cssi/SciSciGPT-SciSciNet huggingface dataset:
Topic Identification for Speech without ASR

Modern topic identification (topic ID) systems for speech use automatic speech recognition (ASR) to produce speech transcripts, and perform supervised classification on such ASR outputs. However, under resource-limited conditions, the manually transcribed speech required to develop standard ASR systems can be severely limited or unavailable. In this paper, we investigate alternative unsupervised solutions to obtaining tokenizations of speech in terms of a vocabulary of automatically discovered word-like or phoneme-like units, without depending on the supervised training of ASR systems. Moreover, using automatic phoneme-like tokenizations, we demonstrate that a convolutional neural network based framework for learning spoken document representations provides competitive performance compared to a standard bag-of-words representation, as evidenced by comprehensive topic ID evaluations on both single-label and multi-label classification tasks.
Testing Poisson binomial distributions

A Poisson Binomial distribution over n variables is the distribution of the sum of n independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution P supported on {0, . . ., n} to which we have sample access is a Poisson Binomial distribution, or far from all Poisson Binomial distributions. The sample complexity of our algorithm is O(n1/4) to which we provide a matching lower bound. We note that our sample complexity improves quadratically upon that of the naive "learn followed by tolerant-test" approach, while instance optimal identity testing [VV14] is not applicable since we are looking to simultaneously test against a whole family of distributions.
Energy-Efficient Interactive Beam Alignment for Millimeter-Wave Networks

Millimeter-wave will be a key technology in next-generation wireless networks thanks to abundant bandwidth availability. However, the use of large antenna arrays with beamforming demands precise beam alignment between the transmitter and the receiver and may entail huge overhead in mobile environments. This paper investigates the design of an optimal interactive beam alignment and data communication protocol, with the goal of minimizing power consumption under a minimum rate constraint. The base station selects beam alignment or data communication and the beam parameters, based on the feedback from the user end. Based on the sectored antenna model and uniform prior on the angles of departure and arrival (AoD/AoA), the optimality of a fixed-length beam-alignment phase followed by a data-communication phase is demonstrated. Moreover, a decoupled fractional beam-alignment method is shown to be optimal, which decouples the alignment of AoD and AoA over time, and iteratively scans a fraction of their region of uncertainty. A heuristic policy is proposed for non-uniform prior on AoD/AoA, with provable performance guarantees, and it is shown that the uniform prior is the worst-case scenario. The performance degradation due to detection errors is studied analytically and via simulation. The numerical results with analog beams depict up to 4dB, 7.5dB, and 14dB gains over a state-of-the-art bisection method and conventional and interactive exhaustive search policies, respectively, and demonstrate that the sectored model provides valuable insights for beam-alignment design.
A Separation Principle for Discrete-Time Fractional-Order Dynamical Systems and Its Implications to Closed-Loop Neurotechnology

Closed-loop neurotechnology requires the capability to predict the state evolution and its regulation under (possibly) partial measurements. There is evidence that neurophysiological dynamics can be modeled by fractional-order dynamical systems (FODS). Therefore, we propose to establish a separation principle for discrete-time FODS, which are inherently nonlinear and are able to capture spatiotemporal relations that exhibit non-Markovian properties. The separation principle states that the problems of controller and state estimator design can be done independently of each other while ensuring proper estimation and control in closed-loop setups. Lastly, we illustrate, as proof-of-concept, the application of the separation principle when designing controllers and estimators for these classes of systems in the context of neurophysiological data. In particular, we rely on real data to derive the models used to assess and regulate the evolution of closed-loop neurotechnologies based on electroencephalographic data.
Quantum electron transport in ohmic edge contacts between two-dimensional materials

In-plane edge contacts can achieve both minimal volume and low contact resistance to further shrink transistor dimensions and increase device performance. However, a quantitative understanding of t...
An oracle property of the Nadaraya–Watson kernel estimator for high‐dimensional nonparametric regression

The celebrated Nadaraya-Watson kernel estimator is among the most studied method for nonparametric regression. A classical result is that its rate of convergence depends on the number of covariates and deteriorates quickly as the dimension grows, which underscores the "curse of dimensionality" and has limited its use in high dimensional settings. In this article, we show that when the true regression function is single or multi-index, the effects of the curse of dimensionality may be mitigated for the Nadaraya-Watson kernel estimator. Specifically, we prove that with $K$-fold cross-validation, the Nadaraya-Watson kernel estimator indexed by a positive semidefinite bandwidth matrix has an oracle property that its rate of convergence depends on the number of indices of the regression function rather than the number of covariates. Intuitively, this oracle property is a consequence of allowing the bandwidths to diverge to infinity as opposed to restricting them all to converge to zero at certain rates as done in previous theoretical studies. Our result provides a theoretical perspective for the use of kernel estimation in high dimensional nonparametric regression and other applications such as metric learning when a low rank structure is anticipated. Numerical illustrations are given through simulations and real data examples.
Quickest Detection of Deviations from Periodic Statistical Behavior

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d. processes. It is shown that the algorithms can be computed recursively and are asymptotically optimal. This problem has applications in anomaly detection in traffic data, social network data, and neural data, where periodic statistical behavior has been observed.
The Ohm-Rush content function II. Noetherian rings, valuation domains, and base change

The notion of an Ohm–Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan–Hochster proof of Stillman’s conjecture....
The information sieve

We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a single latent factor that is maximally informative about multivariate dependence in the data. The data is transformed after each pass so that the remaining unexplained information trickles down to the next layer. Ultimately, we are left with a set of latent factors explaining all the dependence in the original data and remainder information consisting of independent noise. We present a practical implementation of this framework for discrete variables and apply it to a variety of fundamental tasks in unsupervised learning including independent component analysis, lossy and lossless compression, and predicting missing values in data.
Positive Curvature, Partial Vanishing Theorems and Coarse Indices

Let M be a complete Riemannian manifold, D a Dirac-type operator on M whose Weitzenbock curvature is uniformly positive on the complement of a subset Z of M. We show that the coarse index of D is localized to the K-theory of the coarse C*-algebra of Z. Applications are discussed, including a coarse form of the relative index theorem.
Contextual semibandits via supervised learning oracles

We study an online decision making problem where on each round a learner chooses a list of items based on some side information, receives a scalar feedback value for each individual item, and a reward that is linearly related to this feedback. These problems, known as contextual semibandits, arise in crowdsourcing, recommendation, and many other domains. This paper reduces contextual semibandits to supervised learning, allowing us to leverage powerful supervised learning methods in this partial-feedback setting. Our first reduction applies when the mapping from feedback to reward is known and leads to a computationally efficient algorithm with near-optimal regret. We show that this algorithm outperforms state-of-the-art approaches on real-world learning-to-rank datasets, demonstrating the advantage of oracle-based algorithms. Our second reduction applies to the previously unstudied setting when the linear mapping from feedback to reward is unknown. Our regret guarantees are superior to prior techniques that ignore the feedback.
Spectral and geometric bounds on 2-orbifold diffeomorphism type

Abstract We show that a Laplace isospectral family of two-dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collection of 2-orbifolds satisfying lower bounds on sectional curvature and volume, and an upper bound on diameter. An argument converting spectral data to geometric bounds shows that the first result is a consequence of the second.
Low Ply Drawings of Trees and 2-Trees.

Ply number is a recently developed graph drawing metric inspired by studying road networks. Informally, for each vertex v, which is associated with a point in the plane, a disk is drawn centered on v with a radius that is alpha times the length of the longest edge incident to v, for some constant alpha in (0, 0.5]. The ply number is the maximum number of disks that overlap at a single point. We show that any tree with maximum degree Delta has a 1-ply drawing when alpha = O(1 / Delta). We also show that when alpha = 1/2, trees can be drawn with logarithmic ply number, with an area that is polynomial for bounded-degree trees. Lastly, we show that this logarithmic upper bound does not apply to 2-trees, by giving a lower bound of Omega(sqrt(n / log n)) ply for any value of alpha.
Serverless Edge Computing for Green Oil and Gas Industry

Escalating demand of petroleum led the Oil and Gas (O&G) industry to extend oil extraction operation in the remote reservoirs. Oil extraction is a fault intolerant process where the maximum penalty is disaster impacting the environment seriously. Therefore, efficient and nature-friendly green oil extraction is a challenging operation, especially with location constrained in accessing the sites. To overcome these challenges and protect the environment from pollution, smart oil fields with numerous sensors (e.g., for pipeline pressure, gas leakage, air pollution) are established to achieve clean O&G extraction. Conventionally, cloud datacenters are utilized to process the generated data. High-latency satellite communication are used for data transfer, which is not suitable for time-sensitive operations/tasks. To process such latency-sensitive tasks, edge computing can be a suitable candidate, however, their computational power goes downhill at disaster time due to surge demand of many coordinated activities. Therefore, we propose green smart oil fields that operate based on edge computing. To overcome shortage of resources and rapid deployment of the edge computing systems, we propose to use lightweight serverless computing on a federation of edge computing resources from nearby oil rigs. Our solution coordinates urgent coordinated operations/tasks to prevent disasters in oil fields and enable the idea of green smart oil fields. Evaluation results demonstrate the efficacy of our proposed solution in compare to conventional solutions for smart oil fields.
Optimal Power Flow With Step-Voltage Regulators in Multi-Phase Distribution Networks

This paper develops a branch-flow-based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed delta, and open delta step-voltage regulators (SVRs). SVRs are assumed ideal and their taps are represented by continuous decision variables. To tackle the non-linearity, the branch-flow semidefinite programming framework of traditional OPF is expanded to accommodate SVR edges. Three types of non-convexity are addressed: (a) rank-1 constraints on non-SVR edges, (b) nonlinear equality constraints on SVR power flows and taps, and (c) trilinear equalities on SVR voltages and taps. Leveraging a practical phase-separation assumption on the SVR secondary voltage, novel McCormick relaxations are provided for (c) and certain rank-1 constraints of (a), while dropping the rest. A linear relaxation based on conservation of power is used in place of (b). Numerical simulations on standard distribution test feeders corroborate the merits of the proposed convex formulation.
Computing the Gromov-Hausdorff Distance for Metric Trees

The Gromov-Hausdorff (GH) distance is a natural way to measure distance between two metric spaces. We prove that it is NP-hard to approximate the GH distance better than a factor of 3 for geodesic metrics on a pair of trees. We complement this result by providing a polynomial time O(min n, √rn)-approximation algorithm for computing the GH distance between a pair of metric trees, where r is the ratio of the longest edge length in both trees to the shortest edge length. For metric trees with unit length edges, this yields an O(√ n)-approximation algorithm1.
Efficiency of minimizing compositions of convex functions and smooth maps

We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration solves a regularized subproblem formed by linearizing the smooth map. When the subproblems are solved exactly, the method has efficiency $$\mathcal {O}(\varepsilon ^{-2})$$ , akin to gradient descent for smooth minimization. We show that when the subproblems can only be solved by first-order methods, a simple combination of smoothing, the prox-linear method, and a fast-gradient scheme yields an algorithm with complexity $$\widetilde{\mathcal {O}}(\varepsilon ^{-3})$$ . We round off the paper with an inertial prox-linear method that automatically accelerates in presence of convexity.
Much Faster Algorithms for Matrix Scaling

We develop several efficient algorithms for the classical Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input n&#x00D7; n matrix A, this problem asks to find diagonal (scaling) matrices X and Y (if they exist), so that X A Y &#x03B5;-approximates a doubly stochastic matrix, or more generally a matrix with prescribed row and column sums.We address the general scaling problem as well as some important special cases. In particular, if A has m nonzero entries, and if there exist X and Y with polynomially large entries such that X A Y is doubly stochastic, then we can solve the problem in total complexity \tilde{O}(m + n^{4/3}). This greatly improves on the best known previous results, which were either \tilde{O}(n^4) or O(m n^{1/2}/&#x03B5;).Our algorithms are based on tailor-made first and second order techniques, combined with other recent advances in continuous optimization, which may be of independent interest for solving similar problems.
On the Totik–Widom Property for a Quasidisk

Let K be a quasidisk on the complex plane. We construct a sequence of monic polynomials $$p_n=p_n(\cdot ,K)$$ with all their zeros on K such that $$\Vert p_n\Vert _K\le O(1)\text{ cap }(K)^n$$ as $$n\rightarrow \infty $$.
Dimensional crossover and quantum effects of gases adsorbed on nanotube bundles

Adsorption properties of several gases (Ne, ${\mathrm{CH}}_{4},$ Ar, and Xe) on the external surface of a carbon nanotube bundle are investigated. Calculations are performed at low coverage and variable temperature, and for some fixed temperatures as a function of coverage. Within a simple model (in the limit of very low coverage) we are able to study the evolution of the film's thermal properties from those of a one dimensional (1D) fluid to those of a 2D film. In addition, grand canonical Monte Carlo simulations are performed in order to identify a second-layer groove phase that occurs once a monolayer of atoms covers the external surface. We derive from the simulations the isosteric heat, compressibility, and specific heat as a function of coverage. We evaluate alternative models in order to derive quantum corrections to the classical results. We compare our findings with those of recent adsorption experiments.
Learned versus Hand-Designed Feature Representations for 3d Agglomeration

Abstract: For image recognition and labeling tasks, recent results suggest that machine learning methods that rely on manually specified feature representations may be outperformed by methods that automatically derive feature representations based on the data. Yet for problems that involve analysis of 3d objects, such as mesh segmentation, shape retrieval, or neuron fragment agglomeration, there remains a strong reliance on hand-designed feature descriptors. In this paper, we evaluate a large set of hand-designed 3d feature descriptors alongside features learned from the raw data using both end-to-end and unsupervised learning techniques, in the context of agglomeration of 3d neuron fragments. By combining unsupervised learning techniques with a novel dynamic pooling scheme, we show how pure learning-based methods are for the first time competitive with hand-designed 3d shape descriptors. We investigate data augmentation strategies for dramatically increasing the size of the training set, and show how combining both learned and hand-designed features leads to the highest accuracy.
“Irregularization” of systems of conservation laws

We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result in defects which are more singular, and we thus refer to such schemes as “irregularizations”. In particular, we seek to produce delta shock defects which satisfy a condition of stationarity. We are motivated to pursue such exotic defects by a physical example arising from dislocation dynamics in materials physics, which we describe.
Arithmetic Levi–Cività connection

This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer numbers, derivations are replaced by Fermat quotient operators, and connections (respectively curvature) are replaced by certain adelic (respectively global) objects attached to symmetric matrices with integral coefficients. Previous papers were devoted to an arithmetic analogue of the Chern connection. The present paper is devoted to an arithmetic analogue of the Levi–Civita connection.
On concentration properties of disordered Hamiltonians

We present an elementary approach to concentration of disordered Hamiltonians. Assuming differentiability of the limiting free energy $F$ with respect to the inverse temperature $\beta$, we show that the Hamiltonian concentrates around the energy level $F'(\beta)$ under the free energy and Gibbs average.
Bridging the Gap Between 2D and 3D Organ Segmentation with Volumetric Fusion Net

There has been a debate on whether to use 2D or 3D deep neural networks for volumetric organ segmentation. Both 2D and 3D models have their advantages and disadvantages. In this paper, we present an alternative framework, which trains 2D networks on different viewpoints for segmentation, and builds a 3D Volumetric Fusion Net (VFN) to fuse the 2D segmentation results. VFN is relatively shallow and contains much fewer parameters than most 3D networks, making our framework more efficient at integrating 3D information for segmentation. We train and test the segmentation and fusion modules individually, and propose a novel strategy, named cross-cross-augmentation, to make full use of the limited training data. We evaluate our framework on several challenging abdominal organs, and verify its superiority in segmentation accuracy and stability over existing 2D and 3D approaches.
Exact complexity: The spectral decomposition of intrinsic computation

Abstract We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's ϵ-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography.
A LINKING NUMBER DEFINITION OF THE AFFINE INDEX POLYNOMIAL AND APPLICATIONS

This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial. In particular, it proves the Cosmetic Crossing Change Conjecture for odd virtual knots and pure virtual knots. It also demonstrates that the polynomial can detect mutations by positive rotation and proves it cannot detect mutations by positive reflection. Finally it exhibits a pair of mutant knots that can be distinguished by a type 2 vassiliev invariant coming from the polynomial.
Operators preserving orthogonality are isometries

We prove that every operator preserving orthogonality in a real Banach space is an isometry multiplied by a constant.
Brauer–Thrall for totally reflexive modules☆

Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R,m) with m3=0 are commonly regarded as the structurally simplest rings to admit diverse categorical and homological characteristics. For such rings we obtain conclusive results about the category of totally reflexive modules, modeled on the Brauer–Thrall conjectures. Starting from a non-free cyclic totally reflexive module, we construct a family of indecomposable totally reflexive R-modules that contains, for every n∈N, a module that is minimally generated by n elements. Moreover, if the residue field R/m is algebraically closed, then we construct for every n∈N an infinite family of indecomposable and pairwise non-isomorphic totally reflexive R-modules, each of which is minimally generated by n elements. The modules in both families have periodic minimal free resolutions of period at most 2.
Lossy compression with near-uniform encoder outputs

It is well known that lossless compression of a discrete memoryless source with near-uniform encoder output is possible at a rate above its entropy if and only if the encoder and decoder share a common random seed. This work focuses on deriving conditions for near-uniform encoder output(s) in the Wyner-Ziv and the distributed lossy compression problems. We show that in the Wyner-Ziv problem, near-uniform encoder output and operation close to the WZ-rate limit is simultaneously possible, whereas in the distributed lossy compression problem, jointly near-uniform outputs is achievable in the interior of the distributed lossy compression rate region if the sources share non-trivial Gacs-Korner common information.
Griffiths groups of supersingular abelian varieties

The Griffiths group of a smooth projective variety over an algebraically closed field is defined to be the group of homologically trivial algebraic cycles of codimension on modulo the subgroup of algebraically trivial algebraic cycles. The main result of this paper is that the Griffiths group of a supersingular abelian variety over the algebraic closure of a finite field of characteristic is at most a -primary torsion group. As a corollary the same conclusion holds for supersingular Fermat threefolds. In contrast, using methods of . Schoen it is also shown that if the Tate conjecture is valid for all smooth projective surfaces and all finite extensions of the finite ground field of characteristic , then the Griffiths group of any ordinary abelian threefold over the algebraic closure of is non-trivial; in fact, for all but a finite number of primes it is the case that .
Improved predictions of the physical properties of Zn- and Cd-based wide band-gap semiconductors: a validation of the ACBN0 functional

We study the physical properties of ZnX (X = O, S, Se, Te) and CdX (X = O, S, Se, Te) in the zinc-blende, rock-salt, and wurtzite structures using the recently developed fully ab initio pseudohybrid Hubbard density functional ACBN0. We find that both the electronic and vibrational properties of these wide band-gap semiconductors are systematically improved over the PBE values and reproduce closely the experimental measurements. Similar accuracy is found for the structural parameters, especially the bulk modulus. ACBN0 results compare well with hybrid functional calculations at a fraction of the computational cost.
Demystifying Deep Learning: a Geometric Approach to Iterative Projections

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we present an alternative semi-parametric framework which foregoes the ordinarily required feedback, by introducing the novel idea of geometric regularization. We show that certain deep learning techniques such as residual network (ResNet) architecture are closely related to our approach. Hence, our technique can be used to analyze these types of deep learning. Moreover, we present preliminary results which confirm that our approach can be easily trained to obtain complex structures.
Multi-block ADMM for big data optimization in smart grid

In this paper, we review the parallel and distributed optimization algorithms based on alternating direction method of multipliers (ADMM) for solving "big data" optimization problem in smart grid communication networks. We first introduce the canonical formulation of the large-scale optimization problem. Next, we describe the general form of ADMM and then focus on several direct extensions and sophisticated modifications of ADMM from 2-block to N-block settings to deal with the optimization problem. The iterative schemes and convergence properties of each extension/modification are given, and the implementation on large-scale computing facilities is also illustrated. Finally, we numerate several applications in power system for distributed robust state estimation, network energy management and security constrained optimal power flow problem.
Prevalence and recoverability of syntactic parameters in sparse distributed memories

We propose a new method, based on sparse distributed memory, for studying dependence relations between syntactic parameters in the Principles and Parameters model of Syntax. By storing data of syntactic structures of world languages in a Kanerva network and checking recoverability of corrupted data from the network, we identify two different effects: an overall underlying relation between the prevalence of parameters across languages and their degree of recoverability, and a finer effect that makes some parameters more easily recoverable beyond what their prevalence would indicate. The latter can be seen as an indication of the existence of dependence relations, through which a given parameter can be determined using the remaining uncorrupted data.
Transformed Schatten-1 iterative thresholding algorithms for low rank matrix completion

c 2017 International Press C OMMUN. M ATH. S CI. Vol. 15, No. 3, pp. 839–862 TRANSFORMED SCHATTEN-1 ITERATIVE THRESHOLDING ALGORITHMS FOR LOW RANK MATRIX COMPLETION ∗ SHUAI ZHANG † , PENGHANG YIN ‡ , AND JACK XIN § Abstract. We study a non-convex low-rank promoting penalty function, the transformed Schatten- 1 (TS1), and its applications in matrix completion. The TS1 penalty, as a matrix quasi-norm deﬁned on its singular values, interpolates the rank and the nuclear norm through a nonnegative parameter a ∈ (0,+∞). We consider the unconstrained TS1 regularized low-rank matrix recovery problem and develop a ﬁxed point representation for its global minimizer. The TS1 thresholding functions are in closed analytical form for all parameter values. The TS1 threshold values diﬀer in subcritical (supercritical) parameter regime where the TS1 threshold functions are continuous (discontinuous). We propose TS1 iterative thresholding algorithms and compare them with some state-of-the-art algorithms on matrix completion test problems. For problems with known rank, a fully adaptive TS1 iterative thresholding algorithm consistently performs the best under diﬀerent conditions, where ground truth matrices are generated by multivariate Gaussian, (0,1) uniform and Chi-square distributions. For problems with unknown rank, TS1 algorithms with an additional rank estimation procedure approach the level of IRucL-q which is an iterative reweighted algorithm, non-convex in nature and best in performance. Keywords. transformed Schatten-1 penalty; ﬁxed point representation; closed form thresholding function; iterative thresholding algorithms; matrix completion AMS subject classiﬁcations. 90C26; 90C46 1. Introduction Low rank matrix completion problems arise in many applications such as collabora- tive ﬁltering in recommender systems [4,17], minimum order system and low-dimensional Euclidean embedding in control theory [14,15], network localization [18], and others [26]. The mathematical problem is: min rank(X) X∈ m×n s.t. X ∈ L where L is a convex set. In this paper, we are interested in methods for solving the aﬃne rank minimization problem (ARMP) min rank(X) X∈ m×n s.t. A (X) = b in p , where the linear transformation A : m×n → p and vector b ∈ p are given. The matrix completion problem min rank(X) X∈ m×n s.t. X i,j = M i,j , (i,j) ∈ Ω is a special case of (1.2), where X and M are both m × n matrices and Ω is a subset of index pairs {(i,j)}. ∗ Received: September 25, 2016; accepted (in revised form): October 28, 2016. Communicated by Wotao Yin. The work was partially supported by NSF grant DMS-1222507 and DMS-1522383. † Department of Mathematics, University of California, Irvine, CA, 92697, USA (szhang3@uci.edu). Phone: (949)-824-5309. Fax: (949)-824-7993. ‡ Department of Mathematics, University of California, Irvine, CA, 92697, USA (penghany@uci.edu). § Department of Mathematics, University of California, Irvine, CA, 92697, USA (jxin@math.uci.edu).
Sparse Recovery With Graph Constraints

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor the key characteristics of large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse signals in the presence of network topological constraints. Unlike conventional sparse recovery where a measurement can contain any subset of the unknown variables, we use a graph to characterize the topological constraints and allow an additive measurement over nodes (unknown variables) only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs, and the number of measurements by our construction is less than that needed by existing random constructions. Moreover, our construction for a line network is provably optimal in the sense that it requires the minimum number of measurements. A measurement construction algorithm for general graphs is also proposed and evaluated. For any given graph $G$ with $n$ nodes, we derive bounds of the minimum number of measurements needed to recover any $k$ -sparse vector over $G$ ( $M^{G}_{k,n}$ ). Using the Erdős-Renyi random graph as an example, we characterize the dependence of $M^{G}_{k,n}$ on the graph structure. This paper suggests that $M^{G}_{k,n}$ may serve as a graph connectivity metric.
Recognizing Galois representations of K3 surfaces

Under the assumption of the Hodge, Tate and Fontaine–Mazur conjectures we give a criterion for a compatible system of $$\ell $$ -adic representations of the absolute Galois group of a number field to be isomorphic to the second cohomology of a K3 surface. This is achieved by producing a motive M realizing the compatible system, using a local to global argument for quadratic forms to produce a K3 lattice in the Betti realization of M and then applying surjectivity of the period map for K3 surfaces to obtain a complex K3 surface. Finally we use a very general descent argument to show that the complex K3 surface admits a model over a number field.
Hierarchical modeling of seed variety yields and decision making for future planting plans

Eradicating hunger and malnutrition is a key development goal of the twenty first century. This paper addresses the problem of optimally identifying seed varieties to reliably increase crop yield within a risk-sensitive decision making framework. Specifically, a novel hierarchical machine learning mechanism for predicting crop yield (the yield of different seed varieties of the same crop) is introduced. This prediction mechanism is then integrated with a weather forecasting model and three different approaches for decision making under uncertainty to select seed varieties for planting so as to balance yield maximization and risk. The model was applied to the problem of soybean variety selection given in the 2016 Syngenta Crop Challenge. The prediction model achieved a median absolute error of 235 kg/ha and thus provides good estimates for input into the decision models. The decision models identified the selection of soybean varieties that appropriately balance yield and risk as a function of the farmer’s risk aversion level. More generally, the models can support farmers in decision making about which seed varieties to plant.
A "quantum" Ramsey theorem for operator systems

Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP) = 1 or k^2.
Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators

Motivated by recent interest for multi-agent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. By extending methods from synchronization theory and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the classic Kuramoto model. By combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying network parameters and initial conditions.
Reinforcement Learning under Model Mismatch

We study reinforcement learning under model misspecification, where we do not have access to the true environment but only to a reasonably close approximation to it. We address this problem by extending the framework of robust MDPs to the model-free Reinforcement Learning setting, where we do not have access to the model parameters, but can only sample states from it. We define robust versions of Q-learning, Sarsa, and TD-learning and prove convergence to an approximately optimal robust policy and approximate value function respectively. We scale up the robust algorithms to large MDPs via function approximation and prove convergence under two different settings. We prove convergence of robust approximate policy iteration and robust approximate value iteration for linear architectures (under mild assumptions). We also define a robust loss function, the mean squared robust projected Bellman error and give stochastic gradient descent algorithms that are guaranteed to converge to a local minimum.
Rank Two ADHM Invariants and Wallcrossing

Generalized Donaldson-Thomas invariants corresponding to local D6-D2-D0 configurations are defined applying the formalism of Joyce and Song to ADHM sheaves on curves. A wallcrossing formula for invariants of D6-rank two is proven and shown to agree with the wallcrossing formula of Kontsevich and Soibelman. Using this result, the asymptotic D6-rank two invariants of (-1,-1) and (0,-2) local rational curves are computed in terms of the D6-rank one invariants.
GenerationMania: Learning to Semantically Choreograph

Beatmania is a rhythm action game where players must reproduce some of the sounds of a song by pressing specific controller buttons at the correct time. In this paper we investigate the use of deep neural networks to automatically create game stages—called charts—for arbitrary pieces of music. Our technique uses a multi-layer feed-forward network trained on sound sequence summary statistics to predict which sounds in the music are to be played by the player and which will play automatically. We use another neural network along with rules to determine which controls should be mapped to which sounds. We evaluated our system on the ability to reconstruct charts in a held-out test set, achieving an F1-score that significantly beats LSTM baselines.
Brauer equivalent number fields and the geometry of quaternionic Shimura varieties

Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper we prove a variety of number theoretic results about Brauer equivalent number fields (e.g., they must have the same signature). These results are then applied to the geometry of certain arithmetic locally symmetric spaces. As an example, we construct incommensurable arithmetic locally symmetric spaces containing exactly the same set of proper immersed totally geodesic surfaces.
Multivariate stochastic volatility modeling of neural data

Because multivariate autoregressive models have failed to adequately account for the complexity of neural signals, researchers have predominantly relied on non-parametric methods when studying the relations between brain and behavior. Using medial temporal lobe (MTL) recordings from 96 neurosurgical patients, we show that time series models with volatility described by a multivariate stochastic latent-variable process and lagged interactions between signals in different brain regions provide new insights into the dynamics of brain function. The implied volatility inferred from our process positively correlates with high-frequency spectral activity, a signal that correlates with neuronal activity. We show that volatility features derived from our model can reliably decode memory states, and that this classifier performs as well as those using spectral features. Using the directional connections between brain regions during complex cognitive process provided by the model, we uncovered perirhinal-hippocampal desynchronization in the MTL regions that is associated with successful memory encoding.
Fast determinantal point processes via distortion-free intermediate sampling.

Given a fixed $n\times d$ matrix $\mathbf{X}$, where $n\gg d$, we study the complexity of sampling from a distribution over all subsets of rows where the probability of a subset is proportional to the squared volume of the parallelepiped spanned by the rows (a.k.a. a determinantal point process). In this task, it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). To that end, we propose a new determinantal point process algorithm which has the following two properties, both of which are novel: (1) a preprocessing step which runs in time $O(\text{number-of-non-zeros}(\mathbf{X})\cdot\log n)+\text{poly}(d)$, and (2) a sampling step which runs in $\text{poly}(d)$ time, independent of the number of rows $n$. We achieve this by introducing a new regularized determinantal point process (R-DPP), which serves as an intermediate distribution in the sampling procedure by reducing the number of rows from $n$ to $\text{poly}(d)$. Crucially, this intermediate distribution does not distort the probabilities of the target sample. Our key novelty in defining the R-DPP is the use of a Poisson random variable for controlling the probabilities of different subset sizes, leading to new determinantal formulas such as the normalization constant for this distribution. Our algorithm has applications in many diverse areas where determinantal point processes have been used, such as machine learning, stochastic optimization, data summarization and low-rank matrix reconstruction.
Sensitivity of a bayesian source-term estimation model to spatiotemporal sensor resolution

Abstract Source-term estimation (STE) methods attempt to calculate the most-likely source characteristics of an atmospheric release given concentration observations. The quality of the STE depends partially on the time and space scales of the observations, sensor locations, and release parameters. We quantify the sensitivity of a probabilistic STE algorithm that was previously validated using observational data collected during a controlled tracer release experiment to the spatiotemporal resolution of observing networks. We have also made many improvements to the STE algorithm, which extends applicability to coarser-resolution observational datasets. Improvements include the use of a fully-connected deep neural network model emulator with dynamically optimized architecture and better goodness-of-fit (GoF) metrics to measure the discrepancy between model and observational data. The GoF metrics, which are more robust and resilient than previous metrics, are the Spearman rank-based correlation coefficient and a variation of the binary f 1 classification score adapted for regression problems. Using synthetically generated observations over East Asia, the skill of the improved algorithm is quantified over a broad range of sensor configurations and release scenarios. The evaluation is broken into three experiments. First, a validation study shows that the proposed GoF metrics perform more reliably than other possible candidates. Next, data-denial techniques are applied to a single release scenario over the Korean peninsula, where the skill of the inversion is shown to be highly sensitive to the number and location of deployed sensors but less sensitive to temporal resolution. Finally, the STE algorithm is tested for many release locations throughout the geographic model domain, where the STE algorithm performs well for all but a few cases. The results indicate that the STE algorithm provides informative source-parameter posterior probability distributions utilizing data collected by sparse sensor networks; however, the skill of the STE algorithm improves significantly for higher resolution networks.
A glycal-based photoaffinity probe that enriches sialic acid binding proteins

Abstract To identify sialic acid binding proteins from complex proteomes, three photocrosslinking affinity-based probes were constructed using Neu5Ac (5 and 6) and Neu5Ac2en (7) scaffolds. Kinetic inhibition assays and Western blotting revealed the Neu5Ac2en-based 7 to be an effective probe for the labeling of a purified gut microbial sialidase (BDI_2946) and a purified human sialic acid binding protein (hCD33). Additionally, LC–MS/MS affinity-based protein profiling verified the ability of 7 to enrich a low-abundance sialic acid binding protein (complement factor H) from human serum thus validating the utility of this probe in a complex context.
Predicting the Argumenthood of English Prepositional Phrases.

Distinguishing between arguments and adjuncts of a verb is a longstanding, nontrivial problem. In natural language processing, argumenthood information is important in tasks such as semantic role labeling (SRL) and prepositional phrase (PP) attachment disambiguation. In theoretical linguistics, many diagnostic tests for argumenthood exist but they often yield conflicting and potentially gradient results. This is especially the case for syntactically oblique items such as PPs. We propose two PP argumenthood prediction tasks branching from these two motivations: (1) binary argumentadjunct classification of PPs in VerbNet, and (2) gradient argumenthood prediction using human judgments as gold standard, and report results from prediction models that use pretrained word embeddings and other linguistically informed features. Our best results on each task are (1) acc. = 0.955, F1 = 0.954 (ELMo+BiLSTM) and (2) Pearson’s r = 0.624 (word2vec+MLP). Furthermore, we demonstrate the utility of argumenthood prediction in improving sentence representations via performance gains on SRL when a sentence encoder is pretrained with our tasks.