cssi/SciSciGPT-SciSciNet huggingface dataset:
Periodicity Transforms For Multichannel and Multiclass Detection of Visual Evoked Potentials

A repetitive visual stimulus induces a brain response known as the Steady State Visual Evoked Potential (SSVEP) whose frequency matches that of the stimulus. Reliable SSVEP-based Brain-Computer-Interfacing (BCI) is premised in part on the ability to efficiently detect and classify the true underlying frequencies in real time. We pose the problem of detecting different frequencies corresponding to different stimuli as a composite multi-hypothesis test, where measurements from multiple electrodes are assumed to admit a sparse representation in a Ramanujan Periodicity Transform (RPT) dictionary. We develop an RPT detector based on a generalized likelihood ratio test of the underlying periodicity that accounts for the spatial correlation between the electrodes. Unlike the existing supervised methods which are highly data-dependent, the RPT detector only uses data to estimate the per-subject spatial correlation. The RPT detector is shown to yield promising results comparable to state-of-the-art methods such as standard CCA and IT CCA based on experiments with real data. Its ability to yield high accuracy with short epochs holds potential to advance real-time BCI technology.
The flat stable module category of a coherent ring

Abstract Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for constructing model structures, the key step is to show that a module is flat and cotorsion if and only if it is Gorenstein flat and Gorenstein cotorsion.
Learning to attend in a brain-inspired deep neural network

Recent machine learning models have shown that including attention as a component results in improved model accuracy and interpretability, despite the concept of attention in these approaches only loosely approximating the brain's attention mechanism. Here we extend this work by building a more brain-inspired deep network model of the primate ATTention Network (ATTNet) that learns to shift its attention so as to maximize the reward. Using deep reinforcement learning, ATTNet learned to shift its attention to the visual features of a target category in the context of a search task. ATTNet's dorsal layers also learned to prioritize these shifts of attention so as to maximize success of the ventral pathway classification and receive greater reward. Model behavior was tested against the fixations made by subjects searching images for the same cued category. Both subjects and ATTNet showed evidence for attention being preferentially directed to target goals, behaviorally measured as oculomotor guidance to targets. More fundamentally, ATTNet learned to shift its attention to target like objects and spatially route its visual inputs to accomplish the task. This work makes a step toward a better understanding of the role of attention in the brain and other computational systems.
On Jones' subgroup of R. Thompson group F

Abstract Recently Vaughan Jones showed that the R. Thompson group F encodes in a natural way all knots and links in R 3 , and a certain subgroup F → of F encodes all oriented knots and links. We answer several questions of Jones about F → . In particular we prove that the subgroup F → is generated by x 0 x 1 , x 1 x 2 , x 2 x 3 (where x i , i ∈ N are the standard generators of F ) and is isomorphic to F 3 , the analog of F where all slopes are powers of 3 and break points are 3-adic rationals. We also show that F → coincides with its commensurator. Hence the linearization of the permutational representation of F on F / F → is irreducible. We show how to replace 3 in the above results by an arbitrary n , and to construct a series of irreducible representations of F defined in a similar way. Finally we analyze Jones' construction and deduce that the Thompson index of a link is linearly bounded in terms of the number of crossings in a link diagram.
Duluth UROP at SemEval-2018 Task 2: Multilingual Emoji Prediction with Ensemble Learning and Oversampling

This paper describes the Duluth UROP systems that participated in SemEval–2018 Task 2, Multilingual Emoji Prediction. We relied on a variety of ensembles made up of classifiers using Naive Bayes, Logistic Regression, and Random Forests. We used unigram and bigram features and tried to offset the skewness of the data through the use of oversampling. Our task evaluation results place us 19th of 48 systems in the English evaluation, and 5th of 21 in the Spanish. After the evaluation we realized that some simple changes to our pre-processing could significantly improve our results. After making these changes we attained results that would have placed us sixth in the English evaluation, and second in the Spanish.
Alignment-Based Network Coding for Two-Unicast-Z Networks

In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast- $Z$ network is a two-unicast network where the destination intending to decode the second message has a priori side information of the first message. We make three contributions in this paper. First, we describe a new linear network coding algorithm for two-unicast-Z networks over the directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For the graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and the polynomial complexity in terms of the number of edges. Second, we prove that our algorithm achieves the rate pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over the directed acyclic graphs, to an earlier result of Wang et al. , which studied the necessary and sufficient conditions for the feasibility of the rate pair (1, 1) in two-unicast networks. Third, we provide a new proof of the classical max-flow min-cut theorem for the directed acyclic graphs.
Frobenius powers of some monomial ideals

Abstract In this paper, we characterize the (generalized) Frobenius powers and critical exponents of two classes of monomial ideals of a polynomial ring in positive characteristic: powers of the homogeneous maximal ideal, and ideals generated by positive powers of the variables. In doing so, we effectively characterize the test ideals and F-jumping exponents of sufficiently general homogeneous polynomials, and of all diagonal polynomials. Our characterizations make these invariants computable, and show that they vary uniformly with the congruence class of the characteristic modulo a fixed integer. Moreover, we confirm that for a diagonal polynomial over a field of characteristic zero, the test ideals of its reduction modulo a prime agree with the reductions of its multiplier ideals for infinitely many primes.
Correlation Decay in Random Decision Networks

We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the corresponding nodes. The goal is to construct a decision vector that maximizes the total reward. This decision problem encompasses a variety of models, including maximum-likelihood inference in graphical models (Markov Random Fields), combinatorial optimization on graphs, economic team theory, and statistical physics. The network is endowed with a probabilistic structure in which rewards are sampled from a distribution. Our aim is to identify sufficient conditions on the network structure and rewards distributions to guarantee average-case polynomiality of the underlying optimization problem. Additionally, we wish to characterize the efficiency of a decentralized solution generated on the basis of local information. We construct a new decentralized algorithm called Cavity Expans...
Schubert polynomials and classes of Hessenberg varieties

Abstract Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a “Giambelli formula” expressing the classes of regular semisimple Hessenberg varieties in terms of Chern classes. In fact, we show that the cohomology class of each regular semisimple Hessenberg variety is the specialization of a certain double Schubert polynomial, giving a natural geometric interpretation to such specializations. We also decompose such classes in terms of the Schubert basis for the cohomology ring of the flag variety. The coefficients obtained are nonnegative, and we give closed combinatorial formulas for the coefficients in many cases. We introduce a closely related family of schemes called regular nilpotent Hessenberg schemes, and use our results to determine when such schemes are reduced.
A cluster-cumulant expansion at the fixed points of belief propagation

We introduce a new cluster-cumulant expansion (CCE) based on the fixed points of iterative belief propagation (IBP). This expansion is similar in spirit to the loop-series (LS) recently introduced in [1]. However, in contrast to the latter, the CCE enjoys the following important qualities: 1) it is defined for arbitrary state spaces 2) it is easily extended to fixed points of generalized belief propagation (GBP), 3) disconnected groups of variables will not contribute to the CCE and 4) the accuracy of the expansion empirically improves upon that of the LS. The CCE is based on the same Mobius transform as the Kikuchi approximation, but unlike GBP does not require storing the beliefs of the GBP-clusters nor does it suffer from convergence issues during belief updating.
On the Optimal Recovery Threshold of Coded Matrix Multiplication

We provide novel coded computation strategies for distributed matrix–matrix products that outperform the recent “Polynomial code” constructions in recovery threshold, i.e., the required number of successful workers. When a fixed $1/m$ fraction of each matrix can be stored at each worker node, Polynomial codes require $m^{2}$ successful workers, while our MatDot codes only require $2m-1$ successful workers. However, MatDot codes have higher computation cost per worker and higher communication cost from each worker to the fusion node. We also provide a systematic construction of MatDot codes. Furthermore, we propose “PolyDot” coding that interpolates between Polynomial codes and MatDot codes to trade off computation/communication costs and recovery thresholds. Finally, we demonstrate a novel coding technique for multiplying $n$ matrices ( $n \geq 3$ ) using ideas from MatDot and PolyDot codes.
2-Selmer near-companion curves

Let $E$ and $A$ be elliptic curves over a number field $K$. Let $\chi$ be a quadratic character of $K$. We prove the conjecture posed by Mazur and Rubin on $n$-Selmer near-companion curves in the case $n=2$. Namely, we show if the difference of the $2$-Selmer ranks of $E^\chi$ and $A^\chi$ is bounded independent of $\chi$, there is a $G_K$-isomorphism $E[2] \cong A[2]$.
The Whitney Extension Theorem for \(C^1\), Horizontal Curves in the Heisenberg Group

For a real-valued function defined on a compact set \(K \subset {\mathbb {R}}^m\), the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a \(C^k\) extension to \({\mathbb {R}}^m\). In this paper, we prove a version of the Whitney Extension Theorem in the case of \(C^1\), horizontal extensions for mappings defined on compact subsets of \({\mathbb {R}}\) taking values in the sub-Riemannian Heisenberg group \(\mathbb {H}^n\).
Lifting laws and arithmetic invariant theory

In this paper we discuss lifting laws which, roughly, are ways of "lifting" elements of the open orbit of one prehomogeneous vector space to elements of the minimal nonzero orbit of another prehomogeneous vector space. We prove a handful of these lifting laws, and show how they can be used to help solve certain problems in arithmetic invariant theory. Of the results contained in this article are twisted versions of certain parametrization theorems of Bhargava.
Duality theorems for étale gerbes on orbifolds

Abstract Let G be a finite group and Y a G -gerbe over an orbifold B . A disconnected orbifold Y ˆ and a flat U ( 1 ) -gerbe c on Y ˆ is canonically constructed from Y . Motivated by a proposal in physics, we study a mathematical duality between the geometry of the G -gerbe Y and the geometry of Y ˆ twisted by c . We prove several results verifying this duality in the contexts of non-commutative geometry and symplectic topology. In particular, we prove that the category of sheaves on Y is equivalent to the category of c -twisted sheaves on Y ˆ . When Y is symplectic, we show, by a combination of techniques from non-commutative geometry and symplectic topology, that the Chen–Ruan orbifold cohomology of Y is isomorphic to the c -twisted orbifold cohomology of Y ˆ as graded algebras.
Borromean rays and hyperplanes

Three disjoint rays in ℝ3 form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.
Bases of Solutions for Linear Congruences

In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases. This article is a continuation of my article "On linear congruences".
Spatial multiresolution cluster detection method

A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to select the optimal test threshold. The MCD method is compared with single scale testing methods controlling for false discovery rate and the spatial scan statistics using simulation and f-MRI data. The MCD method is shown to be more effective for discovering irregularly shaped clusters, and the implementation of this method does not require heavy computation, making it suitable for cluster detection for large spatial data.
Bilinear Controllability of a Class of Advection–Diffusion–Reaction Systems

In this paper, we investigate the exact controllability properties of an advection–diffusion equation on a bounded domain, using time- and space-dependent velocity fields as the control parameters. This partial differential equation (PDE) is the Kolmogorov forward equation for a reflected diffusion process that models the spatiotemporal evolution of a swarm of agents. We prove that if a target probability density has bounded first-order weak derivatives and is uniformly bounded from below by a positive constant, then it can be reached in finite time using control inputs that are bounded in space and time. We then extend this controllability result to a class of advection–diffusion–reaction PDEs that corresponds to a hybrid switching diffusion process (HSDP), in which case the reaction parameters are additionally incorporated as the control inputs. For the HSDP, we first constructively prove controllability of the associated continuous-time Markov chain (CTMC) system in which the state space is finite. Then, we show that our controllability results for the advection–diffusion equation and the CTMC can be combined to establish controllability of the forward equation of the HSDP. Finally, we provide constructive solutions to the problem of asymptotically stabilizing an HSDP to a target nonnegative stationary distribution using time-independent state feedback laws, which correspond to spatially dependent coefficients of the associated system of PDEs.
Accelerating the evolution of convolutional neural networks with node-level mutations and epigenetic weight initialization

This paper examines three generic strategies for improving the performance of neuro-evolving convolutional neural networks (CNNs): node-level mutation operations, epigenetic weight initialization and pooling connections. These were implemented using the Evolutionary eXploration of Augmenting Convolutional Topologies (EXACT) algorithm. Results were gathered over the period of a month using a volunteer computing project, where over 225,000 CNNs were trained and evaluated across 16 different EXACT searches. The node mutation operations where shown to dramatically improve evolution rates over traditional edge mutation operations (as used by the NEAT algorithm), and epigenetic weight initialization was shown to further increase the accuracy and generalizability of the trained CNNs. As a negative but interesting result, allowing for pooling connections was shown to degrade the evolution progress. The best trained CNNs reached 99.46% accuracy on the MNIST test data in under 13,500 CNN evaluations - accuracy comparable with some of the best human designed CNNs.
Participation and performance on paper- and computer-based low-stakes assessments

High-stakes assessments, such the Graduate Records Examination, have transitioned from paper to computer administration. Low-stakes research-based assessments (RBAs), such as the Force Concept Inventory, have only recently begun this transition to computer administration with online services. These online services can simplify administering, scoring, and interpreting assessments, thereby reducing barriers to instructors’ use of RBAs. By supporting instructors’ objective assessment of the efficacy of their courses, these services can stimulate instructors to transform their courses to improve student outcomes. We investigate the extent to which RBAs administered outside of class with the online Learning About STEM Student Outcomes (LASSO) platform provide equivalent data to tests administered on paper in class, in terms of both student participation and performance. We use an experimental design to investigate the differences between these two assessment conditions with 1310 students in 25 sections of 3 college physics courses spanning 2 semesters. Analysis conducted using hierarchical linear models indicates that student performance on low-stakes RBAs is equivalent for online (out-of-class) and paper-and-pencil (in-class) administrations. The models also show differences in participation rates across assessment conditions and student grades, but that instructors can achieve participation rates with online assessments equivalent to paper assessments by offering students credit for participating and by providing multiple reminders to complete the assessment. We conclude that online out-of-class administration of RBAs can save class and instructor time while providing participation rates and performance results equivalent to in-class paper-and-pencil tests.
Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA

Numerical weather prediction (NWP) has proven to be computationally challenging due to its inherent multiscale nature. Currently, the highest resolution global NWP models use a horizontal resolutio...
Geometry of the contactomorphism group

Abstract In this paper we examine the Riemannian geometry of the group of contactomorphisms of a compact contact manifold. We compute the sectional curvature of D θ ( M ) in the sections containing the Reeb field and show that it is non-negative. We also solve explicitly the Jacobi equation along the geodesic corresponding to the flow of the Reeb field and determine the conjugate points. Finally, we show that the Riemannian exponential map is a non-linear Fredholm map of index zero.
Bounds on variance for symmetric unimodal distributions

We show a direct relationship between the variance and the differential entropy for the general class of symmetric unimodal distributions by providing an upper bound on variance in terms of entropy power. Combining this bound with the well-known entropy power lower bound on variance, we prove that for the general class of symmetric unimodal distributions the variance can be bounded below and above by the scaled entropy power. As differential entropy decreases, the variance is sandwiched between two exponentially decreasing functions in the differential entropy. This establishes that for the general class of symmetric unimodal distributions, the differential entropy can be used as a surrogate for concentration of the distribution.
Efficient approximation of Sparse Jacobians for time-implicit reduced order models

Summary This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation method and uses only samples of the nonzero entries of the matrix series. The proposed approach can approximate very large matrices, unlike the current matrix discrete empirical interpolation method, which is limited by its large computational memory requirements. The empirical interpolation indices obtained by the sparse algorithm slightly differ from the ones computed by the matrix discrete empirical interpolation method as a consequence of the singular vectors round-off errors introduced by the economy or full singular value decomposition (SVD) algorithms when applied to the full matrix snapshots. When appropriately padded with zeros, the economy SVD factorization of the nonzero elements of the snapshots matrix is a valid economy SVD for the full snapshots matrix. Numerical experiments are performed with the 1D Burgers and 2D shallow water equations test problems where the quadratic reduced nonlinearities are computed via tensorial calculus. The sparse matrix approximation strategy is compared against five existing methods for computing reduced Jacobians: (i) matrix discrete empirical interpolation method, (ii) discrete empirical interpolation method, (iii) tensorial calculus, (iv) full Jacobian projection onto the reduced basis subspace, and (v) directional derivatives of the model along the reduced basis functions. The sparse matrix method outperforms all other algorithms. The use of traditional matrix discrete empirical interpolation method is not possible for very large dimensions because of its excessive memory requirements. Copyright © 2016 John Wiley & Sons, Ltd.
Behavioral Malware Classification using Convolutional Recurrent Neural Networks

Behavioral malware detection aims to improve on the performance of static signature-based techniques used by anti-virus systems, which are less effective against modern polymorphic and metamorphic malware. Behavioral malware classification aims to go beyond the detection of malware by also identifying a malware’s family according to a naming scheme such as the ones used by anti-virus vendors. Behavioral malware classification techniques use run-time features, such as file system or network activities, to capture the behavioral characteristic of running processes. The increasing volume of malware samples, diversity of malware families, and the variety of naming schemes given to malware samples by anti-virus vendors present challenges to behavioral malware classifiers. We describe a behavioral classifier that uses a Convolutional Recurrent Neural Network and data from Microsoft Windows Prefetch files. We demonstrate the model’s improvement on the state-of-the-art using a large dataset of malware families and four major anti-virus vendor naming schemes. The model is effective in classifying malware samples that belong to common and rare malware families and can incrementally accommodate the introduction of new malware samples and families.
Antipodes and involutions

Abstract If H is a connected, graded Hopf algebra, then Takeuchi's formula can be used to compute its antipode. However, there is usually massive cancellation in the result. We show how sign-reversing involutions can sometimes be used to obtain cancellation-free formulas. We apply this idea to nine different examples. We rederive known formulas for the antipodes in the Hopf algebra of polynomials, the shuffle Hopf algebra, the Hopf algebra of quasisymmetric functions in both the monomial and fundamental bases, the Hopf algebra of multi-quasisymmetric functions in the fundamental basis, and the incidence Hopf algebra of graphs. We also find cancellation-free expressions for particular values of the antipode in the immaculate basis for the noncommutative symmetric functions as well as the Malvenuto–Reutenauer and Poirier–Reutenauer Hopf algebras, some of which are the first of their kind. We include various conjectures and suggestions for future research.
A Bayesian Approach for Parameter Estimation With Uncertainty for Dynamic Power Systems

We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These methods are used to estimate the maximum a posteriori point of the parameters and their variance, which quantifies their uncertainty. Within this framework, we estimate several parameters of the dynamic power system, such as generator inertias, which are not quantifiable in steady-state models. We illustrate the performance of these approaches on a 9-bus power grid example and analyze the dependence on measurement frequency, estimation horizon, perturbation size, and measurement noise. We assess the computational efficiency, and discuss the expected performance when these methods are applied to large systems.
Conditioning and covariance on caterpillars

Let X 1 , …, X n be joint {±1}-valued random variables. It is known that conditioning on a random subset of O(1/ϵ2) of them reduces their average pairwise covariance to below ϵ (in expectation). We conjecture that O(1/ϵ2) can be improved to O(1/ϵ). The motivation for the problem and our conjectured improvement comes from the theory of global correlation rounding for convex relaxation hierarchies. We suggest attempting the conjecture in the case that X 1 , …, X n are the leaves of an information flow tree. We prove the conjecture in the case that the information flow tree is a caterpillar graph (similar to a two-state hidden Markov model).
Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a coflow, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an O(log n/log log n)-approximation polynomial time algorithm for scheduling circuit-based coflows without given flow paths (here n is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least %22 on average over competing heuristics.
A Derandomized Sparse Johnson-Lindenstrauss Transform

Recent work of [Dasgupta-Kumar-Sarl os, STOC 2010] gave a sparse Johnson-Lindenstrauss transform and left as a main open question whether their construction could be eciently derandomized. We answer their question armatively by giving an alternative proof of their result requiring only bounded independence hash functions. Furthermore, the sparsity bound obtained in our proof is improved. The main ingredient in our proof is a spectral moment bound for quadratic forms that was recently used in [Diakonikolas-Kane-Nelson, FOCS 2010].
Linearly Recurrent Autoencoder Networks for Learning Dynamics

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural network approximations of the underlying Koopman operator. Extended Dynamic...
Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices

Abstract We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero–Grunbaum–Moral–Velazquez, this enables us to study spreading rates for quantum walks in one spatial dimension. We prove several general results which establish quantitative upper and lower bounds on the spreading of a quantum walk in terms of estimates on a pair of associated matrix cocycles. To demonstrate the power and utility of these methods, we apply them to several concrete cases of interest. In the case where the coins are distributed according to an element of the Fibonacci subshift, we are able to rather completely describe the dynamics in a particular asymptotic regime. As a pleasant consequence, this supplies the first concrete example of a quantum walk with anomalous transport, to the best of our knowledge. We also prove ballistic transport for a quantum walk whose coins are periodically distributed.
New Signatures of WIMPless Dark Matter

We consider new signatures of WIMPless dark matter, particularly those which can be used to test models with low dark matter mass. We focus on detection prospects at hadron colliders through the production of new heavy QCD-coupled particles, which decay to WIMPless dark matter plus jets. We find that the Tevatron can probe a significant fraction of the low mass parameter space with data already taken, and the LHC will have even better detection prospects with its first physics run.
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces

This paper contains two improvements on a theorem of S. N. Bernstein for Banach spaces. We show that if $X$ is an arbitrary infinite-dimensional Banach space, ${Y_n}$ is a sequence of strictly nested subspaces of $ X$ and if ${d_n}$ is a non-increasing sequence of non-negative numbers tending to 0, then for any $cin(0,1]$ we can find $x_{c} in X$, such that the distance $rho(x_{c}, Y_n)$ from $x_{c}$ to $Y_n$ satisfies$$c d_n leq rho(x_{c},Y_n) leq 4c d_n,~mbox{for all $ninmathbb N$}.$$We prove the above inequality by first improving Borodin (2006)'s result for Banach spaces by weakening his condition on the sequence ${d_n}$. The weakened condition on $d_n$ requires refinement of Borodin's construction to extract an element in $X$, whose distances from the nested subspaces are precisely the given values $d_n$.
Leavitt path algebras with finitely presented irreducible representations

Abstract Let E be an arbitrary graph, K be any field and let L = L K ( E ) be the corresponding Leavitt path algebra. Necessary and sufficient conditions (both graphical and algebraic) are given under which all the irreducible representations of L are finitely presented. In this case, the graph E turns out to be row-finite and the cycles in E form an artinian partial ordered set under a defined relation ≥. When the graph is E is finite, the above graphical conditions were shown in [6] to be equivalent to L K ( E ) having finite Gelfand–Kirillov dimension. Examples are constructed showing that this equivalence no longer holds for infinite graphs and a complete description is obtained of Leavitt path algebras over arbitrary graphs having finite Gelfand–Kirillov dimensions. The “building blocks” for these algebras seem to be von Neumann rings and the Laurent polynomial ring K [ x , x − 1 ] .
Banach envelopes in symmetric spaces of measurable operators

We study Banach envelopes for commutative symmetric sequence or function spaces, and noncommutative symmetric spaces of measurable operators. We characterize the class (HC) of quasi-normed symmetric sequence or function spaces E for which their Banach envelopes \(\widehat{E}\) are also symmetric spaces. The class of symmetric spaces satisfying (HC) contains but is not limited to order continuous spaces. Let \(\mathcal {M}\) be a non-atomic, semifinite von Neumann algebra with a faithful, normal, \(\sigma \)-finite trace \(\tau \) and E be as symmetric function space on \([0,\tau (\mathbf 1 ))\) or symmetric sequence space. We compute Banach envelope norms on \(E(\mathcal {M},\tau )\) and \(C_E\) for any quasi-normed symmetric space E. Then we show under assumption that \(E\in (HC)\) that the Banach envelope \(\widehat{E(\mathcal {M},\tau )}\) of \(E(\mathcal {M},\tau )\) is equal to \(\widehat{E}\left( \mathcal {M},\tau \right) \) isometrically. We also prove the analogous result for unitary matrix spaces \(C_E\).
Log rationally connected surfaces

In this paper, combining the works of Miyanishi-Tsunoda and Keel-McKernan, we prove the log Castelnuovo's rationality criterion for smooth quasiprojective surfaces over complex numbers.
On the Vinogradov mean value

We discuss the recent work of C. Demeter, L. Guth and the author on the proof of the Vinogradov Main Conjecture using the decoupling theory for curves.
Towards Random Metasurface based Devices

Using full wave simulations and a transmission matrix approach, we design and then realize random metasurface lenses with anisotropic nanorods, and show that we can obtain a diffraction limited focal spot for all polarizations.
Compact group automorphisms, addition formulas and Fuglede-Kadison determinants

For a countable amenable group and an element f in the integral group ring Z being invertible in the group von Neumann algebra of , we show that the entropy of the shift action of on the Pontryagin dual of the quotient of Z by its left ideal generated by f is the logarithm of the Fuglede-Kadison determinant of f. For the proof, we establish an ‘ p -version of Rufus Bowen’s denition of topological entropy, addition formulas for group extensions of countable amenable group actions, and an approximation formula for the Fuglede-Kadison determinant of f in terms of the determinants of perturbations of the compressions of f.
Rigid local systems and alternating groups

We show that some very simple to write one parameter families of exponential sums on the affine line in characteristic p have alternating groups as their geometric monodromy groups.
A Finite Element Method for High-Contrast Interface Problems with Error Estimates Independent of Contrast

We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $$L^2$$ norm and $$H^1$$ weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.
Signature Characters of Highest-Weight Representations of $U_{q}(\mathfrak {gl}_{n})$

We consider \(U_{q}(\mathfrak {gl}_{n})\), the quantum group of type A for |q| = 1, q generic. We provide formulas for signature characters of irreducible finite-dimensional highest weight modules and Verma modules. In both cases, the technique involves combinatorics of the Gelfand-Tsetlin bases. As an application, we obtain information about unitarity of finite-dimensional irreducible representations for arbitrary q: we classify the continuous spectrum of the unitarity locus. We also recover some known results in the classical limit \(q \rightarrow 1\) that were obtained by different means. Finally, we provide several explicit examples of signature characters.
ON MODULI SPACES AND CW STRUCTURES ARISING FROM MORSE THEORY ON HILBERT MANIFOLDS

This paper proves some results on negative gradient dynamical systems of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain compactified moduli spaces, orientation formulas, and CW structures of the underlying manifolds.
Creature forcing and topological Ramsey spaces

Abstract This article introduces a line of investigation into connections between creature forcings and topological Ramsey spaces. Three examples of sets of pure candidates for creature forcings are shown to contain dense subsets which are actually topological Ramsey spaces. A new variant of the product tree Ramsey theorem is proved in order to obtain the pigeonhole principles for two of these examples.
Geometric and Analytic Quasiconformality in Metric Measure Spaces

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism f : X → Y between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When X and Y have locally Q-bounded geometry and Y is contained in an Alexandrov space of curvature bounded above, the sharpness of our results implies that, as in the classical case, the modular and pointwise outer dilatations of f are related by KO(f) = esssupHO(x, f).
Analogical Inference for Multi-relational Embeddings

Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of knowledge-based inference in a broad range of applications. This paper proposes a novel framework for optimizing the latent representations with respect to the \textit{analogical} properties of the embedded entities and relations. By formulating the learning objective in a differentiable fashion, our model enjoys both theoretical power and computational scalability, and significantly outperformed a large number of representative baseline methods on benchmark datasets. Furthermore, the model offers an elegant unification of several well-known methods in multi-relational embedding, which can be proven to be special instantiations of our framework.
A division algorithm approach to p-adic Sylvester expansions

Abstract A method of constructing finite p -adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci–Sylvester (greedy) algorithm by iterating a p -adic division algorithm. The method extends to irrational p -adics that have an embedding in the reals.
CONTINUITY OF THE VOLUME OF SIMPLICES IN CLASSICAL GEOMETRY

It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices. This verifies affirmatively a conjecture of John Minor.
Binary hidden Markov models and varieties

This paper closely examines HMMs in which all the hidden random variables are binary. Its main contributions are (1) a birational parametrization for every such HMM, with an explicit inverse for recovering the hidden parameters in terms of observables, (2) a semialgebraic model membership test for every such HMM, and (3) minimal dening equations for the 4-node fully binary model, comprising 21 quadrics and 29 cubics, which were computed using Grobner bases in the cumulant coordinates of Sturmfels and Zwiernik. The new model parameters in (1) are rationally identiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zariski closure is therefore a rational projective variety of dimension 5. Grobner basis computations for the model and its graph are found to be considerably faster using these parameters. In the case of two hidden states, item (2) supersedes a previous algorithm of Schonhuth which is only generically dened, and the dening equations (3) yield new invariants for HMMs of all lengths 4. Such invariants have been used successfully in model selection problems in phylogenetics, and one can hope for similar applications in the case of HMMs.
Local Regularity for the Modified SQG Patch Equation

We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified surface quasi-geostrophic (SQG) equations. These involve a parameter α that appears in the power of the kernel in their Biot-Savart laws and describes the degree of regularity of the equation. The values α=0 and α=½ correspond to the two-dimensional Euler and SQG equations, respectively. We establish here local-in-time regularity for these models, for all α ∊ (0,½) on the whole plane and for all small α > 0 on the half-plane. We use the latter result in [16], where we show existence of regular initial data on the half-plane that lead to a finite-time singularity.© 2016 Wiley Periodicals, Inc.
Outer automorphism groups of right-angled Coxeter groups are either large or virtually abelian

We generalise the notion of a separating intersection of links (SIL) to give necessary and sufficient criteria on the defining graph $\Gamma$ of a right-angled Coxeter group $W_\Gamma$ so that its outer automorphism group is large: that is, it contains a finite index subgroup that admits the free group $F_2$ as a quotient. When $Out(W_\Gamma)$ is not large, we show it is virtually abelian. We also show that the same dichotomy holds for the outer automorphism groups of graph products of finite abelian groups. As a consequence, these groups have property (T) if and only if they are finite, or equivalently $\Gamma$ contains no SIL.
Efficient Symmetric Norm Regression via Linear Sketching

We provide efficient algorithms for overconstrained linear regression problems with size $n \times d$ when the loss function is a symmetric norm (a norm invariant under sign-flips and coordinate-permutations). An important class of symmetric norms are Orlicz norms, where for a function $G$ and a vector $y \in \mathbb{R}^n$, the corresponding Orlicz norm $\|y\|_G$ is defined as the unique value $\alpha$ such that $\sum_{i=1}^n G(|y_i|/\alpha) = 1$. When the loss function is an Orlicz norm, our algorithm produces a $(1 + \varepsilon)$-approximate solution for an arbitrarily small constant $\varepsilon > 0$ in input-sparsity time, improving over the previously best-known algorithm which produces a $d \cdot \polylog n$-approximate solution. When the loss function is a general symmetric norm, our algorithm produces a $\sqrt{d} \cdot \polylog n \cdot \mathrm{mmc}(\ell)$-approximate solution in input-sparsity time, where $\mathrm{mmc}(\ell)$ is a quantity related to the symmetric norm under consideration. To the best of our knowledge, this is the first input-sparsity time algorithm with provable guarantees for the general class of symmetric norm regression problem. Our results shed light on resolving the universal sketching problem for linear regression, and the techniques might be of independent interest to numerical linear algebra problems more broadly.
AGen: Adaptable Generative Prediction Networks for Autonomous Driving

In highly interactive driving scenarios, accurate prediction of other road participants is critical for safe and efficient navigation of autonomous cars. Prediction is challenging due to the difficulty in modeling various driving behavior, or learning such a model. The model should be interactive and reflect individual differences. Imitation learning methods, such as parameter sharing generative adversarial imitation learning (PS-GAIL), are able to learn interactive models. However, the learned models average out individual differences. When used to predict trajectories of individual vehicles, these models are biased. This paper introduces an adaptable generative prediction framework (AGen), which performs online adaptation of the offline learned models to recover individual differences for better prediction. In particular, we combine the recursive least square parameter adaptation algorithm (RLS-PAA) with the offline learned model from PS-GAIL. RLS-PAA has analytical solutions and is able to adapt the model for every single vehicle efficiently online. The proposed method is able to reduce the root mean squared prediction error in a 2.5 s time window by 60%, compared with PS-GAIL.
MCE 2018: The 1st Multi-Target Speaker Detection and Identification Challenge Evaluation.

The Multi-target Challenge aims to assess how well current speech technology is able to determine whether or not a recorded utterance was spoken by one of a large number of blacklisted speakers. It is a form of multi-target speaker detection based on real-world telephone conversations. Data recordings are generated from call center customer-agent conversations. The task is to measure how accurately one can detect 1) whether a test recording is spoken by a blacklisted speaker, and 2) which specific blacklisted speaker was talking. This paper outlines the challenge and provides its baselines, results, and discussions.
Contextualizing the SAT: Experimental Evidence on College Admission Recommendations for Low-SES Applicants:

Although it is well established that college entrance exams have become a key factor for admission to selective institutions, less is known about the influence of test scores in relation to other a...
Verifiable Registration-Based Encryption

In recent work, Garg, Hajiabadi, Mahmoody, and Rahimi [18] introduced a new encryption framework, which they referred to as Registration-Based Encryption (RBE). The central motivation behind RBE was to provide a novel methodology for solving the well-known key-escrow problem in Identity-Based Encryption (IBE) systems [33]. Informally, in an RBE system, there is no private-key generator unlike IBE systems, but instead, it is replaced with a public key accumulator. Every user in an RBE system samples its own public-secret key pair and sends the public key to the accumulator for registration. The key accumulator has no secret state and is only responsible for compressing all the registered user identity-key pairs into a short public commitment. Here the encryptor only requires the compressed parameters along with the target identity, whereas a decryptor requires supplementary key material along with the secret key associated with the registered public key.