cssi/SciSciGPT-SciSciNet huggingface dataset:
The error-floor of LDPC codes in the Laplacian channel

We analyze the performance of Low-Density-Parity-Check codes in the error-floor domain where the Signal-to-Noise-Ratio, s, is large, s >> 1. We describe how the instanton method of theoretical physics, recently adapted to coding theory, solves the problem of characterizing the error-floor domain in the Laplacian channel. An example of the (155,64,20) LDPC code with four iterations (each iteration consisting of two semi-steps: from bits-to-checks and from checks-to-bits) of the min-sum decoding is discussed. A generalized computational tree analysis is devised to explain the rational structure of the leading instantons. The asymptotic for the symbol Bit-Error-Rate in the error-floor domain is comprised of individual instanton contributions, each estimated as ~ \exp(-l_{inst;L} s), where the effective distances, l_{inst;L}, of the the leading instantons are 7.6, 8.0 and 8.0 respectively. (The Hamming distance of the code is 20.) The analysis shows that the instantons are distinctly different from the ones found for the same coding/decoding scheme performing over the Gaussian channel. We validate instanton results against direct simulations and offer an explanation for remarkable performance of the instanton approximation not only in the extremal, s -> \infty, limit but also at the moderate s values of practical interest.
The Golod property of powers of the maximal ideal of a local ring

We identify minimal cases in which a power $$\mathfrak {m}^i\not =0$$ of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring $$R/\mathfrak {m}^i$$ is not Golod. Complementary to a 2014 result by Rossi and Sega, we prove that for a generic artinian Gorenstein local ring with $$\mathfrak {m}^4=0\ne \mathfrak {m}^3$$ , the quotient $$R/\mathfrak {m}^3$$ is not Golod. This is provided that $$\mathfrak {m}$$ is minimally generated by at least 3 elements. Indeed, we show that if $$\mathfrak {m}$$ is 2-generated, then every power $$\mathfrak {m}^i\ne 0$$ is Golod.
BIRACK SHADOW MODULES AND THEIR LINK INVARIANTS

We introduce an associative algebra ℤ[X, S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations of ℤ[X, S] known as shadow modules. We provide examples which demonstrate that the shadow module enhanced invariants are not determined by the Alexander polynomial or the unenhanced birack counting invariants.
Optimal Noise Adding Mechanisms for Approximate Differential Privacy

We study the (nearly) optimal mechanisms in $(\epsilon , \delta )$ -differential privacy for integer-valued query functions and vector-valued (histogram-like) query functions under a utility-maximization/cost-minimization framework. Within the classes of mechanisms oblivious of the database and the queries beyond the global sensitivity, we characterize the tradeoff between $\epsilon $ and $\delta $ in utility and privacy analysis for histogram-like query functions, and show that the $(\epsilon , \delta )$ -differential privacy is a framework not much more general than the $(\epsilon ,0)$ -differential privacy and $(0,\delta )$ -differential privacy in the context of $\ell ^{1}$ and $\ell ^{2}$ cost functions, i.e., minimum expected noise magnitude and noise power. In the same context of $\ell ^{1}$ and $\ell ^{2}$ cost functions, we show the near-optimality of uniform noise mechanism and discrete Laplacian mechanism in the high privacy regime (as $(\epsilon ,\delta ) \to (0,0)$ ). We conclude that in $(\epsilon ,\delta )$ -differential privacy, the optimal noise magnitude and the noise power are $\Theta (\min (({1}/{\epsilon }), ({1}/{\delta })))$ and $\Theta (\min (({1}/{\epsilon ^{2}}), ({1}/{\delta ^{2}})))$ , respectively, in the high privacy regime.
Deformation bicomplex of module algebras

The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras, comodule-(co)algebras, and (co)module-bialgebras are also considered.
Fairness in Recommendation Ranking through Pairwise Comparisons

Recommender systems are one of the most pervasive applications of machine learning in industry, with many services using them to match users to products or information. As such it is important to ask: what are the possible fairness risks, how can we quantify them, and how should we address them? In this paper we offer a set of novel metrics for evaluating algorithmic fairness concerns in recommender systems. In particular we show how measuring fairness based on pairwise comparisons from randomized experiments provides a tractable means to reason about fairness in rankings from recommender systems. Building on this metric, we offer a new regularizer to encourage improving this metric during model training and thus improve fairness in the resulting rankings. We apply this pairwise regularization to a large-scale, production recommender system and show that we are able to significantly improve the system's pairwise fairness.
Classification of KdV Vessels with Constant Parameters and Two Dimensional Outer Space

In this article we classify vessels producing solutions of some completely integrable partial differential equations (PDEs), presenting a unified approach for them. The classification includes such important examples as Korteweg-de Vries (KdV) and evolutionary non linear Schrodingier (ENLS) equations. In fact, employing basic matrix algebra techniques it is shown that there are exactly two canonical forms of such vessels, so that each canonical form generalize either KdV or ENLS equations. Particularly, Dirac canonical systems, whose evolution was recently inserted into the vessel theory, are shown to be equivalent to the ENLS equation in the sense of vessels. This work is important as a first step to a classification of completely integrable PDEs, which are solvable by the theory of vessels. We note that a recent paper of the author, published in Journal of Mathematical Physics, showed that initial value problem with analytic initial potential for the KdV equation has at least a “narrowing” in time solution. The presented classification inherits this idea and a similar theorem can be easily proved for the presented PDEs. Finally, the results of the work serve as a basis for the investigation of the following problems: (1) hierarchy of the generalized KdV, ENLS equations (by generalizing the vessel equations), (2) new completely integrable PDEs (by changing the dimension of the outer space), (3) addressing the question of integrability of a given arbitrary PDE (the future classification will create a list of solvable by vessels equations, which may eventually include many existing classes of PDEs).
MmWave Vehicle-to-Infrastructure Communication: Analysis of Urban Microcellular Networks

Vehicle-to-infrastructure (V2I) communication may provide high data rates to vehicles via millimeter-wave (mmWave) microcellular networks. This paper uses stochastic geometry to analyze the coverage of urban mmWave microcellular networks. Prior work used a pathloss model with a line-of-sight probability function based on randomly oriented buildings, to determine whether a link was line-of-sight or non-line-of-sight. In this paper, we use a pathloss model inspired by measurements, which uses a Manhattan distance pathloss model and accounts for differences in pathloss exponents and losses when turning corners. In our model, streets are randomly located as a Manhattan poisson line process and the base stations (BSs) are distributed according to a Poisson point process. Our model is well suited for urban microcellular networks where the BSs are deployed at street level. Based on this new approach, we derive the coverage probability under certain BS association rules to obtain closed-form solutions without much complexity. In addition, we draw two main conclusions from our work. First, non-line-of-sight BSs are not a major benefit for association or source of interference most of the time. Second, there is an ultra-dense regime where deploying active BSs does not enhance coverage.
Uniform Lie Algebras and Uniformly Colored Graphs

Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie algebras and we classify uniform Lie algebras with five or fewer generators. We define a type of directed colored graph called a uniformly colored graph and establish a correspondence between uniform Lie algebras and uniformly colored graphs. We present several methods of constructing infinite families of uniformly colored graphs and corresponding uniform Lie algebras.
Beyond Contact Tracing: Community-Based Early Detection for Ebola Response.

INTRODUCTION The 2014 Ebola outbreak in West Africa raised many questions about the control of infectious disease in an increasingly connected global society. Limited availability of contact information made contact tracing diffcult or impractical in combating the outbreak. METHODS We consider the development of multi-scale public health strategies that act on individual and community levels. We simulate policies for community-level response aimed at early screening all members of a community, as well as travel restrictions to prevent inter-community transmission. RESULTS Our analysis shows the policies to be effective even at a relatively low level of compliance and for a variety of local and long range contact transmission networks. In our simulations, 40% of individuals conforming to these policies is enough to stop the outbreak. Simulations with a 50% compliance rate are consistent with the case counts in Liberia during the period of rapid decline after mid September, 2014. We also find the travel restriction to be effective at reducing the risks associated with compliance substantially below the 40% level, shortening the outbreak and enabling efforts to be focused on affected areas. DISCUSSION Our results suggest that the multi-scale approach can be used to further evolve public health strategy for defeating emerging epidemics.
Risk of Cascading Blackouts Given Correlated Component Outages

Cascading blackouts typically occur when nearly simultaneous outages occur in $k$ out of $N$ components in a power system, triggering subsequent failures that propagate through the network and cause significant load shedding. While large cascades are rare, their impact can be catastrophic, so quantifying their risk is important for grid planning and operation. A common assumption in previous approaches to quantifying such risk is that the $k$ initiating component outages are statistically independent events. However, when triggered by a common exogenous cause, initiating outages may actually be correlated. Here, copula analysis is used to quantify the impact of correlation of initiating outages on the risk of cascading failure. The method is demonstrated on two test cases; a 2383-bus model of the Polish grid under varying load conditions and a synthetic 10 000-bus model based on the geography of the Western US. The large size of the Western US test case required development of new approaches for bounding an estimate of the total number of $N-3$ blackout-causing contingencies. The results suggest that both risk of cascading failure, and the relative contribution of higher order contingencies, increase as a function of spatial correlation in component failures.
Simultaneous active parameter estimation and control using sampling-based Bayesian reinforcement learning

Robots performing manipulation tasks must operate under uncertainty about both their pose and the dynamics of the system. In order to remain robust to modeling error and shifts in payload dynamics, agents must simultaneously perform estimation and control tasks. However, the optimal estimation actions are often not the optimal actions for accomplishing the control tasks, and thus agents trade between exploration and exploitation. This work frames the problem as a Bayes-adaptive Markov decision process and solves it online using Monte Carlo tree search and an extended Kalman filter to handle Gaussian process noise and parameter uncertainty in a continuous space. MCTS selects control actions to reduce model uncertainty and reach the goal state nearly optimally. Certainty equivalent model predictive control is used as a benchmark to compare performance in simulations with varying process noise and parameter uncertainty.
Forward reachable sets: Analytically derived properties of connected components for dynamic networks

Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration. FRS are defined as the set of nodes that can be reached from an initial seed via a path of temporally ordered edges; a natural extension of connected component measures to dynamic networks. Working in a stochastic framework, we derive closed-form expressions for the mean and variance of the exponential growth rate of the FRS for temporal networks with both edge and node dynamics. For networks with node dynamics, we calculate thresholds for the growth of the FRS. The effects of finite population size are explored via simulation and approximation. We examine how these properties vary by edge duration and different cross-sectional degree distributions that characterize a range of scientifically interesting normative outcomes (Poisson and Bernoulli). The size of the forward reachable set gives an upper bound for the epidemic size in disease transmission network models, relating this work to epidemic modeling (Ferguson, 2000; Eames, 2004).
Discrete Riesz transforms and sharp metric $X_p$ inequalities

$ \renewcommand{\subset}{\subseteq} \newcommand{\N}{\mathbb N} $For $p\in [2,\infty)$ the metric $X_p$ inequality with sharp scaling parameter is proven here to hold true in $L_p$. The geometric consequences of this result include the following sharp statements about embeddings of $L_q$ into $L_p$ when $2< q<p<\infty$: the maximal $\theta\in (0,1]$ for which $L_q$ admits a bi-$\theta$-Holder embedding into $L_p$ equals $q/p$, and for $m,n\in \N$ the smallest possible bi-Lipschitz distortion of any embedding into $L_p$ of the grid $\{1,\ldots,m\}^n\subset \ell_q^n$ is bounded above and below by constant multiples (depending only on $p,q$) of the quantity $\min\{n^{(p-q)(q-2)/(q^2(p-2))}, m^{(q-2)/q}\}$.
Generating Adversarial Examples with Adversarial Networks

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.
The Liar paradox is a Real Problem

The liar paradox is widely seen as not a serious problem. I try to explain why this view is mistaken.
Degeneracies in quasi-categories

In this note we show that a semisimplicial set with the weak Kan condition admits a simplicial structure, provided any object allows an idempotent self-equivalence. Moreover, any two choices of simplicial structures give rise to equivalent quasi-categories. The method is purely combinatorial and extends to semisimplicial objects in other categories; in particular to semi-simplicial spaces satisfying the Segal condition (semi-Segal spaces).
Multi-Winner Contests for Strategic Diffusion in Social Networks

Strategic diffusion encourages participants to take active roles in promoting stakeholders’ agendas by rewarding successful referrals. As social media continues to transform the way people communicate, strategic diffusion has become a powerful tool for stakeholders to influence people’s decisions or behaviors for desired objectives. Existing reward mechanisms for strategic diffusion are usually either vulnerable to falsename attacks or not individually rational for participants that have made successful referrals. Here, we introduce a novel multi-winner contests (MWC) mechanism for strategic diffusion in social networks. The MWC mechanism satisfies several desirable properties, including false-name-proofness, individual rationality, budget constraint, monotonicity, and subgraph constraint. Numerical experiments on four real-world social network datasets demonstrate that stakeholders can significantly boost participants’ aggregated efforts with proper design of competitions. Our work sheds light on how to design manipulation-resistant mechanisms with appropriate contests.
Efficiently Decodable Codes for the Binary Deletion Channel.

In the random deletion channel, each bit is deleted independently with probability $p$. For the random deletion channel, the existence of codes of rate $(1-p)/9$, and thus bounded away from $0$ for any $p 0$.
The least prime primitive root and the shifted sieve

We derive, for all prime moduli p except those in a very thin set, an upper bound for the least prime primitive root (mod p) of order of magnitude a constant power of log p. The improvement over previous results, where the upper bound was log p to an exponent tending to infinity with p, lies in the use of the linear sieve (a particular version called the shifted sieve) rather than Brun's sieve. The same methods allow us to rederive a conditional result of Shoup on the least prime primitive root (mod p) for all prime moduli p, assuming the generalized Riemann hypothesis. We also extend both results to composite moduli q, where the analogue of a primitive root is an element of maximal multiplicative order (mod q).
Isotone Cones in Banach Spaces and Applications to Best Approximations of Operators without Continuity Conditions

AbstractIn this paper, we introduce the concept of isotone cones in Banach spaces. Then, we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity conditions in partially ordered Banach spaces.
RAVEN: A Dataset for Relational and Analogical Visual REasoNing

Dramatic progress has been witnessed in basic vision tasks involving low-level perception, such as object recognition, detection, and tracking. Unfortunately, there is still enormous performance gap between artificial vision systems and human intelligence in terms of higher-level vision problems, especially ones involving reasoning. Earlier attempts in equipping machines with high-level reasoning have hovered around Visual Question Answering (VQA), one typical task associating vision and language understanding. In this work, we propose a new dataset, built in the context of Raven's Progressive Matrices (RPM) and aimed at lifting machine intelligence by associating vision with structural, relational, and analogical reasoning in a hierarchical representation. Unlike previous works in measuring abstract reasoning using RPM, we establish a semantic link between vision and reasoning by providing structure representation. This addition enables a new type of abstract reasoning by jointly operating on the structure representation. Machine reasoning ability using modern computer vision is evaluated in this newly proposed dataset. Additionally, we also provide human performance as a reference. Finally, we show consistent improvement across all models by incorporating a simple neural module that combines visual understanding and structure reasoning.
Multi-Task Identification of Entities, Relations, and Coreference for Scientific Knowledge Graph Construction

We introduce a multi-task setup of identifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called SciIE with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
Passive Reaction Analysis for Grasp Stability

In this paper, we focus on the following problem in multifingered robotic grasping: assuming that an external wrench is being applied to a grasped object, will the contact forces between the hand and the object, as well as the hand joints, respond in such a way to preserve quasi-static equilibrium? In particular, we assume that there is no change in the joint torques being actively exerted by the motors; any change in contact forces and joint torques is due exclusively to passive effects arising in response to the external disturbance. Such passive effects include, for example, joints that are driven by highly geared motors (a common occurrence in practice) and thus do not back drive in response to external torques. To account for nonlinear phenomena encountered in such cases, and which existing methods do not consider, we formulate the problem as a mixed-integer program used in the inner loop of an iterative solver. We present evidence showing that this formulation captures important effects for assessing the stability of a grasp employing some of the most commonly used actuation mechanisms. Note to Practitioners —Once a grasp of a given object has been chosen, our method has multiple possible applications. First, it can be used to determine how the choice of a preload (i.e., the torques applied to the joints as the grasp is created) affects the stability of the grasp. Second, once a preload has been chosen, our method can be used to determine which external disturbances can be resisted solely through passive effects, without further changes to the commands sent to the motors. We believe this approach is particularly relevant for the large family of grasping devices that are not equipped with tactile or proprioceptive sensors, and are thus unable to sense external disturbances or to control joint torques, but are still effective thanks to passive resistance effects.
Generalized de Bruijn words for primitive words and powers

Abstract We show that for every n ≥ 1 and over any finite alphabet, there is a word whose circular factors of length n have a one-to-one correspondence with the set of primitive words. In particular, we prove that such a word can be obtained by a greedy algorithm, or by concatenating all Lyndon words of length n in increasing lexicographic order. We also look into connections between de Bruijn graphs of primitive words and Lyndon graphs. Finally, we also show that the shortest word that contains every p -power of length p n over a k -letter alphabet has length between p k n and roughly ( p + 1 k ) k n , for all integers p ≥ 1 . An algorithm that generates a word which achieves the upper bound is provided.
Plenoptic Monte Carlo Object Localization for Robot Grasping Under Layered Translucency

In order to fully function in human environments, robot perception needs to account for the uncertainty caused by translucent materials. Translucency poses several open challenges in the form of transparent objects (e.g., drinking glasses), refractive media (e.g., water), and diffuse partial occlusions (e.g., objects behind stained glass panels). This paper presents Plenoptic Monte Carlo Localization (PMCL)as a method for localizing object poses in the presence of translucency using plenoptic (light-field)observations. We propose a new depth descriptor, the Depth Likelihood Volume (DLV), and its use within a Monte Carlo object localization algorithm. We present results of localizing and manipulating objects with translucent materials and objects occluded by layers of translucency. Our PMCL implementation uses observations from a Lytro first generation light field camera to allow a Michigan Progress Fetch robot to perform grasping.
Stereochemical properties of the OH molecule in combined electric and magnetic fields: analytic results

The stereochemical properties of the ultracold ground state OH molecule in the presence of electric and magnetic fields are currently of considerable interest. For example, relevant quantities such as molecular alignment and orientation, calculated numerically by using large basis sets, have lately appeared in the literature. In this work, based on our recent exact solution to an effective eight-dimensional matrix Hamiltonian for the molecular ground state, we present analytic expressions for the stereochemical properties of OH. Our results require the solution of algebraic equations only, agree well with the aforementioned fully numerical calculations, provide compact expressions for simple field geometries, allow ready access to relatively unexplored parameter space, and yield straightforwardly higher moments of the molecular axis distribution.
Multi-task Sequence to Sequence Learning

Abstract: Sequence to sequence learning has recently emerged as a new paradigm in supervised learning. To date, most of its applications focused on only one task and not much work explored this framework for multiple tasks. This paper examines three multi-task learning (MTL) settings for sequence to sequence models: (a) the oneto-many setting - where the encoder is shared between several tasks such as machine translation and syntactic parsing, (b) the many-to-one setting - useful when only the decoder can be shared, as in the case of translation and image caption generation, and (c) the many-to-many setting - where multiple encoders and decoders are shared, which is the case with unsupervised objectives and translation. Our results show that training on a small amount of parsing and image caption data can improve the translation quality between English and German by up to 1.5 BLEU points over strong single-task baselines on the WMT benchmarks. Furthermore, we have established a new state-of-the-art result in constituent parsing with 93.0 F1. Lastly, we reveal interesting properties of the two unsupervised learning objectives, autoencoder and skip-thought, in the MTL context: autoencoder helps less in terms of perplexities but more on BLEU scores compared to skip-thought.
de Bruijn Arrays for L-Fillings

We use modular arithmetic to construct a de Bruijn L-array, which is a k × k2 array consisting of exactly one copy of each L-shaped pattern (a 2 × 2 array with the upper right corner removed) with ...
Thermodynamic calculation of spin scaling functions

Abstract Critical phenomena theory centers on the scaled thermodynamic potential per spin ϕ ( β , h ) = | t | p Y ( h | t | − q ) , with inverse temperature β = 1 / T , h = − β H , ordering field H, reduced temperature t = t ( β ) , critical exponents p and q, and function Y ( z ) of z = h | t | − q . I discuss calculating Y ( z ) with the information geometry of thermodynamics. Scaled solutions are found to obtain with three admissible functions t ( β ) : 1) t = e − J β , 2) t = β − 1 , and 3) t = β C − β , where J and β C are constants. For p = q , information geometry yields Y ( z ) = 1 + z 2 , consistent with the one-dimensional (1D) ferromagnetic Ising model.
Enumerating palindromes and primitives in rank two free groups

Abstract Let F be a free group of rank two. An element of F is primitive if it, along with another group element, generates the group. If F = 〈 A , B 〉 , then a word W ( A , B ) , in A and B, is a palindrome if it reads the same forwards and backwards. It is known that in a rank two free group, for any fixed set of two generators a primitive element will be conjugate either to a palindrome or to the product of two palindromes, but known iteration schemes for all primitive words give only a representative for the conjugacy class. Here we derive a new iteration scheme that gives either the unique palindrome in the conjugacy class or expresses the word as a unique product of two unique palindromes that have already appeared in the scheme. We denote these words by E p / q where p / q is rational number expressed in lowest terms. We prove that E p / q is a palindrome if pq is even and the unique product of two unique palindromes if pq is odd. We prove that the pair ( X , Y ) (or ( X − 1 , Y − 1 ) ) generates the group if and only if X is conjugate to E p / q and Y is conjugate to E r / s where | p s − r q | = 1 . This improves a previously known result that held only for pq and rs both even. The derivation of the enumeration scheme also gives a new proof of the known results about primitive words.
Slip Detection with Combined Tactile and Visual Information

Slip detection plays a vital role in robotic manipulation and it has long been a challenging problem in the robotic community. In this paper, we propose a new method based on deep neural network (DNN) to detect slip. The training data is acquired by a GelSight tactile sensor and a camera mounted on a gripper when we use a robot arm to grasp and lift 94 daily objects with different grasping forces and grasping positions. The DNN is trained to classify whether a slip occurred or not. To evaluate the performance of the DNN, we test 10 unseen objects in 152 grasps. A detection accuracy as high as 88.03 % is achieved. It is anticipated that the accuracy can be further improved with a larger dataset. This method is beneficial for robots to make stable grasps, which can be widely applied to automatic force control, grasping strategy selection and fine manipulation.
Tests of the standard electroweak model at the energy frontier

In this review, we summarize tests of standard electroweak (EW) theory at the highest available energies as a precursor to the Large Hadron Collider (LHC) era. Our primary focus is on the published results (as of March 2010) from proton- antiproton collisions at $\sqrt{s}=1.96$ TeV at the Fermilab Tevatron collected using the CDF and D0 detectors. This review is very timely since the LHC scientific program is nearly underway with the first high-energy ($\sqrt{s}=7$ TeV) collisions about to begin. After presenting an overview of the EW sector of the standard model, we provide a summary of current experimental tests of EW theory. These include gauge boson properties and self-couplings, tests of EW physics from top quark sector, and searches for the Higgs boson.
On Algebraic Proofs of Stability for Homogeneous Vector Fields

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function, which is the ratio of two polynomials (i.e., a rational function ). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sum of squares certificates and, hence, such a Lyapunov function can always be found by semidefinite programming . This generalizes the classical fact that an asymptotically stable linear system admits a quadratic Lyapunov function, which satisfies a certain linear matrix inequality. In addition to homogeneous vector fields, the result can be useful for showing local asymptotic stability of nonhomogeneous systems by proving asymptotic stability of their lowest order homogeneous component. This paper also includes some negative results: We show that in absence of homogeneity, globally asymptotically stable polynomial vector fields may fail to admit a global rational Lyapunov function, and in presence of homogeneity, the degree of the numerator of a rational Lyapunov function may need to be arbitrarily high (even for vector fields of fixed degree and dimension). On the other hand, we also give a family of homogeneous polynomial vector fields that admit a low-degree rational Lyapunov function but necessitate polynomial Lyapunov functions of arbitrarily high degree. This shows the potential benefits of working with rational Lyapunov functions, particularly as the ones whose existence we guarantee have structured denominators and are not more expensive to search for than polynomial ones.
Non-perturbative Heavy Quark Effective Theory: Introduction and Status

Abstract We give an introduction to Heavy Quark Effective Theory (HQET). Our emphasis is on its formulation non-perturbative in the strong coupling, including the non-perturbative determination of the parameters in the HQET Lagrangian. In a second part we review the present status of HQET on the lattice, largely based on work of the ALPHA collaboration in the last few years. We finally discuss opportunities and challenges.
Corner Cases, Singularities, and Dynamic Factoring

In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The “factoring” approach alleviates this difficulty by deriving a PDE for a new (locally smooth) variable while capturing the rarefaction-related singularity in a known (non-smooth) “factor”. Previously this technique was successfully used to address rarefaction fans arising at point sources. In this paper we show how similar ideas can be used to factor the 2D rarefactions arising due to nonsmoothness of domain boundaries or discontinuities in PDE coefficients. Locations and orientations of such rarefaction fans are not known in advance and we construct a “just-in-time factoring” method that identifies them dynamically. The resulting algorithm is a generalization of the Fast Marching Method originally introduced for the regular (unfactored) Eikonal equations. We show that our approach restores the first-order convergence and illustrate it using a range of maze navigation examples with non-permeable and “slowly permeable” obstacles.
A thermodynamic classification of real numbers

Abstract Text A new classification scheme for real numbers is given, motivated by ideas from statistical mechanics in general and work of Knauf (1993) [16] and Fiala and Kleban (2005) [8] in particular. Critical for this classification of a real number will be the Diophantine properties of its continued fraction expansion. Video For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=qnPF2QS4cRg .
Small-loss bounds for online learning with partial information

We consider the problem of adversarial (non-stochastic) online learning with partial information feedback, where at each round, a decision maker selects an action from a finite set of alternatives. We develop a black-box approach for such problems where the learner observes as feedback only losses of a subset of the actions that includes the selected action. When losses of actions are non-negative, under the graph-based feedback model introduced by Mannor and Shamir, we offer algorithms that attain the so called "small-loss" $o(\alpha L^{\star})$ regret bounds with high probability, where $\alpha$ is the independence number of the graph, and $L^{\star}$ is the loss of the best action. Prior to our work, there was no data-dependent guarantee for general feedback graphs even for pseudo-regret (without dependence on the number of actions, i.e. utilizing the increased information feedback). Taking advantage of the black-box nature of our technique, we extend our results to many other applications such as semi-bandits (including routing in networks), contextual bandits (even with an infinite comparator class), as well as learning with slowly changing (shifting) comparators. In the special case of classical bandit and semi-bandit problems, we provide optimal small-loss, high-probability guarantees of $\tilde{O}(\sqrt{dL^{\star}})$ for actual regret, where $d$ is the number of actions, answering open questions of Neu. Previous bounds for bandits and semi-bandits were known only for pseudo-regret and only in expectation. We also offer an optimal $\tilde{O}(\sqrt{\kappa L^{\star}})$ regret guarantee for fixed feedback graphs with clique-partition number at most $\kappa$.
FBG-Based Control of a Continuum Manipulator Interacting with Obstacles*

Tracking and controlling the shape of continuum dexterous manipulators (CDM) in constraint environments is a challenging task. The imposed constraints and interaction with unknown obstacles may conform the CDM's shape and therefore demands for shape sensing methods which do not rely on direct line of sight. To address these issues, we integrate a novel Fiber Bragg Grating (FBG) shape sensing unit into a CDM, reconstruct the shape in real-time, and develop an optimization-based control algorithm using FBG tip position feedback. The CDM is designed for less-invasive treatment of osteolysis (bone degradation). To evaluate the performance of the feedback control algorithm when the CDM interacts with obstacles, we perform a set of experiments similar to the real scenario of the CDM interaction with soft and hard lesions during the treatment of osteolysis. In addition, we propose methods for identification of the CDM collisions with soft or hard obstacles using the jacobian information. Results demonstrate successful control of the CDM tip based on the FBG feedback and indicate repeatability and robustness of the proposed method when interacting with unknown obstacles.
Accessible proof of standard monomial basis for coordinatization of Schubert sets of flags

Abstract The main results of this paper are accessible with only basic linear algebra. Given an increasing sequence of dimensions, a flag in a vector space is an increasing sequence of subspaces with those dimensions. The set of all such flags (the flag manifold) can be projectively coordinatized using products of minors of a matrix. These products are indexed by tableaux on a Young diagram. A basis of “standard monomials” for the vector space generated by such projective coordinates over the entire flag manifold has long been known. A Schubert variety is a subset of flags specified by a permutation. Lakshmibai, Musili, and Seshadri gave a standard monomial basis for the smaller vector space generated by the projective coordinates restricted to a Schubert variety. Reiner and Shimozono made this theory more explicit by giving a straightening algorithm for the products of the minors in terms of the right key of a Young tableau. Since then, Willis introduced scanning tableaux as a more direct way to obtain right keys. This paper uses scanning tableaux to give more-direct proofs of the spanning and the linear independence of the standard monomials. In the appendix it is noted that this basis is a weight basis for the dual of a Demazure module for a Borel subgroup of G L n . This paper contains a complete proof that the characters of these modules (the key polynomials) can be expressed as the sums of the weights for the tableaux used to index the standard monomial bases.
Contextual Search via Intrinsic Volumes

We study the problem of contextual search, a multidimensional generalization of binary search that captures many problems in contextual decision-making. In contextual search, a learner is trying to learn the value of a hidden vector. Every round the learner is provided an adversarially-chosen context vector, submits a guess for the inner product of the context vector with the hidden vector, learns whether their guess was too high or too low, and incurs some loss based on the quality of their guess. The learner's goal is to minimize their total loss over the course of some number of rounds. We present an algorithm for the contextual search problem for the symmetric loss function that achieves constant total loss. We present a new algorithm for the dynamic pricing problem (which can be realized as a special case of the contextual search problem) that achieves doubly-logarithmic total loss, improving exponentially on the previous best known upper bounds and matching the known lower bounds (up to a polynomial dependence on dimension). Both algorithms make significant use of ideas from the field of integral geometry, most notably the notion of intrinsic volumes of a convex set. To the best of our knowledge this is the first application of intrinsic volumes to algorithm design.
Elasticity as the Basis of Allostery in DNA.

Allosteric interactions in DNA are crucial for various biological processes. These interactions are quantified by measuring the change in free energy as a function of the distance between the bindi...
Recognizing and Curating Photo Albums via Event-Specific Image Importance.

Automatic organization of personal photos is a problem with many real world ap- plications, and can be divided into two main tasks: recognizing the event type of the photo collection, and selecting interesting images from the collection. In this paper, we attempt to simultaneously solve both tasks: album-wise event recognition and image- wise importance prediction. We collected an album dataset with both event type labels and image importance labels, refined from an existing CUFED dataset. We propose a hybrid system consisting of three parts: A siamese network-based event-specific image importance prediction, a Convolutional Neural Network (CNN) that recognizes the event type, and a Long Short-Term Memory (LSTM)-based sequence level event recognizer. We propose an iterative updating procedure for event type and image importance score prediction. We experimentally verified that image importance score prediction and event type recognition can each help the performance of the other.
Uniqueness of self-shrinkers to the degree-one curvature flow with a tangent cone at infinity

Given a smooth, symmetric and homogeneous of degree one function $$f\left( \lambda _{1},\ldots ,\lambda _{n}\right) $$ satisfying $$\partial _{i}f>0\quad \forall \,i=1,\ldots , n$$ , and a properly embedded smooth cone $${\mathcal {C}}$$ in $${\mathbb {R}}^{n+1}$$ , we show that under suitable conditions on f, there is at most one f self-shrinker (i.e. a hypersurface $$\Sigma $$ in $${\mathbb {R}}^{n+1}$$ satisfying $$f\left( \kappa _{1},\ldots ,\kappa _{n}\right) +\frac{1}{2}X\cdot N=0$$ , where $$\kappa _{1},\ldots ,\kappa _{n}$$ are principal curvatures of $$\Sigma $$ ) that is asymptotic to the given cone $${\mathcal {C}}$$ at infinity.
Hultman Elements for the Hyperoctahedral Groups

Hultman, Linusson, Shareshian, and Sj o strand gave a pattern avoidance characterization of the permutations for which the number of chambers of its associated inversion arrangement is the same as the size of its lower interval in Bruhat order. Hultman later gave a characterization, valid for an arbitrary finite reflection group, in terms of distances in the Bruhat graph. On the other hand, the pattern avoidance criterion for permutations had earlier appeared in independent work of Sj o strand and of Gasharov and Reiner. We give characterizations of the elements of the hyperoctahedral groups satisfying Hultman's criterion that is in the spirit of those of Sj o strand and of Gasharov and Reiner. We also give a pattern avoidance criterion using the notion of pattern avoidance defined by Billey and Postnikov.
A non-CLP-compact product space whose finite subproducts are CLP-compact

Abstract We construct a family of Hausdorff spaces such that every finite product of spaces in the family (possibly with repetitions) is CLP-compact, while the product of all spaces in the family is non-CLP-compact. Our example will yield a single Hausdorff space X such that every finite power of X is CLP-compact, while no infinite power of X is CLP-compact. This answers a question of Steprāns and Sostak.
Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications

The von Neumann graph entropy (VNGE) facilitates measurement of information divergence and distance between graphs in a graph sequence. It has been successfully applied to various learning tasks driven by network-based data. While effective, VNGE is computationally demanding as it requires the full eigenspectrum of the graph Laplacian matrix. In this paper, we propose a new computational framework, Fast Incremental von Neumann Graph EntRopy (FINGER), which approaches VNGE with a performance guarantee. FINGER reduces the cubic complexity of VNGE to linear complexity in the number of nodes and edges, and thus enables online computation based on incremental graph changes. We also show asymptotic equivalence of FINGER to the exact VNGE, and derive its approximation error bounds. Based on FINGER, we propose efficient algorithms for computing Jensen-Shannon distance between graphs. Our experimental results on different random graph models demonstrate the computational efficiency and the asymptotic equivalence of FINGER. In addition, we apply FINGER to two real-world applications and one synthesized anomaly detection dataset, and corroborate its superior performance over seven baseline graph similarity methods.
Fixed Point Composition and Toeplitz-Composition C*-algebras

Abstract Let φ be a linear-fractional, non-automorphism self-map of D that fixes ζ ∈ T and satisfies φ ′ ( ζ ) ≠ 1 and consider the composition operator C φ acting on the Hardy space H 2 ( D ) . We determine which linear-fractionally-induced composition operators are contained in the unital C ⁎ -algebra generated by C φ and the ideal K of compact operators. We apply these results to show that C ⁎ ( C φ , K ) and C ⁎ ( F ζ ) , the unital C ⁎ -algebra generated by all composition operators induced by linear-fractional, non-automorphism self-maps of D that fix ζ, are each isomorphic, modulo the ideal of compact operators, to a unitization of a crossed product of C 0 ( [ 0 , 1 ] ) . We compute the K-theory of C ⁎ ( C φ , K ) and calculate the essential spectra of a class of operators in this C ⁎ -algebra. We also obtain a full description of the structures, modulo the ideal of compact operators, of the C ⁎ -algebras generated by the unilateral shift T z and a single linear-fractionally-induced composition operator.
Homological dimensions of ring spectra

We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is the global dimension of real K-theory KO and its connective version ko at the prime 2. We show that the global dimension of KO is 2 or 3, and the global dimension of ko is 4 or 5.