cssi/SciSciGPT-SciSciNet huggingface dataset:
Distributionally Adversarial Attack

Recent work on adversarial attack has shown that Projected Gradient Descent (PGD) Adversary is a universal first-order adversary, and the classifier adversarially trained by PGD is robust against a wide range of first-order attacks. It is worth noting that the original objective of an attack/defense model relies on a data distribution p(x), typically in the form of risk maximization/minimization, e.g., max/min Ep(x) L(x) with p(x) some unknown data distribution and L(·) a loss function. However, since PGD generates attack samples independently for each data sample based on L(·), the procedure does not necessarily lead to good generalization in terms of risk optimization. In this paper, we achieve the goal by proposing distributionally adversarial attack (DAA), a framework to solve an optimal adversarial-data distribution, a perturbed distribution that satisfies the L∞ constraint but deviates from the original data distribution to increase the generalization risk maximally. Algorithmically, DAA performs optimization on the space of potential data distributions, which introduces direct dependency between all data points when generating adversarial samples. DAA is evaluated by attacking state-of-the-art defense models, including the adversarially-trained models provided by MIT MadryLab. Notably, DAA ranks the first place on MadryLab’s white-box leaderboards, reducing the accuracy of their secret MNIST model to 88.56% (with l∞ perturbations of e = 0.3) and the accuracy of their secret CIFAR model to 44.71% (with l∞ perturbations of e = 8.0). Code for the experiments is released on https://github.com/tianzheng4/Distributionally-Adversarial-Attack.
SmartEAR: smartwatch-based unsupervised learning for multi-modal signal analysis in opportunistic sensing framework

Wrist-bands such as smartwatches have become an unobtrusive interface for collecting physiological and contextual data from users. Smartwatches are being used for smart healthcare, telecare, and wellness monitoring. In this paper, we used data collected from the AnEAR framework leveraging smartwatches to gather and store physiological data from patients in naturalistic settings. This data included temperature, galvanic skin response (GSR), acceleration, and heart rate (HR). In particular, we focused on HR and acceleration, as these two modalities are often correlated. Since the data was unlabeled we relied on unsupervised learning for multi-modal signal analysis. We propose using k-means clustering, GMM clustering, and Self-Organizing maps based on Neural Networks for group the multi-modal data into homogeneous clusters. This strategy helped in discovering latent structures in our data.
Fourier's law for a granular fluid

Newton's viscosity law for the momentum flux and Fourier's law for the heat flux define Navier-Stokes hydrodynamics for a simple, one-component fluid. There is ample evidence that a hydrodynamic description applies as well to a mesoscopic granular fluid with the same form for Newton's viscosity law. However, theory predicts a qualitative difference for Fourier's law with an additional contribution from density gradients even at uniform temperature. The reasons for the absence of such terms for normal fluids are indicated, and a related microscopic explanation for their existence in granular fluids is presented.
Accelerated flow for probability distributions

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. The maximum principle of optimal control theory is used to derive Hamilton's equations for the optimal gradient flow. The Hamilton's equation are shown to achieve the accelerated form of density transport from any initial probability distribution to a target probability distribution. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. Two numerical approximations are presented to implement the Hamilton's equations as a system of $N$ interacting particles. The continuous limit of the Nesterov's algorithm is shown to be a special case with $N=1$. The algorithm is illustrated with numerical examples.
Discrete homotopies and the fundamental group

Abstract We generalize and strengthen the theorem of Gromov that the fundamental group of any compact Riemannian manifold of diameter at most D has a set of generators g 1 , … , g k of length at most 2 D and relators of the form g i g m = g j . In particular, we obtain an explicit bound for the number k of generators in terms of the number of “short loops” at every point and the number of balls required to cover a given semi-locally simply connected geodesic space. As a corollary we obtain a fundamental group finiteness theorem (new even for Riemannian manifolds) that replaces the curvature and volume conditions of Anderson and the 1-systole bound of Shen–Wei, by more general geometric hypothesis implied by these conditions. This theorem, in turn, is a special case of a theorem for arbitrary compact geodesic spaces, proved using the method of discrete homotopies introduced by the first author and V. N. Berestovskii. Central to the proof is the notion of “homotopy critical spectrum”, introduced in this paper as a natural consequence of discrete homotopy methods. This spectrum is closely related to the Sormani–Wei covering spectrum which is a subset of the classical length spectrum studied by de Verdiere and Duistermaat–Guillemin. It is completely determined (including multiplicity) by special closed geodesics called “essential circles”.
On isolated singularities with noninvertible finite endomorphism

Abstract We prove that if ϕ : ( X , 0 ) → ( X , 0 ) is a finite endomorphism of an isolated singularity such that deg ⁡ ( ϕ ) ≥ 2 and ϕ is etale in codimension 1, then X is Q -Gorenstein and log canonical.
VIGAN: Missing view imputation with generative adversarial networks

In an era when big data are becoming the norm, there is less concern with the quantity but more with the quality and completeness of the data. In many disciplines, data are collected from heterogeneous sources, resulting in multi-view or multi-modal datasets. The missing data problem has been challenging to address in multi-view data analysis. Especially, when certain samples miss an entire view of data, it creates the missing view problem. Classic multiple imputations or matrix completion methods are hardly effective here when no information can be based on in the specific view to impute data for such samples. The commonly-used simple method of removing samples with a missing view can dramatically reduce sample size, thus diminishing the statistical power of a subsequent analysis. In this paper, we propose a novel approach for view imputation via generative adversarial networks (GANs), which we name by VIGAN. This approach first treats each view as a separate domain and identifies domain-to-domain mappings via a GAN using randomly-sampled data from each view, and then employs a multi-modal denoising autoencoder (DAE) to reconstruct the missing view from the GAN outputs based on paired data across the views. Then, by optimizing the GAN and DAE jointly, our model enables the knowledge integration for domain mappings and view correspondences to effectively recover the missing view. Empirical results on benchmark datasets validate the VIGAN approach by comparing against the state of the art. The evaluation of VIGAN in a genetic study of substance use disorders further proves the effectiveness and usability of this approach in life science.
Capacity Region of the Broadcast Channel with Two Deterministic Channel State Components

This paper establishes the capacity region of a class of broadcast channels with random state in which each channel component is selected from two possible functions and each receiver knows its state sequence. This channel model does not fit into any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. The capacity region is shown to coincide with the UV outer bound and is achieved via Marton coding.
Real-Time Prediction of the Duration of Distribution System Outages

This paper addresses the problem of predicting duration of unplanned power outages, using historical outage records to train a series of neural network predictors. The initial duration prediction is made based on environmental factors, and it is updated based on incoming field reports using natural language processing to automatically analyze the text. Experiments using 15 years of outage records show good initial results and improved performance leveraging text. Case studies show that the language processing identifies phrases that point to outage causes and repair steps.
Delocalized epidemics on graphs: A maximum entropy approach

The susceptible-infected-susceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be localized on small subgraphs of the contact network. Localized infections are not interesting because a true outbreak concerns network-wide invasion of the contact graph rather than localized infection of certain sites within the contact network. Existing approaches to localization phenomenon suffer from a major drawback: they fully rely on the steady-state solution of mean-field approximate models in the neighborhood of their phase transition point, where their approximation accuracy is worst; as statistical physics tells us. We propose a dispersion entropy measure that quantifies the localization of infections in a generic contact graph. Formulating a maximum entropy problem, we find an upper bound for the dispersion entropy of the possible metastable state in the exact SIS process. As a result, we find sufficient conditions such that any initial infection over the network either dies out or reaches a localized metastable state. Unlike existing studies relying on the solution of mean-field approximate models, our investigation of epidemic localization is based on characteristics of exact SIS equations. Our proposed method offers a new paradigm in studying spreading processes over complex networks.
Differential Algebras with Banach-Algebra Coefficients II: The Operator Cross-Ratio Tau-Function and the Schwarzian Derivative

Several features of an analytic (infinite-dimensional) Grassmannian of (commensurable) subspaces of a Hilbert space were developed in the context of integrable PDEs (KP hierarchy). We extended some of those features when polarized separable Hilbert spaces are generalized to a class of polarized Hilbert modules and then consider the classical Baker and τ-functions as operator-valued. Following from Part I we produce a pre-determinant structure for a class of τ-functions defined in the setting of the similarity class of projections of a certain Banach *-algebra. This structure is explicitly derived from the transition map of a corresponding principal bundle. The determinant of this map leads to an operator τ-function. We extend to this setting the operator cross-ratio which had previously been used to produce the scalar-valued τ-function, as well as the associated notion of a Schwarzian derivative along curves inside the space of similarity classes of a given projection. We link directly this cross-ratio with Fay’s trisecant identity for the τ-function. By restriction to the image of the Krichever map, we use the Schwarzian to introduce the notion of an operator-valued projective structure on a compact Riemann surface: this allows a deformation inside the Grassmannian (as it varies its complex structure). Lastly, we use our identification of the Jacobian of the Riemann surface in terms of extensions of the Burchnall–Chaundy C*-algebra (Part I) provides a link to the study of the KP hierarchy.
Adaptive Numerical Treatment of Elliptic Systems on Manifolds

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first reviewed, and then adaptive multilevel finite element methods for approximating solutions to this class of problems are considered in some detail. Two a posteriori error indicators are derived, based on local residuals and on global linearized adjoint or dual problems. The design of Manifold Code (MC) is then discussed; MC is an adaptive multilevel finite element software package for 2- and 3-manifolds developed over several years at Caltech and UC San Diego. It employs a posteriori error estimation, adaptive simplex subdivision, unstructured algebraic multilevel methods, global inexact Newton methods, and numerical continuation methods for the numerical solution of nonlinear covariant elliptic systems on 2- and 3-manifolds. Some of the more interesting features of MC are described in detail, including some new ideas for topology and geometry representation in simplex meshes, and an unusual partition of unity-based method for exploiting parallel computers. A short example is then given which involves the Hamiltonian and momentum constraints in the Einstein equations, a representative nonlinear 4-component covariant elliptic system on a Riemannian 3-manifold which arises in general relativity. A number of operator properties and solvability results recently established in [55] are first summarized, making possible two quasi-optimal a priori error estimates for Galerkin approximations which are then derived. These two results complete the theoretical framework for effective use of adaptive multilevel finite element methods. A sample calculation using the MC software is then presented; more detailed examples using MC for this application may be found in [26].
Learning Deep Models for Face Anti-Spoofing: Binary or Auxiliary Supervision

Face anti-spoofing is crucial to prevent face recognition systems from a security breach. Previous deep learning approaches formulate face anti-spoofing as a binary classification problem. Many of them struggle to grasp adequate spoofing cues and generalize poorly. In this paper, we argue the importance of auxiliary supervision to guide the learning toward discriminative and generalizable cues. A CNN-RNN model is learned to estimate the face depth with pixel-wise supervision, and to estimate rPPG signals with sequence-wise supervision. The estimated depth and rPPG are fused to distinguish live vs. spoof faces. Further, we introduce a new face anti-spoofing database that covers a large range of illumination, subject, and pose variations. Experiments show that our model achieves the state-of-the-art results on both intra- and cross-database testing.
A Mayer-Vietoris Theorem for the Kauffman Bracket Skein Module

The nth relative Kauffman bracket skein modules are defined and two theorems are given relating them to the Kauffman bracket skein module of a 3-manifold. The first theorem covers the case when the 3-manifold is split along a separating closed orientable surface and the second theorem addresses the case when the surface is nonseparating.
Fast Exact Matrix Completion with Finite Samples

Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works (Keshavan, 2012; Jain et al., 2013; Hardt, 2014) have proposed fast non-convex optimization based iterative algorithms to solve this problem. However, the sample complexity in all these results is sub-optimal in its dependence on the rank, condition number and the desired accuracy. In this paper, we present a fast iterative algorithm that solves the matrix completion problem by observing O ( nr log n ) entries, which is independent of the condition number and the desired accuracy. The run time of our algorithm is O ( nr log n log 1/ ) which is near linear in the dimension of the matrix. To the best of our knowledge, this is the first near linear time algorithm for exact matrix completion with finite sample complexity (i.e. independent of ). Our algorithm is based on a well known projected gradient descent method, where the projection is onto the (nonconvex) set of low rank matrices. There are two key ideas in our result: 1) our argument is based on a `∞ norm potential function (as opposed to the spectral norm) and provides a novel way to obtain perturbation bounds for it. 2) we prove and use a natural extension of the Davis-Kahan theorem to obtain perturbation bounds on the best low rank approximation of matrices with good eigen gap. Both of these ideas may be of independent interest.
Quadrivariate existence theorems and strong representability

In this article, we give conditions under which we can compute the conjugate of a convex function on the product of two Frechet spaces defined in terms of another convex function on the product of two (possibly different) Frechet spaces. We use this result to give simple proofs of some (both old and new) results for Banach spaces, and deduce some (both old and new) stability results for strongly representable multifunctions. We take as our starting point a result on closed convex cones in the product of two Frechet spaces.
Symmetries and conservation laws of the Euler equations in Lagrangian coordinates

Abstract We consider the Euler equations of incompressible inviscid fluid dynamics. We discuss a variational formulation of the governing equations in Lagrangian coordinates. We compute variational symmetries of the action functional and generate corresponding conservation laws in Lagrangian coordinates. We clarify and demonstrate relationships between symmetries and the classical balance laws of energy, linear momentum, center of mass, angular momentum, and the statement of vorticity advection. Using a newly obtained scaling symmetry, we obtain a new conservation law for the Euler equations in Lagrangian coordinates in n-dimensional space. The resulting integral balance relates the total kinetic energy to a new integral quantity defined in Lagrangian coordinates. This relationship implies an inequality which describes the radial deformation of the fluid, and shows the non-existence of time-periodic solutions with nonzero, finite energy.
An empirical analysis of feature engineering for predictive modeling

Machine learning models, such as neural networks, decision trees, random forests and gradient boosting machines accept a feature vector and provide a prediction. These models learn in a supervised fashion where a set of feature vectors with expected output is provided. It is very common practice to engineer new features from the provided feature set. Such engineered features will either augment, or replace portions of the existing feature vector. These engineered features are essentially calculated fields, based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different types of engineered features. This paper reports on empirical research to demonstrate what types of engineered features are best suited to which machine learning model type. This is accomplished by generating several datasets that are designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model is capable of synthesizing the needed feature on its own. If a model is capable of synthesizing an engineered feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.
Null asymptotics of solutions of the Einstein–Maxwell equations in general relativity and gravitational radiation

We prove that for spacetimes solving the Einstein–Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In Nonlinear nature of gravitation and gravitational-wave experiments, Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a permanent displacement of test masses in a laser interferometer gravitational-wave detector. Christodoulou derived a precise formula for this permanent displacement in the Einstein vacuum (EV) case. We prove in Theorem 2.6 that for the EM equations this permanent displacement exhibits a term coming from the electromagnetic field. This term is at the same highest order as the purely gravitational term that governs the EV situation. On the other hand, in Section 3, we show that to leading order, the presence of the electromagnetic field does not change the instantaneous displacement of the test masses. Following the method introduced by Christodoulou in Nonlinear nature of gravitation and gravitational-wave experiments, and asymptotics derived by Zipser in The global nonlinear stability of the trivial solution of the Einstein–Maxwell equations and Extensions of the stability theorem of the Minkowski space in general relativity: Solutions of the Einstein–Maxwell equations, we investigate gravitational radiation at null infinity in spacetimes solving the EM equations. We study the Bondi mass loss formula at null infinity derived in Extensions of the stability theorem of the Minkowski space in general relativity: Solutions of the Einstein–Maxwell equations. We show that the mass loss formula from Extensions of the stability theorem of the Minkowski space in general relativity: Solutions of the Einstein–Maxwell equations is compatible with the one in Bondi coordinates obtained in Gravitational waves in general relativity X: Asymptotic expansions for the Einstein–Maxwell field. And we observe that the presence of the electromagnetic field increases the total energy radiated to infinity up to leading order. Moreover, we compute the limit of the area radius at null infinity in Theorem 2.7.
Robust photometric stereo using learned image and gradient dictionaries

Photometric stereo is a method for estimating the normal vectors of an object from images of the object under varying lighting conditions. Motivated by several recent works that extend photometric stereo to more general objects and lighting conditions, we study a new robust approach to photometric stereo that utilizes dictionary learning. Specifically, we propose and analyze two approaches to adaptive dictionary regularization for the photometric stereo problem. First, we propose an image preprocessing step that utilizes an adaptive dictionary learning model to remove noise and other non-idealities from the image dataset before estimating the normal vectors. We also propose an alternative model where we directly apply the adaptive dictionary regularization to the normal vectors themselves during estimation. We study the practical performance of both methods through extensive simulations, which demonstrate the state-of-the-art performance of both methods in the presence of noise.
Viehweg’s hyperbolicity conjecture for families with maximal variation

We use the theory of Hodge modules to construct Viehweg–Zuo sheaves on base spaces of families with maximal variation and fibers of general type and, more generally, families whose geometric generic fiber has a good minimal model. Combining this with a result of Campana–Paun, we deduce Viehweg’s hyperbolicity conjecture in this context, namely the fact that the base spaces of such families are of log general type. This is approached as part of a general problem of identifying what spaces can support Hodge theoretic objects with certain positivity properties.
A note on Nahm’s conjecture in rank 2 case

The aim of this paper is to get a complete list of positive definite symmetric matrices with integer entries $\a&b\b&d\$ such that all complex solutions to the system of equations $1-x_1=x_1^ax_2^b\ 1-x_2=x_1^bx_2^d$ are real. This result is related to Nahm's conjecture in rank 2 case.
A fast generalized DFT for finite groups of lie type

We give an arithmetic algorithm using O(|G|ω/2+o(1)) operations to compute the generalized Discrete Fourier Transform (DFT) over group G for finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here ω is the exponent of matrix multiplication, so the exponent ω/2 is optimal if ω = 2. Previously, "exponent one" algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known (even under the assumption ω = 2) for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for SL2 (Fq) had exponent 4/3 despite being the focus of significant effort. We unconditionally achieve exponent at most 1.19 for this group, and exponent one if ω = 2. We also show that ω = 2 implies a [EQUATION] exponent for general finite groups G, which beats the longstanding previous best upper bound (assuming ω = 2) of 3/2.
Data-driven learning of the number of states in multi-state autoregressive models

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new and intuitive model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to identify whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between two AR filters based on the mean squared prediction error, and propose an efficient method to generate stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.
Principal Component Analysis and Higher Correlations for Distributed Data

We consider algorithmic problems in the setting in which the input data has been partitioned arbitrarily on many servers. The goal is to compute a function of all the data, and the bottleneck is the communication used by the algorithm. We present algorithms for two illustrative problems on massive data sets: (1) computing a low-rank approximation of a matrixA = A 1 +A 2 +::: +A s , with matrix A t stored on server t and (2) computing a function of a vector a1 + a2 + ::: + as, where servert has the vectorat; this includes the well-studied special case of computing frequency moments and separable functions, as well as higher-order correlations such as the number of subgraphs of a specified type occurring in a graph. For both problems we give algorithms with nearly optimal communication, and in particular the only dependence on n, the size of the data, is in the number of bits needed to represent indices and words (O(logn)).
Widespread selection and gene flow shape the genomic landscape during a radiation of monkeyflowers

Speciation genomic studies aim to interpret patterns of genome-wide variation in light of the processes that give rise to new species. However, interpreting the genomic "landscape" of speciation is difficult, because many evolutionary processes can impact levels of variation. Facilitated by the first chromosome-level assembly for the group, we use whole-genome sequencing and simulations to shed light on the processes that have shaped the genomic landscape during a radiation of monkeyflowers. After inferring the phylogenetic relationships among the 9 taxa in this radiation, we show that highly similar diversity (π) and differentiation (FST) landscapes have emerged across the group. Variation in these landscapes was strongly predicted by the local density of functional elements and the recombination rate, suggesting that the landscapes have been shaped by widespread natural selection. Using the varying divergence times between pairs of taxa, we show that the correlations between FST and genome features arose almost immediately after a population split and have become stronger over time. Simulations of genomic landscape evolution suggest that background selection (BGS; i.e., selection against deleterious mutations) alone is too subtle to generate the observed patterns, but scenarios that involve positive selection and genetic incompatibilities are plausible alternative explanations. Finally, tests for introgression among these taxa reveal widespread evidence of heterogeneous selection against gene flow during this radiation. Combined with previous evidence for adaptation in this system, we conclude that the correlation in FST among these taxa informs us about the processes contributing to adaptation and speciation during a rapid radiation.
Time-dependent spatially varying graphical models, with application to brain fMRI data analysis

In this work, we present an additive model for space-time data that splits the data into a temporally correlated component and a spatially correlated component. We model the spatially correlated portion using a time-varying Gaussian graphical model. Under assumptions on the smoothness of changes in covariance matrices, we derive strong single sample convergence results, confirming our ability to estimate meaningful graphical structures as they evolve over time. We apply our methodology to the discovery of time-varying spatial structures in human brain fMRI signals.
Activity and circadian rhythm of sepsis patients in the Intensive Care Unit

Early mobilization of critically ill patients in the Intensive Care Unit (ICU) can prevent adverse outcomes such as delirium and post-discharge physical impairment. To date, no studies have characterized activity of sepsis patients in the ICU using granular actigraphy data. This study characterizes the activity of sepsis patients in the ICU to aid in future mobility interventions. We have compared the actigraphy features of 24 patients in four groups: Chronic Critical Illness (CCI) sepsis patients in the ICU, Rapid Recovery (RR) sepsis patients in the ICU, non-sepsis ICU patients (control-ICU), and healthy subjects. We used a total of 15 statistical and circadian rhythm features extracted from the patients' actigraphy data collected over a five-day period. Our results show that the four groups are significantly different in terms of activity features. In addition, we observed that the CCI and control-ICU patients show less regularity in their circadian rhythm compared to the RR patients. These results show the potential of using actigraphy data for guiding mobilization practices, classifying sepsis recovery subtype, as well as for tracking patients' recovery.
Identifying the Social Signals That Drive Online Discussions: A Case Study of Reddit Communities

Increasingly people form opinions based on information they consume on online social media. As a result, it is crucial to understand what type of content attracts people's attention on social media and drive discussions. In this paper we focus on online discussions. Can we predict which comments and what content gets the highest attention in an online discussion? How does this content differ from community to community? To accomplish this, we undertake a unique study of Reddit involving a large sample comments from 11 popular subreddits with different properties. We introduce a large number of sentiment, relevance, content analysis features including some novel features customized to reddit. Through a comparative analysis of the chosen subreddits, we show that our models are correctly able to retrieve top replies under a post with great precision. In addition, we explain our findings with a detailed analysis of what distinguishes high scoring posts in different communities that differ along the dimensions of the specificity of topic and style, audience and level of moderation.
Automated Diagnosis of Clinic Workflows

Outpatient clinics often run behind schedule due to patients who arrive late or appointments that run longer than expected. We sought to develop a generalizable method that would allow healthcare providers to diagnose problems in workflow that disrupt the schedule on any given provider clinic day. We use a constraint optimization problem to identify the least number of appointment modifications that make the rest of the schedule run on-time. We apply this method to an outpatient clinic at Vanderbilt. For patient seen in this clinic between March 27, 2017 and April 21, 2017, long cycle times tended to affect the overall schedule more than late patients. Results from this workflow diagnosis method could be used to inform interventions to help clinics run smoothly, thus decreasing patient wait times and increasing provider utilization.
Concentration of Multilinear Functions of the Ising Model with Applications to Network Data

We prove near-tight concentration of measure for polynomial functions of the Ising model, under high temperature, improving the radius of concentration guaranteed by known results by polynomial factors in the dimension (i.e.~the number of nodes in the Ising model). We show that our results are optimal up to logarithmic factors in the dimension. We obtain our results by extending and strengthening the exchangeable-pairs approach used to prove concentration of measure in this setting by Chatterjee. We demonstrate the efficacy of such functions as statistics for testing the strength of interactions in social networks in both synthetic and real world data.
Intersection patterns of finite sets and of convex sets

The main result is a common generalization of results on lower bounds for the chromatic number of r-uniform hypergraphs and some of the major theorems in Tverberg-type theory, which is concerned with the intersection pattern of faces in a simplicial complex when continuously mapped to Euclidean space. As an application we get a simple proof of a generalization of a result of Kriz for certain parameters. This specializes to a short and simple proof of Kneser's conjecture. Moreover, combining this result with recent work of Mabillard and Wagner we show that the existence of certain equivariant maps yields lower bounds for chromatic numbers. We obtain an essentially elementary proof of the result of Schrijver on the chromatic number of stable Kneser graphs. In fact, we show that every neighborly even-dimensional polytope yields a small induced subgraph of the Kneser graph of the same chromatic number. We furthermore use this geometric viewpoint to give tight lower bounds for the chromatic number of certain small subhypergraphs of Kneser hypergraphs.
Direct-photon + hadron correlations to study parton energy loss with the STAR experiment

Abstract We report new results of γ d i r +hadron and π 0 +hadron azimuthal correlations as a measure of the away-side jet-like correlated yields in central Au+Au and p+p collisions at s N N = 200 GeV in the STAR experiment from years 2011 and 2009 of data taking, respectively. The charged-hadron per-trigger yields at mid-rapidity ( | η | 1 ) and for transverse momenta p T assoc > 1.2 GeV/ c associated with γ d i r and π 0 (for triggers | η | 0.9 , 12 p T t r i g 20 GeV/ c ) in central Au+Au collisions are compared with p+p collisions. The z T ( = p T a s s o c p T t r i g ) dependence, now extending down to z T = 0.1 , of the suppression of the away-side associated yields is presented. We observed that the suppression of away-side associated yields tends to vanish at lower z T . The dependence of the suppression on both p T a s s o c and p T t r i g is also discussed. Finally, these results are compared with various model predictions.
On Detection and Structural Reconstruction of Small-World Random Networks

In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model [29] which aims to describe real-world complex networks that exhibit both high clustering and short average length properties. The WS model with neighborhood size $k$ and rewiring probability probability $\beta$ can be viewed as a continuous interpolation between a deterministic ring lattice graph and the Erdős-Renyi random graph. We study the computational and statistical aspects of detection and recovery of the deterministic ring lattice structure (strong ties) in the presence of random connections (weak ties). The phase diagram in terms of $(k,\beta)$ is shown to consist of several regions according to the difficulty of the problem. We propose distinct methods for these regions.
Odd Khovanov homology is mutation invariant

We prove that odd Khovanov homology is mutation invariant over $\zz$, and therefore that Khovanov homology is mutation invariant over $\zzt$. We also establish mutation invariance for the entire Ozsv\'ath-Szab\'o spectral sequence from reduced Khovanov homology to the Heegaard Floer homology of the branched double-cover.
Attention-Based Natural Language Person Retrieval

Following the recent progress in image classification and captioning using deep learning, we develop a novel natural language person retrieval system based on an attention mechanism. More specifically, given the description of a person, the goal is to localize the person in an image. To this end, we first construct a benchmark dataset for natural language person retrieval. To do so, we generate bounding boxes for persons in a public image dataset from the segmentation masks, which are then annotated with descriptions and attributes using the Amazon Mechanical Turk. We then adopt a region proposal network in Faster R-CNN as a candidate region generator. The cropped images based on the region proposals as well as the whole images with attention weights are fed into Convolutional Neural Networks for visual feature extraction, while the natural language expression and attributes are input to Bidirectional Long Short- Term Memory (BLSTM) models for text feature extraction. The visual and text features are integrated to score region proposals, and the one with the highest score is retrieved as the output of our system. The experimental results show significant improvement over the state-of-the-art method for generic object retrieval and this line of research promises to benefit search in surveillance video footage.
Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift

Abstract We prove existence, uniqueness and optimal regularity of solutions to the stationary obstacle problem defined by the fractional Laplacian operator with drift, in the subcritical regime. As in [4] , we localize our problem by considering a suitable extension operator introduced in [2] . The structure of the extension equation is different from the one constructed in [4] , in that the obstacle function has less regularity, and exhibits some singularities. To take into account the new features of the problem, we prove a new monotonicity formula, which we then use to establish the optimal regularity of solutions.
Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations

We address finding the semi-global solutions to optimal feedback control and the Hamilton–Jacobi–Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum computational load. However, except for systems with two or three state variables, using traditional techniques for numerically finding a semi-global solution to an HJB equation for general nonlinear systems is infeasible due to the curse of dimensionality. Here we present a new computational method for finding feedback optimal control and solving HJB equations which is able to mitigate the curse of dimensionality. We do not discretize the HJB equation directly, instead we introduce a sparse grid in the state space and use the Pontryagin’s maximum principle to derive a set of necessary conditions in the form of a boundary value problem, also known as the characteristic equations, for each grid point. Using this approach, the method is spatially causality free, which enjoys the advantage of perfect parallelism on a sparse grid. Compared with dense grids, a sparse grid has a significantly reduced size which is feasible for systems with relatively high dimensions, such as the 6-D system shown in the examples. Once the solution obtained at each grid point, high-order accurate polynomial interpolation is used to approximate the feedback control at arbitrary points. We prove an upper bound for the approximation error and approximate it numerically. This sparse grid characteristics method is demonstrated with three examples of rigid body attitude control using momentum wheels.
Intermodal group-velocity engineering for broadband nonlinear optics

Interest in the nonlinear properties of multi-mode optical waveguides has seen a recent resurgence on account of the large dimensionality afforded by the platform. The large volume of modes in these waveguides provides a new spatial degree of freedom for phase matching nonlinear optical processes. However, this spatial dimension is quantized, which narrows the conversion bandwidths of intermodal processes and constrains spectral and temporal tailoring of the light. Here we show that by engineering the relative group velocity within the spatial dimension, we can tailor the phase-matching bandwidth of intermodal parametric nonlinearities. We demonstrate group-velocity-tailored parametric nonlinear mixing between higher-order modes in a multi-mode fiber with gain bandwidths that are more than an order of magnitude larger than that previously thought possible for intermodal four-wave mixing. As evidence of the technological utility of this methodology, we seed this process to generate the first high-peak-power wavelength-tunable all-fiber quasi-CW laser in the Ti:sapphire wavelength regime. More generally, with the combination of intermodal interactions, which dramatically expand the phase-matching degrees of freedom for nonlinear optics, and intermodal group-velocity engineering, which enables tailoring of the bandwidth of such interactions, we showcase a platform for nonlinear optics that can be broadband while being wavelength agnostic.
Curvature estimates for steady Ricci solitons

We show that for an $n$ dimensional complete non Ricci flat gradient steady Ricci soliton with potential function $f$ bounded above by a constant and curvature tensor $Rm$ satisfying $\overline{\lim}_{r\to \infty} r|Rm| 0$, improving a result of [36]. For any four dimensional complete non Ricci flat gradient steady Ricci soliton with scalar curvature $S\to 0$ as $r\to \infty$, we prove that $|Rm|\leq cS$ for some constant $c>0$, improving an estimate in [11]. As an application, we show that for a four dimensional complete non Ricci flat gradient steady Ricci soliton, $|Rm|$ decays exponentially provided that $\overline{\lim}_{r\to \infty} rS$ is sufficiently small and $f$ is bounded above by a constant.
A Theory of Selective Prediction.

We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to make the prediction as well as the length of the prediction window, possibly depending on the observations so far. We prove that, even without any distributional assumption on the input data stream, a large family of statistics can be estimated to non-trivial accuracy. To give one concrete example, suppose that we are given access to an arbitrary binary sequence $x_1, \ldots, x_n$ of length $n$. Our goal is to accurately predict the average observation, and we are allowed to choose the window over which the prediction is made: for some $t < n$ and $m \le n - t$, after seeing $t$ observations we predict the average of $x_{t+1}, \ldots, x_{t+m}$. This particular problem was first studied in Drucker (2013) and referred to as the "density prediction game". We show that the expected squared error of our prediction can be bounded by $O(\frac{1}{\log n})$ and prove a matching lower bound, which resolves an open question raised in Drucker (2013). This result holds for any sequence (that is not adaptive to when the prediction is made, or the predicted value), and the expectation of the error is with respect to the randomness of the prediction algorithm. Our results apply to more general statistics of a sequence of observations, and we highlight several open directions for future work.
Uncovering missed indels by leveraging unmapped reads

In current practice, Next Generation Sequencing (NGS) applications start with mapping/aligning short reads to the reference genome, with the aim of identifying genetic variants. Although existing alignment tools have shown great accuracy in mapping short reads to the reference genome, a significant number of short reads still remain unmapped and are often excluded from downstream analyses thereby causing nonnegligible information loss in the subsequent variant calling procedure. This paper describes Genesis-indel, a computational pipeline that explores the unmapped reads to identify novel indels that are initially missed in the original procedure. Genesis-indel is applied to the unmapped reads of 30 breast cancer patients from TCGA. Results show that the unmapped reads are conserved between the two subtypes of breast cancer investigated in this study and might contribute to the divergence between the subtypes. Genesis-indel identifies 72,997 novel high-quality indels previously not found, among which 16,141 have not been annotated in the widely used mutation database. Statistical analysis of these indels shows significant enrichment of indels residing in oncogenes and tumour suppressor genes. Functional annotation further reveals that these indels are strongly correlated with pathways of cancer and can have high to moderate impact on protein functions. Additionally, some of the indels overlap with the genes that do not have any indel mutations called from the originally mapped reads but have been shown to contribute to the tumorigenesis in multiple carcinomas, further emphasizing the importance of rescuing indels hidden in the unmapped reads in cancer and disease studies.
Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals

This paper develops a novel wild bootstrap procedure to construct robust bias-corrected valid confidence intervals for fuzzy regression discontinuity designs, providing an intuitive complement to existing robust bias-corrected methods. The confidence intervals generated by this procedure are valid under conditions similar to the procedures proposed by Calonico et al. (2014) and related literature. Simulations provide evidence that this new method is at least as accurate as the plug-in analytical corrections when applied to a variety of data-generating processes featuring endogeneity and clustering. Finally, we demonstrate its empirical relevance by revisiting Angrist and Lavy (1999) analysis of class size on student outcomes.