cssi/SciSciGPT-SciSciNet huggingface dataset:
Continuous Monitoring of Pareto Frontiers on Partially Ordered Attributes for Many Users.

We study the problem of continuous object dissemination---given a large number of users and continuously arriving new objects, deliver an object to all users who prefer the object. Many real world applications analyze users' preferences for effective object dissemination. For continuously arriving objects, timely finding users who prefer a new object is challenging. In this paper, we consider an append-only table of objects with multiple attributes and users' preferences on individual attributes are modeled as strict partial orders. An object is preferred by a user if it belongs to the Pareto frontier with respect to the user's partial orders. Users' preferences can be similar. Exploiting shared computation across similar preferences of different users, we design algorithms to find target users of a new object. In order to find users of similar preferences, we study the novel problem of clustering users' preferences that are represented as partial orders. We also present an approximate solution of the problem of finding target users which is more efficient than the exact one while ensuring sufficient accuracy. Furthermore, we extend the algorithms to operate under the semantics of sliding window. We present the results from comprehensive experiments for evaluating the efficiency and effectiveness of the proposed techniques.
Using a secret key to foil an eavesdropper

This work addresses secrecy with distributed systems in mind. We consider an adversary who wishes to attack a system and find the optimal communication and use of secret key to share information in such a system. Instead of measuring secrecy by “equivocation,” we define a value function for the system, based on the actions of the system and the adversary, and set out to design a system that maximizes the average value obtained against the worst adversary.
Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)

The interpretation of deep learning models is a challenge due to their size, complexity, and often opaque internal state. In addition, many systems, such as image classifiers, operate on low-level features rather than high-level concepts. To address these challenges, we introduce Concept Activation Vectors (CAVs), which provide an interpretation of a neural net's internal state in terms of human-friendly concepts. The key idea is to view the high-dimensional internal state of a neural net as an aid, not an obstacle. We show how to use CAVs as part of a technique, Testing with CAVs (TCAV), that uses directional derivatives to quantify the degree to which a user-defined concept is important to a classification result--for example, how sensitive a prediction of "zebra" is to the presence of stripes. Using the domain of image classification as a testing ground, we describe how CAVs may be used to explore hypotheses and generate insights for a standard image classification network as well as a medical application.
Ceva's Triangle Inequalities

We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a three-parameter family of inequalities which we call Ceva’s triangle inequalities. Our main result provides the parametrization of the solution set.
Sparse Quadrature for High-Dimensional Integration with Gaussian Measure

In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions of high-dimensional parameters with Gaussian measure. Under certain assumptions on the exactness and boundedness of univariate quadrature rules as well as on the regularity assumptions on the parametric functions with respect to the parameters, we prove that the convergence of the sparse quadrature error is independent of the number of the parameter dimensions. Moreover, we propose both an a priori and an a posteriori schemes for the construction of a practical sparse quadrature rule and perform numerical experiments to demonstrate their dimension-independent convergence rates.
Convergence of densities of some functionals of Gaussian processes

Abstract The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Steinʼs method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.
Downlink Multi-Antenna Heterogeneous Cellular Network With Load Balancing

We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with $K$ classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing signal-to-interference-plus-noise-ratio (SINR) at the receiver, we show that adding an appropriately chosen tier-dependent cell selection bias in the received power yields a close approximation. Assuming arbitrary selection bias for each tier, simple expressions for downlink coverage and rate are derived. For coverage maximization, the required selection bias for each tier is given in closed form. Due to this connection with biasing, multi-antenna HetNets may balance load more naturally across tiers in certain regimes compared to single-antenna HetNets, where a large cell selection bias is often needed to offload traffic to small cells.
Influence Models on Layered Uncertain Networks: A Guaranteed-Cost Design Perspective

Control and estimation on large-scale social networks often necessitate the availability of models for the interactions amongst the agents. However characterizing accurate models of social interactions pose new challenges due to inherent complexity and unpredictability. Moreover, model uncertainty becomes more pronounced for large-scale networks. For certain classes of social networks, the layering structure allows a compositional approach. In this paper, we present such an approach to determine performance guarantees on layered networks with inherent model uncertainties. A factorization method is used to determine robust stability and performance and this is accomplished by a layered cost-guaranteed design via a layered Riccati-type solver, mirroring the network structure. We provide an example of the proposed methodology in the context of opinion dynamics on large-scale social networks.
Towards Zero Shot Frame Semantic Parsing for Domain Scaling

State-of-the-art slot filling models for goal-oriented human/machine conversational language understanding systems rely on deep learning methods. While multi-task training of such models alleviates the need for large in-domain annotated datasets, bootstrapping a semantic parsing model for a new domain using only the semantic frame, such as the back-end API or knowledge graph schema, is still one of the holy grail tasks of language understanding for dialogue systems. This paper proposes a deep learning based approach that can utilize only the slot description in context without the need for any labeled or unlabeled in-domain examples, to quickly bootstrap a new domain. The main idea of this paper is to leverage the encoding of the slot names and descriptions within a multi-task deep learned slot filling model, to implicitly align slots across domains. The proposed approach is promising for solving the domain scaling problem and eliminating the need for any manually annotated data or explicit schema alignment. Furthermore, our experiments on multiple domains show that this approach results in significantly better slot-filling performance when compared to using only in-domain data, especially in the low data regime.
Election predictions are arbitrage-free: response to Taleb

Taleb [Election predictions as martingales: An arbitrage approach. Quant. Finance, 2018, 18, 1–5] claimed a novel approach to evaluating the quality of probabilistic election forecasts via no-arbit...
On the Output of Nonlinear Systems Excited by Discrete Prolate Spheroidal Sequences

The discrete prolate spheroidal sequences (DPSSs)—a set of optimally bandlimited sequences with unique properties—are important to applications in both science and engineering. In this work, properties of nonlinear system response due to DPSS excitation are reported. In particular, the sequences are shown to be approximately orthogonal after passing through a nonlinear, multiple-input multiple-output dynamical system under quite general conditions. This work quantifies these conditions in terms of constraints upon the higher-order generalized transfer functions characterizing the Volterra expansion of a MIMO system, the Volterra order of the system, and the DPSS bandwidth parameter $W$ and time-bandwidth parameter $NW$ . The approximate system output orthogonality allows multiple-input, multiple-output characterization of the linear narrowband response of a nonlinear system using simultaneous, DPSS excitation.
Detector considerations for a HAWC southern observatory

The High-Altitude Water Cherenkov (HAWC) observatory in central Mexico is currently the world’s only synoptic survey instrument for gamma rays above 1 TeV. Because there is significant interest in covering the full TeV sky with a survey instrument, we have examined options for a Southern Hemisphere extension to HAWC. In addition to providing all-sky coverage of TeV sources, a southern site could complement existing surveys of the densest part of the Galactic Plane, provide continuous monitoring of Galactic and extragalactic transient sources in both Hemispheres, and simplify the analysis of spatially extended signals such as diffuse gamma rays and the TeV cosmic-ray anisotropy. To take advantage of the air-shower physics and lower the energy threshold of the experiment as much as possible, a high altitude site above 5000 m a.s.l (vs. 4100 m a.s.l. at the current site in Mexico) has been specified. To facilitate efficient detector construction at such altitudes, the detector tanks would be assembled at lower altitude and delivered to the site. An all-digital communications and data acquisition scheme is proposed. Possible designs include taking advantage of digital optical module technology from the IceCube experiment as well as new custom electronics. We discuss the physics potential of such an experiment, focusing on the energy threshold, angular resolution, and background suppression capability of the experiment, as well as the advantages of full-sky coverage above 1 TeV.
Elliptic curves with maximally disjoint division fields

One of the many interesting algebraic objects associated to a given elliptic curve defined over the rational numbers, E/Q, is its full-torsion representation ρE : Gal(Q/Q)→ GL2(Ẑ). Generalizing this idea, one can create another full-torsion Galois representation, ρ(E1,E2) : Gal(Q/Q)→ ( GL2(Ẑ) )2 associated to a pair (E1, E2) of elliptic curves defined over Q. The goal of this paper is to provide an infinite number of concrete examples of pairs of elliptic curves whose associated full-torsion Galois representation ρ(E1,E2) has maximal image. The size of the image is inversely related to the size of the intersection of various division fields defined by E1 and E2. The representation ρ(E1,E2) has maximal image when these division fields are maximally disjoint, and most of the paper is devoted to studying these intersections.
Privacy preserving Distance computation using somewhat-trusted third parties

A critically important component of most signal processing procedures is that of computing the distance between signals. In multiparty processing applications where these signals belong to different parties, this introduces privacy challenges. The signals may themselves be private, and the parties to the computation may not be willing to expose them. Solutions proposed to the problem in the literature generally invoke homomorphic encryption schemes, secure multi-party computation, or other cryptographic methods which introduce significant computational complexity into the proceedings, often to the point of making more complex computations requiring repeated computations unfeasible. Other solutions invoke third parties, making unrealistic assumptions about their trustworthiness. In this paper we propose an alternate approach, also based on third party computation, but without assuming as much trust in the third party. Individual participants to the computation “secure” their data through a proposed secure hashing scheme with shared keys, prior to sharing it with the third party. The hashing ensures that the third party cannot recover any information about the individual signals or their statistics, either from analysis of individual computations or their long-term aggregate patterns. We provide theoretical proof of these properties and empirical demonstration of the feasibility of the computation.
Corners in Tree-Like Tableaux

In this paper, we study tree – like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of corners in tree – like tableaux and the total number of corners in symmetric tree – like tableaux. In this paper, we prove both conjectures. Our proofs are based off of the bijection with permutation tableaux or type – B permutation tableaux and consequently, we also prove results for these tableaux. In addition, we derive the limiting distribution of the number of occupied corners in random tree – like tableaux and random symmetric tree – like tableaux.
Convex billiards on convex spheres

Abstract In this paper we study the dynamical billiards on a convex 2D sphere. We investigate some generic properties of the convex billiards on a general convex sphere. We prove that C ∞ generically, every periodic point is either hyperbolic or elliptic with irrational rotation number. Moreover, every hyperbolic periodic point admits some transverse homoclinic intersections. A new ingredient in our approach is Herman's result on Diophantine invariant curves that we use to prove the nonlinear stability of elliptic periodic points for a dense subset of convex billiards.
Carries, Shuffling and An Amazing Matrix

For this example, 19/40=47.5% of the columns have a carry of 1. Holte shows that if the binary digits are chosen at random, uniformly, in the limit 50% of all the carries are zero. This holds no matter what the base. More generally, if one adds n integers (base b) that are produced by choosing their digits uniformly at random in {0, 1, . . . , b− 1}, the sequence of carries κ0 = 0, κ1, κ2, . . . is a Markov chain taking values in {0, 1, 2, . . . , n − 1}. The Markov property holds because to compute the amount carried to the next column, one only needs to know the carry and numbers in the current column: the past does not matter. We let P (i, j) = P (κ′ = j|κ = i) denote an entry of the transition matrix between successive carries κ, κ′. Holte found the following:
Descent for n-bundles☆

Abstract Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U → X , specifying a transition cocycle on the cover, and descending the trivialized bundle U × G along the cover. We demonstrate the existence of an analogous construction for local n-bundles for general n. We establish analogues for simplicial Lie groups of Moore's results on simplicial groups; these imply that bundles for strict Lie n-groups arise from local n-bundles. Our construction leads to simple finite dimensional models of Lie 2-groups such as String ( n ) from cocycle data.
On the Dec group of finite Abelian Galois extensions over global fields

Abstract If K / F is a finite Abelian Galois extension of global fields whose Galois group has exponent t, we prove that there exists a short exact sequence 0 → Dec ( K / F ) → Br t ( K / F ) → ⊕ q ∈ P r q Z / Z → 0 where r q ∈ Q and P is a finite set of primes of F that is empty if t is square free. In particular, we obtain that if t is square free, then Dec ( K / F ) = Br t ( K / F ) which we use to show that prime exponent division algebras over Henselian valued fields with global residue fields are isomorphic to a tensor product of cyclic algebras. Finally, we construct a counterexample to the result for higher exponent division algebras.
The lamplighter group of rank two generated by a bireversible automaton

We construct a 4-state 2-letter bireversible automaton generating the lamplighter group (ℤ22)≀ℤ of rank two. The action of the generators on the boundary of the tree can be induced by the affine tr...
Regularizing effect of the forward energy cascade in the inviscid dyadic model

We study the inviscid dyadic model of the Euler equations and prove some regularizing properties of the nonlinear term that occur due to forward energy cascade. We show every solution must have 3 L 2 -based (or 1 10 L 3 -based) regularity for all positive time. We conjecture this holds up to Onsager's scaling, where the L2-based exponent is 5 and the L 3-based exponent is 1 .
Confounds and Consequences in Geotagged Twitter Data

Twitter is often used in quantitative studies that identify geographically-preferred topics, writing styles, and entities. These studies rely on either GPS coordinates attached to individual messages, or on the user-supplied location field in each profile. In this paper, we compare these data acquisition techniques and quantify the biases that they introduce; we also measure their effects on linguistic analysis and textbased geolocation. GPS-tagging and selfreported locations yield measurably different corpora, and these linguistic differences are partially attributable to differences in dataset composition by age and gender. Using a latent variable model to induce age and gender, we show how these demographic variables interact with geography to affect language use. We also show that the accuracy of text-based geolocation varies with population demographics, giving the best results for men above the age of 40.
Particle traces for detecting divergent robot behavior

The motion of robots and objects in our world is often highly dependent upon contact. When contact is expected but does not occur or when contact is not expected but does occur, robot behavior diverges from plan, often disastrously. This paper describes an approach that uses simulation to detect possible such behavioral divergences on real robots. This approach, and others like it, could be applied to validation of robot behaviors, mechanism design, and even online planning. The particle trace approach samples robot modeling parameters, sensory readings, and state estimates to evaluate a robot's behavior statistically over a range of conditions. We demonstrate that combining even coarse estimates of state and modeling parameters with fast multibody simulation can be sufficient to detect divergent robot behavior and characterize robot performance in the real world. Correspondingly, this approach could be used to assess risk and find and analyze likely failures, given the extensive data that such simulations can generate. We assess this approach on actuated, high degree-of-freedom robot locomotion examples, a picking task with a fixed-base manipulator, and an unpowered passive dynamic walker. This research works toward understanding how multi-rigid body simulations can better characterize the behavior of non-soft robots.
Residual Unfairness in Fair Machine Learning from Prejudiced Data

Recent work in fairness in machine learning has proposed adjusting for fairness by equalizing accuracy metrics across groups and has also studied how datasets affected by historical prejudices may lead to unfair decision policies. We connect these lines of work and study the residual unfairness that arises when a fairness-adjusted predictor is not actually fair on the target population due to systematic censoring of training data by existing biased policies. This scenario is particularly common in the same applications where fairness is a concern. We characterize theoretically the impact of such censoring on standard fairness metrics for binary classifiers and provide criteria for when residual unfairness may or may not appear. We prove that, under certain conditions, fairness-adjusted classifiers will in fact induce residual unfairness that perpetuates the same injustices, against the same groups, that biased the data to begin with, thus showing that even state-of-the-art fair machine learning can have a "bias in, bias out" property. When certain benchmark data is available, we show how sample reweighting can estimate and adjust fairness metrics while accounting for censoring. We use this to study the case of Stop, Question, and Frisk (SQF) and demonstrate that attempting to adjust for fairness perpetuates the same injustices that the policy is infamous for.
Maximally supersymmetric Yang-Mills on the lattice

We summarize recent progress in lattice studies of four-dimensional 𝒩 = 4 supersymmetric Yang–Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.
Hecke operators on differential modular forms mod p

Abstract A description is given of all primitive δ-series mod p of order 1 which are eigenvectors of all the Hecke operators n T κ ( n ) , “ p T κ ( p ) ”, ( n , p ) = 1 , and which are δ-Fourier expansions of δ-modular forms of arbitrary order and weight w with deg ( w ) = κ ⩾ 0 ; this set of δ-series is shown to be in a natural one-to-one correspondence with the set of series mod p (of order 0) which are eigenvectors of all the Hecke operators T κ + 2 ( n ) , T κ + 2 ( p ) , ( n , p ) = 1 and which are Fourier expansions of (classical) modular forms of weight ≡ κ + 2 mod p − 1 .
Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models

Model-based reinforcement learning (RL) algorithms can attain excellent sample efficiency, but often lag behind the best model-free algorithms in terms of asymptotic performance. This is especially true with high-capacity parametric function approximators, such as deep networks. In this paper, we study how to bridge this gap, by employing uncertainty-aware dynamics models. We propose a new algorithm called probabilistic ensembles with trajectory sampling (PETS) that combines uncertainty-aware deep network dynamics models with sampling-based uncertainty propagation. Our comparison to state-of-the-art model-based and model-free deep RL algorithms shows that our approach matches the asymptotic performance of model-free algorithms on several challenging benchmark tasks, while requiring significantly fewer samples (e.g. 8 and 125 times fewer samples than Soft Actor Critic and Proximal Policy Optimization respectively on the half-cheetah task).
TOPOLOGY ON COHOMOLOGY OF LOCAL FIELDS

Arithmetic duality theorems over a local field -algebraic stacks. Geometric arguments prove that these ‘classifying stack topologies’ enjoy the properties expected from the Cech topologies. With this as the key input, we prove that the Cech and the classifying stack topologies actually agree. The expected properties of the Cech topologies follow, and these properties streamline a number of arithmetic duality proofs given elsewhere.
Torsion in tensor powers of modules

Tensor products usually have nonzero torsion. This is a central theme of Auslander's 1961 paper; the theme continues in the work of Huneke and Wiegand in the 1990s. The main focus in this article is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modules N with the property that M ⊗R N has nonzero torsion unless M is very special. An important example of such a module N is the Frobenius power pe R over a complete intersection domain R of characteristic p > 0.
Machine generalization and human categorization: an information-theoretic view

In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types of concepts and categories people naturally use. The psychological literature on concept learning and categorization provides strong evidence that certain categories are more easily learned, recalled, and recognized than others. We show here how a measure of the informational value of a category predicts the results of several important categorization experiments better than standard alternative explanations. This suggests that information-based approaches to machine generalization may prove particularly useful and natural for human users of the systems.
Interior regularity for nonlocal fully nonlinear equations with Dini continuous terms

Abstract This paper is concerned with interior regularity of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations with Dini continuous terms. We obtain C σ regularity estimates for the nonlocal equations by perturbative methods and a version of a recursive Evans–Krylov theorem.
Medial/Skeletal Linking Structures for Multi-region Configurations

We consider a generic configuration of regions, consisting of a collection of distinct compact regions {Ωi} in R n+1 which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries Bi in a generic way. We introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions’ individual shapes and geometric properties as well as the “positional geometry” of the collection. The linking structure extends in a minimal way the individual “skeletal structures” on each of the regions. This allows us to significantly extend the mathematical methods introduced for single regions to the configuration of regions. We prove for a generic configuration of regions the existence of a special type of Blum linking structure which builds upon the Blum medial axes of the individual regions. As part of this, we introduce the “spherical axis”, which is the analogue of the medial axis but for directions. These results require proving several transversality theorems for certain associated “multi-distance” and “height-distance” functions for such configurations. We show that by relaxing the conditions on the Blum linking structures we obtain the more general class of skeletal linking structures which still capture the geometric properties. The skeletal linking structure is used to analyze the “positional geometry” of the configuration. This involves using the “linking flow” to identify neighborhoods of the configuration regions which capture their positional relations. As well as yielding geometric invariants which capture the shapes and geometry of individual regions, these structures are used to define invariants which measure positional properties of the configuration such as: measures of relative closeness of neighboring regions and relative significance of the individual regions for the configuration. All of these invariants are computed by formulas involving “skeletal linking integrals” on the internal skeletal structures of the regions. These invariants are then used to construct a “tiered linking graph”, which for given thresholds of closeness and/or significance, identifies subconfigurations and provides a hierarchical ordering in terms of order of significance. 1991 Mathematics Subject Classification. Primary: 53A07, 58A35, Secondary: 68U05.
Increasing indoor spectrum sharing capacity using smart reflect-array

The radio frequency (RF) spectrum becomes overly crowded in some indoor environments due to the high density of users and bandwidth demands. To accommodate the tremendous wireless data demands, efficient spectrum-sharing approaches are highly desired. To this end, this paper introduces a new spectrum sharing solution for indoor environments based on the usage of a reconfigurable reflect-array in the middle of the wireless channel. By optimally controlling the phase shift of each element on the reflect-array, the useful signals for each transmission pair can be enhanced while the interferences can be canceled. As a result, multiple wireless users in the same room can access the same spectrum band at the same time without interfering each other. Hence, the network capacity can be dramatically increased. To prove the feasibility of the proposed solution, an experimental testbed is first developed and evaluated. Then, the effects of the reflect-array on transport capacity of the indoor wireless networks are investigated. Through experiments, theoretical deduction, and simulations, this paper demonstrates that significantly higher spectrum-spatial efficiency can be achieved by using the smart reflect-array without any modification of the hardware and software in the users' devices.
Gender, Productivity, and Prestige in Computer Science Faculty Hiring Networks

Women are dramatically underrepresented in computer science at all levels in academia and account for just 15% of tenure-track faculty. Understanding the causes of this gender imbalance would inform both policies intended to rectify it and employment decisions by departments and individuals. Progress in this direction, however, is complicated by the complexity and decentralized nature of faculty hiring and the non-independence of hires. Using comprehensive data on both hiring outcomes and scholarly productivity for 2659 tenure-track faculty across 205 Ph.D.-granting departments in North America, we investigate the multi-dimensional nature of gender inequality in computer science faculty hiring through a network model of the hiring process. Overall, we find that hiring outcomes are most directly affected by (i) the relative prestige between hiring and placing institutions and (ii) the scholarly productivity of the candidates. After including these, and other features, the addition of gender did not significantly reduce modeling error. However, gender differences do exist, e.g., in scholarly productivity, postdoctoral training rates, and in career movements up the rankings of universities, suggesting that the effects of gender are indirectly incorporated into hiring decisions through gender's covariates. Furthermore, we find evidence that more highly ranked departments recruit female faculty at higher than expected rates, which appears to inhibit similar efforts by lower ranked departments. These findings illustrate the subtle nature of gender inequality in faculty hiring networks and provide new insights to the underrepresentation of women in computer science.
Polynomials with divisors of every degree

Abstract We consider polynomials of the form t n − 1 and determine when members of this family have a divisor of every degree in Z [ t ] . With F ( x ) defined to be the number of such integers n ⩽ x , we prove the existence of two positive constants c 1 and c 2 such that c 1 x log x ⩽ F ( x ) ⩽ c 2 x log x .
On 2-Dimensional Dijkgraaf-Witten Theory with Defects

In this paper, we provide a construction of a state-sum model for finite gauge-group Dijkgraaf-Witten theory on surfaces with codimension 1 defects. The construction requires not only that the triangulation be subordinate to the filtration, but flag-like: each simplex of the triangulation is either disjoint from the defect curve, or intersects it in a closed face. The construction allows internal degrees of freedom in the defect curves by introducing a second gauge-group from which edges of the curve are labeled in the state-sum construction. Edges incident with the defect, but not lying in it, have states lying in a set with commuting actions of the two gauge-groups. We determine the appropriate generalizations of the 2-cocycles specifying twistings of defect-free 2D Dijkgraaf-Witten theory. Examples arising by restriction of group 2-cocycles, and constructed from characters of the 2-dimensional gauge group are presented.
A new type of the Gronwall-Bellman inequality and its application to fractional stochastic differential equations

This paper presents a new type of Gronwall-Bellman inequality, which arises from a class of integral equations with a mixture of nonsingular and singular integrals. The new idea is to use a binomial function to combine the known Gronwall-Bellman inequalities for integral equations having nonsingular integrals with those having singular integrals. Based on this new type of Gronwall-Bellman inequality, we investigate the existence and uniqueness of the solution to a fractional stochastic differential equation (SDE) with fractional order 0<α<1. Finally, the fractional type Fokker-Planck-Kolmogorov equation associated to the solution of the fractional SDE is derived using Ito’s formula.
Active Target Tracking With Self-Triggered Communications in Multi-Robot Teams

We study the problem of reducing the amount of communication in decentralized target tracking. We focus on the scenario, where a team of robots is allowed to move on the boundary of the environment. Their goal is to seek a formation so as to best track a target moving in the interior of the environment. The robots are capable of measuring distances to the target. Decentralized control strategies have been proposed in the past, which guarantees that the robots asymptotically converge to the optimal formation. However, existing methods require that the robots exchange information with their neighbors at all time steps. Instead, we focus on decentralized strategies to reduce the amount of communication among robots. We propose a self-triggered communication strategy that decides when a particular robot should seek up-to-date information from its neighbors and when it is safe to operate with possibly outdated information. We prove that this strategy converges asymptotically to the desired formation when the target is stationary. For the case of a mobile target, we use a decentralized Kalman filter with covariance intersection to share the beliefs of neighboring robots. We evaluate all the approaches through simulations and a proof-of-concept experiment. Note to Practitioners —We study the problem of tracking a target using a team of coordinating robots. Target tracking problems are prevalent in a number of applications, such as co-robots, surveillance, and wildlife monitoring. Coordination between robots typically requires communication amongst them. Most multi-robot coordination algorithms implicitly assume that the robots can communicate at all time steps. Communication can be a considerable source of energy consumption, especially for small robots. Furthermore, communicating at all time steps may be redundant in many settings. With this as motivation, we propose an algorithm where the robots do not necessarily communicate at all times and instead choose specific triggering time instances to share information with their neighbors. Despite the limitation of limited communication, we show that the algorithm converges to the optimal configuration both in theory as well as in simulations.
Probabilism for stochastic theories

Abstract I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C * -algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or ‘Dutch book’) in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent.
Realizing spaces as classifying spaces

Which spaces occur as a classifying space for fibrations with a given fibre? We address this question in the context of rational homotopy theory. We construct an infinite family of finite complexes realized (up to rational homotopy) as classifying spaces. We also give several non-realization results, including the following: the rational homotopy types of $\mathbb{C}P^2$ and $S^4$ are not realized as the classifying space of any simply connected, rational space with finite-dimensional homotopy groups.
Factor models for matrix-valued high-dimensional time series

Abstract In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many companies are reported over time. Although it is natural to turn a matrix observation into a long vector then use standard vector time series models or factor analysis, it is often the case that the columns and rows of a matrix represent different sets of information that are closely interrelated in a very structural way. We propose a novel factor model that maintains and utilizes the matrix structure to achieve greater dimensional reduction as well as finding clearer and more interpretable factor structures. Estimation procedure and its theoretical properties are investigated and demonstrated with simulated and real examples.
Distributed Inexact Damped Newton Method: Data Partitioning and Load-Balancing.

In this paper we study inexact dumped Newton method implemented in a distributed environment. We start with an original DiSCO algorithm [Communication-Efficient Distributed Optimization of Self-Concordant Empirical Loss, Yuchen Zhang and Lin Xiao, 2015]. We will show that this algorithm may not scale well and propose an algorithmic modifications which will lead to less communications, better load-balancing and more efficient computation. We perform numerical experiments with an regularized empirical loss minimization instance described by a 273GB dataset.
Nuclear and mitochondrial genomic resources for the meltwater stonefly (Plecoptera: Nemouridae), Lednia tumana (Ricker, 1952)

With more than 3,700 described species, stoneflies (Order Plecoptera) are an important component of global aquatic biodiversity. The meltwater stonefly Lednia tumana (Ricker, 1952) is endemic to al...
Multiscale Computational Modeling of Tubulin-Tubulin Lateral Interaction

Microtubules are multistranded polymers in eukaryotic cells that support key cellular functions such as chromosome segregation, motor-based cargo transport, and maintenance of cell polarity. Microtubules self-assemble via "dynamic instability," in which the dynamic plus ends switch stochastically between alternating phases of polymerization and depolymerization. A key question in the field is what are the atomistic origins of this switching, i.e., what is different between the GTP- and GDP-tubulin states that enables microtubule growth and shortening, respectively? More generally, a major challenge in biology is how to connect theoretical frameworks across length- and timescales, from atoms to cellular behavior. In this study, we describe a multiscale model by linking atomistic molecular dynamics (MD), molecular Brownian dynamics (BD), and cellular-level thermokinetic modeling of microtubules. Here, we investigated the underlying interaction energy when tubulin dimers associate laterally by performing all-atom MD simulations. We found that the lateral potential energy is not significantly different among three nucleotide states of tubulin, GTP, GDP, and GMPCPP and is estimated to be ≅ -11 kBT. Furthermore, using MD potential energy in our BD simulations of tubulin dimers confirms that the lateral bond is weak on its own, with a mean lifetime of ∼0.1 μs, implying that the longitudinal bond is required for microtubule assembly. We conclude that nucleotide-dependent lateral-bond strength is not the key mediator microtubule dynamic instability, implying that GTP acts elsewhere to exert its stabilizing influence on microtubule polymer. Furthermore, the estimated lateral-bond strength (ΔGlat0≅ -5 kBT) is well-aligned with earlier estimates based on thermokinetic modeling and light microscopy measurements. Thus, we have computationally connected atomistic-level structural information, obtained by cryo-electron microscopy, to cellular-scale microtubule assembly dynamics using a combination of MD, BD, and thermokinetic models to bridge from Angstroms to micrometers and from femtoseconds to minutes.
A gelatin hydrogel to study endometrial angiogenesis and trophoblast invasion.

The endometrium is the lining of the uterus and site of blastocyst implantation. Each menstrual cycle, the endometrium cycles through rapid phases of growth, remodelling and breakdown. Significant ...
Hall Effect Measurements of the Double-Layer Capacitance of the Graphene–Electrolyte Interface

There is an ongoing effort to improve the energy storage capacity of graphene-based supercapacitors. These supercapacitors store energy in the electric field between the charge carriers in the graphene and the counter ions in a liquid electrolyte. To characterize this double layer, we use the Hall effect to determine the charge carrier density in graphene as a function of voltage. We disentangle the separate roles of double-layer capacitance (the electrostatic contribution) and quantum capacitance and compare the performance of different electrolytes. Our results highlight the advantages of Hall effect measurements for probing the electrostatics of graphene–electrolyte interfaces.
The constant factor in the asymptotic for practical numbers

An integer n ≥ 1 is said to be practical if every natural number m ≤ n can be expressed as a sum of distinct positive divisors of n. The number of practical numbers up to x is asymptotic to cx/log ...
Symmetry breaking transition towards directional locomotion in Physarum microplasmodia

True slime mold Physarum polycephalum has been widely used as a model organism to study ﬂow-driven amoeboid locomotion as well as the dynamics of its complex mechanochemical self-oscillations. The aim of this work is to quantify the mechanical aspects of symmetry breaking and its transition into directional ﬂow-driven amoeboid locomotion in small (alt;~ 200 µm) fragments of Physarum polycephalum. To this end, we combined measurements of traction stresses, fragment morphology, and ectoplasmic microrheology with experimental manipulations of cell-substrate adhesion, cortical strength and microplasmodium size. These measurements show that initiation of locomotion is accompanied by the symmetry breaking of traction stresses and the polarization of ectoplasmic mechanical properties, with the rear part of the microplasmodium becoming signiﬁcantly stiﬀer after the onset of locomotion. Our experimental data suggests that the initiation of locomotion in Physarum could be analogous to an interfacial instability process and that microplasmodial size is a critical parameter governing the instability. Speciﬁcally, our results indicate that the instability driving the onset of locomotion is strengthened by substrate adhesiveness and weakened by cortical stiﬀness. Furthermore, the Fourier spectral analysis of morphology revealed lobe number n = 2 as the consistent dominant mode number across various experimental manipulations, suggesting that the instability mechanism driving the onset of Physarum locomotion is robust with respect to changes in environmental conditions and microplasmodial properties.
Kernel Truncated Randomized Ridge Regression: Optimal Rates and Low Noise Acceleration

In this paper we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our algorithm has faster finite-time and asymptotic rates on problems where the Bayes risk with respect to the square loss is small. We state our results using standard tools from the theory of least square regression in RKHSs, namely, the decay of the eigenvalues of the associated integral operator and the complexity of the optimal predictor measured through the integral operator.
Thin compactifications and relative fundamental classes

We define a notion of relative fundamental class that applies to moduli spaces in gauge theory and in symplectic Gromov-Witten theory. For universal moduli spaces over a parameter space, the relative fundamental class specifies an element of the Cech homology of the compactification of each fiber; it is defined if the compactification is "thin" in the sense that its boundary has homological codimension at least two.
The population genetics of structural variants in grapevine domestication

Structural variants (SVs) are a largely unexplored feature of plant genomes. Little is known about the type and size of SVs, their distribution among individuals and, especially, their population dynamics. Understanding these dynamics is critical for understanding both the contributions of SVs to phenotypes and the likelihood of identifying them as causal genetic variants in genome-wide associations. Here, we identify SVs and study their evolutionary genomics in clonally propagated grapevine cultivars and their outcrossing wild progenitors. To catalogue SVs, we assembled the highly heterozygous Chardonnay genome, for which one in seven genes is hemizygous based on SVs. Using an integrative comparison between Chardonnay and Cabernet Sauvignon genomes by whole-genome, long-read and short-read alignment, we extended SV detection to population samples. We found that strong purifying selection acts against SVs but particularly against inversion and translocation events. SVs nonetheless accrue as recessive heterozygotes in clonally propagated lineages. They also define outlier regions of genomic divergence between wild and cultivated grapevines, suggesting roles in domestication. Outlier regions include the sex-determination region and the berry colour locus, where independent large, complex inversions have driven convergent phenotypic evolution. This study identified structural variants in grapevine populations, including wild progenitors, using a de novo assembly and comparative genomics approach, and examined their evolutionary genomics and roles in domestication and phenotypic evolution.