cssi/SciSciGPT-SciSciNet huggingface dataset:
Degenerations of Abelian differentials

Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, give dimension bounds for their moduli spaces, and establish smoothability criteria. As applications, we show that the spin parity of holomorphic and meromorphic differentials extends to distinguish twisted canonical divisors in the locus of stable pointed curves of pseudocompact type. We also justify whether zeros and poles on general curves in a stratum of differentials can be Weierstrass points. Moreover, we classify twisted canonical divisors on curves with at most two nodes in the minimal stratum in genus three. Our techniques combine algebraic geometry and flat geometry. Their interplay is a main flavor of the paper.
Equiangular tight frames from group divisible designs

An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that many of the known constructions of ETFs are of one of two types. We further provide a new method for combining a given ETF of one of these two types with an appropriate group divisible design (GDD) in order to produce a larger ETF of the same type. By applying this method to known families of ETFs and GDDs, we obtain several new infinite families of ETFs. The real instances of these ETFs correspond to several new infinite families of strongly regular graphs. Our approach was inspired by a seminal paper of Davis and Jedwab which both unified and generalized McFarland and Spence difference sets. Our main result is a combinatorial analog of their algebraic results.
Wandering Bumps in Stochastic Neural Fields

We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions between neurons in different spatial locations of the network. Translationally symmetric neural fields support a continuum of stationary bump solutions, which may be centered at any spatial location. Random fluctuations are introduced by modeling the system as a spatially extended Langevin equation whose noise term we take to be additive. For nonzero noise, bumps are shown to wander about the domain in a purely diffusive way. We can approximate the associated diffusion coefficient using a small noise expansion. Upon breaking the (continuous) translation symmetry of the system using spatially heterogeneous inputs or synapses, bumps in the stochastic neural field can become temporarily pinned to a finite number of locations in the network. As a result, the effective diffusion of the bump is reduced, in comparison to the homogeneous case. As the modulation frequency of this heterogeneity increases, the effective diffusion of bumps in the network approaches that of the network with spatially homogeneous weights.
Audio-Visual Scene Analysis with Self-Supervised Multisensory Features

The thud of a bouncing ball, the onset of speech as lips open—when visual and audio events occur together, it suggests that there might be a common, underlying event that produced both signals. In this paper, we argue that the visual and audio components of a video signal should be modeled jointly using a fused multisensory representation. We propose to learn such a representation in a self-supervised way, by training a neural network to predict whether video frames and audio are temporally aligned. We use this learned representation for three applications: (a) sound source localization, i.e. visualizing the source of sound in a video; (b) audio-visual action recognition; and (c) on/off-screen audio source separation, e.g. removing the off-screen translator’s voice from a foreign official’s speech. Code, models, and video results are available on our webpage: http://andrewowens.com/multisensory.
Harvesting Paragraph-Level Question-Answer Pairs from Wikipedia

We study the task of generating from Wikipedia articles question-answer pairs that cover content beyond a single sentence. We propose a neural network approach that incorporates coreference knowledge via a novel gating mechanism. As compared to models that only take into account sentence-level information (Heilman and Smith, 2010; Du et al., 2017; Zhou et al., 2017), we find that the linguistic knowledge introduced by the coreference representation aids question generation significantly, producing models that outperform the current state-of-the-art. We apply our system (composed of an answer span extraction system and the passage-level QG system) to the 10,000 top ranking Wikipedia articles and create a corpus of over one million question-answer pairs. We provide qualitative analysis for the this large-scale generated corpus from Wikipedia.
Radon inversion formulas over local fields

Let F be a local field and n ≥ 2 an integer. We study the Radon transform as an operator M : C+ → C− from the space of smooth K-finite functions on Fn \ {0} with bounded support to the space of smooth K-finite functions on Fn \{0} supported away from a neighborhood of 0. These spaces naturally arise in the theory of automorphic forms. We prove that M is an isomorphism and provide formulas for M−1. In the real case, we show that when K-finiteness is dropped from the definitions, the analog of M is not surjective.
Chebyshev polynomials, moment matching, and optimal estimation of the unseen

We consider the problem of estimating the support size of a discrete distribution whose minimum nonzero mass is at least $\frac{1}{k}$. Under the independent sampling model, we show that the sample complexity, that is, the minimal sample size to achieve an additive error of $\varepsilon k$ with probability at least 0.1 is within universal constant factors of $\frac{k}{\log k}\log^{2}\frac{1}{\varepsilon }$, which improves the state-of-the-art result of $\frac{k}{\varepsilon^{2}\log k}$ in [In Advances in Neural Information Processing Systems (2013) 2157–2165]. Similar characterization of the minimax risk is also obtained. Our procedure is a linear estimator based on the Chebyshev polynomial and its approximation-theoretic properties, which can be evaluated in $O(n+\log^{2}k)$ time and attains the sample complexity within constant factors. The superiority of the proposed estimator in terms of accuracy, computational efficiency and scalability is demonstrated in a variety of synthetic and real datasets.
The Dehn functions of Stallings–Bieri groups

We show that the Stallings–Bieri groups, along with certain other Bestvina–Brady groups, have quadratic Dehn function.
Mixture Selection, Mechanism Design, and Signaling

We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function g from the n-dimensional hypercube to the bounded interval [-1, 1], and an n × m matrix A with bounded entries, maximize g(Ax) over x in the m-dimensional simplex. This problem arises naturally when one seeks to design a lottery over items for sale in an auction, or craft the posterior beliefs for agents in a Bayesian game through the provision of information (a.k.a. Signaling). We present an approximation algorithm for this problem when g simultaneously satisfies two "smoothness" properties: Lipschitz continuity with respect to the La#x221E; norm, and noise stability. The latter notion, which we define and cater to our setting, controls the degree to which low-probability -- and possibly correlated -- errors in the inputs of g can impact its output. The approximation guarantee of our algorithm degrades gracefully as a function of the Lipschitz continuity and noise stability of g. In particular, when g is both O(1)-Lipschitz continuous and O(1)-stable, we obtain an (additive) polynomial-time approximation scheme (PTAS) for mixture selection. We also show that neither assumption suffices by itself for an additive PTAS, and both assumptions together do not suffice for an additive fully polynomial-time approximation scheme (FPTAS). We apply our algorithm for mixture selection to a number of different game-theoretic applications, focusing on problems from mechanism design and optimal signaling. In particular, we make progress on a number of open problems suggested in prior work by easily reducing them to mixture selection: we resolve an important special case of the small-menu lottery design problem posed by Dughmi, Han, and Nisan, we resolve the problem of revenue-maximizing signaling in Bayesian second-price auctions posed by Emek et al. And Miltersen and Sheffet, we design a quasipolynomial-time approximation scheme for the optimal signaling problem in normal form games suggested by Dughmi, and we design an approximation algorithm for the optimal signaling problem in the voting model of Alonso and Camara.
Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)

We present the first provably sublinear time hashing algorithm for approximate Maximum Inner Product Search (MIPS). Searching with (un-normalized) inner product as the underlying similarity measure is a known difficult problem and finding hashing schemes for MIPS was considered hard. While the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, in this paper we extend the LSH framework to allow asymmetric hashing schemes. Our proposal is based on a key observation that the problem of finding maximum inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search in classical settings. This key observation makes efficient sublinear hashing scheme for MIPS possible. Under the extended asymmetric LSH (ALSH) framework, this paper provides an example of explicit construction of provably fast hashing scheme for MIPS. Our proposed algorithm is simple and easy to implement. The proposed hashing scheme leads to significant computational savings over the two popular conventional LSH schemes: (i) Sign Random Projection (SRP) and (ii) hashing based on p-stable distributions for L2 norm (L2LSH), in the collaborative filtering task of item recommendations on Netflix and Movielens (10M) datasets.
Analysis of MEMS electrostatic energy harvesters electrically configured as voltage multipliers

Abstract This paper presents the analysis of an efficient alternative interface circuit for MEMS electrostatic energy harvesters. It is entirely composed of diodes and capacitors. Based on modeling and simulation, an anti-phase gap-closing structure is investigated. We find that when configured as a voltage multiplier, it can operate at very low acceleration amplitudes. In addition, the allowed maximum voltage between electrodes is barely limited by the pull-in effect. The parasitic capacitance of the harvester and non-ideal characteristics of electronic components are taken into account. A lumped-model of the harvesting system has been implemented in a circuit simulator. Simulation results show that an output voltage of 22 V is obtained with 0.15 g input acceleration. The minimum necessary ratio between the maximum and minimum capacitances of the generators, which allows operation of the circuit, can be lower than 2. This overcomes a crucial obstacle in low-power energy harvesting devices. A comparison between the voltage multiplier against other current topologies is highlighted. An advantage of the former over the latter is to generate much higher saturation voltage, while the minimum required initial bias and the minimum capacitance ratio in both cases are at similar levels.
On totally real spheres in complex space

Let M ,N be two totally real and real analytic submanifolds in Cn . We say that M and N are biholomorphically equivalent if there is a biholomorphic mapping F defined in a neighborhood of M such that F (M ) = N . As a standard fact of complexification, one knows that all totally real and real analytic embeddings of M in C n are biholomorphically equivalent if M is of maximal dimension n . However, the topology of the manifold plays a major role in the existence of totally real immersions or embeddings. For instance, R.O. Wells [23] proved that if an n-dimensional compact and orientable manifold M admits a totally real embedding in Cn , then its Euler number must vanish. It was also observed by Wells that if M is a manifold of dimension n and it admits a totally real immersion in Cn , then its complexified tangent bundle T cM = TM⊗C is trivial. Conversely, the triviality of T cM also implies the existence of totally real immersions of M in Cn . This was obtained by M.L. Gromov in [11] through the method of convex integration. A stronger result due to J.A. Lees [17] says that M also admits Lagrangian immersions in Cn . The sphere S k : x 2 1 + . . . + x 2 k+1 = 1 in R k+1 gives us a trivial totally real embedding of S k in Ck+1. On the other hand, the works of Gromov [11], AhernRudin [1] and Stout-Zame [21] tell us that S k admits a totally real and real analytic embedding in Ck if and only if k = 1, 3. Our main result is the following. Theorem 1.1. If k ≤ 4, all totally real and real analytic embeddings of S k in Cn are biholomorphically equivalent. If k ≥ 5 and nk = k + 2[ k−1 4 ], there exist totally
Pseudo-Prikry sequences

We generalize results of Gitik, Dzamonja-Shelah, and Magidor-Sinapova on the existence of pseudo-Prikry sequences, which are sequences that approximate the behavior of the generic objects introduced by Prikry-type forcings, in outer models of set theory. Such sequences play an important role in the study of singular cardinal combinatorics by placing restrictions on the type of behavior that can consistently be obtained in outer models. In addition, we provide results about the existence of diagonal pseudo-Prikry sequences, which approximate the behavior of the generic objects introduced by diagonal Prikry-type forcings. Our proof techniques are substantially different from those of previous results and rely on an analysis of PCF-theoretic objects in the outer model.
Distributed learning with infinitely many hypotheses

We consider a distributed learning setup where a network of agents sequentially access realizations of a set of random variables with unknown distributions. The network objective is to find a parametrized distribution that best describes their joint observations in the sense of the Kullback-Leibler divergence. We analyze the case of countably many hypotheses and the case of a continuum of hypotheses. We provide non-asymptotic bounds for the concentration rate of the agents' beliefs around the correct hypothesis in terms of the number of agents, the network parameters, and the learning abilities of the agents. Additionally, we provide a novel motivation for a general set of distributed non-Bayesian update rules as instances of the distributed stochastic mirror descent algorithm.
Formal Theory of Cornered Asymptotically Hyperbolic Einstein Metrics

This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the usual infinite boundary and a corner where the two meet. On the finite boundary, a constant mean curvature umbilic condition is imposed. First, recent work of Nozaki, Takayanagi, and Ugajin is generalized and extended showing that such metrics cannot have smooth compactifications for generic corners embedded in the infinite boundary. A model linear problem is then studied: a formal expansion at the corner is derived for eigenfunctions of the scalar Laplacian subject to certain boundary conditions. In doing so, scalar ODEs are studied that are of relevance for a broader class of boundary value problems and also for the Einstein problem. Next, unique formal existence at the corner, up to order at least equal to the boundary dimension, of Einstein metrics in a cornered asymptotically hyperbolic normal form which are polyhomogeneous in polar coordinates is demonstrated for arbitrary smooth conformal infinity. Finally it is shown that, in the special case that the finite boundary is taken to be totally geodesic, there is an obstruction to existence beyond this order, which defines a conformal hypersurface invariant.
Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives

In this paper we propose a novel method that provides contrastive explanations justifying the classification of an input by a black box classifier such as a deep neural network. Given an input we find what should be minimally and sufficiently present (viz. important object pixels in an image) to justify its classification and analogously what should be minimally and necessarily \emph{absent} (viz. certain background pixels). We argue that such explanations are natural for humans and are used commonly in domains such as health care and criminology. What is minimally but critically \emph{absent} is an important part of an explanation, which to the best of our knowledge, has not been explicitly identified by current explanation methods that explain predictions of neural networks. We validate our approach on three real datasets obtained from diverse domains; namely, a handwritten digits dataset MNIST, a large procurement fraud dataset and a brain activity strength dataset. In all three cases, we witness the power of our approach in generating precise explanations that are also easy for human experts to understand and evaluate.
Ensemble Estimation of Information Divergence

Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Renyi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem.
Applying Deep Learning to the Newsvendor Problem

The newsvendor problem is one of the most basic and widely applied inventory models. If the probability distribution of the demand is known, the problem can be solved analytically. However, approxi...
Well-Posedness for Constrained Hamilton-Jacobi Equations

The goal of this paper is to study a Hamilton-Jacobi equation $$ \textstyle\begin{cases} u_{t}=H(Du)+R(x,I(t)) &\text{in }\mathbb{R}^{n} \times (0,\infty ), \\ \sup_{\mathbb{R}^{n}} u(\cdot ,t)=0 &\text{on }[0,\infty ), \end{cases} $$ with initial conditions $I(0)=I_{0}>0$, $u(x,0)=u_{0}(x)$ on $\mathbb{R}^{n}$. Here $(u,I)$ is a pair of unknowns and the Hamiltonian $H$ and the reaction term $R$ are given. Moreover, $I(t)$ is an unknown constraint (Lagrange multiplier) that constrains the supremum of $u$ to be always zero. We construct a solution in the viscosity setting using a fixed point argument when the reaction term $R(x,I)$ is strictly decreasing in $I$. We also discuss both uniqueness and nonuniqueness. For uniqueness, a certain structural assumption on $R(x,I)$ is needed. We also provide an example with infinitely many solutions when the reaction term is not strictly decreasing in $I$.
Person re-identification using visual attention

Despite recent attempts for solving the person re-identification problem, it remains a challenging task since a person's appearance can vary significantly when large variations in view angle, human pose and illumination are involved. The concept of attention is one of the most interesting recent architectural innovations in neural networks. Inspired by that, in this paper we propose a novel approach based on using a gradient-based attention mechanism in deep convolution neural network for solving the person re-identification problem. Our model learns to focus selectively on parts of the input image for which the networks' output is most sensitive to. Extensive comparative evaluations demonstrate that the proposed method outperforms state-of-the-art approaches, including both traditional and deep neural network-based methods on the challenging CUHK01 and CUHK03 datasets.
Poisson–Gerstenhaber brackets in representation algebras

Abstract We introduce cyclic bilinear forms on coalgebras and use them to generalize Van den Berghʼs Poisson brackets in representation algebras.
Detecting flatness over smooth bases

Given an essentially finite type morphism of schemes f: X --> Y and a positive integer d, let f^{d}: X^{d} --> Y denote the natural map from the d-fold fiber product, X^{d}, of X over Y and \pi_i: X^{d} --> X the i'th canonical projection. When Y smooth over a field and F is a coherent sheaf on X, it is proved that F is flat over Y if (and only if) f^{d} maps the associated points of the tensor product sheaf \otimes_{i=1}^d \pi_i^*(F) to generic points of Y, for some d greater than or equal to dim Y. The equivalent statement in commutative algebra is an analog---but not a consequence---of a classical criterion of Auslander and Lichtenbaum for the freeness of finitely generated modules over regular local rings.
Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Abstract: Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos.
Instantons and affine algebras I: The Hilbert scheme and vertex operators

This is the first in a series of papers which describe the action of an affine Lie algebra with central charge $n$ on the moduli space of $U(n)$-instantons on a four manifold $X$. This generalises work of Nakajima, who considered the case when $X$ is an ALE space. In particular, this describes the combinatorial complexity of the moduli space as being precisely that of representation theory, and thus will lead to a description of the Betti numbers of moduli space as dimensions of weight spaces. This Lie algebra acts on the space of conformal blocks (i\.e\., the cohomology of a determinant line bundle on the moduli space) generalising the ``insertion'' and ``deletion'' operations of conformal field theory, and indeed on any cohomology theory. In the particular case of $U(1)$-instantons, which is essentially the subject of this present paper, the construction produces the basic representation after Frenkel-Kac. Then the well known quadratic nature of $ch_2$, $$ch_2 = \frac{1}{2} c_1\cdot c_1 - c_2 $$ becomes precisely the formula for the eigenvalue of the degree operator, i\.e\. the well known quadratic behaviour of affine Lie algebras.
Optimizing neural network hyperparameters with Gaussian processes for dialog act classification

Systems based on artificial neural networks (ANNs) have achieved state-of-the-art results in many natural language processing tasks. Although ANNs do not require manually engineered features, ANNs have many hyperparameters to be optimized. The choice of hyperparameters significantly impacts models' performances. However, the ANN hyperparameters are typically chosen by manual, grid, or random search, which either requires expert experiences or is computationally expensive. Recent approaches based on Bayesian optimization using Gaussian processes (GPs) is a more systematic way to automatically pinpoint optimal or near-optimal machine learning hyperparameters. Using a previously published ANN model yielding state-of-the-art results for dialog act classification, we demonstrate that optimizing hyperparameters using GP further improves the results, and reduces the computational time by a factor of 4 compared to a random search. Therefore it is a useful technique for tuning ANN models to yield the best performances for NLP tasks.
MM Algorithms For Variance Components Models.

Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticia...
A note on the minimum size of an orthogonal array

ABSTRACTIt is an elementary fact that the size of an orthogonal array of strength t on k factors must be a multiple of a certain number, say Lt, that depends on the orders of the factors. Thus Lt is a lower bound on the size of arrays of strength t on those factors, and is no larger than Lk, the size of the complete factorial design. We investigate the relationship between the numbers Lt, and two questions in particular: For what t is Lt < Lk? And when Lt = Lk, is the complete factorial design the only array of that size and strength t? Arrays are assumed to be mixed-level.We refer to an array of size less than Lk as a proper fraction. Guided by our main result, we construct a variety of mixed-level proper fractions of strength k − 1 that also satisfy a certain group-theoretic condition.
Heegaard–Floer homology of broken fibrations over the circle

Abstract We extend Perutz’s Lagrangian matching invariants to 3-manifolds which are not necessarily fibered using the technology of holomorphic quilts. We prove an isomorphism of these invariants with Ozsvath–Szabo’s Heegaard–Floer invariants for certain extremal spin c structures. As applications, we give new calculations of Heegaard–Floer homology of certain classes of 3-manifolds, and a characterization of Juhasz’s sutured Floer homology.
Did the model understand the question

We analyze state-of-the-art deep learning models for three tasks: question answering on (1) images, (2) tables, and (3) passages of text. Using the notion of “attribution” (word importance), we find that these deep networks often ignore important question terms. Leveraging such behavior, we perturb questions to craft a variety of adversarial examples. Our strongest attacks drop the accuracy of a visual question answering model from 61.1% to 19%, and that of a tabular question answering model from 33.5% to 3.3%. Additionally, we show how attributions can strengthen attacks proposed by Jia and Liang (2017) on paragraph comprehension models. Our results demonstrate that attributions can augment standard measures of accuracy and empower investigation of model performance. When a model is accurate but for the wrong reasons, attributions can surface erroneous logic in the model that indicates inadequacies in the test data.
Focused stochastic local search and the lovász local lemma

We develop tools for analyzing focused stochastic local search algorithms. These are algorithms that search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random nearby state which, hopefully, addresses the violation without introducing many new ones. A large class of such algorithms arise from algorithmizations of the Lovasz Local Lemma, a non-constructive tool for proving the existence of satisfying states. Here we give tools that provide a unified analysis of such algorithms and of many more, expressing them as instances of a general framework.
On the birationality of complete intersections associated to nef-partitions

We prove that generic complete intersections associated to multiple mirror nef-partitions are all birational. This result solves a conjecture by Batyrev and Nill in [6] under some mild assumptions.
Free boundary minimal surfaces in the unit ball with low cohomogeneity

We study free boundary minimal surfaces in the unit ball of low cohomogeneity. For each pair of positive integers $(m,n)$ such that $m, n >1$ and $m+n\geq 8$, we construct a free boundary minimal surface $\Sigma_{m, n} \subset B^{m+n}$(1) invariant under $O(m)\times O(n)$. When $m+n<8$, an instability of the resulting equation allows us to find an infinite family $\{\Sigma_{m,n, k}\}_{k\in \mathbb{N}}$ of such surfaces. In particular, $\{\Sigma_{2, 2, k}\}_{k\in \mathbb{N}}$ is a family of solid tori which converges to the cone over the Clifford Torus as $k$ goes to infinity. These examples indicate that a smooth compactness theorem for Free Boundary Minimal Surfaces due to Fraser and Li does not generally extend to higher dimensions. For each $n\geq 3$, we prove there is a unique nonplanar $SO(n)$-invariant free boundary minimal surface (a "catenoid") $\Sigma_n \subset B^n(1)$. These surfaces generalize the "critical catenoid" in $B^3(1)$ studied by Fraser and Schoen.
Investigations of Auditory Filters Based Excitation Patterns for Assessment of Noise Induced Hearing Loss

Noise induced hearing loss (NIHL) as one of the major avoidable occupational related health issues has been studied for decades. To assess NIHL, the excitation pattern (EP) has been considered as one of the mechanisms to estimate the movements of the basilar membrane (BM) in the cochlea. In this study, two auditory filters, dual resonance nonlinear (DRNL) filter and rounded-exponential (ROEX) filter are applied to create two EPs, the velocity EP and the loudness EP respectively. Two noise hazard metrics are proposed based on two proposed EPs to evaluate hazardous levels caused by different types of noise. Moreover Gaussian noise and tone signals are simulated to evaluate performances of the proposed EPs and the noise metrics. The results show that both EPs can reflect the responses of the BM to different types of noise. For Gaussian noise there is a frequency shift between the velocity EP and the loudness EP. The results suggest that both EPs can be used for assessment of NIHL.
Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networks

Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local convergence theory for smooth two-player games, which subsumes several discrete-time gradient-based saddle point dynamics. The analysis reveals the surprising nature of the off-diagonal interaction term as both a blessing and a curse. On the one hand, this interaction term explains the origin of the slow-down effect in the convergence of Simultaneous Gradient Ascent (SGA) to stable Nash equilibria. On the other hand, for the unstable equilibria, exponential convergence can be proved thanks to the interaction term, for four modified dynamics proposed to stabilize GAN training: Optimistic Mirror Descent (OMD), Consensus Optimization (CO), Implicit Updates (IU) and Predictive Method (PM). The analysis uncovers the intimate connections among these stabilizing techniques, and provides detailed characterization on the choice of learning rate. As a by-product, we present a new analysis for OMD proposed in Daskalakis, Ilyas, Syrgkanis, and Zeng [2017] with improved rates.
Solid solution strengthening and softening due to collective nanocrystalline deformation physics

Solid solution effects on the strength of the finest nanocrystalline grain sizes are studied with molecular dynamics simulations of different Cu-based alloys. We find evidence of both solid solution strengthening and softening, with trends in strength controlled by how alloying affects the elastic modulus of the material. This behavior is consistent with a shift to collective grain boundary deformation physics, and provides a link between the mechanical behavior of very fine-grained nanocrystalline metals and metallic glasses.
A NOTE ON LEFSCHETZ FIBRATIONS ON COMPACT STEIN 4-MANIFOLDS

Loi–Piergallini and Akbulut–Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the disk D2 with bounded fibers. In this note we give a more intrinsic alternative proof of this result.
What's in a Question: Using Visual Questions as a Form of Supervision

Collecting fully annotated image datasets is challenging and expensive. Many types of weak supervision have been explored: weak manual annotations, web search results, temporal continuity, ambient sound and others. We focus on one particular unexplored mode: visual questions that are asked about images. The key observation that inspires our work is that the question itself provides useful information about the image (even without the answer being available). For instance, the question what is the breed of the dog? informs the AI that the animal in the scene is a dog and that there is only one dog present. We make three contributions: (1) providing an extensive qualitative and quantitative analysis of the information contained in human visual questions, (2) proposing two simple but surprisingly effective modifications to the standard visual question answering models that allow them to make use of weak supervision in the form of unanswered questions associated with images and (3) demonstrating that a simple data augmentation strategy inspired by our insights results in a 7.1% improvement on the standard VQA benchmark.
Trajectory Modeling and Prediction with Waypoint Information Using a Conditionally Markov Sequence

Information about the waypoints of a moving object, e.g., an airliner in an air traffic control (ATC) problem, should be considered in trajectory modeling and prediction. Due to the ATC regulations, trajectory design criteria, and restricted motion capability of airliners there are long range dependencies in trajectories of airliners. Waypoint information can be used for modeling such dependencies in trajectories. This paper proposes a conditionally Markov (CM) sequence for modeling trajectories passing by waypoints. A dynamic model governing the proposed sequence is obtained. Filtering and trajectory prediction formulations are presented. The use of the proposed sequence for modeling trajectories with waypoints is justified.
Discrete reproducing kernel Hilbert spaces: sampling and distribution of Dirac-masses

We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) H over infinite, discrete and countable sets V. In this setting we analyze in detail the distributions of the corresponding Dirac point-masses of V. Illustrations include certain models from neural networks: An Extreme Learning Machine (ELM) is a neural network-configuration in which a hidden layer of weights are randomly sampled, and where the object is then to compute resulting output. For RKHSs H of functions defined on a prescribed countable infinite discrete set V, we characterize those which contain the Dirac masses δx for all points x in V. Further examples and applications where this question plays an important role are: (i) discrete Brownian motion-Hilbert spaces, i.e., discrete versions of the Cameron-Martin Hilbert space; (ii) energy-Hilbert spaces corresponding to graph-Laplacians where the set V of vertices is then equipped with a resistance metric; and finally (iii) the study of Gaussian free fields.
Minimizing lifetime poverty with a penalty for bankruptcy

Abstract We provide investment advice for an individual who wishes to minimize her lifetime poverty, with a penalty for bankruptcy or ruin. We measure poverty via a non-negative, non-increasing function of (running) wealth. Thus, the lower wealth falls and the longer wealth stays low, the greater the penalty. This paper generalizes the problems of minimizing the probability of lifetime ruin and minimizing expected lifetime occupation, with the poverty function serving as a bridge between the two. To illustrate our model, we compute the optimal investment strategies for a specific poverty function and two consumption functions, and we prove some interesting properties of those investment strategies.
Compositional Semantic Parsing on Semi-Structured Tables

Two important aspects of semantic parsing for question answering are the breadth of the knowledge source and the depth of logical compositionality. While existing work trades off one aspect for another, this paper simultaneously makes progress on both fronts through a new task: answering complex questions on semi-structured tables using question-answer pairs as supervision. The central challenge arises from two compounding factors: the broader domain results in an open-ended set of relations, and the deeper compositionality results in a combinatorial explosion in the space of logical forms. We propose a logical-form driven parsing algorithm guided by strong typing constraints and show that it obtains significant improvements over natural baselines. For evaluation, we created a new dataset of 22,033 complex questions on Wikipedia tables, which is made publicly available.
Pitt's inequality and the fractional Laplacian: Sharp error estimates

Sharp error estimates in terms of the fractional Laplacian and a weighted Besov norm are obtained for Pitt's inequality by using the spectral representation with weights for the fractional Laplacian due to Frank, Lieb and Seiringer and the sharp Stein-Weiss inequality. Dilation invariance, group symmetry on a non-unimodular group and a nonlinear Stein-Weiss lemma are used to provide short proofs of the Frank-Seiringer "Hardy inequalities" where fractional smoothness is measured by a Besov norm.
Pattern-based Modeling of High-Performance Computing Resilience

With the growing scale and complexity of high-performance computing (HPC) systems, resilience solutions that ensure continuity of service despite frequent errors and component failures must be methodically designed to balance the reliability requirements with the overheads to performance and power. Design patterns enable a structured approach to the development of resilience solutions, providing hardware and software designers with the building block elements for the rapid development of novel solutions and for adapting existing technologies for emerging, extreme-scale HPC environments. In this paper, we develop analytical models that enable designers to evaluate the reliability and performance characteristics of the design patterns. These models are particularly useful in building a unified framework that analyzes and compares various resilience solutions built using a combination of patterns.
Benedetto’s trick and existence of rational preperiodic structures for quadratic polynomials

We refine a result of R. Benedetto in p-adic analysis in order to exhibit infinitely many quadratic polynomials with rational coefficients having a specified graph of rational preperiodic points.
A Novel View of the Drift: Method for Heavy Traffic Limits of Queueing Systems

The drift method has been recently developed to study queueing systems in heavy traffic [3]. This method was successfully used to obtain the heavy traffic scaled sum queue lengths of several systems, even when the so-called complete resource pooling condition is not satisfied. In this poster, we present a novel view of the drift method to explain why this methodworks.We believe that this view can be exploited to obtain the joint distribution of the steady-state heavy-traffic scaled queue lengths.
Homogenization of parabolic equations with large time-dependent random potential

Abstract This paper concerns the homogenization problem of a parabolic equation with large, time-dependent, random potentials in high dimensions d ≥ 3 . Depending on the competition between temporal and spatial mixing of the randomness, the homogenization procedure turns to be different. We characterize the difference by proving the corresponding weak convergence of Brownian motion in random scenery. When the potential depends on the spatial variable macroscopically, we prove a convergence to SPDE.
A two-dimensional resistor network model for transition-edge sensors with normal metal features

Transition-edge sensors (TESs) can be used in high-resolution photon detection, exploiting the steep slope of the resistance in the superconducting-to-normal transition edge. Normal metal bars on the TES film are commonly used to engineer its transition shape, namely the dependence of resistance on temperature and current. This problem has been studied in one dimension, however until now, there have been no predictive models of the influence of two-dimensional (2-D) normal metal features on the TES transition shape. In this work, we approach this problem by treating the TES as a 2-D network of resistors, the values of which are based on the two-fluid model. We present a study of the behavior of devices with different 2-D geometric features. Our 2-D network model is capable of predicting how typical TES geometry parameters, such as number of bars, bar spacing, and overall dimensions, influence device behavior and thus is a powerful tool to guide the engineering of new TES devices.
Infinitude of k-Lehmer numbers which are not Carmichael

In this paper, we prove that there are infinitely many n’s for which rad(φ(n))|n − 1 but n is not a Carmichael number. Additionally, we prove that for any k ≥ 3, there exist infinitely many n’s such that φ(n)|(n − 1)k but φ(n) ∤ (n − 1)k−1. The constructions that we consider here are generalizations of Carmichael and Lehmer numbers, respectively, that were first formulated by Grau and Oller-Marcen.
Coarse embeddings into superstable spaces

Krivine and Maurey proved in 1981 that every stable Banach space contains almost isometric copies of lp, for some p ∊ [1, ∞). In 1983, Raynaud showed that if a Banach space uniformly embeds into a superstable Banach space, then X must contain an isomorphic copy of lp, for some p ∊ [1, ∞). In these notes, we show that if a Banach space coarsely embeds into a superstable Banach space, then X has a spreading model isomorphic to lp, for some p ∊ [1, ∞). In particular, we obtain that there exist reflexive Banach spaces which do not coarsely embed into any superstable Banach space.
Teaching an Old Elephant New Tricks

In recent years, column stores (or C-stores for short) have emerged as a novel approach to deal with read-mostly data warehousing applications. Experimental evidence suggests that, for cert ain types of queries, the new features of C-stores result in orders of magnitude improvement over traditional relational engines. At the same time, some C-store proponents argue that C-stores are fundamentally different from traditional engines, and therefore their benefi ts cannot be incorporated into a relational engine short of a complete rewrite. In this paper we challenge this claim and show that many of the benefits of C-stores can indeed be simulated in traditional e ngines with no changes whatsoever. We then identify some limitations of our “pure-simulation” approach for the case of more complex queries. Finally, we predict that traditional relational e ngines will eventually leverage most of the benefits of C-stores nativel y, as is currently happening in other domains such as XML data.
Extracting flexibility of heterogeneous deferrable loads via polytopic projection approximation

This paper develops a novel approach to extract the aggregate flexibility of deferrable loads with heterogeneous parameters via polytopic projection approximation. First, an exact characterization of their aggregate flexibility is derived analytically, which in general contains exponentially many inequality constraints with respect to the number of loads. In order to have a tractable solution, we develop a numerical algorithm that gives a sufficient approximation of the exact aggregate flexibility. Geometrically, the flexibility of each individual load is a polytope and their aggregation is the Minkowski sum of these polytopes. Our method is motivated by an alternative interpretation of the Minkowski sum as a projection operation. The aggregate flexibility can be viewed as the projection of a high-dimensional polytope onto the subspace representing the aggregate power. We formulate a robust optimization problem to optimally approximate the polytopic projection with respect to the homothets of a given polytope. To enable efficient and parallel computation of the aggregate flexibility for a large number of loads, a muti-stage aggregation strategy is proposed. Finally, an energy arbitrage problem is solved to demonstrate the effectiveness of the proposed method.
Pattern formation, traveling fronts and consensus versus fragmentation in a model of opinion dynamics

Abstract We consider a continuous version of the Hegselmann–Krause model of opinion dynamics. Interaction between agents either leads to a state of consensus, where agents converge to a single opinion as time evolves, or to a fragmented state with multiple opinions. In this work, we linearize the system about a uniform density solution and predict consensus or fragmentation based on properties of the resulting dispersion relation. This prediction is different depending on whether the initial agent distribution is uniform or nearly uniform. In the uniform case, we observe traveling fronts in the agent based model and make predictions for the speed and pattern selected by this front.
Feynman integrals and critical modular $L$-values

Broadhurst conjectured that the Feynman integral associated to the polynomial corresponding to $t=1$ in the one-parameter family $(1+x_1+x_2+x_3)(1+x_1^{-1}+x_2^{-1}+x_3^{-1})-t$ is expressible in terms of $L(f,2),$ where $f$ is a cusp form of weight $3$ and level $15$. Bloch, Kerr and Vanhove have recently proved that the conjecture holds up to a rational factor. In this paper, we prove that Broadhurst's conjecture is true. Similar identities involving Feynman integrals associated to other polynomials in the same family are also established.