cssi/SciSciGPT-SciSciNet huggingface dataset:
On tensor third $L$-functions of automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$

Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. We study these problems in a setting related to the Langlands $L$-functions $L(s,\pi,\,\otimes^3),$ where $\pi$ is a cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_F)$ where $F$ is a global field.
Operation of the ATLAS detector with first collisions at 7 TeV at the LHC

The ATLAS experiment has successfully recorded over 300 nb^-1 of pp collisions at 7 TeV provided by the Large Hadron Collider, with an efficiency of 94%. We describe the data acquisition, trigger, reconstruction, calibration, monitoring, and luminosity measurement infrastructure that have made this possible.
Optimizing Star-Convex Functions

Star-convexity is a significant relaxation of the notion of convexity, that allows for functions that do not have (sub)gradients at most points, and may even be discontinuous everywhere except at the global optimum. We introduce a polynomial time algorithm for optimizing the class of star-convex functions, under no Lipschitz or other smoothness assumptions whatsoever, and no restrictions except exponential boundedness on a region about the origin, and Lebesgue measurability. The algorithm’s performance is polynomial in the requested number of digits of accuracy and the dimension of the search domain. This contrasts with the previous best known algorithm of Nesterov and Polyak which has exponential dependence on the number of digits of accuracy, but only n! dependence on the dimension n (where ! is the matrix multiplication exponent), and which further requires Lipschitz second differentiability of the function [1].
Enhancing ICA performance by exploiting sparsity: Application to FMRI analysis

Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete statistical independence can be too restrictive an assumption in practice. Additionally, important prior information about the data, such as sparsity, is usually available. Sparsity is a natural property of the data, a form of diversity, which, if incorporated into the ICA model, can relax the independence assumption, resulting in an improvement in the overall separation performance. In this work, we propose a new variant of ICA by entropy bound minimization (ICA-EBM)—a flexible, yet parameter-free algorithm—through the direct exploitation of sparsity. Using this new SparseICA-EBM algorithm, we study the synergy of independence and sparsity through simulations on synthetic as well as functional magnetic resonance imaging (fMRI)-like data.
Periodic orbits of Gross–Pitaevskii in the disc with vortices following point vortex flow

We prove the existence of non-constant time periodic vortex solutions to the Gross–Pitaevskii equations for small but fixed $$\varepsilon > 0.$$ The vortices of these solutions follow periodic orbits to the point vortex system of ordinary differential equations for all time. The construction uses two approaches—constrained minimization techniques adapted from Gelantalis and Sternberg (J Math Phys 53:083701, 2012) and topological minimax techniques adapted from Lin and Lin (Sel Math New Ser 3:99–113, 1997), applied to a formulation of the problem within a rotational ansatz.
On a class of degenerate parabolic equations with dynamic boundary conditions

We consider a quasi-linear parabolic (possibly, degenerate) equation with nonlinear dynamic boundary conditions. The corresponding class of initial and boundary value problems has already been studied previously, proving well-posedness of weak solutions and the existence of the global attractor, assuming that the nonlinearities are subcritical to a given exponent. The goal of this article is to show that the previous analysis can be redone for supercritical nonlinearities by proving an additional L∞-estimate on the solutions. In particular, we derive new conditions which reflect an exact balance between the internal and the boundary mechanisms involved, even when both the nonlinear sources contribute in opposite directions. Then, we show how to construct a trajectory attractor for the weak solutions of the associated parabolic system, and prove that any solution belonging to the attractor is bounded, which implies uniqueness. Finally, we also prove for the (semilinear) reaction–diffusion equation with nonlinear dynamic boundary conditions, that the fractal dimension of the global attractor is of the order ν−(N−1), as diffusion ν→0+, in any space dimension N⩾2, improving some recent results in Gal (2012) [23].
Automated Design using Neural Networks and Gradient Descent

We propose a novel method that makes use of deep neural networks and gradient decent to perform automated design on complex real world engineering tasks. Our approach works by training a neural network to mimic the fitness function of a design optimization task and then, using the differential nature of the neural network, perform gradient decent to maximize the fitness. We demonstrate this methods effectiveness by designing an optimized heat sink and both 2D and 3D airfoils that maximize the lift drag ratio under steady state flow conditions. We highlight that our method has two distinct benefits over other automated design approaches. First, evaluating the neural networks prediction of fitness can be orders of magnitude faster then simulating the system of interest. Second, using gradient decent allows the design space to be searched much more efficiently then other gradient free methods. These two strengths work together to overcome some of the current shortcomings of automated design.
On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions

Abstract We show existence of infinitely many homoclinic orbits at the origin for a class of singular second-order Hamiltonian systems u ¨ + V u ( t , u ) = 0 , − ∞ t ∞ . We use variational methods under the assumption that V ( t , u ) satisfies the so-called “Strong-Force” condition.
Connectivity and giant component of stochastic Kronecker graphs

Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix k-by-k matrix P with entries in [0,1]. We develop a novel correspondence between the adjacencies in a general stochastic Kronecker graph and the action of a fixed Markov chain. Using this correspondence we are able to generalize the arguments of Horn and Radcliffe on the emergence of the giant component from the case where k = 2 to arbitrary k. We are also able to use this correspondence to completely analyze the connectivity of a general stochastic Kronecker graph.
Antilinearity rather than Hermiticity as a guiding principle for quantum theory

Currently there is much interest in Hamiltonians that are not Hermitian but instead possess an antilinear PT symmetry. Here we seek to put such PT symmetric theories into as general a context as possible. After providing a brief overview of the PT symmetry program, we show that having an antilinear symmetry that acts on a well-defined Hilbert space is the most general condition that one can impose on a quantum theory for which one can have a well-defined inner product that is time independent, have a Hamiltonian that is self-adjoint, and have energy eigenvalues that are all real. For each of these properties Hermiticity is only a sufficient condition but not a necessary one, with Hermiticity thus being the special case in which the Hamiltonian has both antilinearity and Hermiticity. As well as being the necessary condition for the reality of energy eigenvalues, antilinearity in addition allows for the physically interesting cases of manifestly non-Hermitian but nonetheless self-adjoint Hamiltonians that have energy eigenvalues that appear in complex conjugate pairs, or that are Jordan block and cannot be diagonalized at all. We show that one can extend these ideas to quantum field theory, with the dual requirements of the existence of time independent inner products and invariance under complex Lorentz transformations forcing the antilinear symmetry to uniquely be CPT. We thus extend the CPT theorem to non-Hermitian Hamiltonians. For theories that are separately charge conjugation invariant, PT symmetry then follows, with the case for the physical relevance of the PT-symmetry program thus being advanced. While CPT symmetry can be defined at the classical level for every classical path in a path integral quantization procedure, in contrast, in such a path integral there is no reference at all to the Hermiticity of the Hamiltonian or the quantum Hilbert space on which it acts, as they are strictly quantum-mechanical concepts that can only be defined after the path integral quantization has been performed and the quantum Hilbert space has been constructed. CPT symmetry thus goes beyond Hermiticity and has primacy over it, with our work raising the question of how Hermiticity ever comes into quantum theory at all. To this end we show that whether or not a CPT-invariant theory has a Hamiltonian that is Hermitian is a property of the solutions to the theory and not of the Hamiltonian itself. Hermiticity thus never needs to be postulated at all.
Convexity of mutual information along the Ornstein-Uhlenbeck flow

We study the convexity of mutual information as a function of time along the flow of the Ornstein-Uhlenbeck process. We prove that if the initial distribution is strongly log-concave, then mutual information is eventually convex, i.e., convex for all large time. In particular, if the initial distribution is sufficiently strongly log-concave compared to the target Gaussian measure, then mutual information is always a convex function of time. We also prove that if the initial distribution is either bounded or has finite fourth moment and Fisher information, then mutual information is eventually convex. Finally, we provide counterexamples to show that mutual information can be nonconvex at small time.
Sigma Models and Phase Transitions for Complete Intersections

We study a one-parameter family of gauged linear sigma models (GLSMs) naturally associated to a complete intersection in weighted projective space. In the positive phase of the family we recover Gromov-Witten theory of the complete intersection, while in the negative phase we obtain a Landau--Ginzburg-type theory. Focusing on the negative phase, we develop foundational properties which allow us to state and prove a genus-zero comparison theorem that generalizes the multiple log-canonical correspondence and should be viewed as analogous to quantum Serre duality in the positive phase. Using this comparison result, along with the crepant transformation conjecture and quantum Serre duality, we prove a genus-zero correspondence between the GLSMs which arise at the two phases, thereby generalizing the Landau-Ginzburg/Calabi-Yau correspondence to complete intersections.
Spectral Methods for Correlated Topic Models

Author(s): Arabshahi, Forough; Anandkumar, Animashree | Abstract: In this paper, we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations, by assuming that the hidden topic proportions are drawn from a flexible class of Normalized Infinitely Divisible (NID) distributions. NID distributions are generated through the process of normalizing a family of independent Infinitely Divisible (ID) random variables. The Dirichlet distribution is a special case obtained by normalizing a set of Gamma random variables. We prove that this flexible topic model class can be learned via spectral methods using only moments up to the third order, with (low order) polynomial sample and computational complexity. The proof is based on a key new technique derived here that allows us to diagonalize the moments of the NID distribution through an efficient procedure that requires evaluating only univariate integrals, despite the fact that we are handling high dimensional multivariate moments. In order to assess the performance of our proposed Latent NID topic model, we use two real datasets of articles collected from New York Times and Pubmed. Our experiments yield improved perplexity on both datasets compared with the baseline.
Lipschitz parametrization of probabilistic graphical models

We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the lp-norm of differences of parameters as the minimization of that upper bound. The expected log-likelihood is lower bounded by the negative lp-norm, which allows understanding the generalization ability of probabilistic models. The exponential of the negative lp-norm is involved in the lower bound of the Bayes error rate, which shows that it is reasonable to use parameters as features in algorithms that rely on metric spaces (e.g. classification, dimensionality reduction, clustering). Our results do not rely on specific algorithms for learning the structure or parameters. We show preliminary results for activity recognition and temporal segmentation.
Mitigating hardware cyber-security risks in error correcting decoders

This paper investigates hardware cyber-security risks associated with channel decoders, which are commonly acquired as a black box in semiconductor industry. It is shown that channel decoders are potentially attractive targets for hardware cyber-security attacks and can be easily embedded with malicious blocks. Several attack scenarios are considered in this work and suitable methods for mitigating the risks are proposed. A homomorphic channel decoding is devised that obstructs the communications between attackers and the malicious blocks, ideally without changing the decoding performance.
Leavitt path algebras with bounded index of nilpotence

In this paper we completely describe graphically Leavitt path algebras with bounded index of nilpotence. We show that the Leavitt path algebra LK(E) has index of nilpotence at most n if and only if...
Generalized Rybicki Press algorithm

Summary This article discusses a more general and numerically stable Rybicki Press algorithm, which enables inverting and computing determinants of covariance matrices, whose elements are sums of exponentials. The algorithm is true in exact arithmetic and relies on introducing new variables and corresponding equations, thereby converting the matrix into a banded matrix of larger size. Linear complexity banded algorithms for solving linear systems and computing determinants on the larger matrix enable linear complexity algorithms for the initial semi-separable matrix as well. Benchmarks provided illustrate the linear scaling of the algorithm. Copyright © 2015 John Wiley & Sons, Ltd.
Cloud-based optimization: A quasi-decentralized approach to multi-agent coordination

New architectures and algorithms are needed to reflect the mixture of local and global information that is available as multi-agent systems connect over the cloud. We present a novel architecture for multi-agent coordination where the cloud is assumed to be able to gather information from all agents, perform centralized computations, and disseminate the results in an intermittent manner. This architecture is used to solve a multi-agent optimization problem in which each agent has a local objective function unknown to the other agents and in which the agents are collectively subject to global inequality constraints. Leveraging the cloud, a dual problem is formulated and solved by finding a saddle point of the associated Lagrangian.
Bandwidth selection for nonparametric modal regression

In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are u...
An Integrated Framework for Treebanks and Multilayer Annotations

Treebank formats and associated software tools are proliferating rapidly, with little consideration for interoperability. We survey a wide variety of treebank structures and operations, and show how they can be mapped onto the annotation graph model, and leading to an integrated framework encompassing tree and non-tree annotations alike. This development opens up new possibilities for managing and exploiting multilayer annotations.
Second-order ergodic theorem for self-similar tiling systems

We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space . We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a graph-directed self-similar set associated with the substitution rule.
Decentralized nonparametric multiple testing

ABSTRACTConsider a big data multiple testing task, where, due to storage and computational bottlenecks, one is given a very large collection of p-values by splitting into manageable chunks and dist...
Local spectrum of truncations of Kronecker products of Haar distributed unitary matrices

We address the local spectral behavior of the random matrix where U is a Haar distributed unitary matrix of size n × n, the factor k is at most c0lgn for a small constant c0 > 0, and Π1, Π2 are arbitrary projections on of ranks proportional to nk. We prove that in this setting the k-fold Kronecker product behaves similarly to the well-studied case when k = 1.
Maximum Area Rectangle Separating Red and Blue Points

Given a set R of n red points and a set B of m blue points, we study the problem of finding a rectangle that contains all the red points, the minimum number of blue points and has the largest area. We call such rectangle a maximum separating rectangle. We address the planar, axis-aligned (2D) version, and present an O(mlogm+n) time, O(m+n) space algorithm. The running time reduces to O(m + n) if the points are pre-sorted by one of the coordinates. We further prove that our algorithm is optimal in the decision model of computation.
IdentityFinder and Some New Identities of Rogers–Ramanujan Type

The Rogers–Ramanujan identities and various analogous identities (Gordon, Andrews–Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partitions. These identities (written in generating function form) are typically of the form “product side” equals “sum side,” with the product side enumerating partitions obeying certain congruence conditions and the sum side obeying certain initial conditions and difference conditions (along with possibly other restrictions). We use symbolic computation to generate various such sum sides and then use Euler’s algorithm to see which of them actually do produce elegant conjectured product sides. We not only rediscover many of the known identities but also discover some apparently new ones, as conjectures supported by strong mathematical evidence.
Storage allocation under processor sharing II: Further asymptotic results

We consider a processor-sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items. All of the spaces are numbered and ordered. An arriving customer takes the lowest available space. Dynamic storage allocation and the fragmentation of computer memory are wellknown applications of this model. We define the traffic intensity ρ to be λ/μ, where λ is the customers’ arrival rate and μ is the service rate of the processor. We study the joint probability distribution of the numbers of occupied primary and secondary spaces. We study the problem in two asymptotic limits: (1) m → ∞ with a fixed ρ < 1, and (2) ρ ↑ 1, m → ∞ with m(1 − ρ) = O(1). The asymptotics yield insight into how many secondary spaces tend to be needed, and into the sample paths leading to the occupation of the two types of spaces. We show that the asymptotics lead to accurate numerical approximations. 1 Introduction
Regions of Attraction for Hybrid Limit Cycles of Walking Robots

Abstract This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the “rimless wheel”, and the “compass gait”, the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle into tangential and transverse components, and a search for a Lyapunov function in the transverse dynamics using sum-of-squares analysis (semidefinite programming). Each example illuminates different aspects of the procedure, including optimization of transversal surfaces, the handling of impact maps, optimization of the Lyapunov function, and orbitally-stabilizing control design.
A Discrete Divergence-Free Weak Galerkin Finite Element Method for the Stokes Equations

Abstract A discrete divergence free weak Galerkin finite element method is developed for the Stokes equations based on a weak Galerkin (WG) method introduced in [17] . Discrete divergence free bases are constructed explicitly for the lowest order weak Galerkin elements in two and three dimensional spaces. These basis functions can be derived on general meshes of arbitrary shape of polygons and polyhedrons. With the divergence free basis derived, the discrete divergence free WG scheme can eliminate pressure variable from the system and reduces a saddle point problem to a symmetric and positive definite system with many fewer unknowns. Numerical results are presented to demonstrate the robustness and accuracy of this discrete divergence free WG method.
Big-Little Net: An Efficient Multi-Scale Feature Representation for Visual and Speech Recognition

In this paper, we propose a novel Convolutional Neural Network (CNN) architecture for learning multi-scale feature representations with good tradeoffs between speed and accuracy. This is achieved by using a multi-branch network, which has different computational complexity at different branches. Through frequent merging of features from branches at distinct scales, our model obtains multi-scale features while using less computation. The proposed approach demonstrates improvement of model efficiency and performance on both object recognition and speech recognition tasks,using popular architectures including ResNet and ResNeXt. For object recognition, our approach reduces computation by 33% on object recognition while improving accuracy with 0.9%. Furthermore, our model surpasses state-of-the-art CNN acceleration approaches by a large margin in accuracy and FLOPs reduction. On the task of speech recognition, our proposed multi-scale CNNs save 30% FLOPs with slightly better word error rates, showing good generalization across domains. The codes are available at this https URL
Charged Point Normalization: An Efficient Solution to the Saddle Point Problem.

Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to escape saddle points. Unlike other saddle point escaping algorithms, second order information is not utilized, and the system can be trained with an arbitrary gradient descent learner. The system drastically improves learning in a range of deep neural networks on various data-sets in comparison to non-CPN neural networks.
Inducing Language Networks from Continuous Space Word Representations

Recent advancements in unsupervised feature learning have developed powerful latent representations of words. However, it is still not clear what makes one representation better than another and how we can learn the ideal representation. Understanding the structure of latent spaces attained is key to any future advancement in unsupervised learning. In this work, we introduce a new view of continuous space word representations as language networks.We explore two techniques to create language networks from learned features by inducing them for two popular word representation methods and examining the properties of their resulting networks. We find that the induced networks differ from other methods of creating language networks, and that they contain meaningful community structure.
Thermal to Visible Synthesis of Face Images Using Multiple Regions

Synthesis of visible spectrum faces from thermal facial imagery is a promising approach for heterogeneous face recognition; enabling existing face recognition software trained on visible imagery to be leveraged, and allowing human analysts to verify cross-spectrum matches more effectively. We propose a new synthesis method to enhance the discriminative quality of synthesized visible face imagery by leveraging both global (e.g., entire face) and local regions (e.g., eyes, nose, and mouth). Here, each region provides (1) an independent representation for the corresponding area, and (2) additional regularization terms, which impact the overall quality of synthesized images. We analyze the effects of using multiple regions to synthesize a visible face image from a thermal face. We demonstrate that our approach improves cross-spectrum verification rates over recently published synthesis approaches. Moreover, using our synthesized imagery, we report the results on facial landmark detection—commonly used for image registration— which is a critical part of the face recognition process.
Leading digit laws on linear Lie groups

We study the leading digit laws for the matrix entries of a linear Lie group G. For non-compact G, these laws generalize the following observations: (1) the normalized Haar measure of the Lie group $\mathbb {R}^{+}$ is d x/x and (2) the scale invariance of d x/x implies the distribution of the digits follow Benford’s law. Viewing this scale invariance as left invariance of Haar measure, we see either Benford or power law behavior in the significands from one matrix entry of various such G. When G is compact, the leading digit laws we obtain come as a consequence of digit laws for a fixed number of components of a unit sphere. The sequence of digit laws for the unit sphere exhibits periodic behavior as the dimension tends to infinity.
DeGroot–Friedkin Map in Opinion Dynamics Is Mirror Descent

We provide a variational interpretation of the DeGroot–Friedkin map in opinion dynamics. Specifically, we show that the nonlinear dynamics for the DeGroot–Friedkin map can be viewed as mirror descent on the standard simplex with the associated Bregman divergence being equal to the generalized Kullback–Leibler divergence, i.e., an entropic mirror descent. Our results reveal that the DeGroot–Friedkin map elicits an individual’s social power to be close to her social influence while minimizing the so called “extropy”—the entropy of the complimentary opinion.
Homogenization of the g-equation with incompressible random drift in two dimensions

We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is statistically stationary and ergodic, we prove sufficient conditions for homogenization to hold with probability one. These conditions are expressed in terms of travel times for the associated control problem. When the spatial dimension is equal to two and the fluid velocity is divergence-free, we verify that these conditions hold under suitable assumptions about the growth of the random stream function.
An ensemble diversity approach to supervised binary hashing

Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization. We propose a much simpler approach: we train each hash function (or bit) independently from each other, but introduce diversity among them using techniques from classifier ensembles. Surprisingly, we find that not only is this faster and trivially parallelizable, but it also improves over the more complex, coupled objective function, and achieves state-of-the-art precision and recall in experiments with image retrieval.
A measure-conjugacy invariant for free group actions

This paper introduces a new measure-conjugacy invariant for actions of free groups. Using this invariant, it is shown that two Bernoulli shifts over a finitely generated free group are measurably conjugate if and only if their base measures have the same entropy. This answers a question of Ornstein and Weiss.
Detecting and Explaining Crisis

Individuals on social media may reveal themselves to be in various states of crisis (e.g. suicide, self-harm, abuse, or eating disorders). Detecting crisis from social media text automatically and accurately can have profound consequences. However, detecting a general state of crisis without explaining why has limited applications. An explanation in this context is a coherent, concise subset of the text that rationalizes the crisis detection. We explore several methods to detect and explain crisis using a combination of neural and non-neural techniques. We evaluate these techniques on a unique data set obtained from Koko, an anonymous emotional support network available through various messaging applications. We annotate a small subset of the samples labeled with crisis with corresponding explanations. Our best technique significantly outperforms the baseline for detection and explanation.
Limit linear series for curves not of compact type

We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding specialization result. For a more restricted class of curves which simultaneously generalizes two-component curves and curves of compact type, we give an equivalent definition of limit linear series, which is visibly a generalization of the Eisenbud-Harris definition. Finally, for the same class of curves, we prove a smoothing theorem which constitutes an improvement over known results even in the compact-type case.
On nef subvarieties

Abstract In this paper, we first study generalizations of Fujita vanishing theorems for q-ample divisors. We then apply them to study positivity of subvarieties with nef normal bundle in the sense of intersection theory. After Ottem's work on ample subschemes, we introduce the notion of a nef subscheme, which generalizes the notion of a subvariety with nef normal bundle. We show that restriction of a pseudoeffective (resp. big) divisor to a nef subvariety is pseudoeffective (resp. big). We also show that ampleness and nefness are transitive properties. We define the weakly movable cone as the cone generated by the pushforward of cycle classes of nef subvarieties via proper surjective maps. This cone contains the movable cone and shares similar intersection-theoretic properties with it, thanks to the aforementioned properties of nef subvarieties. On the other hand, we prove that if Y ⊂ X is an ample subscheme of codimension r and D | Y is q-ample, then D is ( q + r ) -ample. This is analogous to a result proved by Demailly-Peternell-Schneider and Kuronya.
Rigidity of complex convex divisible sets

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts cocompactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have C1 boundary, and have word hyperbolic dividing group. In this paper we study a notion of convexity in complex projective space and show that the only divisible complex convex sets with C1 boundary are the projective balls.
Aperiodic Crosscorrelation of Sequences Derived From Characters

It is shown that the pairs of maximal linear recursive sequences ( $m$ -sequences) typically have mean square aperiodic crosscorrelation on par with that of random sequences, but that if one takes a pair of $m$ -sequences where one is the reverse of the other, and shifts them appropriately, one can get significantly lower mean square aperiodic crosscorrelation. Sequence pairs with even lower mean square aperiodic crosscorrelation are constructed by taking a Legendre sequence, cyclically shifting it, and then cutting it (approximately) in half and using the halves as the sequences of the pair. In some of these constructions, the mean square aperiodic crosscorrelation can be lowered further if one truncates or periodically extends (appends) the sequences. Exact asymptotic formulas for mean squared aperiodic crosscorrelation are proved for sequences derived from additive characters (including $m$ -sequences and modified versions thereof) and multiplicative characters (including Legendre sequences and their relatives). Data are presented that show that the sequences of modest length have performance that closely approximates the asymptotic formulas.
DeepDeath: Learning to predict the underlying cause of death with Big Data

Multiple cause-of-death data provides a valuable source of information that can be used to enhance health standards by predicting health related trajectories in societies with large populations. These data are often available in large quantities across U.S. states and require Big Data techniques to uncover complex hidden patterns. We design two different classes of models suitable for large-scale analysis of mortality data, a Hadoop-based ensemble of random forests trained over N-grams, and the DeepDeath, a deep classifier based on the recurrent neural network (RNN). We apply both classes to the mortality data provided by the National Center for Health Statistics and show that while both perform significantly better than the random classifier, the deep model that utilizes long short-term memory networks (LSTMs), surpasses the N-gram based models and is capable of learning the temporal aspect of the data without a need for building ad-hoc, expert-driven features.
Work Analysis with Resource-Aware Session Types

While there exist several successful techniques for supporting programmers in deriving static resource bounds for sequential code, analyzing the resource usage of message-passing concurrent processes poses additional challenges. To meet these challenges, this article presents an analysis for statically deriving worst-case bounds on the total work performed by message-passing processes. To decompose interacting processes into components that can be analyzed in isolation, the analysis is based on novel resource-aware session types, which describe protocols and resource contracts for inter-process communication. A key innovation is that both messages and processes carry potential to share and amortize cost while communicating. To symbolically express resource usage in a setting without static data structures and intrinsic sizes, resource contracts describe bounds that are functions of interactions between processes. Resource-aware session types combine standard binary session types and type-based amortized resource analysis in a linear type system. This type system is formulated for a core session-type calculus of the language SILL and proved sound with respect to a multiset-based operational cost semantics that tracks the total number of messages that are exchanged in a system. The effectiveness of the analysis is demonstrated by analyzing standard examples from amortized analysis and the literature on session types and by a comparative performance analysis of different concurrent programs implementing the same interface.
Dynamic Instability of the Standard Model and the Fine-Tuning Problem

The Standard Model for particle physics (SM) is a nonlinear field theory in which both Yang-Mills and Higgs bosons are self-interacting objects. Their classical or quantum evolution is inevitably sensitive to the transition from order to chaos. With some noteworthy exceptions, the mainstream of theoretical particle physics has ignored the dynamical contribution of chaos in Quantum Field Theory. Here we point out that quantum corrections to the classical interaction of the Higgs with gauge bosons may lower the threshold for the onset of chaos and destabilize the vacuum in the low or intermediate TeV scale. The inability of the vacuum to survive in this energy region hints to a straightforward solution for the fine-tuning problem. It also implies that perturbative estimates on vacuum stability well above the LHC scale are likely to be invalid.
Morph: flexible acceleration for 3D CNN-based video understanding

The past several years have seen both an explosion in the use of Convolutional Neural Networks (CNNs) and accelerators to make CNN inference practical. In the architecture community, the lion share of effort has targeted CNN inference for image recognition. The closely related problem of video recognition has received far less attention as an accelerator target. This is surprising, as video recognition is more computationally intensive than image recognition, and video traffic is predicted to be the majority of internet traffic in the coming years. This paper fills the gap between algorithmic and hardware advances for video recognition by providing a design space exploration and flexible architecture for accelerating 3D Convolutional Neural Networks (3D CNNs)—the core kernel in modern video understanding. When compared to (2D) CNNs used for image recognition, efficiently accelerating 3D CNNs poses a significant engineering challenge due to their large (and variable over time) memory footprint and higher dimensionality. To address these challenges, we design a novel accelerator called "Morph," that can adaptively support different spatial and temporal tiling strategies depending on the needs of each layer of each target 3D CNN. We codesign a software infrastructure alongside the Morph hardware to find good-fit parameters to control the hardware. Evaluated on state-of-the-art 3D CNNs, Morph achieves up to 2.7× (1.9× average) reduction in energy consumption and improves performance/watt up to 4.4× (3× average) compared to a baseline 3D CNN accelerator, with an area overhead of 2%. Morph further achieves a 11.6× average energy reduction on 3D CNNs when compared to Eyeriss, a popular 2D CNN accelerator, while reducing efficiency compared to Eyeriss on a 2D CNN by 71%.
The Calabi Flow with Rough Initial Data

In this paper, we prove that there exists a dimensional constant $\delta > 0$ such that given any background K\"ahler metric $\omega$, the Calabi flow with initial data $u_0$ satisfying \begin{equation*} \partial \bar \partial u_0 \in L^\infty (M) \text{ and } (1- \delta )\omega 0, \end{equation*} which should be interpreted as a "continuous K\"ahler metric". A main technical ingredient is Schauder-type estimates for biharmonic heat equation on Riemannian manifolds with time weighted H\"older norms.
Fair Scheduling Policies Exploiting Multiuser Diversity in Cellular Systems With Device-to-Device Communications

We consider the resource allocation problem in cellular networks which support device-to-device communications (D2D). For systems that enable D2D via only orthogonal resource sharing, we propose and analyze two resource allocation policies that guarantee access fairness among all users, while taking advantage of multi-user diversity and local D2D communications, to provide marked improvements over existing cellular-only policies. The first policy, the Cellular Fairness Scheduling (CFS) Policy, provides the simplest D2D extension to existing cellular systems, while the second policy, the D2D Fairness Scheduling (DFS) Policy, harnesses maximal performance from D2D-enabled systems under the orthogonal sharing setting. For even higher spectral efficiency, cellular systems with D2D can schedule the same frequency resource for more than one D2D pairs. Under this non-orthogonal sharing environment, we propose a novel group scheduling policy, the Group Fairness Scheduling (GFS) Policy, that exploits both spatial frequency reuse and multiuser diversity to deliver dramatic improvements to system performance with perfect fairness among the users, regardless of whether they are cellular or D2D users.
Singularities of Richardson varieties

We give a short proof that essentially all questions concerning singularities of Richardson varieties reduce to corresponding questions about Schubert varieties. Consequently, we quickly deduce some new and previously known results.
Current Injection Attack against the KLJN Secure Key Exchange

The Kirchhoff-law-Johnson-noise (KLJN) scheme is a statistical/physical secure key exchange system based on the laws of classical statistical physics to provide unconditional security. We used the LTSPICE industrial cable and circuit simulator to emulate one of the major active (invasive) attacks, the current injection attack, against the ideal and a practical KLJN system, respectively. We show that two security enhancement techniques, namely, the instantaneous voltage/current comparison method, and a simple privacy amplification scheme, independently and effectively eliminate the information leak and successfully preserve the system’s unconditional security.
Learning Unknown Markov Decision Processes: A Thompson Sampling Approach

We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth rate of episode length. The second stopping criterion happens when the number of visits to any state-action pair is doubled. We establish $\tilde O(HS\sqrt{AT})$ bounds on expected regret under a Bayesian setting, where $S$ and $A$ are the sizes of the state and action spaces, $T$ is time, and $H$ is the bound of the span. This regret bound matches the best available bound for weakly communicating MDPs. Numerical results show it to perform better than existing algorithms for infinite horizon MDPs.
Algorithmic Regularization in Over-parameterized Matrix Sensing and Neural Networks with Quadratic Activations

We show that the gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations. Concretely, we show that given $\tilde{O}(dr^{2})$ random linear measurements of a rank $r$ positive semidefinite matrix $X^{\star}$, we can recover $X^{\star}$ by parameterizing it by $UU^\top$ with $U\in \mathbb R^{d\times d}$ and minimizing the squared loss, even if $r \ll d$. We prove that starting from a small initialization, gradient descent recovers $X^{\star}$ in $\tilde{O}(\sqrt{r})$ iterations approximately. The results solve the conjecture of Gunasekar et al.'17 under the restricted isometry property. The technique can be applied to analyzing neural networks with one-hidden-layer quadratic activations with some technical modifications.
A multi-scale approach to describe electrical impulses propagating along actin filaments in both intracellular and in vitro conditions

An accurate and efficient characterization of the polyelectrolyte properties for cytoskeleton filaments are key to the molecular understanding of electrical signal propagation, bundle and network formation, as well as their potential nanotechnological applications. In this article, we introduce an innovative multi-scale approach able to account for the atomistic details of a protein molecular structure, its biological environment, and their impact on electrical impulses propagating along wild type Actin filaments. The formulation includes non trivial contributions to the ionic electrical conductivity and capacitance coming from the diffuse part of the electrical double layer of G-actins. We utilize this monomer characterization in a nonlinear inhomogeneous transmission line prototype model to account for the monomer-monomer interactions, dissipation and damping perturbations along the filament length. A novel, simple, accurate, approximate analytic expression has been obtained for the transmission line model. Our results reveal the propagation of electrical signal impulses in the form of solitons for the range of voltage stimulus and electrolyte solutions typically present for intracellular and in-vitro conditions. The approach predicts a lower electrical conductivity with higher linear capacitance and nonlinear accumulation of charge for intracellular conditions. Our results show a significant influence of the voltage input on the electrical impulse shape, attenuation and kern propagation velocity. The filament is able to sustain the soliton propagation at almost constant kern velocity for the in-vitro condition, whereas the intracellular condition displays a remarkable deceleration. Additionally, the solitons are narrower and travel faster at higher voltage input. As a unique feature, this multi-scale theory is able to account for molecular structure conformation (mutation) and biological environment (protonations/deprotonations) changes often present in pathological conditions. It is also applicable to other highly charged rod-like polyelectrolytes with relevance in biomedicine and biophysics.
Finite Time Blowup for Lagrangian Modifications of the Three-Dimensional Euler Equation

In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as $$\begin{aligned} \partial _t \omega + {\mathcal {L}}_u \omega&= 0\\ u&= \delta \tilde{\eta }^{-1} \Delta ^{-1} \omega \end{aligned}$$ where $$\omega $$ is the vorticity 2-form, $${\mathcal {L}}_u$$ denotes the Lie derivative with respect to the velocity field u, $$\Delta $$ is the Hodge Laplacian, $$\delta $$ is the codifferential (the negative of the divergence operator), and $$\tilde{\eta }^{-1}$$ is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric $$\eta $$ . In this paper we consider a generalisation of these Euler equations in three spatial dimensions, in which the vector potential operator $$\tilde{\eta }^{-1} \Delta ^{-1}$$ is replaced by a more general operator A of order $$-2$$ ; this retains the Lagrangian structure of the Euler equations, as well as most of its conservation laws and local existence theory. Despite this, we give three different constructions of such an operator A which admits smooth solutions that blow up in finite time, including an example on $$\mathbb {R}^3$$ which is self-adjoint and positive definite. This indicates a barrier to establishing global regularity for the three-dimensional Euler equations, in that any method for achieving this must use some property of those equations that is not shared by the generalised Euler equations considered here.