cssi/SciSciGPT-SciSciNet huggingface dataset:
The free-boundary Brakke flow

We develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must "pop" upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White to the free-boundary setting. We use Ilmanen's elliptic regularization procedure to prove existence of free-boundary Brakke flows.
Compressed sensing for tactile skins

Whole body tactile perception via tactile skins offers large benefits for robots in unstructured environments. To fully realize this benefit, tactile systems must support real-time data acquisition over a massive number of tactile sensor elements. We present a novel approach for scalable tactile data acquisition using compressed sensing. We first demonstrate that the tactile data is amenable to compressed sensing techniques. We then develop a solution for fast data sampling, compression, and reconstruction that is suited for tactile system hardware and has potential for reducing the wiring complexity. Finally, we evaluate the performance of our technique on simulated tactile sensor networks. Our evaluations show that compressed sensing, with a compression ratio of 3 to 1, can achieve higher signal acquisition accuracy than full data acquisition of noisy sensor data.
Multistage Robust Unit Commitment With Dynamic Uncertainty Sets and Energy Storage

The deep penetration of wind and solar power is a critical component of the future power grid. However, the intermittency and stochasticity of these renewable resources bring significant challenges to the reliable and economic operation of power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the unit commitment (UC) problem, which models the sequential nature of the dispatch process and utilizes a new type of dynamic uncertainty sets to capture the temporal and spatial correlations of wind and solar power. The model also considers the operation of energy storage devices. We propose a simplified and effective affine policy for dispatch decisions, and develop an efficient algorithmic framework using a combination of constraint generation and duality-based reformulation with various improvements. Extensive computational experiments show that the proposed method can efficiently solve multistage robust UC problems on the Polish 2736-bus system under high dimensional uncertainty of 60 wind farms and 30 solar farms. The computational results also suggest that the proposed model leads to significant benefits in both costs and reliability over robust models with traditional uncertainty sets as well as deterministic models with reserve rules.
Quotients of representation rings

We give a proof, using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(\infinity)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to \infinity. This in turn allows a detailed description of the quotient map in terms of a reflection group. As an application, one obtains a general description of the branching rules for the restriction of representations of Gl(N) to O(N) and Sp(N) as well as detailed information about the structure of the q-Brauer algebras in the nonsemisimple case for certain specializations.
Superstability and Symmetry

Abstract This paper continues the study of superstability in abstract elementary classes (AECs) satisfying the amalgamation property. In particular, we consider the definition of μ -superstability which is based on the local character characterization of superstability from first order logic. Not only is μ -superstability a potential dividing line in the classification theory for AECs, but it is also a tool in proving instances of Shelah's Categoricity Conjecture. In this paper, we introduce a formulation, involving towers, of symmetry over limit models for μ -superstable abstract elementary classes. We use this formulation to gain insight into the problem of the uniqueness of limit models for categorical AECs.
Learning without recall by random walks on directed graphs

We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might not be able to distinguish the true state based only on her private observations. This occurs when some other states are observationally equivalent to the true state from the agent's perspective. To overcome this shortcoming, agents must communicate with each other to benefit from local observations. We propose a model where each agent selects one of her neighbors randomly at each time. Then, she refines her opinion using her private signal and the prior of that particular neighbor. The proposed rule can be thought of as a Bayesian agent who cannot recall the priors based on which other agents make inferences. This learning without recall approach preserves some aspects of the Bayesian inference while being computationally tractable. By establishing a correspondence with a random walk on the network graph, we prove that under the described protocol, agents learn the truth exponentially fast in the almost sure sense. The asymptotic rate is expressed as the sum of the relative entropies between the signal structures of every agent weighted by the stationary distribution of the random walk.
Beating the SDP bound for the floor layout problem: A simple combinatorial idea

For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through sem...
Solving for high-dimensional committor functions using artificial neural networks

In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of transition path theory, which satisfies a high-dimensional Fokker–Planck equation. By working with the variational formulation of such partial differential equation and parameterizing the committor function in terms of a neural network, approximations can be obtained via optimizing the neural network weights using stochastic algorithms. The numerical examples show that moderate accuracy can be achieved for high-dimensional problems.
Trace formulas and a Borg-type theorem for CMV operators with matrix-valued coefficients

We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velazquez [13]) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result [39] for CMV operators with scalar-valued coefficients. In the course of deriving the Borg-type result we also use exponential Herglotz representations of Caratheodory matrix-valued functions to prove an infinite sequence of trace formulas connected with CMV operators
Mirror-Prox SCA Algorithm for Multicast Beamforming and Antenna Selection

This paper considers the (NP-)hard problem of joint multicast beamforming and antenna selection. Prior work has focused on using Semi-Definite relaxation (SDR) techniques in an attempt to obtain a high quality sub-optimal solution. However, SDR suffers from the drawback of having high computational complexity, as SDR lifts the problem to higher dimensional space, effectively squaring the number of variables. This paper proposes a high performance, low complexity Successive Convex Approximation (SCA) algorithm for max-min SNR “fair” joint multicast beamforming and antenna selection under a sum power constraint. The proposed approach relies on iteratively approximating the non-convex objective with a series of non-smooth convex subproblems, and then, a first order-based method called Saddle Point Mirror-Prox (SP-MP) is used to compute optimal solutions for each SCA subproblem. Simulations reveal that the SP-MP SCA algorithm provides a higher quality and lower complexity solution compared to the one obtained using SDR.
Upper triangular matrices and Billiard Arrays

Abstract Fix a nonnegative integer d , a field F , and a vector space V over F with dimension d + 1 . Let T denote an invertible upper triangular matrix in Mat d + 1 ( F ) . Using T we construct three flags on V . We find a necessary and sufficient condition on T for these three flags to be totally opposite. In this case, we use these three totally opposite flags to construct a Billiard Array B on V . It is known that B is determined up to isomorphism by a certain triangular array of scalar parameters called the B -values. We compute these B -values in terms of the entries of T . We describe the set of isomorphism classes of Billiard Arrays in terms of upper triangular matrices.
A new achievable rate region for multiple-access channel with states

The problem of reliable communication over the multiple-access channel (MAC) with states is investigated. We propose a new coding scheme for this problem which uses quasi-group codes (QGC). We derive a new computable single-letter characterization of the achievable rate region. As an example, we investigate the problem of doubly-dirty MAC with modulo-4 addition. It is shown that the sum rate R 1 + R 2 =1 bits per channel use is achievable using the new scheme. Whereas, the natural extension of the Gel'fand-Pinsker scheme, sum-rates greater than 0.32 are not achievable.
Anisotropic challenges in pedestrian flow modeling

Macroscopic models of crowd flow incorporating individual pedestrian choices present many analytic and computational challenges. Anisotropic interactions are particularly subtle, both in terms of describing the correct "optimal" direction field for the pedestrians and ensuring that this field is uniquely defined. We develop sufficient conditions, which establish a range of "safe" densities and parameter values for each model. We illustrate our approach by analyzing several established intra-crowd and inter-crowd models. For the two-crowd case, we also develop sufficient conditions for the uniqueness of Nash Equilibria in the resulting non-zero-sum game.
Investigating the necessity of distribution markets in accomodating high penetration microgrids

The increased need for reliable, resilient, and high quality power combined with a falling cost of distributed generation technologies has resulted in a rapid growth of microgrid in power systems. Although providing multitude of benefits, the microgrid power transfer with the main grid, which is commonly obtained using economy and reliability consideration, may result in major operational drawbacks, most notably, a large mismatch between actual and forecasted system loads. This paper investigates the impact of high penetration microgrids on the power system net load, and further proposes three paradigms that can be adopted to address the emerging operational issues. The IEEE 6-bus test system is used for numerical studies and to further support the discussions.
Stabilizers of Ergodic Actions of Lattices and Commensurators

We prove that any ergodic measure-preserving action of an irreducible lattice in a semisimple group, with finite center and each simple factor having rank at least two, either has finite orbits or has finite stabilizers. The same dichotomy holds for many commensurators of such lattices. The above are derived from more general results on groups with the Howe-Moore property and property (T). We prove similar results for commensurators in such groups and for irreducible lattices (and commensurators) in products of at least two such groups, at least one of which is totally disconnected.
Dirichlet eigenvalue sums on triangles are minimal for equilaterals

Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first n eigenvalues of the Dirichlet Laplacian, for each n ≥ 1. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains. 1. Results and Conjectures This paper establishes geometrically sharp lower bounds for the Dirichlet eigenvalues of the Laplacian on triangular domains. These eigenvalues are important in solving the wave, diffusion and Schrodinger equations. The eigenfunctions satisfy −∆u = λu with boundary condition u = 0, and the eigenvalues satisfy 0 < λ1 < λ2 ≤ λ3 ≤ · · · → ∞. We start with a sharp bound on eigenvalue sums. Notice we normalize the eigenvalues to be scale invariant, by multiplying with the square of the diameter D of the domain. Theorem 1.1. Among all triangular domains of given diameter, the equilateral triangle minimizes the sum of the first n eigenvalues of the Dirichlet Laplacian, for each n. That is, if T is a triangular domain, E is equilateral, and n ≥ 1, then (λ1 + · · ·+ λn)D ∣∣∣ T ≥ (λ1 + · · ·+ λn)D ∣∣∣ E with equality if and only if T is equilateral. The theorem is proved in Section 3. The case n = 1 for the fundamental tone was known already, by combining Polya and Szegő’s result [32, Note A] that λ1A is minimal for the equilateral triangle with the elementary isodiametric inequality that D2/A is minimal Date: November 30, 2010. 2000 Mathematics Subject Classification. Primary 35P15. Secondary 35J20.
A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis

Abstract We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions.
Multinomial Adversarial Networks for Multi-Domain Text Classification

Many text classification tasks are known to be highly domain-dependent. Unfortunately, the availability of training data can vary drastically across domains. Worse still, for some domains there may not be any annotated data at all. In this work, we propose a multinomial adversarial network (MAN) to tackle this real-world problem of multi-domain text classification (MDTC) in which labeled data may exist for multiple domains, but in insufficient amounts to train effective classifiers for one or more of the domains. We provide theoretical justifications for the MAN framework, proving that different instances of MANs are essentially minimizers of various f-divergence metrics (Ali and Silvey, 1966) among multiple probability distributions. MANs are thus a theoretically sound generalization of traditional adversarial networks that discriminate over two distributions. More specifically, for the MDTC task, MAN learns features that are invariant across multiple domains by resorting to its ability to reduce the divergence among the feature distributions of each domain. We present experimental results showing that MANs significantly outperform the prior art on the MDTC task. We also show that MANs achieve state-of-the-art performance for domains with no labeled data.
The Role of Data Analysis in Uncertainty Quantification: Case Studies for Materials Modeling

In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that can propagate into final predictions in unexpected ways. Thus, modelers require data analysis tools that (i) address the problems posed by simulated data, and (ii) facilitate uncertainty quantification. In this manuscript, we discuss three case studies in materials modeling where careful data analysis can be leveraged to address specific instances of these issues. As a unifying theme, we highlight the idea that attention to physical and mathematical constraints surrounding the generation of computational data can significantly enhance its analysis.
A Low-Complexity Recursive Approach Toward Code-Domain NOMA for Massive Communications

Nonorthogonal multiple access (NOMA) is a promising technology to meet the demands of the next generation wireless networks on massive connectivity, high throughput and reliability, improved fairness, and low latency. In this context, code-domain NOMA which attempts to serve $K$ users in $M \leq K$ orthogonal resource blocks, using a pattern matrix, is of utmost interest. However, extending the pattern matrix dimensions severely increases the detection complexity and hampers on the significant advantages that can be achieved using large pattern matrices. In this paper, we propose a novel approach toward code-domain NOMA which factorizes the pattern matrix as the Kronecker product of some other factor matrices each with a smaller dimension. Therefore, both the pattern matrix design at the transmitter side and the mixed symbols' detection at the receiver side can be performed over much smaller dimensions and with a remarkably reduced complexity and latency. As a consequence, the system can significantly be overloaded to effectively support the requirements of the next generation wireless networks without any considerable increase on the system complexity.
Prime parking functions on rooted trees

Abstract For a labeled, rooted tree with edges oriented towards the root, we consider the vertices as parking spots and the edge orientation as a one-way street. Each driver, starting with her preferred parking spot, searches for and parks in the first unoccupied spot along the directed path to the root. If all n drivers park, the sequence of spot preferences is called a parking function. We consider the sequences, called prime parking functions, for which each driver parks and each edge in the tree is traversed by some driver after failing to park at her preferred spot. We prove that the total number of prime parking functions on trees with n vertices is ( 2 n − 2 ) ! . Additionally, we generalize increasing parking functions, those in which the drivers park with a weakly-increasing order of preference, to trees and prove that the total number of increasing prime parking functions on trees with n vertices is ( n − 1 ) ! S n − 1 , where { S i } i ≥ 0 are the large Schroder numbers.
Gamma-ray bursts

Gamma-ray bursts are the most luminous explosions in the Universe, and their origin and mechanism are the focus of intense research and debate. More than three decades after their discovery, and after pioneering breakthroughs from space and ground experiments, their study is entering a new phase with the recently launched Swift satellite. The interplay between these observations and theoretical models of the prompt gamma-ray burst and its afterglow is reviewed.
Special subgroups of gyrogroups: Commutators, nuclei and radical

‎A gyrogroup is a nonassociative group-like structure modelled on the ‎space of relativistically admissible velocities with a binary ‎operation given by Einstein's velocity addition law‎. ‎In this ‎article‎, ‎we present a few of groups sitting inside a gyrogroup G‎, ‎including the commutator subgyrogroup‎, ‎the left nucleus‎, ‎and the ‎radical of G‎. ‎The normal closure of the commutator subgyrogroup‎, ‎the left nucleus‎, ‎and the radical of G are in particular normal ‎subgroups of G‎. ‎We then give a criterion to determine when a ‎subgyrogroup H of a finite gyrogroup G‎, ‎where the index ‎$[Gcolon H]$ is the smallest prime dividing |G|‎, ‎is normal in G‎.
The deformable mirror demonstration mission (DeMi) CubeSat: optomechanical design validation and laboratory calibration

Coronagraphs on future space telescopes will require precise wavefront correction to detect Earth-like exoplanets near their host stars. High-actuator count microelectromechanical system (MEMS) deformable mirrors provide wavefront control with low size, weight, and power. The Deformable Mirror Demonstration Mission (DeMi) payload will demonstrate a 140 actuator MEMS Deformable Mirror (DM) with 5:5 μm maximum stroke. We present the flight optomechanical design, lab tests of the flight wavefront sensor and wavefront reconstructor, and simulations of closed-loop control of wavefront aberrations. We also present the compact flight DM controller, capable of driving up to 192 actuator channels at 0-250V with 14-bit resolution. Two embedded Raspberry Pi 3 compute modules are used for task management and wavefront reconstruction. The spacecraft is a 6U CubeSat (30 cm x 20 cm x 10 cm) and launch is planned for 2019.
On the Convergence Rate of Average Consensus and Distributed optimization over Unreliable Networks

We consider the problems of reaching average consensus and solving consensus-based optimization over unreliable communication networks wherein packets may be dropped accidentally during transmission. Existing work either assumes that the link failures affect the communication on both directions or that the message senders know exactly, in each iteration, how many of their outgoing links are functioning properly. In this paper, we consider directed links, and we do not require each node know its current outgoing degree.First, we propose and characterize the convergence rate of reaching average consensus. Then we apply our robust consensus update to the classical distributed dual averaging method wherein the consensus update is used as the information aggregation primitive. We show that the local iterates converge to a common optimum of the global objective at rate $O\left(\frac{1}{\sqrt{t}}\right)$, where t is the number of iterations, matching the failure-free performance of the distributed dual averaging method.
Slow motion for the 1D Swift–Hohenberg equation

Abstract The goal of this paper is to study the behavior of certain solutions to the Swift–Hohenberg equation on a one-dimensional torus T . Combining results from Γ-convergence and ODE theory, it is shown that solutions corresponding to initial data that is L 1 -close to a jump function v, remain close to v for large time. This can be achieved by regarding the equation as the L 2 -gradient flow of a second order energy functional, and obtaining asymptotic lower bounds on this energy in terms of the number of jumps of v.
Collaborative Deep Learning in Fixed Topology Networks

There is significant recent interest to parallelize deep learning algorithms in order to handle the enormous growth in data and model sizes. While most advances focus on model parallelization and engaging multiple computing agents via using a central parameter server, aspect of data parallelization along with decentralized computation has not been explored sufficiently. In this context, this paper presents a new consensus-based distributed SGD (CDSGD) (and its momentum variant, CDMSGD) algorithm for collaborative deep learning over fixed topology networks that enables data parallelization as well as decentralized computation. Such a framework can be extremely useful for learning agents with access to only local/private data in a communication constrained environment. We analyze the convergence properties of the proposed algorithm with strongly convex and nonconvex objective functions with fixed and diminishing step sizes using concepts of Lyapunov function construction. We demonstrate the efficacy of our algorithms in comparison with the baseline centralized SGD and the recently proposed federated averaging algorithm (that also enables data parallelism) based on benchmark datasets such as MNIST, CIFAR-10 and CIFAR-100.
Parton fragmentation in nuclear collisions

The hydrodynamic (hydro) model has been extensively applied to heavy ion data from the relativistic heavy ion collider (RHIC). Results are interpreted to conclude that a dense QCD medium nearly opaque to most partons, a strongly-coupled quark-gluon plasma (sQGP), is formed in more-central Au-Au collisions. The sQGP may have a very small viscosity (“perfect liquid”). However, other analysis methods provide contradictory evidence. Two-component analysis of single-particle hadron spectra reveals a spectrum hard component consistent with a parton fragment distribution described by pQCD which can masquerade as “radial flow” in some hydromotivated analysis. Minimum-bias angular correlations reveal that a large number of back-toback jets from initial-state scattered partons with energies as low as 3 GeV survive as “minijet” hadron correlations even in central Au-Au collisions, suggesting near transparency to partons. In this talk I present methods by which almost all spectrum and correlation structure, even in the most-central Au-Au collisions at 200 GeV, can be described quantitatively by pQCD calculations. The evolution of nuclear collisions is apparently dominated by parton scattering and fragmentation even in the most-central A-A collisions, albeit the fragmentation process is strongly modified.
Constrained Bayesian inference for low rank multitask learning

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the feasible set of densities and propose a general recipe for such problems. We apply the proposed constrained Bayesian inference approach to multitask learning subject to rank constraints on the weight matrix. Further, constrained parameter estimation is applied to recover the sparse conditional independence structure encoded by prior precision matrices. Our approach is motivated by reverse inference for high dimensional functional neuroimaging, a domain where the high dimensionality and small number of examples requires the use of constraints to ensure meaningful and effective models. For this application, we propose a model that jointly learns a weight matrix and the prior inverse covariance structure between different tasks. We present experimental validation showing that the proposed approach outperforms strong baseline models in terms of predictive performance and structure recovery.
Self-conjugate core partitions and modular forms

Abstract A recent paper by Hanusa and Nath states many conjectures in the study of self-conjugate core partitions. We prove all but two of these conjectures asymptotically by number-theoretic means. We also obtain exact formulas for the number of self-conjugate t -core partitions for “small” t via explicit computations with modular forms. For instance, self-conjugate 9-core partitions are related to counting points on elliptic curves over Q with conductor dividing 108, and self-conjugate 6-core partitions are related to the representations of integers congruent to 11 mod 24 by 3 X 2 + 32 Y 2 + 96 Z 2 , a form with finitely many (conjecturally five) exceptional integers in this arithmetic progression, by an ineffective result of Duke–Schulze-Pillot.
Constant slope maps on the extended real line

For a transitive countably piecewise monotone Markov interval map we consider the question of whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous, whether it is mixing or not, what slope we consider and whether the conjugate map is defined on a bounded interval, half-line or the whole real line (with the infinities included).
UNITARY REPRESENTATIONS OF WAVELET GROUPS AND ENCODING OF ITERATED FUNCTION SYSTEMS IN SOLENOIDS.

For points in d real dimensions, we introduce a geometry for general digit sets. We introduce a positional number system where the basis for our representation is a fixed d by d matrix over Z. Our starting point is a given pair (A,D) with the matrix A assumed expansive, and D a chosen complete digit set, i.e., in bijective correspondence with the points in Z d /A T Z d . We give an explicit geometric representation and encoding with infinite words in letters from D. We show that the attractor X(A T ,D) for an affine Iterated Function System (IFS) based on (A,D) is a set of fractions for our digital representation of points in R d . Moreover our positional "number representation" is spelled out in the form of an explicit IFS-encoding of a compact solenoid SA associated with the pair (A,D). The intricate part (Theorem 6.15) is played by the cycles in Z d for the initial (A,D)-IFS. Using these cycles we are able to write down formulas for the two maps which do the encoding as well as the decoding in our positional D-representation. We show how some wavelet representations can be realized on the solenoid, and on symbolic spaces.
Energy Efficiency and Emission Testing for Connected and Automated Vehicles Using Real-World Driving Data

By using the onboard sensing and external connectivity technology, connected and automated vehicles (CAV) could lead to improved energy efficiency, better routing, and lower traffic congestion. With the rapid development of the technology and adaptation of CAV, it is critical to developing the universal evaluation method and the testing standard which could evaluate the impacts on energy consumption and environmental pollution of CAV fairly, especially under the various traffic conditions. In this paper, we proposed a new method and framework to evaluate the energy efficiency and emission of the vehicle based on the unsupervised learning methods. Both the real-world driving data of the evaluated vehicle and the large naturalistic driving dataset are used to perform the driving primitive analysis and coupling. Then the linear weighted estimation method could be used to calculate the testing result of the evaluated vehicle. The results show that this method can successfully identify the typical driving primitives. The couples of the driving primitives from the evaluated vehicle and the typical driving primitives from the large real-world driving dataset coincide with each other very well. This new method could enhance the standard development of the energy efficiency and emission testing of CAV and other off-cycle credits.
A Bayesian matrix factorization model for relational data

Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metropolis-Hastings is impractically slow, and so we develop a block Metropolis-Hastings sampler which uses the gradient and Hessian of the likelihood to dynamically tune the proposal. We demonstrate that a predictive model of brain response to stimuli can be improved by augmenting it with side information about the stimuli.
Exploring Tradeoffs in Models for Low-Latency Speech Enhancement

We explore a variety of neural networks configurations for one- and two-channel spectrogram-mask-based speech enhancement. Our best model improves on previous state-of-the-art performance on the CHiME2 speech enhancement task by 0.4 decibels in signal-to-distortion ratio (SDR). We examine trade-offs such as non-causal look-ahead, computation, and parameter count versus enhancement performance and find that zero-look-ahead models can achieve, on average, within 0.03 dB SDR of our best bidirectional model. Further, we find that 200 milliseconds of look-ahead is sufficient to achieve equivalent performance to our best bidirectional model.
Online Learning of Optimal Bidding Strategy in Repeated Multi-Commodity Auctions

We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $\Omega(\sqrt{T})$ for any strategy, we conclude that DPDS is order optimal up to a $\sqrt{\log{T}}$ term. We evaluate the performance of DPDS empirically in the context of virtual trading in wholesale electricity markets by using historical data from the New York market. Empirical results show that DPDS consistently outperforms benchmark heuristic methods that are derived from machine learning and online learning approaches.
A distance for HMMS based on aggregated wasserstein metric and state registration

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly match, aka register, the states in two HMMs. We refer to such HMMs as Gaussian mixture model-HMM (GMM-HMM). The registration of states is inspired by the intrinsic relationship of optimal transport and the Wasserstein metric between distributions. Specifically, the components of the marginal GMMs are matched by solving an optimal transport problem where the cost between components is the Wasserstein metric for Gaussian distributions. The solution of the optimization problem is a fast approximation to the Wasserstein metric between two GMMs. The new Aggregated Wasserstein distance is a semi-metric and can be computed without generating Monte Carlo samples. It is invariant to relabeling or permutation of the states. This distance quantifies the dissimilarity of GMM-HMMs by measuring both the difference between the two marginal GMMs and the difference between the two transition matrices. Our new distance is tested on the tasks of retrieval and classification of time series. Experiments on both synthetic data and real data have demonstrated its advantages in terms of accuracy as well as efficiency in comparison with existing distances based on the Kullback-Leibler divergence.
Start late or finish early: a distributed graph processing system with redundancy reduction

Graph processing systems are important in the big data domain. However, processing graphs in parallel often introduces redundant computations in existing algorithms and models. Prior work has proposed techniques to optimize redundancies for out-of-core graph systems, rather than distributed graph systems. In this paper, we study various state-of-the-art distributed graph systems and observe root causes for these pervasively existing redundancies. To reduce redundancies without sacrificing parallelism, we further propose SLFE, a distributed graph processing system, designed with the principle of "start late or finish early". SLFE employs a novel preprocessing stage to obtain a graph's topological knowledge with negligible overhead. SLFE's redundancy-aware vertex-centric computation model can then utilize such knowledge to reduce the redundant computations at runtime. SLFE also provides a set of APIs to improve programmability. Our experiments on an 8-machine high-performance cluster show that SLFE outperforms all well-known distributed graph processing systems with the inputs of real-world graphs, yielding up to 75x speedup. Moreover, SLFE outperforms two state-of-the-art shared memory graph systems on a high-end machine with up to 1644x speedup. SLFE's redundancy-reduction schemes are generally applicable to other vertex-centric graph processing systems.
Mean Field Games in Nudge Systems for Societal Networks

We consider the general problem of resource sharing in societal networks, consisting of interconnected communication, transportation, energy, and other networks important to the functioning of society. Participants in such network need to take decisions daily, both on the quantity of resources to use as well as the periods of usage. With this in mind, we discuss the problem of incentivizing users to behave in such a way that society as a whole benefits. To perceive societal level impact, such incentives may take the form of rewarding users with lottery tickets based on good behavior and periodically conducting a lottery to translate these tickets into real rewards. We will pose the user decision problem as a mean field game and the incentives question as one of trying to select a good mean field equilibrium (MFE). In such a framework, each agent (a participant in the societal network) takes a decision based on an assumed distribution of actions of his/her competitors and the incentives provided by the social planner. The system is said to be at MFE if the agent’s action is a sample drawn from the assumed distribution. We will show the existence of such an MFE under general settings, and also illustrate how to choose an attractive equilibrium using as an example demand-response in the (smart) electricity network.
On the p-adic meromorphy of the function field height zeta function

Abstract In this brief note, we will investigate the number of points of bounded height in a projective variety defined over a function field, where the function field comes from a projective variety of dimension greater than or equal to 2. A first step in this investigation is to understand the p -adic analytic properties of the height zeta function. In particular, we will show that for a large class of projective varieties this function is p -adic meromorphic.
Coupling Geometry on Binary Bipartite Networks: Hypotheses Testing on Pattern Geometry and Nestedness

Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the intrinsic structures of the system, so that the coupling geometry should be taken as information contents, or even the nonparametric minimum sufficient statistics of the network data. Then pertinent null and alternative hypotheses, such as nestedness, are to be formulated according to the macrostate. That is, any efficient testing statistic needs to be a function of this coupling geometry. These conceptual architectures and mechanisms are by and large still missing in community ecology literature, and rendered misconceptions prevalent in this research area. Here the algorithmically computed coupling geometry is shown consisting of deterministic multiscale block patterns, which are framed by two marginal ultrametric trees on row and column axes, and stochastic uniform randomness within each block found on the finest scale. Functionally a series of increasingly larger ensembles of matrix mimicries is derived by conforming to the multiscale block configurations. Here matrix mimicking is meant to be subject to constraints of row and column sums sequences. Based on such a series of ensembles, a profile of distributions becomes a natural device for checking the validity of testing statistics or structural indexes. An energy based index is used for testing whether network data indeed contains structural geometry. A new version block-based nestedness index is also proposed. Its validity is checked and compared with the existing ones. A computing paradigm, called Data Mechanics, and its application on one real data network are illustrated throughout the developments and discussions in this paper.
Scaling of the detonation product state with reactant kinetic energy

Abstract Chemical explosives provide one of the most high-power and energy-dense storage materials available. During detonation, transfer of this energy to adjacent materials is governed by the detonation product equation of state. No accurate methodology exists for prediction of this thermodynamic relationship and equation-of-state data continues to be experimentally characterized for each new formulation or charge density. Here we present a universal detonation product equation of state derived from several newly discovered empirical correlations in prior condensed-phase detonation product measurements. This model depends only on initial charge density and detonation velocity as inputs, dramatically simplifying the calibration process relative to existing models, which require measurement of up to seven formulation-specific parameters. This new result implies the product energy density scales with reactant kinetic energy density, which is the product of the explosive initial density and detonation velocity squared, for all condensed-phase energetic materials and that explosive microstructural or chemical details only influence the product energy density though these two parameters.
Background Subtraction via Fast Robust Matrix Completion

Background subtraction is the primary task of the majority of video inspection systems. The most important part of the background subtraction which is common among different algorithms is background modeling. In this regard, our paper addresses the problem of background modeling in a computationally efficient way, which is important for current eruption of "big data" processing coming from high resolution multi-channel videos. Our model is based on the assumption that background in natural images lies on a low-dimensional subspace. We formulated and solved this problem in a low-rank matrix completion framework. In modeling the background, we benefited from the in-face extended Frank-Wolfe algorithm for solving a defined convex optimization problem. We evaluated our fast robust matrix completion (fRMC) method on both background models challenge (BMC) and Stuttgart artificial background subtraction (SABS) datasets. The results were compared with the robust principle component analysis (RPCA) and low-rank robust matrix completion (RMC) methods, both solved by inexact augmented Lagrangian multiplier (IALM). The results showed faster computation, at least twice as when IALM solver is used, while having a comparable accuracy even better in some challenges, in subtracting the backgrounds in order to detect moving objects in the scene.
Grace: A cross-platform micromagnetic simulator on graphics processing units

Abstract A micromagnetic simulator running on graphics processing units (GPUs) is presented. Different from GPU implementations of other research groups which are predominantly running on NVidia’s CUDA platform, this simulator is developed with C++ Accelerated Massive Parallelism (C++ AMP) and is hardware platform independent. It runs on GPUs from venders including NVidia, AMD and Intel, and achieves significant performance boost as compared to previous central processing unit (CPU) simulators, up to two orders of magnitude. The simulator paved the way for running large size micromagnetic simulations on both high-end workstations with dedicated graphics cards and low-end personal computers with integrated graphics cards, and is freely available to download.
Multi-parameter singular Radon transforms III: Real analytic surfaces

Abstract The goal of this paper is to study operators of the form, T f ( x ) = ψ ( x ) ∫ f ( γ t ( x ) ) K ( t ) d t , where γ is a real analytic function defined on a neighborhood of the origin in ( t , x ) ∈ R N × R n , satisfying γ 0 ( x ) ≡ x , ψ is a cutoff function supported near 0 ∈ R n , and K is a “multi-parameter singular kernel” supported near 0 ∈ R N . A main example is when K is a “product kernel.” We also study maximal operators of the form, M f ( x ) = ψ ( x ) sup 0 δ 1 , … , δ N ≪ 1 ∫ | t | 1 | f ( γ δ 1 t 1 , … , δ N t N ( x ) ) | d t . We show that M is bounded on L p ( 1 p ⩽ ∞ ). We give conditions on γ under which T is bounded on L p ( 1 p ∞ ); these conditions hold automatically when K is a Calderon–Zygmund kernel. This is the final paper in a three part series. The first two papers consider the more general case when γ is C ∞ .
The family of analytic Poisson brackets for the Camassa--Holm hierarchy

We consider the integrable Camassa--Holm hierarchy on the line with positive initial data rapidly decaying at infinity. It is known that flows of the hierarchy can be formulated in a Hamiltonian form using two compatible Poisson brackets. In this note we propose a new approach to Hamiltonian theory of the CH equation. In terms of associated Riemann surface and the Weyl function we write an analytic formula which produces a family of compatible Poisson brackets. The formula includes an entire function $f(z)$ as a parameter. The simplest choice $f(z)=1$ or $f(z)=z$ corresponds to the rational or trigonometric solutions of the Yang-Baxter equation and produces two original Poisson brackets. All other Poisson brackets corresponding to other choices of the function $f(z)$ are new.
Hierarchical models for relational event sequences

Abstract Interaction within small groups can often be represented as a sequence of events, each event involving a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner—we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics from 297 sessions.
A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs

The Capacitated Vehicle Routing problem is to find a minimum-cost set of tours that collectively cover clients in a graph, such that each tour starts and ends at a specified depot and is subject to a capacity bound on the number of clients it can serve. In this paper, we present a polynomial-time approximation scheme (PTAS) for instances in which the input graph is planar and the capacity is bounded. Previously, only a quasipolynomial-time approximation scheme was known for these instances. To obtain this result, we show how to embed planar graphs into bounded-treewidth graphs while preserving, in expectation, the client-to-client distances up to a small additive error proportional to client distances to the depot.
An Optimal Task Allocation Strategy for Heterogeneous Multi-Robot Systems

For a team of heterogeneous robots executing multiple tasks, we propose a novel algorithm to optimally allocate tasks to robots while accounting for their different capabilities. Motivated by the need that robot teams have in many real-world applications of remaining operational for long periods of time, we allow each robot to choose tasks taking into account the energy consumed by executing them, besides the global specifications on the task allocation. The tasks are encoded as constraints in an energy minimization problem solved at each point in time by each robot. The prioritization of a task over others—effectively signifying the allocation of the task to that particular robot—occurs via the introduction of slack variables in the task constraints. Moreover, the suitabilities of certain robots towards certain tasks are also taken into account to generate a task allocation algorithm for a team of robots with heterogeneous capabilities. The efficacy of the developed approach is demonstrated both in simulation and on a team of real robots.