cssi/SciSciGPT-SciSciNet huggingface dataset:
Braided Hochschild cohomology and Hopf actions

We show that the braided Hochschild cohomology, of an algebra in a suitably algebraic braided monoidal category, admits a graded ring structure under which it is braided commutative. We then give a canonical identification between the usual Hochschild cohomology ring of a smash product and the (derived) invariants of its braided Hochschild cohomology ring. We apply our results to identify the associative formal deformation theory of a smash product with its formal deformation theory as a module algebra over the given Hopf algebra (when the Hopf algebra is sufficiently semisimple). As a second application we deduce some structural results for the usual Hochschild cohomology of a smash product, and discuss specific implications for finite group actions on smooth affine schemes.
A Coupled CFD-FEA study of the Sound Generated in a Stenosed Artery and Transmitted Through Tissue Layers

A new computational approach for simulating the blood flow-induced sound generation and propagation in a stenosed artery with one-sided constriction was investigated. This computational hemoacoustic method is based on mapping the transient pressure (force) fluctuations on the vessel wall and solving for the structural vibrations in frequency domain. These vibrations were detected as sound on the epidermal surface. The current hydro-vibroacoustic method employs a two-step, one-way coupled approach for the sound generation in the flow domain and its propagation through the tissue layers. The results were validated by comparing with previous analytical and computational solutions. It was found that the bruits (generated from the flow around the stenosis) are related primarily to the time-derivative of the integrated pressure force on the arterial wall downstream of the stenosis. Advantages of the methods used in the current study include: (a) capability of providing accurate solution with a faster solution time; (b) accurately capturing the break frequency of the velocity fluctuation measured on epidermal surface; (c) inclusion of the fluid-structure interaction between blood flow and the arterial wall.
Symmetric powers do not stabilize

We discuss the stabilization of symmetric products Sym^n(X) of a smooth projective variety X in the Grothendieck ring of varieties. For smooth projective surfaces X with non-zero h^0(X, \omega_X), these products do not stabilize; we conditionally show that they do not stabilize in another related sense, in response to a question of R. Vakil and M. Wood. There are analogies between such stabilization, the Dold-Thom theorem, and the analytic class number formula. Finally, we discuss Hodge-theoretic obstructions to the stabilization of symmetric products, and provide evidence for these obstructions in terms of a relationship between the Newton polygon of a certain "motivic zeta function" associated to a curve, and its Hodge polygon.
On dependence structure of copula-based Markov chains

We consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential ρ -mixing. We analyse the example of the Mardia and Frechet copula families using small sets.
Panning for gold: ‘model‐X’ knockoffs for high dimensional controlled variable selection

Many contemporary large‐scale applications involve building interpretable models linking a large set of potential covariates to a response in a non‐linear fashion, such as when the response is binary. Although this modelling problem has been extensively studied, it remains unclear how to control the fraction of false discoveries effectively even in high dimensional logistic regression, not to mention general high dimensional non‐linear models. To address such a practical problem, we propose a new framework of ‘model‐X’ knockoffs, which reads from a different perspective the knockoff procedure that was originally designed for controlling the false discovery rate in linear models. Whereas the knockoffs procedure is constrained to homoscedastic linear models with n⩾p, the key innovation here is that model‐X knockoffs provide valid inference from finite samples in settings in which the conditional distribution of the response is arbitrary and completely unknown. Furthermore, this holds no matter the number of covariates. Correct inference in such a broad setting is achieved by constructing knockoff variables probabilistically instead of geometrically. To do this, our approach requires that the covariates are random (independent and identically distributed rows) with a distribution that is known, although we provide preliminary experimental evidence that our procedure is robust to unknown or estimated distributions. To our knowledge, no other procedure solves the controlled variable selection problem in such generality but, in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case–control study of Crohn's disease in the UK, making twice as many discoveries as the original analysis of the same data.
Performance and sensitivity of vortex coronagraphs on segmented space telescopes

The detection of molecular species in the atmospheres of earth-like exoplanets orbiting nearby stars requires an optical system that suppresses starlight and maximizes the sensitivity to the weak planet signals at small angular separations. Achieving sufficient contrast performance on a segmented aperture space telescope is particularly challenging due to unwanted diffraction within the telescope from amplitude and phase discontinuities in the pupil. Apodized vortex coronagraphs are a promising solution that theoretically meet the performance needs for high contrast imaging with future segmented space telescopes. We investigate the sensitivity of apodized vortex coronagraphs to the expected aberrations, including segment co-phasing errors in piston and tip/tilt as well as other low-order and mid-spatial frequency aberrations. Coronagraph designs and their associated telescope requirements are identified for conceptual HabEx and LUVOIR telescope designs.
UNIQUELY 2-DIVISIBLE BOL LOOPS

Although any finite Bol loop of odd prime exponent is solvable, we show there exist such Bol loops with trivial center. We also construct finitely generated, infinite, simple Bruck loops of odd prime exponent for sufficiently large primes. This shows that the Burnside problem for Bruck loops has a negative answer.
Precision Annealing Monte Carlo Methods for Statistical Data Assimilation: Metropolis-Hastings Procedures

Abstract. Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the information transfer addresses properties of the conditional probability distribution of the states of the model conditioned on the observations. The quantities of interest in SDA are the conditional expected values of functions of the model state, and these require the approximate evaluation of high dimensional integrals. We introduce a conditional probability distribution and use the Laplace method with annealing to identify the maxima of the conditional probability distribution. The annealing method slowly increases the precision term of the model as it enters the Laplace method. In this paper, we extend the idea of precision annealing (PA) to Monte Carlo calculations of conditional expected values using Metropolis-Hastings methods.
Noise control in gene regulatory networks with negative feedback

Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the lower bound for noise suppression in terms of the number of signaling events, shows that a tetracycline repressor-based negative-regulatory gene circuit behaves as a WK filter. For the class of Hill-like nonlinear regulatory functions, this type of filter provides the optimal reduction in noise. Our theoretical approach can be readily combined with experimental measurements of response functions in a wide variety of gen...
Preparing a highly degenerate fermi gas in an optical lattice

We propose a method to prepare fermionic atoms in a three-dimensional optical lattice at unprecedentedly low temperatures and uniform filling factors. The process involves adiabatic loading of degenerate atoms into multiple energy bands of an optical lattice followed by a filtering stage whereby atoms from all but the lowest band are removed. Of critical importance is the use of a nonharmonic trapping potential to provide external confinement for the atoms. For realistic experimental parameters, this procedure will produce a Fermi gas in a lattice with a reduced temperature $T/{T}_{F}~0.003$ and an entropy per particle of $s~0.02 {k}_{B}$.
The fourth moment of quadratic Dirichlet L-functions over function fields

We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet L-functions over $${\mathbb{F}_q[x]}$$ , as the base field $${\mathbb{F}_q}$$ is fixed and the genus of the family goes to infinity. According to conjectures of Andrade and Keating, we expect the fourth moment to be asymptotic to $${q^{2g+1} P(2g+1)}$$ up to an error of size $${o(q^{2g+1})}$$ , where P is a polynomial of degree 10 with explicit coefficients. We prove an asymptotic formula with the leading three terms, which agrees with the conjectured result.
>The SEIS model, or, the contact process with a latent stage

The susceptible→exposed→infectious→susceptible (SEIS) model is well known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The compartment model is well studied, but the corresponding particle system has so far received no attention. For the particle system model in one spatial dimension, we give upper and lower bounds on the critical values, prove convergence of critical values in the limit of small and large latent time, and identify a limiting process to which the SEIS model converges in the limit of large latent time.
Non-Flat Regular Polytopes and Restrictions on Chiral Polytopes

An abstract polytope is flat if every facet is incident on every vertex. In this paper, we prove that no chiral polytope has flat finite regular facets and finite regular vertex-figures. We then determine the three smallest non-flat regular polytopes in each rank, and use this to show that for $n \geq 8$, a chiral $n$-polytope has at least $48(n-2)(n-2)!$ flags.
The topology of the zero locus of a genus 2 theta function

Mess showed that the genus 2 Torelli group $T_2$ is isomorphic to a free group of countably infinite rank by showing that genus 2 Torelli space is homotopy equivalent to an infinite wedge of circles. As an application of his computation, we compute the homotopy type of the zero locus of any classical genus 2 theta function in $\mathfrak{h}_2 \times \mathbb{C}^2$, where $\mathfrak{h}_2$ denotes rank 2 Siegel space. Specifically, we show that the zero locus of any such function is homotopy equivalent to an infinite wedge of 2-spheres.
Remarks on non-commutative crepant resolutions of complete intersections

Abstract We study obstructions to existence of non-commutative crepant resolutions, in the sense of Van den Bergh, over local complete intersections.
The hidden convexity of spectral clustering

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by certain Indepenent Component Analysis techniques, are simple, easy to implement and efficient. Geometrically, the proposed algorithms can be interpreted as hidden basis recovery by means of function optimization. We give a complete characterization of the contrast functions admissible for provable basis recovery. We show how these conditions can be interpreted as a "hidden convexity" of our optimization problem on the sphere; interestingly, we use efficient convex maximization rather than the more common convex minimization. We also show encouraging experimental results on real and simulated data.
Stable Grothendieck rings of wreath product categories

Let k be an algebraically closed field of characteristic zero, and let $${\mathcal {C}} = {\mathcal {R}} -\hbox {mod}$$ be the category of finite-dimensional modules over a fixed Hopf algebra over k. One may form the wreath product categories $$ {\mathcal {W}}_{n}({\mathcal {C}}) = ( {\mathcal {R}} \wr S_n)-\hbox {mod}$$ whose Grothendieck groups inherit the structure of a ring. Fixing distinguished generating sets (called basic hooks) of the Grothendieck rings, the classification of the simple objects in $$ {\mathcal {W}}_{n}({\mathcal {C}}) $$ allows one to demonstrate stability of structure constants in the Grothendieck rings (appropriately understood), and hence define a limiting Grothendieck ring. This ring is the Grothendieck ring of the wreath product Deligne category $$S_t({\mathcal {C}})$$ . We give a presentation of the ring and an expression for the distinguished basis arising from simple objects in the wreath product categories as polynomials in basic hooks. We discuss some applications when $$ {\mathcal {R}} $$ is the group algebra of a finite group, and some results about stable Kronecker coefficients. Finally, we explain how to generalise to the setting where $${\mathcal {C}}$$ is a tensor category.
A Comparison of Five Multiple Instance Learning Pooling Functions for Sound Event Detection with Weak Labeling

Sound event detection (SED) entails two subtasks: recognizing what types of sound events are present in an audio stream (audio tagging), and pinpointing their onset and offset times (localization). In the popular multiple instance learning (MIL) framework for SED with weak labeling, an important component is the pooling function. This paper compares five types of pooling functions both theoretically and experimentally, with special focus on their performance of localization. Although the attention pooling function is currently receiving the most attention, we find the linear softmax pooling function to perform the best among the five. Using this pooling function, we build a neural network called TALNet. It is the first system to reach state-of-the-art audio tagging performance on Audio Set, while exhibiting strong localization performance on the DCASE 2017 challenge at the same time.
A Complete Dichotomy Rises from the Capture of Vanishing Signatures

We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions $\mathcal{F}$ on Boolean variables. This extends and unifies all previous dichotomies for Holant problems on symmetric constraint functions (taking values without a finite modulus). We define and characterize all symmetric vanishing signatures; they turn out to be essential to the complete classification of Holant problems. The dichotomy theorem has an explicit tractability criterion expressible in terms of holographic transformations. A Holant problem defined by a set of constraint functions $\mathcal{F}$ is solvable in polynomial time if it satisfies this tractability criterion, and is #P-hard otherwise. The tractability criterion can be intuitively stated as follows: A set $\mathcal{F}$ is tractable if (1) every function in $\mathcal{F}$ has arity at most two; or (2) $\mathcal{F}$ is transformable to an affine type; or (3) $\mathcal{F}$ is transformable to a product type; o...
Testing Core Membership in Public Goods Economies.

This paper develops a recent line of economic theory seeking to understand public goods economies using methods of topological analysis. Our first main result is a very clean characterization of the economy's core (the standard solution concept in public goods). Specifically, we prove that a point is in the core iff it is Pareto efficient, individually rational, and the set of points it dominates is path connected. While this structural theorem has a few interesting implications in economic theory, the main focus of the second part of this paper is on a particular algorithmic application that demonstrates its utility. Since the 1960s, economists have looked for an efficient computational process that decides whether or not a given point is in the core. All known algorithms so far run in exponential time (except in some artificially restricted settings). By heavily exploiting our new structure, we propose a new algorithm for testing core membership whose computational bottleneck is the solution of $O(n)$ convex optimization problems on the utility function governing the economy. It is fairly natural to assume that convex optimization should be feasible, as it is needed even for very basic economic computational tasks such as testing Pareto efficiency. Nevertheless, even without this assumption, our work implies for the first time that core membership can be efficiently tested on (e.g.) utility functions that admit "nice" analytic expressions, or that appropriately defined $\varepsilon$-approximate versions of the problem are tractable (by using modern black-box $\varepsilon$-approximate convex optimization algorithms).
Getting Path Integrals Physically and Technically Right

Feynman’s Lagrangian path integral was an outgrowth of Dirac’s vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton’s first equation of motion, so their use contravenes the uncertainty principle, but they are relevant to semiclassical approximations and relatedly to the ubiquitous case that the Hamiltonian is quadratic in the canonical momenta, which accounts for the Lagrangian path integral’s “success”. Feynman also invented the Hamiltonian phase-space path integral, which is fully compatible with the uncertainty principle. We recast this as an ordinary functional integral by changing direct integration over subpaths constrained to all have the same two endpoints into an equivalent integration over those subpaths’ unconstrained second derivatives. Function expansion with generalized Legendre polynomials of time then enables the functional integral to be unambiguously evaluated through first order in the elapsed time, yielding the Schrodinger equation with a unique quantization of the classical Hamiltonian. Widespread disbelief in that uniqueness stemmed from the mistaken notion that no subpath can have its two endpoints arbitrarily far separated when its nonzero elapsed time is made arbitrarily short. We also obtain the quantum amplitude for any specified configuration or momentum path, which turns out to be an ordinary functional integral over, respectively, all momentum or all configuration paths. The first of these results is directly compared with Feynman’s mistaken Lagrangian-action hypothesis for such a configuration path amplitude, with special heed to the case that the Hamiltonian is quadratic in the canonical momenta.
Chiral magnetic effect search in p(d)+Au, Au+Au collisions at RHIC

The chiral magnetic effect (CME) refers to charge separation along a strong magnetic field of single-handed quarks, caused by interactions with topological gluon fields from QCD vacuum fluctuations. A major background of CME measurements in heavy-ion collisions comes from resonance decays coupled with elliptical flow anisotropy. These proceedings present two new studies from STAR to shed further light on the background issue: (1) small system p+Au and d+Au collisions where the CME signal is not expected, and (2) pair invariant mass dependence where resonance peaks can be identified.
Channel assignment in dense MC-MR wireless networks: Scaling laws and algorithms

We investigate optimal channel assignment algorithms that maximize per node throughput in dense multi-channel multi-radio (MC-MR) wireless networks. Specifically, we consider an MC-MR network where all nodes are within the transmission range of each other. This situation is encountered in many real-life settings such as students in a lecture hall, delegates attending a conference, or soldiers in a battlefield. In this scenario, we show that intelligent assignment of the available channels results in a significantly higher per node throughput. We first propose a class of channel assignment algorithms, parameterized by T (the number of transceivers per node), that can achieve Θ(1/N1/T) per node throughput using Θ(TN1-1/T ) channels. In view of practical constraints on T, we then propose another algorithm that can achieve Θ((1/log2n)2) per node throughput using only two transceivers per node. Finally, we identify a fundamental relationship between the achievable per node throughput, the total number of channels used, and the network size under any strategy. Using analysis and simulations, we show that our algorithms achieve close to optimal performance at different operating points on this curve. Our work has several interesting implications on the optimal network design for dense MC-MR wireless networks.
On q-commutative power and Laurent series rings at roots of unity

We continue the first and second authors’ study of q-commutative power series rings R=kq[[x1,…,xn]] and Laurent series rings L=kq[[x1±1,…,xn±1]], specializing to the case in which the commutation p...
Positive motivic measures are counting measures

Let K be a field. A positive motivic measure on the Grothendieck ring K_0(Var_K) is a homomorphism from K_0(Var_K) to the real numbers assigning a nonnegative value to every variety. In this note we show that the only positive motivic measures are the counting measures: measures on K_0(Var_{F_q}) which send a variety to its number of rational points over some fixed finite extension of F_q.
Atomistic Simulation of Nearly Defect-Free Models of Amorphous Silicon: An Information-Based Approach

We present an information-based total-energy optimization method to produce nearly defect-free structural models of amorphous silicon. Using geometrical, structural, and topological information from disordered tetrahedral networks, we have shown that it is possible to generate structural configurations of amorphous silicon, which are superior than the models obtained from conventional reverse Monte Carlo and molecular dynamics simulations. The new data-driven hybrid approach presented here is capable of producing atomistic models with structural and electronic properties which are on a par with those obtained from the modified Wooten-Winer-Weaire (WWW) models of amorphous silicon. Structural, electronic, and thermodynamic properties of the hybrid models are compared with the best dynamical models obtained from using machine-intelligence-based algorithms and efficient classical molecular dynamics simulations, reported in the recent literature. We have shown that, together with the WWW models, our hybrid models represent one of the best structural models so far produced by total-energy-based Monte Carlo methods in conjunction with experimental diffraction data.
DEEP NEURAL NETWORKS FOR NON-LINEAR MODEL-BASED ULTRASOUND RECONSTRUCTION

Ultrasound reflection tomography is widely used to image large complex specimens that are only accessible from a single side, such as well systems and nuclear power plant containment walls. Typical methods for inverting the measurement rely on delay-and-sum algorithms that rapidly produce reconstructions but with significant artifacts. Recently, model-based reconstruction approaches using a linear forward model have been shown to significantly improve image quality compared to the conventional approach. However, even these techniques result in artifacts for complex objects because of the inherent non-linearity of the ultrasound forward model.In this paper, we propose a non-iterative model-based reconstruction method for inverting measurements that are based on non-linear forward models for ultrasound imaging. Our approach involves obtaining an approximate estimate of the reconstruction using a simple linear back-projection and training a deep neural network to refine this to the actual reconstruction. We apply our method to simulated and experimental ultrasound data to demonstrate dramatic improvements in image quality compared to the delay-and-sum approach and the linear model-based reconstruction approach.
On the density function on moduli spaces of toric 4-manifolds

The optimal density function assigns to each symplectic toric manifold $M$ a number $0 < d \leq 1$ obtained by considering the ratio between the maximum volume of $M$ which can be filled by symplectically embedded disjoint balls and the total symplectic volume of $M$. In the toric version of this problem, $M$ is toric and the balls need to be embedded respecting the toric action on $M$. The goal of this note is first to give a brief survey of the notion of toric symplectic manifold and the recent constructions of moduli space structure on them, and recall how to define a natural density function on this moduli space. Then we review previous works which explain how the study of the density function can be reduced to a problem in convex geometry, and use this correspondence to to give a simple description of the regions of continuity of the maximal density function when the dimension is $4$.
Automatic estimation of ice bottom surfaces from radar imagery

Ground-penetrating radar on planes and satellites now makes it practical to collect 3D observations of the subsurface structure of the polar ice sheets, providing crucial data for understanding and tracking global climate change. But converting these noisy readings into useful observations is generally done by hand, which is impractical at a continental scale. In this paper, we propose a computer vision-based technique for extracting 3D ice-bottom surfaces by viewing the task as an inference problem on a probabilistic graphical model. We first generate a seed surface subject to a set of constraints, and then incorporate additional sources of evidence to refine it via discrete energy minimization. We evaluate the performance of the tracking algorithm on 7 topographic sequences (each with over 3000 radar images) collected from the Canadian Arctic Archipelago with respect to human-labeled ground truth.
Variational information maximization for feature selection

Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class labels. Practical methods are forced to rely on approximations due to the difficulty of estimating mutual information. We demonstrate that approximations made by existing methods are based on unrealistic assumptions. We formulate a more flexible and general class of assumptions based on variational distributions and use them to tractably generate lower bounds for mutual information. These bounds define a novel information-theoretic framework for feature selection, which we prove to be optimal under tree graphical models with proper choice of variational distributions. Our experiments demonstrate that the proposed method strongly outperforms existing information-theoretic feature selection approaches.
Temporal Gaussian Mixture Layer for Videos

We introduce a new convolutional layer named the Temporal Gaussian Mixture (TGM) layer and present how it can be used to efficiently capture longer-term temporal information in continuous activity videos. The TGM layer is a temporal convolutional layer governed by a much smaller set of parameters (e.g., location/variance of Gaussians) that are fully differentiable. We present our fully convolutional video models with multiple TGM layers for activity detection. The extensive experiments on multiple datasets, including Charades and MultiTHUMOS, confirm the effectiveness of TGM layers, significantly outperforming the state-of-the-arts.
Robustness May Be at Odds with Accuracy

We show that there may exist an inherent tension between the goal of adversarial robustness and that of standard generalization. Specifically, training robust models may not only be more resource-consuming, but also lead to a reduction of standard accuracy. We demonstrate that this trade-off between the standard accuracy of a model and its robustness to adversarial perturbations provably exists in a fairly simple and natural setting. These findings also corroborate a similar phenomenon observed empirically in more complex settings. Further, we argue that this phenomenon is a consequence of robust classifiers learning fundamentally different feature representations than standard classifiers. These differences, in particular, seem to result in unexpected benefits: the representations learned by robust models tend to align better with salient data characteristics and human perception.
Rare event simulation via importance sampling for linear SPDE’s

The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations. We find that if a spectral gap of appropriate size exists, then one can identify a lower dimensional manifold where the rare event takes place. This allows one to build importance sampling changes of measures that perform provably well even pre-asymptotically (i.e. for small but non-zero size of the noise) without degrading in performance due to infinite dimensionality or due to long simulation time horizons. Simulation studies supplement and illustrate the theoretical results.
Storage capacity as an information-theoretic analogue of vertex cover

Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from the information stored at the neighboring vertices. Computing the storage capacity is a fundamental problem in network coding and is related, or equivalent, to some well-studied problems such as index coding with side information and generalized guessing games. In this paper, we consider storage capacity as a natural information-theoretic analogue of the minimum vertex cover of a graph. Indeed, while it was known that storage capacity is upper bounded by minimum vertex cover, we show that by treating it as such we can get a 3/2 approximation for planar graphs, and a 4/3 approximation for triangle-free planar graphs. Since the storage capacity is closely related to the index coding rate, we get a 1.923 approximation of index coding rate for planar graphs and 3/2 approximation for triangle-free planar graphs. Previously only an obvious 4 approximation of the index coding rate was known for planar graphs. We then develop a general method of “gadget covering” to upper bound the storage capacity in terms of the average of a set of vertex covers. This method is intuitive and leads to the exact characterization of storage capacity for various families of graphs, such as cycles with chords and certain Cartesian product graphs. Finally, we generalize the storage capacity notion to include recovery from partial failures in distributed storage. We show tight upper and lower bounds on this partial recovery capacity that scales nicely with the fraction of failure in a vertex.
On ranges of variants of the divisor functions that are dense

For a real number t, let st be the multiplicative arithmetic function defined by for all primes p and positive integers α. We show that the range of a function s-r is dense in the interval (0, 1] whenever r ∈ (0, 1]. We then find a constant ηA ≈ 1.9011618 and show that if r > 1, then the range of the function s-r is a dense subset of the interval if and only if r ≤ ηA. We end with an open problem.
Geometry of integral binary hermitian forms

Abstract We generalize Conwayʼs approach to integral binary quadratic forms to study integral binary hermitian forms over quadratic imaginary extensions of Q . We show that every indefinite anisotropic form determines a plane (“ocean”) in Mendozaʼs spine associated to the corresponding Bianchi group in the hyperbolic 3-space. The ocean can be used to compute the group of integral transformations preserving the hermitian form.
GUIDES: Geospatial Urban Infrastructure Data Engineering Solutions

As the underground infrastructure systems of cities age, maintenance and repair become an increasing concern. Cities face difficulties in planning maintenance, predicting and responding to infrastructure related issues, and in realizing their vision to be a smart city due to their incomplete understanding of the existing state of the infrastructure. Only few cities have accurate and complete digital information on their underground infrastructure (e.g., electricity, water, natural gas) systems, which poses problems to those planning and performing construction projects. To address these issues, we introduce GUIDES as a new data conversion and management framework for urban underground infrastructure systems that enable city administrators, workers, and contractors along with the general public and other users to query digitized and integrated data to make smarter decisions. This demo paper presents the GUIDES architecture and describes two of its central components: (i) mapping of underground infrastructure systems, and (ii) integration of heterogeneous geospatial data.
Configuration Spaces of Graphs with Certain Permitted Collisions

If G is a graph with vertex set V, let $${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$ be the space of n-tuples of points on G, which are only allowed to overlap on elements of V. We think of $${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$ as a configuration space of points on G, where points are allowed to collide on vertices. In this paper, we attempt to understand these spaces from two separate, but closely related, perspectives. Using techniques of combinatorial topology we compute the fundamental groups and homology groups of $${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$ in the case where G is a tree. Next, we use techniques of asymptotic algebra to prove statements about $${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$ , for general graphs G, whenever n is sufficiently large. It is proven that, for general graphs, the homology groups exhibit generalized representation stability in the sense of Ramos ( arXiv:1606.02673 , 2016).
Van den Essen’s theorem on the de Rham cohomology of a holonomic D-module over a formal power series ring

Abstract In this expository paper, we give a complete proof of van den Essen’s theorem that the de Rham cohomology spaces of a holonomic D -module are finite-dimensional in the case of a formal power series ring over a field of characteristic zero. This proof requires results from at least five of van den Essen’s papers as well as his unpublished thesis, and until now has not been available in a self-contained document.
Some requests for machine learning research from the east african tech scene

Based on 46 in-depth interviews with scientists, engineers, and CEOs, this document presents a list of concrete machine research problems, progress on which would directly benefit tech ventures in East Africa.
Schatten-class truncated Toeplitz operators

We let H2 denote the Hardy space H2(D) of the open unit disk D in the complex plane. Recall that H2 is the Hilbert space of holomorphic functions which are power series centered at 0 with square-summable coefficients. As usual, we identify H2 with its space of boundary values, the subspace of L2(∂D) spanned by {1, z, z2, . . . }, where the functions in this set are considered as functions on ∂D. We let P denote the Cauchy projection, the orthogonal projection from L2(∂D) to H2. This projection may be extended in a natural way to a map from L1(∂D) to H(D), the set of holomorphic functions on D (see [12]). A (possibly unbounded) classical Toeplitz operator is defined by starting with a function φ ∈ L2(∂D), called a symbol function, and compressing the multiplication operator Mφ to H 2. That is, we define
Load synchronization and sustained oscillations induced by transactive control

Transactive or market-based coordination strategies have recently been proposed for controlling the aggregate demand of a large number of electric loads. Such schemes offer operational benefits such as enforcing distribution feeder capacity limits and providing users with flexibility to consume energy based on the price they are willing to pay. However, this paper demonstrates that they are also prone to load synchronization and power oscillations. A transactive energy framework has been adopted and applied to a population of thermostatically controlled loads (TCLs). A modified TCL switching logic takes into account market coordination signals, alongside the natural hysteresis-based switching conditions. Studies of this market-based coordination scheme suggest that several factors may contribute to load synchronism, including sharp changes in the market prices that are broadcast to loads, lack of diversity in user specified bid curves, low feeder limits that are encountered periodically, and the form of user bid curves. Case studies illustrate challenges associated with market-based coordination strategies and provide insights into modifications that address those issues.
Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds

In this article, we consider the Floer cohomology (with $\Z_2$ coefficients) between torus fibers and the real Lagrangian in Fano toric manifolds. We first investigate the conditions under which the Floer cohomology is defined, and then develop a combinatorial description of the Floer complex based on the polytope of the toric manifold. We show that if the Floer cohomology is defined, and the Floer cohomology of the torus fiber is non-zero, then the Floer cohomology of the pair is non-zero. We use this result to develop some applications to non-displaceability and the minimum number of intersection points under Hamiltonian isotopy.
Sampling and Optimization on Convex Sets in Riemannian Manifolds of Non-Negative Curvature

The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex sets also have meaningful counterparts in the manifold setting. Geodesically convex optimization is a well-studied problem with ongoing research and considerable recent interest in machine learning and theoretical computer science. In this paper, we study sampling and convex optimization problems over manifolds of non-negative curvature proving polynomial running time in the dimension and other relevant parameters. Our algorithms assume a warm start. We first present a random walk based sampling algorithm and then combine it with simulated annealing for solving convex optimization problems. To our knowledge, these are the first algorithms in the general setting of positively curved manifolds with provable polynomial guarantees under reasonable assumptions, and the first study of the connection between sampling and optimization in this setting.
A language hierarchy and Kitchens-type theorem for self-similar groups

Abstract We generalize the notion of self-similar groups of infinite tree automorphisms to allow for groups which are defined on a tree but may not act faithfully on it. The elements of such a group correspond to labeled trees which may be recognized by a tree automaton (e.g. Rabin, Buchi, etc.), or considered as elements of a tree shift (e.g. of finite type, sofic) as in symbolic dynamics. We give examples to show how self-similar groups defined in this way can be separated into different tree language hierarchies. As the main result, extending the classical result of Kitchens on one-dimensional group shifts, we provide a sufficient condition for a self-similar group whose elements form a sofic tree shift to be a tree shift of finite type. As an application, we show that the closures of certain self-similar groups of rooted k-ary tree automorphisms that satisfy an algebraic law are not Rabin-recognizable, that is, they can not be described within the second order theory of k successors. In both the main result and in the application a crucial role is played by a distinguished branched subgroup structure of the groups under consideration.
Swimming on limit cycles with nonholonomic constraints

The control and motion planning of bioinspired swimming robots is complicated by the fluid–robot interaction, which is governed by a very high (infinite)-dimensional nonlinear system. Many high-dimensional nonlinear systems, often have low-dimensional attractors. From the perspective of swimming robots, such low-dimensional attractors simplify the analysis of the mechanics of swimming and prove to be useful to design controllers. This paper describes such a low-dimensional model for the swimming of a class of robots that are propelled by the motion of an internal reaction wheel. The model of swimming on a low-dimensional attractor is itself motivated by recent work on the dissipative Chaplygin sleigh, a well-known nonholonomic system, that exhibits limit cycle dynamics. We show that the governing equations of the Chaplygin sleigh are a very useful surrogate model for the swimming robot. The Chaplygin sleigh model is used to demonstrate certain maneuvers by the robot through computations. Experiments with such a robot provide evidence of limit cycle dynamics. Computational models based on discrete-point vortex–body interaction confirm this behavior. Our work also suggests that there is a close phenomenological and mathematical similarity between the dynamics of swimming robots and those of ground-based nonholonomic robots, which could motivate the development of very low-dimensional mathematical models for the motion of other fish-like swimming robots.
Statistical Analysis of Some Evolution Equations Driven by Space-only Noise

We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations have been studied, little is known about inverse problems for these equations. We exploit the somewhat unusual structure of the observations coming from these equations that leads to an interesting interplay between classical and non-traditional statistical models. We derive several types of estimators for the drift and/or diffusion coefficients of these equations, and prove their relevant properties.
Finite-Time Error Bounds For Linear Stochastic Approximation and TD Learning

We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an associated ordinary differential equation (ODE). We obtain finite-time bounds on the mean-square error in the case of constant step-size algorithms by considering the drift of an appropriately chosen Lyapunov function. The Lyapunov function can be interpreted either in terms of Stein's method to obtain bounds on steady-state performance or in terms of Lyapunov stability theory for linear ODEs. We also provide a comprehensive treatment of the moments of the square of the 2-norm of the approximation error. Our analysis yields the following results: (i) for a given step-size, we show that the lower-order moments can be made small as a function of the step-size and can be upper-bounded by the moments of a Gaussian random variable; (ii) we show that the higher-order moments beyond a threshold may be infinite in steady-state; and (iii) we characterize the number of samples needed for the finite-time bounds to be of the same order as the steady-state bounds. As a by-product of our analysis, we also solve the open problem of obtaining finite-time bounds for the performance of temporal difference learning algorithms with linear function approximation and a constant step-size, without requiring a projection step or an i.i.d. noise assumption.
A polygenic score for body mass index is associated with depressive symptoms via early life stress: Evidence for gene-environment correlation

Abstract Increasing childhood obesity rates are associated with not only adverse physical, but also mental health outcomes, including depression. These negative outcomes may be caused and/or exacerbated by the bullying and shaming overweight individuals experience. As body mass index (BMI) can be highly heritable, we hypothesized that a genetic risk for higher BMI, will predict higher early life stress (ELS), which in turn will predict higher depressive symptoms in adulthood. Such a process will reflect an evocative gene-environment correlation (rGE) wherein an individual's genetically influenced phenotype evokes a reaction from the environment that subsequently shapes the individual's health. We modeled genetic risk using a polygenic score of BMI derived from a recent large GWAS meta-analysis. Self-reports were used for the assessment of ELS and depressive symptoms in adulthood. The discovery sample consisted of 524 non-Hispanic Caucasian university students from the Duke Neurogenetics Study (DNS; 278 women, mean age 19.78 ± 1.23 years) and the independent replication sample consisted of 5930 white British individuals from the UK biobank (UKB; 3128 women, mean age 62.66 ± 7.38 years). A significant mediation effect was found in the DNS (indirect effect = 0.207, bootstrapped SE = .10, bootstrapped 95% CI: 0.014 to 0.421), and then replicated in the UKB (indirect effect = 0.04, bootstrapped SE = .01, bootstrapped 95% CI: 0.018 to 0.066). Higher BMI polygenic scores predicted higher ELS, which in turn predicted higher depressive symptoms. Our findings suggest that evocative rGE may contribute to weight-related mental health problems and stress the need for interventions that aim to reduce weight bias, specifically during childhood.
Information-Theoretic Confidence Bounds for Reinforcement Learning

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments, including linear bandits, tabular MDPs, and factored MDPs. These examples demonstrate the potential of a general information-theoretic approach for the design and analysis of reinforcement learning algorithms.
Isomorphism in Wavelets

Two scaling functions \(\varphi _A\) and \(\varphi _B\) for Parseval frame wavelets are algebraically isomorphic, \(\varphi _A \simeq \varphi _B\), if they have matching solutions to their (reduced) isomorphic systems of equations. Let A and B be \(d\times d\) and \(s\times s\) expansive dyadic integral matrices with \(d, s\ge 1\) respectively and let \(\varphi _A\) be a scaling function associated with matrix A and generated by a finite solution. There always exists a scaling function \(\varphi _B\) associated with matrix B such that $$\begin{aligned} \varphi _B \simeq \varphi _A. \end{aligned}$$ An example shows that the assumption on the finiteness of the solutions can not be removed. An algebraic isomorphism with consistency has orthogonality as an invariant.