cssi/SciSciGPT-SciSciNet huggingface dataset:
Multiple Dirichlet series and moments of zeta and L-functions

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments of zeta functions and quadratic L-series. As an application of the theory, in a third section, we obtain the current best known error term for mean values of cubes of cent ral values of Dirichlet L-series. The methods utilized to derive this result are the convexity principle for functions of several complex-variables combined with a knowledge of groups of functional equations for certain multiple Dirichlet series.
PageRank on inhomogeneous random digraphs

Abstract We study the typical behavior of Google’s PageRank algorithm on inhomogeneous random digraphs, including directed versions of the Erdős–Renyi model, the Chung–Lu model, the Poissonian random graph and the generalized random graph. Specifically, we show that the rank of a randomly chosen vertex converges weakly to the attracting endogenous solution to the stochastic fixed-point equation R = D ∑ i = 1 N C i R i + Q , where ( N , Q , { C i } i ≥ 1 ) is a real-valued vector with N ∈ N , and the { R i } are i.i.d. copies of R , independent of ( N , Q , { C i } i ≥ 1 ) ; = D denotes equality in distribution. This result provides further evidence of the power-law behavior of PageRank on graphs whose in-degree distribution follows a power law.
Fixed Points of Competitive Threshold-Linear Networks.

Threshold-linear networks (TLNs) are models of neural networks that consist of simple, perceptron-like neurons and exhibit nonlinear dynamics determined by the network's connectivity. The fixed poi...
Distributed average tracking for second-order agents with nonlinear dynamics

This paper addresses distributed average tracking of physical second-order agents with nonlinear dynamics, where the interaction among the agents is described by an undirected graph. In both agents' and reference inputs' dynamics, there is a nonlinear term that satisfying the Lipschitz-type condition. To achieve the distributed average tracking problem in the presence of nonlinear term, a non-smooth filter and a control input are designed for each agent. The idea is that each filter outputs converge to the average of the reference inputs and the reference velocities asymptotically and in parallel each agent's position and velocity are driven to track its filter outputs. To overcome the nonlinear term unboundedness effect, novel state-dependent time varying gains are employed in each agent's filter and control input. In the proposed algorithm, each agent needs its neighbors' filters outputs besides its own filter outputs, absolute position and absolute velocity and its neighbors' reference inputs and reference velocities. Finally, the algorithm is simplified to achieve the distributed average tracking of physical second-order agents in the presence of an unknown bounded term in both agents' and reference inputs' dynamics.
Stochastic optimization for deep CCA via nonlinear orthogonal iterations

Deep CCA is a recently proposed deep neural network extension to the traditional canonical correlation analysis (CCA), and has been successful for multi-view representation learning in several domains. However, stochastic optimization of the deep CCA objective is not straightforward, because it does not decouple over training examples. Previous optimizers for deep CCA are either batch-based algorithms or stochastic optimization using large minibatches, which can have high memory consumption. In this paper, we tackle the problem of stochastic optimization for deep CCA with small minibatches, based on an iterative solution to the CCA objective, and show that we can achieve as good performance as previous optimizers and thus alleviate the memory requirement.
Clustering with capacity and size constraints: A deterministic approach

This paper discusses a deterministic clustering approach to capacitated resource allocation problems. In particular, the Deterministic Annealing (DA) algorithm from the data-compression literature, which bears a distinct analogy to the phase transformation under annealing process in statistical physics, is adapted to address problems pertaining to clustering with several forms of size constraints. These constraints are addressed through appropriate modifications of the basic DA formulation by judiciously adjusting the free-energy function in the DA algorithm. At a given value of the annealing parameter, the iterations of the DA algorithm are of the form of a Descent Method, which motivate scaling principles for faster convergence.
Ricci flow with surgery in higher dimensions

We present a new curvature condition which is preserved by the Ricci flow in higher dimensions. For initial metrics satisfying this condition, we establish a higher dimensional version of Hamilton's neck-like curvature pinching estimate. Using this estimate, we are able to prove a version of Perelman's Canonical Neighborhood Theorem in higher dimensions. This makes it possible to extend the flow beyond singularities by a surgery procedure in the spirit of Hamilton and Perelman. As a corollary, we obtain a classification of all diffeomorphism types of such manifolds in terms of a connected sum decomposition. In particular, the underlying manifold cannot be an exotic sphere. Our result is sharp in many interesting situations. For example, the curvature tensors of $\mathbb{CP}^{n/2}$, $\mathbb{HP}^{n/4}$, $S^{n-k} \times S^k$ ($2 \leq k \leq n-2$), $S^{n-2} \times \mathbb{H}^2$, $S^{n-2} \times \mathbb{R}^2$ all lie on the boundary of our curvature cone. Another borderline case is the pseudo-cylinder: this is a rotationally symmetric hypersurface which is weakly, but not strictly, two-convex. Finally, the curvature tensor of $S^{n-1} \times \mathbb{R}$ lies in the interior of our curvature cone.
Automatic renal segmentation in DCE-MRI using convolutional neural networks

Kidney function evaluation using dynamic contrast-enhanced MRI (DCE-MRI) images could help in diagnosis and treatment of kidney diseases of children. Automatic segmentation of renal parenchyma is an important step in this process. In this paper, we propose a time and memory efficient fully automated segmentation method which achieves high segmentation accuracy with running time in the order of seconds in both normal kidneys and kidneys with hydronephrosis. The proposed method is based on a cascaded application of two 3D convolutional neural networks that employs spatial and temporal information at the same time in order to learn the tasks of localization and segmentation of kidneys, respectively. Segmentation performance is evaluated on both normal and abnormal kidneys with varying levels of hydronephrosis. We achieved a mean dice coefficient of 91.4 and 83.6 for normal and abnormal kidneys of pediatric patients, respectively.
Direct Observation of Branching MT Nucleation in Living Animal Cells

Centrosome-mediated microtubule (MT) nucleation has been well characterized; however, numerous noncentrosomal MT nucleation mechanisms exist. The branching MT nucleation pathway envisages that the γ-tubulin ring complex (γ-TuRC) is recruited to MTs by the augmin complex to initiate nucleation of new MTs. While the pathway is well conserved at a molecular and functional level, branching MT nucleation by core constituents has never been directly observed in animal cells. Here, multicolor TIRF microscopy was applied to visualize and quantitatively define the entire process of branching MT nucleation in dividing Drosophila cells during anaphase. The steps of a stereotypical branching nucleation event entailed augmin binding to a mother MT and recruitment of γ-TuRC after 15 s, followed by nucleation 16 s later of a daughter MT at a 36° branch angle. Daughters typically remained attached throughout their ∼40-s lifetime unless the mother depolymerized past the branch point. Assembly of branched MT arrays, which did not require Drosophila TPX2, enhanced localized RhoA activation during cytokinesis.
Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures

We demonstrate a tandem neural network architecture that tolerates inconsistent training instances in inverse design of nanophotonic devices. It provides a way to train large neural networks for the inverse design of complex photonic structures. © 2019 The Author(s)
NoFAQ: synthesizing command repairs from examples

Command-line tools are confusing and hard to use due to their cryptic error messages and lack of documentation. Novice users often resort to online help-forums for finding corrections to their buggy commands, but have a hard time in searching precisely for posts that are relevant to their problem and then applying the suggested solutions to their buggy command. We present NoFAQ, a tool that uses a set of rules to suggest possible fixes when users write buggy commands that trigger commonly occurring errors. The rules are expressed in a language called FIXIT and each rule pattern-matches against the user's buggy command and corresponding error message, and uses these inputs to produce a possible fixed command. NoFAQ automatically learns FIXIT rules from examples of buggy and repaired commands. We evaluate NoFAQ on two fronts. First, we use 92 benchmark problems drawn from an existing tool and show that NoFAQ is able to synthesize rules for 81 benchmark problems in real time using just 2 to 5 input-output examples for each rule. Second, we run our learning algorithm on the examples obtained through a crowd-sourcing interface and show that the learning algorithm scales to large sets of examples.
A Sharp Rate of Convergence for the Empirical Spectral Measure of a Random Unitary Matrix

We consider the convergence of the empirical spectral measures of random N × N unitary matrices. We give upper and lower bounds showing that the Kolmogorov distance between the spectral measure and uniform measure on the unit circle is of order log N/N, both in expectation and almost surely. This implies, in particular, that the convergence happens more slowly for Kolmogorov distance than for the L1-Kantorovich distance. The proof relies on the determinantal structure of the eigenvalue process.
Ordering-based search: a simple and effective algorithm for learning Bayesian networks

One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hill-climbing with tabu lists; moreover, many of the proposed algorithms are quite complex and hard to implement. In this paper, we propose a very simple and easy-to-implement method for addressing this task. Our approach is based on the well-known fact that the best network (of bounded in-degree) consistent with a given node ordering can be found very efficiently. We therefore propose a search not over the space of structures, but over the space of orderings, selecting for each ordering the best network consistent with it. This search space is much smaller, makes more global search steps, has a lower branching factor, and avoids costly acyclicity checks. We present results for this algorithm on both synthetic and real data sets, evaluating both the score of the network found and in the running time. We show that ordering-based search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement.
Greedy Variance Estimation for the LASSO

Recent results have proven the minimax optimality of LASSO and related algorithms for noisy linear regression. However, these results tend to rely on variance estimators that are inefficient or optimizations that are slower than LASSO itself. We propose an efficient estimator for the noise variance in high dimensional linear regression that is faster than LASSO, only requiring p matrix–vector multiplications. We prove this estimator is consistent with a good rate of convergence, under the condition that the design matrix satisfies the restricted isometry property (RIP). In practice, our estimator scales incredibly well into high dimensions, is highly parallelizable, and only incurs a modest bias.
Intrinsic tunneling in phase separated manganites.

We present evidence of direct electron tunneling across intrinsic insulating regions in submicrometer wide bridges of the phase-separated ferromagnet $(\mathrm{La},\mathrm{Pr},\mathrm{Ca}){\mathrm{MnO}}_{3}$. Upon cooling below the Curie temperature, a predominantly ferromagnetic supercooled state persists where tunneling across the intrinsic tunnel barriers (ITBs) results in metastable, temperature-independent, high-resistance plateaus over a large range of temperatures. Upon application of a magnetic field, our data reveal that the ITBs are extinguished resulting in sharp, colossal, low-field resistance drops. Our results compare well to theoretical predictions of magnetic domain walls coinciding with the intrinsic insulating phase.
More Voices Than Ever? Quantifying Media Bias in Networks

Social media, such as blogs, are often seen as democratic entities that allow more voices to be heard than the conventional mass or elite media. Some also feel that social media exhibits a balancing force against the arguably slanted elite media. A systematic comparison between social and mainstream media is necessary but challenging due to the scale and dynamic nature of modern communication. Here we propose empirical measures to quantify the extent and dynamics of social (blog) and mainstream (news) media bias. We focus on a particular form of bias— coverage quantity—as applied to stories about the 111th US Congress. We compare observed coverage of Members of Congress against a null model of unbiased coverage, testing for biases with respect to political party, popular front runners, regions of the country, and more. Our measures suggest distinct characteristics in news and blog media. A simple generative model, in agreement with data, reveals differences in the process of coverage selection between the two media. “In the end, we’ll have more voices and more options.” ‐ Dan Gillmor, We the media
Multi-Rees algebras and toric dynamical systems

This paper explores the relation between multi-Rees algebras and ideals that arise in the study of toric dynamical systems from the theory of chemical reaction networks.
Combinatorial descriptions of the crystal structure on certain PBW bases

Using the theory of PBW bases, one can realize the crystal B(∞) for any semisimple Lie algebra over C using Kostant partitions as the underlying set. In fact there are many such realizations, one for each reduced expression for the longest element of the Weyl group. There is an algorithm to calculate the actions of the crystal operators, but it can be quite complicated. Here we show that, for certain reduced expressions, the crystal operators can also be described by a much simpler bracketing rule. We give conditions describing these reduced expressions, and show that there is at least one example in every type except possibly E8, F4 and G2. We then discuss some examples.
Likelihood‐based inference for discretely observed birth–death‐shift processes, with applications to evolution of mobile genetic elements

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.
Reduced cracking in polycrystalline ZrO2-CeO2 shape-memory ceramics by meeting the cofactor conditions

Abstract Cracking is generally regarded as an unavoidable consequence of martensitic transformation in polycrystalline ZrO2-based ceramics. This shortcoming has limited ZrO2-based shape-memory ceramics (SMCs) to micron-sized single- or oligo-crystals to reduce bulk transformation stresses. In this paper we explore an alternate approach to reduce transformation-induced cracking by manipulating the crystallographic phase compatibility in polycrystalline ZrO2-CeO2 ceramics. For a range of compositions 12.5-15 mol% CeO2, we present lattice parameter measurements for the tetragonal and monoclinic phases from in situ X-ray diffraction, direct observation of lattice correspondences by electron backscatter diffraction, and calculations of interface and bulk compatibility. We identify ZrO2-13.5 mol% CeO2 as having preferred interface compatibility in that it closely meets the crystallographic cofactor conditions. This composition resists cracking through 10 thermal cycles, whereas other compositions all crack. These results suggest that interface compatibility may contribute more strongly to transformation-induced cracking in ZrO2-based SMCs than previously believed and opens a strategy for designing crack-resistant polycrystalline SMCs.
Transitive representations of inverse semigroups

Abstract While every group is isomorphic to a transitive group of permutations, the analogous property fails for inverse semigroups: not all inverse semigroups are isomorphic to transitive inverse semigroups of one-to-one partial transformations of a set. We describe those inverse semigroups that are.
Differential algebra of cubic planar graphs

Abstract In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In addition, in the appendix by K. Sackel the F q -rational points of its graded augmentation variety are shown to coincide with ( q + 1 ) -colorings of the dual graph.
Minimax Estimation of Neural Net Distance

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance based on samples drawn from the distributions. We develop the first known minimax lower bound on the estimation error of the neural net distance, and an upper bound tighter than an existing bound on the estimator error for the empirical neural net distance. Our lower and upper bounds match not only in the order of the sample size but also in terms of the norm of the parameter matrices of neural networks, which justifies the empirical neural net distance as a good approximation of the true neural net distance for training GANs in practice.
PhaseLiftOff: An accurate and stable phase retrieval method based on difference of trace and Frobenius norms

Phase retrieval aims to recover a signal x∈Cn from its amplitude measurements |〈x,ai〉|, i= 1,2, · ·· ,m, where ai’s are over-complete basis vectors, with m at least 3n−2 to ensure a unique solution up to a constant phase factor. The quadratic measurement becomes linear in terms of the rank-one matrix X=xx∗. Phase retrieval is then a rank-one minimization problem subject to linear constraint for which a convex relaxation based on trace-norm minimization (PhaseLift) has been extensively studied recently. At m=O(n), PhaseLift recovers with high probability the rank-one solution. In this paper, we present a precise proxy of the rank-one condition via the difference of trace and Frobenius norms which we call PhaseLiftOff. The associated least squares minimization with this penalty as regularization is equivalent to the rank-one least squares problem under a mild condition on the measurement noise. Stable recovery error estimates are valid at m=O(n) with high probability. Computation of PhaseLiftOff minimization is carried out by a convergent difference of convex functions algorithm. In our numerical example, ai’s are Gaussian distributed. Numerical results show that PhaseLiftOff outperforms PhaseLift and its nonconvex variant (log-determinant regularization), and successfully recovers signals near the theoretical lower limit on the number of measurements without the noise.
Sequential nonparametric testing with the law of the iterated logarithm

We propose a new algorithmic framework for sequential hypothesis testing with i.i.d. data, which includes A/B testing, nonparametric two-sample testing, and independence testing as special cases. It is novel in several ways: (a) it takes linear time and constant space to compute on the fly, (b) it has the same power guarantee (up to a small factor) as a nonsequential version of the test with the same computational constraints, and (c) it accesses only as many samples as are required - its stopping time adapts to the unknown difficulty of the problem. All our test statistics are constructed to be zero-mean martingales under the null hypothesis, and the rejection threshold is governed by a uniform non-asymptotic law of the iterated logarithm (LIL). For nonparametric two-sample mean testing, we also provide a finite-sample power analysis, and the first non-asymptotic stopping time analysis for this class of problems. We verify our predictions for type I and II errors and stopping times using simulations.
Global Well-Posedness and Scattering for the Defocusing, Mass-Critical Generalized KdV Equation

In this paper we prove that the defocusing, mass-critical generalized KdV initial value problem is globally well-posed and scattering for $$u_{0} \in L^{2}(\mathbf {R})$$ . To prove this, we combine the profile decomposition of Killip et al. (Discrete Contin Dyn Syst Ser A 32(1):191–221, 2012) with an interaction Morawetz estimate constructed from the monotonicity formula of Tao (Discrete Contin Dyn Syst Ser A 18(1):1–14, 2007).
Work/Precision Tradeoffs in Continuum Models of Biomolecular Electrostatics

The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule’s ubiquitous atomic charges and polar chemical groups. In this work, we investigate a simple approach to numerical calculation of this model using boundary-integral equation (BIE) methods and boundary-element methods (BEM). Traditional BEM discretizes the protein–solvent boundary into a set of boundary elements, or panels, and the approximate solution is defined as a weighted combination of basis functions with compact support. The resulting BEM matrix then requires integrating singular or near singular functions, which can be slow and challenging to compute. Here we investigate the accuracy and convergence of a simpler representation, namely modeling the unknown surface charge distribution as a set of discrete point charges on the surface. We find that at low resolution, point-based BEM is more accurate than panel-based methods, due to the fact that the protein surface is sampled directly, and can be of significant value for numerous important calculations that require only moderate accuracy, such as the preliminary stages of rational drug design and protein engineering.Copyright © 2015 by ASME
Trend filtering on graphs

We introduce a family of adaptive estimators on graphs, based on penalizing the l1 norm of discrete graph differences. This generalizes the idea of trend filtering (Kim et al., 2009; Tibshirani, 2014), used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filtering exhibits a level of local adaptivity unmatched by the usual l2-based graph smoothers. It is also defined by a convex minimization problem that is readily solved (e.g., by fast ADMM or Newton algorithms). We demonstrate the merits of graph trend filtering through both examples and theory.
Tensor Decomposition for Compressing Recurrent Neural Network

In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and inference. In this paper, we are trying to reduce the number of parameters and maintain the expressive power from RNN simultaneously. We utilize several tensor decompositions method including CANDECOMP/PARAFAC (CP), Tucker decomposition and Tensor Train (TT) to re-parameterize the Gated Recurrent Unit (GRU) RNN. We evaluate all tensor-based RNNs performance on sequence modeling tasks with a various number of parameters. Based on our experiment results, TT-GRU achieved the best results in a various number of parameters compared to other decomposition methods.
Bayesian Multi-Plate High-Throughput Screening of Compounds

High-throughput screening of compounds (chemicals) is an essential part of drug discovery, involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross-plate correlation or statistical strength among plates. We present a new statistical framework for high-throughput screening of compounds based on Bayesian nonparametric modeling. The proposed approach is able to identify candidate hits from multiple plates simultaneously, sharing statistical strength among plates and providing more robust estimates of compound activity. It can flexibly accommodate arbitrary distributions of compound activities and is applicable to any plate geometry. The algorithm provides a principled statistical approach for hit identification and false discovery rate control. Experiments demonstrate significant improvements in hit identification sensitivity and specificity over the B-score and R-score methods, which are highly sensitive to threshold choice. These improvements are maintained at low hit rates. The framework is implemented as an efficient R extension package BHTSpack and is suitable for large scale data sets.
Error Analysis for the Linear Feedback Particle Filter

This paper is concerned with the convergence and the error analysis for the feedback particle filter (FPF) algorithm. The FPF is a controlled interacting particle system where the control law is designed to solve the nonlinear filtering problem. For the linear Gaussian case, certain simplifications arise whereby the linear FPF reduces to one form of the ensemble Kalman filter. For this and for the more general nonlinear non-Gaussian case, it has been an open problem to relate the convergence and error properties of the finite- $N$ algorithm to the mean-field limit (where the exactness results have been obtained). In this paper, the equations for empirical mean and covariance are derived for the finite- $N$ linear FPF. Remarkably, for a certain deterministic form of FPF, the equations for mean and variance are identical to the Kalman filter. This allows strong conclusions on convergence and error properties based on the classical filter stability theory for the Kalman filter. It is shown that the error converges to zero even with finite number of particles. The paper also presents propagation of chaos estimates for the finite- $N$ linear filter. The error estimates are illustrated with numerical experiments.
Abelian networks II. Halting on all inputs

Abelian networks are systems of communicating automata satisfying a local commutativity condition. We show that a finite irreducible abelian network halts on all inputs if and only if all eigenvalues of its production matrix lie in the open unit disk.
Systems Perturbation Analysis of a Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates for Cancer Therapeutics.

Dysregulation in signal transduction pathways can lead to a variety of complex disorders, including cancer. Computational approaches such as network analysis are important tools to understand system dynamics as well as to identify critical components that could be further explored as therapeutic targets. Here, we performed perturbation analysis of a large-scale signal transduction model in extracellular environments that stimulate cell death, growth, motility, and quiescence. Each of the model's components was perturbed under both loss-of-function and gain-of-function mutations. Using 1,300 simulations under both types of perturbations across various extracellular conditions, we identified the most and least influential components based on the magnitude of their influence on the rest of the system. Based on the premise that the most influential components might serve as better drug targets, we characterized them for biological functions, housekeeping genes, essential genes, and druggable proteins. The most influential components under all environmental conditions were enriched with several biological processes. The inositol pathway was found as most influential under inactivating perturbations, whereas the kinase and small lung cancer pathways were identified as the most influential under activating perturbations. The most influential components were enriched with essential genes and druggable proteins. Moreover, known cancer drug targets were also classified in influential components based on the affected components in the network. Additionally, the systemic perturbation analysis of the model revealed a network motif of most influential components which affect each other. Furthermore, our analysis predicted novel combinations of cancer drug targets with various effects on other most influential components. We found that the combinatorial perturbation consisting of PI3K inactivation and overactivation of IP3R1 can lead to increased activity levels of apoptosis-related components and tumor suppressor genes, suggesting that this combinatorial perturbation may lead to a better target for decreasing cell proliferation and inducing apoptosis. Lastly, our approach shows a potential to identify and prioritize therapeutic targets through systemic perturbation analysis of large scale computational models of signal transduction. While some components of the presented computational results have been validated against independent gene expression data sets, more laboratory experiments are warranted to more comprehensively validate the presented results.
Non-Gaussian observations in nonlinear compressed sensing via Stein discrepancies

Performance guarantees for compression in nonlinear models under non-Gaussian observations can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the value of zero under Gaussian or linear sensing. The use of these characteristics, or discrepancies, improves some previous results in this area by relaxing conditions and tightening performance bounds. In addition, these characteristics are tractable to compute when Gaussian sensing is corrupted by either additive errors or mixing.
On expansions of the real field by complex subgroups

Abstract We construct a class of finite rank multiplicative subgroups of the complex numbers such that the expansion of the real field by such a group is model-theoretically well-behaved. As an application we show that a classification of expansions of the real field by cyclic multiplicative subgroups of the complex numbers due to Hieronymi does not even extend to expansions by subgroups with two generators.
Free pluriharmonic functions on noncommutative polyballs

In this paper, we study free k-pluriharmonic functions on noncommutative regular polyballs. These regular polyballs have universal operator models consisting of left creation operators acting on tensor products of full Fock spaces. We introduce and determine the class of kmulti- Toeplitz operators acting on these tensor products and show that the bounded free k-pluriharmonic functions on regular polyballs are precisely the noncommutative Berezin transforms of k-multi-Toeplitz operators. The Dirichlet extension problem on regular polyballs is also solved. It is proved that a free k-pluriharmonic function has continuous extension to the closed polyball if and only if it is the noncommutative Berezin transform of a k-multi-Toeplitz operator in a certain class, which we determine. We provide a Naimark type dilation theorem for direct products of unital free semigroups, and use it to obtain a structure theorem which characterizes the positive free k-pluriharmonic functions on the regular polyball, with operator-valued coefficients. We define the noncommutative the Berezin (resp. Poisson) transform of a completely bounded linear map on the C*-algebra generated by the universal operator model and give necessary an sufficient conditions for a function to be the Poisson transform of a completely bounded (resp. completely positive) map. In the last section of the paper, we obtain Herglotz-Riesz representation theorems for free holomorphic functions on regular polyballs with positive real parts, extending the classical result as well as Korannyi-Pukanszky version in scalar polydisks.
The geometry of blueprints: Part I: Algebraic background and scheme theory

Abstract In this paper, we introduce the category of blueprints, which is a category of algebraic objects that include both commutative (semi)rings and commutative monoids. This generalization allows a simultaneous treatment of ideals resp. congruences for rings and monoids and leads to a common scheme theory. In particular, it bridges the gap between usual schemes and F 1 -schemes (after Kato, Deitmar and Connes–Consani). Beside this unification, the category of blueprints contains new interesting objects as “improved” cyclotomic field extensions F 1 n of F 1 and “archimedean valuation rings”. It also yields a notion of semiring schemes. This first paper lays the foundation for subsequent projects, which are devoted to the following problems: Titsʼ idea of Chevalley groups over F 1 , congruence schemes, sheaf cohomology, K-theory and a unified view on analytic geometry over F 1 , adic spaces (after Huber), analytic spaces (after Berkovich) and tropical geometry.
An Original Mechanism for the Acceleration of Ultra-High-Energy Cosmic Rays

Abstract We suggest that ultra-high-energy (UHE) cosmic rays (CRs) may be accelerated in ultra-relativistic flows via a one-shot mechanism, the “espresso” acceleration, in which already-energetic particles are generally boosted by a factor of ∼ Γ 2 in energy, where Γ is the flow Lorentz factor. More precisely, we consider blazar-like ultra-relativistic jets propagating into a halo of “seed” CRs produced in supernova remnants, which can accelerate UHECRs up to 1020 eV. Such a re-acceleration process naturally accounts for the chemical composition measured by the Pierre Auger Collaboration, which resembles the one around and above the knee in the CR spectrum, and is consistent with the distribution of potential sources in the local universe; particularly intriguing is the coincidence of the powerful blazar Mrk 421 with the hotspot reported by the Telescope Array Collaboration.
On the Secure Degrees of Freedom of the K-user Interference Channel with Delayed CSIT

In this paper, the $K$ -user interference channel with confidential messages is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure transmission scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving confidentiality is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: phase one in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the confidentiality constraints. The proposed scheme achieves a sum secure degrees of freedom (SDoF) of at least $\frac{1}{2}(\sqrt{K}-6)$ . To the best of our knowledge, this is the first result on the $K$ -user interference channel with confidential messages and delayed CSIT that achieves a SDoF which scales with $K$ -.
Information-Theoretic Lower Bounds for Distributed Function Computation

We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the network initially has a random observation and aims to compute a common function of all observations to a given accuracy with a given confidence by exchanging messages with its neighbors. We obtain the lower bounds on computation time by examining the conditional mutual information between the actual function value and its estimate at an arbitrary node, given the observations in an arbitrary subset of nodes containing that node. The main contributions include the following. First, a lower bound on the conditional mutual information via so-called small ball probabilities, which captures the dependence of the computation time on the joint distribution of the observations at the nodes, the structure of the function, and the accuracy requirement. For linear functions, the small ball probability can be expressed by Levy concentration functions of sums of independent random variables, for which tight estimates are available that lead to strict improvements over existing lower bounds on computation time. Second, an upper bound on the conditional mutual information via strong data processing inequalities, which complements and strengthens existing cutset-capacity upper bounds. Finally, a multi-cutset analysis that quantifies the loss (dissipation) of the information needed for computation as it flows across a succession of cutsets in the network. This analysis is based on reducing a general network to a line network with bidirectional links and self-links, and the results highlight the dependence of the computation time on the diameter of the network, a fundamental parameter that is missing from most of the existing lower bounds on computation time.
Denoising and completion of 3D data via multidimensional dictionary learning

In this paper a new dictionary learning algorithm for multidimensional data is proposed. Unlike most conventional dictionary learning methods which are derived for dealing with vectors or matrices, our algorithm, named K-TSVD, learns a multidimensional dictionary directly via a novel algebraic approach for tensor factorization as proposed in [Braman, 2010; Kilmer et al., 2011; Kilmer and Martin, 2011]. Using this approach one can define a tensor-SVD and we propose to extend K-SVD algorithm used for 1-D data to a K-TSVD algorithm for handling 2-D and 3-D data. Our algorithm, based on the idea of sparse coding (using group-sparsity over multidimensional coefficient vectors), alternates between estimating a compact representation and dictionary learning. We analyze our K-TSVD algorithm and demonstrate its result on video completion and video/multispectral image denoising.
Variational Knowledge Graph Reasoning

Inferring missing links in knowledge graphs (KG) has attracted a lot of attention from the research community. In this paper, we tackle a practical query answering task involving predicting the relation of a given entity pair. We frame this prediction problem as an inference problem in a probabilistic graphical model and aim at resolving it from a variational inference perspective. In order to model the relation between the query entity pair, we assume that there exists an underlying latent variable (paths connecting two nodes) in the KG, which carries the equivalent semantics of their relations. However, due to the intractability of connections in large KGs, we propose to use variation inference to maximize the evidence lower bound. More specifically, our framework (Diva) is composed of three modules, i.e. a posterior approximator, a prior (path finder), and a likelihood (path reasoner). By using variational inference, we are able to incorporate them closely into a unified architecture and jointly optimize them to perform KG reasoning. With active interactions among these sub-modules, Diva is better at handling noise and coping with more complex reasoning scenarios. In order to evaluate our method, we conduct the experiment of the link prediction task on multiple datasets and achieve state-of-the-art performances on both datasets.
Inference in hybrid Bayesian networks using mixtures of Gaussians

The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG Bayesian networks, and there exists a commercial implementation of this algorithm. However, this algorithm can only be used for MoG BNs. Some limitations of such networks are as follows. All continuous chance variables must have conditional linear Gaussian distributions, and discrete chance nodes cannot have continuous parents. The methods described in this paper will enable us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This includes networks with continuous chance nodes with non-Gaussian distributions, networks with no restrictions on the topology of discrete and continuous variables, networks with conditionally deterministic variables that are a nonlinear function of their continuous parents, and networks with continuous chance variables whose variances are functions of their parents.
Temperature dependence in rainbow scattering of hyperthermal Ar atoms from LiF(001)

Abstract Recent experiments have reported measurements of rainbow scattering features in the angular distributions of hyperthermal Ar colliding with LiF(001) [Kondo et al., J. Chem. Phys. 122, 244713 (2005)]. A theory of atom–surface collisions recently developed by the authors, based on the eikonal approximation, that includes multiphonon energy transfers is used to explain the temperature dependence of the measured scattered angular distribution spectra.
Optimal linear estimation under unknown nonlinear transform

Linear regression studies the problem of estimating a model parameter β* ∈ ℝp, from n observations {(yi, xi)}ni=1 from linear model yi = 〈xi, β*〉 + ∊i. We consider a significant generalization in which the relationship between 〈xi, β*〉 and yi is noisy, quantized to a single bit, potentially nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover β* in settings (i.e., classes of link function f) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between yi and 〈xi, β*〉. We also consider the high dimensional setting where β* is sparse, and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where p ≫ n. For a broad class of link functions between 〈xi, β*〉 and yi, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
Bilipschitz equivalence of trees and hyperbolic fillings

We combine conditions found in [Wh] with results from [MPR] to show that quasi-isometries between uniformly discrete bounded geometry spaces that satisfy linear isoperimetric inequalities are within bounded distance to bilipschitz equivalences. We apply this result to regularly branching trees and hyperbolic fillings of metric spaces.
Exact bounds on the truncated-tilted mean, with applications

Exact upper bounds on the Winsorised-tilted mean, E Xe h(X^ w) E eh(X^ w) , of a random variable X in terms of its first two moments are given. Such results are needed in work on nonuniform Berry-Esseen-type bounds for general nonlinear statistics. As another application, optimal upper bounds on the Bayes posterior mean are provided. Certain monotonicity properties of the tilted mean are also presented. AMS 2000 subject classifications: Primary 60E15; secondary 60E10, 60F10, 60F05. Keywords and phrases: exact upper bounds, Winsorization, truncation, large deviations, nonuniform Berry-Esseen bounds, Cramer tilt transform, monotonicity, Bayes posterior mean.
Concept drift learning with alternating learners

Data-driven predictive analytics are in use today across a number of industrial applications, but further integration is hindered by the requirement of similarity among model training and test data distributions. This paper addresses the need of learning from possibly nonstationary data streams, or under concept drift, a commonly seen phenomenon in practical applications. A simple dual-learner ensemble strategy, alternating learners framework, is proposed. A long-memory model learns stable concepts from a long relevant time window, while a short-memory model learns transient concepts from a small recent window. The difference in prediction performance of these two models is monitored and induces an alternating policy to select, update and reset the two models. The method features an online updating mechanism to maintain the ensemble accuracy, and a concept-dependent trigger to focus on relevant data. Through empirical studies the method demonstrates effective tracking and prediction when the steaming data carry abrupt and/or gradual changes.
Input-aware auto-tuning of compute-bound HPC kernels

Efficient implementations of HPC applications for parallel architectures generally rely on external software packages (e.g., BLAS, LAPACK, CUDNN). While these libraries provide highly optimized routines for certain characteristics of inputs (e.g., square matrices), they generally do not retain optimal performance across the wide range of problems encountered in practice. In this paper, we present an input-aware auto-tuning framework for matrix multiplications and convolutions, ISAAC, which uses predictive modeling techniques to drive highly parameterized PTX code templates towards not only hardware-, but also application-specific kernels. Numerical experiments on the NVIDIA Maxwell and Pascal architectures show up to 3x performance gains over both cuBLAS and cuDNN after only a few hours of auto-tuning.