Datasets:

debajyotidasgupta

/

dblp_2022_2023

like 0

Title: Role detection in bicycle-sharing networks using multilayer stochastic block models Abstract: In urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Our models successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.

Title: Predicting Network Controllability Robustness: A Convolutional Neural Network Approach Abstract: Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node removals or edge removals. The measure of network controllability is quantified by the number of external control inputs needed to recover or to retain the controllability after the occurrence of an unexpected attack. The measure of the network controllability robustness, on the other hand, is quantified by a sequence of values that record the remaining controllability of the network after a sequence of attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming. In this article, a method to predict the controllability robustness based on machine learning using a convolutional neural network (CNN) is proposed, motivated by the observations that: 1) there is no clear correlation between the topological features and the controllability robustness of a general network; 2) the adjacency matrix of a network can be regarded as a grayscale image; and 3) the CNN technique has proved successful in image processing without human intervention. Under the new framework, a fairly large number of training data generated by simulations are used to train a CNN for predicting the controllability robustness according to the input network-adjacency matrices, without performing conventional attack simulations. Extensive experimental studies were carried out, which demonstrate that the proposed framework for predicting controllability robustness of different network configurations is accurate and reliable with very low overheads.

Title: Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups Abstract: We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M, Polish group G of permutations of M, and $$n \ge 1$$ , G has a comeager n-diagonal conjugacy class iff the family of all n-tuples of G-extendable bijections between finitely generated substructures of M, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.

Title: Eco-Mobility-on-Demand Fleet Control With Ride-Sharing Abstract: Shared Mobility-on-Demand using automated vehicles can reduce energy consumption and cost for future mobility. However, its full potential in energy saving has not been fully explored. An algorithm to minimize fleet fuel consumption while satisfying customers’ travel time constraints is developed in this article. Numerical simulations with realistic travel demand and route choice are performed, sh...

Title: MetaMixUp: Learning Adaptive Interpolation Policy of MixUp With Metalearning Abstract: MixUp is an effective data augmentation method to regularize deep neural networks via random linear interpolations between pairs of samples and their labels. It plays an important role in model regularization, semisupervised learning (SSL), and domain adaption. However, despite its empirical success, its deficiency of randomly mixing samples has poorly been studied. Since deep networks are capable of memorizing the entire data set, the corrupted samples generated by vanilla MixUp with a badly chosen interpolation policy will degrade the performance of networks. To overcome overfitting to corrupted samples, inspired by metalearning (learning to learn), we propose a novel technique of learning to a mixup in this work, namely, MetaMixUp. Unlike the vanilla MixUp that samples interpolation policy from a predefined distribution, this article introduces a metalearning-based online optimization approach to dynamically learn the interpolation policy in a data-adaptive way (learning to learn better). The validation set performance via metalearning captures the noisy degree, which provides optimal directions for interpolation policy learning. Furthermore, we adapt our method for pseudolabel-based SSL along with a refined pseudolabeling strategy. In our experiments, our method achieves better performance than vanilla MixUp and its variants under SL configuration. In particular, extensive experiments show that our MetaMixUp adapted SSL greatly outperforms MixUp and many state-of-the-art methods on CIFAR-10 and SVHN benchmarks under the SSL configuration.

Title: Monitoring procedures for strict stationarity based on the multivariate characteristic function. Abstract: We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Asymptotic as well as Monte Carlo results are presented. The new methods are also employed in order to test for possible stationarity breaks in time-series data from the financial sector.

Title: Reflection algebras and conservation results for theories of iterated truth Abstract: We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original system of arithmetic. Much stronger systems, however, are obtained by adding either induction axioms or reflection axioms on top of them. Theories of this kind can interpret some well-known predicatively reducible fragments of second-order arithmetic such as iterated arithmetical comprehension.

Title: Switch-based hybrid beamforming for massive MIMO communications in mmWave bands Abstract: •Switch-based hybrid networks provide a promising implementation for beamforming.•Binary nature of the switch-based structure hinders design of analog beamformer.•Decoupling and optimizing in a rank-constrained subspace is an effective method.•Frobenius norm and QR lower bound can be used as effective surrogate cost functions.•Any partially network can be designed by imposing suitable linear constraints.

Title: Bloom filter variants for multiple sets: a comparative assessment Abstract: In this paper we compare two probabilistic data structures for association queries derived from the well-known Bloom filter: the shifting Bloom filter (ShBF), and the spatial Bloom filter (SBF). With respect to the original data structure, both variants add the ability to store multiple subsets in the same filter, using different strategies. We analyse the performance of the two data structures with respect to false positive probability, and the inter-set error probability (the probability for an element in the set of being recognised as belonging to the wrong subset). As part of our analysis, we extended the functionality of the shifting Bloom filter, optimising the filter for any non-trivial number of subsets. We propose a new generalised ShBF definition with applications outside of our specific domain, and present new probability formulas. Results of the comparison show that the ShBF provides better space efficiency, but at a significantly higher computational cost than the SBF.

Title: RATE OF STRONG CONVERGENCE TO MARKOV-MODULATED BROWNIAN MOTION Abstract: Latouche and Nguyen (2015b) constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). Here, we construct a different sequence of stochastic fluid processes and show that it converges strongly to an MMBM. To the best of our knowledge, this is the first result on strong convergence to a Markov-modulated Brownian motion. Besides implying weak convergence, such a strong approximation constitutes a powerful tool for developing deep results for sophisticated models. Additionally, we prove that the rate of this almost sure convergence is o(n (-1/2) log n). When reduced to the special case of standard Brownian motion, our convergence rate is an improvement over that obtained by a different approximation in Gorostiza and Griego (1980), which is o(n(-1/2) ( log n)(5/2)).

Title: Dissipativity analysis of negative resistance circuits Abstract: This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of negative resistance. Active elements are necessary to design physical circuits that switch and oscillate. We generalize the classical passivity theory of circuit analysis to develop a port interconnection theory for such non-equilibrium behaviors. The approach closely mimics the classical methodology of (incremental) dissipativity theory, but with dissipation inequalities that combine signed storage functions and signed supply rates to account for the port interconnection of passive and active elements.

Title: A Survey of Automated Programming Hint Generation: The HINTS Framework Abstract: AbstractAutomated tutoring systems offer the flexibility and scalability necessary to facilitate the provision of high-quality and universally accessible programming education. To realise the potential of these systems, recent work has proposed a diverse range of techniques for automatically generating feedback in the form of hints to assist students with programming exercises. This article integrates these apparently disparate approaches into a coherent whole. Specifically, it emphasises that all hint techniques can be understood as a series of simpler components with similar properties. Using this insight, it presents a simple framework for describing such techniques, the Hint Iteration by Narrow-down and Transformation Steps framework, and surveys recent work in the context of this framework. Findings from this survey include that (1) hint techniques share similar properties, which can be used to visualise them together, (2) the individual steps of hint techniques should be considered when designing and evaluating hint systems, (3) more work is required to develop and improve evaluation methods, and (4) interesting relationships, such as the link between automated hints and data-driven evaluation, should be further investigated. Ultimately, this article aims to facilitate the development, extension, and comparison of automated programming hint techniques to maximise their educational potential.

Title: A Decentralized Primal-Dual Method for Constrained Minimization of a Strongly Convex Function Abstract: We propose decentralized primal-dual methods for cooperative multiagent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for suboptimality, infeasibility, and consensus violation in terms of the number of communications required; examine the effect of underlying network topology on the convergence rates.

Title: Open Named Entity Modeling From Embedding Distribution Abstract: In this paper, we report our discovery on named entity distribution in a general word embedding space, which helps an open definition on multilingual named entity definition rather than previous closed and constraint definition on named entities through a named entity dictionary, which is usually derived from human labor and replies on schedule update. Our initial visualization of monolingual word embeddings indicates named entities tend to gather together despite of named entity types and language difference, which enable us to model all named entities using a specific geometric structure inside embedding space, namely, the named entity hypersphere. For monolingual cases, the proposed named entity model gives an open description of diverse named entity types and different languages. For cross-lingual cases, mapping the proposed named entity model provides a novel way to build a named entity dataset for resource-poor languages. At last, the proposed named entity model may be shown as a handy clue to enhance state-of-the-art named entity recognition systems generally.

Title: Gaussian mixture model decomposition of multivariate signals Abstract: We propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the following features: (1) It accepts multivariate signals, i.e., sampled multivariate functions, histograms, time series, images, etc., as input. (2) The method can handle general (i.e., ellipsoidal) Gaussians. (3) No prior assumption on the number of mixture components is needed. To the best of our knowledge, no previous method for Gaussian mixture model decomposition simultaneously enjoys all these features. We also prove an upper bound, which cannot be improved by a global constant, for the distance from any mode of a Gaussian mixture model to the set of corresponding means. For mixtures of spherical Gaussians with common variance sigma(2), the bound takes the simple form root n sigma. We evaluate our method on one- and two-dimensional signals. Finally, we discuss the relation between clustering and signal decomposition, and compare our method to the baseline expectation maximization algorithm.

Title: Sparse noncommutative polynomial optimization Abstract: This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity in the input data. A converging hierarchy of semidefinite relaxations for eigenvalue and trace optimization is provided. This hierarchy is a noncommutative analogue of results due to Lasserre (SIAM J Optim 17(3):822–843, 2006) and Waki et al. (SIAM J Optim 17(1):218–242, 2006). The Gelfand–Naimark–Segal construction is applied to extract optimizers if flatness and irreducibility conditions are satisfied. Among the main techniques used are amalgamation results from operator algebra. The theoretical results are utilized to compute lower bounds on minimal eigenvalue of noncommutative polynomials from the literature.

Title: Approximations for Pareto and Proper Pareto solutions and their KKT conditions Abstract: In this article, we view the Pareto and weak Pareto solutions of the multiobjective optimization by using an approximate version of KKT type conditions. In one of our main results Ekeland’s variational principle for vector-valued maps plays a key role. We also focus on an improved version of Geoffrion proper Pareto solutions and it’s approximation and characterize them through saddle point and KKT type conditions.

Title: CrowdOS: A Ubiquitous Operating System for Crowdsourcing and Mobile Crowd Sensing Abstract: With the rise of crowdsourcing and mobile crowdsensing techniques, a large number of crowdsourcing applications or platforms ( <inline-formula><tex-math notation="LaTeX">$\mathbb {CAP}$</tex-math></inline-formula> ) have appeared. In the mean time, <inline-formula><tex-math notation="LaTeX">$\mathbb {CAP}$</tex-math></inline-formula> -related models and frameworks based on different research hypotheses are rapidly emerging, and they usually address specific issues from a certain perspective. Due to different settings and conditions, different models are not compatible with each other. However, <inline-formula><tex-math notation="LaTeX">$\mathbb {CAP}$</tex-math></inline-formula> urgently needs to combine these techniques to form a unified framework. In addition, these models needs to be learned and updated online with the extension of crowdsourced data and task types; thus, requiring a unified architecture that integrates lifelong learning concepts and breaks down the barriers between different modules. This paper draws on the idea of ubiquitous operating systems and proposes a novel OS (CrowdOS), which is an abstract software layer running between native OS and application layer. In particular, based on an in-depth analysis of the complex crowd environment and diverse characteristics of heterogeneous tasks, we construct the OS kernel and three core frameworks including task resolution and assignment framework ( <i>TRAF</i> ), integrated resource management ( <i>IRM</i> ), and task result quality optimization ( <i>TRO</i> ). In addition, we validate the usability of CrowdOS, module correctness and development efficiency. Our evaluation further reveals <i>TRO</i> brings enormous improvement in efficiency and a reduction in energy consumption.

Title: Simplified decision making in the belief space using belief sparsification Abstract: In this work, we introduce a new and efficient solution approach for the problem of decision making under uncertainty, which can be formulated as decision making in a belief space, over a possibly high-dimensional state space. Typically, to solve a decision problem, one should identify the optimal action from a set of candidates, according to some objective. We claim that one can often generate and solve an analogous yet simplified decision problem, which can be solved more efficiently. A wise simplification method can lead to the same action selection, or one for which the maximal loss in optimality can be guaranteed. Furthermore, such simplification is separated from the state inference and does not compromise its accuracy, as the selected action would finally be applied on the original state. First, we present the concept for general decision problems and provide a theoretical framework for a coherent formulation of the approach. We then practically apply these ideas to decision problems in the belief space, which can be simplified by considering a sparse approximation of their initial belief. The scalable belief sparsification algorithm we provide is able to yield solutions which are guaranteed to be consistent with the original problem. We demonstrate the benefits of the approach in the solution of a realistic active-SLAM problem and manage to significantly reduce computation time, with no loss in the quality of solution. This work is both fundamental and practical and holds numerous possible extensions.

Title: INDEPENDENCE NUMBER AND CONNECTIVITY FOR FRACTIONAL (a, b, k)-CRITICAL COVERED GRAPHS Abstract: A graph G is a fractional (a, b, k)-critical covered graph if G-U is a fractional [a, b]-covered graph for every U subset of V(G) with |U| - K, which is first defined by (Zhou, Xu and Sun, Inf. Process. Lett. 152 (2019) 105838). Furthermore, they derived a degree condition for a graph to be a fractional (a, b, k)-critical covered graph. In this paper, we gain an independence number and connectivity condition for a graph to be a fractional (a, b, k)-critical covered graph and verify that G is a fractional (a, b, k)-critical covered graph if k(G) >= max {2b(a + 1)(b + 1) + 4bk + 5/4b, (a + 1)(2)alpha(G) + 4bk +5/4b}.

Title: High order discretization methods for spatial-dependent epidemic models Abstract: In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size of the populations differs in space. The use of local spatial dependence yields a system of partial-differential equations with integral terms. The uniqueness and qualitative properties of the continuous model are analyzed. Furthermore, different spatial and temporal discretizations are employed, and step-size restrictions for the discrete model’s positivity, monotonicity preservation, and population conservation are investigated. We provide sufficient conditions under which high-order numerical schemes preserve the stability of the computational process and provide sufficiently accurate numerical approximations. Computational experiments verify the convergence and accuracy of the numerical methods.

Title: Efficient elimination of Skolem functions in $$\text {LK}^\text {h}$$ LK h Abstract: We present a sequent calculus with the Henkin constants in the place of the free variables. By disposing of the eigenvariable condition, we obtained a proof system with a strong locality property—the validity of each inference step depends only on its active formulas, not its context. Our major outcomes are: the cut elimination via a non-Gentzen-style algorithm without resorting to regularization and the elimination of Skolem functions with linear increase in the proof length for a subclass of derivations with cuts.

Title: Extending the Scope of Robust Quadratic Optimization Abstract: We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. Our results provide extensions to known results from the literature. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations. As an application, we show how to construct a natural uncertainty set based on a statistical confidence set around a sample mean vector and covariance matrix and use this to provide a tractable reformulation of the robust counterpart of an uncertain portfolio optimization problem. We also apply the results of this paper to norm approximation problems. Summary of Contribution: This paper develops new theoretical results and algorithms that extend the scope of a robust quadratic optimization problem. More specifically, we derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations.

Title: On perfectness in Gaussian graphical models Abstract: Knowing when a graphical model perfectly encodes the conditional independence structure of a distribution is essential in applications, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional independence statements in the distribution and separation statements in the graph. Previous work has shown that almost all models based on linear directed acyclic graphs as well as Gaussian chain graphs are perfect, the latter of which subsumes Gaussian graphical models (i.e., the undirected Gaussian models) as a special case. In this paper, we directly approach the problem of perfectness for the Gaussian graphical models, and provide a new proof, via a more transparent parametrization, that almost all such models are perfect. Our approach is based on, and substantially extends, a construction of Lnenicka and Matus showing the existence of a perfect Gaussian distribution for any graph. The analysis involves constructing a probability measure on the set of normalized covariance matrices Markov with respect to a graph that may be of independent interest.

Title: Accelerated Information Gradient Flow Abstract: We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo algorithms for Bayesian inverse problems. Here four examples of information metrics are considered, including Fisher-Rao metric, Wasserstein-2 metric, Kalman-Wasserstein metric and Stein metric. For both Fisher-Rao and Wasserstein-2 metrics, we prove convergence properties of accelerated gradient flows. In implementations, we propose a sampling-efficient discrete-time algorithm for Wasserstein-2, Kalman-Wasserstein and Stein accelerated gradient flows with a restart technique. We also formulate a kernel bandwidth selection method, which learns the gradient of logarithm of density from Brownian-motion samples. Numerical experiments, including Bayesian logistic regression and Bayesian neural network, show the strength of the proposed methods compared with state-of-the-art algorithms.

Title: Finding the dimension of a non-empty orthogonal array polytope Abstract: By using representation theory, we reduce the size of the set of possible values for the dimension of the convex hull of all feasible points of an orthogonal array (OA) defining integer linear description (ILD). Our results address the conjecture that if this polytope is non-empty, then it is full-dimensional within the affine space where all the feasible points of the ILD’s linear description (LD) relaxation lie, raised by Appa et al. (2006). In particular, our theoretical results provide a sufficient condition for this polytope to be full-dimensional within the LD relaxation affine space when it is non-empty. This sufficient condition implies all the known non-trivial values of the dimension of the (k,s) assignment polytope. However, our results suggest that the conjecture mentioned above may not be true. More generally, we provide previously unknown restrictions on the feasible values of the dimension of the convex hull of all feasible points of our OA defining ILD. We also determine all possible corresponding sets of equality constraints up to equivalence that can potentially be implied by the integrality constraints of this ILD. Moreover, we find additional restrictions on the dimension of the convex hull of all feasible points, and larger sets of corresponding equality constraints for the n=2 and even s cases. Each of these cases possesses symmetries that do not necessarily exist in the 3≤n or odd s cases. Finally, we discuss how to decrease the number of possible values for the dimension of the convex hull of all feasible points of an arbitrary ILD as well as generate sets of corresponding equality constraints with the zero right hand side. These are the only sets of zero right hand side equality constraints up to equivalence that can potentially be implied by the integrality constraints of the ILD.

Title: Chromatic number is Ramsey distinguishing Abstract: A graph G is Ramsey for a graph H if every colouring of the edges of G in two colours contains a monochromatic copy of H. Two graphs H 1 and H 2 are Ramsey equivalent if any graph G is Ramsey for H 1 if and only if it is Ramsey for H 2. A graph parameter s is Ramsey distinguishing if s ( H 1 ) not equal s ( H 2 ) implies that H 1 and H 2 are not Ramsey equivalent. In this paper we show that the chromatic number is a Ramsey distinguishing parameter. We also extend this to the multicolour case and use a similar idea to find another graph parameter which is Ramsey distinguishing.

Title: Restricted Minimum Error Entropy Criterion for Robust Classification Abstract: The minimum error entropy (MEE) criterion is a powerful approach for non-Gaussian signal processing and robust machine learning. However, the instantiation of MEE on robust classification is a rather vacancy in the literature. The original MEE purely focuses on minimizing Renyi’s quadratic entropy of the prediction errors, which could exhibit inferior capability in noisy classification tasks. To this end, we analyze the optimal error distribution with adverse outliers and introduce a specific codebook for restriction, which optimizes the error distribution toward the optimal case. Half-quadratic-based optimization and convergence analysis of the proposed learning criterion, called restricted MEE (RMEE), are provided. The experimental results considering logistic regression and extreme learning machine on synthetic data and UCI datasets, respectively, are presented to demonstrate the superior robustness of RMEE. Furthermore, we evaluate RMEE on a noisy electroencephalogram dataset, so as to strengthen its practical impact.

Title: NEAR: Neighborhood Edge AggregatoR for Graph Classification Abstract: AbstractLearning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis, and data mining. Recent GNN algorithms are based on neural message passing, which enables GNNs to integrate local structures and node features recursively. However, past GNN algorithms based on 1-hop neighborhood neural message passing are exposed to a risk of loss of information on local structures and relationships. In this article, we propose Neighborhood Edge AggregatoR (NEAR), a framework that aggregates relations between the nodes in the neighborhood via edges. NEAR, which can be orthogonally combined with Graph Isomorphism Network (GIN), gives integrated information that describes which nodes in the neighborhood are connected. Therefore, NEAR can reflect additional information of a local structure of each node beyond the nodes themselves in 1-hop neighborhood. Experimental results on multiple graph classification tasks show that our algorithm makes a good improvement over other existing 1-hop based GNN-based algorithms.

Title: On Guaspari's problem about partially conservative sentences Abstract: We investigate sentences which are simultaneously partially conservative over several theories. First, we generalize Bennet's results on this topic to the case of more than two theories. In particular, for any finite family {Ti}i≤k of consistent r.e. extensions of Peano Arithmetic, we give a necessary and sufficient condition for the existence of a Πn sentence which is unprovable in Ti and Σn-conservative over Ti for all i≤k. Secondly, we prove that for any finite family of such theories, there exists a Σn sentence which is simultaneously unprovable and Πn-conservative over each of these theories. This constitutes a positive solution to a particular case of Guaspari's problem. Finally, we demonstrate several non-implications among related properties of families of theories.

Title: Meyniel Extremal Families of Abelian Cayley Graphs Abstract: We study the game of Cops and Robbers, where cops try to capture a robber on the vertices of a graph. Meyniel’s conjecture states that for every connected graph G on n vertices, the cop number of G is upper bounded by $$O(\sqrt{n})$$ . That is, for every graph G on n vertices $$O(\sqrt{n})$$ cops suffice to catch the robber. We present several families of abelian Cayley graphs that are Meyniel extremal, i.e., graphs whose cop number is $$O(\sqrt{n})$$ . This proves that the $$O(\sqrt{n})$$ upper bound for Cayley graphs proved by Bradshaw (Discret Math 343:1, 2019) is tight. In particular, this shows that Meyniel’s conjecture, if true, is tight even for abelian Cayley graphs. In order to prove the result, we construct Cayley graphs on n vertices with $$\Omega (\sqrt{n})$$ generators that are $$K_{2,3}$$ -free. This shows that the Kövári, Sós, and Turán theorem, stating that any $$K_{2,3}$$ -free graph of n vertices has at most $$O(n^{3/2})$$ edges, is tight up to a multiplicative constant even for abelian Cayley graphs.

Title: On Learning Disentangled Representations for Gait Recognition Abstract: Gait, the walking pattern of individuals, is one of the important biometrics modalities. Most of the existing gait recognition methods take silhouettes or articulated body models as gait features. These methods suffer from degraded recognition performance when handling confounding variables, such as clothing, carrying and viewing angle. To remedy this issue, we propose a novel AutoEncoder framewor...

Title: Multitarget Multiple-Instance Learning for Hyperspectral Target Detection Abstract: In remote sensing, it is often challenging to acquire or collect a large data set that is accurately labeled. This difficulty is usually due to several issues, including but not limited to the study sitex2019;s spatial area and accessibility, errors in the global positioning system (GPS), and mixed pixels caused by an imagex2019;s spatial resolution. We propose an approach, with two variations, that estimates multiple-target signatures from training samples with imprecise labels: multitarget multiple-instance adaptive cosine estimator (MTMI-ACE) and multitarget multiple-instance spectral match filter (MTMI-SMF). The proposed methods address the abovementioned problems by directly considering the multiple-instance, imprecisely labeled data set. They learn a dictionary of target signatures that optimizes detection against a background using the adaptive cosine estimator (ACE) and spectral match filter (SMF). Experiments were conducted to test the proposed algorithms using a simulated hyperspectral data set, the MUUFL Gulfport hyperspectral data set collected over the University of Southern Mississippix2013;Gulfpark Campus, and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral data set collected over Santa Barbara County, CA, USA. Both simulated and real hyperspectral target detection experiments show that the proposed algorithms are effective at learning target signatures and performing target detection.

Title: On the Convergence Properties of Social Hegselmann–Krause Dynamics Abstract: We study the convergence properties of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">social Hegselmann–Krause (HK) dynamics</i> , a variant of the HK model of opinion dynamics where a physical connectivity graph that accounts for the extrinsic factors that could prevent interaction between certain pairs of agents is incorporated. As opposed to the original HK dynamics (which terminates in finite time), we show that for any underlying connected and incomplete graph, under a certain mild assumption, the expected termination time of social HK dynamics is infinity. We then investigate the rate of convergence to the steady state, and provide bounds on the maximum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -convergence time in terms of the properties of the physical connectivity graph. We extend this discussion and observe that for almost all <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> , there exists an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -vertex physical connectivity graph on which social HK dynamics may not even <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -converge to the steady state within a bounded time frame. We then provide nearly tight necessary and sufficient conditions for arbitrarily slow merging (a phenomenon that is essential for arbitrarily slow <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -convergence to the steady state). Using the necessary conditions, we show that complete <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> -partite graphs have bounded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -convergence times.

Title: Estimating the Potential for Shared Autonomous Scooters Abstract: Recent technological developments have shown significant potential for transforming urban mobility. Considering first- and last-mile travel and short trips, the rapid adoption of dockless bike-share systems showed the possibility of disruptive change, while simultaneously presenting new challenges, such as fleet management or the use of public spaces. In this paper, we evaluate the operational cha...

Title: Policy space identification in configurable environments Abstract: We study the problem of identifying the policy space available to an agent in a learning process, having access to a set of demonstrations generated by the agent playing the optimal policy in the considered space. We introduce an approach based on frequentist statistical testing to identify the set of policy parameters that the agent can control, within a larger parametric policy space. After presenting two identification rules (combinatorial and simplified), applicable under different assumptions on the policy space, we provide a probabilistic analysis of the simplified one in the case of linear policies belonging to the exponential family. To improve the performance of our identification rules, we make use of the recently introduced framework of the Configurable Markov Decision Processes, exploiting the opportunity of configuring the environment to induce the agent to reveal which parameters it can control. Finally, we provide an empirical evaluation, on both discrete and continuous domains, to prove the effectiveness of our identification rules.

Title: Hypergraph Partitioning With Embeddings. Abstract: The problem of placing circuits on a chip or distributing sparse matrix operations can be modeled as the hypergraph partitioning problem. A hypergraph is a generalization of the traditional graph wherein each "hyperedge" may connect any number of nodes. Hypergraph partitioning, therefore, is the NP-Hard problem of dividing nodes into $k$ similarly sized disjoint sets while minimizing the number of hyperedges that span multiple partitions. Due to this problem's complexity, many partitioners leverage the multilevel heuristic of iteratively "coarsening" their input to a smaller approximation until an inefficient algorithm becomes feasible. The initial solution is then propagated back to the original hypergraph, which produces a reasonably accurate result provided the coarse representation preserves structural properties of the original. The multilevel hypergraph partitioners are considered today as state-of-the-art solvers that achieve an excellent quality/running time trade-off on practical large-scale instances of different types. In order to improve the quality of multilevel hypergraph partitioners, we propose leveraging graph embeddings to better capture structural properties during the coarsening process. Our approach prioritizes dense subspaces found at the embedding, and contracts nodes according to both traditional and embedding-based similarity measures. Reproducibility: All source code, plots and experimental data are available at https://sybrandt.com/2019/partition.

Title: Storage-Computation-Communication Tradeoff in Distributed Computing: Fundamental Limits and Complexity Abstract: Distributed computing has become one of the most important frameworks in dealing with large computation tasks. In this paper, we propose a systematic construction of coded computing schemes for MapReduce-type distributed systems. The construction builds upon placement delivery arrays (PDA), originally proposed by Yan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> for coded caching schemes. The main contributions of our work are three-fold. First, we identify a class of PDAs, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Comp-PDAs</i> , and show how to obtain a coded computing scheme from any Comp-PDA. We also characterize the normalized number of stored files ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">storage load</i> ), computed intermediate values ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">computation load</i> ), and communicated bits ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">communication load</i> ), of the obtained schemes in terms of the Comp-PDA parameters. Then, we show that the performance achieved by Comp-PDAs describing Maddah-Ali and Niesen’s coded caching schemes matches a new information-theoretic converse, thus establishing the fundamental region of all achievable performance triples. In particular, we characterize <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">all</i> the Comp-PDAs achieving the pareto-optimal storage, computation, and communication (SCC) loads of the fundamental region. Finally, we investigate the file complexity of the proposed schemes, i.e., the smallest number of files required for implementation. In particular, we describe Comp-PDAs that achieve pareto-optimal SCC triples with significantly lower file complexity than the originally proposed Comp-PDAs.

Title: Bringing runtime verification home: a case study on the hierarchical monitoring of smart homes using decentralized specifications Abstract: We use runtime verification (RV) to check various specifications in a smart apartment. The specifications can be broken down into three types: behavioral correctness of the apartment sensors, detection of specific user activities (known as activities of daily living), and composition of specifications of the previous types. The context of the smart apartment provides us with a complex system with a large number of components with two different hierarchies to group specifications and sensors: geographically within the same room, floor or globally in the apartment, and logically following the different types of specifications. We leverage a recent approach to decentralized RV of decentralized specifications, where monitors have their own specifications and communicate together to verify more general specifications. We leverage the hierarchies, modularity and re-use afforded by decentralized specifications to: (1) scale beyond existing centralized RV techniques, and (2) greatly reduce computation and communication costs.

Title: Fractional Isomorphism of Graphons Abstract: We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is characterized in terms of distributions on iterated degree measures, Markov operators, weak isomorphism of a conditional expectation with respect to invariant sub-σ-algebras and isomorphism of certain quotients of given graphons.

Title: Self-Reinforcing Unsupervised Matching Abstract: Remarkable gains in deep learning usually benefit from large-scale supervised data. Ensuring the intra-class modality diversity in training set is critical for generalization capability of cutting-edge deep models, but it burdens human with heavy manual labor on data collection and annotation. In addition, some rare or unexpected modalities are new for the current model, causing reduced performance under such emerging modalities. Inspired by the achievements in speech recognition, psychology and behavioristics, we present a practical solution, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self-reinforcing unsupervised matching</i> (SUM), to annotate the images with 2D structure-preserving property in an emerging modality by cross-modality matching. Specifically, we propose a dynamic programming algorithm, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dynamic position warping</i> (DPW), to reveal the underlying element correspondence relationship between two matrix-form data in an order-preserving fashion, and devise a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local feature adapter</i> (LoFA) to allow for cross-modality similarity measurement. On these bases, we develop a two-tier self-reinforcing learning mechanism on both feature level and image level to optimize the LoFA. The proposed SUM framework requires no any supervision in emerging modality and only one template in seen modality, providing a promising route towards incremental learning and continual learning. Extensive experimental evaluation on two proposed challenging one-template visual matching tasks demonstrate its efficiency and superiority.

Title: Gramians, Energy Functionals, and Balanced Truncation for Linear Dynamical Systems With Quadratic Outputs Abstract: In this article, we investigate a balancing-based model order reduction method for dynamical systems with a linear dynamical equation and a quadratic output function. With this aim, we propose a new algebraic observability Gramian for the system based on the Hilbert space adjoint theory. We then show that the proposed Gramian satisfies a particular type of generalized Lyapunov equation and we investigate its connection to energy functionals. It allows one to find states that are hard to control and hard to observe via an appropriate balancing transformation. Truncation of such states yields reduced-order models. Finally, based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_2$</tex-math></inline-formula> energy considerations, we derive error bounds, depending on the neglected singular values. We demonstrate the efficiency of the proposed methodology using a numerical example.

Title: Hard edge statistics of products of Pólya ensembles and shifted GUE’s Abstract: Very recently, we have shown how the harmonic analysis approach can be modified to deal with products of general Hermitian and complex random matrices at finite matrix dimension. In the present work, we consider the particular product of a multiplicative Pólya ensemble on the complex square matrices and a Gaussian unitary ensemble (GUE) shifted by a constant multiplicative of the identity. The shift shall show that the limiting hard edge statistics of the product matrix is weakly dependent on the local spectral statistics of the GUE, but depends more on the global statistics via its Stieltjes transform (Green function). Under rather mild conditions for the Pólya ensemble, we prove formulas for the hard edge kernel of the singular value statistics of the Pólya ensemble alone and the product matrix to highlight their very close similarity. Due to these observations, we even propose a conjecture for the hard edge statistics of a multiplicative Pólya ensemble on the complex matrices and a polynomial ensemble on the Hermitian matrices.

Title: Faster quantum and classical SDP approximations for quadratic binary optimization Abstract: We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-theart algorithms. Such instances include approximating the ground state of spin glasses and MAxeuT on Erdos-Renyi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.

Title: DUAL LINEAR PROGRAMMING BOUNDS FOR SPHERE PACKING VIA MODULAR FORMS Abstract: We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions 8 and 24, where the linear programming bound is sharp, we show that it comes nowhere near the best packing densities known in dimensions 12, 16, 20, 28, and 32. More generally, we provide a systematic technique for proving separations of this sort.

Title: Boltzmann Machine Learning and Regularization Methods for Inferring Evolutionary Fields and Couplings From a Multiple Sequence Alignment Abstract: The inverse Potts problem to infer a Boltzmann distribution for homologous protein sequences from their single-site and pairwise amino acid frequencies recently attracts a great deal of attention in the studies of protein structure and evolution. We study regularization and learning methods and how to tune regularization parameters to correctly infer interactions in Boltzmann machine learning. Using <inline-formula><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula> regularization for fields, group <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula> for couplings is shown to be very effective for sparse couplings in comparison with <inline-formula><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula> . Two regularization parameters are tuned to yield equal values for both the sample and ensemble averages of evolutionary energy. Both averages smoothly change and converge, but their learning profiles are very different between learning methods. The Adam method is modified to make stepsize proportional to the gradient for sparse couplings and to use a soft-thresholding function for group <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula> . It is shown by first inferring interactions from protein sequences and then from Monte Carlo samples that the fields and couplings can be well recovered, but that recovering the pairwise correlations in the resolution of a total energy is harder for the natural proteins than for the protein-like sequences. Selective temperature for folding/structural constrains in protein evolution is also estimated.

Title: Discrete Choice Prox-Functions on the Simplex Abstract: We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps. As illustration, we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming adjusts demand within a consumption cycle.

Title: Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains Abstract: We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

Title: Riemannian proximal gradient methods Abstract: In the Euclidean setting the proximal gradient method and its accelerated variants are a class of efficient algorithms for optimization problems with decomposable objective. In this paper, we develop a Riemannian proximal gradient method (RPG) and its accelerated variant (ARPG) for similar problems but constrained on a manifold. The global convergence of RPG is established under mild assumptions, and the O(1/k) is also derived for RPG based on the notion of retraction convexity. If assuming the objective function obeys the Rimannian Kurdyka–Łojasiewicz (KL) property, it is further shown that the sequence generated by RPG converges to a single stationary point. As in the Euclidean setting, local convergence rate can be established if the objective function satisfies the Riemannian KL property with an exponent. Moreover, we show that the restriction of a semialgebraic function onto the Stiefel manifold satisfies the Riemannian KL property, which covers for example the well-known sparse PCA problem. Numerical experiments on random and synthetic data are conducted to test the performance of the proposed RPG and ARPG.

Title: New lower bounds on the size-Ramsey number of a path Abstract: We prove that for all graphs with at most (3.75 - o(1))n edges there exists a 2-coloring of the edges such that every monochromatic path has order less than n. This was previously known to be true for graphs with at most 2.5n - 7.5 edges. We also improve on the best-known lower bounds in the r-color case.

Title: Horizontal Flows and Manifold Stochastics in Geometric Deep Learning Abstract: We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a w...

Title: Adversarial Attack on Skeleton-Based Human Action Recognition Abstract: Deep learning models achieve impressive performance for skeleton-based human action recognition. Graph convolutional networks (GCNs) are particularly suitable for this task due to the graph-structured nature of skeleton data. However, the robustness of these models to adversarial attacks remains largely unexplored due to their complex spatiotemporal nature that must represent sparse and discrete s...

Title: Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm Abstract: As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of a color image. Motivated by two kinds of low-rank approximation approaches (low-rank decomposition and nuclear norm minimization) in traditional matrix-based methods, we combine the two approaches in our quaternion matrix-based model. Furthermore, the nuclear norm of the quaternion matrix is replaced by the sum of the Frobenius norm of its two low-rank factor quaternion matrices. Based on the relationship between the quaternion matrix and its equivalent complex matrix, the problem eventually is converted from the quaternion number domain to the complex number domain. An alternating minimization method is applied to solve the model. Simulation results on color image recovery show the superior performance and efficiency of the proposed algorithm over some tensor-based and quaternion-based ones.

Title: Propagation complete encodings of smooth DNNF theories Abstract: We investigate conjunctive normal form (CNF) encodings of a function represented with a decomposable negation normal form (DNNF). Several encodings of DNNFs and decision diagrams were considered by (Abío et al., 2016). The authors differentiate between encodings which implement consistency or domain consistency by unit propagation from encodings which are unit refutation complete or propagation complete. The difference is that in the former case we do not care about propagation strength of the encoding with respect to the auxiliary variables while in the latter case we treat all variables (the main and the auxiliary ones) in the same way. The currently known encodings of DNNF theories implement domain consistency. Building on these encodings we generalize the result of (Abío et al., 2016) on a propagation complete encoding of decision diagrams and present a propagation complete encoding of a DNNF and its generalization for variables with finite domains.

Title: ChOracle: A Unified Statistical Framework for Churn Prediction Abstract: User churn is an important issue in online services that threatens the health and profitability of services. Most of the previous works on churn prediction convert the problem into a binary classification task where the users are labeled as churned and non-churned. More recently, some works have tried to convert the user churn prediction problem into the prediction of user return time. In this app...

Title: Efficient rational creative telescoping Abstract: We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the important feature that the computation of a telescoper is independent of its certificate. In addition, our algorithm uses a compact representation of the certificate, which allows it to be easily manipulated and analyzed without knowing the precise expanded form. This representation hides potential expression swell until the final (and optional) expansion, which can be accomplished in time polynomial in the size of the expanded certificate. A complexity analysis, along with a Maple implementation, indicates that our algorithm has better theoretical and practical performance than the reduction-based approach in the rational case.

Title: Generation Of Off-Critical Zeros For Hypercubic Epstein Zeta Functions Abstract: We study the Epstein zeta-function formulated on the d-dimensional hypercubic lattice zeta((d))(s) = 1/2 Sigma' (n1,...,nd) (n(1)(2) +... + n(d)(2))(-s/2) where the real part R(s) > dand the summation runs over all integers except of the origin (0, 0,..., 0). An analytical continuation of the Epstein zeta-function to the whole complex s-plane is constructed for the spatial dimension dbeing a continuous variable ranging from 0 to infinity. Zeros of the Epstein zeta-function rho = rho x + i rho(y) are defined by zeta((d)) (rho) = 0. The nontrivial zeros split into the "critical" zeros (on the critical line) with rho(x) = d/2 and the "off-critical" zeros (offthe critical line) with rho(x) not equal d/2. Numerical calculations reveal that the critical zeros form closed or semi-open curves rho(y) (d) which enclose disjunctive regions of the plane (rho(x) = d/2,rho(y)). Each curve involves a number of left/right edge points rho*= (d */2,rho*(y)), defined by a divergent tangent d(rho y)/dd|(rho'). Every edge point gives rise to two conjugate tails of off-critical zeros with continuously varying dimension dwhich exhibit a singular expansion around the edge point, in analogy with critical phenomena for second-order phase transitions. For each dimension d > 9.24555... there exists a conjugate pair of real off-critical zeros which tend to the boundaries 0 and dof the critical strip in the limit d ->infinity. As a by-product of the formalism, we derive an exact formula for lim(d -> 0)zeta((d)) (s)/d. An equidistant distribution of critical zeros along the imaginary axis is obtained for large d, with spacing between the nearest-neighbour zeros vanishing as 2 pi/ ln din the limit d ->infinity. (C) 2021 Elsevier Inc. All rights reserved.

Title: Packing and covering directed triangles asymptotically Abstract: A well-known conjecture of Tuza asserts that if a graph has at most t pairwise edge-disjoint triangles, then it can be made triangle-free by removing at most 2t edges. If true, the factor 2 would be best possible. In the directed setting, also asked by Tuza, the analogous statement has recently been proven, however, the factor 2 is not optimal. In this paper, we show that if an n-vertex directed graph has at most t pairwise arc-disjoint directed triangles, then there exists a set of at most 1.8t + o(n(2)) arcs that meets all directed triangles. We complement our result by presenting two constructions of large directed graphs with t is an element of Omega(n(2)) whose smallest such set has 1.5t - o(n(2)) arcs. (C) 2021 Elsevier Ltd. All rights reserved.

Title: MFCC-based Recurrent Neural Network for automatic clinical depression recognition and assessment from speech Abstract: Clinical depression or Major Depressive Disorder (MDD) is a common and serious medical illness. In this paper, a deep Recurrent Neural Network-based framework is presented to detect depression and to predict its severity level from speech. Low-level and high-level audio features are extracted from audio recordings to predict the 24 scores of the Patient Health Questionnaire and the binary class of depression diagnosis. To overcome the problem of the small size of Speech Depression Recognition (SDR) datasets, expanding training labels and transferred features are considered. The proposed approach outperforms the state-of-art approaches on the DAIC-WOZ database with an overall accuracy of 76.27% and a root mean square error of 0.4 in assessing depression, while a root mean square error of 0.168 is achieved in predicting the depression severity levels. The proposed framework has several advantages (fastness, non-invasiveness, and non-intrusion), which makes it convenient for real-time applications. The performances of the proposed approach are evaluated under a multi-modal and a multi-features experiments. MFCC based high-level features hold relevant information related to depression. Yet, adding visual action units and different other acoustic features further boosts the classification results by 20% and 10% to reach an accuracy of 95.6% and 86%, respectively. Considering visual-facial modality needs to be carefully studied as it sparks patient privacy concerns while adding more acoustic features increases the computation time.

Title: Higher dimensional cardinal characteristics for sets of functions Abstract: Much recent work in cardinal characteristics has focused on generalizing results about ω to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces κκ and 2κ. In this note I look at generalizations to other function spaces, focusing particularly on the space of functions f:ωω→ωω. By considering classical cardinal invariants on Baire space in this setting I derive a number of “higher dimensional” analogues of such cardinals, ultimately introducing 18 new cardinal invariants, alongside a framework that allows for numerous others. These 18 form two separate diagrams consisting of 6 and 12 cardinals respectively, each resembling versions of the Cichoń diagram. These ZFC-inequalities are the first main result of the paper. I then consider other relations between these cardinals, as well as the cardinal c+ and show that these results rely on additional assumptions about cardinal characteristics on ω. Finally, using variations of Cohen, Hechler, and localization forcing I prove a number of consistency results for possible values of the new cardinals.

Title: Reachability games with relaxed energy constraints Abstract: We study games with reachability objectives under energy constraints. We first prove that under strict energy constraints (either only lower-bound constraint or interval constraint), those games are LOGSPACE-equivalent to energy games with the same energy constraints but without reachability objective (i.e., for infinite runs). We then consider two relaxations of the upper-bound constraints (while keeping the lower-bound constraint strict): in the first one, called weak upper bound, the upper bound is absorbing, i.e., when the upper bound is reached, the extra energy is not stored; in the second one, we allow for temporary violations of the upper bound, imposing limits on the number or on the amount of violations.

Title: Weak Edge Identification Network for Ocean Front Detection Abstract: Ocean fronts have an important influence on global ocean–atmosphere interactions and marine fishery. Hence, it is of great significance to obtain the positions of the ocean fronts. However, current ocean front detection research confronts two challenges: scarcity of labeled data and limitations of ocean front detection algorithms. To address these two problems, we have collected and labeled an oce...

Title: Fractional matching preclusion number of graphs? Abstract: The fractional matching preclusion number of a graph G, denoted by fmp(G), is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings. In this paper, we first give some sharp upper and lower bounds of fractional matching preclusion number. Next, graphs with large and small fractional matching preclusion number are characterized, respectively. In the end, we investigate some extremal problems on fractional matching preclusion number. (c) 2022 Elsevier B.V. All rights reserved. <comment>Superscript/Subscript Available</comment

Title: Deterministic algorithms for the Lovász Local Lemma: simpler, more general, and more parallel Abstract: The Lovasz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\mathcal B$ of "bad" events which are mostly independent and have low probability. In its simplest "symmetric" form, it asserts that whenever a bad-event has probability $p$ and affects at most $d$ bad-events, and $e p d < 1$, then a configuration avoiding all $\mathcal B$ exists. A seminal algorithm of Moser & Tardos (2010) gives nearly-automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms have lagged behind. We address three specific shortcomings of the prior deterministic algorithms. First, our algorithm applies to the LLL criterion of Shearer (1985); this is more powerful than alternate LLL criteria and also removes a number of nuisance parameters and leads to cleaner and more legible bounds. Second, we provide parallel algorithms with much greater flexibility in the functional form of of the bad-events. Third, we provide a derandomized version of the MT-distribution, that is, the distribution of the variables at the termination of the MT algorithm. We show applications to non-repetitive vertex coloring, independent transversals, strong coloring, and other problems. These give deterministic algorithms which essentially match the best previous randomized sequential and parallel algorithms.

Title: Survey on rain removal from videos or a single image Abstract: Rain can cause performance degradation of outdoor computer vision tasks. Thus, the exploration of rain removal from videos or a single image has drawn considerable attention in the field of image processing. Recently, various deraining methodologies have been proposed. However, no comprehensive survey work has yet been conducted to summarize existing deraining algorithms and quantitatively compare their generalization ability, and especially, no off-the-shelf toolkit exists for accumulating and categorizing recent representative methods for easy performance reproduction and deraining capability evaluation. In this regard, herein, we present a comprehensive overview of existing video and single image deraining methods as well as reproduce and evaluate current state-of-the-art deraining methods. In particular, these approaches are mainly classified into model- and deep-learning-based methods, and more elaborate branches of each method are presented. Inherent abilities, especially generalization performance, of the state-of-the-art methods have been both quantitatively and visually analyzed through thorough experiments conducted on synthetic and real benchmark datasets. Moreover, to facilitate the reproduction of existing deraining methods for general users, we present a comprehensive repository with detailed classification, including direct links to 85 deraining papers, 24 relevant project pages, source codes of 12 and 25 algorithms for video and single image deraining, respectively, 5 and 10 real and synthesized datasets, respectively, and 7 frequently used image quality evaluation metrics, along with the corresponding computation codes. Research limitations worthy of further exploration have also been discussed for future research along this direction.

Title: LMI-based robust stability and stabilization analysis of fractional-order interval systems with time-varying delay Abstract: This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results, a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in LMI form, which is more suitable to check due to various existing efficient convex optimization parsers and solvers. Finally, some numerical examples have shown the effectiveness of our results.

Title: Regular Matroids Have Polynomial Extension Complexity Abstract: We prove that the extension complexity of the independence polytope of every regular matroid on n elements is O(n(6)). Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a O(n(2)) bound for the special case of (co)graphic matroids. However, the case of a general regular matroid was open, despite recent attempts. We also consider the extension complexity of circuit dominants of regular matroids, for which we give a O(n(2)) bound.

Title: Specification and optimal reactive synthesis of run-time enforcement shields Abstract: A run time enforcement shield is a controller which corrects the output O of a system with sporadic errors (SSE) so as to guarantee the invariance of a critical requirement. Moreover, the shield output O′ must deviate from the SSE output O “as little as possible” to maintain the quality. We give a method for logical specification of shields using logic QDDC. The specification consists of a correctness requirement REQ, a mandatory hard deviation constraint HDC, and a soft deviation constraint SDC whose satisfaction must be optimized in an H-optimal fashion. We show how a tool DCSynth implementing soft requirement guided synthesis is used for the automatic synthesis of shields from such specifications. Next, we give logical formulation of various notions of shields including Bloem's k-Stabilizing shield, Wu's Burst-error shield, as well as new EK-shield and Windowed-EK-shield. We experimentally compare the performance of the shields synthesized under these notions.

Title: Poset Ramsey Numbers for Boolean Lattices Abstract: For each positive integer n, let Qn denote the Boolean lattice of dimension n. For posets $P, P^{\prime }$ , define the poset Ramsey number $R(P,P^{\prime })$ to be the least N such that for any red/blue coloring of the elements of QN, there exists either a subposet isomorphic to P with all elements red, or a subposet isomorphic to $P^{\prime }$ with all elements blue. Axenovich and Walzer introduced this concept in Order (2017), where they proved R(Q2,Qn) ≤ 2n + 2 and R(Qn,Qm) ≤ mn + n + m. They later proved 2n ≤ R(Qn,Qn) ≤ n2 + 2n. Walzer later proved R(Qn,Qn) ≤ n2 + 1. We provide some improved bounds for R(Qn,Qm) for various $n,m \in \mathbb {N}$ . In particular, we prove that R(Qn,Qn) ≤ n2 − n + 2, $R(Q_{2}, Q_{n}) \le \frac {5}{3}n + 2$ , and $R(Q_{3}, Q_{n}) \le \lceil \frac {37}{16}n + \frac {55}{16}\rceil $ . We also prove that R(Q2,Q3) = 5, and $R(Q_{m}, Q_{n}) \le \left \lceil \left (m - 1 + \frac {2}{m+1} \right )n + \frac {1}{3} m + 2\right \rceil $ for all n > m ≥ 4.

Title: Grid Anchor Based Image Cropping: A New Benchmark and An Efficient Model Abstract: Image cropping aims to improve the composition as well as aesthetic quality of an image by removing extraneous content from it. Most of the existing image cropping databases provide only one or several human-annotated bounding boxes as the groundtruths, which can hardly reflect the non-uniqueness and flexibility of image cropping in practice. The employed evaluation metrics such as intersection-over-union cannot reliably reflect the real performance of a cropping model, either. This work revisits the problem of image cropping, and presents a grid anchor based formulation by considering the special properties and requirements (e.g., local redundancy, content preservation, aspect ratio) of image cropping. Our formulation reduces the searching space of candidate crops from millions to no more than ninety. Consequently, a grid anchor based cropping benchmark is constructed, where all crops of each image are annotated and more reliable evaluation metrics are defined. To meet the practical demands of robust performance and high efficiency, we also design an effective and lightweight cropping model. By simultaneously considering the region of interest and region of discard, and leveraging multi-scale information, our model can robustly output visually pleasing crops for images of different scenes. With less than 2.5M parameters, our model runs at a speed of 200 FPS on one single GTX 1080Ti GPU and 12 FPS on one i7-6800K CPU. The code is available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/HuiZeng/Grid-Anchor-based-Image-Cropping-Pytorch</uri> .

Title: A characterization of circle graphs in terms of total unimodularity Abstract: A graph G has an associated multimatroid Z(3)(G), which is equivalent to the isotropic system of G studied by Bouchet. In previous work it was shown that G is a circle graph if and only if for every field F, the rank function of Z(3)(G) can be extended to the rank function of an F-representable matroid. In the present paper we strengthen this result using a multimatroid analogue of total unimodularity. As a consequence we obtain a characterization of matroid planarity in terms of this total-unimodularity analogue. (C)& nbsp;2021 Elsevier Ltd. All rights reserved.

Title: New Results Relating Independence and Matchings Abstract: In this paper we study relationships between the matching number, written mu(G), and the independence number, written alpha(G). Our first main result is to show alpha(G) <= mu(G) + |X| - mu(G[N-G[X]]), where X is any intersection of maximum independent sets in G. Our second main result is to show delta(G) alpha(G) <= Delta(G)mu(G), where delta(G) and Delta(G) denote the minimum and maximum vertex degrees of G, respectively. These results improve on and generalize known relations between mu(G) and alpha(G). Further, we also give examples showing these improvements.

Title: Regularized Diffusion Adaptation via Conjugate Smoothing Abstract: The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, while the regularizers are assumed deterministic, but are not required to be differentiable or even continuous. The individual, regularized, cos...

Title: Genetic Neural Architecture Search for automatic assessment of human sperm images Abstract: Male infertility is a disease that affects approximately 7% of men. Sperm morphology analysis (SMA) is one of the main diagnosis methods for this problem. However, manual SMA is an inexact, subjective, non-reproducible, and hard to teach process. Therefore, in this paper, we introduce a novel automatic SMA technique that is based on the neural architecture search algorithm, named Genetic Neural Architecture Search (GeNAS). For this purpose, we used a collection of images termed MHSMA dataset, which contains 1540 sperm images that have been collected from 235 patients with infertility problems. In detail, GeNAS consists of a special genetic algorithm that acts as a meta-controller which explores the constrained search space of plain convolutional neural network architectures. Every individual of this genetic algorithm is a convolutional neural network trained to predict morphological deformities in different segments of human sperm (head, vacuole, and acrosome). The fitness of each individual is calculated by a novel proposed method, named GeNAS Weighting Factor (GeNAS-WF). This technique is specially designed to evaluate the fitness of neural networks which, during their learning process, validation accuracy highly fluctuates. To speed up the algorithm, a hashing method is practiced to save each trained neural architecture fitness, so we could reuse them during fitness evaluation. In terms of running time and computational power, our proposed architecture search method is far more efficient than most of the other existing neural architecture search algorithms. Moreover, whereas most of the existing neural architecture search algorithms are designed to work well with well-prepared benchmark datasets, the overall paradigm of GeNAS is specially designed to address the challenges of real-world datasets, particularly shortage of data and class imbalance. In our experiments, the best neural architecture found by GeNAS has reached an accuracy of 91.66%, 77.33%, and 77.66% in the vacuole, head, and acrosome abnormality detection, respectively. In comparison to other proposed algorithms for MHSMA dataset, GeNAS achieved state-of-the-art results.

Title: Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference Abstract: We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model – an actively studied topic in statistics and machine learning. In the noiseless case, matching upper and lower bounds on sample complexity are established for the exact recovery of sparse vectors and for stable estimation of approximately sparse vectors, respectively. In the noisy case, upper and matching minimax lower bounds for estimation error are obtained. We also consider the debiased sparse group Lasso and investigate its asymptotic property for the purpose of statistical inference. Finally, numerical studies are provided to support the theoretical results.

Title: Whitney Numbers of Combinatorial Geometries and Higher-Weight Dowling Lattices Abstract: We study the Whitney numbers of the first kind of combinatorial geometries, in connection with the theory of error-correcting codes. The first part of the paper is devoted to general results relating the Mo "\bius functions of nested atomistic lattices, extending some classical theorems in combinatorics. We then specialize our results to restriction geometries, i.e., to sublattices \scrA of the lattice of subspaces of an \BbbFq-linear space, say, X, generated by a set of projective points A \subseteq X. In this context, we introduce the notion of subspace distribution and show that partial knowledge of the latter is equivalent to partial knowledge of the Whitney numbers of \scrA. This refines a classical result by Dowling. The most interesting applications of our results are to be seen in the theory of higher -weight Dowling lattices (HWDLs), to which we devote the second and most substantive part of the paper. These combinatorial geometries were introduced by Dowling in 1971 in connection with fundamental problems in coding theory, most notably the famous MDS conjecture. They were further studied by, among others, Zaslavsky, Bonin, Kung, Brini, and Games. To date, still very little is known about these lattices and the techniques to compute their Whitney numbers have not been discovered yet. In this paper, we bring forward the theory of HWDLs, computing their Whitney numbers for new infinite families of parameters. We also show that the second Whitney numbers of HWDLs are polynomials in the underlying field size q, whose coefficients are curious expressions involving the Bernoulli numbers. In passing, we obtain new results intersecting coding theory and enumerative combinatorics.

Title: Edge Isoperimetric Inequalities for Powers of the Hypercube Abstract: For positive integers n and r, we let Q(n)(r) denote the rth power of the n-dimensional discrete hypercube graph, i.e., the graph with vertex-set {0,1}(n), where two 0-1 vectors are joined if they are Hamming distance at most r apart. We study edge isoperimetric inequalities for this graph. Harper, Bernstein, Lindsey and Hart proved a best-possible edge isoperimetric inequality for this graph in the case r = 1. For each r >= 2, we obtain an edge isoperimetric inequality for Q(n)(r); our inequality is tight up to a constant factor depending only upon r. Our techniques also yield an edge isoperimetric inequality for the 'Kleitman-West graph' (the graph whose vertices are all the k-element subsets of {1, 2, ..., n}, where two k-element sets have an edge between them if they have symmetric difference of size two); this inequality is sharp up to a factor of 2 + o(1) for sets of size ((n-s)(k-s)), where k = o(n) and s is an element of N.

Title: Elasticity detection: a building block for internet congestion control Abstract: This paper introduces a new metric, "elasticity," which characterizes the nature of cross-traffic competing with a flow. Elasticity captures whether the cross traffic reacts to changes in available bandwidth. We show that it is possible to robustly detect the elasticity of cross traffic at a sender without router support, and that elasticity detection can reduce delays in the Internet by enabling delay-controlling congestion control protocols to be deployed without hurting flow throughput. Our results show that the proposed method achieves more than 85% accuracy under a variety of network conditions, and that congestion control using elasticity detection achieves throughput comparable to Cubic but with delays that are 50--70 ms lower when cross traffic is inelastic.

Title: Decreasing the maximum average degree by deleting an independent set or a d-degenerate subgraph Abstract: The maximum average degree mad(G) of a graph G is the maximum over all subgraphs of G, of the average degree of the subgraph. In this paper, we prove that for every G and positive integer k such that mad(G) >= k there exists S subset of V (G) such that mad(G - S) <= mad(G) - k and G[S] is (k - 1)-degenerate. Moreover, such S can be computed in polynomial time. In particular, if G contains at least one edge then there exists an independent set I in G such that mad(G - I) <= mad(G) - 1 and if G contains a cycle then there exists an induced forest F such that mad(G - F) <= mad(G) - 2. As a side result, we also obtain a subexponential bound on the diameter of reconfiguration graphs of generalized colourings of graphs with bounded value of their mad.

Title: High-Dimensional Clustering via Random Projections Abstract: This work addresses the unsupervised classification issue for high-dimensional data by exploiting the general idea of Random Projection Ensemble. Specifically, we propose to generate a set of low-dimensional independent random projections and to perform model-based clustering on each of them. The top B∗ projections, i.e., the projections which show the best grouping structure, are then retained. The final partition is obtained by aggregating the clusters found in the projections via consensus. The performances of the method are assessed on both real and simulated datasets. The obtained results suggest that the proposal represents a promising tool for high-dimensional clustering.

Title: Permuting 2-uniform Tolerances on Lattices Abstract: A 2-uniform tolerance on a lattice is a compatible tolerance relation such that all of its blocks are 2-element. We characterize permuting pairs of 2-uniform tolerances on lattices of finite length. In particular, any two 2-uniform congruences on such a lattice permute.

Title: A Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections Abstract: Cooperative Adaptive Cruise Control (CACC) is considered as a key potential enabler to improve driving safety and traffic efficiency. It allows for automated vehicle following using wireless communication in addition to onboard sensors. To achieve string stability in CACC platoons, constant time gap (CTG) spacing policies have prevailed in research; namely, vehicle interspacing grows with the speed. While constant distance gap (CDG) spacing policies provide superior potential to increase traffic capacity than CTG, their major drawbacks are a smaller safety margin at high velocities and that string stability cannot be achieved using a one-vehicle look-ahead communication. In this work, we propose to apply CDG only in a few driving situations, when traffic throughput is of highest importance and safety requirements can be met due to relatively low velocities. As the most relevant situations where CDG could be applied, we identify starting platoons at signalized intersections. With this application scenario we show that applying CDG only in a few specific and crucial situation can have a major impact on traffic efficiency. Specifically, we compare CTG with CDG regarding its potential to increase the capacity of traffic lights. Starting with the elementary situation of single traffic lights we expand our scope to whole traffic networks including several thousand vehicles in simulation. Using real world data to calibrate and validate vehicle dynamics simulation and traffic simulation, the study discusses the most relevant working parameters of CDG, CTG, and the traffic system in which both are applied.

Title: Two Remarks on Graph Norms Abstract: For a graph H, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions W in $$L^p$$ , $$p\ge e(H)$$ , denoted by t(H, W). One may then define corresponding functionals $$\Vert W\Vert _{H}\,{:}{=}\,|t(H,W)|^{1/e(H)}$$ and $$\Vert W\Vert _{r(H)}\,{:}{=}\,t(H,|W|)^{1/e(H)}$$ , and say that H is (semi-)norming if $$\Vert \,{\cdot }\,\Vert _{H}$$ is a (semi-)norm and that H is weakly norming if $$\Vert \,{\cdot }\,\Vert _{r(H)}$$ is a norm. We obtain two results that contribute to the theory of (weakly) norming graphs. Firstly, answering a question of Hatami, who estimated the modulus of convexity and smoothness of $$\Vert \,{\cdot }\,\Vert _{H}$$ , we prove that $$\Vert \,{\cdot }\,\Vert _{r(H)}$$ is neither uniformly convex nor uniformly smooth, provided that H is weakly norming. Secondly, we prove that every graph H without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of H when studying graph norms. In particular, we correct a negligence in the original statement of the aforementioned theorem by Hatami.

Title: Posture and sequence recognition for Bharatanatyam dance performances using machine learning approaches Abstract: Understanding the underlying semantics of performing arts like dance is a challenging task. Analysis of dance is useful to preserve cultural heritage, make video recommendation systems, and build tutoring systems. To create such a dance analysis application, three aspects of dance analysis must be addressed: (1) segment the dance video to find representative action elements, (2) recognize the detected action elements, and (3) recognize sequences formed by combining action elements according to specific rules. This paper attempts to address the three fundamental problems of dance analysis raised above, with a focus on Indian Classical Dance, em Bharatanatyam. Since dance is driven by music, we use both musical and motion information to extract action elements. The action elements are then recognized using machine learning and deep learning techniques. Finally, the Hidden Markov Model (HMM) and Long Short-Term Memory (LSTM) are used to recognize the dance sequence.

Title: Classification Logit Two-Sample Testing by Neural Networks for Differentiating Near Manifold Densities Abstract: The recent success of generative adversarial networks and variational learning suggests that training a classification network may work well in addressing the classical two-sample problem, which asks to differentiate two densities given finite samples from each one. Network-based methods have the computational advantage that the algorithm scales to large datasets. This paper considers using the classification logit function, which is provided by a trained classification neural network and evaluated on the testing set split of the two datasets, to compute a two-sample statistic. To analyze the approximation and estimation error of the logit function to differentiate near-manifold densities, we introduce a new result of near-manifold integral approximation by neural networks. We then show that the logit function provably differentiates two sub-exponential densities given that the network is sufficiently parametrized, and for on or near manifold densities, the needed network complexity is reduced to only scale with the intrinsic dimensionality. In experiments, the network logit test demonstrates better performance than previous network-based tests using classification accuracy, and also compares favorably to certain kernel maximum mean discrepancy tests on synthetic datasets and hand-written digit datasets.

Title: Matchings and squarefree powers of edge ideals Abstract: Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper, we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such powers are linearly related or have linear resolution. We also consider the so-called squarefree Ratliff property.

Title: Matroids arising from electrical networks Abstract: This paper introduces Dirichlet matroids, a generalization of graphic matroids arising from electrical networks. We present four main theorems. First, we exhibit a matroid quotient involving geometric duals of networks embedded in surfaces with boundary. Second, we characterize the Bergman fans of Dirichlet matroids as subfans of graphic Bergman fans. Third, we prove an interlacing result on the real zeros and poles of the trace of the response matrix. And fourth, we bound the coefficients of the precoloring polynomial of a network by the coefficients of the associated chromatic polynomial.

Title: Robust and Adaptive Sequential Submodular Optimization Abstract: Emerging applications of control, estimation, and machine learning, from target tracking to decentralized model fitting, pose resource constraints that limit which of the available sensors, actuators, or data can be simultaneously used across time. Therefore, many researchers have proposed solutions within discrete optimization frameworks where the optimization is performed over finite sets. By ex...

Title: Adversarial Deep Embedded Clustering: On a Better Trade-off Between Feature Randomness and Feature Drift Abstract: To overcome the absence of concrete supervisory signals, deep clustering models construct their own labels based on self-supervision and pseudo-supervision. However, applying these techniques can cause Feature Randomness and Feature Drift. In this paper, we formally characterize these two new concepts. On one hand, Feature Randomness takes place when a considerable portion of the pseudo-labels is ...

Title: Elastic Deep Learning in Multi-Tenant GPU Clusters Abstract: We study how to support elasticity, that is, the ability to dynamically adjust the parallelism (i.e., the number of GPUs), for deep neural network (DNN) training in a GPU cluster. Elasticity can benefit multi-tenant GPU cluster management in many ways, for example, achieving various scheduling objectives (e.g., job throughput, job completion time, GPU efficiency) according to cluster load variations, utilizing transient idle resources, and supporting performance profiling, job migration, and straggler mitigation. We propose EDL, which enables elastic deep learning with a simple API and can be easily integrated with existing deep learning frameworks such as TensorFlow and PyTorch. EDL also incorporates techniques that are necessary to reduce the overhead of parallelism adjustments, such as stop-free scaling and dynamic data pipeline. We demonstrate with experiments that EDL can indeed bring significant benefits to the above-listed applications in GPU cluster management.

Title: A Re-classification of Information Seeking Tasks and Their Computational Solutions Abstract: AbstractThis article presents a re-classification of information seeking (IS) tasks, concepts, and algorithms. The proposed taxonomy provides new dimensions to look into information seeking tasks and methods. The new dimensions include number of search iterations, search goal types, and procedures to reach these goals. Differences along these dimensions for the information seeking tasks call for suitable computational solutions. The article then reviews machine learning solutions that match each new category. The article ends with a review of evaluation campaigns for IS systems.

Title: Dynamic Interference Management for UAV-Assisted Wireless Networks Abstract: We investigate a transmission mechanism aiming to improve the data rate between a base station (BS) and a user equipment (UE) through deploying multiple relaying UAVs. We consider the effect of interference incurred by another established communication network, which makes our problem challenging and different from the state of the art. We aim to design the 3D trajectories and power allocation for...

Title: H-Kernels by Walks Abstract: Let $$D=(V,E)$$ and $$H=(U,F)$$ be digraphs and consider a colouring of the arcs of D with the vertices of H; we say that D is H coloured. We study a natural generalisation of the notion of kernel, as introduced by V. Neumann and Morgenstern (1944), to prove that If every cycle of D is an H-cycle, then D has an H-kernel by walks. As a consequence of this, we are able to give several sufficient conditions for the existence of H-kernels by walks; in particular, we solve partially a conjecture by Bai et al. in this context [2]; viz., they work with complete H without loops, and use paths rather than walks, so whenever the existence of H-paths is implied by the existence of H-walks our result can be use to corroborate Bai’s conjecture—in particular, if D is two coloured, and each cycle is alternating, then each alternating walk contains an alternating path.

Title: Kissing Numbers of Regular Graphs Abstract: We prove a sharp upper bound on the number of shortest cycles contained inside any connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds only for Moore graphs, which gives a new characterization of these graphs. In the case of regular graphs, our result improves an inequality of Teo and Koh. We also show that a subsequence of the Ramanujan graphs of Lubotzky-Phillips-Sarnak have super-linear kissing numbers.

Title: A Scalable Algorithm for Sparse Portfolio Selection Abstract: The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities and minimum investment constraints. Existing certifiably optimal approaches to this problem do not converge within a practical amount of time at real world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic which supplies high-quality warm-starts, a preprocessing technique for decreasing the gap at the root node, and an analytic technique for strengthening our cuts. We also study the problem's Boolean relaxation, establish that it is second-order-cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.

Title: PINE : Universal Deep Embedding for Graph Nodes via Partial Permutation Invariant Set Functions Abstract: Graph node embedding aims at learning a vector representation for all nodes given a graph. It is a central problem in many machine learning tasks (e.g., node classification, recommendation, community detection). The key problem in graph node embedding lies in how to define the dependence to neighbors. Existing approaches specify (either explicitly or implicitly) certain dependencies on neighbors, ...

Title: A varying terminal time mean-variance model Abstract: To improve the efficient frontier of the classical mean-variance model in continuous time, we propose a varying terminal time mean-variance model with a constraint on the mean value of the portfolio asset, which moves with the varying terminal time. Using the embedding technique from stochastic optimal control in continuous time and varying the terminal time, we determine an optimal strategy and related deterministic terminal time for the model. The results of this paper suggest that for an investment plan requires minimizing the variance with a varying terminal time. (C) 2022 Elsevier B.V. All rights reserved.

Title: Spatiotemporal Co-Attention Recurrent Neural Networks for Human-Skeleton Motion Prediction Abstract: Human motion prediction aims to generate future motions based on the observed human motions. Witnessing the success of Recurrent Neural Networks (RNN) in modeling sequential data, recent works utilize RNNs to model human-skeleton motions on the observed motion sequence and predict future human motions. However, these methods disregard the existence of the spatial coherence among joints and the tem...

Title: A Method for Geodesic Distance on Subdivision of Trees With Arbitrary Orders and Their Applications Abstract: Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the exact solutions to geodesic distances on two different families of growth trees which are recursively created upon an arbitrary tree <tex-math no...

Title: Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics Abstract: Whilst influence functions for linear discriminant analysis (LDA) have been found for a single discriminant when dealing with two groups, until now these have not been derived in the setting of a general number of groups. In this paper we explore the relationship between Sliced Inverse Regression (SIR) and LDA, and exploit this relationship to develop influence functions for LDA from those already derived for SIR. These influence functions can be used to understand robustness properties of LDA and also to detect influential observations in practice. We illustrate the usefulness of these via their application to a real data set.