cssi/SciSciGPT-SciSciNet huggingface dataset:
Patchwork Kriging for large-scale Gaussian process regression

This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patching together the local GP models nearly seamlessly to ensure that the local GP models for two neighboring regions produce nearly the same response prediction and prediction error variance on the boundary between the two regions. This largely mitigates the well-known discontinuity problem that degrades the prediction accuracy of existing local partitioned GP methods over regional boundaries. Our main innovation is to represent the continuity conditions as additional pseudoobservations that the differences between neighboring GP responses are identically zero at an appropriately chosen set of boundary input locations. To predict the response at any input location, we simply augment the actual response observations with the pseudo-observations and apply standard GP prediction methods to the augmented data. In contrast to heuristic continuity adjustments, this has an advantage of working within a formal GP framework, so that the GP-based predictive uncertainty quantification remains valid. Our approach also inherits a sparse block-like structure for the sample covariance matrix, which results in computationally efficient closed-form expressions for the predictive mean and variance. In addition, we provide a new spatial partitioning scheme based on a recursive space partitioning along local principal component directions, which makes the proposed approach applicable for regression domains having more than two dimensions. Using three spatial datasets and three higher dimensional datasets, we investigate the numerical performance of the approach and compare it to several state-of-the-art approaches.
Perfect sampling of GI/GI/c queues

We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling from the past protocol. In particular, we use a coupled multi-server vacation system as the upper bound process and develop an algorithm to simulate the vacation system backward in time from stationarity at time zero. The algorithm has finite expected termination time with mild moment assumptions on the interarrival time and service time distributions.
SU(2)-Cyclic Surgeries on Knots

A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two SU(2)-cyclic surgery coefficients is bounded by the sum of the absolute values of their numerators. This is an analog of Culler-Gordon-Luecke-Shalen's cyclic surgery theorem.
Banach algebras, Samelson products, and the Wang differential

Assume that given a principal G bundle ζ : P → Sk (with k ≥ 2) and a Banach algebra B upon which G acts continuously. Let denote the associated bundle and let denote the associated Banach algebra of sections. Then π*GLAζ⊗B is determined by a mostly degenerate spectral sequence and by a Wang differential We show that if B is a C*-algebra then the differential is given explicitly in terms of an enhanced Samelson product with the clutching map of the principal bundle. Analogous results hold after localization and in the setting of topological K-theory. We illustrate our technique with a close analysis of the invariants associated to the C*-algebra of sections of the bundle constructed from the Hopf bundle ζ : S7 → S4 and by the conjugation action of S3 on M2 = M2(ℂ). We compare and contrast the information obtained from the homotopy groups π*(U◦Aζ⊗M2), the rational homotopy groups π*(U◦Aζ⊗M2) ⊗ ℚ and the topological K-theory groups K*(Aζ⊗M2), where U◦B is the connected component of the unitary group of the C*-algebra B.
On tame subgroups of finitely presented groups

We prove that the free product of two finitely presented locally tame groups is locally tame and describe many examples of tame subgroups of finitely presented groups. We also include some open problems related to tame subgroups.
Some examples of quasiisometries of nilpotent Lie groups

We construct quasiisometries of nilpotent Lie groups. In particular, for any simply connected nilpotent Lie group N , we construct quasiisometries from N to itself that is not at finite distance from any map that is a composition of left translations and automorphisms. We also construct biLipschitz maps of the Heisenberg groups that send vertical lines to curves that are not vertical lines.
A Faster Solution to Smale's 17th Problem I: Real Binomial Systems

Suppose F:=(f_1,ldots,f_n) is a system of random n-variate polynomials with f_i having degree leq\!d_i and the coefficient of x^a_1 _1\cdots x^a_n _n in f_i being an independent complex Gaussian of mean 0 and variance \fracd_i! a_1!\cdots a_n!left(d_i-\sum^n_j=1 a_j \right)! . Recent progress on Smale's 17þth Problem by Lairez --- building upon seminal work of Shub, Beltran, Pardo, Bu rgisser, and Cucker --- has resulted in a deterministic algorithm that finds a single (complex) approximate root of F using just N^O(1) arithmetic operations on average, where N\!:=\!\sum^n_i=1 \frac(n+d_i)! n!d_i! (=n(n+\max_i d_i)^O(\min\n,\max_i d_i)\ ) is the maximum possible total number of monomial terms for such an F. However, can one go faster when the number of terms is smaller, and we restrict to real coefficient and real roots? And can one still maintain average-case polynomial-time with more general probability measures? We show the answer is yes when F is instead a binomial system --- a case whose numerical solution is a key step in polyhedral homotopy algorithms for solving arbitrary polynomial systems. We give a deterministic algorithm that finds a real approximate root (or correctly decides there are none) using just O(n^3log^2(n\max_i d_i)) arithmetic operations on average. Furthermore, our approach allows real Gaussians with arbitrary variance. We also discuss briefly the obstructions to maintaining average-case time polynomial in nlog \max_i d_i when F has more terms.
Real Interpolation between Row and Column Spaces

We give an equivalent expression for the $K$-functional associated to the pair of operator spaces $(R,C)$ formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair $(M_n(R), M_n(C))$ (uniformly over $n$). More generally, the same result is valid when $M_n$ (or $B(\ell_2)$) is replaced by any semi-finite von Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust--Piquard) that is valid for the Lorentz spaces $L_{p,q}(\tau)$ associated to a non-commutative measure $\tau$, simultaneously for the whole range $1\le p,q 2$. Actually, the main novelty is the case $p=2,q\not=2$. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert-Schmidt one.
UWB Channel Sounding and Modeling for UAV Air-to-Ground Propagation Channels

Unmanned aerial vehicles (UAVs) are expected to be used extensively in the near future in applications such as aerial surveillance, transportation, and disaster assistance. The conditions under which UAVs operate are different from those of conventional piloted aircrafts. This necessitates development of new air-to-ground (AG) propagation channel models for UAVs. To our best knowledge, there are limited studies in the literature on sounding and modeling of ultrawideband (UWB) AG propagation channels. In this work, comprehensive UWB measurements are conducted for various UAV communication scenarios using Time Domain P410 UWB kits. Both time and frequency domain analysis of the measured data are carried out. Based on the measured data, stochastic path loss and multipath channel models are developed to characterize AG UWB propagation channels
Testing for high‐dimensional geometry in random graphs

We study the problem of detecting the presence of an underlying high-dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erdős-Renyi random graph G(n, p). Under the alternative, the graph is generated from the G(n,p,d) model, where each vertex corresponds to a latent independent random vector uniformly distributed on the sphere Sd−1, and two vertices are connected if the corresponding latent vectors are close enough. In the dense regime (i.e., p is a constant), we propose a near-optimal and computationally efficient testing procedure based on a new quantity which we call signed triangles. The proof of the detection lower bound is based on a new bound on the total variation distance between a Wishart matrix and an appropriately normalized GOE matrix. In the sparse regime, we make a conjecture for the optimal detection boundary. We conclude the paper with some preliminary steps on the problem of estimating the dimension in G(n,p,d). © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 503–532, 2016
Shear-transformation-zone theory of viscosity, diffusion, and stretched exponential relaxation in amorphous solids.

The shear-transformation-zone (STZ) theory has been remarkably successful in accounting for broadly peaked, frequency-dependent, viscoelastic responses of amorphous systems near their glass temperatures ${T}_{g}$. This success is based on the theory's first-principles prediction of a wide range of internal STZ transition rates. Here, I show that the STZ rate distribution causes the Newtonian viscosity to be strongly temperature dependent; and I propose that it is this temperature dependence, rather than any heterogeneity-induced enhancement of diffusion, that is at least in part responsible for Stokes-Einstein violations near ${T}_{g}$. I also show that stretched-exponential relaxation of density fluctuations emerges naturally from the same distribution of STZ transition rates that predicts the viscoelastic behavior. To be consistent with observations of Fickian diffusion near ${T}_{g}$, however, an STZ-based diffusion theory somehow must include the cascades of correlated displacement events that are seen in low-temperature numerical simulations.
Required behavior of sequence diagrams: Semantics and conformance

Many reusable software artifacts such as design patterns and design aspects make use of UML sequence diagrams to describe interaction behaviors. When a pattern or an aspect is reused in an application, it is important to ensure that the sequence diagrams for the application conform to the corresponding sequence diagrams for the pattern or aspect. Reasoning about conformance relationship between sequence diagrams has not been addressed adequately in literature. In this article, we focus on required behaviors specified by a UML sequence diagram and provide a semantic-based formalization of conformance relationships between sequence diagrams. A novel trace semantics is first given that captures precisely required behaviors. A refinement relation between sequence diagrams is then defined based on the semantics. The refinement relation allows a sequence diagram to be refined by changing its structure so long as its required behaviors are preserved. A conformance relation between sequence diagrams is finally given that includes the refinement relation as a special case. It allows one to introduce and rename lifelines, messages, and system variables when reusing sequence diagrams. Properties of the semantics, refinement, and conformance relations are studied. Two case studies are provided to illustrate the efficacy of semantic-based conformance reasoning.
On the longest common pattern contained in two or more random permutations

AbstractWeprovideupperandlowerboundsfortheexpectedlengthE(L n,m )ofthelongestcommonpatterncontainedinmrandompermutationsoflengthn. WealsoaddressthetightnessoftheconcentrationofL n,m aroundE(L n,m ). 1 Introduction Let π = π 1 π 2 ...π n and σ = σ 1 σ 2 ...σ k be permutations, where k < n.We say that σ is a pattern contained in π if there are a series of entriesin π, not necessarily consecutive, which have the same relative ordering asσ. For instance, when π = 153642 and σ = 132, we see that π containsthe subsequence 1,6,4, which has the same relative ordering as 1,3,2 in thesense that both have their smallest entry ﬁrst, their largest second, and theirmiddle last. Thus π = 153642 contains the pattern σ = 132. Formally, wesay σ is a pattern contained in π if there exist indices i 1 < i 2 < ... < i k suchthat the sequence π i 1 π i 2 ...π i k is order isomorphic to σ; i.e., for any a and b,π i a < π i b if and only if σ a < σ b .Given m permutations π 1 ,...,π m ∈ S n , a common pattern is a permuta-tion σ which is a pattern contained in all of the π
Algorithms for item categorization based on ordinal ranking data

We present a new method for identifying the latent categorization of items based on their rankings. Complimenting a recent work that uses a Dirichlet prior on preference vectors and variational inference, we show that this problem can be effectively dealt with using existing community detection algorithms, with the communities corresponding to item categories. In particular we convert the bipartite ranking data to a unipartite graph of item affinities, and apply community detection algorithms. In this context we modify an existing algorithm - namely the label propagation algorithm to a variant that uses the distance between the nodes for weighting the label propagation - to identify the categories. We propose and analyze a synthetic ordinal ranking model and show its relation to the recently much studied stochastic block model. We test our algorithms on synthetic data and compare performance with several popular community detection algorithms. We also test the method on real data sets of movie categorization from the Movie Lens database. In all of the cases our algorithm is able to identify the categories for a suitable choice of tuning parameter.
Statistical Inference for Cluster Trees

A cluster tree provides an intuitive summary of a density function that reveals essential structure about the high-density clusters. The true cluster tree is estimated from a finite sample from an unknown true density. This paper addresses the basic question of quantifying our uncertainty by assessing the statistical significance of different features of an empirical cluster tree. We first study a variety of metrics that can be used to compare different trees, analyzing their properties and assessing their suitability for our inference task. We then propose methods to construct and summarize confidence sets for the unknown true cluster tree. We introduce a partial ordering on cluster trees which we use to prune some of the statistically insignificant features of the empirical tree, yielding interpretable and parsimonious cluster trees. Finally, we provide a variety of simulations to illustrate our proposed methods and furthermore demonstrate their utility in the analysis of a Graft-versus-Host Disease (GvHD) data set.
A Study of MAC Address Randomization in Mobile Devices and When it Fails

MAC address randomization is a privacy technique whereby mobile devices rotate through random hardware addresses in order to prevent observers from singling out their traffic or physical location from other nearby devices. Adoption of this technology, however, has been sporadic and varied across device manufacturers. In this paper, we present the first wide-scale study of MAC address randomization in the wild, including a detailed breakdown of different randomization techniques by operating system, manufacturer, and model of device. We then identify multiple flaws in these implementations which can be exploited to defeat randomization as performed by existing devices. First, we show that devices commonly make improper use of randomization by sending wireless frames with the true, global address when they should be using a randomized address. We move on to extend the passive identification techniques of Vanhoef et al. to effectively defeat randomization in ~96% of Android phones. Finally, we show a method that can be used to track 100% of devices using randomization, regardless of manufacturer, by exploiting a previously unknown flaw in the way existing wireless chipsets handle low-level control frames.
Spectral uniqueness of radial semiclassical Schrodinger operators

We prove that the spectrum of an n-dimensional semiclassical radial Schrodinger operator determines the potential within a large class of potentials for which we assume no symmetry or analyticity. Our proof is based on the first two semiclassical trace invariants and on the isoperimetric inequality.
Deep compressive macroscopic fluorescence lifetime imaging

Compressive Macroscopic Fluorescence Lifetime Imaging (MFLI) is a novel technical implementation that enables monitoring multiple molecular interactions in macroscopic scale. Especially, we reported recently on the development of a hyperspectral wide-field time-resolved single-pixel imaging platform that facilitates whole-body in vivo lifetime imaging in less than 14 minutes. However, despite efficient data acquisition, the data processing of a Compressed Sensing (CS) based inversion plus lifetime fitting remain very time consuming. Herein, we propose to investigate the potential of deep learning for fast and accurate image formation. More precisely we developed a Convolutional Neural Network (CNN) called Net-FLICS (Network for Fluorescence Lifetime Imaging with Compressive Sensing) that reconstructs both intensity and lifetime images directly from raw CS measurements. Results show that better quality reconstruction can be obtained using Net-FLICS, for both simulation and experimental dataset, with almost negligible time compared to the traditional analytic methods. This first investigation suggests that Net-FLICS may be a powerful tool to enable CS-based lifetime imaging for real-time applications.
Detecting Relative Anomaly

System states that are anomalous from the perspective of a domain expert occur with high density in some anomaly detection problems. The performance of commonly used unsupervised anomaly detection methods may suffer in that setting, because they use density as a proxy for anomaly. We propose a novel concept for anomaly detection, called relative anomaly detection. It is tailored to be robust towards anomalies that have high density, by taking into account their location relative to the most typical observations. The approaches we develop are computationally feasible even for large data sets, and they allow real-time detection. We illustrate using data sets of potential scraping attempts and Wi-Fi channel utilization, both from Google.
Convolutional neural network steganalysis's application to steganography

This paper presents a novel approach to increase the performance bounds of image steganography under the criteria of minimizing distortion. The proposed approach utilizes a steganalysis convolutional neural network (CNN) framework to understand an image's model and embed in less detectable regions to preserve the model. In other word, the trained steganalysis CNN is used to calculate derivatives of the statistical model of an image with respect to embedding changes. The experimental results show that the proposed algorithm outperforms previous state-of-the-art methods in a wide range of low relative payloads when compared with HUGO, S-UNIWARD, and HILL by the state-of-the-art steganalysis.
Imaging with electromagnetic waves in terminating waveguides

We study an inverse scattering problem for Maxwell's equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered returns. The mathematical formulation of the inverse scattering problem is based on the electromagnetic Lippmann-Schwinger integral equation and an explicit calculation of the Green tensor. The image formation is carried with reverse time migration and with $\ell_1$ optimization.
Generalization for Adaptively-chosen Estimators via Stable Median

Datasets are often reused to perform multiple statistical analyses in an adaptive way, in which each analysis may depend on the outcomes of previous analyses on the same dataset. Standard statistical guarantees do not account for these dependencies and little is known about how to provably avoid overfitting and false discovery in the adaptive setting. We consider a natural formalization of this problem in which the goal is to design an algorithm that, given a limited number of i.i.d.~samples from an unknown distribution, can answer adaptively-chosen queries about that distribution. We present an algorithm that estimates the expectations of $k$ arbitrary adaptively-chosen real-valued estimators using a number of samples that scales as $\sqrt{k}$. The answers given by our algorithm are essentially as accurate as if fresh samples were used to evaluate each estimator. In contrast, prior work yields error guarantees that scale with the worst-case sensitivity of each estimator. We also give a version of our algorithm that can be used to verify answers to such queries where the sample complexity depends logarithmically on the number of queries $k$ (as in the reusable holdout technique). Our algorithm is based on a simple approximate median algorithm that satisfies the strong stability guarantees of differential privacy. Our techniques provide a new approach for analyzing the generalization guarantees of differentially private algorithms.
Geometric view on noneikonal waves

Abstract An axiomatic theory of classical nondissipative waves is proposed that is constructed based on the definition of a wave as a multidimensional oscillator. Waves are represented as abstract vectors | ψ 〉 in the appropriately defined space Ψ with a Hermitian metric. The metric is usually positive-definite but can be more general in the presence of negative-energy waves (which are typically unstable and must not be confused with negative-frequency waves). The very form of wave equations is derived from properties of Ψ. The generic wave equation is shown to be a quantumlike Schrodinger equation; hence one-to-one correspondence with the mathematical framework of quantum mechanics is established, and the quantum-mechanical machinery becomes applicable to classical waves “as is”. The classical wave action is defined as the density operator, | ψ 〉 〈 ψ | . The coordinate and momentum spaces, not necessarily Euclidean, need not be postulated but rather emerge when applicable. Various kinetic equations flow as projections of the von Neumann equation for | ψ 〉 〈 ψ | . The previously known action conservation theorems for noneikonal waves and the conventional Wigner–Weyl–Moyal formalism are generalized and subsumed under a unifying invariant theory. Whitham's equations are recovered as the corresponding fluid limit in the geometrical-optics approximation. The Liouville equation is also yielded as a special case, yet in a somewhat different limit; thus ray tracing, and especially nonlinear ray tracing, is found to be more subtle than commonly assumed. Applications of this axiomatization are also discussed, briefly, for some characteristic equations.
Riley's Conjecture on SL(2,R) Representations of 2-Bridge Knots

We prove a conjecture of Riley on SL(2, ℝ) representations of 2-bridge knot groups. As a consequence we show that if K is a 2-bridge knot with non-zero signature, then the fundamental group of the n-fold cyclic branched cover of K is left-orderable for n sufficiently large.
Minimum Probability Flow Learning

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable normalization factor or sampling from the equilibrium distribution of the model. This is achieved by establishing dynamics that would transform the observed data distribution into the model distribution, and then setting as the objective the minimization of the KL divergence between the data distribution and the distribution produced by running the dynamics for an infinitesimal time. Score matching, minimum velocity learning, and certain forms of contrastive divergence are shown to be special cases of this learning technique. We demonstrate parameter estimation in Ising models, deep belief networks and an independent component analysis model of natural scenes. In the Ising model case, current state of the art techniques are outperformed by at least an order of magnitude in learning time, with lower error in recovered coupling parameters.
Sparse linear isotonic models

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predictors; in particular, additive isotonic models (AIMs) assume the unknown transformations to be monotone. In this paper, we introduce sparse linear isotonic models (SLIMs) for highdimensional problems by hybridizing ideas in parametric sparse linear models and AIMs, which enjoy a few appealing advantages over both. In the high-dimensional setting, a two-step algorithm is proposed for estimating the sparse parameters as well as the monotone functions over predictors. Under mild statistical assumptions, we show that the algorithm can accurately estimate the parameters. Promising preliminary experiments are presented to support the theoretical results.
Onions in the Crosshairs: When The Man really is out to get you

We introduce and investigate targeting adversaries who selectively attack users of Tor or other secure-communication networks. We argue that attacks by such adversaries are more realistic and more significant threats to those most relying on Tor's protection than are attacks in prior analyses of Tor security. Previous research and Tor design decisions have focused on protecting against adversaries who are equally interested in any user of the network. Our adversaries selectively target users - e.g., those who visit a particular website or chat on a particular private channel - and essentially disregard Tor users other than these. We investigate three example cases where particular users might be targeted: a cabal conducting meetings using MTor, a published Tor multicast protocol; a cabal meeting on a private IRC channel; and users visiting a particular .onion website. In general for our adversaries, compromise is much faster and provides more feedback and possibilities for adaptation than do attacks examined in prior work. We also discuss selection of websites for targeting of their users based on the distribution across users of site activity. We describe adversaries attempting to learn the size of either a cabal meeting online or a set of sufficiently active visitors to a targeted site, and we describe adversaries attempting to identify guards of each targeted user. We compare the threat of targeting adversaries versus previously considered adversaries, and we briefly sketch possible countermeasures for resisting targeting adversaries.
Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries

In many applications, one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampled set of linear projections of the composite signal. In this study, the authors propose using the Dantzig selector model incorporating an overcomplete dictionary to separate a noisy undersampled collection of composite signals, and present an algorithm to efficiently solve the model. The Dantzig selector is a statistical approach to finding a solution to a noisy linear regression problem by minimising the l1 norm of candidate coefficient vectors while constraining the scope of the residuals. The Dantzig selector performs well in the recovery and separation of an unknown composite signal when the underlying coefficient vector is sparse. They propose a proximity operator-based algorithm to recover and separate unknown noisy undersampled composite signals using the Dantzig selector. They present numerical simulations comparing the proposed algorithm with the competing alternating direction method, and the proposed algorithm is found to be faster, while producing similar quality results. In addition, they demonstrate the utility of the proposed algorithm by applying it in various applications including the recovery of complex-valued coefficient vectors, the removal of impulse noise from smooth signals, and the separation and classification of a composition of handwritten digits.
Singular Lorentz-violating Lagrangians and associated Finsler structures

Several Lagrangians associated with classical limits of Lorentz-violating fermions in the standard model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin couplings are present, the Lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive-definite quadratic form defined on a desingularized variety.
Toward a fundamental theorem of quantal measure theory

In this paper we address the extension problem for quantal measures of path-integral type, concentrating on two cases: sequential growth of causal sets and a particle moving on the finite lattice ? n . In both cases, the dynamics can be coded into a vector-valued measure µ on ?, the space of all histories. Initially, µ is just defined on special subsets of ? called cylinder events, and we would like to extend it to a larger family of subsets (events) in analogy to the way this is done in the classical theory of stochastic processes. Since quantally µ is generally not of bounded variation, a new method is required. We propose a method that defines the measure of an event by means of a sequence of simpler events that in a suitable sense converges to the event whose measure we are seeking to define. To this end, we introduce canonical sequences approximating certain events, and we propose a measure-based criterion for the convergence of such sequences. Applying the method, we encounter a simple event whose measure is zero classically but non-zero quantally.
Renormalization group invariance in the Pinch Technique

We show how to construct, using an elementary extension of the Pinch Technique (PT), all offshell Green’s functions of a non-Abelian gauge theory so tha t they are locally gauge-invariant and renormalization-group invariant (RGI), as the S-matrix is , as well as being process-independent, coupling-constant independent (dimensional transmutation) and satisfying QED-like Ward identities. These PT-RGI Green’s functions are those of the gaug e potentials gAν , which is RGI itself in the PT. They differ from the standard PT Green’s functions by a simple multiplicative factor that removes their dependence on the renormalization point μ. Closed quark and ghost loops do not change this. We outline how to construct an approximate PT-RGI three-gluon vertex with three physical momentum scales but no μ-dependence, possibly phenomenologically useful. PTRGI Green’s functions obey a hierarchy of Schwinger-Dyson e quations (SDEs) that is organized by their momentum dependence in the UV, which can be found exactly from this hierarchy using the PT Ward identities. One of these Ward identities yields the gluon propagator as a functional of the vertex, allowing for an SDE truncation that is just the opposite of the often-used gauge technique that expresses the vertex approximately as a functional of the propagator, but which mishandles the UV behavior. Gluonic spin furnishes complications that would take too long to explain fully here, so we give details of this SDE hierarchy f or an analogous vertex and propagator in a modified form of φ 3 6 theory. The PT-RGI property of all off-shell Green’s functi ons, plus other long-known features of NAGTs coupled to quarks, leads to near-realization of the dreams of S-matrix theorists of the sixties: An effectively finite t heory whose symmetry structure (that of an NAGT) follows from unitarity, and having no fixed singul arities in angular momentum. Effective finiteness means that all Green’s functions, incl uding matrix elements of condensates, depend neither on a cutoff nor on a renormalization point μ; in conventional treatments, an offshell Green’s function will depend either on one (unrenorma lized, cutoff-dependent) or the other (renormalized, μ-dependent).
Robustness of causal claims

A causal claim is any assertion that invokes causal relationships between variables, for example, that a drug has a certain effect on preventing a disease. Causal claims are established through a combination of data and a set of causal assumptions called a "causal model." A claim is robust when it is insensitive to violations of some of the causal assumptions embodied in the model. This paper gives a formal definition of this notion of robustness, and establishes a graphical condition for quantifying the degree of robustness of a given causal claim. Algorithms for computing the degree of robustness are also presented.
SIEGEL MODULAR FORMS OF DEGREE TWO ATTACHED TO HILBERT MODULAR FORMS

Abstract Let E / Q be a real quadratic field and π 0 a cuspidal, irreducible, automorphic representation of GL ( 2 , A E ) with trivial central character and infinity type ( 2 , 2 n + 2 ) for some non-negative integer n. We show that there exists a non-zero Siegel paramodular newform F : H 2 → C with weight, level, Hecke eigenvalues, epsilon factor and L-function determined explicitly by π 0 . We tabulate these invariants in terms of those of π 0 for every prime p of Q .
A Framework for Coupled Deformation-Diffusion Analysis with Application to Degradation/Healing

SUMMARY This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation–diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framework for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework, we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always snon-negative, which is one of the main contributions of this paper. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution of this paper is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice versa, and their implication in modeling degradation/healing of materials. We show that the coupled response is both qualitatively and quantitatively different from the uncoupled response. Copyright © 2011 John Wiley & Sons, Ltd.
Almost-everywhere algorithmic stability and generalization error

We explore in some detail the notion of algorithmic stability as a viable framework for analyzing the generalization error of learning algorithms. We introduce the new notion of training stability of a learning algorithm and show that, in a general setting, it is sufficient for good bounds on generalization error. In the PAC setting, training stability is both necessary and sufficient for learnability. The approach based on training stability makes no reference to VC dimension or VC entropy. There is no need to prove uniform convergence, and generalization error is bounded directly via an extended McDiarmid inequality. As a result it potentially allows us to deal with a broader class of learning algorithms than Empirical Risk Minimization. We also explore the relationships among VC dimension, generalization error, and various notions of stability. Several examples of learning algorithms are considered.
Some quantum vertex algebras of Zamolodchikov-Faddeev type

This is a continuation of a previous study of quantum vertex algebras of the Zamolodchikov–Faddeev type. In this paper, we focus our attention on the special case associated to diagonal unitary rational quantum Yang–Baxter operators. We prove that the associated weak quantum vertex algebras, if not zero, are irreducible quantum vertex algebras with a normal basis in a certain sense.
An O(Log Log m)-Competitive Algorithm for Online Machine Minimization

This paper considers the online machine minimization problem, a basic real time scheduling problem. The setting for this problem consists of n jobs that arrive over time, where each job has a deadline by which it must be completed. The goal is to design an online scheduler that feasibly schedules the jobs on a nearly minimal number of machines. An algorithm is c-machine optimal if the algorithm will feasibly schedule a collection of jobs on c ·m machines if there exists a feasible schedule on m machines. For over two decades the best known result was a O(log P)-machine optimal algorithm, where P is the ratio of the maximum to minimum job size. In a recent breakthrough, a O(log m)-machine optimal algorithm was given. In this paper, we exponentially improve on this recent result by giving a O(log log m)-machine optimal algorithm.
The colored Kauffman skein relation and the head and tail of the colored Jones polynomial

Using the colored Kauffman skein relation, we study the highest and lowest 4n coefficients of the nth unreduced colored Jones polynomial of alternating links. This gives a natural extension of a re...
Theory @ Hard Probes 2015

Abstract Overview of the latest theory developments presented at the Hard Probes 2015 conference, held at McGill University, Montreal, Canada, in July 2015.
Monotonic Chunkwise Attention

Sequence-to-sequence models with soft attention have been successfully applied to a wide variety of problems, but their decoding process incurs a quadratic time and space cost and is inapplicable to real-time sequence transduction. To address these issues, we propose Monotonic Chunkwise Attention (MoChA), which adaptively splits the input sequence into small chunks over which soft attention is computed. We show that models utilizing MoChA can be trained efficiently with standard backpropagation while allowing online and linear-time decoding at test time. When applied to online speech recognition, we obtain state-of-the-art results and match the performance of a model using an offline soft attention mechanism. In document summarization experiments where we do not expect monotonic alignments, we show significantly improved performance compared to a baseline monotonic attention-based model.
SafeSpec: Banishing the Spectre of a Meltdown with Leakage-Free Speculation

Speculative attacks, such as Spectre and Meltdown, target speculative execution to access privileged data and leak it through a side-channel. In this paper, we introduce (SafeSpec), a new model for supporting speculation in a way that is immune to the side-channel leakage by storing side effects of speculative instructions in separate structures until they commit. Additionally, we address the possibility of a covert channel from speculative instructions to committed instructions before these instructions are committed. We develop a cycle accurate model of modified design of an x86-64 processor and show that the performance impact is negligible.
Reliability of layered neural oscillator networks

We study the reliability of large networks of pulse-coupled oscillators in response to fluctuating stimuli. Reliability means that a stimulus elicits essentially identical responses upon repeated presentations. We view the problem on two scales: neuronal reliability, which concerns the repeatability of spike times of individual oscillators embedded within a network, and pooled-response reliability, which addresses the repeatability of the total output from the network. We find that individual embedded oscillators can be reliable or unreliable depending on network conditions, whereas pooled responses of sufficiently large networks are mostly reliable.
Using a distributional semantic vector space with a knowledge base for reasoning in uncertain conditions

Abstract The inherent inflexibility and incompleteness of commonsense knowledge bases (KB) has limited their usefulness. We describe a system called Displacer for performing KB queries extended with the analogical capabilities of the word2vec distributional semantic vector space (DSVS). This allows the system to answer queries with information which was not contained in the original KB in any form. By performing analogous queries on semantically related terms and mapping their answers back into the context of the original query using displacement vectors, we are able to give approximate answers to many questions which, if posed to the KB alone, would return no results. We also show how the hand-curated knowledge in a KB can be used to increase the accuracy of a DSVS in solving analogy problems. In these ways, a KB and a DSVS can make up for each other’s weaknesses.
SPACE-TIME FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract We consider non-linear time-fractional stochastic heat type equation ∂ t β u t ( x ) = − ν ( − Δ ) α / 2 u t ( x ) + I t 1 − β [ σ ( u ) W ⋅ ( t , x ) ] in ( d + 1 ) dimensions, where ν > 0 , β ∈ ( 0 , 1 ) , α ∈ ( 0 , 2 ] and d min { 2 , β − 1 } α , ∂ t β is the Caputo fractional derivative, − ( − Δ ) α / 2 is the generator of an isotropic stable process, I t 1 − β is the fractional integral operator, W ⋅ ( t , x ) is space–time white noise, and σ : R → R is Lipschitz continuous. Time fractional stochastic heat type equations might be used to model phenomenon with random effects with thermal memory. We prove existence and uniqueness of mild solutions to this equation and establish conditions under which the solution is continuous. Our results extend the results in the case of parabolic stochastic partial differential equations obtained in Foondun and Khoshnevisan (2009), Walsh (1986). In sharp contrast to the stochastic partial differential equations studied earlier in Foondun and Khoshnevisan (2009), Khoshnevisan (2014) and Walsh (1986), in some cases our results give existence of random field solutions in spatial dimensions d = 1 , 2 , 3 . Under faster than linear growth of σ , we show that time fractional stochastic partial differential equation has no finite energy solution. This extends the result of Foondun and Parshad (in press) in the case of parabolic stochastic partial differential equations. We also establish a connection of the time fractional stochastic partial differential equations to higher order parabolic stochastic differential equations.
ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR VARIETIES

Let E/ℚ be a totally real number field that is Galois over ℚ, and let π be a cuspidal, nondihedral automorphic representation of GL2(&#x1d538;E) that is in the lowest weight discrete series at every real place of E. The representation π cuts out a "motive" Met(π∞) from the l-adic middle degree intersection cohomology of an appropriate Hilbert modular variety. If l is sufficiently large in a sense that depends on π we compute the dimension of the space of Tate classes in Met(π∞). Moreover if the space of Tate classes on this motive over all finite abelian extensions k/E is at most of rank one as a Hecke module, we prove that the space of Tate classes in Met(π∞) is spanned by algebraic cycles.
A Double-Edged Sword: Security Threats and Opportunities in One-Sided Network Communication

One-sided network communication technologies such as RDMA and NVMe-over-Fabrics are quickly gaining adoption in production software and in datacenters. Although appealing for their low CPU utilization and good performance, they raise new security concerns that could seriously undermine datacenter software systems building on top of them. At the same time, they offer unique opportunities to help enhance security. Indeed, one-sided network communication is a double-edged sword in security. This paper presents our insights into security implications and opportunities of one-sided communication.
Generalized Batch Normalization: Towards Accelerating Deep Neural Networks

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appropriate choice for the centering and scaling procedure within the BN transformation, particularly if ReLU follows the normalization step. We present a Generalized Batch Normalization (GBN) transformation, which can utilize a variety of alternative deviation measures for scaling and statistics for centering, choices which naturally arise from the theory of generalized deviation measures and risk theory in general. When used in conjunction with the ReLU non-linearity, the underlying risk theory suggests natural, arguably optimal choices for the deviation measure and statistic. Utilizing the suggested deviation measure and statistic, we show experimentally that training is accelerated more so than with conventional BN, often with improved error rate as well. Overall, we propose a more flexible BN transformation supported by a complimentary theoretical framework that can potentially guide design choices.
On the atomicity of monoid algebras

Abstract Let M be a commutative cancellative monoid, and let R be an integral domain. The question of whether the monoid ring R [ x ; M ] is atomic provided that both M and R are atomic dates back to the 1980s. In 1993, Roitman gave a negative answer to the question for M = N 0 : he constructed an atomic integral domain R such that the polynomial ring R [ x ] is not atomic. However, the question of whether a monoid algebra F [ x ; M ] over a field F is atomic provided that M is atomic has been open since then. Here we offer a negative answer to this question. First, we exhibit for any infinite cardinal κ a torsion-free atomic monoid M of rank κ satisfying that the monoid domain R [ x ; M ] is not atomic for any integral domain R. Then for every n ≥ 2 and for each field F of finite characteristic we find a torsion-free atomic monoid M of rank n such that F [ x ; M ] is not atomic. Finally, we construct a torsion-free atomic monoid M of rank 1 such that Z 2 [ x ; M ] is not atomic.