cssi/SciSciGPT-SciSciNet huggingface dataset:
Continuity properties of best analytic approximation

Let $\A$ be the operator which assigns to each $m \times n$ matrix-valued function on the unit circle with entries in $H^\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \times n$ matrix-valued functions in the open unit disc. We study the continuity of $\A$ with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, $\A$ is continuous at any function whose superoptimal singular values are non-zero and is such that certain associated integer indices are equal to 1. We also obtain necessary conditions for continuity of $\A$ at point and a sufficient condition for the continuity of superoptimal singular values.
Robust Environmental Mapping by Mobile Sensor Networks

Constructing a spatial map of environmental parameters is a crucial step to preventing hazardous chemical leakages, forest fires, or while estimating a spatially distributed physical quantities such as terrain elevation. Although prior methods can do such mapping tasks efficiently via dispatching a group of autonomous agents, they are unable to ensure satisfactory convergence to the underlying ground truth distribution in a decentralized manner when any of the agents fail. Since the types of agents utilized to perform such mapping are typically inexpensive and prone to failure, this results in poor overall mapping performance in real-world applications, which can in certain cases endanger human safety. This paper presents a Bayesian approach for robust spatial mapping of environmental parameters by deploying a group of mobile robots capable of ad-hoc communication equipped with short-range sensors in the presence of hardware failures. Our approach first utilizes a variant of the Voronoi diagram to partition the region to be mapped into disjoint regions that are each associated with at least one robot. These robots are then deployed in a decentralized manner to maximize the likelihood that at least one robot detects every target in their associated region despite a non-zero probability of failure. A suite of simulation results is presented to demonstrate the effectiveness and robustness of the proposed method when compared to existing techniques.
A polynomial bound on the regularity of an ideal in terms of half of the syzygies

Let K be a field and let S = K[x_1, ..., x_n] be a polynomial ring. Consider a homogenous ideal I in S. Let t_i denote reg(Tor_i (S/I, K)), the maximal degree of an ith syzygy of S/I. We prove bounds on the numbers t_i for i > n/2 purely in terms of the previous t_i. As a result, we give bounds on the regularity of S/I in terms of as few as half of the numbers t_i. We also prove related bounds for arbitrary modules. These bounds are often much smaller than the known doubly exponential bound on regularity purely in terms of t_1.
A Sparse Estimate for Multisublinear Forms Involving Vector-valued Maximal Functions

We prove a sparse bound for the m -sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multisublinear operators are preserved via l r -valued extension. This observation is in turn used to deduce vector-valued, multilinear weighted norm inequalities for multisublinear operators obeying sparse bounds, which are out of reach for the extrapolation theory developed by Cruz-Uribe and Martell in Limited range multilinear extrapolation with applications to the bilinear Hilbert transform , preprint arXiv:1704.06833 (2017). As an example, vector-valued multilinear weighted inequalities for bilinear Hilbert transforms are deduced from the scalar sparse domination theorem of Domination of multilinear singular integrals by positive sparse forms , preprint arXiv:1603.05317.
Generalized direct change estimation in ising model structure

We consider the problem of estimating change in the dependency structure of two p-dimensional Ising models, based on respectively n1 and n2 samples drawn from the models. The change is assumed to be structured, e.g., sparse, block sparse, node-perturbed sparse, etc., such that it can be characterized by a suitable (atomic) norm. We present and analyze a norm-regularized estimator for directly estimating the change in structure, without having to estimate the structures of the individual Ising models. The estimator can work with any norm, and can be generalized to other graphical models under mild assumptions. We show that only one set of samples, say n2, needs to satisfy the sample complexity requirement for the estimator to work, and the estimation error decreases as c/√ min(n1, n2), where c depends on the Gaussian width of the unit norm ball. For example, for l1 norm applied to s- sparse change, the change can be accurately estimated with min(n1, n2) = O(s log p) which is sharper than an existing result n1 = O(s2 log p) and n2 = O(n21). Experimental results illustrating the effectiveness of the proposed estimator are presented.
Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterization

Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks~(RNNs). In this paper, we present an efficient parametrization of the transition matrix of an RNN that allows us to stabilize the gradients that arise in its training. Specifically, we parameterize the transition matrix by its singular value decomposition(SVD), which allows us to explicitly track and control its singular values. We attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD. By explicitly controlling the singular values, our proposed Spectral-RNN method allows us to easily solve the exploding gradient problem and we observe that it empirically solves the vanishing gradient issue to a large extent. We note that the SVD parameterization can be used for any rectangular weight matrix, hence it can be easily extended to any deep neural network, such as a multi-layer perceptron. Theoretically, we demonstrate that our parameterization does not lose any expressive power, and show how it controls generalization of RNN for the classification task. %, and show how it potentially makes the optimization process easier. Our extensive experimental results also demonstrate that the proposed framework converges faster, and has good generalization, especially in capturing long range dependencies, as shown on the synthetic addition and copy tasks, as well as on MNIST and Penn Tree Bank data sets.
Holographic pomeron and entropy

In dipole-dipole scattering at large rapidity $\ensuremath{\chi}=\mathrm{ln}﻿(s/{s}_{0})$, the induced instanton on the string world sheet carries entropy ${\mathbf{S}}_{k}=2({\ensuremath{\alpha}}_{\mathbf{P}k}\ensuremath{-}1)\ensuremath{\chi}$, with ${\ensuremath{\alpha}}_{\mathbf{P}k}\ensuremath{-}1$ the Pomeron intercept for a dipole source of N-ality $k$. We argue that this entropy is released promptly over a time ${t}_{R}\ensuremath{\approx}({\mathbf{b}}_{\ensuremath{\perp}}/\ensuremath{\chi}{)}^{3}/(4{\ensuremath{\alpha}}^{\ensuremath{'}})$, with ${\ensuremath{\alpha}}^{\ensuremath{'}}/2$ the Pomeron slope and ${\mathbf{b}}_{\ensuremath{\perp}}$ the impact parameter. This stringy entropy may explain the $3/2$ jump in the total charged multiplicities at about ten participants reported over a wide range of collider energies by PHOBOS. We predict the charged multiplicities in $pp$, $pA$ and central $AA$ collisions at LHC.
A Survey of Quantum Enhancements

In this short survey article we collect the current state of the art in the nascent field of quantum enhancements, a type of knot invariant defined by collecting values of quantum invariants of knots with colorings by various algebraic objects over the set of such colorings. This class of invariants includes classical skein invariants and quandle and biquandle cocycle invariants as well as new invariants.
Coalitional game with opinion exchange

In coalitional games, traditional coalitional game theory does not apply if different participants hold different opinions about the payoff function that corresponds to each subset of the coalition. In this paper, we propose a framework in which players can exchange opinions about their views of payoff functions and then decide the distribution of the value of the grand coalition. When all players are truth-telling, the problem of opinion consensus is decoupled from the coalitional game, but interesting dynamics will arise when players are strategic in the consensus phase. Assuming that all players are rational, the model implies that, if influential players are risk-averse, an efficient fusion of the distributed data is achieved at pure strategy Nash equilibrium, meaning that the average opinion will not drift. Also, without the assumption that all players are rational, each player can use an algorithmic R-learning process, which gives the same result as the pure strategy Nash equilibrium with rational players.
A Note on High-Dimensional Linear Regression With Interactions

ABSTRACTThe problem of interaction selection in high-dimensional data analysis has recently received much attention. This note aims to address and clarify several fundamental issues in interaction selection for linear regression models, especially when the input dimension p is much larger than the sample size n. We first discuss how to give a formal definition of “importance” for main and interaction effects. Then we focus on two-stage methods, which are computationally attractive for high-dimensional data analysis but thus far have been regarded as heuristic. We revisit the counterexample of Turlach and provide new insight to justify two-stage methods from the theoretical perspective. In the end, we suggest new strategies for interaction selection under the marginality principle and provide some simulation results.
Segmenting a surface mesh into pants using Morse theory

Two Morse theory based algorithms for pants decomposition of a surface mesh are proposed.Both of our pants decomposition algorithms run in much less time than the existing state- of-the-art method.The algorithms handle surfaces with and without boundaries.Our algorithms are robust against noise and other mesh imperfections. A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple closed curves embedded in the surface that decompose the surface into pants. In this paper, we present two Morse theory based algorithms for pants decomposition of a surface mesh. Both algorithms operates on a choice of an appropriate Morse function on the surface. The first algorithm uses this Morse function to identify handles that are glued systematically to obtain a pants decomposition. The second algorithm uses the Reeb graph of the Morse function to obtain a pants decomposition. Both algorithms work for surfaces with or without boundaries. Our preliminary implementation of the two algorithms shows that both algorithms run in much less time than an existing state-of-the-art method, and the Reeb graph based algorithm achieves the best time efficiency. Finally, we demonstrate the robustness of our algorithms against noise.
Freeze casting – A review of processing, microstructure and properties via the open data repository, FreezeCasting.net

Abstract Freeze-casting produces materials with complex, three-dimensional pore structures which may be tuned during the solidification process. The range of potential applications of freeze-cast materials is vast, and includes: structural materials, biomaterials, filtration membranes, pharmaceuticals, and foodstuffs. Fabrication of materials with application-specific microstructures is possible via freeze casting, however, the templating process is highly complex and the underlying principles are only partially understood. Here, we report the creation of a freeze-casting experimental data repository, which contains data extracted from ∼800 different freeze-casting papers (as of August 2017). These data pertain to variables that link processing conditions to microstructural characteristics, and finally, mechanical properties. The aim of this work is to facilitate broad dissemination of relevant data to freeze-casting researchers, promote better informed experimental design, and encourage modeling efforts that relate processing conditions to microstructure formation and material properties. An initial, systematic analysis of these data is provided and key processing-structure-property relationships posited in the freeze-casting literature are discussed and tested against the database. Tools for data visualization and exploration available through the web interface are also provided.
Random rigidity in the free group

We prove a rigidity theorem for the geometry of the unit ball in random subspaces of the scl norm in B1H of a free group. In a free group F of rank k, a random word w of length n (conditioned to lie in [F,F]) has scl(w)= log(2k−1)n∕6log(n)+o(n∕log(n)) with high probability, and the unit ball in a subspace spanned by d random words of length O(n) is C0 close to a (suitably affinely scaled) octahedron. A conjectural generalization to hyperbolic groups and manifolds (discussed in the appendix) would show that the length of a random geodesic in a hyperbolic manifold can be recovered from the bounded cohomology of the fundamental group.
Contaminant remediation decision analysis using information gap theory

Decision making under severe lack of information is a ubiquitous situation in nearly every applied field of engineering, policy, and science. A severe lack of information precludes our ability to determine a frequency of occurrence of events or conditions that impact the decision; therefore, decision uncertainties due to a severe lack of information cannot be characterized probabilistically. To circumvent this problem, information gap (info-gap) theory has been developed to explicitly recognize and quantify the implications of a severe lack of information in decision making. This paper presents a decision analysis based on info-gap theory developed for a contaminant remediation scenario. The analysis provides decision support in determining the fraction of contaminant mass to remove from the environment. An info-gap uncertainty model is developed to characterize uncertainty due to a lack of information concerning the contaminant flux. The info-gap uncertainty model groups nested, convex sets of functions defining contaminant flux over time based on their level of deviation from a nominal contaminant flux. The nominal contaminant flux defines a best estimate of contaminant flux over time based on existing, though incomplete, information. A robustness function is derived to quantify the maximum level of deviation from nominal that still ensures compliance for alternative decisions. An opportuneness function is derived to characterize the possibility of meeting a desired contaminant concentration level. The decision analysis evaluates how the robustness and opportuneness change as a function of time since remediation and as a function of the fraction of contaminant mass removed.
Primary Components of Codimension Two Lattice Basis Ideals

We provide explicit combinatorial descriptions of the primary components of codimension two lattice basis ideals. As an application, we compute the set of parameters for which a bivariate Horn system of hypergeometric differential equations is holonomic.
Dynamic Attack Detection in Cyber-Physical Systems With Side Initial State Information

This technical note studies the impact of side initial state information on the detectability of data deception attacks against cyber-physical systems. We assume the attack detector has access to a linear function of the initial system state that cannot be altered by an attacker. First, we provide a necessary and sufficient condition for an attack to be undetectable by any dynamic attack detector under each specific side information pattern. Second, we characterize attacks that can be sustained for arbitrarily long periods without being detected. Third, we define the zero state inducing attack, the only type of attack that remains dynamically undetectable regardless of the side initial state information available to the attack detector. Finally, we design a dynamic attack detector that detects detectable attacks.
Multiscale convergence properties for spectral approximations of a model kinetic equation

In this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of the kinetic distribution and, as such, is accompanied by standard algebraic estimates of the form $N^{-q}$, where $N$ is the number of modes and $q>0$ depends on the regularity of the solution. However, in the multiscale setting, the error estimate can be expressed in terms of the scaling parameter $\epsilon$, which measures the ratio of the mean-free-path to the characteristic domain length. We show that, for isotropic initial conditions, the error in the spectral approximation is $\mathcal{O}(\epsilon^{N+1})$. More surprisingly, the coefficients of the expansion satisfy super convergence properties. In particular, the error of the $\ell^{th}$ coefficient of the expansion scales like $\mathcal{O}(\epsilon^{2N})$ when $\ell =0$ and $\mathcal{O}(\epsilon^{2N+2-\ell})$ for all $1\leq \ell \leq N$. This result is significant, because the low-order coefficients correspond to physically relevant quantities of the underlying system. All the above estimates involve constants depending on $N$, the time $t$, and the initial condition. We investigate specifically the dependence on $N$, in order to assess whether increasing $N$ actually yields an additional factor of $\epsilon$ in the error. Numerical tests will also be presented to support the theoretical results.
Non-classification of Cartan subalgebras for a class of von Neumann algebras

Abstract We study the complexity of the classification problem for Cartan subalgebras in von Neumann algebras. We construct a large family of II1 factors whose Cartan subalgebras up to unitary conjugacy are not classifiable by countable structures, providing the first such examples. Additionally, we construct examples of II1 factors whose Cartan subalgebras up to conjugacy by an automorphism are not classifiable by countable structures. Finally, we show directly that the Cartan subalgebras of the hyperfinite II1 factor up to unitary conjugacy are not classifiable by countable structures, and deduce that the same holds for any McDuff II1 factor with at least one Cartan subalgebra.
Unimodular binary hierarchical models

Abstract Associated to each simplicial complex is a binary hierarchical model. We classify the simplicial complexes that yield unimodular binary hierarchical models. Our main theorem provides both a construction of all unimodular binary hierarchical models, together with a characterization in terms of excluded minors, where our definition of a minor allows the taking of links and induced complexes. A key tool in the proof is the lemma that the class of unimodular binary hierarchical models is closed under the Alexander duality operation on simplicial complexes.
Cryptographic Applications of Capacity Theory: On the Optimality of Coppersmith’s Method for Univariate Polynomials

We draw a new connection between Coppersmith’s method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic curves. Coppersmith’s method uses lattice basis reduction to construct an auxiliary polynomial that vanishes at the desired solutions. Capacity theory provides a toolkit for proving when polynomials with certain boundedness properties do or do not exist. Using capacity theory, we prove that Coppersmith’s bound for univariate polynomials is optimal in the sense that there are no auxiliary polynomials of the type he used that would allow finding roots of size \(N^{1/d+\epsilon }\) for any monic degree-d polynomial modulo N. Our results rule out the existence of polynomials of any degree and do not rely on lattice algorithms, thus eliminating the possibility of improvements for special cases or even superpolynomial-time improvements to Coppersmith’s bound. We extend this result to constructions of auxiliary polynomials using binomial polynomials, and rule out the existence of any auxiliary polynomial of this form that would find solutions of size \(N^{1/d+\epsilon }\) unless N has a very small prime factor.
Vision as an Interlingua: Learning Multilingual Semantic Embeddings of Untranscribed Speech

In this paper, we explore the learning of neural network embeddings for natural images and speech waveforms describing the content of those images. These embeddings are learned directly from the waveforms without the use of linguistic transcriptions or conventional speech recognition technology. While prior work has investigated this setting in the monolingual case using English speech data, this work represents the first effort to apply these techniques to languages beyond English. Using spoken captions collected in English and Hindi, we show that the same model architecture can be successfully applied to both languages. Further, we demonstrate that training a multilingual model simultaneously on both languages offers improved performance over the monolingual models. Finally, we show that these models are capable of performing semantic cross-lingual speech-to-speech retrieval.
Crystal Ball: On the Future High Energy Colliders

High energy particle colliders have been in the forefront of particle physics for more than three decades. At present the near term US, European and international strategies of the particle physics community are centered on full exploitation of the physics potential of the Large Hadron Collider (LHC) through its high-luminosity upgrade (HL-LHC). A number of next generation collider facilities have been proposed and are currently under consideration for the medium- and far-future of the accelerator-based high energy physics. In this paper we offer a uniform approach to evaluation of various accelerators based on the feasibility of their energy reach, performance reach and cost range. We briefly review such post-LHC options as linear e+e- colliders in Japan (ILC) or at CERN (CLIC), muon collider, and circular lepton or hadron colliders in China (CepC/SppC) and Europe (FCC). We conclude with a look into ultimate energy reach accelerators based on plasmas and crystals, and some perspectives for the far future of accelerator-based particle physics.
The culmination of an inverse cascade: Mean flow and fluctuations

Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained and what determines them and the fluctuations around them. A recent theory for the mean flow will be reviewed. The theory assumes that turbulence is excited by a forcing supported on small scales and uses a linear shear model to relate the turbulent momentum flux to the mean shear rate. Extending the theory, it will be shown here that the relation between the momentum flux and mean shear is valid, and the momentum flux is non-zero, for both an isotropic forcing and an anisotropic forcing, independent of the dissipation mechanism at small scales. This conclusion requires taking into account that the linear shear model is an approximation to the real system. The proportionality between the momentum flux and the inverse of the shear can then be inferred most simply on dimensional grounds. Moreover, for a homoge...
The simplification of singularities of Lagrangian and Legendrian fronts

We establish a full h-principle ( $$C^0$$ -close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy.
Non-rational centers of log canonical singularities

Abstract We show that if ( X , B ) is a log canonical pair with dim X ⩾ d + 2 , whose non-klt centers have dimension ⩾d, then X has depth ⩾ d + 2 at every closed point.
MDS Matrices over Small Fields: A Proof of the GM-MDS Conjecture

An MDS matrix is a matrix whose minors all have full rank. A question arising in coding theory is, what zero patterns can MDS matrices have. There is a natural combinatorial necessary condition (called the MDS condition) which is necessary over any field, and sufficient over very large fields by a probabilistic argument. Dau et al. (ISIT 2014) conjectured that the MDS condition is sufficient over small fields as well, and gave an algebraic conjecture which would imply this. In this work, we prove this conjecture.
Shape-constrained partial identification of a population mean under unknown probabilities of sample selection

Summary Estimating a population mean from a sample obtained with unknown selection probabilities is important in the biomedical and social sciences. Using a ratio estimator, Aronow & Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed values. In this paper, we show how to use auxiliary shape constraints on the population outcome distribution, such as symmetry or log-concavity, to obtain tighter bounds on the population mean. We use this method to estimate the performance of Aymara students, an ethnic minority in the north of Chile, in a national educational standardized test. We implement this method in the R package scbounds.
Phase-Sensitive Imaging of Ferromagnetic Resonance Using Ultrafast Heat Pulses

Researchers in spintronics seek to harness the spins of electrons to efficiently manipulate magnetization, for digital logic and data-storage applications. It is a challenge, however, to develop an instrument both fast and sensitive enough to track microscopic magnetic dynamics. The authors demonstrate an approach based on ultrafast laser heating to simultaneously image magnetic orientation and electric current, capturing the dynamics of both at gigahertz frequencies. This could be used to directly study current-induced torques in magnetic devices\char22{}a boon to both basic research and working technology.
SANTA: Self-aligned nanotrench ablation via Joule heating for probing sub-20 nm devices

Manipulating materials at the nanometer scale is challenging, particularly if alignment with nanoscale electrodes is desired. Here, we describe a lithography-free, self-aligned nanotrench ablation (SANTA) technique to create nanoscale “trenches” in a polymer like poly(methyl methacrylate) (PMMA). The nanotrenches are self-aligned with carbon nanotube (CNT) or graphene ribbon electrodes through a simple Joule heating process. Using simulations and experiments we investigated how the Joule power, ambient temperature, PMMA thickness, and substrate properties affect the spatial resolution of this technique. We achieved sub-20 nm nanotrenches, for the first time, by lowering the ambient temperature and reducing the PMMA thickness. We also demonstrated a functioning nanoscale resistive memory (RRAM) bit selfaligned with a CNT control device, achieved through the SANTA approach. This technique provides an elegant and inexpensive method to probe nanoscale devices using self-aligned electrodes, without the use of conventional alignment or lithography steps.
Semiparametric Estimation of a CES Demand System with Observed and Unobserved Product Characteristics

We develop a demand estimation framework with observed and unobserved product char- acteristics based on CES preferences. We show that our demand system can nest the logit demand system with observed and unobserved product characteristics, which has been widely used since Berry (1994); Berry et al. (1995). Furthermore, the demand system we develop can directly accommodate zero market shares by separating the extensive and the intensive margins. We apply our framework to the scanner data of cola sales, which shows that the estimated demand curves can even be upward sloping if zero market shares are not properly accommodated.
Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments

Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper develops a method to perform trajectory design by considering a low-fidelity model that accounts for model mismatch. The presented method begins by computing a conservative Forward Reachable Set (FRS) of a high-fidelity model's trajectories produced when tracking trajectories of a low-fidelity model over a finite time horizon. At runtime, the vehicle intersects this FRS with obstacles in the environment to eliminate trajectories that can lead to a collision, then selects an optimal plan from the remaining safe set. By bounding the time for this set intersection and subsequent path selection, this paper proves a lower bound for the FRS time horizon and sensing horizon to guarantee safety. This method is demonstrated in simulation using a kinematic Dubin's car as the low-fidelity model and a dynamic unicycle as the high-fidelity model.
Non-convex Finite-Sum Optimization Via SCSG Methods

We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods , for the smooth nonconvex finite-sum optimization problem. Only assuming the smoothness of each component, the complexity of SCSG to reach a stationary point with $E \|\nabla f(x)\|^{2}\le \epsilon$ is $O(\min\{\epsilon^{-5/3}, \epsilon^{-1}n^{2/3}\})$, which strictly outperforms the stochastic gradient descent. Moreover, SCSG is never worse than the state-of-the-art methods based on variance reduction and it significantly outperforms them when the target accuracy is low. A similar acceleration is also achieved when the functions satisfy the Polyak-Lojasiewicz condition. Empirical experiments demonstrate that SCSG outperforms stochastic gradient methods on training multi-layers neural networks in terms of both training and validation loss.
The integral chow ring of the stack of hyperelliptic curves of even genus

Let $g$ be an even positive integer. In this paper we compute the integral Chow ring of the stack of smooth hyperelliptic curves of genus $g$.
On the Strength of Connectedness of a Random Hypergraph

Bollob a s and Thomason (1985) proved that for each $k=k(n) \in [1, n-1]$, with high probability, the random graph process, where edges are added to vertex set $V=[n]$ uniformly at random one after another, is such that the stopping time of having minimal degree $k$ is equal to the stopping time of becoming $k$-(vertex-)connected. We extend this result to the $d$-uniform random hypergraph process, where $k$ and $d$ are fixed. Consequently, for $m=\frac{n}{d}(\ln n +(k-1)\ln \ln n +c)$ and $p=(d-1)! \frac{\ln n + (k-1) \ln \ln n +c}{n^{d-1}}$, the probability that the random hypergraph models $H_d(n, m)$ and $H_d(n, p)$ are $k$-connected tends to $e^{-e^{-c}/(k-1)!}.$
Metric mean dimension for algebraic actions of Sofic groups

Recently Bingbing Liang and Hanfeng Li computed the mean dimension and metric mean dimension for algebraic actions of amenable groups. We show how to extend their computation of metric mean dimension to the case of sofic groups, provided that the dual module is finitely generated. Additionally, we show that when the dual module is finitely presented that the mean dimension is the von Neumann rank. The proof also goes through introducing \ell^{p}-analogues of metric mean dimension, which may be seen as an obstruction to the equality of mean dimension and metric mean dimension.
Optimal quantization for the Cantor distribution generated by infinite similutudes

Let P be a Borel probability measure on ℝ generated by an infinite system of similarity mappings {Sj : j ∈ ℕ} such that $$P=\Sigma_{j=1}^{\infty}\frac{1}{2^{j}}P\circ{S}_j^{-1}$$ , where for each j ∈ ℕ and x ∈ ℝ, $$S_j(x)=\frac{1}{3^j}x+1-\frac{1}{3^{j-1}}$$ . Then, the support of P is the dyadic Cantor set C generated by the similarity mappings f1, f2 : ℝ → ℝ such that f1(x) = 1/3x and f2(x) = 1/3x+ 2/3 for all x ∈ ℝ. In this paper, using the infinite system of similarity mappings {Sj : j ∈ ℕ} associated with the probability vector $$(\frac{1}{2},\frac{1}{{{2^2}}},...)$$ , for all n ∈ ℕ, we determine the optimal sets of n-means and the nth quantization errors for the infinite self-similar measure P. The technique obtained in this paper can be utilized to determine the optimal sets of n-means and the nth quantization errors for more general infinite self-similar measures.
Sequence Classification with Neural Conditional Random Fields

The proliferation of sensor devices monitoring human activity generates voluminous amount of temporal sequences needing to be interpreted and categorized. Moreover, complex behavior detection requires the personalization of multi-sensor fusion algorithms. Conditional random fields (CRFs) are commonly used in structured prediction tasks such as part-of-speech tagging in natural language processing. Conditional probabilities guide the choice of each tag/label in the sequence conflating the structured prediction task with the sequence classification task where different models provide different categorization of the same sequence. The claim of this paper is that CRF models also provide discriminative models to distinguish between types of sequence regardless of the accuracy of the labels obtained if we calibrate the class membership estimate of the sequence. We introduce and compare different neural network based linear-chain CRFs and we present experiments on two complex sequence classification and structured prediction tasks to support this claim.
Pretentiously detecting power cancellation

Granville and Soundararajan have recently introduced the notion of pretentiousness in the study of multiplicative functions of modulus bounded by 1, essentially the idea that two functions which are similar in a precise sense should exhibit similar behavior. It turns out, somewhat surprisingly, that this does not directly extend to detecting power cancellation there are multiplicative functions which exhibit as much cancellation as possible in their partial sums that, modified slightly, give rise to functions which exhibit almost as little as possible. We develop two new notions of pretentiousness under which power cancellation can be detected, one of which applies to a much broader class of multiplicative functions.
Asymptotics for polynomials orthogonal in an indefinite metric

Abstract We continue studying polynomials generated by the Szegő recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results for the corresponding orthogonal polynomials and then translate them to the real line to obtain the Szegő asymptotics for the resulting polynomials. The latter polynomials give rise to a non-symmetric tridiagonal matrix but it is a finite-rank perturbation of a symmetric Jacobi matrix.
A SIEVE PROBLEM AND ITS APPLICATION

Let $\theta$ be an arithmetic function and let $\mathcal{B}$ be the set of positive integers $n=p_1^{\alpha_1} \cdots p_k^{\alpha_k}$, which satisfy $p_{j+1} \le \theta ( p_1^{\alpha_1}\cdots p_{j}^{\alpha_{j}})$ for $0\le j < k$. We show that $\mathcal{B}$ has a natural density, provide a criterion to determine whether this density is positive, and give various estimates for the counting function of $\mathcal{B}$. When $\theta(n)/n$ is non-decreasing, the set $\mathcal{B}$ coincides with the set of integers $n$ whose divisors $1=d_1< d_2 < \ldots <d_{\tau(n)}=n$ satisfy $d_{j+1} \le \theta( d_j )$ for $1\le j <\tau(n)$.
A model for rank one measure preserving transformations

Abstract We define a model for rank one measure preserving transformations in the sense of [2] . This is done by defining a new Polish topology on the space of codes, which are infinite rank one words, for symbolic rank one systems. We establish that this space of codes has the same generic dynamical properties as the space of (rank one) measure preserving transformations on the unit interval.
Detecting epistasis via Markov bases

Rapid research progress in genotyping techniques have allowed large genome-wide as- sociation studies. Existing methods often focus on determining associations between single loci and a specific phenotype. However, a particular phenotype is usually the result of complex relation- ships between multiple loci and the environment. In this paper, we describe a two-stage method for detecting epistasis by combining the traditionally used single-locus search with a search for multiway interactions. Our method is based on an extended version of Fisher's exact test. To perform this test, a Markov chain is constructed on the space of multidimensional contingency tables using the elements of a Markov basis as moves. We test our method on simulated data and compare it to a two-stage logistic regression method and to a fully Bayesian method, showing that we are able to detect the interacting loci when other methods fail to do so. Finally, we apply our method to a genome-wide data set consisting of 685 dogs and identify epistasis associated with canine hair length for four pairs of single nucleotide polymorphisms (SNPs).
Universality and clustering in 1 + 1 dimensional superstring-bit models

We construct a 1+1 dimensional superstring-bit model for {ital D}=3 type IIB superstring. This low dimension model escapes the problems encountered in higher dimension models: (1) It possesses full Galilean supersymmetry. (2) For noninteracting polymers of bits, the exactly soluble linear superpotential describing bit interactions is in a large universality class of superpotentials which includes ones bounded at spatial infinity. (3) The latter are used to construct a superstring-bit model with the clustering properties needed to define an {ital S} matrix for closed polymers of superstring bits. {copyright} {ital 1996 The American Physical Society.}
Tropical spectral theory of tensors

Abstract We introduce and study tropical eigenpairs of tensors, a generalization of the tropical spectral theory of matrices. We show the existence and uniqueness of an eigenvalue. We associate with a tensor a directed hypergraph and define a new type of cycle on such a hypergraph, which we call an H-cycle. The eigenvalue of a tensor turns out to be equal to the minimal normalized weighted length of H-cycles of the associated hypergraph. We show that the eigenvalue can be computed efficiently via a linear program.
ER=EPR, GHZ, and the consistency of quantum measurements

This paper illustrates various aspects of the ER=EPR conjecture. It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges. The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-Zeilinger pattern. The last part of the paper is about entanglement as a resource for quantum communication. ER=EPR provides a way to visualize protocols like quantum teleportation. In some sense teleportation takes place through the wormhole, but as usual, classical communication is necessary to complete the protocol.
How many randomly colored edges make a randomly colored dense graph rainbow Hamiltonian or rainbow connected

In this paper we study the randomly edge colored graph that is obtained by adding randomly colored random edges to an arbitrary randomly edge colored dense graph. In particular we ask how many colors and how many random edges are needed so that the resultant graph contains a fixed number of edge disjoint rainbow Hamilton cycles. We also ask when in the resultant graph every pair of vertices is connected by a rainbow path.
Levi Subgroup Actions on Schubert Varieties, Induced Decompositions of their Coordinate Rings, and Sphericity Consequences

Let L w be the Levi part of the stabilizer Q w in G L N (for left multiplication) of a Schubert variety X(w) in the Grassmannian G d,N . For the natural action of L w on $\mathbb {C}[X(w)]$ , the homogeneous coordinate ring of X(w) (for the Plucker embedding), we give a combinatorial description of the decomposition of $\mathbb {C}[X(w)]$ into irreducible L w -modules; in fact, our description holds more generally for the action of the Levi part L of any parabolic subgroup Q that is contained in Q w . This decomposition is then used to show that all smooth Schubert varieties, all determinantal Schubert varieties, and all Schubert varieties in G2,N are spherical L w -varieties.
Learning Generic Sentence Representations Using Convolutional Neural Networks

We propose a new encoder-decoder approach to learn distributed sentence representations that are applicable to multiple purposes. The model is learned by using a convolutional neural network as an encoder to map an input sentence into a continuous vector, and using a long short-term memory recurrent neural network as a decoder. Several tasks are considered, including sentence reconstruction and future sentence prediction. Further, a hierarchical encoder-decoder model is proposed to encode a sentence to predict multiple future sentences. By training our models on a large collection of novels, we obtain a highly generic convolutional sentence encoder that performs well in practice. Experimental results on several benchmark datasets, and across a broad range of applications, demonstrate the superiority of the proposed model over competing methods.
Automated Diagnosis of Lymphoma with Digital Pathology Images Using Deep Learning

Recent studies have shown promising results in using Deep Learning to detect malignancy in whole slide imaging, however, they were limited to just predicting a positive or negative finding for a specific neoplasm. We attempted to use Deep Learning with a convolutional neural network (CNN) algorithm to build a lymphoma diagnostic model for four diagnostic categories: (1) benign lymph node, (2) diffuse large B-cell lymphoma, (3) Burkitt lymphoma, and (4) small lymphocytic lymphoma. Our software was written in Python language. We obtained digital whole-slide images of Hematoxylin and Eosin stained slides of 128 cases including 32 cases for each diagnostic category. Four sets of 5 representative images, 40x40 pixels in dimension, were taken for each case. A total of 2,560 images were obtained from which 1,856 were used for training, 464 for validation, and 240 for testing. For each test set of 5 images, the predicted diagnosis was combined from the prediction of five images. The test results showed excellent diagnostic accuracy at 95% for image-by-image prediction and at 100% for set-by-set prediction. This preliminary study provided a proof of concept for incorporating automated lymphoma diagnostic screen into future pathology work-flow to augment the pathologists' productivity.
A class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature

We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a so-called global supersolution but does not require a global subsolution. As a consequence, we construct a class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature, extending a recent result of Holst, Nagy, and Tsogtgerel [HNT07] which constructed similar solutions in the presence of matter. We give a second proof of this result showing that vacuum solutions can be obtained as a limit of [HNT07] non-vacuum solutions. Our principal existence theorem is of independent interest in the near-CMC case, where it simplifies previously known hypotheses required for existence.
Gundy–Varopoulos martingale transforms and their projection operators on manifolds and vector bundles

This paper proves the $$L^p$$ boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms a la Gundy–Varopoulos for quite general diffusions on manifolds and vector bundles. Several specific examples and applications are presented: Lie groups of compact type, the Heisenberg group, $$\mathbb {SU}(2)$$ , and Riesz transforms on forms and spinors.
Connectivity of the coset poset and the subgroup poset of a group

We study the connectivity of the coset poset and the subgroup poset of a group, focusing in particular on simple connectivity. The coset poset was recently introduced by K. S. Brown in connection with the probabilistic zeta function of a group. We take Brown's study of the homotopy type of the coset poset further, and in particular generalize his results on direct products and classify direct products with simply connected coset posets. The homotopy type of the subgroup poset LðGÞ has been examined previously by Kratzer, Thevenaz, and Shareshian. We generalize some results of Kratzer and Thevenaz, and deter- mine p1ðLðGÞÞ in nearly all cases.
Testing separability of space--time functional processes

SummarySeparability is a common simplifying assumption on the covariance structure of spatiotemporal functional data. We present three tests of separability, one a functional extension of the Monte Carlo likelihood method of Mitchell et al. (2006) and two based on quadratic forms. Our tests are based on asymptotic distributions of maximum likelihood estimators and do not require Monte Carlo simulation. The main theoretical contribution of this paper is the specification of the joint asymptotic distribution of these estimators, which can be used to derive many other tests. The main methodological finding is that one of the quadratic form methods, which we call a norm approach, emerges as a clear winner in terms of finite-sample performance in nearly every setting we considered. This approach focuses directly on the Frobenius distance between the spatiotemporal covariance function and its separable approximation. We demonstrate the efficacy of our methods via simulations and application to Irish wind data.
Fast, Trainable, Multiscale Denoising

Denoising is a fundamental imaging problem. Versatile but fast filtering has been demanded for mobile camera systems. We present an approach to multiscale filtering which allows real-time applications on low-powered devices. The key idea is to learn a set of kernels that upscales, filters, and blends patches of different scales guided by local structure analysis. This approach is trainable so that learned filters are capable of treating diverse noise patterns and artifacts. Experimental results show that the presented approach produces comparable results to state-of-the-art algorithms while processing time is orders of magnitude faster.
Chemically non-equilibrated QGP and thermal photon elliptic flow

Abstract It has been discovered in recent heavy-ion experiments that elliptic and triangular flow of direct photons are underpredicted by most hydrodynamic models. I discuss possible enhancement mechanisms based on late chemical equilibration of the QGP and in-medium modification of parton distributions. Numerical hydrodynamic analyses indicate that they suppress early photon emission and visibly enhance thermal photon elliptic flow.
Wavelet ensemble Kalman filters

We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an example.