cssi/SciSciGPT-SciSciNet huggingface dataset:
Economic Analysis of Software Defined Networking (SDN) Under Various Network Failure Scenarios

Failures are inevitable in an operational network. They can happen anytime in different sizes and components of a network. They impact the network economics regarding CAPEX (Capital Expenditure), OPEX (Operational Expenditure), revenue lost due to service provisioning cut and so on. In order to mitigate the damages resulting from these failures, reactions of network architectures and designs are crucial for the future of the network. Recently, Software Defined Networking (SDN) has got the attention of researchers from both academia and industry as a means in order to increase network availability and reliability due to features, such as centralized automated control and global network view, it promises in networking. To this end, we explore the effects of programmable network architectures, i.e. SDN technology, and traditional network architectures, i.e. MPLS (Multiprotocol Label Switching) technology, on network economics by exploiting Number of Satisfied Service Requests and our predefined Unit Service Cost Scalability metrics under network failure scenarios: i) a random single data plane link failure and ii) a random controller (i.e. control plane) failure. To the best of our knowledge, this study is the first to consider a comparison of a programmable network architecture, i.e. SDN, along with different control plane models, Centralized (Single) Control Plane (CCP), Distributed (Flat) Control Plane (DCP), and Hierarchical Control Plane (HCP), and a non-programmable network architecture, i.e. MPLS, regarding network economics in case of network failures.
Defining the patient experience in medical oncology.

Higher patient satisfaction is associated with improved health outcomes, treatment adherence, and quality of life. The goal of this study was to explore oncology patients’ perceptions on their hospital experience, focusing on the quality of care in medical oncology. A qualitative and quantitative study design was implemented with a sample of 58 patients at Smilow Yale New Haven Hospital. Data were collected from patient interviews and observation of rounds. Two themes emerged: hospital experience and physician communication skills. Within hospital experience, subthemes identified include: attended to (49%), facility/staff (35%), nurses (33%), long wait time (29%), doctors (20%), coordination of care (18%), unnecessary medical procedures (10%), medications (6%), night awakenings (4%), pain (4%), not getting better (4%), and decreased mobility (2%). Within physician communication skills, subthemes identified include: involving the patient and/or family in the care process (41%), method of information sharing (18%), lack of coordination of care (15%), use of medical jargon (10%), attending to patient’s needs (8%), and lack of patient’s perspective (8%). Patients reported that effective engagement of patients in the care process and attending to patient-specific needs were desired qualities in their hospital experience as well as patient-centered communication with their physician. The quantitative data supported qualitative results with 72% of patients giving the highest score in overall satisfaction with their patient experience. Physician attentiveness or lack thereof is a defining aspect of the quality of patient experience and physician communication. The results are intended to inform clinical and operational interventions that care providers might incorporate into practice.
A Multi-Physics Battery Model with Particle Scale Resolution of Porosity Evolution Driven by Intercalation Strain and Electrolyte Flow

We present a coupled continuum formulation for the electrostatic, chemical, thermal, mechanical and fluid physics in battery materials. Our treatment is at the particle scale, at which the active particles held together by carbon-binders, the porous separator, current collectors and the perfusing electrolyte are explicitly modeled. Starting with the description common to the field, in terms of reaction-transport partial differential equations for ions, variants of the classical Poisson equation for electrostatics, and the heat equation, we introduce solid-fluid interaction to the problem. Our main contribution is to model the electrolyte as an incompressible fluid driven by elastic, thermal and lithium intercalation strains in the active material. Our treatment is in the finite strain setting, and uses the Arbitrary Lagrangian-Eulerian (ALE) framework to account for mechanical coupling of the solid and fluid. We present a detailed computational study of the influence of solid-fluid interaction and magnitude of intercalation strain upon porosity evolution, ion distribution and electrostatic potential fields in the cell.
Minimax structured normal means inference

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means inference. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different means, the distribution that produced some observed data. Recent work has studied several special cases including sparse vectors, biclusters, and graph-based structures. We establish nearly matching upper and lower bounds on the minimax probability of error for any structured normal means problem, and we derive an optimality certificate for the maximum likelihood estimator, which can be applied to many instantiations. We also consider an experimental design setting, where we generalize our minimax bounds and derive an algorithm for computing a design strategy with a certain optimality property. We show that our results give tight minimax bounds for many structure recovery problems and consider some consequences for interactive sampling.
Geometric rounding and feature separation in meshes

Abstract Geometric rounding of a 3D triangle mesh is the task of approximating the vertex coordinates by floating point numbers while preserving the topology. We present a practical geometric rounding algorithm based on a novel strategy: (1) modify the mesh to achieve a feature separation that prevents topology changes when the coordinates change by the rounding unit; and (2) round each vertex coordinate to the closest floating point number. The geometric rounding algorithm allows computational geometry algorithms to interface with numerical algorithms. Mesh feature separation is also useful on its own, for example for enforcing minimum feature sizes in CAD models. We demonstrate a robust, efficient implementation.
Unavoidable disorder and entropy in multi-component systems

The need for improved functionalities is driving the search for more complicated multi-component materials. Despite the factorially increasing composition space, ordered compounds with four or more species are rare. Here, we unveil the competition between the gain in enthalpy and entropy with increasing number of species by statistical analysis of the AFLOW data repositories. A threshold in the number of species is found where entropy gain exceeds enthalpy gain. Beyond that, enthalpy can be neglected, and disorder—complete or partial—is unavoidable.
Sum-integral interpolators and the Euler-Maclaurin formula for polytopes

A local lattice point counting formula, and more generally a local Euler-Maclaurin formula follow by comparing two natural families of meromorphic functions on the dual of a rational vector space V , namely the family of exponential sums (S) and the family of exponential integrals (I) parametrized by the set of rational polytopes in V. The paper introduces the notion of an interpolator between these two families of meromorphic functions. We prove that every rigid complement map in V gives rise to an effectively computable SI-interpolator (and a local Euler-MacLaurin formula), an IS-interpolator (and a reverse local Euler-MacLaurin formula) and an IS 0 -interpolator (which interpolates between integrals and sums over interior lattice points.) Rigid complement maps can be constructed by choosing an inner product on V or by choosing a complete flag in V. The corresponding interpolators generalize and unify the work of Berline-Vergne, Pommersheim-Thomas, and Morelli.
The limitations of simple gene set enrichment analysis assuming gene independence

Since its first publication in 2003, the Gene Set Enrichment Analysis method, based on the Kolmogorov-Smirnov statistic, has been heavily used, modified, and also questioned. Recently a simplified approach using a one-sample t-test score to assess enrichment and ignoring gene-gene correlations was proposed by Irizarry et al. 2009 as a serious contender. The argument criticizes Gene Set Enrichment Analysis’s nonparametric nature and its use of an empirical null distribution as unnecessary and hard to compute. We refute these claims by careful consideration of the assumptions of the simplified method and its results, including a comparison with Gene Set Enrichment Analysis’s on a large benchmark set of 50 datasets. Our results provide strong empirical evidence that gene–gene correlations cannot be ignored due to the significant variance inflation they produced on the enrichment scores and should be taken into account when estimating gene set enrichment significance. In addition, we discuss the challenges th...
Relaxed Byzantine Vector Consensus

Byzantine vector consensus requires that non-faulty processes reach agreement on adecision (or output) that is in the convex hull of the inputs at the non-faulty processes. Recent work has shown that, for n processes with up to f Byzantine failures, when the inputs are d-dimensional vectors of reals, n >= max (3f + 1, (d + 1)f + 1) is the tight bound for synchronous systems, and n >= (d + 2)f + 1 is tight for approximate consensus in asynchronous systems. Due to the dependence of the lower bound on vector dimension d, the number of processes necessary becomes large when the vector dimension is large. With the hope of reducing the lower bound on n, we propose relaxed versions of Byzantine vector consensus: k-relaxed Byzantine vector consensus and (delta, p)-relaxed Byzantine vector consensus. k-relaxed consensus only requires consensus for projections of inputs on every subset of k dimensions. (delta, p)-relaxed consensus requires that the output be within distance d of the convex hull of the non-faulty inputs, where distance is defined using the L_{p}-norm. An input-dependent delta allows the distance from the non-faulty convex hull to be dependent on the maximum distance between the non-faulty inputs. We show that for k-relaxed consensus with k > 1, and for (delta, p)-relaxed consensus with constant delta >= 0, the bound on n is identical to the bound stated above for the original vector consensus problem. On the other hand, when k = 1 or d depends on the inputs, we show that the bound on n is smaller when d >= 3. Input-dependent delta may be of interest in practice. In essence, input-dependent delta scales with the spread of the inputs.
The Gauss-Bonnet-Chern theorem: A probabilistic perspective

We prove that the Euler form of a metric connection on a real oriented vector bundle E over a compact oriented manifold M can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section of the bundle. We also explain how to reconstruct probabilistically the metric and the connection on E from the statistics of random sections of E. CONTENTS
Upper Bounds on L-Functions at the Edge of the Critical Strip

The problem of finding upper bounds for L-functions at the edge of the critical strip has a long and interesting history. Here, the situation for classical L-functions such as Dirichlet L-functions is relatively well understood. The reason for this is because the size of the coefficients of these L-functions is known to be small. Although L-functions are generally expected to have coefficients which are bounded by a constant at the primes, this has only been proven for a small class of familiar examples. Our main focus here is on the problem of finding upper bounds for L-functions for which we have comparatively bad bounds for the size of the coefficients.
Minimality and fiber sum decompositions of Lefschetz fibrations

We give a short proof of a conjecture of Stipsicz on the minimality of fiber sums of Lefschetz fibrations, which was proved earlier by Usher. We then construct the first examples of genus g > 1 Lefschetz fibrations on minimal symplectic 4-manifolds which, up to diffeomorphisms of the summands, admit unique decompositions as fiber sums.
Conflict-driven Hybrid Observer-based Anomaly Detection

This paper presents an anomaly detection method using a hybrid observer - which consists of a discrete state observer and a continuous state observer. We focus our attention on anomalies caused by intelligent attacks, which may bypass existing anomaly detection methods because neither the event sequence nor the observed residuals appear to be anomalous. Based on the relation between the continuous and discrete variables, we define three conflict types and give the conditions under which the detection of the anomalies is guaranteed. We call this method conflict-driven anomaly detection. The effectiveness of this method is demonstrated mathematically and illustrated on a Train-Gate (TG) system.
Label-Free Supervision of Neural Networks with Physics and Domain Knowledge

In many machine learning applications, labeled data is scarce and obtaining more labels is expensive. We introduce a new approach to supervising neural networks by specifying constraints that should hold over the output space, rather than direct examples of input-output pairs. These constraints are derived from prior domain knowledge, e.g., from known laws of physics. We demonstrate the effectiveness of this approach on real world and simulated computer vision tasks. We are able to train a convolutional neural network to detect and track objects without any labeled examples. Our approach can significantly reduce the need for labeled training data, but introduces new challenges for encoding prior knowledge into appropriate loss functions.
Open-World Knowledge Graph Completion

Knowledge Graphs (KGs) have been applied to many tasks including Web search, link prediction, recommendation, natural language processing, and entity linking. However, most KGs are far from complete and are growing at a rapid pace. To address these problems, Knowledge Graph Completion (KGC) has been proposed to improve KGs by filling in its missing connections. Unlike existing methods which hold a closed-world assumption, i.e., where KGs are fixed and new entities cannot be easily added, in the present work we relax this assumption and propose a new open-world KGC task. As a first attempt to solve this task we introduce an open-world KGC model called ConMask. This model learns embeddings of the entity's name and parts of its text-description to connect unseen entities to the KG. To mitigate the presence of noisy text descriptions, ConMask uses a relationship-dependent content masking to extract relevant snippets and then trains a fully convolutional neural network to fuse the extracted snippets with entities in the KG. Experiments on large data sets, both old and new, show that ConMask performs well in the open-world KGC task and even outperforms existing KGC models on the standard closed-world KGC task.
Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"

This special issue collects contributions from the participants of the “Information in Dynamical Systems and Complex Systems” workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported here in reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.
Grammar as a foreign language

Syntactic constituency parsing is a fundamental problem in natural language processing and has been the subject of intensive research and engineering for decades. As a result, the most accurate parsers are domain specific, complex, and inefficient. In this paper we show that the domain agnostic attention-enhanced sequence-to-sequence model achieves state-of-the-art results on the most widely used syntactic constituency parsing dataset, when trained on a large synthetic corpus that was annotated using existing parsers. It also matches the performance of standard parsers when trained only on a small human-annotated dataset, which shows that this model is highly data-efficient, in contrast to sequence-to-sequence models without the attention mechanism. Our parser is also fast, processing over a hundred sentences per second with an unoptimized CPU implementation.
The impact of global nuclear mass model uncertainties on r-process abundance predictions

Rapid neutron capture or ‘r -process’ nucleosynthesis may be responsible for half the production of heavy elements above iron on the periodic table. Masses are one of the most important nuclear physics ingredients that go into calculations of r -process nucleosynthesis as they enter into the calculations of reaction rates, decay rates, branching ratios and Q-values. We explore the impact of uncertainties in three nuclear mass models on r -process abundances by performing global monte carlo simulations. We show that root-mean-square (rms) errors of current mass models are large so that current r -process predictions are insufficient in predicting features found in solar residuals and in r -process enhanced metal poor stars. We conclude that the reduction of global rms errors below 100 keV will allow for more robust r -process predictions.
A Resolvent Criterion for Normality

AbstractGiven a normal matrix A and an arbitrary square matrix B (not necessarily of the same size), what relationships between A and B, if any, guarantee that B is also a normal matrix? We provide an answer to this question in terms of pseudospectra and norm behavior. In doing so, we prove that a certain distance formula, known to be a necessary condition for normality, is in fact sufficient and demonstrates that the spectrum of a matrix can be used to recover the spectral norm of its resolvent precisely when the matrix is normal. These results lead to new normality criteria and other interesting consequences.
Global analysis of multi-host and multi-vector epidemic models.

Abstract We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression S E I R framework and the dynamics of vectors is captured by an SI framework. The proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by m host species and transmitted by p arthropod vector species. In each host, the infectious period is structured into n stages with a corresponding infectiousness parameter to each vector species. We determine the basic reproduction number R 0 2 ( m , n , p ) and investigate the dynamics of the systems when this threshold is less or greater than one. We show that the dynamics of the multi-host, multi-stage, and multi-vector system is completely determined by the basic reproduction number and the structure of the host-vector network configuration. Particularly, we prove that the disease-free equilibrium is globally asymptotically stable (GAS) whenever R 0 2 ( m , n , p ) 1 , and a unique strongly endemic equilibrium exists and is GAS if R 0 2 ( m , n , p ) > 1 and the host-vector configuration is irreducible. That is, either the disease dies out or persists in all hosts and all vector species.
Clustering on Multiple Incomplete Datasets via Collective Kernel Learning

Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors and credit history to group users. Each dataset contains different information and suffices for learning. A number of clustering algorithms on multiple datasets were proposed during the past few years. These algorithms assume that at least one dataset is complete. So far as we know, all the previous methods will not be applicable if there is no complete dataset available. However, in reality, there are many situations where no dataset is complete. As in building a recommendation system, some new users may not have profiles or historical behaviors, while some may not have credit history. Hence, no available dataset is complete. In order to solve this problem, we propose an approach called Collective Kernel Learning to infer hidden sample similarity from multiple incomplete datasets. The idea is to collectively completes the kernel matrices of incomplete datasets by optimizing the alignment of shared instances of the datasets. Furthermore, a clustering algorithm is proposed based on the kernel matrix. The experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed approach. The proposed clustering algorithm outperforms the comparison algorithms by as much as two times in normalized mutual information.
Analytic computable structure theory and $L^p$ spaces

We continue the investigation of analytic spaces from the perspective of computable structure theory. We show that if $p \geq 1$ is a computable real, and if $\Omega$ is a nonzero, non-atomic, and separable measure space, then every computable presentation of $L^p(\Omega)$ is computably linearly isometric to the standard computable presentation of $L^p[0,1]$; in particular, $L^p[0,1]$ is computably categorical. We also show that there is a measure space $\Omega$ that does not have a computable presentation even though $L^p(\Omega)$ does for every computable real $p \geq 1$.
Cognitive mechanisms for human flocking dynamics

Low-level “adaptive” and higher-level “sophisticated” human reasoning processes have been proposed to play opposing roles in the emergence of unpredictable collective behaviors such as crowd panics, traffic jams, and market bubbles. While adaptive processes are widely recognized drivers of emergent social complexity, complementary theories of sophistication predict that incentives, education, and other inducements to rationality will suppress it. We show in a series of multiplayer laboratory experiments that, rather than suppressing complex social dynamics, sophisticated reasoning processes can drive them. Our experiments elicit an endogenous collective behavior and show that it is driven by the human ability to recursively anticipate the reasoning of others. We identify this behavior, “sophisticated flocking”, across three games, the Beauty Contest and the “Mod Game” and “Runway Game”. In supporting our argument, we also present evidence for mental models and social norms constraining how players express their higher-level reasoning abilities. By implicating sophisticated recursive reasoning in the kind of complex dynamic that it has been predicted to suppress, we support interdisciplinary perspectives that emergent complexity is typical of even the most intelligent populations and carefully designed social systems.
Rado’s Conjecture and its Baire version

Rado’s Conjecture is a compactness/reflection principle that says any nonspecial tree of height ω1 has a nonspecial subtree of size ℵ1. Though incompatible with Martin’s Axiom, Rado’s Conjecture tu...
A non-linear convex cost model for economic dispatch in microgrids

Abstract This paper proposes a convex non-linear cost saving model for optimal economic dispatch in a microgrid. The model incorporates energy storage degradation cost and intermittent renewable generation. Cell degradation cost being a non-linear model, its incorporation in an objective function alters the convexity of the optimization problem and stochastic algorithms are required for its solution. This paper builds on the scope for usage of macroscopically semi-empirical models for degradation cost in economic dispatch problems and proves that these cost models derived from the existing semi-empirical capacity fade equations for LiFePO4 cells are convex under some operating conditions. The proposed non-linear model was tested on two data sets of varying size which portray different trends of seasonality. The results show that the model reflects the trends of seasonality existing in the data sets and it minimizes the total fuel cost globally when compared to conventional systems of economic dispatch. The results thus indicate that the model achieves a more accurate estimate of fuel cost in the system and can be effectively utilized for cost analysis in power system applications.
Approximation beats concentration? An approximation view on inference with smooth radial kernels

Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view to explore various aspects of smooth kernels related to their inferential properties. We analyze eigenvalue decay of kernels operators and matrices, properties of eigenfunctions/eigenvectors and "Fourier" coefficients of functions in the kernel space restricted to a discrete set of data points. We also investigate the fitting capacity of kernels, giving explicit bounds on the fat shattering dimension of the balls in Reproducing Kernel Hilbert spaces. Interestingly, the same properties that make kernels very effective approximators for functions in their "native" kernel space, also limit their capacity to represent arbitrary functions. We discuss various implications, including those for gradient descent type methods. It is important to note that most of our bounds are measure independent. Moreover, at least in moderate dimension, the bounds for eigenvalues are much tighter than the bounds which can be obtained from the usual matrix concentration results. For example, we see that the eigenvalues of kernel matrices show nearly exponential decay with constants depending only on the kernel and the domain. We call this "approximation beats concentration" phenomenon as even when the data are sampled from a probability distribution, some of their aspects are better understood in terms of approximation theory.
Deterministic Search for CNF Satisfying Assignments in Almost Polynomial Time

We consider the fundamental derandomization problem of deterministically finding a satisfying assignment to a CNF formula that has many satisfying assignments. We give a deterministic algorithm which, given an n-variable \poly(n)-clause CNF formula F that has at least &#x2265; 2^n satisfying assignments, runs in time \[ n^{\tilde{O}(\log\log n)^2} \] for &#x2265; \ge 1/\polylog(n) and outputs a satisfying assignment of F. Prior to our work the fastest known algorithm for this problem was simply to enumerate over all seeds of a pseudorandom generator for CNFs; using the best known PRGs for CNFs \cite{DETT10, this takes time n^{\tilde{&#x03A9;}(\log n)} even for constant &#x2265;. Our approach is based on a new general framework relating deterministic search and deterministic approximate counting, which we believe may find further applications.
Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modeling

We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are often required for identification. The new algorithm is particularly suitable for cases where the available sample size is large enough to accurately estimate second-order output probabilities, but not higher-order ones. We show that if one is only able to obtain a reliable estimate of the pairwise co-occurrence probabilities of the emissions, it is still possible to uniquely identify the HMM if the emission probability is \emph{sufficiently scattered}. We apply our method to hidden topic Markov modeling, and demonstrate that we can learn topics with higher quality if documents are modeled as observations of HMMs sharing the same emission (topic) probability, compared to the simple but widely used bag-of-words model.
Colorful Coverings of Polytopes and Piercing Numbers of Colorful d-Intervals

We prove a common strengthening of Barany’s colorful Caratheodory theorem and the KKMS theorem. In fact, our main result is a colorful polytopal KKMS theorem, which extends a colorful KKMS theorem due to Shih and Lee [Math. Ann. 296 (1993), no. 1, 35–61] as well as a polytopal KKMS theorem due to Komiya [Econ. Theory 4 (1994), no. 3, 463–466]. The (seemingly unrelated) colorful Caratheodory theorem is a special case as well. We apply our theorem to establish an upper bound on the piercing number of colorful d-interval hypergraphs, extending earlier results of Tardos [Combinatorica 15 (1995), no. 1, 123–134] and Kaiser [Discrete Comput. Geom. 18 (1997), no. 2, 195–203].
Tensor products of cyclic algebras of degree 4 and their Kummer subspaces

ABSTRACTWe prove that the maximal dimension of a Kummer space in the generic tensor product of n cyclic algebras of degree 4 is 4n + 1.
Solving the Conjugacy Decision Problem via Machine Learning

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented no...
The Sample Complexity of Online One-Class Collaborative Filtering

We consider the online one-class collaborative filtering (CF) problem that consists of recommending items to users over time in an online fashion based on positive ratings only. This problem arises when users respond only occasionally to a recommendation with a positive rating, and never with a negative one. We study the impact of the probability of a user responding to a recommendation, p_f, on the sample complexity, i.e., the number of ratings required to make `good' recommendations, and ask whether receiving positive and negative ratings, instead of positive ratings only, improves the sample complexity. Both questions arise in the design of recommender systems. We introduce a simple probabilistic user model, and analyze the performance of an online user-based CF algorithm. We prove that after an initial cold start phase, where recommendations are invested in exploring the user's preferences, this algorithm makes---up to a fraction of the recommendations required for updating the user's preferences---perfect recommendations. The number of ratings required for the cold start phase is nearly proportional to 1/p_f, and that for updating the user's preferences is essentially independent of p_f. As a consequence we find that, receiving positive and negative ratings instead of only positive ones improves the number of ratings required for initial exploration by a factor of 1/p_f, which can be significant.
A convergent Gradient descent algorithm for rank minimization and semidefinite programming from random linear measurements

We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With O(r3K2n log n) random measurements of a positive semidefinite n x n matrix of rank r and condition number K, our method is guaranteed to converge linearly to the global optimum.
A remark on the Kottwitz homomorphism

We prove that for any split, almost simple, connected reductive group G over a p-adic field F, the Kottwitz homomorphism $$\kappa : G(F) \rightarrow \Omega $$ exhibits a homomorphic section $$\Omega \hookrightarrow G(F)$$ . We then extend this result to certain additional split connected reductive groups.
Finite Blocklength and Dispersion Bounds for the Arbitrarily- Varying Channel

Finite blocklength and second-order (dispersion) results are presented for the arbitrarily-varying channel (AVC), a classical model wherein an adversary can transmit arbitrary signals into the channel. A novel finite blocklength achievability bound is presented, roughly analogous to the random coding union bound for non-adversarial channels. This finite blocklength bound, along with a known converse bound, is used to derive bounds on the dispersion of discrete memoryless AVCs without shared randomness, and with cost constraints on the input and the state. These bounds are tight for many channels of interest, including the binary symmetric AVC. However, the bounds are not tight if the deterministic and random code capacities differ.
Frobenius splittings of toric varieties

We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that section rings of nef line bundles on diagonally split toric varieties are normally presented and Koszul, and that Schubert varieties are not diagonally split in general.
Recurrent random walks, Liouville's theorem and circle packings

It has been shown that univalent circle packings filling the complex plane C are unique up to similarities of C. Here we prove that bounded degree branched circle packings properly covering C are uniquely determined, up to similarities of C, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result.We also establish a circle packing analogue of Liouville's theorem: if f is a circle packing map whose domain packing is infinite, univalent, and has recurrent tangency graph, then the ratio map associated with f is either unbounded or constant.
Learning From Graph Neighborhoods Using LSTMs

Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or predictions. We present an approach for applying machine learning directly to such graph neighborhoods, yielding predicitons for graph nodes on the basis of the structure of their local neighborhood and the features of the nodes in it. Our approach allows predictions to be learned directly from examples, bypassing the step of creating and tuning an inference model or summarizing the neighborhoods via a fixed set of hand-crafted features. The approach is based on a multi-level architecture built from Long Short-Term Memory neural nets (LSTMs); the LSTMs learn how to summarize the neighborhood from data. We demonstrate the effectiveness of the proposed technique on a synthetic example and on real-world data related to crowdsourced grading, Bitcoin transactions, and Wikipedia edit reversions.
Weak equivalence and non-classifiability of measure preserving actions

Abert and Weiss have shown that the Bernoulli shift s_Γ of a countably infinite group Γ is weakly contained in any free measure preserving action ɑ of Γ. Proving a conjecture of Ioana, we establish a strong version of this result by showing that s_Γ×ɑ is weakly equivalent to ɑ. Using random Bernoulli shifts introduced by Abert, Glasner, and Virag, we generalize this to non-free actions, replacing s_Γ with a random Bernoulli shift associated to an invariant random subgroup, and replacing the product action with a relatively independent joining. The result for free actions is used along with the theory of Borel reducibility and Hjorth’s theory of turbulence to show that, on the weak equivalence class of a free measure preserving action, the equivalence relations of isomorphism, weak isomorphism, and unitary equivalence are not classifiable by countable structures. This in particular shows that there are no free weakly rigid actions, that is, actions whose weak equivalence class and isomorphism class coincide, answering negatively a question of Abert and Elek. We also answer a question of Kechris regarding two ergodic theoretic properties of residually finite groups. A countably infinite residually finite group Γ is said to have property EMD∗ if the action p_Γ of Γ on its profinite completion weakly contains all ergodic measure preserving actions of Γ, and Γ is said to have property MD if ι×p_Γ weakly contains all measure preserving actions of Γ, where ι denotes the identity action on a standard non-atomic probability space. Kechris has shown that EMD∗ implies MD and asked if the two properties are actually equivalent. We provide a positive answer to this question by studying the relationship between convexity and weak containment in the space of measure preserving actions.
NeuralPower: Predict and Deploy Energy-Efficient Convolutional Neural Networks

"How much energy is consumed for an inference made by a convolutional neural network (CNN)?" With the increased popularity of CNNs deployed on the wide-spectrum of platforms (from mobile devices to workstations), the answer to this question has drawn significant attention. From lengthening battery life of mobile devices to reducing the energy bill of a datacenter, it is important to understand the energy efficiency of CNNs during serving for making an inference, before actually training the model. In this work, we propose NeuralPower: a layer-wise predictive framework based on sparse polynomial regression, for predicting the serving energy consumption of a CNN deployed on any GPU platform. Given the architecture of a CNN, NeuralPower provides an accurate prediction and breakdown for power and runtime across all layers in the whole network, helping machine learners quickly identify the power, runtime, or energy bottlenecks. We also propose the "energy-precision ratio" (EPR) metric to guide machine learners in selecting an energy-efficient CNN architecture that better trades off the energy consumption and prediction accuracy. The experimental results show that the prediction accuracy of the proposed NeuralPower outperforms the best published model to date, yielding an improvement in accuracy of up to 68.5%. We also assess the accuracy of predictions at the network level, by predicting the runtime, power, and energy of state-of-the-art CNN architectures, achieving an average accuracy of 88.24% in runtime, 88.34% in power, and 97.21% in energy. We comprehensively corroborate the effectiveness of NeuralPower as a powerful framework for machine learners by testing it on different GPU platforms and Deep Learning software tools.
Eigenvector Computation and Community Detection in Asynchronous Gossip Models

We give a simple distributed algorithm for computing adjacency matrix eigenvectors for the communication graph in an asynchronous gossip model. We show how to use this algorithm to give state-of-the-art asynchronous community detection algorithms when the communication graph is drawn from the well-studied stochastic block model. Our methods also apply to a natural alternative model of randomized communication, where nodes within a community communicate more frequently than nodes in different communities. Our analysis simplifies and generalizes prior work by forging a connection between asynchronous eigenvector computation and Oja's algorithm for streaming principal component analysis. We hope that our work serves as a starting point for building further connections between the analysis of stochastic iterative methods, like Oja's algorithm, and work on asynchronous and gossip-type algorithms for distributed computation.
Restricted Boltzmann Machines: Introduction and Review

The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Boltzmann machines carry a rich structure, with connections to geometry, applied algebra, probability, statistics, machine learning, and other areas. The analysis of these models is attractive in its own right and also as a platform to combine and generalize mathematical tools for graphical models with hidden variables. This article gives an introduction to the mathematical analysis of restricted Boltzmann machines, reviews recent results on the geometry of the sets of probability distributions representable by these models, and suggests a few directions for further investigation.
On Robust Trimming of Bayesian Network Classifiers

This paper considers the problem of removing costly features from a Bayesian network classifier. We want the classifier to be robust to these changes, and maintain its classification behavior. To this end, we propose a closeness metric between Bayesian classifiers, called the expected classification agreement (ECA). Our corresponding trimming algorithm finds an optimal subset of features and a new classification threshold that maximize the expected agreement, subject to a budgetary constraint. It utilizes new theoretical insights to perform branch-and-bound search in the space of feature sets, while computing bounds on the ECA. Our experiments investigate both the runtime cost of trimming and its effect on the robustness and accuracy of the final classifier.
Strategic communication between prospect theoretic agents over a Gaussian test channel

In this paper, we model a Stackelberg game in a simple Gaussian test channel where a human transmitter (leader) communicates a source message to a human receiver (follower). We model human decision making using prospect theory models proposed for continuous decision spaces. Assuming that the value function is the squared distortion at both the transmitter and the receiver, we analyze the effects of the weight functions at both the transmitter and the receiver on optimal communication strategies, namely encoding at the transmitter and decoding at the receiver, in the Stackelberg sense. We show that the optimal strategies for the behavioral agents in the Stackelberg sense are identical to those designed for unbiased agents. At the same time, we also show that the prospect-theoretic distortions at both the transmitter and the receiver are both larger than the expected distortion, thus making behavioral agents less contended than unbiased agents. Consequently, the presence of cognitive biases increases the need for transmission power in order to achieve a given distortion at both transmitter and receiver.
Optimizing affinity-based binary hashing using auxiliary coordinates

In supervised binary hashing, one wants to learn a function that maps a high-dimensional feature vector to a vector of binary codes, for application to fast image retrieval. This typically results in a difficult optimization problem, nonconvex and nonsmooth, because of the discrete variables involved. Much work has simply relaxed the problem during training, solving a continuous optimization, and truncating the codes a posteriori. This gives reasonable results but is quite suboptimal. Recent work has tried to optimize the objective directly over the binary codes and achieved better results, but the hash function was still learned a posteriori, which remains suboptimal. We propose a general framework for learning hash functions using affinity-based loss functions that uses auxiliary coordinates. This closes the loop and optimizes jointly over the hash functions and the binary codes so that they gradually match each other. The resulting algorithm can be seen as an iterated version of the procedure of optimizing first over the codes and then learning the hash function. Compared to this, our optimization is guaranteed to obtain better hash functions while being not much slower, as demonstrated experimentally in various supervised datasets. In addition, our framework facilitates the design of optimization algorithms for arbitrary types of loss and hash functions.
What Your Username Says About You

Usernames are ubiquitous on the Internet, and they are often suggestive of user demographics. This work looks at the degree to which gender and language can be inferred from a username alone by making use of unsupervised morphology induction to decompose usernames into sub-units. Experimental results on the two tasks demonstrate the effectiveness of the proposed morphological features compared to a character n-gram baseline.
Learning Policies for Adaptive Tracking with Deep Feature Cascades

Visual object tracking is a fundamental and time-critical vision task. Recent years have seen many shallow tracking methods based on real-time pixel-based correlation filters, as well as deep methods that have top performance but need a high-end GPU. In this paper, we learn to improve the speed of deep trackers without losing accuracy. Our fundamental insight is to take an adaptive approach, where easy frames are processed with cheap features (such as pixel values), while challenging frames are processed with invariant but expensive deep features. We formulate the adaptive tracking problem as a decision-making process, and learn an agent to decide whether to locate objects with high confidence on an early layer, or continue processing subsequent layers of a network. This significantly reduces the feedforward cost for easy frames with distinct or slow-moving objects. We train the agent offline in a reinforcement learning fashion, and further demonstrate that learning all deep layers (so as to provide good features for adaptive tracking) can lead to near real-time average tracking speed of 23 fps on a single CPU while achieving state-of-the-art performance. Perhaps most tellingly, our approach provides a 100X speedup for almost 50% of the time, indicating the power of an adaptive approach.
Avoiding The Man on the Wire: Improving Tor's Security with Trust-Aware Path Selection.

Tor users are vulnerable to deanonymization by an adversary that can observe some Tor relays or some parts of the network. We propose that users use trust to choose paths through Tor that are less likely to be observed. We present a system to model this trust as probability distributions on the location of the user’s adversaries. We propose the Trust-Aware Path Selection algorithm for Tor that helps users avoid traffic-analysis attacks while still choosing paths that could have been selected by many other users. We evaluate this algorithm in two settings using a high-level map of Internet routing: (i) users try to avoid a single global adversary that has an independent chance to control each Autonomous System organization, Internet Exchange Point organization, and Tor relay family, and (ii) users try to avoid deanonymization by any single country. We also examine the performance of trust-aware path selection using the Shadow Tor network simulator.
On clustering network-valued data

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being able to cluster within a network is important, there are emerging needs to be able to \emph{cluster multiple networks}. This is largely motivated by the routine collection of network data that are generated from potentially different populations. These networks may or may not have node correspondence. When node correspondence is present, we cluster networks by summarizing a network by its graphon estimate, whereas when node correspondence is not present, we propose a novel solution for clustering such networks by associating a computationally feasible feature vector to each network based on trace of powers of the adjacency matrix. We illustrate our methods using both simulated and real data sets, and theoretical justifications are provided in terms of consistency.