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Title: Differential Privacy via a Truncated and Normalized Laplace Mechanism Abstract: When querying databases containing sensitive information, the privacy of individuals stored in the database has to be guaranteed. Such guarantees are provided by differentially private mechanisms which add controlled noise to the query responses. However, most such mechanisms do not take into consideration the valid range of the query being posed. Thus, noisy responses that fall outside of this range may potentially be produced. To rectify this and therefore improve the utility of the mechanism, the commonly-used Laplace distribution can be truncated to the valid range of the query and then normalized. However, such a data-dependent operation of normalization leaks additional information about the true query response, thereby violating the differential privacy guarantee. Here, we propose a new method which preserves the differential privacy guarantee through a careful determination of an appropriate scaling parameter for the Laplace distribution. We adapt the privacy guarantee in the context of the Laplace distribution to account for data-dependent normalization factors and study this guarantee for different classes of range constraint configurations. We provide derivations of the optimal scaling parameter (i.e., the minimal value that preserves differential privacy) for each class or provide an approximation thereof. As a result of this work, one can use the Laplace distribution to answer queries in a range-adherent and differentially private manner. To demonstrate the benefits of our proposed method of normalization, we present an experimental comparison against other range-adherent mechanisms. We show that our proposed approach is able to provide improved utility over the alternative mechanisms.

Title: ProbMinHash – A Class of Locality-Sensitive Hash Algorithms for the (Probability) Jaccard Similarity Abstract: The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a hash algorithm that maps those weighted sets to compact signatures which allow fast estimation of pairwise similarities, it constitutes a valuable method for big data applications such as near-duplicate detection, nearest neighbor search, or clustering. This paper introduces a class of one-pass locality-sensitive hash algorithms that are orders of magnitude faster than the original approach. The performance gain is achieved by calculating signature components not independently, but collectively. Four different algorithms are proposed based on this idea. Two of them are statistically equivalent to the original approach and can be used as drop-in replacements. The other two may even improve the estimation error by introducing statistical dependence between signature components. Moreover, the presented techniques can be specialized for the conventional Jaccard similarity, resulting in highly efficient algorithms that outperform traditional minwise hashing and that are able to compete with the state of the art.

Title: Efficient Global MOT Under Minimum-Cost Circulation Framework Abstract: We developed a minimum-cost circulation framework for solving the global data association problem, which plays a key role in the tracking-by-detection paradigm of multi-object tracking (MOT). The global data association problem was extensively studied under the minimum-cost flow framework, which is theoretically attractive as being flexible and globally solvable. However, the high computational bu...

Title: ON THE CONVERGENCE OF STOCHASTIC PRIMAL-DUAL HYBRID GRADIENT Abstract: In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution with convexity and linear convergence with further structure, using standard step sizes independent of strong convexity or other regularity constants. In the general convex case, we also prove the \scrO (1/k) convergence rate for the ergodic sequence, on expected primal-dual gap function. Our assumption for linear convergence is metric subregularity, which is satisfied for strongly convex-strongly concave problems in addition to many nonsmooth and/or nonstrongly convex problems, such as linear programs, Lasso, and support vector machines. We also provide numerical evidence showing that SPDHG with standard step sizes shows a competitive practical performance against its specialized strongly convex variant SPDHG-\mu and other state-of-the-art algorithms, including variance reduction methods.

Title: Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems. Abstract: In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the local shape around a boundary point with a high magnitude of mean curvature can be reconstructed more easily and stably. In proving this, we develop a novel mathematical scheme by analyzing the generalized polarisation tensors (GPTs) and the scattering coefficients (SCs) coming from the associated scattered fields, which in turn boils down to the analysis of the layer potential operators that sit inside the GPTs and SCs via microlocal analysis. In a delicate and subtle manner, we decompose the reconstruction process into several steps, where all but one steps depend on the global geometry, and one particular step depends on the mean curvature at a given boundary point. Then by a sensitivity analysis with respect to local perturbations of the curvature of the boundary surface, we establish the local resolution effects. Our study opens up a new field of mathematical analysis on wave super-resolution imaging.

Title: Stochastic Optimal Control of HVAC System for Energy-Efficient Buildings Abstract: The heating, ventilation, and air-conditioning (HVAC) system account for substantial energy use in buildings, whereas a large group of occupants is still not actually feeling comfortable staying inside. This poses the issue of developing energy-efficient HVAC control, i.e., reduce energy use (cost) while simultaneously enhancing human comfort. This brief pursues the objective and studies the stoch...

Title: A discontinuous Galerkin method for shock capturing using a mixed high-order and sub-grid low-order approximation space Abstract: •(Non-linear) stability of high-order methods for conservation laws is an open issue.•This paper introduces a new discontinuous Galerkin method.•An approximation space is considered with high-order and sub-grid basis functions.•The high-order modes can additionally suppressed by penalty using a new sensor.

Title: Fast reliability ranking of matchstick minimal networks Abstract: In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices n=2m we define the set of all the possible compositions of series and parallel networks of two devices. We then define several partial orders over this set and study their properties. As far as we know the ranking problem has not been addressed before in this context, and this article establishes the first results in this direction. The usual approach when dealing with reliability of two-terminal networks is to determine existence or nonexistence of uniformly most reliable networks. The problem of ranking two-terminal networks is thus more complex, but by restricting our study to the set of compositions we manage to determine and demonstrate the existence of at least a graded poset.

Title: Circular specifications and "predicting" with information from the future: Errors in the empirical SAOM-TERGM comparison of Leifeld & Cranmer. Abstract: We review the empirical comparison of SAOMs and TERGMs by Leifeld and Cranmer (2019) in Network Science. We note that their model specification uses nodal covariates calculated from observed degrees instead of using structural effects, thus turning endogeneity into circularity. In consequence, their out-of-sample predictions using TERGMs are based on out-of-sample information and thereby predict the future using observations from the future. We conclude that their analysis rest on erroneous model specifications that render the article's conclusions meaningless. Consequently, researchers should disregard recommendations from the criticized paper when making informed modelling choices.

Title: Personalized Robo-Advising: Enhancing Investment Through Client Interaction Abstract: Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. The viability of robo-advisors crucially depends on their ability to offer personalized financial advice. We introduce a novel framework in which a robo-advisor interacts with a client to solve an adaptive mean-variance portfolio optimization problem. The risk-return tradeoff adapts to the client???s risk profile, which depends on idiosyncratic characteristics, market returns, and economic conditions. We show that the optimal investment strategy includes both myopic and intertemporal hedging terms that reflect the dynamic risk profile of the client. We characterize the optimal portfolio personalization via a tradeoff faced by the robo-advisor between receiving information from the client in a timely manner and mitigating behavioral biases in the communicated risk profile. We argue that the optimal portfolio???s Sharpe ratio and return distribution improve if the robo-advisor counters the client???s tendency to reduce market exposure during economic contractions when the market risk-return tradeoff is more favorable.

Title: Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension Abstract: Let p be an odd prime and let r be the smallest generator of the multiplicative group Z(p)*. We show that there exists a correlation of size Theta(r(2)) that selftests a maximally entangled state of local dimension p - 1. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set {2, 3, 5} ( D.R. Heath-Brown The Quarterly Journal of Mathematics (1986) and M. Murty The Mathematical Intelligencer (1988)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.

Title: Scalable and Data Privacy Conserving Controller Tuning for Large-Scale Power Networks Abstract: The increasing share of renewable generation leads to new challenges in reliable power system operation, such as the rising volatility of power generation, which leads to time-varying dynamics and behavior of the system. To counteract the changing dynamics, we propose to adapt the parameters of existing controllers to the changing conditions. Doing so, however, is challenging, as large power systems often involve multiple subsystem operators, which, for safety and privacy reasons, do not want to exchange detailed information about their subsystems. Furthermore, centralized tuning of structured controllers for large-scale systems, such as power networks, is often computationally very challenging. For this reason, we present a hierarchical decentralized approach for controller tuning, which increases data security and scalability. The proposed method is based on the exchange of structured reduced models of subsystems, which conserves data privacy and reduces computational complexity. For this purpose, suitable methods for model reduction and model matching are introduced. Furthermore, we demonstrate how increased renewable penetration leads to time-varying dynamics on the IEEE 68-bus power system, which underlines the importance of the problem. Then, we apply the proposed approach on simulation studies to show its effectiveness. As shown, similar system performance as with a centralized method can be obtained. Finally, we show the scalability of the approach on a large power system with more than 2500 states and about 1500 controller parameters.

Title: <italic>embComp</italic>: Visual Interactive Comparison of Vector Embeddings Abstract: This article introduces <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">embComp</i> , a novel approach for comparing two embeddings that capture the similarity between objects, such as word and document embeddings. We survey scenarios where comparing these embedding spaces is useful. From those scenarios, we derive common tasks, introduce visual analysis methods that support these tasks, and combine them into a comprehensive system. One of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">embComp</i> ’s central features are overview visualizations that are based on metrics for measuring differences in the local structure around objects. Summarizing these local metrics over the embeddings provides global overviews of similarities and differences. Detail views allow comparison of the local structure around selected objects and relating this local information to the global views. Integrating and connecting all of these components, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">embComp</i> supports a range of analysis workflows that help understand similarities and differences between embedding spaces. We assess our approach by applying it in several use cases, including understanding corpora differences via word vector embeddings, and understanding algorithmic differences in generating embeddings.

Title: Properly Colored Short Cycles In Edge-Colored Graphs Abstract: Properly colored cycles in edge-colored graphs are closely related to directed cycles in oriented graphs. As an analogy of the well-known Caccetta-Haggkvist Conjecture, we study the existence of properly colored cycles of bounded length in an edge-colored graph. We first prove that for all integers s and t with t >= s >= 2, every edge-colored graph G with no properly colored K-s,(t) contains a spanning subgraph H which admits an orientation D such that every directed cycle in D is a properly colored cycle in G. Using this result, we show that for r >= 4, if the Caccetta-Haggkvist Conjecture holds, then every edge-colored graph of order n with minimum color degree at least n/r + 2 root n + 1 contains a properly colored cycle of length at most r. In addition, we also obtain an asymptotically tight total color degree condition which ensures a properly colored (or rainbow) K-s,K-t. (C) 2021 Published by Elsevier Ltd.

Title: Reversible Data Hiding in Encrypted Images Based on Pixel Prediction and Bit-Plane Compression Abstract: Reversible data hiding in encrypted images (RDHEI) receives growing attention because it protects the content of the original image while the embedded data can be accurately extracted and the original image can be reconstructed losslessly. To make full use of the correlation of the adjacent pixels, this article proposes an RDHEI scheme based on pixel prediction and bit-plane compression. First, th...

Title: A fast two-point gradient algorithm based on sequential subspace optimization method for nonlinear ill-posed problems Abstract: In this paper, we propose a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. The key idea, in contrast to the standard two-point gradient method, is to use multiple search directions in each iteration without extra computation, and to get the step size by metric projection. Moreover, a modified discrete backtracking search algorithm is proposed to select the combination parameters in the accelerated two-point gradient method. Under the basic assumptions for iterative regularization methods, we establish the convergence results of the method in the noise-free case. Furthermore, stability and regularity are presented when the algorithm terminated by the discrepancy principle for the case of noisy data. Finally, some numerical simulations are presented, which exhibit that the proposed method leads to a significant reduction of the iteration numbers and the overall computational time.

Title: The correlation-assisted missing data estimator Abstract: We introduce a novel approach to estimation problems in settings with missing data. Our proposal - the Correlation-Assisted Missing data (CAM) estimator - works by exploiting the relationship between the observations with missing features and those without missing features in order to obtain improved prediction accuracy. In particular, our theoretical results elucidate general conditions under which the proposed CAM estimator has lower mean squared error than the widely used complete-case approach in a range of estimation problems. We showcase in detail how the CAM estimator can be applied to U-Statistics to obtain an unbiased, asymptotically Gaussian estimator that has lower variance than the complete-case U-Statistic. Further, in nonparametric density estimation and regression problems, we construct our CAM estimator using kernel functions, and show it has lower asymptotic mean squared error than the corresponding complete-case kernel estimator. We also include practical demonstrations throughout the paper using simulated data and the Terneuzen birth cohort and Brandsma datasets available from CRAN.

Title: Mixed Social Optima and Nash Equilibrium in Linear-Quadratic-Gaussian Mean-Field System Abstract: This article investigates a class of mixed stochastic linear-quadratic-Gaussian social optimization and Nash game in the context of a large-scale system. Two types of interactive agents are involved: a major agent and a large number of weakly coupled minor agents. All minor agents are cooperative to minimize the social cost as the sum of their individual costs, whereas such social cost is conflictive to that of the major agent. Thus, the major agent and all minor agents are further competitive to reach some nonzero-sum Nash equilibrium. Applying the mean-field approximations and person-by-person optimality, we obtain auxiliary control problems for the major agent and minor agents, respectively. The decentralized social strategy is derived by a class of new consistency condition (CC) system, which consists of mean-field forward–backward stochastic differential equations. The well-posedness of CC system is obtained by the discounting method. The related asymptotic social optimality for minor agents and Nash equilibrium for major–minor agents are also verified.

Title: Scalable Variational Gaussian Processes for Crowdsourcing: Glitch Detection in LIGO Abstract: In the last years, crowdsourcing is transforming the way classification training sets are obtained. Instead of relying on a single expert annotator, crowdsourcing shares the labelling effort among a large number of collaborators. For instance, this is being applied in the laureate laser interferometer gravitational waves observatory (LIGO), in order to detect glitches which might hinder the identification of true gravitational-waves. The crowdsourcing scenario poses new challenging difficulties, as it has to deal with different opinions from a heterogeneous group of annotators with unknown degrees of expertise. Probabilistic methods, such as Gaussian processes (GP), have proven successful in modeling this setting. However, GPs do not scale up well to large data sets, which hampers their broad adoption in real-world problems (in particular LIGO). This has led to the very recent introduction of deep learning based crowdsourcing methods, which have become the state-of-the-art for this type of problems. However, the accurate uncertainty quantification provided by GPs has been partially sacrificed. This is an important aspect for astrophysicists in LIGO, since a glitch detection system should provide very accurate probability distributions of its predictions. In this work, we first leverage a standard sparse GP approximation (SVGP) to develop a GP-based crowdsourcing method that factorizes into mini-batches. This makes it able to cope with previously-prohibitive data sets. This first approach, which we refer to as scalable variational Gaussian processes for crowdsourcing (SVGPCR), brings back GP-based methods to a state-of-the-art level, and excels at uncertainty quantification. SVGPCR is shown to outperform deep learning based methods and previous probabilistic ones when applied to the LIGO data. Its behavior and main properties are carefully analyzed in a controlled experiment based on the MNIST data set. Moreover, recent GP inference techniques are also adapted to crowdsourcing and evaluated experimentally.

Title: Perceived Intensities of Normal and Shear Skin Stimuli Using a Wearable Haptic Bracelet Abstract: Our aim is to provide effective interaction with virtual objects, despite the lack of co-location of virtual and real-world contacts, while taking advantage of relatively large skin area and ease of mounting on the forearm. We performed two human participant studies to determine the effects of haptic feedback in the normal and shear directions during virtual manipulation using haptic devices worn near the wrist. In the first study, participants performed significantly better while discriminating stiffness values of virtual objects when the feedback consisted of normal displacements compared to shear displacements. Participants also commented that they could detect normal cues much easier than shear, which motivated us to perform a second study to find the point of subjective equality (PSE) between normal and shear stimuli. Our results show that shear stimuli require a larger actuator displacement but less force than normal stimuli to achieve perceptual equality for our haptic bracelets. We found that normal and shear stimuli cannot be equalized through skin displacement nor the interaction forces across all users. Rather, a calibration method is needed to find the point of equality for each user where normal and shear stimuli create the same intensity on the user’s skin.

Title: Super Domination in Trees Abstract: For S subset of V(G), we define (S) over bar = V(G)\S. A set S subset of V(G) is called a super dominating set if for every vertex u is an element of (S) over bar, there exists v is an element of S such that N (v) boolean AND (S) over bar = {u}. The super domination number gamma(sp)(G) of G is the minimum cardinality among all super dominating sets in G. The super domination subdivision number sd(gamma sp) (G) of a graph G is the minimum number of edges that must be subdivided in order to increase the super domination number of G. In this paper, we investigate the ratios between super domination and other domination parameters in trees. In addition, we show that for any nontrivial tree T, 1 <= sd(gamma sp) (T) <= 2, and give constructive characterizations of trees whose super domination subdivision number are 1 and 2, respectively.

Title: CONVERGENCE ACCELERATION OF ENSEMBLE KALMAN INVERSION IN NONLINEAR SETTINGS Abstract: Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often needed. The ensemble Kalman filter (EnKF) is a particle-based derivative-free Bayesian algorithm originally designed for data assimilation. Recently, it has been applied to inverse problems for computational efficiency. The resulting algorithm, known as ensemble Kalman inversion (EKI), involves running an ensemble of particles with EnKF update rules so they can converge to a minimizer. In this article, we investigate EKI convergence in general nonlinear settings. To improve convergence speed and stability, we consider applying EKI with non-constant step-sizes and covariance inflation. We prove that EKI can hit critical points with finite steps in non-convex settings. We further prove that EKI converges to the global minimizer polynomially fast if the loss function is strongly convex. We verify the analysis presented with numerical experiments on two inverse problems.

Title: High-Dimensional Black-Box Optimization Under Uncertainty Abstract: Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research-unimportant input variables and inefficient treatment of uncertainty associated with the black-box output. We first design a new flexible non-interpolating parsimonious surrogate model using a partitioning-based multivariate adaptive regression splines approach, Tree Knot MARS (TK-MARS). The proposed model is specifically designed for optimization by capturing the structure of the function, bending at near-optimal locations, and is capable of screening unimportant input variables. Furthermore, we develop a novel replication approach called Smart-Replication, to overcome the uncertainty associated with the black-box output. The Smart-Replication approach identifies promising input points to replicate and avoids unnecessary evaluations of other data points. Smart-Replication is agnostic to the choice of a surrogate and can adapt itself to an unknown noise level. Finally to demonstrate the effectiveness of our proposed approaches we consider different complex global optimization test functions from the surrogate optimization literature. The results indicate that TKMARS outperforms original MARS within a surrogate optimization algorithm and successfully detects important variables. The results also show that although non-interpolating surrogates can mitigate uncertainty, replication is still beneficial for optimizing highly complex black-box functions. The robustness and the quality of the final optimum solution found through Smart-Replication are competitive with that using no replications in environments with low levels of noise and using a fixed number of replications in highly noisy environments.

Title: Option compatible reward inverse reinforcement learning Abstract: •New method of assigning reward functions for a hierarchical IRL problem is introduced.•The recovered reward functions can be used to transfer knowledge across related tasks.•It also shows better robustness to noise included in expert demonstrations.

Title: A Q-Wadge Hierarchy in quasi-Polish Spaces Abstract: The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it here to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g. several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.

Title: Solving inverse problems for steady-state equations using a multiple criteria model with collage distance, entropy, and sparsity Abstract: In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the entropy and minimizes the sparsity. In this extended formulation, the parameter estimation minimization problem can be understood as a multiple criteria problem, with three different and conflicting criteria: The generalized collage error, the entropy associated with the unknown parameters, and the sparsity of the set of unknown parameters. We implement a scalarization technique to reduce the multiple criteria program to a single criterion one, by combining all objective functions with different trade-off weights. Numerical examples confirm that the collage method produces good, but sub-optimal, results. A relatively low-weighted entropy term allows for better approximations while the sparsity term decreases the complexity of the solution in terms of the number of elements in the basis.

Title: Counting extensions revisited Abstract: We consider rooted subgraphs in random graphs, that is, extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three connecting two given vertices. In 1989, Spencer gave sufficient conditions for the event that, with high probability, these extension counts are asymptotically equal for all choices of the root vertices. For the important strictly balanced case, Spencer also raised the fundamental question as to whether these conditions are necessary. We answer this question by a careful second moment argument, and discuss some intriguing problems that remain open.

Title: SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION Abstract: In this paper, we justify the semiclassical limit of the Gross-Pitaevskii equation with Dirichlet boundary condition on the three-dimensional upper space under the assumption that the leading-order terms to both initial amplitude and initial phase function are sufficiently small in some high enough Sobolev norms. We remark that the main difficulty of the proof lies in the fact that the boundary layer appears in the leading-order terms of the amplitude functions and the gradient of the phase functions to the WKB expansions of the solutions. In particular, we partially solved the open question proposed in [D. Chiron and F. Rousset, Comm. Math. Phys., 288 (2009), pp. 503-546; C. T. Pham, C. Nore, and M. E. Brachet, Phys. D, 210 (2005), pp. 203-226] concerning the semiclassical limit of the Gross-Pitaevskii equation with Dirichlet boundary condition.

Title: Towards Automated Monitoring of Parkinson's Disease Following Drug Treatment. Abstract: Background and Objective: It is commonly accepted that accurate monitoring of neurodegenerative diseases is crucial for effective disease management and delivery of medication and treatment. This research develops automatic clinical monitoring techniques for PD, following treatment, using the novel application of EAs. Specifically, the research question addressed was: Can accurate monitoring of PD be achieved using EAs on rs-fMRI data for patients prescribed Modafinil (typically prescribed for PD patients to relieve physical fatigue)? Methods: This research develops novel clinical monitoring tools using data from a controlled experiment where participants were administered Modafinil versus placebo, examining the novel application of EAs to both map and predict the functional connectivity in participants using rs-fMRI data. Specifically, CGP was used to classify DCM analysis and timeseries data. Results were validated with two other commonly used classification methods (ANN and SVM) and via k-fold cross-validation. Results: Findings revealed a maximum accuracy of 74.57% for CGP. Furthermore, CGP provided comparable performance accuracy relative to ANN and SVM. Nevertheless, EAs enable us to decode the classifier, in terms of understanding the data inputs that are used, more easily than in ANN and SVM. Conclusions: These findings underscore the applicability of both DCM analyses for classification and CGP as a novel classification technique for brain imaging data with medical implications for medication monitoring. Furthermore, classification of fMRI data for research typically involves statistical modelling techniques being often hypothesis driven, whereas EAs use data-driven explanatory modelling methods resulting in numerous benefits. DCM analysis is novel for classification and advantageous as it provides information on the causal links between different brain regions.

Title: An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges Abstract: In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional case. For higher dimensions, the result is the rise of two new contributions to the first law of thermodynamics. The first term corresponds to corrections of the usual definition of thermodynamic volumes at the horizon due to the presence of the higher curvature terms. The second term arises in odd dimensions, comes from the asymptotic region, and corresponds to a scale transformation of the form proportional to delta<^>ln(l/l), with l the AdS radius and l a parameter. A particularly interesting case corresponds to the Chern Simons gravity where the change scale does not generate a contribution at the asymptotic region, likely due to the Chern Simons AdS local symmetry.

Title: Distributed Redundant Placement for Microservice-based Applications at the Edge Abstract: Multi-access edge computing (MEC) is booming as a promising paradigm to push the computation and communication resources from cloud to the network edge to provide services and to perform computations. With container technologies, mobile devices with small memory footprint can run composite microservice-based applications without time-consuming backbone. Service placement at the edge is of importance to put MEC from theory into practice. However, current state-of-the-art research does not sufficiently take the composite property of services into consideration. Besides, although Kubernetes has certain abilities to heal container failures, high availability cannot be ensured due to heterogeneity and variability of edge sites. To deal with these problems, we propose a distributed redundant placement framework SAA-RP and a GA-based Server Selection (GASS) algorithm for microservice-based applications with sequential combinatorial structure. We formulate a stochastic optimization problem with the uncertainty of microservice request considered, and then decide for each microservice, how it should be deployed and with how many instances as well as on which edge sites to place them. Benchmark policies are implemented in two scenarios, where redundancy is allowed and not, respectively. Numerical results based on a real-world dataset verify that GASS significantly outperforms all the benchmark policies.

Title: Factored Latent-Dynamic Conditional Random Fields for single and multi-label sequence modeling Abstract: •We propose a single and multi-label generalization of LDCRF (Morency et al., 2007), called the Factored LDCRF.•FLDCRF unifies the concepts of LDCRF and Dynamic CRFs (DCRF, Sutton et al., 2007) and extends the CRF family.•The single-label variant of FLDCRF (FLDCRF-s) outperforms state-of-the-art models, viz., CRF, LDCRF, LSTM and LSTM-CRF across 5 experiments over 2 different datasets.•The multi-label variant of FLDCRF-m outperforms state-of-the-art single-label, viz., CRF, LDCRF, LSTM and LSTM-CRF, and multi-label, viz., Coupled CRF, Factorial CRF and multi-label LSTM models on the multi-label sequence tagging experiment.•We compare FLDCRF and LSTM model families not only on the test data, but also across several other modeling aspects, e.g., model selection, consistency and computation times.

Title: MINNAERT RESONANCES FOR BUBBLES IN SOFT ELASTIC MATERIALS Abstract: Minnaert resonance is a widely known acoustic phenomenon, and it has many important applications, in particular in the effective realization of acoustic metamaterials using bubbly media in recent years. In this paper, motivated by the Minnaert resonance in acoustics, we consider the low-frequency resonance for acoustic bubbles embedded in soft elastic materials. This is a hybrid physical process that couples the acoustic and elastic wave propagations. By delicately and subtly balancing the acoustic and elastic parameters as well as the geometry of the bubble, we show that Minnaert resonance can occur (at least approximately) for rather general constructions. Our study highlights the great potential for the effective realization of negative elastic materials by using bubbly elastic media.

Title: Parameter Estimation in Adaptive Control of Time-Varying Systems Under a Range of Excitation Conditions Abstract: This article presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast toward a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis.

Title: Deep Reinforcement Learning Based Dynamic Trajectory Control for UAV-Assisted Mobile Edge Computing Abstract: In this paper, we consider a platform of flying mobile edge computing (F-MEC), where unmanned aerial vehicles (UAVs) serve as equipment providing computation resource, and they enable task offloading from user equipment (UE). We aim to minimize energy consumption of all UEs via optimizing user association, resource allocation and the trajectory of UAVs. To this end, we first propose a Convex optimizAtion based Trajectory control algorithm (CAT), which solves the problem in an iterative way by using block coordinate descent (BCD) method. Then, to make the real-time decision while taking into account the dynamics of the environment (i.e., UAV may take off from different locations), we propose a deep Reinforcement leArning based trajectory control algorithm (RAT). In RAT, we apply the Prioritized Experience Replay (PER) to improve the convergence of the training procedure. Different from the convex optimization based algorithm which may be susceptible to the initial points and requires iterations, RAT can be adapted to any taking off points of the UAVs and can obtain the solution more rapidly than CAT once training process has been completed. Simulation results show that the proposed CAT and RAT achieve the considerable performance and both outperform traditional algorithms.

Title: Projective and Reedy Model Category Structures for (Infinitesimal) Bimodules over an Operad Abstract: We construct and study projective and Reedy model category structures for bimodules and infinitesimal bimodules over topological operads. Both model structures produce the same homotopy categories. For the model categories in question, we build explicit cofibrant and fibrant replacements. We show that these categories are right proper and under some conditions left proper. We also study the extension/restriction adjunctions.

Title: A spanning bandwidth theorem in random graphs. Abstract: The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $(\frac{k-1}{k}+o(1))n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and bandwidth $o(n)$. In [arXiv:1612.00661] a random graph analogue of this statement is proved: for $p\gg (\frac{\log n}{n})^{1/\Delta}$ a.a.s. each spanning subgraph $G$ of $G(n,p)$ with minimum degree $(\frac{k-1}{k}+o(1))pn$ contains all $n$-vertex $k$-colourable graphs $H$ with maximum degree $\Delta$, bandwidth $o(n)$, and at least $C p^{-2}$ vertices not contained in any triangle. This restriction on vertices in triangles is necessary, but limiting. In this paper we consider how it can be avoided. A special case of our main result is that, under the same conditions, if additionally all vertex neighbourhoods in $G$ contain many copies of $K_\Delta$ then we can drop the restriction on $H$ that $Cp^{-2}$ vertices should not be in triangles.

Title: Time-Optimal Coordination for Connected and Automated Vehicles at Adjacent Intersections Abstract: In this paper, we provide a hierarchical coordination framework for connected and automated vehicles (CAVs) at two adjacent intersections. This framework consists of an upper-level scheduling problem and a low-level optimal control problem. By partitioning the area around two adjacent intersections into different zones, we formulate a scheduling problem for each individual CAV aimed at minimizing its total travel time. For each CAV, the solution of the upper-level problem designates the arrival times at each zones on its path which becomes the inputs of the low-level problem. The solution of the low-level problem yields the optimal control input (acceleration/deceleration) of each CAV to exit the intersections at the time specified in the upper-level scheduling problem. We validate the performance of our proposed hierarchical framework through extensive numerical simulations and comparison with signalized intersections, centralized scheduling, and FIFO queuing policy.

Title: Paired domination versus domination and packing number in graphs Abstract: Given a graph $$G=(V(G), E(G))$$ , the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by $$\gamma (G)$$ , $$\gamma _{pr}(G)$$ , and $$\gamma _{t}(G)$$ , respectively. For a positive integer k, a k-packing in G is a set $$S \subseteq V(G)$$ such that for every pair of distinct vertices u and v in S, the distance between u and v is at least $$k+1$$ . The k-packing number is the order of a largest k-packing and is denoted by $$\rho _{k}(G)$$ . It is well known that $$\gamma _{pr}(G) \le 2\gamma (G)$$ . In this paper, we prove that it is NP-hard to determine whether $$\gamma _{pr}(G) = 2\gamma (G)$$ even for bipartite graphs. We provide a simple characterization of trees with $$\gamma _{pr}(G) = 2\gamma (G)$$ , implying a polynomial-time recognition algorithm. We also prove that even for a bipartite graph, it is NP-hard to determine whether $$\gamma _{pr}(G)=\gamma _{t}(G)$$ . We finally prove that it is both NP-hard to determine whether $$\gamma _{pr}(G)=2\rho _{4}(G)$$ and whether $$\gamma _{pr}(G)=2\rho _{3}(G)$$ .

Title: Streaming Convolutional Neural Networks for End-to-End Learning With Multi-Megapixel Images Abstract: Due to memory constraints on current hardware, most convolution neural networks (CNN) are trained on sub-megapixel images. For example, most popular datasets in computer vision contain images much less than a megapixel in size (0.09MP for ImageNet and 0.001MP for CIFAR-10). In some domains such as medical imaging, multi-megapixel images are needed to identify the presence of disease accurately. We propose a novel method to directly train convolutional neural networks using any input image size end-to-end. This method exploits the locality of most operations in modern convolutional neural networks by performing the forward and backward pass on smaller tiles of the image. In this work, we show a proof of concept using images of up to 66-megapixels (8192×8192), saving approximately 50GB of memory per image. Using two public challenge datasets, we demonstrate that CNNs can learn to extract relevant information from these large images and benefit from increasing resolution. We improved the area under the receiver-operating characteristic curve from 0.580 (4MP) to 0.706 (66MP) for metastasis detection in breast cancer (CAMELYON17). We also obtained a Spearman correlation metric approaching state-of-the-art performance on the TUPAC16 dataset, from 0.485 (1MP) to 0.570 (16MP). Code to reproduce a subset of the experiments is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/DIAGNijmegen/StreamingCNN</uri> .

Title: Matchings in 1-planar graphs with large minimum degree Abstract: In 1979, Nishizeki and Baybars showed that every planar graph with minimum degree 3 has a matching of size n3+c (where the constant c depends on the connectivity), and even better bounds hold for planar graphs with minimum degree 4 and 5. In this paper, we investigate similar matching-bounds for 1-planar graphs, that is, graphs that can be drawn such that every edge has at most one crossing. We show that every 1-planar graph with minimum degree 3 has a matching of size at least 17n+127, and this is tight for some graphs. We provide similar bounds for 1-planar graphs with minimum degree 4 and 5, while the case of minimum degree 6 and 7 remains open.

Title: Gorenstein projective objects in comma categories Abstract: Let $$\mathcal {A}$$ and $$\mathcal {B}$$ be abelian categories and $${\mathbf {F}} :\mathcal {A}\rightarrow \mathcal {B}$$ an additive and right exact functor which is perfect, and let $$({\mathbf {F}},\mathcal {B})$$ be the left comma category. We give an equivalent characterization of Gorenstein projective objects in $$({\mathbf {F}},\mathcal {B})$$ in terms of Gorenstein projective objects in $$\mathcal {B}$$ and $$\mathcal {A}$$ . We prove that there exists a left recollement of the stable category of the subcategory of $$({\mathbf {F}},\mathcal {B})$$ consisting of Gorenstein projective objects modulo projectives relative to the same kind of stable categories in $$\mathcal {B}$$ and $$\mathcal {A}$$ . Moreover, this left recollement can be filled into a recollement when $$\mathcal {B}$$ is Gorenstein and $${\mathbf {F}}$$ preserves projectives.

Title: A TFC-based homotopy continuation algorithm with application to dynamics and control problems Abstract: A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms’ success highly relies on empirical knowledge, due to manually, inherently selected homotopy paths. This work introduces a homotopy method based on the Theory of Functional Connections (TFC). The TFC-based method implicitly defines infinite homotopy paths, from which the most promising ones are selected. A two-layer continuation algorithm is devised, where the first layer tracks the homotopy path by monotonously varying the continuation parameter, while the second layer recovers possible failures resorting to a TFC representation of the homotopy function. Compared to pseudo-arclength methods, the proposed TFC-based method retains the simplicity of direct continuation while allowing a flexible path switching. Numerical simulations illustrate the effectiveness of the presented method.

Title: Efficient fair principal component analysis Abstract: It has been shown that dimension reduction methods such as Principal Component Analysis (PCA) may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality reduction, using the notion of Pareto optimality, we propose an adaptive first-order algorithm to learn a subspace that preserves fairness, while slightly compromising the reconstruction loss. Theoretically, we provide sufficient conditions that the solution of the proposed algorithm belongs to the Pareto frontier for all sensitive groups; thereby, the optimal trade-off between overall reconstruction loss and fairness constraints is guaranteed. We also provide the convergence analysis of our algorithm and show its efficacy through empirical studies on different datasets, which demonstrates superior performance in comparison with state-of-the-art algorithms. The proposed fairness-aware PCA algorithm can be efficiently generalized to multiple group sensitive features and effectively reduce the unfairness decisions in downstream tasks such as classification.

Title: The power of two choices for random walks. Abstract: We apply the power-of-two-choices paradigm to random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the controller to significantly accelerate the hitting and cover times in several natural graph classes. In particular, we show that the cover time becomes linear in the number $n$ of vertices on discrete tori and bounded degree trees, of order $\mathcal{O}(n \log \log n)$ on expanders, and of order $\mathcal{O}(n (\log \log n)^2)$ on the Erd\H{o}s-R\'{e}nyi random graph in a certain sparsely connected regime. We also consider the algorithmic question of computing an optimal strategy, and prove a dichotomy in efficiency between computing strategies for hitting and cover times.

Title: On the constructions of MDS self-dual codes via cyclotomy Abstract: MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and extended generalized Reed-Solomon codes as the candidates of MDS codes and taking their evaluation sets as a union of cyclotomic classes. The conditions on such MDS codes being self-dual are expressed in terms of cyclotomic numbers.

Title: SimVODIS: Simultaneous Visual Odometry, Object Detection, and Instance Segmentation Abstract: Intelligent agents need to understand the surrounding environment to provide meaningful services to or interact intelligently with humans. The agents should perceive geometric features as well as semantic entities inherent in the environment. Contemporary methods in general provide one type of information regarding the environment at a time, making it difficult to conduct high-level tasks. Moreove...

Title: AMP₀: Species-Specific Prediction of Anti-microbial Peptides Using Zero and Few Shot Learning Abstract: AbstractEvolution of drug-resistant microbial species is one of the major challenges to global health. Development of new antimicrobial treatments such as antimicrobial peptides needs to be accelerated to combat this threat. However, the discovery of novel antimicrobial peptides is hampered by low-throughput biochemical assays. Computational techniques can be used for rapid screening of promising antimicrobial peptide candidates prior to testing in the wet lab. The vast majority of existing antimicrobial peptide predictors are non-targeted in nature, i.e., they can predict whether a given peptide sequence is antimicrobial, but they are unable to predict whether the sequence can target a particular microbial species. In this work, we have used zero and few shot machine learning to develop a targeted antimicrobial peptide activity predictor called AMP0. The proposed predictor takes the sequence of a peptide and any N/C-termini modifications together with the genomic sequence of a microbial species to generate targeted predictions. Cross-validation results show that the proposed scheme is particularly effective for targeted antimicrobial prediction in comparison to existing approaches and can be used for screening potential antimicrobial peptides in a targeted manner with only a small number of training examples for novel species. AMP0 webserver is available at http://ampzero.pythonanywhere.com.

Title: Sparse Density Estimation with Measurement Errors Abstract: This paper aims to estimate an unknown density of the data with measurement errors as a linear combination of functions from a dictionary. The main novelty is the proposal and investigation of the corrected sparse density estimator (CSDE). Inspired by the penalization approach, we propose the weighted Elastic-net penalized minimal l(2)-distance method for sparse coefficients estimation, where the adaptive weights come from sharp concentration inequalities. The first-order conditions holding a high probability obtain the optimal weighted tuning parameters. Under local coherence or minimal eigenvalue assumptions, non-asymptotic oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with a high probability. Some numerical experiments for discrete and continuous distributions confirm the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed in a meteorology dataset. It shows that our method has potency and superiority in detecting multi-mode density shapes compared with other conventional approaches.

Title: LGN-CNN: A biologically inspired CNN architecture Abstract: In this paper we introduce a biologically inspired Convolutional Neural Network (CNN) architecture called LGN-CNN that has a first convolutional layer composed of a single filter that mimics the role of the Lateral Geniculate Nucleus (LGN). The first layer of the neural network shows a rotational symmetric pattern justified by the structure of the net itself that turns up to be an approximation of a Laplacian of Gaussian (LoG). The latter function is in turn a good approximation of the receptive field profiles (RFPs) of the cells in the LGN. The analogy with the visual system is established, emerging directly from the architecture of the neural network. A proof of rotation invariance of the first layer is given on a fixed LGN-CNN architecture and the computational results are shown. Thus, contrast invariance capability of the LGN-CNN is investigated and a comparison between the Retinex effects of the first layer of LGN-CNN and the Retinex effects of a LoG is provided on different images. A statistical study is done on the filters of the second convolutional layer with respect to biological data. In conclusion, the model we have introduced approximates well the RFPs of both LGN and V1 attaining similar behavior as regards long range connections of LGN cells that show Retinex effects.

Title: Mutual algebraicity and cellularity Abstract: We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure M is cellular if and only if M is $$\omega $$ -categorical and mutually algebraic. Second, if a countable structure M in a finite relational language is mutually algebraic non-cellular, we show it admits an elementary extension adding infinitely many infinite MA-connected components. Towards these results, we introduce MA-presentations of a mutually algebraic structure, in which every atomic formula is mutually algebraic. This allows for an improved quantifier elimination and a decomposition of the structure into independent pieces. We also show this decomposition is largely independent of the MA-presentation chosen.

Title: On the Maximum Number of Non-Confusable Strings Evolving under Short Tandem Duplications Abstract: The set of all $$q$$ -ary strings that do not contain repeated substrings of length $${\le\! 3}$$ (i.e., that do not contain substrings of the form $$a a$$ , $$a b a b$$ , and $$a b c a b c$$ ) constitutes a code correcting an arbitrary number of tandem-duplication mutations of length $${\le\! 3}$$ . In other words, any two such strings are non-confusable in the sense that they cannot produce the same string while evolving under tandem duplications of length $${\le\! 3}$$ . We demonstrate that this code is asymptotically optimal in terms of rate, meaning that it represents the largest set of non-confusable strings up to subexponential factors. This result settles the zero-error capacity problem for the last remaining case of tandem-duplication channels satisfying the “root-uniqueness” property.

Title: Fixed-Horizon Active Hypothesis Testing Abstract: Two active hypothesis testing problems are formulated. In these problems, the agent can perform a fixed number of experiments and then decide on one of the hypotheses or declare its experiments inconclusive. The first problem is an asymmetric formulation in which the objective is to minimize the probability of incorrectly declaring a particular hypothesis to be true while ensuring that the probabi...

Title: Large N behaviour of the two-dimensional Yang-Mills partition function. Abstract: We compute the large N limit of the partition function of the Euclidean Yang--Mills measure with structure group SU(N) or U(N) on all closed compact surfaces, orientable or not, excepted for the sphere and the projective plane. This limit is finite as opposed to the case of the sphere and presumably the projective plane. We expect that the results we present might give an insight towards the master field on these surfaces.

Title: Toward efficient polynomial preconditioning for GMRES Abstract: We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many previous polynomial preconditioners. Our current implementation of this polynomial using its roots is naturally more stable than previous methods of computing the same polynomial. We implement further stability control using added roots, and this allows for high degree polynomials. We discuss the effectiveness and challenges of root-adding and give an additional check for stability. In this article, we study the polynomial preconditioner applied to GMRES; however it could be used with any Krylov solver. This polynomial preconditioning algorithm can dramatically improve convergence for some problems, especially for difficult problems, and can reduce dot products by an even greater margin.

Title: Ultra-Fast Accurate AoA Estimation via Automotive Massive-MIMO Radar Abstract: Massive multiple-input multiple-output (MIMO) radar, enabled by millimeter-wave virtual MIMO techniques, provides great promises to the high-resolution automotive sensing and target detection in unmanned ground/aerial vehicles (UGA/UAV). As a long-established problem, however, existing subspace methods suffer from either high complexity or low accuracy. In this work, we propose two efficient methods, to accomplish fast subspace computation and accurate angle of arrival (AoA) acquisition. By leveraging randomized low-rank approximation, our fast multiple signal classification (MUSIC) methods, relying on random sampling and projection techniques, substantially accelerate the subspace estimation by orders of magnitude. Moreover, we establish the theoretical bounds of our proposed methods, which ensure the accuracy of the approximated pseudo-spectrum. As demonstrated, the pseudo-spectrum acquired by our fast-MUSIC would be highly precise; and the estimated AoA is almost as accurate as standard MUSIC. In contrast, our new methods are tremendously faster than standard MUSIC. Thus, our fast-MUSIC enables the high-resolution real-time environmental sensing with massive MIMO radars, which has great potential in the emerging unmanned systems.

Title: Asymptotic Analysis of Skolem&apos;s exponential Functions Abstract: Skolem (1956) studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant $1$, the identity function $x$, and such that whenever $f$ and $g$ are in the set, $f+g,fg$ and $f^g$ are in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz (1984) computed the order type of the fragment below $2^{2^x}$. Here we prove that the set of asymptotic classes within any archimedean class of Skolem functions has order type $\omega$. As a consequence we obtain, for each positive integer $n$, an upper bound for the fragment below $2^{n^x}$. We deduce an epsilon-zero upper bound for the fragment below $2^{x^x}$, improving the previous epsilon-omega bound by Levitz (1978). A novel feature of our approach is the use of Conway's surreal number for asymptotic calculations.

Title: Convex Formulation of Overparameterized Deep Neural Networks Abstract: The analysis of over-parameterized neural networks has drawn significant attention in recent years. It was shown that such systems behave like convex systems under various restricted settings, such as for two-layer neural networks, and when learning is only restricted locally in the so-called neural tangent kernel space around specialized initializations. However, there is a lack of powerful theoretical techniques that can analyze fully trained deep neural networks under general conditions. This paper considers this fundamental problem by investigating such overparameterized deep neural networks when fully trained. Specifically, we characterize a deep neural network by its features’ distributions and propose a metric to intuitively measure the usefulness of feature representations. Under certain regularizers that bounds the metric, we show deep neural networks can be reformulated as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">convex</i> optimization and the system can guarantee effective feature representations in terms of the metric. Our new analysis is more consistent with empirical observations that deep neural networks are capable of learning efficient feature representations. Empirical studies confirm that predictions of our theory are consistent with results observed in practice.

Title: Efficient function approximation on general bounded domains using splines on a Cartesian grid Abstract: Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a regular but oversampled grid that is defined on a bounding box. This approach allows the use of high-order and highly structured splines as a basis for piecewise polynomials. The methodology is analogous to that of Fourier extensions, using Fourier series on a bounding box, which leads to spectral accuracy for smooth functions. However, Fourier extension approximations involve solving a highly ill-conditioned linear system, and this is an expensive step. The computational complexity of recent algorithms is $\mathcal {O}\left (N\log ^{2}\left (N\right )\right )$ in 1-D and $\mathcal {O}\left (N^{2}\log ^{2}\left (N\right )\right )$ in 2-D. We show that, compared to Fourier extension, the compact support of B-splines enables improved complexity for multivariate approximations, namely $\mathcal {O}(N)$ in 1-D, $\mathcal {O}\left (N^{3/2}\right )$ in 2-D and more generally $\mathcal {O}\left (N^{3(d-1)/d}\right )$ in d-D with d > 1. By using a direct sparse QR solver for a related linear system, we also observe that the computational complexity can be nearly linear in practice. This comes at the cost of achieving only algebraic rates of convergence. Our statements are corroborated with numerical experiments and Julia code is available.

Title: WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis Abstract: Convolutional neural network (CNN), with the ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, an explanation on the physical meaning of a CNN architecture has rarely been studied. In this article, a novel wavelet-driven deep neural network, termed as WaveletKernelNet (WKN), is presented, where a continuous wavelet convolutional (CWConv) layer is designed to replace the first convolutional layer of the standard CNN. This enables the first CWConv layer to discover more meaningful kernels. Furthermore, only the scale parameter and translation parameter are directly learned from raw data at this CWConv layer. This provides a very effective way to obtain a customized kernel bank, specifically tuned for extracting defect-related impact component embedded in the vibration signal. In addition, three experimental studies using data from laboratory environment are carried out to verify the effectiveness of the proposed method for mechanical fault diagnosis. The experimental results show that the accuracy of the WKNs is higher than CNN by more than 10%, which indicate the importance of the designed CWConv layer. Besides, through theoretical analysis and feature map visualization, it is found that the WKNs are interpretable, have fewer parameters, and have the ability to converge faster within the same training epochs.

Title: A Hypergraph Turán Problem with No Stability Abstract: A fundamental barrier in extremal hypergraph theory is the presence of many near-extremal constructions with very different structures. Indeed, the classical constructions due to Kostochka imply that the notorious extremal problem for the tetrahedron exhibits this phenomenon assuming Turán’s conjecture. Our main result is to construct a finite family of triple systems $${\cal M}$$ , determine its Turán number, and prove that there are two near-extremal $${\cal M}$$ -free constructions that are far from each other in edit-distance. This is the first extremal result for a hypergraph family that fails to have a corresponding stability theorem.

Title: Improved Clustering Algorithms for the Bipartite Stochastic Block Model Abstract: We establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by spectral clustering algorithms in BSBM. Next, we propose a new computationally simple and fast procedure achieving exact recovery under milder conditions than the state of the art. Namely, if the vertex sets <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{2}$ </tex-math></inline-formula> in BSBM have sizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{2}$ </tex-math></inline-formula> , we show that the condition <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ p = \Omega \left ({\max \left ({\sqrt {\frac {\log {n_{1}}}{n_{1}n_{2}}},\frac {\log {n_{1}}}{n_{2}}}\right )}\right )$ </tex-math></inline-formula> on the edge intensity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> is sufficient for exact recovery within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{1}$ </tex-math></inline-formula> . This condition exhibits an elbow at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{2} \asymp n_{1}\log {n_{1}}$ </tex-math></inline-formula> between the low-dimensional and high-dimensional regimes. The suggested procedure is a variant of Lloyd’s iterations initialized with a well-chosen spectral estimator leading to what we expect to be the optimal condition for exact recovery in BSBM. The optimality conjecture is supported by showing that, for a supervised oracle procedure, such a condition is necessary to achieve exact recovery. The key elements of the proof techniques are different from classical community detection tools on random graphs. Numerical studies confirm our theory, and show that the suggested algorithm is both very fast and achieves almost the same performance as the supervised oracle. Finally, using the connection between planted satisfiability problems and the BSBM, we improve upon the sufficient number of clauses to completely recover the planted assignment.

Title: Quasigroup Words and Reversible Automata Abstract: This paper examines two related topics: the linearization of the reversible automata of Gvaramiya and Plotkin, and the problem of finding a faithful representation of the words in a central quasigroup that respects the triality symmetry of the language of quasigroups. In particular, it is shown that every central pique is a module over a ring on which the triality group acts.

Title: On the path partition number of 6-regular graphs Abstract: A path partition (also referred to as a linear forest) of a graph G $G$ is a set of vertex-disjoint paths which together contain all the vertices of G $G$. An isolated vertex is considered to be a path in this case. The path partition conjecture states that every n $n$-vertex d $d$-regular graph has a path partition with at most n d + 1 $\frac{n}{d+1}$ paths. The conjecture has been proved for all d < 6 $d\lt 6$. We prove the conjecture for d = 6 $d=6$.

Title: Optimal complexity and certification of Bregman first-order methods Abstract: We provide a lower bound showing that the O(1/k) convergence rate of the NoLips method (a.k.a. Bregman Gradient or Mirror Descent) is optimal for the class of problems satisfying the relative smoothness assumption. This assumption appeared in the recent developments around the Bregman Gradient method, where acceleration remained an open issue. The main inspiration behind this lower bound stems from an extension of the performance estimation framework of Drori and Teboulle (Mathematical Programming, 2014) to Bregman first-order methods. This technique allows computing worst-case scenarios for NoLips in the context of relatively-smooth minimization. In particular, we used numerically generated worst-case examples as a basis for obtaining the general lower bound.

Title: Network Flows That Solve Sylvester Matrix Equations Abstract: In this article, we study methods to solve a Sylvester equation in the form of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {A}\mathbf {X}+\mathbf {X}\mathbf {B}=\mathbf {C}$</tex-math></inline-formula> for given matrices <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {A}, \mathbf {B}, \mathbf {C}\in \mathbb {R}^{n\times n}$</tex-math></inline-formula> , inspired by the distributed linear equation flows. The entries of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {A}, \mathbf {B},$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {C}$</tex-math></inline-formula> are separately partitioned into a number of pieces (or sometimes we permit these pieces to overlap), which are allocated to nodes in a network. Nodes hold a dynamic state shared among their neighbors defined from the network structure. Natural partial or full row/column partitions and block partitions of the data <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {A}, \mathbf {B},$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {C}$</tex-math></inline-formula> are formulated by use of the vectorized matrix equation. We show that existing network flows for distributed linear algebraic equations can be extended to solve this special form of matrix equations over networks. A “consensus <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$+$</tex-math></inline-formula> projection <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$+$</tex-math></inline-formula> symmetrization” flow is also developed for equations with symmetry constraints on the matrix variables. We prove the convergence of these flows and obtain the fastest convergence rates that these flows can achieve regardless of the choices of node interaction strengths and network structures.

Title: Joint emotion label space modeling for affect lexica Abstract: Emotion lexica are commonly used resources to combat data poverty in automatic emotion detection. However, vocabulary coverage issues, differences in construction method and discrepancies in emotion framework and representation result in a heterogeneous landscape of emotion detection resources, calling for a unified approach to utilizing them. To combat this, we present an extended emotion lexicon of 30,273 unique entries, which is a result of merging eight existing emotion lexica by means of a multi-view variational autoencoder (VAE). We showed that a VAE is a valid approach for combining lexica with different label spaces into a joint emotion label space with a chosen number of dimensions, and that these dimensions are still interpretable. We tested the utility of the unified VAE lexicon by employing the lexicon values as features in an emotion detection model. We found that the VAE lexicon outperformed individual lexica, but contrary to our expectations, it did not outperform a naive concatenation of lexica, although it did contribute to the naive concatenation when added as an extra lexicon. Furthermore, using lexicon information as additional features on top of state-of-the-art language models usually resulted in a better performance than when no lexicon information was used.

Title: Exact and Approximation Algorithms for the Expanding Search Problem Abstract: Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. Starting from a fixed root node, an expanding search visits the vertices sequentially until it finds the target, where the next vertex can be reached from any of the previously visited vertices. That is, the time to reach the next vertex equals the shortest-path distance from the set of all previously visited vertices. The expanding search problem then asks for a sequence of the nodes, so as to minimize the expected time to finding the target. This problem has numerous applications, such as searching for hidden explosives, mining coal, and disaster relief. In this paper, we develop exact algorithms and heuristics, including a branch-and-cut procedure, a greedy algorithm with a constant-factor approximation guarantee, and a local search procedure based on a spanning-tree neighborhood. Computational experiments show that our branch-and-cut procedure outperforms existing methods for instances with nonuniform probability distributions and that both our heuristics compute near-optimal solutions with little computational effort. Summary of Contribution: This paper studies new algorithms for the expanding search problem, which asks to search a graph for a target hidden in one of the nodes according to a known probability distribution. This problem has applications such as searching for hidden explosives, mining coal, and disaster relief. We propose several new algorithms, including a branch-and-cut procedure, a greedy algorithm, and a local search procedure; and we analyze their performance both experimentally and theoretically. Our analysis shows that the algorithms improve on the performance of existing methods and establishes the first constant-factor approximation guarantee for this problem.

Title: Multi-Source Spatial Entity Linkage Abstract: Besides the traditional cartographic data sources, spatial information can also be derived from location-based sources. However, even though different location-based sources refer to the same physical world, each one has only partial coverage of the spatial entities, describe them with different attributes, and sometimes provide contradicting information. Hence, we introduce the spatial entity linkage problem, which finds which pairs of spatial entities belong to the same physical spatial entity. Our proposed solution ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QuadSky</i> ) starts with a time-efficient spatial blocking technique ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QuadFlex</i> ), compares pairwise the spatial entities in the same block, ranks the pairs using Pareto optimality with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SkyRank</i> algorithm, and finally, classifies the pairs with our novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SkyEx-*</i> family of algorithms that yield 0.85 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precision</i> and 0.85 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">recall</i> for a manually labeled dataset of 1,500 pairs and 0.87 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precision</i> and 0.6 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">recall</i> for a semi-manually labeled dataset of 777,452 pairs. Moreover, we provide a theoretical guarantee and formalize the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SkyEx-FES</i> algorithm that explores only 27 percent of the skylines without any loss in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F-measure</i> . Furthermore, our fully unsupervised algorithm <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SkyEx-D</i> approximates the optimal result with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F-measure</i> loss of just 0.01. Finally, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QuadSky</i> provides the best trade-off between <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precision</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">recall</i> , and the best <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F-measure</i> compared to the existing baselines and clustering techniques, and approximates the results of supervised learning solutions.

Title: Incompressibility of Classical Distributions Abstract: In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $\rho $ drawn from a known ensemble (but without knowing what $\rho $ is), and she transmits sufficient quantum data to a receiver Bob so that ...

Title: Motion Control for Autonomous Heterogeneous Multiagent Area Search in Uncertain Conditions Abstract: Using multiple mobile robots in search missions offers a lot of benefits, but one needs a suitable and competent motion control algorithm that is able to consider sensor characteristics, the uncertainty of target detection, and complexity of needed maneuvers in order to make a multiagent search autonomous. This article provides a methodology for an autonomous 2-D search using multiple unmanned (aerial or possibly other) vehicles. The proposed methodology relies on an accurate calculation of target occurrence probability distribution based on the initial estimated target distribution and continuous action of spatial variant search agent sensors. The core of the autonomous search process is a high-level motion control for multiple search agents which utilizes the probabilistic model of target occurrence via a heat equation-driven area coverage (HEDAC) method. This centralized motion control algorithm is tailored for handling a group of search agents that are heterogeneous in both motion and sensing characteristics. The motion of agents is directed by the gradient of the potential field which provides a near-ergodic exploration of the search space. The proposed method is tested on three realistic search mission simulations and compared with three alternative methods, where HEDAC outperforms all alternatives in all tests. Conventional search strategies need about double the time to achieve the proportionate detection rate when compared to HEDAC controlled search. The scalability test showed that increasing the number of an HEDAC controlled search agents, although somewhat deteriorating the search efficiency, provides needed speed-up of the search. This study shows the flexibility and competence of the proposed method and gives a strong foundation for possible real-world applications.

Title: Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces Abstract: This paper investigates properties of $$\sigma $$ -closed forcings which generate ultrafilters satisfying weak partition relations. The Ramsey degree of an ultrafilter $${\mathcal {U}}$$ for n-tuples, denoted $$t({\mathcal {U}},n)$$ , is the smallest number t such that given any $$l\ge 2$$ and coloring $$c:[\omega ]^n\rightarrow l$$ , there is a member $$X\in {\mathcal {U}}$$ such that the restriction of c to $$[X]^n$$ has no more than t colors. Many well-known $$\sigma $$ -closed forcings are known to generate ultrafilters with finite Ramsey degrees, but finding the precise degrees can sometimes prove elusive or quite involved, at best. In this paper, we utilize methods of topological Ramsey spaces to calculate Ramsey degrees of several classes of ultrafilters generated by $$\sigma $$ -closed forcings. These include a hierarchy of forcings due to Laflamme which generate weakly Ramsey and weaker rapid p-points, forcings of Baumgartner and Taylor and of Blass and generalizations, and the collection of non-p-points generated by the forcings $${\mathcal {P}}(\omega ^k)/\mathrm {Fin}^{\otimes k}$$ . We provide a general approach to calculating the Ramsey degrees of these ultrafilters, obtaining new results as well as streamlined proofs of previously known results. In the second half of the paper, we calculate pseudointersection and tower numbers for these $$\sigma $$ -closed forcings and their relationships with the classical pseudointersection number $${\mathfrak {p}}$$ .

Title: Who Are the Phishers? Phishing Scam Detection on Ethereum via Network Embedding Abstract: Recently, blockchain technology has become a topic in the spotlight but also a hotbed of various cybercrimes. Among them, phishing scams on blockchain have been found to make a notable amount of money, thus emerging as a serious threat to the trading security of the blockchain ecosystem. In order to create a favorable environment for investment, an effective method for detecting phishing scams is ...

Title: Computer Model Emulation with High-Dimensional Functional Output in Large-Scale Observing System Uncertainty Experiments Abstract: Observing system uncertainty experiments (OSUEs) have been recently proposed as a cost-effective way to perform probabilistic assessment of retrievals for NASA's Orbiting Carbon Observatory-2 (OCO-2) mission. One important component in the OCO-2 retrieval algorithm is a full-physics forward model that describes the mathematical relationship between atmospheric variables such as carbon dioxide and radiances measured by the remote sensing instrument. This complex forward model is computationally expensive but large-scale OSUEs require evaluation of this model numerous times, which makes it infeasible for comprehensive experiments. To tackle this issue, we develop a statistical emulator to facilitate large-scale OSUEs in the OCO-2 mission. Within each distinct spectral band, the emulator represents radiance output at irregular wavelengths as a linear combination of basis functions and random coefficients. These random coefficients are then modeled with nearest-neighbor Gaussian processes with built-in input dimension reduction via active subspace. The proposed emulator reduces dimensionality in both input space and output space, so that fast computation is achieved within a fully Bayesian inference framework. Validation experiments demonstrate that this emulator outperforms other competing statistical methods and a reduced order model that approximates the full-physics forward model.

Title: Rule extraction in unsupervised anomaly detection for model explainability: Application to OneClass SVM Abstract: OneClass SVM is a popular method for unsupervised anomaly detection. As many other methods, it suffers from the black box problem: it is difficult to justify, in an intuitive and simple manner, why the decision frontier is identifying data points as anomalous or non anomalous. This problem is being widely addressed for supervised models. However, it is still an uncharted area for unsupervised learning. In this paper, we evaluate several rule extraction techniques over OneClass SVM models, while presenting alternative designs for some of those algorithms. Furthermore, we propose algorithms for computing metrics related to eXplainable Artificial Intelligence (XAI) regarding the “comprehensibility”, “representativeness”, “stability” and “diversity” of the extracted rules. We evaluate our proposals with different data sets, including real-world data coming from industry. Consequently, our proposal contributes to extending XAI techniques to unsupervised machine learning models.

Title: The Linear Algebra Mapping Problem. Current State of Linear Algebra Languages and Libraries Abstract: We observe a disconnect between developers and end-users of linear algebra libraries. On the one hand, developers invest significant effort in creating sophisticated numerical kernels. On the other hand, end-users are progressively less likely to go through the time consuming process of directly using said kernels; instead, languages and libraries, which offer a higher level of abstraction, are becoming increasingly popular. These languages offer mechanisms that internally map the input program to lower level kernels. Unfortunately, our experience suggests that, in terms of performance, this translation is typically suboptimal.In this paper, we define the problem of mapping a linear algebra expression to a set of available building blocks as the “Linear Algebra Mapping Problem” (LAMP); we discuss its NP-complete nature, and investigate how effectively a benchmark of test problems is solved by popular high-level programming languages and libraries. Specifically, we consider Matlab, Octave, Julia, R, Armadillo (C++), Eigen (C++), and NumPy (Python); the benchmark is meant to test both compiler optimizations, as well as linear algebra specific optimizations, such as the optimal parenthesization of matrix products. The aim of this study is to facilitate the development of languages and libraries that support linear algebra computations.

Title: JANOS: An Integrated Predictive and Prescriptive Modeling Framework Abstract: Business research practice is witnessing a surge in the integration of predictive modeling and prescriptive analysis. We describe a modeling framework JANOS that seamlessly integrates the two streams of analytics, allowing researchers and practitioners to embed machine learning models in an end-to-end optimization framework. JANOS allows for specifying a prescriptive model using standard optimization modeling elements such as constraints and variables. The key novelty lies in providing modeling constructs that enable the specification of commonly used predictive models within an optimization model, have the features of the predictive model as variables in the optimization model, and incorporate the output of the predictive models as part of the objective. The framework considers two sets of decision variables: regular and predicted. The relationship between the regular and the predicted variables is specified by the user as pretrained predictive models. JANOS currently supports linear regression, logistic regression, and neural network with rectified linear activation functions. In this paper, we demonstrate the flexibility of the framework through an example on scholarship allocation in a student enrollment problem and provide a numeric performance evaluation. Summary of Contribution. This paper describes a new software tool, JANOS, that integrates predictive modeling and discrete optimization to assist decision making. Specifically, the proposed solver takes as input user-specified pretrained predictive models and formulates optimization models directly over those predictive models by embedding them within an optimization model through linear transformations.

Title: Uniform chain decompositions and applications Abstract: The Boolean lattice 2[n] is the family of all subsets of [n] = {1,., n} ordered by inclusion, and a chain is a family of pairwise comparable elements of 2[n]. Let s = 2n/ ( n.n/2.), which is the average size of a chain in a minimal chain decomposition of 2[n]. We prove that 2[n] can be partitioned into ( n.n/2.) chains such that all but at most o(1) proportion of the chains have size s(1+ o(1)). This asymptotically proves a conjecture of Furedi from1985. Our proof is based on probabilistic arguments. To analyze our random partition we develop a weighted variant of the graph container method. Using this result, we also answer a Kalai-type question raised recently by Das, Lamaison, and Tran. What is theminimum number of forbidden comparable pairs forcing that the largest subfamily of 2[n] not containing any of them has size at most ( n.n/2.) ? We show that the answer is (v.. 8 + o(1))2nv n. Finally, we discuss how these uniform chain decompositions can be used to optimize and simplify various results in extremal set theory.

Title: A Continuous Teleoperation Subspace With Empirical and Algorithmic Mapping Algorithms for Nonanthropomorphic Hands Abstract: Teleoperation is a valuable tool for robotic manipulators in highly unstructured environments. However, finding an intuitive mapping between a human hand and a nonanthropomorphic robot hand can be difficult, due to the hands’ dissimilar kinematics. In this article, we seek to create a mapping between the human hand and a fully actuated, nonanthropomorphic robot hand that is intuitive enough to enable effective real-time teleoperation, even for novice users. To accomplish this, we propose a low-dimensional teleoperation subspace that can be used as an intermediary for mapping between hand pose spaces. We present two different methods to define the teleoperation subspace: an empirical definition, which requires a person to define hand motions in an intuitive, hand-specific way, and an algorithmic definition, which is kinematically independent and uses objects to define the subspace. We use each of these definitions to create a teleoperation mapping for different hands. One of the main contributions of this article is the validation of both the empirical and algorithmic mappings with teleoperation experiments controlled by ten novices and performed on two kinematically distinct hands. The experiments show that the proposed subspace is relevant to teleoperation, intuitive enough to enable control by novices, and can generalize to nonanthropomorphic hands with different kinematics. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As robots move into our warehouses, workplaces, and homes, it is important to develop robotic controls that are intuitive and easy for novices to use. In particular, teleoperation can be valuable to guide robots when they encounter situations that autonomous programs are not prepared to deal with. In this article, we focus specifically on robotic grasping using nonanthropomorphic hands. Our method is intended for novice users to intuitively teleoperate such robots. We show that the teleoperation subspace we use can effectively enable pick-and-place tasks and in-hand manipulation tasks and that it is intuitive for novice operators. Our subspace outperforms state-of-the-art methods for pick-and-place tasks and performs as well as state-of-the-art methods for in-hand manipulation.

Title: Ocular recognition databases and competitions: a survey Abstract: The use of the iris and periocular region as biometric traits has been extensively investigated, mainly due to the singularity of the iris features and the use of the periocular region when the image resolution is not sufficient to extract iris information. In addition to providing information about an individual's identity, features extracted from these traits can also be explored to obtain other information such as the individual's gender, the influence of drug use, the use of contact lenses, spoofing, among others. This work presents a survey of the databases created for ocular recognition, detailing their protocols and how their images were acquired. We also describe and discuss the most popular ocular recognition competitions (contests), highlighting the submitted algorithms that achieved the best results using only iris trait and also fusing iris and periocular region information. Finally, we describe some relevant works applying deep learning techniques to ocular recognition and point out new challenges and future directions. Considering that there are a large number of ocular databases, and each one is usually designed for a specific problem, we believe this survey can provide a broad overview of the challenges in ocular biometrics.

Title: WaveRange: wavelet-based data compression for three-dimensional numerical simulations on regular grids Abstract: A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data. The effectiveness of this method is demonstrated by applying it to example numerical tests, ranging from idealized configurations to realistic global-scale simulations. The novelty of this study is in its focus on assessing the impact of compression on post-processing and restart of numerical simulations.

Title: Graph pruning for model compression Abstract: Previous AutoML pruning works utilized individual layer features to automatically prune filters. We analyze the correlation for two layers from the different blocks which have a short-cut structure. It shows that, in one block, the deeper layer has many redundant filters which can be represented by filters in the former layer. So, it is necessary to take information from other layers into consideration in pruning. In this paper, a novel pruning method, named GraphPruning, is proposed. Any series of the network is viewed as a graph. To automatically aggregate neighboring features for each node, a graph aggregator based on graph convolution networks (GCN) is designed. In the training stage, a PruningNet that is given aggregated node features generates reasonable weights for any size of the sub-network. Subsequently, the best configuration of the Pruned Network is searched by reinforcement learning. Different from previous work, we take the node features from a well-trained graph aggregator instead of the hand-craft features, as the states in reinforcement learning. Compared with other AutoML pruning works, our method has achieved the state-of-the-art under the same conditions on ImageNet-2012.

Title: Robust Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Unknown Dynamics and State Constraints Abstract: Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this article, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopman operator-based prediction model obtained offline from precollected input–output datasets. Unlike classic tube-based MPC, in each prediction time interval of r-LPC, we use an actor–critic structure to learn a near-optimal feedback control policy rather than a control sequence. The resulting closed-loop control policy can be learned offline and deployed online or learned online in an asynchronous way. In the latter case, online learning can be activated whenever necessary; for instance, the safety constraint is violated with the deployed policy. The closed-loop recursive feasibility, robustness, and asymptotic stability are proven under function approximation errors of the actor–critic networks. Simulation and experimental results on two nonlinear systems with unknown dynamics and disturbances have demonstrated that our approach has better or comparable performance when compared with tube-based MPC and linear quadratic regulator, and outperforms a recently developed actor–critic learning approach.

Title: Bribery in Rating Systems: A Game-Theoretic Perspective Abstract: Rating systems play a vital role in the exponential growth of service-oriented markets. As highly rated online services usually receive substantial revenue in the markets, malicious sellers seek to boost their service evaluation by manipulating the rating system with fake ratings. One effective way to improve the service evaluation is to hire fake rating providers by bribery. The fake ratings given by the bribed buyers influence the evaluation of the service, which further impacts the decision-making of potential buyers. In this paper, we study the bribery of a rating system with multiple sellers and buyers via a game-theoretic perspective. In detail, we examine whether there exists an equilibrium state in the market in which the rating system is expected to be bribery-proof: no bribery strategy yields a strictly positive gain. We first collect real-world data for modeling the bribery problem in rating systems. On top of that, we analyze the problem of bribery in a rating system as a static game. From our analysis, we conclude that at least a Nash equilibrium can be reached in the bribery game of rating systems.

Title: LINEAR FILTERING WITH FRACTIONAL NOISES: LARGE TIME AND SMALL NOISE ASYMPTOTICS Abstract: The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated operator equation in general, simplifies to the Riccati ordinary differential equation in the martingale case. This reduction lies in the foundations of the Kalman--Bucy approach to linear optimal filtering. In this paper we consider a basic KalmanBucy model with noises, generated by independent fractional Brownian motions, and develop a new method of asymptotic analysis of the integro-differential filtering equation arising in this case. We establish existence of the steady-state error limit and find its asymptotic scaling in the high signalto-noise regime. Closed form expressions are derived in a number of important cases.

Title: Learnable Pooling in Graph Convolutional Networks for Brain Surface Analysis Abstract: Brain surface analysis is essential to neuroscience, however, the complex geometry of the brain cortex hinders computational methods for this task. The difficulty arises from a discrepancy between 3D imaging data, which is represented in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Euclidean</i> space, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-Euclidean</i> geometry of the highly-convoluted brain surface. Recent advances in machine learning have enabled the use of neural networks for non-Euclidean spaces. These facilitate the learning of surface data, yet pooling strategies often remain constrained to a single fixed-graph. This paper proposes a new learnable graph pooling method for processing multiple surface-valued data to output subject-based information. The proposed method innovates by learning an intrinsic aggregation of graph nodes based on graph spectral embedding. We illustrate the advantages of our approach with in-depth experiments on two large-scale benchmark datasets. The ablation study in the paper illustrates the impact of various factors affecting our learnable pooling method. The flexibility of the pooling strategy is evaluated on four different prediction tasks, namely, subject-sex classification, regression of cortical region sizes, classification of Alzheimer’s disease stages, and brain age regression. Our experiments demonstrate the superiority of our learnable pooling approach compared to other pooling techniques for graph convolutional networks, with results improving the state-of-the-art in brain surface analysis.

Title: On the Existence and Computation of Minimum Attention Optimal Control Laws Abstract: One means of capturing the cost of control implementation of a general nonlinear control system is via Brockett’s minimum attention criterion, defined as a multidimensional integral of the rate of change of the control with respect to state and time. Although shown to be important in human motor control and robotics applications, a practical difficulty with this criterion is that the existence of ...

Title: A Fully Natural Gradient Scheme for Improving Inference of the Heterogeneous Multioutput Gaussian Process Model Abstract: A recent novel extension of multioutput Gaussian processes (GPs) handles heterogeneous outputs, assuming that each output has its own likelihood function. It uses a vector-valued GP prior to jointly model all likelihoods’ parameters as latent functions drawn from a GP with a linear model of coregionalization (LMC) covariance. By means of an inducing points’ framework, the model is able to obtain tractable variational bounds amenable to stochastic variational inference (SVI). Nonetheless, the strong conditioning between the variational parameters and the hyperparameters burdens the adaptive gradient optimization methods used in the original approach. To overcome this issue, we borrow ideas from variational optimization introducing an exploratory distribution over the hyperparameters, allowing inference together with the posterior’s variational parameters through a fully natural gradient (NG) optimization scheme. Furthermore, in this work, we introduce an extension of the heterogeneous multioutput model, where its latent functions are drawn from convolution processes. We show that our optimization scheme can achieve better local optima solutions with higher test performance rates than adaptive gradient methods for both the LMC and the convolution process model. We also show how to make the convolutional model scalable by means of SVI and how to optimize it through a fully NG scheme. We compare the performance of the different methods over the toy and real databases.

Title: Design and Evaluation of a Multi-Domain Trojan Detection Method on Deep Neural Networks Abstract: Trojan attacks on deep neural networks (DNNs) exploit a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">backdoor</i> embedded in a DNN model that can hijack any input with an attacker’s chosen signature trigger. Emerging defence mechanisms are mainly designed and validated on vision domain tasks (e.g., image classification) on 2D Convolutional Neural Network (CNN) model architectures; a defence mechanism that is general across vision, text, and audio domain tasks is demanded. This work designs and evaluates a run-time Trojan detection method exploiting <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STR</u> ong <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</u> ntentional <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</u> erturbation of inputs that is a multi-domain input-agnostic Trojan detection defence across <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Vi</u> sion, <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</u> ext and <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</u> udio domains—thus termed as STRIP-ViTA. Specifically, STRIP-ViTA is demonstratively independent of not only task domain but also model architectures. Most importantly, unlike other detection mechanisms, it requires neither machine learning expertise nor expensive computational resource, which are the reason behind DNN model outsourcing scenario—one main attack surface of Trojan attack. We have extensively evaluated the performance of STRIP-ViTA over: i) CIFAR10 and GTSRB datasets using 2D CNNs for vision tasks; ii) IMDB and consumer complaint datasets using both LSTM and 1D CNNs for text tasks; and iii) speech command dataset using both 1D CNNs and 2D CNNs for audio tasks. Experimental results based on more than 30 tested Trojaned models (including publicly Trojaned model) corroborate that STRIP-ViTA performs well across all nine architectures and five datasets. Overall, STRIP-ViTA can effectively detect trigger inputs with small false acceptance rate (FAR) with an acceptable preset false rejection rate (FRR). In particular, for vision tasks, we can always achieve a 0 percent FRR and FAR given strong attack success rate always preferred by the attacker. By setting FRR to be 3 percent, average FAR of 1.1 and 3.55 percent are achieved for text and audio tasks, respectively. Moreover, we have evaluated STRIP-ViTA against a number of advanced backdoor attacks and compare its effectiveness with other recent state-of-the-arts.

Title: AN ALGORITHMIC APPROACH TO CHEVALLEY'S THEOREM ON IMAGES OF RATIONAL MORPHISMS BETWEEN AFFINE VARIETIES Abstract: The goal of this paper is to introduce a new constructive geometric proof of the affine version of Chevalley's Theorem. This proof is algorithmic and a verbatim implementation resulted in an efficient code for computing the constructible image of rational maps between affine varieties. Our approach extends the known descriptions of uniform matrix product states to uMPS(2, 2, 5).

Title: Constructions of optimal Hermitian self-dual codes from unitary matrices Abstract: We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual codes by means of unitary matrices, where some of them generalize the quadratic double circulant constructions. Many optimal Hermitian self-dual codes over large finite fields with new parameters are obtained. More precisely MDS or almost MDS Hermitian self-dual codes of lengths up to 18 are constructed over finite fields Fq, where q=32,42,52,72,82,92,112,132,172,192. Comparisons with classical constructions are made.

Title: An iterative security game for computing robust and adaptive network flows Abstract: We study the robust and adaptive maximum network flow problem in an uncertain environment where the network parameters (e.g., capacities) are known and deterministic, but the network structure (e.g., edges) is vulnerable to adversarial attacks or failures. We propose a robust and sustainable network flow model to effectively and proactively counter plausible attacking behaviors of an adversary operating under a budget constraint. Specifically, we introduce a novel scenario generation approach based on an iterative two-player game between a defender and an adversary. We assume that the adversary always takes a best myopic response (out of some feasible attacks) against the current flow scenario prepared by the defender. On the other hand, we assume that the defender considers all the attacking behaviors revealed by the adversary in previous iterations of the game in order to generate a new conservative flow strategy that is robust (maximin) against all those attacks. This iterative game continues until the objectives of the adversary and the administrator both converge. We show that the robust network flow problem to be solved by the defender is NP-hard and that the complexity of the adversary's decision problem grows exponentially with the network size and the adversary's budget value. We propose two principled heuristic approaches for solving the adversary's problem at the scale of a large urban network. Extensive computational results on multiple synthetic and real-world data sets demonstrate that the solution provided by the defender's problem significantly increases the amount of flow pushed through the network and reduces the expected amount of lost flow over four state-of-the-art benchmark approaches.

Title: Functional Bayesian Filter Abstract: We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). By applying the kernel method and the representer theorem to perform linear quadratic estimation in a functional space, we derive a Bayesian recursive state estimator for a general nonlinear dynamical system in the original input space. Unlike existing n...

Title: Does Set Theory Really Ground Arithmetic Truth? Abstract: We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth. Our method is to emphasize the incomplete picture of both theories and to treat models as their syntactical counterparts. Insisting on the incomplete picture will allow us to argue in favor of the revisability of the standard-model interpretation. We start briefly characterizing the expansion of arithmetic 'truth' provided by the interpretation in a set theory. Interpreted versions of an arithmetic theory into set theories generally have more theorems than the original. This theorem expansion is not complete however. Using this, the set theoretic multiversalist concludes that there are multiple legitimate standard models of arithmetic. We suggest a different multiversalist conclusion: while there is a single arithmetic structure, its interpretation in each universe may vary or even not be possible. We continue by defining the coordination problem. We consider two independent communities of mathematicians responsible for deciding over new axioms for ZF and PA. How likely are they to be coordinated regarding PA's interpretation in ZF? We prove that it is possible to have extensions of PA not interpretable in a given set theory ST. We further show that the number of extensions of arithmetic is uncountable, while interpretable extensions in ST are countable. We finally argue that this fact suggests that coordination can only work if it is assumed from the start.

Title: Stochastic Graphon Games: I. The Static Case Abstract: We consider static finite-player network games and their continuum analogs graphon games. Existence and uniqueness results are provided as well as convergence of the finite-player network game optimal strategy profiles to their analogs for the graphon games. We also show that equilibrium strategy profiles of a graphon game provide approximate Nash equilibria for the finite-player games. Connections with mean field games are discussed. A motivating application of Cournot competition is presented, and explicit computation of its Nash equilibrium is provided.

Title: Semiconvergence of the extended PSS method for singular generalized saddle point problems Abstract: Recently, an extension of the positive definite and skew-Hermitian splitting (EPSS) iteration method for nonsingular generalized saddle point problems has been stated by Masoudi and Salkuyeh. In this article, we study the semiconvergence of the EPSS method for singular generalized saddle problems. Then a special case of the EPSS (SEPSS) preconditioner is applied to accelerate the convergence of the GMRES method for solving singular generalized saddle point problems. Some numerical results are given to demonstrate the robustness of the preconditioner.

Title: Fine-Grained Attention and Feature-Sharing Generative Adversarial Networks for Single Image Super-Resolution Abstract: Traditional super-resolution (SR) methods by minimize the mean square error usually produce images with over-smoothed and blurry edges, due to the lack of high-frequency details. In this paper, we propose two novel techniques within the generative adversarial network framework to encourage generation of photo-realistic images for image super-resolution. Firstly, instead of producing a single score to discriminate real and fake images, we propose a variant, called Fine-grained Attention Generative Adversarial Network (FASRGAN), to discriminate each pixel of real and fake images. FASRGAN adopts a UNet-like network as the discriminator with two outputs: an image score and an image score map. The score map has the same spatial size as the HR/SR images, serving as the fine-grained attention to represent the degree of reconstruction difficulty for each pixel. Secondly, instead of using different networks for the generator and the discriminator, we introduce a feature-sharing variant (denoted as Fs-SRGAN) for both the generator and the discriminator. The sharing mechanism can maintain model express power while making the model more compact, and thus can improve the ability of producing high-quality images. Quantitative and visual comparisons with state-of-the-art methods on benchmark datasets demonstrate the superiority of our methods. We further apply our super-resolution images for object recognition, which further demonstrates the effectiveness of our proposed method. The code is available at https://github.com/Rainyfish/FASRGAN-and-Fs-SRGAN.

Title: An Investigation on Semismooth Newton based Augmented Lagrangian Method for Image Restoration Abstract: The augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging and optimal control. However, one usually needs to solve a coupled and nonlinear system of equations, which is very challenging. In this paper, we propose several semismooth Newton methods to solve arising nonlinear subproblems for image restoration in finite dimensional spaces, which leads to several highly efficient and competitive algorithms for imaging processing. With the analysis of the metric subregularities of the corresponding functions, we give both the global convergence and local linear convergence rate for the proposed augmented Lagrangian methods with semismooth Newton solvers.

Title: Gating Revisited: Deep Multi-Layer RNNs That can be Trained Abstract: We propose a new STAckable Recurrent cell (STAR) for recurrent neural networks (RNNs), which has fewer parameters than widely used LSTM [16] and GRU [10] while being more robust against vanishing or exploding gradients. Stacking recurrent units into deep architectures suffers from two major limitations: (i) many recurrent cells (e.g., LSTMs) are costly in terms of parameters and computation resources; and (ii) deep RNNs are prone to vanishing or exploding gradients during training. We investigate the training of multi-layer RNNs and examine the magnitude of the gradients as they propagate through the network in the ”vertical” direction. We show that, depending on the structure of the basic recurrent unit, the gradients are systematically attenuated or amplified. Based on our analysis we design a new type of gated cell that better preserves gradient magnitude. We validate our design on a large number of sequence modelling tasks and demonstrate that the proposed STAR cell allows to build and train deeper recurrent architectures, ultimately leading to improved performance while being computationally more efficient.

Title: Orienting Ordered Scaffolds: Complexity and Algorithms Abstract: Despite the recent progress in genome sequencing and assembly, many of the currently available assembled genomes come in a draft form. Such draft genomes consist of a large number of genomic fragments (scaffolds), whose order and/or orientation (i.e., strand) in the genome are unknown. There exist various scaffold assembly methods, which attempt to determine the order and orientation of scaffolds along the genome chromosomes. Some of these methods (e.g., based on FISH physical mapping, chromatin conformation capture, etc.) can infer the order of scaffolds, but not necessarily their orientation. This leads to a special case of the scaffold orientation problem (i.e., deducing the orientation of each scaffold) with a known order of the scaffolds. We address the problem of orientating ordered scaffolds as an optimization problem based on given weighted orientations of scaffolds and their pairs (e.g., coming from pair-end sequencing reads, long reads, or homologous relations). We formalize this problem using notion of a scaffold graph (i.e., a graph, where vertices correspond to the assembled contigs or scaffolds and edges represent connections between them). We prove that this problem is $$\textsf {NP}$$ -hard, and present a polynomial-time algorithm for solving its special case, where orientation of each scaffold is imposed relatively to at most two other scaffolds. We further develop a fixed-parameter tractable algorithm for the general case of the orientation of ordered scaffolds problem.