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Title: Edge-isoperimetric inequalities and ball-noise stability: Linear programming and probabilistic approaches Abstract: Let Qnr be the graph with vertex set {−1,1}n in which two vertices are joined if their Hamming distance is at most r. The edge-isoperimetric problem for Qnr is that: For every (n,r,M) such that 1≤r≤n and 1≤M≤2n, determine the minimum edge-boundary size of a subset of vertices of Qnr with a given size M. In this paper, we apply two different approaches to prove bounds for this problem. The first approach is a linear programming approach and the second is probabilistic. Our bound derived by the first approach generalizes the tight bound for M=2n−1 derived by Kahn, Kalai, and Linial in 1989. Moreover, our bound is also tight for M=2n−2 and r≤n2−1. Our bounds derived by the second approach are expressed in terms of the noise stability, and they are shown to be asymptotically tight as n→∞ when r=2⌊βn2⌋+1 and M=⌊α2n⌋ for fixed α,β∈(0,1), and is tight up to a factor 2 when r=2⌊βn2⌋ and M=⌊α2n⌋. In fact, the edge-isoperimetric problem is equivalent to a ball-noise stability problem which is a variant of the traditional (i.i.d.-) noise stability problem. Our results can be interpreted as bounds for the ball-noise stability problem.

Title: MathOptInterface: A Data Structure for Mathematical Optimization Problems Abstract: We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining predefined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP. Summary of Contribution: This paper describes a new abstract data structure for representing mathematical optimization models with a corresponding file format and automatic transformation system. The advances are useful for algebraic modeling languages, allowing practitioners to model problems more naturally and more generally than before.

Title: Before the Page Time: Maximum Entanglements or the Return of the Monster? Abstract: The conservation of information of evaporating black holes is a very natural consequence of unitarity, which is the fundamental symmetry of quantum mechanics. In order to study the conservation of information, we need to understand the nature of the entanglement entropy. The entropy of Hawking radiation is approximately equal to the maximum of entanglement entropy if a black hole is in a state before the Page time, i.e., when the entropy of Hawking radiation is smaller than the entropy of the black hole. However, if there exists a process generating smaller entanglements rather than maximal entanglements, the entropy of Hawking radiation will become smaller than the maximum of the entanglement entropy before the Page time. If this process accumulates, even though the probability is small, the emitted radiation can eventually be distinguished from the exactly thermal state. In this paper, we provide several interpretations of this phenomenon: (1) information of the collapsed matter emitted before the Page time, (2) there exists a firewall or a non-local effect before the Page time, or (3) the statistical entropy is greater than the areal entropy; a monster is formed. Our conclusion will help resolve the information loss paradox by providing groundwork for further research.

Title: On the Convergence of the Monte Carlo Exploring Starts Algorithm for Reinforcement Learning Abstract: A simple and natural algorithm for reinforcement learning (RL) is Monte Carlo Exploring Starts (MCES), where the Q-function is estimated by averaging the Monte Carlo returns, and the policy is improved by choosing actions that maximize the current estimate of the Q-function. Exploration is performed by "exploring starts", that is, each episode begins with a randomly chosen state and action, and then follows the current policy to the terminal state. In the classic book on RL by Sutton & Barto (2018), it is stated that establishing convergence for the MCES algorithm is one of the most important remaining open theoretical problems in RL. However, the convergence question for MCES turns out to be quite nuanced. Bertsekas & Tsitsiklis (1996) provide a counter-example showing that the MCES algorithm does not necessarily converge. Tsitsiklis (2002) further shows that if the original MCES algorithm is modified so that the Q-function estimates are updated at the same rate for all state-action pairs, and the discount factor is strictly less than one, then the MCES algorithm converges. In this paper we make headway with the original and more efficient MCES algorithm given in Sutton & Barto (1998), establishing almost sure convergence for Optimal Policy Feed-Forward MDPs, which are MDPs whose states are not revisited within any episode when using an optimal policy. Such MDPs include a large class of environments such as all deterministic environments and all episodic environments with a timestep or any monotonically changing values as part of the state. Different from the previous proofs using stochastic approximations, we introduce a novel inductive approach, which is very simple and only makes use of the strong law of large numbers.

Title: Acyclic matchings in graphs of bounded maximum degree Abstract: A matching M in a graph G is acyclic if the subgraph of G induced by the set of vertices that are incident to an edge in M is a forest. We prove that every graph with n vertices, maximum degree at most delta, and no isolated vertex, has an acyclic matching of size at least (1 - o(1)) 6n/delta(2), and we explain how to find such an acyclic matching in polynomial time. (C) 2022 Elsevier B.V. All rights reserved.

Title: Distributed Bayesian Matrix Decomposition for Big Data Mining and Clustering Abstract: Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine. Moreover, big data are often distributedly collected and stored on different machines. Thus, such data generally bear strong heterogeneous noise. It is essential and useful to develop distributed matrix decomposition for big data analytics. Such a method should scale up well, model the heterogeneous noise, and address the communication issue in a distributed system. To this end, we propose a distributed Bayesian matrix decomposition model (DBMD) for big data mining and clustering. Specifically, we adopt three strategies to implement the distributed computing including 1) the accelerated gradient descent, 2) the alternating direction method of multipliers (ADMM), and 3) the statistical inference. We investigate the theoretical convergence behaviors of these algorithms. To address the heterogeneity of the noise, we propose an optimal plug-in weighted average that reduces the variance of the estimation. Synthetic experiments validate our theoretical results, and real-world experiments show that our algorithms scale up well to big data and achieves superior or competing performance compared to two typical distributed methods including Scalable-NMF and scalable k-means++.

Title: Learning End-to-End Lossy Image Compression: A Benchmark Abstract: Image compression is one of the most fundamental techniques and commonly used applications in the image and video processing field. Earlier methods built a well-designed pipeline, and efforts were made to improve all modules of the pipeline by handcrafted tuning. Later, tremendous contributions were made, especially when data-driven methods revitalized the domain with their excellent modeling capacities and flexibility in incorporating newly designed modules and constraints. Despite great progress, a systematic benchmark and comprehensive analysis of end-to-end learned image compression methods are lacking. In this paper, we first conduct a comprehensive literature survey of learned image compression methods. The literature is organized based on several aspects to jointly optimize the rate-distortion performance with a neural network, i.e., network architecture, entropy model and rate control. We describe milestones in cutting-edge learned image-compression methods, review a broad range of existing works, and provide insights into their historical development routes. With this survey, the main challenges of image compression methods are revealed, along with opportunities to address the related issues with recent advanced learning methods. This analysis provides an opportunity to take a further step towards higher-efficiency image compression. By introducing a coarse-to-fine hyperprior model for entropy estimation and signal reconstruction, we achieve improved rate-distortion performance, especially on high-resolution images. Extensive benchmark experiments demonstrate the superiority of our model in rate-distortion performance and time complexity on multi-core CPUs and GPUs.

Title: Attentional networks for music generation Abstract: Realistic music generation has always remained as a challenging problem as it may lack structure or rationality. In this work, we propose a deep learning based music generation method in order to produce old style music particularly JAZZ with rehashed melodic structures utilizing a Bi-directional Long Short Term Memory (Bi-LSTM) Neural Network with attention. Owing to the success in modelling long-term temporal dependencies in sequential data and its success in case of videos, Bi-LSTMs with attention serves as a natural choice and early utilization in music generation. We validate in our experiments that Bi-LSTMs with attention are able to preserve the richness and technical nuances of the music performed.

Title: K-bMOM: A robust Lloyd-type clustering algorithm based on bootstrap median-of-means Abstract: The median-of-means is an estimator of the mean of a random variable that has emerged as an efficient and flexible tool to design robust learning algorithms with optimal theoretical guarantees. However, its use for the clustering task suggests dividing the dataset into blocks, which may provoke the disappearance of some clusters in some blocks and lead to bad performances. To overcome this difficulty, a procedure termed "bootstrap median-of-means" is proposed, where the blocks are generated with a replacement in the dataset. Considering the estimation of the mean of a random variable, the bootstrap median-of-means has a better breakdown point than the median-of-means if enough blocks are generated. A clustering algorithm called K-bMOM is designed, by performing Lloyd-type iterations together with the use of the bootstrap median-of-means strategy. Good performances are obtained on simulated and real-world datasets for color quantization and an emphasis is put on the benefits of our robust intialization procedure. On the theoretical side, K-bMOM is also proven to have a non-trivial probabilistic breakdown point in well-clusterizable situations. (c) 2021 Elsevier B.V. All rights reserved.

Title: Controllability of a Linear System With Nonnegative Sparse Controls Abstract: This article studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems, where the external influence on the system is unidirectional, and activating each input node adds to the cost of control. We derive the necessary and sufficient conditions for the controllability of th...

Title: Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-Shape Priors for Image Segmentation Abstract: Deep Convolutional Neural Networks (DCNNs) can well extract the features from natural images. However, the classification functions in the existing network architecture of CNNs are simple and lack capabilities to handle important spatial information as have been done by many well-known traditional variational image segmentation models. Priors such as spatial regularization, volume prior and shapes priors cannot be handled by existing DCNNs. We propose a novel Soft Threshold Dynamics (STD) framework which can integrate many spatial priors of the classic variational models into the DCNNs for image segmentation. The novelty of our method is to interpret the softmax activation function as a dual variable in a variational problem, and thus many spatial priors can be imposed in the dual space. From this viewpoint, we can build a STD based framework which can enable the outputs of DCNNs to have many special priors such as spatial regularization, volume preservation and star-shape prior. The proposed method is a general mathematical framework and it can be applied to any image segmentation DCNNs with a softmax classification layer. To show the efficiency of our method, we applied it to the popular DeepLabV3+ image segmentation network, and the experiments results show that our method can work efficiently on data-driven image segmentation DCNNs.

Title: Toward Multidiversified Ensemble Clustering of High-Dimensional Data: From Subspaces to Metrics and Beyond Abstract: The rapid emergence of high-dimensional data in various areas has brought new challenges to current ensemble clustering research. To deal with the curse of dimensionality, recently considerable efforts in ensemble clustering have been made by means of different subspace-based techniques. However, besides the emphasis on subspaces, rather limited attention has been paid to the potential diversity in similarity/dissimilarity metrics. It remains a surprisingly open problem in ensemble clustering how to create and aggregate a large population of diversified metrics, and furthermore, how to jointly investigate the multilevel diversity in the large populations of metrics, subspaces, and clusters in a unified framework. To tackle this problem, this article proposes a novel multidiversified ensemble clustering approach. In particular, we create a large number of diversified metrics by randomizing a scaled exponential similarity kernel, which are then coupled with random subspaces to form a large set of metric-subspace pairs. Based on the similarity matrices derived from these metric-subspace pairs, an ensemble of diversified base clusterings can be thereby constructed. Furthermore, an entropy-based criterion is utilized to explore the cluster wise diversity in ensembles, based on which three specific ensemble clustering algorithms are presented by incorporating three types of consensus functions. Extensive experiments are conducted on 30 high-dimensional datasets, including 18 cancer gene expression datasets and 12 image/speech datasets, which demonstrate the superiority of our algorithms over the state of the art. The source 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/huangdonghere/MDEC</uri> .

Title: Dynamic impact for ant colony optimization algorithm Abstract: •This paper proposes probability calculation extension for ACO algorithm called dynamic impact.•2 problems were solved using this method. Real-world MMPPFO problem, and theoretical benchmark MKP problem.•MMPPFO problem final solution fitness has been improved by 33.2%.•MKP small instances results were 100% success rate, and for large instances average gap was improved by 4.26 times.•Algorithm showed superior performance across small and large datasets and sparse optimization problems.

Title: Maximizing products of linear forms, and the permanent of positive semidefinite matrices Abstract: We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite (HPSD) matrices. By analyzing a constructive randomized rounding algorithm, we obtain an improved multiplicative approximation factor to the permanent of HPSD matrices, as well as computationally efficient certificates for this approximation. We also propose an analog of van der Waerden’s conjecture for HPSD matrices, where the polynomial optimization problem is interpreted as a relaxation of the permanent.

Title: Learning structured communication for multi-agent reinforcement learning Abstract: This work explores the large-scale multi-agent communication mechanism for multi-agent reinforcement learning (MARL). We summarize the general topology categories for communication structures, which are often manually specified in MARL literature. A novel framework termed Learning Structured Communication (LSC) is proposed by learning a flexible and efficient communication topology (hierarchical structure). It contains two modules: structured communication module and communication-based policy module. The structured communication module learns to form a hierarchical structure by maximizing the cumulative reward of the agents under the current communication-based policy. The communication-based policy module adopts hierarchical graph neural networks to generate messages, propagate information based on the learned communication structure, and select actions. In contrast to existing communication mechanisms, our method has a learnable and hierarchical communication structure. Experiments on large-scale battle scenarios show that the proposed LSC has high communication efficiency and global cooperation capability.

Title: On numerical approximations to fluid–structure interactions involving compressible fluids Abstract: In this paper we introduce a numerical scheme for fluid–structure interaction problems in two or three space dimensions. A flexible elastic plate is interacting with a viscous, compressible barotropic fluid. Hence the physical domain of definition (the domain of Eulerian coordinates) is changing in time. We introduce a fully discrete scheme that is stable, satisfies geometric conservation, mass conservation and the positivity of the density. We also prove that the scheme is consistent with the definition of continuous weak solutions.

Title: A Catlin-type theorem for graph partitioning avoiding prescribed subgraphs Abstract: As an extension of the Brooks theorem, Catlin in 1979 showed that if H is neither an odd cycle nor a complete graph with maximum degree Delta(H), then H has a vertex Delta(H)-coloring such that one of the color classes is a maximum independent set. Let G be a connected graph of order at least 2. A G-free k-coloring of a graph H is a partition of the vertex set of H into V-1, ... , V-k such that H[Vi], the subgraph induced on Vi, does not contain any subgraph isomorphic to G. As a generalization of Catlin's Theorem we show that a graph H has a G-free (sic)(H)/delta(G)(sic)-coloring for which one of the color classes is a maximum G-free subset of V (H) if H satisfies the following conditions; (1) H is not isomorphic to G if G is regular, (2) H is not isomorphic to K-k delta(G)+1 if G (sic)& nbsp; K delta(G)+1, and (3) H is not an odd cycle if G is isomorphic to K-2. Indeed, we show even more, by proving that if G(1), ... , G(k) are connected graphs with minimum degrees d(1), ... , d(k), respectively, and (H) = sigma(k)(i =1) d(k), then there is a partition of vertices of H to V-1, ... , V-k such that each H[Vi] is G(i)-free and moreover one of Vi's can be chosen in a way that H[V-i] is a maximum G(i)-free subset of V (H) except either k =1 and H is isomorphic to G(1), each G(i) is isomorphic to Kdi+1 and H is not isomorphic to K Delta(H)+1, or each G(i) is isomorphic to K-2 and H is not an odd cycle. (C) 2022 Elsevier B.V. All rights reserved.

Title: Rowmotion Orbits of Trapezoid Posets Abstract: Rowmotion is an invertible operator on the order ideals of a poset which has been extensively studied and is well understood for the rectangle poset. In this paper, we show that rowmotion is equivariant with respect to a bijection of Hamaker, Patrias, Pechenik and Williams between order ideals of rectangle and trapezoid posets, thereby affirming a conjecture of Hopkins that the rectangle and trapezoid posets have the same rowmotion orbit structures for order ideals. Our main tools in proving this are K-jeu-de-taquin and (weak) K-Knuth equivalence of increasing tableaux. We define almost minimal tableaux as a family of tableaux naturally arising from order ideals and show that for any partition lambda, the almost minimal tableaux of shape lambda are in different (weak) :K-Knuth equivalence classes.

Title: Force-Sensor-Less Bilateral Teleoperation Control of Dissimilar Master–Slave System With Arbitrary Scaling Abstract: This study designs a high-precision bilateral teleoperation control for a dissimilar master–slave system. The proposed nonlinear control design takes advantage of a novel subsystem-dynamics-based control method that allows designing of individual (decentralized) model-based controllers for the manipulators locally at the subsystem level. Very importantly, a dynamic model of the human operator is incorporated into the control of the master manipulator. The individual controllers for the dissimilar master and slave manipulators are connected in a specific communication channel for the bilateral teleoperation to function. Stability of the overall control design is rigorously guaranteed with arbitrary time delays. Novel features of this study include the completely force-sensor-less design for the teleoperation system with a solution for a uniquely introduced computational algebraic loop, a method of estimating the exogenous operating force of an operator and the use of a commercial haptic manipulator. Most importantly, we conduct experiments on a dissimilar system in two degrees of freedom (DOFs). As an illustration of the performance of the proposed system, a force scaling factor of up to 800 and position scaling factor of up to 4 was used in the experiments. The experimental results show an exceptional tracking performance, verifying the real-world performance of the proposed concept.

Title: Beyond Single-Shot Fault-Tolerant Quantum Error Correction Abstract: Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return incorrect outcomes or inject additional faults into the qubits. To achieve fault-tolerant error correction, Shor proposed to repeat the sequence of parity check measu...

Title: Assortment optimization with repeated exposures and product-dependent patience cost Abstract: In this paper, we study the assortment optimization problem faced by many online retailers such as Amazon. We develop a cascade multinomial logit model, based on the classic multinomial logit model, to capture the consumers' purchasing behavior across multiple stages. Unlike most of existing studies, our model allows for repeated exposures of a product. In addition, each consumer has a patience budget that is sampled from a known distribution and each product is associated with a patience cost, which is the required amount of the cognitive efforts on browsing that product. We propose an approximation solution to the assortment optimization problem under cascade multinomial logit model.

Title: Adaptivity of Stochastic Gradient Methods for Nonconvex Optimization. Abstract: Adaptivity is an important yet under-studied property in modern optimization theory. The gap between the state-of-the-art theory and the current practice is striking in that algorithms with desirable theoretical guarantees typically involve drastically different settings of hyperparameters, such as step-size schemes and batch sizes, in different regimes. Despite the appealing theoretical results, such divisive strategies provide little, if any, insight to practitioners to select algorithms that work broadly without tweaking the hyperparameters. In this work, blending the "geometrization" technique introduced by Lei & Jordan 2016 and the \texttt{SARAH} algorithm of Nguyen et al., 2017, we propose the Geometrized \texttt{SARAH} algorithm for non-convex finite-sum and stochastic optimization. Our algorithm is proved to achieve adaptivity to both the magnitude of the target accuracy and the Polyak-\L{}ojasiewicz (PL) constant if present. In addition, it achieves the best-available convergence rate for non-PL objectives simultaneously while outperforming existing algorithms for PL objectives.

Title: APPROXIMABILITY OF MONOTONE SUBMODULAR FUNCTION MAXIMIZATION UNDER CARDINALITY AND MATROID CONSTRAINTS IN THE STREAMING MODEL Abstract: Maximizing a monotone submodular function under various constraints is a classical and intensively studied problem. However, in the single-pass streaming model, where the elements arrive one by one and an algorithm can store only a small fraction of input elements, there is large gap in our knowledge, even though several approximation algorithms have been proposed in the literature. In this work, we present the first lower bound on the approximation ratios for cardinality and matroid constraints that beat 1 - 1/e the single-pass streaming model. Let n be the number of elements in the stream. Then, we prove that any (randomized) streaming algorithm for a cardinality constraint with approximation ratio 2-root 2+epsilon requires Omega(n/K-2) space for any epsilon > 0, where K is the size limit of the output set. We also prove that any (randomized) streaming algorithm for a (partition) matroid constraint with approximation ratio K/2K-1 requires Omega(n/K-2) space for any epsilon > 0, where K is the rank of the given matroid. In addition, we give streaming algorithms that assume access to the objective function via a weak oracle that can only be used to evaluate function values on feasible sets. Specifically, we show weak-oracle streaming algorithms for cardinality and matroid constraints with approximation ratios K/2K-1 and 1/2, respectively, whose space complexity is exponential in K but is independent of n. The former one exactly matches the known inapproximability result for a cardinality constraint in the weak oracle model. The latter one almost matches our lower bound of K for a matroid constraint, which almost settles the approximation ratio for a matroid constraint K/2K-1 that can be obtained by a streaming algorithm whose space complexity is independent of n.

Title: Minimum Length Scheduling for Discrete-Rate Full-Duplex Wireless Powered Communication Networks Abstract: Wireless powered communication networks (WPCNs) will act as a major enabler of massive machine type communications (MTCs), which is a major service domain for 5G and beyond systems. The MTC networks will be deployed by using low-power transceivers with finite discrete configurations. This paper considers minimum length scheduling problem for full-duplex WPCNs, where users transmit information to a...

Title: Harvesting Ambient RF for Presence Detection Through Deep Learning Abstract: This article explores the use of ambient radio frequency (RF) signals for human presence detection through deep learning. Using Wi-Fi signal as an example, we demonstrate that the channel state information (CSI) obtained at the receiver contains rich information about the propagation environment. Through judicious preprocessing of the estimated CSI followed by deep learning, reliable presence dete...

Title: Learning to Rank for Uplift Modeling Abstract: Causal classification concerns the estimation of the net effect of a treatment on an outcome of interest at the instance level, i.e., of the individual treatment effect (ITE). For binary treatment and outcome variables, causal classification models produce ITE estimates that essentially allow one to rank instances from a large positive effect to a large negative effect. Often, as in uplift modeling (UM), one is merely interested in this ranking, rather than in the ITE estimates themselves. In this regard, we investigate the potential of learning to rank (L2R) techniques to learn a ranking of the instances directly. We propose a unified formalization of different binary causal classification performance measures from the UM literature and explore how these can be integrated into the L2R framework. Additionally, we introduce a new metric for UM with L2R called the <i>promoted cumulative gain</i> (PCG). We employ the L2R technique LambdaMART to optimize the ranking according to PCG and show improved results over the use of standard L2R metrics and equal to improved results when compared with state-of-the-art UM. Finally, we show how L2R techniques can be used to specifically optimize for the top- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> fraction of the ranking in a UM context, however, these results do not generalize to the test set.

Title: Human perception of intrinsically motivated autonomy in human-robot interaction Abstract: A challenge in using robots in human-inhabited environments is to design behavior that is engaging, yet robust to the perturbations induced by human interaction. Our idea is to imbue the robot with intrinsic motivation (IM) so that it can handle new situations and appears as a genuine social other to humans and thus be of more interest to a human interaction partner. Human-robot interaction (HRI) experiments mainly focus on scripted or teleoperated robots, that mimic characteristics such as IM to control isolated behavior factors. This article presents a "robotologist" study design that allows comparing autonomously generated behaviors with each other and, for the first time, evaluates the human perception of IM-based generated behavior in robots. We conducted a within-subjects user study (N = 24) where participants interacted with a fully autonomous Sphero BB8 robot with different behavioral regimes: one realizing an adaptive, intrinsically motivated behavior and the other being reactive, but not adaptive. The robot and its behaviors are intentionally kept minimal to concentrate on the effect induced by IM. A quantitative analysis of post-interaction questionnaires showed a significantly higher perception of the dimension "Warmth" compared to the reactive baseline behavior. Warmth is considered a primary dimension for social attitude formation in human social cognition. A human perceived as warm (friendly, trustworthy) experiences more positive social interactions.

Title: Scalable and Practical Natural Gradient for Large-Scale Deep Learning Abstract: Large-scale distributed training of deep neural networks results in models with worse generalization performance as a result of the increase in the effective mini-batch size. Previous approaches attempt to address this problem by varying the learning rate and batch size over epochs and layers, or ad hoc modifications of batch normalization. We propose scalable and practical natura...

Title: Analyzing Differentiable Fuzzy Logic Operators Abstract: The AI community is increasingly putting its attention towards combining symbolic and neural approaches, as it is often argued that the strengths and weaknesses of these approaches are complementary. One recent trend in the literature is weakly supervised learning techniques that employ operators from fuzzy logics. In particular, these use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks, this background knowledge can be added to regular loss functions, hence making reasoning a part of learning.

Title: Multivariate Monotone Inclusions in Saddle Form Abstract: We introduce the notion of a saddle operator for highly structured multivariate monotone inclusions involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators, as well as various monotonicity-preserving operations among them. The properties of this saddle operator are investigated, and an asynchronous block-iterative algorithm to find its zeros is designed and analyzed. In turn, this allows us to solve the original system via a novel splitting algorithm of great flexibility in terms of processing the constituent operators individually and exploiting their specific attributes. The case of multivariate minimization problems is discussed.

Title: Optimally weighted loss functions for solving PDEs with Neural Networks Abstract: Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks (Raissi et al., 2007). We introduce a generalization for these methods that manifests as a scaling parameter which balances the relative importance of the different constraints imposed by partial differential equations. A mathematical motivation of these generalized methods is provided, which shows that for linear and well-posed partial differential equations, the functional form is convex. We then derive a choice for the scaling parameter that is optimal with respect to a measure of relative error. Because this optimal choice relies on having full knowledge of analytical solutions, we also propose a heuristic method to approximate this optimal choice. The proposed methods are compared numerically to the original methods on a variety of model partial differential equations, with the number of data points being updated adaptively. For several problems, including high-dimensional PDEs the proposed methods are shown to significantly enhance accuracy.

Title: A Robust Traffic Control Model Considering Uncertainties in Turning Ratios Abstract: The effects of model parameter uncertainty on traffic flow control problems have recently drawn research attention. While the uncertainty in fundamental diagram related parameters has been investigated in the past, few articles have focused on network parameters uncertainty, including turning ratio uncertainty. To fill this gap, this article proposes a robust control model to deal with the uncertainties in the turning ratio by using distributionally robust chance constraints. The model allows one to compute the optimal control action that maximizes some objective, under all possible distributions of network parameters. We then apply this robust control framework to both a freeway network and an urban network, and evaluate the impact of uncertainty on optimal control inputs, over the test networks. The case studies show that compared to non-robust control, the proposed robust model can reduce congestion brought by the uncertainties and improve the overall throughput.

Title: Bitcoin's Blockchain Data Analytics: A Graph Theoretic Perspective. Abstract: Bitcoin is the most popular cryptocurrency used worldwide. It provides pseudonymity to its users by establishing identity using public keys as transaction end-points. These transactions are recorded on an immutable public ledger called Blockchain which is an append-only data structure. The popularity of Bitcoin has increased unreasonably. The general trend shows a positive response from the common masses indicating an increase in trust and privacy concerns which makes an interesting use case from the analysis point of view. Moreover, since the blockchain is publicly available and up-to-date, any analysis would provide a live insight into the usage patterns which ultimately would be useful for making a number of inferences by law-enforcement agencies, economists, tech-enthusiasts, etc. In this paper, we study various applications and techniques of performing data analytics over Bitcoin blockchain from a graph theoretic perspective. We also propose a framework for performing such data analytics and explored a couple of use cases using the proposed framework.

Title: Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures Abstract: We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements with edges/faces that may be in arbitrary number (potentially unlimited) and whose measure may be arbitrarily small. Our approach is then very well suited to tame the geometrical complexity featured by most of applications in the computational geoscience field. From the modelling point of view, we adopt a reduction strategy that treats fractures as manifolds of codimension one and we employ the primal version of Darcy's law to describe the flow in both the bulk and in the fracture network. In addition, some physically consistent conditions couple the two problems, allowing for jump of pressure at their interface, and they as well prescribe the behaviour of the fluid along the intersections, imposing pressure continuity and flux conservation. Both the bulk and fracture discretizations are obtained employing the Symmetric Interior Penalty DG method extended to the polytopic setting. The key instrument to obtain a polyDG approximation of the problem in the fracture network is the generalization of the concepts of jump and average at the intersection, so that the contribution from all the fractures is taken into account. We prove the well-posedness of the discrete formulation and perform an error analysis obtaining a priori hp-error estimates. All our theoretical results are validated performing preliminary numerical tests with known analytical solution.

Title: Coordinate-Free Circumnavigation of a Moving Target Via a PD-Like Controller Abstract: This article proposes a coordinate-free controller for a nonholonomic vehicle to circumnavigate a fully- actuated moving target by using range-only measurements. If the range rate is available, our proportional derivative (PD) like controller has a simple structure as the standard PD controller, except the design of an additive constant bias and a saturation function in the error feedback. We show that if the target is stationary, the vehicle asymptotically encloses the target with a predefined radius at an exponential convergence rate, i.e., an exact circumnavigation pattern can be completed. For a moving target, the circumnavigation error converges to a small region whose size is shown proportional to the maneuverability of the target, e.g., the maximum linear speed and acceleration. Moreover, we design a second-order sliding mode (SOSM) filter to estimate the range rate and show that the SOSM filter can recover the range rate in a finite time. Finally, the effectiveness and advantages of our controller are validated via both numerical simulations and real experiments.

Title: Elastool: An Automated Toolkit For Elastic Constants Calculation Abstract: We present the ELASTooL package, an automated toolkit for calculating the second-order elastic constants (SOECs) of any two-(2D) and three-dimensional (3D) crystal systems. ELASTooL uses three kinds of strain-matrix sets, i.e., the high-efficiency strain-matrix sets (OHESS), the universal linear-independent coupling strains (ULICS), and the all-single-element strain-matrix sets (ASESS), to calculate the SOECs automatically. ELASTooL can efficiently compute both zero-and high-temperature elastic constants. We describe in detail the theoretical background and computational method of elastic constants, the package structure, the installation, and run, the input/output files, the controlling parameters, and two representative examples of how to use the ELASTooL package. ELASTooL is useful for either the exploration of materials' elastic properties or high-throughput new materials screening and design. ELASTooL is freely available on GitHub: https://github .com /elastool Program summary Program Title: ElasTool CPC Library link to program files: https://doi .org /10 .17632 /ktvmxrdhpz .1 Code Ocean capsule: https://codeocean .com /capsule /1893813 Licensing provisions: GNU General Public License, version 3 Programming language: Python 3 External routines: NumPy [1], Spglib [2], ASE [3], Pandas [4] Nature of problem: The stress-strain method of elastic constants calculation depends on accurate stresses calculated with first-principles methods, such as the density functional theory (DFT). Compared to the energy-strain method, the stress-strain approach needs a smaller number of strain sets to solve the equation sets needed to deduce the elastic constants; it is also more straightforward to implement. However, accurate stresses take a lot of time to compute within DFT. Thus, a smaller number of strain sets and more efficient strain sets are urgently needed to improve the computational efficiency of elastic constants. An automated solution coupled with DFT is necessary for the exploration of materials' elastic properties and high-throughput new materials screening and design. Solution method: The solution to improve the computational efficiency of the stress-strain method is to decrease the number of strain-matrix sets and optimize the strain-matrix sets. We coupled our previously proposed high-efficiency strain-matrix sets (OHESS) with DFT and automated the processes of calculating the elastic tensor using the stress-strain method in the ELASTooL package. ELASTooL can also adopt the all single-element strain-matrix sets (ASESS) and the universal linear-independent coupling strains (ULICS) approaches. It can deal with both zero-and high-temperature elastic constants of any crystal systems belonging to 2D or 3D. Having obtained the elastic moduli, ELASTooL also gives other essential mechanical and elastic properties of materials such as Young's modulus, bulk modulus, elastic anisotropy, Debye temperature, and the sound velocities. Additional comments including restrictions and unusual features: Currently, this package interfaces with Vienna Ab initio Simulation Package (VASP) code as the stress tensors calculator. [5-7] Extension to other electronic structures is straightforward. References [1] https://numpy.org/ [2] https://atztogo.github.io /spglib/ [3] https://wiki.fysik.dtu.dk/ase/ [4] https://pandas.pydata.org/ [5] https://www.vasp.at/ [6] G. Kresse, J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169. [7] G. Kresse, D.Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999) 1758. (c) 2021 Elsevier B.V. All rights reserved.

Title: Frequency Regulation With Thermostatically Controlled Loads: Aggregation of Dynamics and Synchronization Abstract: Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency-control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior, which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e., simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this article, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions, which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared with existing implementations.

Title: LDPC codes constructed from cubic symmetric graphs Abstract: Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The codes constructed are (3, 3)-regular and the vast majority of the corresponding Tanner graphs have girth greater than four. We analyse properties of the codes obtained and present bounds for the code parameters, the dimension and the minimum distance. Furthermore, we give an expression for the variance of the syndrome weight of the codes constructed. Information on the LDPC codes constructed from bipartite cubic symmetric graphs with less than 200 vertices is presented as well. Some of the codes constructed are optimal, and some have an additional property of being self-orthogonal or linear codes with complementary dual (LCD codes).

Title: Structures of Spurious Local Minima in k -Means Abstract: The $k\text {-means}$ clustering problem concerns finding a partition of the data points into $k$ clusters such that the total within-cluster squared distance is minimized. This optimization objective is non-convex, and not everywhere differentiable. In ...

Title: Directional Deep Embedding and Appearance Learning for Fast Video Object Segmentation Abstract: Most recent semisupervised video object segmentation (VOS) methods rely on fine-tuning deep convolutional neural networks online using the given mask of the first frame or predicted masks of subsequent frames. However, the online fine-tuning process is usually time-consuming, limiting the practical use of such methods. We propose a directional deep embedding and appearance learning (DDEAL) method, which is free of the online fine-tuning process, for fast VOS. First, a global directional matching module (GDMM), which can be efficiently implemented by parallel convolutional operations, is proposed to learn a semantic pixel-wise embedding as an internal guidance. Second, an effective directional appearance model-based statistics is proposed to represent the target and background on a spherical embedding space for VOS. Equipped with the GDMM and the directional appearance model learning module, DDEAL learns static cues from the labeled first frame and dynamically updates cues of the subsequent frames for object segmentation. Our method exhibits the state-of-the-art VOS performance without using online fine-tuning. Specifically, it achieves a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ J}}$ </tex-math></inline-formula> & <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ F}}$ </tex-math></inline-formula> mean score of 74.8% on DAVIS 2017 data set and an overall score <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ G}}$ </tex-math></inline-formula> of 71.3% on the large-scale YouTube-VOS data set, while retaining a speed of 25 fps with a single NVIDIA TITAN Xp GPU. Furthermore, our faster version runs 31 fps with only a little accuracy loss.

Title: Second-Order Conic Programming Approach for Wasserstein Distributionally Robust Two-Stage Linear Programs Abstract: This article proposes a second-order conic programming (SOCP) approach to solve distributionally robust two-stage linear programs over 1-Wasserstein balls. We start from the case with distribution uncertainty only in the objective function and then explore the case with distribution uncertainty only in constraints. The former program is exactly reformulated as a tractable SOCP problem, whereas the...

Title: Lyapunov Characterization of Uniform Exponential Stability for Nonlinear Infinite-Dimensional Systems Abstract: In this article, we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to uncertainties. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to uncertainties) local, semi-global, and global exponential stability, through the...

Title: Unique key Horn functions Abstract: Given a relational database, a key is a set of attributes such that a value assignment to this set uniquely determines the values of all other attributes. The database uniquely defines a pure Horn function h, representing the functional dependencies. If the knowledge of the attribute values in set A determines the value for attribute v, then A→v is an implicate of h. If K is a key of the database, then K→v is an implicate of h for all attributes v.

Title: A Newton Frank–Wolfe method for constrained self-concordant minimization Abstract: We develop a new Newton Frank–Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds globally, the class of self-concordant functions only has local bounds, making it difficult to estimate the number of linear minimization oracle (LMO) calls for the underlying optimization algorithm. Fortunately, we can still prove that the number of LMO calls of our method is nearly the same as that of the standard Frank-Wolfe method in the L-smooth case. Specifically, our method requires at most $${\mathcal {O}}\big (\varepsilon ^{-(1 + \nu )}\big )$$ LMO’s, where $$\varepsilon $$ is the desired accuracy, and $$\nu \in (0, 0.139)$$ is a given constant depending on the chosen initial point of the proposed algorithm. Our intensive numerical experiments on three applications: portfolio design with the competitive ratio, D-optimal experimental design, and logistic regression with elastic-net regularizer, show that the proposed Newton Frank–Wolfe method outperforms different state-of-the-art competitors.

Title: Asymptotic properties of Dirichlet kernel density estimators Abstract: We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the d-dimensional simplex. The simplex is an important case as it is the natural domain of compositional data and has been neglected in the literature on asymmetric kernels. The Dirichlet kernel estimator, which generalizes the (non-modified) unidimensional Beta kernel estimator from Chen (1999), is free of boundary bias and non-negative everywhere on the simplex. We show that it achieves the optimal convergence rate O(n−4/(d+4)) for the mean squared error and the mean integrated squared error, we prove its asymptotic normality and uniform strong consistency, and we also find an asymptotic expression for the mean integrated absolute error. To illustrate the Dirichlet kernel method and its favorable boundary properties, we present a case study on minerals processing.

Title: WHEN SYMMETRIES ARE NOT ENOUGH: A HIERARCHY OF HARD CONSTRAINT SATISFACTION PROBLEMS Abstract: We produce a class of w-categorical structures with finite signature by applying a model-theoretic construction---a refinement of the Hrushovski-enco ding---to w-categorical structures in a possibly infinite signature. We show that the encoded structures retain desirable algebraic properties of the original structures, but that the constraint satisfaction problems (CSPs) associated with these structures can be badly behaved in terms of computational complexity. This method allows us to systematically generate w-categorical templates whose CSPs are complete for a variety of complexity classes of arbitrarily high complexity and w-categorical templates that show that membership in any given complexity class containing AC0 cannot be expressed by a set of identities on the polymorphisms. It moreover enables us to prove that recent results about the relevance of topology on polymorphism clones of w-categorical structures also apply for CSP templates, i.e., structures in a finite language. Finally, we obtain a concrete algebraic criterion which could constitute a description of the delineation between tractability and NP-hardness in the dichotomy conjecture for first-order reducts of finitely bounded homogeneous structures.

Title: The probabilistic model checker Storm Abstract: We present the probabilistic model checker Storm. Storm supports the analysis of discrete- and continuous-time variants of both Markov chains and Markov decision processes. Storm has three major distinguishing features. It supports multiple input languages for Markov models, including the Jani and Prism modeling languages, dynamic fault trees, generalized stochastic Petri nets, and the probabilistic guarded command language. It has a modular setup in which solvers and symbolic engines can easily be exchanged. Its Python API allows for rapid prototyping by encapsulating Storm’s fast and scalable algorithms. This paper reports on the main features of Storm and explains how to effectively use them. A description is provided of the main distinguishing functionalities of Storm. Finally, an empirical evaluation of different configurations of Storm on the QComp 2019 benchmark set is presented.

Title: Blossoming bijection for bipartite pointed maps and parametric rationality of general maps of any surface. Abstract: We construct an explicit bijection between bipartite pointed maps of an arbitrary surface $\mathbb{S}$, and specific unicellular blossoming maps of the same surface. Our bijection gives access to the degrees of all the faces, and distances from the pointed vertex in the initial map. The main construction generalizes recent work of the second author which covered the case of an orientable surface. Our bijection gives rise to a first combinatorial proof of a parametric rationality result concerning the bivariate generating series of maps of a given surface with respect to their numbers of faces and vertices. In particular, it provides a combinatorial explanation of the structural difference between the aforementioned bivariate parametric generating series in the case of orientable and non-orientable maps.

Title: Sampling Kaczmarz-Motzkin method for linear feasibility problems: generalization and acceleration Abstract: Randomized Kaczmarz, Motzkin Method and Sampling Kaczmarz Motzkin (SKM) algorithms are commonly used iterative techniques for solving a system of linear inequalities (i.e., $$Ax \le b$$ ). As linear systems of equations represent a modeling paradigm for solving many optimization problems, these randomized and iterative techniques are gaining popularity among researchers in different domains. In this work, we propose a Generalized Sampling Kaczmarz Motzkin (GSKM) method that unifies the iterative methods into a single framework. In addition to the general framework, we propose a Nesterov-type acceleration scheme in the SKM method called Probably Accelerated Sampling Kaczmarz Motzkin (PASKM). We prove the convergence theorems for both GSKM and PASKM algorithms in the $$L_2$$ norm perspective with respect to the proposed sampling distribution. Furthermore, we prove sub-linear convergence for the Cesaro average of iterates for the proposed GSKM and PASKM algorithms. From the convergence theorem of the GSKM algorithm, we find the convergence results of several well-known algorithms like the Kaczmarz method, Motzkin method and SKM algorithm. We perform thorough numerical experiments using both randomly generated and real-world (classification with support vector machine and Netlib LP) test instances to demonstrate the efficiency of the proposed methods. We compare the proposed algorithms with SKM, Interior Point Method and Active Set Method in terms of computation time and solution quality. In the majority of the problem instances, the proposed generalized and accelerated algorithms significantly outperform the state-of-the-art methods.

Title: <p>Distributed adaptive Newton methods with global superlinear convergence</p> Abstract: This paper considers the distributed optimization problem where each node of a peer-to-peer network minimizes a finite sum of objective functions by communicating with its neighboring nodes. In sharp contrast to the existing literature where the fastest distributed algorithms converge either with a global linear or a local superlinear rate, we propose a distributed adaptive Newton (DAN) algorithm with a global quadratic convergence rate. Our key idea lies in the design of a finite-time set-consensus method with Polyak's adaptive stepsize. Moreover, we introduce a low-rank matrix approximation (LA) technique to compress the innovation of Hessian matrix so that each node only needs to transmit message of dimension O(p) (where p is the dimension of decision vectors) per iteration, which is essentially the same as that of first-order methods. Nevertheless, the resulting DAN-LA converges to an optimal solution with a global superlinear rate. Numerical experiments on logistic regression problems are conducted to validate their advantages over existing methods. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.

Title: Computing the k densest subgraphs of a graph Abstract: •We study a new problem for finding k densest subgraphs in a graph.•We give a PTAS for constant k.•We give an FPT algorithm for parameter k.

Title: Sampling in software engineering research: a critical review and guidelines Abstract: Representative sampling appears rare in empirical software engineering research. Not all studies need representative samples, but a general lack of representative sampling undermines a scientific field. This article therefore reports a critical review of the state of sampling in recent, high-quality software engineering research. The key findings are: (1) random sampling is rare; (2) sophisticated sampling strategies are very rare; (3) sampling, representativeness and randomness often appear misunderstood. These findings suggest that software engineering research has a generalizability crisis. To address these problems, this paper synthesizes existing knowledge of sampling into a succinct primer and proposes extensive guidelines for improving the conduct, presentation and evaluation of sampling in software engineering research. It is further recommended that while researchers should strive for more representative samples, disparaging non-probability sampling is generally capricious and particularly misguided for predominately qualitative research.

Title: A Flexible Outlier Detector Based on a Topology Given by Graph Communities Abstract: Outlier detection is essential for optimal performance of machine learning methods and statistical predictive models. Their detection is especially determinant in small sample size unbalanced problems, since in such settings outliers become highly influential and significantly bias models. This particular experimental settings are usual in medical applications, like diagnosis of rare pathologies, outcome of experimental personalized treatments or pandemic emergencies. In contrast to population-based methods, neighborhood based local approaches compute an outlier score from the neighbors of each sample, are simple flexible methods that have the potential to perform well in small sample size unbalanced problems. A main concern of local approaches is the impact that the computation of each sample neighborhood has on the method performance. Most approaches use a distance in the feature space to define a single neighborhood that requires careful selection of several parameters, like the number of neighbors.

Title: Clustered variants of Hajós' conjecture Abstract: Hajós conjectured that every graph containing no subdivision of the complete graph Ks+1 is properly s-colorable. This conjecture was disproved by Catlin. Indeed, the maximum chromatic number of such graphs is Ω(s2/log⁡s). We prove that O(s) colors are enough for a weakening of this conjecture that only requires every monochromatic component to have bounded size (so-called clustered coloring).

Title: Deep transform and metric learning network: Wedding deep dictionary learning and neural network Abstract: •Reformulate Dictionary Learning (DL) as Transform and Metric learning.•The above reformulation is implemented as a tandem of a linear layer and an RNN.•This is the first work which bridges deep DL and the combination of linear and RNNs.•The proposed method demonstrates efficiency, scalability and discrimination power.•The combinations of CNN architectures achieve better accuracy and stronger robustness.

Title: Majority Logic Decoding for Certain Schubert Codes Using Lines in Schubert Varieties Abstract: In this article, we consider Schubert codes, linear codes associated to Schubert varieties, and discuss minimum weight codewords for dual Schubert codes. The notion of lines in Schubert varieties is looked closely at, and it has been proved that the supports of the minimum weight codewords of the dual Schubert codes lie on lines and any three points on a line in the Schubert variety correspond to ...

Title: The sum of its parts: Analysis of federated byzantine agreement systems Abstract: Federated Byzantine Agreement Systems (FBASs) are a fascinating new paradigm in the context of consensus protocols. Originally proposed for powering the Stellar payment network, FBASs can instantiate Byzantine quorum systems without requiring out-of-band agreement on a common set of validators; every node is free to decide for itself with whom it requires agreement. Sybil-resistant and yet energy-efficient consensus protocols can therefore be built upon FBASs, and the “decentrality” possible with the FBAS paradigm might be sufficient to reduce the use of environmentally unsustainable proof-of-work protocols. In this paper, we first demonstrate how the robustness of individual FBASs can be determined, by precisely determining their safety and liveness buffers and therefore enabling a comparison with threshold-based quorum systems. Using simulations and example node configuration strategies, we then empirically investigate the hypothesis that while FBASs can be bootstrapped in a bottom-up fashion from individual preferences, strategic considerations should additionally be applied by node operators in order to arrive at FBASs that are robust and amenable to monitoring. Finally, we investigate the reported “open-membership” property of FBASs. We observe that an often small group of nodes is exclusively relevant for determining liveness buffers and prove that membership in this top tier is conditional on the approval by current top tier nodes if maintaining safety is a core requirement.

Title: CoLES: Contrastive Learning for Event Sequences with Self-Supervision Abstract: We address the problem of self-supervised learning on discrete event sequences generated by real-world users. Self-supervised learning incorporates complex information from the raw data in low-dimensional fixed-length vector representations that could be easily applied in various downstream machine learning tasks. In this paper, we propose a new method "CoLES", which adapts contrastive learning, previously used for audio and computer vision domains, to the discrete event sequences domain in a self-supervised setting. We deployed CoLES embeddings based on sequences of transactions at the large European financial services company. Usage of CoLES embeddings significantly improves the performance of the pre-existing models on downstream tasks and produces significant financial gains, measured in hundreds of millions of dollars yearly. We also evaluated CoLES on several public event sequences datasets and showed that CoLES representations consistently outperform other methods on different downstream tasks.

Title: Opportunistic Routing for Opto-Acoustic Internet of Underwater Things Abstract: Internet of Underwater Things (IoUT) is a technological revolution that could mark a new era for scientific, industrial, and military underwater applications. To mitigate the hostile underwater channel characteristics, this article considers a multimodal underwater network that hybridizes acoustic and optical wireless communications to achieve an ubiquitous control and high-speed low-latency netwo...

Title: On contact loci of hyperplane arrangements Abstract: We give an explicit expression for the contact loci of hyperplane arrangements and show that their cohomology rings are combinatorial invariants. We also give an expression for the restricted contact loci in terms of Milnor fibers of associated hyperplane arrangements. We prove the degeneracy of a spectral sequence related to the restricted contact loci of a hyperplane arrangement and which conjecturally computes algebraically the Floer cohomology of iterates of the Milnor monodromy. We give formulas for the Betti numbers of contact loci and restricted contact loci in generic cases.

Title: Continuous Influence-Based Community Partition for Social Networks Abstract: Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under Linear Threshold (LT) model in social networks, which is a combinatorial optimization problem that divides the social network to disjoint <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> communities. Our goal is to maximize the sum of influence propagation within each community. As the influence propagation function of community partition problem is supermodular under LT model, we use the method of Lov <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\acute{a}}$</tex-math></inline-formula> sz Extension to relax the target influence function and transfer our goal to maximize the relaxed function over a matroid polytope. Next, we propose a continuous greedy algorithm using the properties of the relaxed function to solve our problem, which needs to be discretized in concrete implementation. Then, random rounding technique is used to convert the fractional solution to the integer solution. We present a theoretical analysis with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1-1/e$</tex-math></inline-formula> approximation ratio for the proposed algorithms. Extensive experiments are conducted to evaluate the performance of the proposed continuous greedy algorithms on real-world online social networks datasets. The results demonstrate that continuous community partition method can improve influence spread and accuracy of the community partition effectively.

Title: Unsupervised Multi-Class Domain Adaptation: Theory, Algorithms, and Practice Abstract: In this paper, we study the formalism of unsupervised multi-class domain adaptation (multi-class UDA), which underlies a few recent algorithms whose learning objectives are only motivated empirically. Multi-Class Scoring Disagreement (MCSD) divergence is presented by aggregating the absolute margin violations in multi-class classification, and this proposed MCSD is able to fully characterize the r...

Title: Local Balance in Graph Decompositions Abstract: In an equireplicate graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various other types of local regularity conditions in graph decompositions. In the basic case where a single graph with colored loops is used as a block, an existence theory for such decompositions follows as a straightforward generalization of previous work on graph decompositions.

Title: Reactive navigation in partially familiar planar environments using semantic perceptual feedback Abstract: This article solves the planar navigation problem by recourse to an online reactive scheme that exploits recent advances in simultaneous localization and mapping (SLAM) and visual object recognition to recast prior geometric knowledge in terms of an offline catalog of familiar objects. The resulting vector field planner guarantees convergence to an arbitrarily specified goal, avoiding collisions along the way with fixed but arbitrarily placed instances from the catalog as well as completely unknown fixed obstacles so long as they are strongly convex and well separated. We illustrate the generic robustness properties of such deterministic reactive planners as well as the relatively modest computational cost of this algorithm by supplementing an extensive numerical study with physical implementation on both a wheeled and legged platform in different settings.

Title: Two-wavelet theory in Weinstein setting Abstract: In this paper, we establish the concept of a two-wavelet in Weinstein setting. Then we introduce and demonstrate the resolution of the identity formula for the continuous Weinstein wavelet transform. In the end, we show few results on Calderon's-type reproducing kernels in the context of the two-wavelet transform in Weinstein setting.

Title: NEW SAV-PRESSURE CORRECTION METHODS FOR THE NAVIER-STOKES EQUATIONS: STABILITY AND ERROR ANALYSIS Abstract: We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require solving a sequence of Poisson type equations at each time step. Furthermore, they are unconditionally energy stable. We also establish rigorous error estimates in the two dimensional case for the velocity and pressure approximation of the first-order scheme without any condition on the time step.

Title: PIANO: A fast parallel iterative algorithm for multinomial and sparse multinomial logistic regression Abstract: •An iterative algorithm named PIANO is proposed to estimate the weights of the Multinomial.•Logistic Regression (MLR) and the Sparse MLR classifiers.•PIANO can parallely update each element of the weight vectors.•Simulation results indicate that PIANO has faster convergence when compared to state-of-the-art algorithms.

Title: Kullback–Leibler Divergence-Based Fuzzy <italic>C</italic>-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frames for Image Segmentation Abstract: In this article, we elaborate on a Kullback–Leibler (KL) divergence-based Fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${C}$ </tex-math></inline-formula> -Means (FCM) algorithm by incorporating a tight wavelet frame transform and morphological reconstruction (MR). To make membership degrees of each image pixel closer to those of its neighbors, a KL divergence term on the partition matrix is introduced as a part of FCM, thus resulting in KL divergence-based FCM. To make the proposed FCM robust, a filtered term is augmented in its objective function, where MR is used for image filtering. Since tight wavelet frames provide redundant representations of images, the proposed FCM is performed in a feature space constructed by tight wavelet frame decomposition. To further improve its segmentation accuracy (SA), a segmented feature set is reconstructed by minimizing the inverse process of its objective function. Each reconstructed feature is reassigned to the closest prototype, thus modifying abnormal features produced in the reconstruction process. Moreover, a segmented image is reconstructed by using tight wavelet frame reconstruction. Finally, supporting experiments coping with synthetic, medical, and real-world images are reported. The experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other peers. In a quantitative fashion, its average SA improvements over its peers are 4.06%, 3.94%, and 4.41%, respectively, when segmenting synthetic, medical, and real-world images. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms.

Title: Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact Abstract: We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk functional over a class of absolutely continuous and signal-adaptive strategies. The stochastic control problem is solved by following a probabilistic and convex analytic approach. We show that the optimal trading strategy is given by a system of four coupled forward backward SDEs, which can be solved explicitly. Our results reveal how the induced transient price distortion provides together with the predictive signal an additional predictor about future price changes. As a consequence, the optimal signal-adaptive trading rate trades off exploiting the predictive signal against incurring the transient displacement of the execution price from its unaffected level. This answers an open question from [C. A. Lehalle and E. Neuman, Finance Stoch., 23 (2019), pp. 275--311] as we show how to derive the unique optimal signal-adaptive liquidation strategy when price impact is not only temporary but also transient.

Title: A characterization of proportionally representative committees Abstract: A well-known axiom for proportional representation is Proportionality for Solid Coalitions (PSC). We characterize committees satisfying PSC as the range of outcomes obtained by the class of Minimal Demand rules, which generalizes an approach pioneered by eminent philosopher Sir Michael Dummett.

Title: Multi-representation knowledge distillation for audio classification Abstract: Audio classification aims to discriminate between different audio signal types, and it has received intensive attention due to its wide applications. In deep learning-based audio classification methods, researchers usually transform the raw signal of audios into different feature representations (such as Short Time Fourier Transform and Mel Frequency Cepstral Coefficients) as the inputs of networks. However, selecting the feature representation requires expert knowledge and extensive experimental verification. Besides, using a single type of feature representation may cause suboptimal results as the information implied in different kinds of feature representations may be complementary. Previous works show that ensembling the networks trained on different representations can greatly boost classification performance. However, making inferences using multiple networks is cumbersome and computation expensive. In this paper, we propose a novel end-to-end collaborative training framework for the audio classification task. The framework takes multiple representations as inputs to train the networks jointly with a knowledge distillation method. Consequently, our framework significantly promotes the performance of networks without increasing the computational overhead in the inference stage. Extensive experimental results demonstrate that the proposed approach improves classification performance and achieves competitive results on both acoustic scene classification tasks and general audio tagging tasks.

Title: Conceptual Game Expansion Abstract: Automated game design is the problem of automatically producing games through computational processes. Traditionally, these methods have relied on the authoring of search spaces by a designer, defining the space of all possible games for the system to the author. In this article, we instead learn representations of existing games from gameplay video and use these to approximate a search space of n...

Title: Appropriate Learning Rates of Adaptive Learning Rate Optimization Algorithms for Training Deep Neural Networks Abstract: This article deals with nonconvex stochastic optimization problems in deep learning. Appropriate learning rates, based on theory, for adaptive-learning-rate optimization algorithms (e.g., Adam and AMSGrad) to approximate the stationary points of such problems are provided. These rates are shown to allow faster convergence than previously reported for these algorithms. Specifically, the algorithms are examined in numerical experiments on text and image classification and are shown in experiments to perform better with constant learning rates than algorithms using diminishing learning rates.

Title: Performance Analysis of Intelligent Reflecting Surface Assisted NOMA Networks Abstract: Intelligent reflecting surface (IRS) is a promising technology to enhance the coverage and performance of wireless networks. We consider the application of IRS to non-orthogonal multiple access (NOMA), where a base station transmits superposed signals to multiple users by the virtue of an IRS. The performance of an IRS-assisted NOMA networks with imperfect successive interference cancellation (ipS...

Title: Suboptimal Control of Unknown Second-Order Nonlinear Systems With Guaranteed Global Convergence Abstract: A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal solution by means of dynamic control gains, based on the estimated main and extended state variables obtained through a high-gain observer. Three numerical examples compare the performance of the proposed control scheme applied to linear and nonlinear systems with that of a fixed-gain conventional ADRC as well as several model-based optimal and suboptimal controllers.

Title: LeafGAN: An Effective Data Augmentation Method for Practical Plant Disease Diagnosis Abstract: Many applications for the automated diagnosis of plant disease have been developed based on the success of deep learning techniques. However, these applications often suffer from overfitting, and the diagnostic performance is drastically decreased when used on test data sets from new environments. In this article, we propose LeafGAN, a novel image-to-image translation system with own attention mec...

Title: A Hybrid Deep Dependency Parsing Approach Enhanced With Rules and Morphology: A Case Study for Turkish Abstract: Fully data-driven, deep learning-based models are usually designed as language-independent and have been shown to be successful for many natural language processing tasks. However, when the studied language is not high-resource and the amount of training data is insufficient, these models can benefit from the integration of natural language grammar-based information. We propose two approaches to dependency parsing especially for languages with restricted amount of training data. Our first approach combines a state-of-the-art deep learning-based parser with a rule-based approach and the second one incorporates morphological information into the parser. In the rule-based approach, the parsing decisions made by the rules are encoded and concatenated with the vector representations of the input words as additional information to the deep network. The morphology-based approach proposes different methods to include the morphological structure of words into the parser network. Experiments are conducted on three different Turkish treebanks and the results suggest that integration of explicit knowledge about the target language to a neural parser through a rule-based parsing system and morphological analysis leads to more accurate annotations and hence, increases the parsing performance in terms of attachment scores. The proposed methods are developed for Turkish, but can be adapted to other languages as well.

Title: Optimal strategies in the fighting fantasy gaming system: Influencing stochastic dynamics by gambling with limited resource Abstract: In many games and other processes, participants can choose to intervene in some way that does not follow the usual progress of the game (for example, cheating at cards, or spying on rivals) which may provide benefits, but also possibly incur substantial costs. Here, repeated interventions may be more likely to incur negative outcomes - for example, as the chance of getting caught increases. How to optimally employ these risky interventions, trading off potential advantages and disadvantages, can then be challenging to identify. Here, we study such a game, taken from the popular 'Fighting Fantasy' gamebook series. This stochastic game involves a series of rounds, each of which may be won or lost. Each round, a unit of limited resource ('Luck') may be spent on a gamble to amplify benefits from a win or to mitigate deficits from a loss. However, the success of this gamble depends on the number of units of remaining resource, and if the gamble is unsuccessful, benefits are reduced and deficits increased. By choosing to expending resource, a player thus has diminishing probability of positive return, as in the cheating and espionage examples above. We characterise the dynamics of this system using stochastic analysis and dynamic programming, solve the Bellman equation for the complete system with diminishing returns, and identify the optimal strategy for any given state during the game. We use classification tools to distil general principles for this and related problems, informing resource allocation problems with diminishing returns in stochastic decision theory. (C) 2022 The Author(s). Published by Elsevier B.V.

Title: Resources for Turkish dependency parsing: introducing the BOUN Treebank and the BoAT annotation tool Abstract: In this paper, we introduce the resources that we developed for Turkish dependency parsing, which include a novel manually annotated treebank (BOUN Treebank), along with the guidelines we adopted, and a new annotation tool (BoAT). The manual annotation process that we employed was shaped and implemented by a team of four linguists and five Natural Language Processing (NLP) specialists. Decisions regarding the annotation of the BOUN Treebank were made in line with the Universal Dependencies (UD) framework as well as our recent efforts for unifying the Turkish UD treebanks through manual re-annotation. To the best of our knowledge, the BOUN Treebank is the largest Turkish UD treebank. It contains a total of 9761 sentences from various topics including biographical texts, national newspapers, instructional texts, popular culture articles, and essays. In addition, we report the parsing results of a state-of-the-art dependency parser obtained over the BOUN Treebank as well as two other treebanks in Turkish. Our results demonstrate that the unification of the Turkish annotation scheme and the introduction of a more comprehensive treebank lead to improved performance with regards to dependency parsing.

Title: Physics constrained learning for data-driven inverse modeling from sparse observations Abstract: •We propose a method for training neural networks in PDE systems.•The training requires sparse observations only.•We develop techniques for both explicit and implicit numerical schemes.•We show the superiority of our method in terms of accuracy and convergence rates.•We compare with methods based on imposing penalty terms in the error functional.

Title: Millimeter Wave Communications With an Intelligent Reflector: Performance Optimization and Distributional Reinforcement Learning Abstract: In this paper, a novel framework is proposed to optimize the downlink multi-user communication of a millimeter wave base station, which is assisted by a reconfigurable intelligent reflector (IR). In particular, a channel estimation approach is developed to measure the channel state information (CSI) in real-time. First, for a perfect CSI scenario, the precoding transmission of the BS and the refle...

Title: A decomposition method by interaction prediction for the optimization of maintenance scheduling Abstract: Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components of the same family: either a set of turbines, a set of transformers or a set of generators. The components share a common stock of spare parts and experience random failures that occur according to known failure distributions. We seek a deterministic preventive maintenance strategy that minimizes an expected cost depending on maintenance and forced outages of the system. The Auxiliary Problem Principle is used to decompose the original large-scale optimization problem into a sequence of independent subproblems of smaller dimension while ensuring their coordination. Each subproblem consists in optimizing the maintenance on a single component. Decomposition-coordination techniques are based on variational techniques but the maintenance optimization problem is a mixed-integer problem. Therefore, we relax the dynamics and the cost functions of the system. The resulting algorithm iteratively solves the subproblems on the relaxed system with a blackbox method and coordinates the components. Relaxation parameters have an important influence on the optimization and must be appropriately chosen. An admissible maintenance strategy is then derived from the resolution of the relaxed problem. We apply the decomposition algorithm on a system with 80 components. It outperforms the reference blackbox method applied directly on the original problem.

Title: RANDOM HORIZON PRINCIPAL-AGENT PROBLEMS Abstract: We consider a general formulation of the random horizon principal-agent problem with a continuous payment and a lump-sum payment at termination. In the European version of the problem, the random horizon is chosen solely by the principal with no other possible action from the agent than exerting effort on the dynamics of the output process. We also consider the American version of the contract, where the agent can also quit by optimally choosing the termination time of the contract. Our main result reduces such nonzero-sum stochastic differential games to appropriate stochastic control problems which may be solved by standard methods of stochastic control theory. This reduction is obtained by following the Sannikov [Rev. Econom. Stud., 75 (2008), pp. 957--984] approach, further developed in [J. Cvitanic'\, D. Possama{\i}\", and N. Touzi, Finance Stoch., 22 (2018), pp. 1--37]. We first introduce an appropriate class of contracts for which the agent's optimal effort is immediately characterized by the standard verification argument in stochastic control theory. We then show that this class of contracts is dense in an appropriate sense, so that the optimization over this restricted family of contracts represents no loss of generality. The result is obtained by using the recent well-posedness result of random horizon second-order backward SDEs in [Y. Lin, Z. Ren, N. Touzi, and J. Yang, Electron. J. Probab., 25 (2020), 99].

Title: Identifying Self-Admitted Technical Debts With Jitterbug: A Two-Step Approach Abstract: Keeping track of and managing Self-Admitted Technical Debts (SATDs) are important to maintaining a healthy software project. This requires much time and effort from human experts to identify the SATDs manually. The current automated solutions do not have satisfactory precision and recall in identifying SATDs to fully automate the process. To solve the above problems, we propose a two-step framework called <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jitterbug</b> for identifying SATDs. <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jitterbug</b> first identifies the “easy to find” SATDs automatically with close to 100 percent precision using a novel pattern recognition technique. Subsequently, machine learning techniques are applied to assist human experts in manually identifying the remaining “hard to find” SATDs with reduced human effort. Our simulation studies on ten software projects show that <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jitterbug</b> can identify SATDs more efficiently (with less human effort) than the prior state-of-the-art methods.

Title: Clique minors in graphs with a forbidden subgraph Abstract: The classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at least r has the clique of order r as a minor. Hadwiger's conjecture is an example of a well-studied class of problems asking how large a clique minor one can guarantee in a graph with certain restrictions. One problem of this type asks what is the largest size of a clique minor in a graph on n vertices of independence number alpha(G) at most r. If true Hadwiger's conjecture would imply the existence of a clique minor of order n/alpha(G). Results of Kuhn and Osthus and Krivelevich and Sudakov imply that if one assumes in addition that G is H-free for some bipartite graph H then one can find a polynomially larger clique minor. This has recently been extended to triangle-free graphs by Dvorak and Yepremyan, answering a question of Norin. We complete the picture and show that the same is true for arbitrary graph H, answering a question of Dvorak and Yepremyan. In particular, we show that any Ks-free graph has a clique minor of order cs(n/alpha(G))1+110(s-2), for some constant cs depending only on s. The exponent in this result is tight up to a constant factor in front of the 1s-2 term.

Title: Stochastic makespan minimization in structured set systems Abstract: We study stochastic combinatorial optimization problems where the objective is to minimize the expected maximum load (a.k.a. the makespan). In this framework, we have a set of n tasks and m resources, where each task j uses some subset of the resources. Tasks have random sizes $$X_j$$ , and our goal is to non-adaptively select t tasks to minimize the expected maximum load over all resources, where the load on any resource i is the total size of all selected tasks that use i. For example, when resources are points and tasks are intervals in a line, we obtain an $$O(\log \log m)$$ -approximation algorithm. Our technique is also applicable to other problems with some geometric structure in the relation between tasks and resources; e.g., packing paths, rectangles, and “fat” objects. Our approach uses a strong LP relaxation using the cumulant generating functions of the random variables. We also show that this LP has an $$\varOmega (\log ^* m)$$ integrality gap, even for the problem of selecting intervals on a line; here $$\log ^* m$$ is the iterated logarithm function.

Title: NEURAL PARAMETRIC FOKKER-PLANCK EQUATION Abstract: In this paper, we develop and analyze numerical methods for high-dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker-Planck equation as a system of ordinary differential equations (ODEs) on finite-dimensional parameter space with the parameters inherited from generative models such as normalizing flows. We call such ODEs neural parametric Fokker-Planck equations. The fact that the Fokker-Planck equation can be viewed as the L2-Wasserstein gradient flow of Kullbackflow of KL divergence on the set of probability densities generated by neural networks. For numerical computation, we design a variational semi-implicit scheme for the time discretization of the proposed ODE. Such an algorithm is sampling-based, which can readily handle the Fokker-Planck equations in higher dimensional spaces. Moreover, we also establish bounds for the asymptotic convergence analysis of the neural parametric Fokker-Planck equation as well as the error analysis for both the continuous and discrete versions. Several numerical examples are provided to illustrate the performance of the proposed algorithms and analysis.

Title: Gini index based initial coin offering mechanism Abstract: As a fundraising method, Initial Coin Offering (ICO) has raised billions of dollars for thousands of startups. Existing ICO mechanisms place more emphasis on the short-term benefits of maximal fundraising while ignoring the problem of unbalanced token allocation, which negatively impacts subsequent fundraising and has bad effects on introducing new investors and resources. We propose a new ICO mechanism which uses the concept of Gini index for the very first time as a mechanism design constraint to control allocation inequality. Our mechanism has an elegant and straightforward structure, which makes it explainable. It allows the agents to modify their bids as a price discovery process, while limiting the bids of whales. Under natural technical assumptions, we show that under our mechanism most agents have simple dominant strategies and the equilibrium revenue approaches the optimal revenue asymptotically in the number of agents. We verify our mechanism using real ICO dataset we collected, and confirm that our mechanism performs well in terms of both allocation fairness and revenue.

Title: NeuralSens: Sensitivity Analysis of Neural Networks Abstract: This article presents the NeuralSens package that can be used to perform sensitivity analysis of neural networks using the partial derivatives method. The main function of the package calculates the partial derivatives of the output with regard to the input variables of a multi-layer perceptron model, which can be used to evaluate variable importance based on sensitivity measures and characterize relationships between input and output variables. Methods to calculate partial derivatives are provided for objects trained using common neural network packages in R, and a ???numeric??? method is provided for objects from packages which are not included. The package also includes functions to plot the information obtained from the sensitivity analysis. The article contains an overview of techniques for obtaining information from neural network models, a theoretical foundation of how partial derivatives are calculated, a description of the package functions, and applied examples to compare NeuralSens functions with analogous functions from other available R packages.

Title: Computation of Dynamic Equilibria in Series-Parallel Networks Abstract: We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a dynamic equilibrium, every infinitesimally small flow particle reaches the sink as early as possible given the pattern of the rest of the flow. Although this model has been examined for many decades, progress has been relatively recent. In particular, the derivatives of dynamic equilibria have been characterized as thin flows with resetting, which allows for more structural results. Our two main results are based on the formulation of thin flows with resetting as a linear complementarity problem and its analysis. We present a constructive proof of existence for dynamic equilibria if the inflow rate is right-monotone. The complexity of computing thin flows with resetting, which occurs as a subproblem in this method, is still open. We settle it for the class of two-terminal, series-parallel networks by giving a recursive algorithm that solves the problem for all flow values simultaneously in polynomial time.

Title: Arnold-Liouville Theorem for Integrable PDEs: A Case Study of the Focusing NLS Equation. Abstract: We prove an infinite dimensional version of the Arnold-Liouville theorem for integrable non-linear PDEs: In a case study we consider the {\em focusing} NLS equation with periodic boundary conditions.

Title: The stabilizing index and cyclic index of the coalescence and Cartesian product of uniform hypergraphs Abstract: Let G be connected uniform hypergraph and let A(G) be the adjacency tensor of G. The stabilizing index of G is exactly the number of eigenvectors of A(G) associated with the spectral radius, and the cyclic index of G is exactly the number of eigenvalues of A(G) with modulus equal to the spectral radius. Let G1⊙G2 and G1□G2 be the coalescence and Cartesian product of connected m-uniform hypergraphs G1 and G2 respectively. In this paper, we give explicit formulas for the stabilizing indices and cyclic indices of G1⊙G2 and G1□G2 in terms of those of G1 and G2 or the invariant divisors of their incidence matrices over Zm, respectively.

Title: Clustered 3-colouring graphs of bounded degree. Abstract: A (not necessarily proper) vertex colouring of a graph has "clustering" $c$ if every monochromatic component has at most $c$ vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$. The previous best bound was $O(\Delta^{37})$. This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$. The best previous bound for this result was exponential in $\Delta$.

Title: Knowledge cores in large formal contexts Abstract: Knowledge computation tasks, such as computing a base of valid implications, are often infeasible for large data sets. This is in particular true when deriving canonical bases in formal concept analysis (FCA). Therefore, it is necessary to find techniques that on the one hand reduce the data set size, but on the other hand preserve enough structure to extract useful knowledge. Many successful methods are based on random processes to reduce the size of the investigated data set. This, however, makes them hardly interpretable with respect to the discovered knowledge. Other approaches restrict themselves to highly supported subsets and omit rare and (maybe) interesting patterns. An essentially different approach is used in network science, called k-cores. These cores are able to reflect rare patterns, as long as they are well connected within the data set. In this work, we study k-cores in the realm of FCA by exploiting the natural correspondence of bi-partite graphs and formal contexts. This structurally motivated approach leads to a comprehensible extraction of knowledge cores from large formal contexts.

Title: A Deep Unsupervised Feature Learning Spiking Neural Network With Binarized Classification Layers for the EMNIST Classification Abstract: End user AI is trained on large server farms with data collected from the users. With ever increasing demand for IoT devices, there is a need for deep learning approaches that can be implemented at the Edge in an energy efficient manner. In this work we approach this using spiking neural networks. The unsupervised learning technique of spike timing dependent plasticity (STDP) and binary activation...

Title: Supervised Dimensionality Reduction and Visualization using Centroid-Encoder Abstract: We propose a new tool for visualizing complex, and potentially large and high-dimensional, data sets called Centroid-Enco der (CE). The architecture of the Centroid-Enco der is similar to the autoencoder neural network but it has a modified target, i.e., the class centroid in the ambient space. As such, CE incorporates label information and performs a supervised data visualization. The training of CE is done in the usual way with a training set whose parameters are tuned using a validation set. The evaluation of the resulting CE visualization is performed on a sequestered test set where the generalization of the model is assessed both visually and quantitatively. We present a detailed comparative analysis of the method using a wide variety of data sets and techniques, both supervised and Isomap, Parametric Embedding, supervised Neighbor Retrieval Visualizer, and Multiple Relational Embedding. An analysis of variance using PCA demonstrates that a non-linear preprocessing by the CE transformation of the data captures more variance than PCA by dimension.

Title: Impact of Information Placement and User Representations in VR on Performance and Embodiment Abstract: Human sensory processing is sensitive to the proximity of stimuli to the body. It is therefore plausible that these perceptual mechanisms also modulate the detectability of content in VR, depending on its location. We evaluate this in a user study and further explore the impact of the user's representation during interaction. We also analyze how embodiment and motor performance are influenced by these factors. In a dual-task paradigm, participants executed a motor task, either through virtual hands, virtual controllers, or a keyboard. Simultaneously, they detected visual stimuli appearing in different locations. We found that, while actively performing a motor task in the virtual environment, performance in detecting additional visual stimuli is higher when presented near the user's body. This effect is independent of how the user is represented and only occurs when the user is also engaged in a secondary task. We further found improved motor performance and increased embodiment when interacting through virtual tools and hands in VR, compared to interacting with a keyboard. This article contributes to better understanding the detectability of visual content in VR, depending on its location in the virtual environment, as well as the impact of different user representations on information processing, embodiment, and motor performance.

Title: Canonical trees of tree-decompositions Abstract: We prove that every graph has a canonical tree of tree-decompositions that distinguishes all principal tangles (these include the ends and various kinds of large finite dense structures) efficiently.

Title: Discrete adjoint implicit Peer methods in optimal control Abstract: It is well known that in the first-discretize-then-optimize approach in the control of ordinary differential equations the discrete adjoint method may converge under additional order conditions only. For Peer two-step methods we derive such adjoint order conditions and pay special attention to different formulations and boundary steps. For s-stage methods, we prove convergence of order s for the state variables if the adjoint method satisfies the conditions for order s−1, at least. We remove some bottlenecks at the boundaries encountered in an earlier paper of Schröder et al. (2014) and discuss the construction of 3-stage methods for the order pair (3,2) in detail. The impact of nodes having equal differences is highlighted. It turns out that the most attractive methods are related to backward differentiation formulas. Three 3-stage methods are constructed, which show the expected orders in numerical tests.

Title: Solving non-monotone equilibrium problems via a DIRECT-type approach Abstract: A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the DIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.