cssi/SciSciGPT-SciSciNet huggingface dataset:
DeepTriage: Exploring the Effectiveness of Deep Learning for Bug Triaging

For a given software bug report, identifying an appropriate developer who could potentially fix the bug is the primary task of bug triaging. Automatic bug triaging is formulated as a classification problem, which takes the bug title and description as the input, and maps it to one of the available developers. A major challenge in doing this is that the bug description usually contains a combination of unstructured text, code snippets, and stack traces making the input data highly noisy. The existing bag-of-words (BOW) models do not consider the semantic information in the unstructured text.In this research, we propose a novel bug report representation using a deep bidirectional recurrent neural network with attention (DBRNN-A) that learns the syntactic and semantic features from long word sequences in an unsupervised manner. Using attention enables the model to remember and attend to important parts of text in a bug report. For training the model, we use unfixed bug reports (which constitute about 70% of bugs in a typical open source bug tracking system) which were ignored in previous studies.Another major contribution of this work is the release of a public benchmark dataset of bug reports from three open source bug tracking systems: Google Chromium, Mozilla Core, and Mozilla Firefox. The dataset consists of 383,104 bug reports from Google Chromium, 314,388 bug reports from Mozilla Core, and 162,307 bug reports from Mozilla Firefox. When compared to other systems, we observe that DBRNN-A provides a higher rank-10 average accuracy.
Nonparametric Stochastic Contextual Bandits

We analyze the $K$-armed bandit problem where the reward for each arm is a noisy realization based on an observed context under mild nonparametric assumptions. We attain tight results for top-arm identification and a sublinear regret of $\widetilde{O}\Big(T^{\frac{1+D}{2+D}}\Big)$, where $D$ is the context dimension, for a modified UCB algorithm that is simple to implement ($k$NN-UCB). We then give global intrinsic dimension dependent and ambient dimension independent regret bounds. We also discuss recovering topological structures within the context space based on expected bandit performance and provide an extension to infinite-armed contextual bandits. Finally, we experimentally show the improvement of our algorithm over existing multi-armed bandit approaches for both simulated tasks and MNIST image classification.
Initial-to-Interface Maps for the Heat Equation on Composite Domains

A map from the initial conditions to the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with n interfaces. The existence of this map allows changing the problem at hand from an interface problem to a boundary value problem which allows for an alternative to the approach of finding a closed-form solution to the interface problem.
Universally near-optimal online power control for energy harvesting nodes

We consider online power control for an energy harvesting system with random i.i.d. energy arrivals and a finite size battery. We propose a simple online power control policy for this channel that requires minimal information regarding the distribution of the energy arrivals and prove that it is universally near-optimal for all parameter values. In particular, the policy depends on the distribution of the energy arrival process only through its mean and achieves the optimal long-term average throughput of the channel within a constant gap. Existing heuristics for online power control fail to achieve such universal performance. This result also allows us to obtain a simple constant-gap approximation for the long-term average throughput of the system, which sheds some light on the qualitative behavior of the throughput, namely how it depends on the distribution of the energy arrivals and the size of the battery.
Learning to Prune Filters in Convolutional Neural Networks

Many state-of-the-art computer vision algorithms use large scale convolutional neural networks (CNNs) as basic building blocks. These CNNs are known for their huge number of parameters, high redundancy in weights, and tremendous computing resource consumptions. This paper presents a learning algorithm to simplify and speed up these CNNs. Specifically, we introduce a “try-and-learn” algorithm to train pruning agents that remove unnecessary CNN filters in a data-driven way. With the help of a novel reward function, our agents removes a significant number of filters in CNNs while maintaining performance at a desired level. Moreover, this method provides an easy control of the tradeoff between network performance and its scale. Performance of our algorithm is validated with comprehensive pruning experiments on several popular CNNs for visual recognition and semantic segmentation tasks.
The NLS approximation for two dimensional deep gravity waves

This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet data, and to show that this is well approximated by the cubic nonlinear Schrodinger equation (NLS) on the natural cubic time scale.
A supercharacter approach to Heilbronn sums

Abstract Various algebraic properties of Heilbronn's exponential sum can be deduced through the use of supercharacter theory, a novel extension of classical character theory due to Diaconis–Isaacs and Andre. This perspective yields a variety of formulas and provides a method for computing the number of solutions to Fermat-type congruences.
Exponents of operator self-similar random fields ☆

Abstract If X ( c E t ) and c H X ( t ) have the same finite-dimensional distributions for some pair of linear operators E and H, we say that the random vector field X ( t ) is operator self-similar. The exponents E and H are not unique in general, due to symmetry. This paper characterizes the possible set of range exponents H for a given domain exponent, and conversely, the set of domain exponents E for a given range exponent.
End-to-End Reinforcement Learning for Automatic Taxonomy Induction

We present a novel end-to-end reinforcement learning approach to automatic taxonomy induction from a set of terms. While prior methods treat the problem as a two-phase task (i.e.,, detecting hypernymy pairs followed by organizing these pairs into a tree-structured hierarchy), we argue that such two-phase methods may suffer from error propagation, and cannot effectively optimize metrics that capture the holistic structure of a taxonomy. In our approach, the representations of term pairs are learned using multiple sources of information and used to determine which term to select and where to place it on the taxonomy via a policy network. All components are trained in an end-to-end manner with cumulative rewards, measured by a holistic tree metric over the training taxonomies. Experiments on two public datasets of different domains show that our approach outperforms prior state-of-the-art taxonomy induction methods up to 19.6% on ancestor F1.
Equiangular Tight Frames From Hyperovals

An equiangular tight frame (ETF) is a set of equal norm vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications, such as waveform design, quantum information theory, compressed sensing, and algebraic coding theory. ETFs seem to be rare, and only a few methods of constructing them are known. In this paper, we present a new infinite family of complex ETFs that arises from hyperovals in finite projective planes. In particular, we give the first ever construction of a complex ETF of 76 vectors in a space of dimension 19. Recently, a computer-assisted approach was used to show that real ETFs of this size do not exist, resolving a longstanding open problem in this field. Our construction is a modification of a previously known technique for constructing ETFs from balanced incomplete block designs.
Formalizing atom-typing and the dissemination of force fields with foyer

Abstract A key component to enhancing reproducibility in the molecular simulation community is reducing ambiguity in the parameterization of molecular models used to perform a study. Ambiguity in molecular models often stems from inadequate usage documentation of molecular force fields and the fact that force fields are not typically disseminated in a format that is directly usable by software. Specifically, the lack of a generally applicable scheme for the annotation of the rules of a particular force field and a general purpose tool for performing automated parameterization (i.e., atom-typing) based on these rules, may lead to errors in model parameterization that are not easily identified. Here, we present Foyer , an open-source Python tool that enables users to define and apply force field atom-typing rules in a format that is both human- and machine-readable and provides a framework for force field dissemination, thus eliminating ambiguity in atom-typing and improving reproducibility. Foyer defines force fields in an XML format, where SMARTS strings are used to define the chemical context of a particular atom type and “overrides” are used to set rule precedence, rather than a rigid hierarchical scheme. Herein we describe the underlying methodology and force field annotation scheme of the Foyer software, demonstrate its application in several use-cases, and discuss specific aspects of the Foyer approach that are designed to improve reproducibility.
Independent component models for replicated point processes

Abstract We propose a semiparametric independent-component model for the intensity functions of replicated point processes. We show that the maximum likelihood estimators of the model parameters are consistent and asymptotically normal when the number of replications goes to infinity. The finite-sample behavior of the estimators is studied by simulation. As an example of application, we analyze the temporal variation in the spatial distribution of street robberies in Chicago.
Generalized Coordinated Transaction Scheduling: A Market Approach to Seamless Interfaces

A generalization of the coordinated transaction scheduling (CTS)—the state-of-the-art interchange scheduling—is proposed. Referred to as generalized coordinated transaction scheduling (GCTS), the proposed approach addresses major seams issues of CTS: the ad hoc use of proxy buses, the presence of loop flow as a result of proxy bus approximation, and difficulties in dealing with multiple interfaces. By allowing market participants to submit bids across market boundaries, GCTS also generalizes the joint economic dispatch that achieves seamless interchange without market participants. It is shown that GCTS asymptotically achieves seamless interface under certain conditions. GCTS is also shown to be revenue adequate in that each regional market has a nonnegative net revenue that is equal to its congestion rent. Numerical examples are presented to illustrate the quantitative improvement of the proposed approach.
Global stabilization of triangulated formations

Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a tar...
Planning random path distributions for ambush games in unstructured environments

Operating vehicles in adversarial environments require non-conventional planning techniques. A two-player, zero-sum non-cooperative game is introduced, and solved via a linear program. An extension is proposed to construct networks displaying good representations of the environment characteristics, while offering acceptable results for the technique used. Sensitivity of the solution to the LP solver algorithm is identified. The planner's performances are finally assessed by comparison with those of conventional planners. Results are used to formulate secondary objectives to the problem.
Formal Calculus and Umbral Calculus

We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a certain crucial "associativity" property of an important class of vertex operator algebras. Very similar (somewhat forgotten) proofs had appeared by the 19-th century, of course without any motivation related to vertex operator algebras. Using this formula, we derive certain results, including especially the calculation of certain adjoint operators, of the classical umbral calculus. This is, roughly speaking, a reversal of the logical development of some standard treatments, which have obtained formulas for the higher derivatives of a composite function, most notably Faa di Bruno's formula, as a consequence of umbral calculus. We also show a connection between the Virasoro algebra and the classical umbral shifts. This leads naturally to a more general class of operators, which we introduce, and which include the classical umbral shifts as a special case. We prove a few basic facts about these operators.
Super-flaring Active Region 12673 Has One of the Fastest Magnetic Flux Emergence Ever Observed

The flux emergence rate of AR 12673 is greater than any values reported in the literature of which we are aware.
Determinants of Seidel matrices and a conjecture of Ghorbani

Abstract Let G n be a simple graph on V n = { v 1 , … , v n } . The Seidel matrix S ( G n ) of G n is the n × n matrix whose ( i j ) 'th entry, for i ≠ j is −1 if v i ∼ v j and 1 otherwise, and whose diagonal entries are 0. We show that the proportion of simple graphs G n such that | det ⁡ ( S ( G n ) ) | ≥ n − 1 tends to one as n tends to infinity.
A REMARK ON THE ARCSINE DISTRIBUTION AND THE HILBERT TRANSFORM.

It is known that if $$(p_n)_{n \in \mathbb {N}}$$ is a sequence of orthogonal polynomials in $$L^2([-1,1], w(x)dx)$$ , then the roots are distributed according to an arcsine distribution $$\pi ^{-1} (1-x^2)^{-1}dx$$ for a wide variety of weights w(x). We connect this to a result of the Hilbert transform due to Tricomi: if $$f(x)(1-x^2)^{1/4} \in L^2(-1,1)$$ and its Hilbert transform Hf vanishes on $$(-1,1)$$ , then the function f is a multiple of the arcsine distribution $$\begin{aligned} f(x) = \frac{c}{\sqrt{1-x^2}}\chi _{(-1,1)} \qquad \text{ where }~c~\in \mathbb {R}. \end{aligned}$$ We also prove a localized Parseval-type identity that seems to be new: if $$f(x)(1-x^2)^{1/4} \in L^2(-1,1)$$ and $$f(x) \sqrt{1-x^2}$$ has mean value 0 on $$(-1,1)$$ , then $$\begin{aligned} \int _{-1}^{1}{ (Hf)(x)^2 \sqrt{1-x^2} dx} = \int _{-1}^{1}{ f(x)^2 \sqrt{1-x^2} dx}. \end{aligned}$$
Optimal succinct rank data structure via approximate nonnegative tensor decomposition

Given an n-bit array A, the succinct rank data structure problem asks to construct a data structure using space n+r bits for r≪ n, supporting rank queries of form rank(u)=∑i=0u−1A[i]. In this paper, we design a new succinct rank data structure with r=n/(logn)Ω(t)+n1−c and query time O(t) for some constant c>0, improving the previous best-known by Pǎtrascu, which has r=n/(logn/t)Ω(t)+O(n3/4) bits of redundancy. For r>n1−c, our space-time tradeoff matches the cell-probe lower bound by Pǎtrascu and Viola, which asserts that r must be at least n/(logn)O(t). Moreover, one can avoid an n1−c-bit lookup table when the data structure is implemented in the cell-probe model, achieving r=⌈ n/(logn)Ω(t)⌉. It matches the lower bound for the full range of parameters. En route to our new data structure design, we establish an interesting connection between succinct data structures and approximate nonnegative tensor decomposition. Our connection shows that for specific problems, to construct a space-efficient data structure, it suffices to approximate a particular tensor by a sum of (few) nonnegative rank-1 tensors. For the rank problem, we explicitly construct such an approximation, which yields an explicit construction of the data structure.
Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimization

We develop a family of accelerated stochastic algorithms that optimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression, across a wide range of problem settings. To achieve this, we establish a framework, based on the classical proximal point algorithm, useful for accelerating recent fast stochastic algorithms in a black-box fashion. Empirically, we demonstrate that the resulting algorithms exhibit notions of stability that are advantageous in practice. Both in theory and in practice, the provided algorithms reap the computational benefits of adding a large strongly convex regularization term, without incurring a corresponding bias to the original ERM problem.
Improving Classification Accuracy of Feedforward Neural Networks for Spiking Neuromorphic Chips

Deep Neural Networks (DNN) achieve human level performance in many image analytics tasks but DNNs are mostly deployed to GPU platforms that consume a considerable amount of power. New hardware platforms using lower precision arithmetic achieve drastic reductions in power consumption. More recently, brain-inspired spiking neuromorphic chips have achieved even lower power consumption, on the order of milliwatts, while still offering real-time processing. However, for deploying DNNs to energy efficient neuromorphic chips the incompatibility between continuous neurons and synaptic weights of traditional DNNs, discrete spiking neurons and synapses of neuromorphic chips need to be overcome. Previous work has achieved this by training a network to learn continuous probabilities, before it is deployed to a neuromorphic architecture, such as IBM TrueNorth Neurosynaptic System, by random sampling these probabilities. The main contribution of this paper is a new learning algorithm that learns a TrueNorth configuration ready for deployment. We achieve this by training directly a binary hardware crossbar that accommodates the TrueNorth axon configuration constrains and we propose a different neuron model. Results of our approach trained on electroencephalogram (EEG) data show a significant improvement with previous work (76% vs 86% accuracy) while maintaining state of the art performance on the MNIST handwritten data set.
Abnormality Detection in Correlated Gaussian Molecular Nano-Networks: Design and Analysis

A nano-abnormality detection scheme (NADS) in molecular nano-networks is studied. This is motivated by the fact that early detection of diseases such as cancer plays a crucial role in their successful treatment. The proposed NADS is in fact a two-tier network of sensor nano-machines (SNMs) in the first tier and a data-gathering node (DGN) at the sink. The SNMs detect the presence of competitor cells (abnormality) by variations in input and/or parameters of a nano-communications channel. The noise of SNMs as their nature suggest is considered correlated in time and space and herein assumed additive Gaussian. In the second step, the SNMs transmit micro-scale messages over a noisy micro-communications channel (MCC) to the DGN, where a decision is made upon fusing the received signals. We find an optimum design of detectors for each of the NADS tiers based on the end-to-end NADS performance. The detection performance of each SNM is analyzed by setting up a generalized likelihood ratio test. Next, taking into account the effect of the MCC, the overall performance of the NADS is analyzed in terms of probabilities of misdetection and false alarm. In addition, computationally efficient expressions to quantify the NADS performance are derived by providing, respectively, an approximation and an upper bound for the probabilities of misdetection and false alarm. This in turn enables formulating a design problem, where the optimized concentration of SNMs in a sample is obtained for a high probability of detection and a limited probability of false alarm. The results indicate that otherwise ignoring the spatial and temporal correlation of SNM noise in the analysis, leads to an NADS that noticeably underperforms in operations.The results indicate how effective fusion of the noisy observations collected from a number of SNMs with limited capabilities could provide an acceptable detection performance.
Bounds on the length of a game of Cops and Robbers

Abstract In the game of Cops and Robbers, a team of cops attempts to capture a robber on a graph G . All players occupy vertices of G . The game operates in rounds; in each round the cops move to neighboring vertices, after which the robber does the same. The minimum number of cops needed to guarantee capture of a robber on G is the cop number of G , denoted c ( G ) , and the minimum number of rounds needed for them to do so is the capture time. It has long been known that the capture time of an n -vertex graph with cop number k is O ( n k + 1 ) . More recently, Bonato et al. (2009) and Gavenciak (2010) showed that for k = 1 , this upper bound is not asymptotically tight: for graphs with cop number 1, the cop can always win within n − 4 rounds. In this paper, we show that the upper bound is tight when k ≥ 2 : for fixed k ≥ 2 , we construct arbitrarily large graphs G having capture time at least V ( G ) 40 k 4 k + 1 . In the process of proving our main result, we establish results that may be of independent interest. In particular, we show that the problem of deciding whether k cops can capture a robber on a directed graph is polynomial-time equivalent to deciding whether k cops can capture a robber on an undirected graph. As a corollary of this fact, we obtain a relatively short proof of a major conjecture of Goldstein and Reingold (1995), which was recently proved through other means (Kinnersley, 2015). We also show that n -vertex strongly-connected directed graphs with cop number 1 can have capture time Ω ( n 2 ) , thereby showing that the result of Bonato et al. (2009) does not extend to the directed setting.
A Computational Framework for Multivariate Convex Regression and Its Variants

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with O(n2) linear constraints (n being t...
Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS

In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and their time derivatives by polynomials and express stability as optimization over polynomials. We use Sum-of-Squares and Positivstellensatz results to numerically search for a solution to the optimization over polynomials. We also show that our algorithm can be used to estimate the rate of decay of the solution to PDE in the L2 norm. Finally, we validate the technique by applying our conditions to the 2D biological KISS PDE model of population growth and an additional example.
Reflexivity and rigidity for complexes, II: Schemes

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing com- plexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with respect to semidualizing complexes, in particular, rela- tive dualizing complexes for Gorenstein-perfect maps. Our results include the- orems of Yekutieli and Zhang concerning rigid dualizing complexes on schemes. This work is a continuation of part I, which dealt with commutative rings.
On the $\Sigma$-Invariants of Generalized Thompson Groups and Houghton Groups

We compute the higher $\Sigma$-invariants $\Sigma^m(F_{n,\infty})$ of the generalized Thompson groups $F_{n,\infty}$, for all $m,n\ge 2$. This extends the $n=2$ case done by Bieri, Geoghegan and Kochloukova, and the $m=2$ case done by Kochloukova. Our approach differs from those used in the $n=2$ and $m=2$ cases; we look at the action of $F_{n,\infty}$ on a $\textrm{CAT}(0)$ cube complex, and use Morse theory to compute all the $\Sigma^m(F_{n,\infty})$. We also obtain lower bounds on $\Sigma^m(H_n)$, for the Houghton groups $H_n$, again using actions on $\textrm{CAT}(0)$ cube complexes, and discuss evidence that these bounds are sharp.
Nonparametric Bayesian Modeling for Automated Database Schema Matching

The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametricBayesian models.
On a problem of S.L. Sobolev

Abstract In his famous works of 1930 [1,2] Sergey L. Sobolev has proposed a construction of the solution of the Cauchy problem for the hyperbolic equation of the second order with variable coefficients in Rs. Although Sobolev did not construct the fundamental solution, his construction was modified later by Romanov (2002) and Smirnov (1964) to obtain the fundamental solution. However, these works impose a restrictive assumption of the regularity of geodesic lines in a large domain. In addition, it is unclear how to realize those methods numerically. In this paper a simple construction of a function, which is associated in a clear way with the fundamental solution of the acoustic equation with the variable speed in 3-d, is proposed. Conditions on geodesic lines are not imposed. An important feature of this construction is that it lends itself to effective computations.
Average Error Probability Analysis in mmWave Cellular Networks

In this paper, a mathematical framework for the analysis of average symbol error probability (ASEP) in millimeter wave (mmWave) cellular networks with Poisson Point Process (PPP) distributed base stations (BSs) is developed using tools from stochastic geometry. The distinguishing features of mmWave communications such as directional beamforming and having different path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links are incorporated in the average error probability analysis. First, average pairwise error probability (APEP) expression is obtained by averaging pairwise error probability (PEP) over fading and random shortest distance from mobile user (MU) to its serving BS. Subsequently, average symbol error probability is approximated from APEP using the nearest neighbor (NN) approximation. ASEP is analyzed for different antenna gains and base station densities. Finally, the effect of beamforming alignment errors on ASEP is investigated to get insight on more realistic cases.
Fast Escape in Incompressible Vector Fields

Swimmers caught in a rip current flowing away from the shore are advised to swim orthogonally to the current to escape it. We describe a mathematical principle in a similar spirit. More precisely, we consider flows $$\gamma $$ in the plane induced by incompressible vector fields $$\mathbf v :{\mathbb {R}}^2 \rightarrow {\mathbb {R}}^2$$ satisfying $$ c_1< \Vert v\Vert < c_2.$$ The length $$\ell $$ a flow curve $$\dot{\gamma }(t) = \mathbf v (\gamma (t))$$ until $$\gamma $$ leaves a disk of radius 1 centered at the initial position can be as long as $$\ell \sim c_2/c_1$$ . The same is true for the orthogonal flow $$\mathbf v ^{\perp } = (-\mathbf v _2, \mathbf v _1)$$ . We show that a combination does strictly better: there always exists a curve flowing first along $$\mathbf v ^{\perp }$$ and then along $$\mathbf v $$ which escapes the unit disk before reaching the length $$ \sqrt{4\pi c_2 / c_1}$$ . Moreover, if the escape length of $$\mathbf v $$ is uniformly $$\sim c_2/c_1$$ , then the escape length of $$\mathbf v ^{\perp }$$ is uniformly $$\sim 1$$ (allowing for a fast escape from the current). We also prove an elementary quantitative Poincare–Bendixson theorem that seems to be new.
Fast trajectory simplification algorithm for natural user interfaces in Robot programming by demonstration

Trajectory simplification is a problem encountered in areas like Robot programming by demonstration, CAD/CAM, computer vision, and in GPS-based applications like traffic analysis. This problem entails reduction of the points in a given trajectory while keeping the relevant points which preserve important information. The benefits include storage reduction, computational expense, while making data more manageable.
On Rademacher sums, the largest Mathieu group and the holographic modularity of moonshine

Recently a conjecture has been proposed which attaches (mock) modular forms to the largest Mathieu group. This may be compared to monstrous moonshine, in which modular functions are attached to elements of the Monster group. One of the most remarkable aspects of monstrous moonshine is the following genus zero property: the modular functions turn out to be the generators for the function fields of their invariance groups. In particular, these invariance groups define genus zero quotients of the upper half plane. It is therefore natural to ask if there is an analogue of this property in the Mathieu case, and at first glance the answer appears to be negative since not all the discrete groups arising there have genus zero. On the other hand, in this article we prove that each (mock) modular form appearing in the Mathieu correspondence coincides with the Rademacher sum constructed from its polar part. This property, inspired by the AdS/CFT correspondence in physics, was shown previously to be equivalent to the genus zero property of monstrous moonshine. Hence we conclude that this “Rademacher summability” property serves as the natural analogue of the genus zero property in the Mathieu case. Our result constitutes further evidence that the Rademacher method provides a powerful framework for understanding the modularity of moonshine, and leads to interesting physical questions regarding the gravitational duals of the relevant conformal field theories.
Equating the achievable exponent region to the achievable entropy region by partitioning the source

In this paper we investigate the image size characterization problem. We show that any arbitrary source set may be decomposed into sets whose image size characterization is the same as its entropy characterization. We also show that the number of these sets required is small enough that one may consider that from a coding perspective the achievable entropy region and achievable exponent region are equal. This has an impact on many source networks and network problems whose solution heretofore could not have the image size characterization applied to them.
Decoupled Potential Integral Equations for Electromagnetic Scattering From Dielectric Objects

Recent work on developing novel integral equation formulations has involved using potentials as opposed to fields as unknown variables. This is a consequence of additional flexibility offered by potentials that enable development of well-conditioned systems. Until recently, most of the work in this area focused on formulations for analysis of scattering perfectly conducting objects. In this paper, we present well-conditioned decoupled potential integral equations (DPIEs) formulated for electromagnetic scattering from homogeneous dielectric objects. The formulation is based on decoupled boundary conditions derived for scalar and vector potentials. The resulting DPIE is a second kind integral equation, and does not suffer from either low frequency or dense mesh breakdown. Analytical properties of the DPIE are studied for spherical systems, and results provided demonstrate well-conditioned nature (and bounded spectrum) of the resulting linear system.
Generating mapping class groups with elements of fixed finite order

Abstract We show that for k ≥ 6 and g sufficiently large, the mapping class group of a surface of genus g can be generated by three elements of order k. We also show that this can be done with four elements of order 5 when g is at least 8.
Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem

Abstract We prove the existence of chaotic motions in an equilateral planar circular restricted four body problem (CRFBP), establishing that the system is not integrable. The proof works by verifying the hypotheses of a topological forcing theorem for Hamiltonian vector fields on R 4 which hypothesizes the existence of a transverse homoclinic orbit in the energy manifold of a saddle focus equilibrium. We develop mathematically rigorous computer assisted arguments for verifying these hypotheses, and provide an implementation for CRFBP. Due to the Hamiltonian structure, this also establishes the existence of a “blue sky catastrophe”, and hence an analytic family of periodic orbits of arbitrarily long period at nearby energy levels. Our method works far from any perturbative regime and requires no mass symmetry. Additionally, the method is constructive and yields additional byproducts such as the locations of transverse connecting orbits, quantitative information about the invariant manifolds, and bounds on transport times.
Resilient Active Target Tracking With Multiple Robots

The problem of target tracking with multiple robots consists of actively planning the motion of the robots to track the targets. A major challenge for practical deployments is to make the robots resilient to failures. In particular, robots may be attacked in adversarial scenarios, or their sensors may fail or get occluded. In this letter, we introduce planning algorithms for multi-target tracking that are resilient to such failures. In general, resilient target tracking is computationally hard. Contrary to the case where there are no failures, no scalable approximation algorithms are known for resilient target tracking when the targets are indistinguishable, or unknown in number, or with unknown motion model. In this letter, we provide the first such algorithm, which also has the following properties: First, it achieves maximal resiliency, since the algorithm is valid for any number of failures. Second, it is scalable, as our algorithm terminates with the same running time as state-of-the-art algorithms for (non-resilient) target tracking. Third, it provides provable approximation bounds on the tracking performance, since our algorithm guarantees a solution that is guaranteed to be close to the optimal. We quantify our algorithm's approximation performance using a novel notion of curvature for monotone set functions subject to matroid constraints. Finally, we demonstrate the efficacy of our algorithm through MATLAB and Gazebo simulations and a sensitivity analysis; we focus on scenarios that involve a known number of distinguishable targets.
Sharp Inequalities for $f$ -Divergences

f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics, and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance, and so on. In this paper, we study the problem of maximizing or minimizing an f-divergence between two probability measures subject to a finite number of constraints on other f-divergences. We show that these infinite-dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable. Our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between f-divergences. We demonstrate that many of the existing results on inequalities between f-divergences can be obtained as special cases of our results. We also improve on some existing non-sharp inequalities.
Dynamic network surgery for efficient DNNs

Deep learning has become a ubiquitous technology to improve machine intelligence. However, most of the existing deep models are structurally very complex, making them difficult to be deployed on the mobile platforms with limited computational power. In this paper, we propose a novel network compression method called dynamic network surgery, which can remarkably reduce the network complexity by making on-the-fly connection pruning. Unlike the previous methods which accomplish this task in a greedy way, we properly incorporate connection splicing into the whole process to avoid incorrect pruning and make it as a continual network maintenance. The effectiveness of our method is proved with experiments. Without any accuracy loss, our method can efficiently compress the number of parameters in LeNet-5 and AlexNet by a factor of 108x and 17.7x respectively, proving that it outperforms the recent pruning method by considerable margins. Code and some models are available at https://github.com/yiwenguo/Dynamic-Network-Surgery.
Whittaker Modules for the Insertion-Elimination Lie Algebra

This paper addresses the representation theory of the insertion-elimination Lie algebra, a Lie algebra that can be naturally realized in terms of tree-inserting and tree-eliminating operations on rooted trees. The insertion-elimination algebra admits a triangular decomposition in the sense of Moody and Pianzola, and thus it is natural to define Whittaker modules corresponding to a given algebra homomorphism. Among other results, we show that the standard Whittaker modules are simple under certain constraints on the corresponding algebra homomorphism.
Noetherian Hopf algebra domains of Gelfand–Kirillov dimension two☆

Abstract We classify all noetherian Hopf algebras H over an algebraically closed field k of characteristic zero which are integral domains of Gelfand–Kirillov dimension two and satisfy the condition Ext H 1 ( k , k ) ≠ 0 . The latter condition is conjecturally redundant, as no examples are known (among noetherian Hopf algebra domains of GK-dimension two) where it fails.
Variations on a Generating-Function Theme: Enumerating Compositions with Parts Avoiding an Arithmetic Sequence

A composition of a positive integer n is a k-tuple (λ1, λ2, …, λk) ∈ ℤk>0 such that n = λ1 + λ2 + … + λk. Our goal is to enumerate those compositions whose parts λ1, λ2, …, λk avoid a fixed arithme...
A brief survey on lattice zonotopes

Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections to combinatorics, both in the sense of enumeration (e.g. Ehrhart theory) and combinatorial structures (e.g. graphs and permutations).
Eigenvalues and Linear Quasirandom Hypergraphs

Let p(k) denote the partition function of k. For each k 2, we describe a list of p(k) 1 quasirandom properties that a k-uniform hypergraph can have. Our work connects previous notions on linear hypergraph quasirandomness of Kohayakawa- Rodl-Skokan and Conlon-H an-Person-Schacht and the spectral approach of Friedman- Wigderson. For each of the quasirandom properties that are described, we dene a largest and second largest eigenvalue. We show that a hypergraph satises these quasirandom properties if and only if it has a large spectral gap. This answers a ques- tion of Conlon-H an-Person-Schacht. Our work can be viewed as a partial extension to hypergraphs of the seminal spectral results of Chung-Graham-Wilson for graphs.
Extracting and Exploiting Inherent Sparsity for Efficient IoT Support in 5G: Challenges and Potential Solutions

Besides enabling an enhanced mobile broadband, the next generation of mobile networks (5G) are envisioned for the support of massive connectivity for heterogeneous Internets of Things. These IoTs are envisioned for a large number of use cases including smart cities, environment monitoring, smart vehicles, and so on. Unfortunately, most IoTs have very limited computing and storage capabilities and need cloud services. Hence, connecting these devices through 5G systems requires huge spectrum resources in addition to handling massive connectivity and improved security. This article discusses the challenges facing the support of IoTs through 5G systems. The focus is devoted to discussing physical layer limitations in terms of spectrum resources and radio access channel connectivity. We show how sparsity can be exploited for addressing these challenges, especially in terms of enabling wideband spectrum management and handling the connectivity by exploiting device-to-device communications and edge cloud. Moreover, we identify major open problems and research directions that need to be explored toward enabling the support of massive heterogeneous IoTs through 5G systems.
Cubic preferences and the character admissibility problem

Abstract The notion of separability is important in a variety of fields, including economics, political science, computer science, and operations research. Separability formalizes the idea that a decision-maker’s preferred ordering of outcomes on some dimensions within a multidimensional alternative space may depend on the values of other dimensions. The character admissibility deals with the construction of preferences that are separable on specific sets of dimensions. In this paper, we develop a graph-theoretic approach to the character admissibility problem, using Hamiltonian paths to generate preference orderings. We apply this method specifically to hypercube graphs, defining the class of cubic preferences. We then explore how the algebraic structure of the group of symmetries of the hypercube impacts the separability structures exhibited by cubic preferences. We prove that the characters of cubic preferences satisfy set theoretic properties distinct from those produced by previous methods, and we define two functions to construct cubic preferences. Our methods have potential applications to a variety of multiple-criteria decision-making problems, including multiple-question referendum elections.
Quantum Schur–Weyl duality and projected canonical bases

Let Hr be the generic type A Hecke algebra defined over Z[u,u−1]. The Kazhdan–Lusztig bases {Cw}w∈Sr and {Cw′}w∈Sr of Hr give rise to two different bases of the Specht module Mλ, λ⊢r, of Hr. These bases are not equivalent and we show that the transition matrix S(λ) between the two is the identity at u=0 and u=∞. To prove this, we first prove a similar property for the transition matrices T˜, T˜′ between the Kazhdan–Lusztig bases and their projected counterparts {C˜w}w∈Sr, {C˜w′}w∈Sr, where C˜w:=Cwpλ, C˜w′:=Cw′pλ and pλ is the minimal central idempotent corresponding to the two-sided cell containing w. We prove this property of T˜,T˜′ using quantum Schur–Weyl duality and results about the upper and lower canonical basis of V⊗r (V the natural representation of Uq(gln)) from [14,11,7]. We also conjecture that the entries of S(λ) have a certain positivity property.
Kernel-Based Reconstruction of Space-Time Functions on Dynamic Graphs

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly diffe-rent time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the sampling cost. Alleviating the limited flexibility of the existing approaches, the present paper broadens the kernel-based graph function estimation framework to reconstruct time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths: the first facilitates judicious control of regularization on a space-time frequency plane, whereas the second accommodates time-varying topologies. Batch and online estimators are also put forth. The latter comprise a novel kernel Kalman filter, developed to reconstruct space-time functions at affordable computational cost. Numerical tests with real datasets corroborate the merits of the proposed methods relative to competing alternatives.
Finite-time analysis of the distributed detection problem

This paper addresses the problem of distributed detection in fixed and switching networks. A network of agents observe partially informative signals about the unknown state of the world. Hence, they collaborate with each other to identify the true state. We propose an update rule building on distributed, stochastic optimization methods. Our main focus is on the finite-time analysis of the problem. For fixed networks, we bring forward the notion of Kullback-Leibler cost to measure the efficiency of the algorithm versus its centralized analog. We bound the cost in terms of the network size, spectral gap and relative entropy of agents' signal structures. We further consider the problem in random networks where the structure is realized according to a stationary distribution. We then prove that the convergence is exponentially fast (with high probability), and the non-asymptotic rate scales inversely in the spectral gap of the expected network.
Inner Bound for the Capacity Region of Noisy Channels with an Authentication Requirement

The rate regions of many variations of the standard and wire-tap channels have been thoroughly explored. Secrecy capacity characterizes the loss of rate required to ensure that the adversary gains no information about the transmissions. Authentication does not have a standard metric, despite being an important counterpart to secrecy. While some results have taken an information-theoretic approach to the problem of authentication coding, the full rate region and accompanying trade-offs have yet to be characterized. In this paper, we provide an inner bound of achievable rates with an average authentication and reliability constraint. The bound is established by combining and analyzing two existing authentication schemes for both noisy and noiseless channels. We find that our coding scheme improves upon existing schemes.
Deployment and trajectory optimization for UAVs: A quantization theory approach

Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The scenarios of variable data rate with fixed transmission power, and variable transmission power with fixed data rate are considered. First, the optimal deployment of UAVs is studied for the static case of a fixed ground terminal (GT) density. Using high resolution quantization theory, the corresponding best achievable performance (average data rate or transmission power) is determined in the asymptotic regime of a large number of UAVs. Next, the dynamic case where the GT density is allowed to vary periodically through time is considered. For one-dimensional networks, an accurate formula for the total amount of UAV movement that guarantees the best time-averaged performance is determined. In general, the tradeoff between the total UAV movement and the achievable performance is obtained through a Lagrangian approach. A corresponding trajectory optimization algorithm is introduced and shown to guarantee a convergent Lagrangian. Numerical simulations are also carried out to confirm the analytical findings.
On the solvability of systems of bilinear equations in finite fields

Given k sets A i ⊆ F d q and a non-degenerate bilinear form B in F d q , we consider the system of l ≤ ( k 2 ) bilinear equations B(a i ,a j )=λ ij , a i ∈ A i , i=1,...,k. We show that the system is solvable for any λ ij ∈ F* q , 1 ≤ i, j ≤ k, given that the restricted sets A i are sufficiently large.