cssi/SciSciGPT-SciSciNet huggingface dataset:
A brief history of the multiverse

The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of low-energy laws of physics. Since these parts are extremely large, the interior of each of them behaves as if it were a separate universe, practically unaffected by the rest of the world. This picture, combined with the theory of eternal inflation and anthropic considerations, may help to solve many difficult problems of modern physics, including the cosmological constant problem. In this article I will briefly describe this theory and provide links to the some hard to find papers written during the first few years of the development of the inflationary multiverse scenario.
Marketing impact on diffusion in social networks

The article proposes a way to add marketing into the standard threshold model of social networks. Within this framework, the article studies logical properties of the influence relation between sets of agents in social networks. Two different forms of this relation are considered: one for promotional marketing and the other for preventive marketing. In each case a sound and complete logical system describing properties of the influence relation is proposed. Both systems could be viewed as extensions of Armstrong's axioms of functional dependency from the database theory.
Online learning to rank with top-k feedback

We consider two settings of online learning to rank where feedback is restricted to top ranked items. The problem is cast as an online game between a learner and sequence of users, over T rounds. In both settings, the learners objective is to present ranked list of items to the users. The learner's performance is judged on the entire ranked list and true relevances of the items. However, the learner receives highly restricted feedback at end of each round, in form of relevances of only the top k ranked items, where k ≪ m. The first setting is non-contextual, where the list of items to be ranked is fixed. The second setting is contextual, where lists of items vary, in form of traditional query-document lists. No stochastic assumption is made on the generation process of relevances of items and contexts. We provide efficient ranking strategies for both the settings. The strategies achieve O(T2/3) regret, where regret is based on popular ranking measures in first setting and ranking surrogates in second setting. We also provide impossibility results for certain ranking measures and a certain class of surrogates, when feedback is restricted to the top ranked item, i.e. k = 1. We empirically demonstrate the performance of our algorithms on simulated and real world data sets.
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H2 and liquid Al–Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.
O(2) Hopf bifurcation of viscous shock waves in a channel

Abstract Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O ( 2 ) transverse Hopf bifurcation, or “cellular instability”, of viscous shock waves in a channel, for a class of quasilinear hyperbolic–parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Frechet differentiability of the time- T solution operator by appropriate hyperbolic–parabolic energy estimates, and (ii) handle O ( 2 ) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic–parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov–Schmidt reduction of the time- T map, yielding a four-dimensional problem with O ( 2 ) plus approximate S 1 symmetry, which we treat “by hand” using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.
On Conjectures of Andrews and Curtis

It is shown that the original Andrews--Curtis conjecture on balanced presentations of the trivial group is equivalent to its "cyclic" version in which, in place of arbitrary conjugations, one can use only cyclic permutations. This, in particular, proves a satellite conjecture of Andrews and Curtis made in 1966. We also consider a more restrictive "cancellative" version of the cyclic Andrews--Curtis conjecture with and without stabilizations and show that the restriction does not change the Andrews--Curtis conjecture when stabilizations are allowed. On the other hand, the restriction makes the conjecture false when stabilizations are not allowed.
Separate source-channel coding for broadcasting correlated Gaussians

The problem of broadcasting a pair of correlated Gaussian sources using optimal separate source and channel codes is studied. Considerable performance gains over previously known separate source-channel schemes are observed. Although source-channel separation yields suboptimal performance in general, it is shown that the proposed scheme is very competitive for any bandwidth compression/expansion scenarios. In particular, for a high channel SNR scenario, it can be shown to achieve optimal power-distortion tradeoff.
Pseudo-Dirac structures

Abstract A Dirac structure is a Lagrangian subbundle of a Courant algebroid, L ⊂ E , which is involutive with respect to the Courant bracket. In particular, L inherits the structure of a Lie algebroid. In this paper, we introduce the more general notion of a pseudo-Dirac structure: an arbitrary subbundle, W ⊂ E , together with a pseudo-connection on its sections, satisfying a natural integrability condition. As a consequence of the definition, W will be a Lie algebroid. Allowing non-isotropic subbundles of E incorporates non-skew tensors and connections into Dirac geometry. Novel examples of pseudo-Dirac structures arise in the context of quasi-Poisson geometry, Lie theory, generalized Kahler geometry, and Dirac Lie groups, among others. Despite their greater generality, we show that pseudo-Dirac structures share many of the key features of Dirac structures. In particular, they behave well under composition with Courant relations.
A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN–PCA method is inspired by recent developments in computer vision using deep learning. CNN–PCA can be viewed as a generalization of an existing optimization-based PCA (O-PCA) method. Both CNN–PCA and O-PCA entail post-processing a PCA model to better honor complex geological features. In CNN–PCA, rather than use a histogram-based regularization as in O-PCA, a new regularization involving a set of metrics for multipoint statistics is introduced. The metrics are based on summary statistics of the nonlinear filter responses of geological models to a pre-trained deep CNN. In addition, in the CNN–PCA formulation presented here, a convolutional neural network is trained as an explicit transform function that can post-process PCA models quickly. CNN–PCA is shown to provide both unconditional and conditional realizations that honor the geological features present in reference SGeMS geostatistical realizations for a binary channelized system. Flow statistics obtained through simulation of random CNN–PCA models closely match results for random SGeMS models for a demanding case in which O-PCA models lead to significant discrepancies. Results for history matching are also presented. In this assessment CNN–PCA is applied with derivative-free optimization, and a subspace randomized maximum likelihood method is used to provide multiple posterior models. Data assimilation and significant uncertainty reduction are achieved for existing wells, and physically reasonable predictions are also obtained for new wells. Finally, the CNN–PCA method is extended to a more complex nonstationary bimodal deltaic fan system, and is shown to provide high-quality realizations for this challenging example.
Partitions of equiangular tight frames

Abstract We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as a corollary yields a positive solution to the Kadison–Singer problem. In particular, we prove that certain diagonal partitions of complex ETFs generated by recursive skew-symmetric conference matrices yield a refinement of the MSS bound. Moreover, we prove that all partitions of ETFs whose largest subset has cardinality three or less also satisfy the MSS bound.
Reconciling Graphs and Sets of Sets

We explore a generalization of set reconciliation, where the goal is to reconcile sets of sets. Alice and Bob each have a parent set consisting of s child sets, each containing at most h elements from a universe of size u. They want to reconcile their sets of sets in a scenario where the total number of differences between all of their child sets (under the minimum difference matching between their child sets) is d. We give several algorithms for this problem, and discuss applications to reconciliation problems on graphs, databases, and collections of documents. We specifically focus on graph reconciliation, providing protocols based on sets of sets reconciliation for random graphs from G(n,p) and for forests of rooted trees.
An integral equation-based numerical solver for Taylor states in toroidal geometries

Abstract We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
Tango: A Deep Neural Network Benchmark Suite for Various Accelerators

Deep neural networks (DNNs) have been proving the effectiveness in various computing fields. To provide more efficient computing platforms for DNN applications, it is essential to have evaluation environments that include assorted benchmark workloads. Though a few DNN benchmark suites have been recently released, most of them require to install proprietary DNN libraries or resource-intensive DNN frameworks, which are hard to run on resource-limited mobile platforms or architecture simulators. To provide a more scalable evaluation environment, we propose a new DNN benchmark suite that can run on any platform that supports CUDA and OpenCL. The proposed benchmark suite includes the most widely used five convolution neural networks and two recurrent neural networks. We provide architectural statistics of these networks while running them on an architecture simulator, a server- and a mobile-GPU, and a mobile FPGA.
Anharmonicity of vibrational modes in fullerenes

Abstract We report a computational study of the anharmonicity of the vibrational modes of fullerenes using the “moments method” (Gao et al., 2015) with a Tersoff-style potential for carbon. We find that the frequencies of all vibrational modes drop systematically with temperature and that the size of the fullerene does not strongly determine the anharmonicity of its modes. Favorable comparison is made with experiments.
Large monochromatic components and long monochromatic cycles in random hypergraphs

Abstract We extend results of Gyarfas and Furedi on the largest monochromatic component in r -colored complete k -uniform hypergraphs to the setting of random hypergraphs. We also study long monochromatic loose cycles in r -colored random hypergraphs. In particular, we obtain a random analog of a result of Gyarfas, Sarkozy, and Szemeredi on the longest monochromatic loose cycle in 2-colored complete k -uniform hypergraphs.
Intermediate asymptotics for critical and supercritical aggregation equations and patlak-keller-segel models

We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose of this work is to identify when solutions decay to the self-similar spreading solutions of the homogeneous diffusion equations. Combined with strong decay estimates, entropy-entropy dissipation methods provide a natural solution to this question and make it possible to derive quantitative convergence rates in $L^1$. The estimated rate depends only on the nonlinearity of the diffusion and the strength of the interaction kernel at long range.
Quadratic harnesses from generalized beta integrals

We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.
Learning Probability Measures with respect to Optimal Transport Metrics

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal quantization, and learning theory, we derive new probabilistic bounds for the performance of a classic algorithm in unsupervised learning (k-means), when used to produce a probability measure derived from the data. In the course of the analysis, we arrive at new lower bounds, as well as probabilistic upper bounds on the convergence rate of empirical to population measures, which, unlike existing bounds, are applicable to a wide class of measures.
LP/SDP Hierarchy Lower Bounds for Decoding Random LDPC Codes

Random $(d_{v},d_{c})$ - regular low-density parity-check (LDPC) codes, where each variable is involved in $d_{v}$ parity checks and each parity check involves $d_{c}$ variables are well-known to achieve the Shannon capacity of the binary symmetric channel, for sufficiently large $d_{v}$ and $d_{c}$ , under exponential time decoding. However, polynomial time algorithms are only known to correct a much smaller fraction of errors. One of the most powerful polynomial-time algorithms with a formal analysis is the linear programming (LP) decoding algorithm of Feldman et al., which is known to correct an $\Omega (1/d_{c})$ fraction of errors. In this paper, we show that fairly powerful extensions of LP decoding, based on the Sherali–Adams and Lasserre hierarchies, fail to correct much more errors than the basic LP-decoder. In particular, we show that: 1) for any values of $d_{v}$ and $d_{c}$ , a linear number of rounds of the Sherali–Adams LP hierarchy cannot correct more than an $O(1/d_{c})$ fraction of errors on a random $(d_{v},d_{c})$ -regular LDPC code; and 2) for any value of $d_{v}$ and infinitely many values of $d_{c}$ , a linear number of rounds of the Lasserre SDP hierarchy cannot correct more than an $O(1/d_{c})$ fraction of errors on a random $(d_{v},d_{c})$ -regular LDPC code. Our proofs use a new stretching and collapsing technique that allows us to leverage recent progress in the study of the limitations of LP/SDP hierarchies for Maximum Constraint Satisfaction Problems (Max-CSPs). The problem then reduces to the construction of special balanced pairwise independent distributions for Sherali–Adams and special cosets of balanced pairwise independent subgroups for Lasserre. Our (algebraic) construction for the Lasserre hierarchy is based on designing sets of points in ${\mathbb F}_{q}^{d}$ (for $q$ any power of 2 and $d = 2,3$ ) with special hyperplane-incidence properties—constructions that may be of independent interest. An intriguing consequence of our work is that expansion seems to be both the strength and the weakness of random regular LDPC codes. Some of our techniques are more generally applicable to a large class of Boolean CSPs called Min-Ones. In particular, for $k$ -Hypergraph Vertex Cover, we obtain an improved integrality gap of $k-1-\epsilon $ that holds after a linear number of rounds of the Lasserre hierarchy, for any $k = q+1$ with $q$ an arbitrary prime power. The best previous gap for a linear number of rounds was equal to $2-\epsilon $ and due to Schoenebeck.
Comparing introductory physics and astronomy students’ attitudes and approaches to problem solving

We examined how introductory physics students' attitudes and approaches to problem solving compare to those of introductory astronomy students, using a previously validated survey, the Attitudes and Approaches to Problem Solving (AAPS) survey. In addition, we compared the performance of the introductory physics and astronomy students on the factors which were identified in a factor analysis in the original validation study. We found that introductory astronomy students' overall average AAPS score was significantly more favorable than that of introductory physics students (p < 0.01), and the effect size was large (Cohen's d = 0.81). We also found that introductory astronomy students' scores were more favorable in all clusters of questions except for one factor involving drawing diagrams and writing scratchwork while solving problems. We also found that introductory physics and astronomy students were equally capable of solving two isomorphic problems posed to them, and that the majority of introductory physics and introductory astronomy students reported that the problem posed in the astronomy context was more interesting to them. Interviews suggest that the context of astronomy in problem solving may be more interesting for students and could be one possible explanation for the more favorable AAPS scores amongst introductory astronomy students compared to introductory physics students. Instructors of introductory physics courses should heed these findings which indicate that it may be beneficial for instructors of introductory physics courses to incorporate problems into their instruction which contain real-world contexts, which may serve to increase student interest-level, and which could help create more favorable attitudes and approaches towards problem solving.
On Lagrangian algebras in group-theoretical braided fusion categories

We describe Lagrangian algebras in twisted Drinfeld centres for finite groups. Using the full centre construction, we establish a 1-1 correspondence between Lagrangian algebras and module categories over pointed fusion categories.
Symmetry protected topological Luttinger liquids and the phase transition between them

We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet d xy in the non-trivial phase and triplet S z = 0 in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.
Castor: Contextual IoT Time Series Data and Model Management at Scale

We demonstrate Castor, a cloud-based system for contextual IoT time series data and model management at scale. Castor is designed to assist Data Scientists in (a) exploring and retrieving all relevant time series and contextual information that is required for their predictive modelling tasks; (b) seamlessly storing and deploying their predictive models in a cloud production environment; (c) monitoring the performance of all predictive models in productions and (semi-)automatically retraining them in case of performance deterioration. The main features of Castor are: (1) an efficient pipeline for ingesting IoT time series data in real time; (2) a scalable, hybrid data management service for both time series and contextual data; (3) a versatile semantic model for contextual information which can be easily adopted to different application domains; (4) an abstract framework for developing and storing predictive models in R or Python; (5) deployment services which automatically train and/or score predictive models upon user-defined conditions. We demonstrate Castor for a real-world Smart Grid use case and discuss how it can be adopted to other application domains such as Smart Buildings, Telecommunication, Retail or Manufacturing.
A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions

We study Sigma-Delta ( $\Sigma \Delta $ ) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then down-sampling, a process known as decimation, can efficiently encode the associated $\Sigma \Delta $ bit-stream. It allows a large reduction in the bit-rate while still permitting good approximation of the underlying bandlimited function via an appropriate reconstruction kernel. Specifically, in the case of stable $r$ th order $\Sigma \Delta $ schemes we show that the reconstruction error decays exponentially in the bit-rate. For example, this result applies to the 1-bit, greedy, first-order $\Sigma \Delta $ scheme.
Complex Network Analysis in Cricket : Community structure, player's role and performance index

This paper describes the applications of network methods for understanding interaction within members of sport teams. We analyze the interaction of batsmen in international cricket matches. We generate batting partnership network (BPN) for different teams and determine the exact values of clustering coefficient, average degree, average shortest path length of the networks and compare them with the Erdos–Renyi model. We observe that the networks display small-world behavior. We find that most connected batsman is not necessarily the most central and most central players are not necessarily the one with high batting averages. We study the community structure of the BPNs and identify each player's role based on inter-community and intra-community links. We observe that Sir DG Bradman, regarded as the best batsman in cricket history does not occupy the central position in the network — the so-called connector hub. We extend our analysis to quantify the performance, relative importance and effect of removing a player from the team, based on different centrality scores.
Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections

Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to bivariate relationships. Linear project can be considered as a compromise between complexity and interpretability, as they allow explicit axes labels, yet provide significantly more degrees of freedom compared to axis-aligned projections. Nevertheless, interpreting the axes directions, which are linear combinations often with many non-trivial components, remains difficult. To address this problem we introduce a structure aware decomposition of (multiple) linear projections into sparse sets of axis aligned projections, which jointly capture all information of the original linear ones. In particular, we use tools from Dempster-Shafer theory to formally define how relevant a given axis aligned project is to explain the neighborhood relations displayed in some linear projection. Furthermore, we introduce a new approach to discover a diverse set of high quality linear projections and show that in practice the information of $k$ linear projections is often jointly encoded in $\sim k$ axis aligned plots. We have integrated these ideas into an interactive visualization system that allows users to jointly browse both linear projections and their axis aligned representatives. Using a number of case studies we show how the resulting plots lead to more intuitive visualizations and new insight.
Controlling Elections through Social Influence

Election control considers the problem of an adversary who attempts to tamper with a voting process, in order to either ensure that their favored candidate wins (constructive control) or another candidate loses (destructive control). As online social networks have become significant sources of information for potential voters, a new tool in an attacker's arsenal is to effect control by harnessing social influence, for example, by spreading fake news and other forms of misinformation through online social media. We consider the computational problem of election control via social influence, studying the conditions under which finding good adversarial strategies is computationally feasible. We consider two objectives for the adversary in both the constructive and destructive control settings: probability and margin of victory (POV and MOV, respectively). We present several strong negative results, showing, for example, that the problem of maximizing POV is inapproximable for any constant factor. On the other hand, we present approximation algorithms which provide somewhat weaker approximation guarantees, such as bicriteria approximations for the POV objective and constant-factor approximations for MOV. Finally, we present mixed integer programming formulations for these problems. Experimental results show that our approximation algorithms often find near-optimal control strategies, indicating that election control through social influence is a salient threat to election integrity.
Loading monotonicity of weighted premiums, and total positivity properties of weight functions

Abstract We consider the construction of insurance premiums that are monotonically increasing with respect to a loading parameter. By introducing weight functions that are totally positive of higher order, we derive higher monotonicity properties of generalized weighted premiums; in particular, we deduce for weight functions that are totally positive of order three a monotonicity property of the variance-to-mean ratio, or index of dispersion, of the loss variable. We derive the higher order total positivity properties of some ratios that arise in actuarial and insurance analysis of combined risks. Further, we examine seven classes of weight functions that have appeared in the literature and we ascertain the higher order total positivity properties of those functions.
A Reflectance Based Method For Shadow Detection and Removal

Shadows are common aspect of images and when left undetected can hinder scene understanding and visual processing. We propose a simple yet effective approach based on reflectance to detect shadows from single image. An image is first segmented and based on the reflectance, illumination and texture characteristics, segments pairs are identified as shadow and non-shadow pairs. The proposed method is tested on two publicly available and widely used datasets. Our method achieves higher accuracy in detecting shadows compared to previous reported methods despite requiring fewer parameters. We also show results of shadow-free images by relighting the pixels in the detected shadow regions.
ClusterGAN : Latent Space Clustering in Generative Adversarial Networks

Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection in GANs to cluster, we demonstrate that the cluster structure is not retained in the GAN latent space. In this paper, we propose ClusterGAN as a new mechanism for clustering using GANs. By sampling latent variables from a mixture of one-hot encoded variables and continuous latent variables, coupled with an inverse network (which projects the data to the latent space) trained jointly with a clustering specific loss, we are able to achieve clustering in the latent space. Our results show a remarkable phenomenon that GANs can preserve latent space interpolation across categories, even though the discriminator is never exposed to such vectors. We compare our results with various clustering baselines and demonstrate superior performance on both synthetic and real datasets.
Lipschitz–Volume rigidity in Alexandrov geometry

Abstract We prove a Lipschitz–Volume rigidity theorem in Alexandrov geometry, that is, if a 1-Lipschitz map f : X = ⨿ X l → Y between Alexandrov spaces preserves volume, then it is a path isometry and an isometry when restricted to the interior of X. We furthermore characterize the metric structure on Y with respect to X when f is also onto. This implies the converse of Petrunin's Gluing Theorem: if a gluing of two Alexandrov spaces via a bijection between their boundaries produces an Alexandrov space, then the bijection must be an isometry.
Geodesic excursions into an embedded disc on a hyperbolic Riemann surface

We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic 2-orbifold returns to an embedded disc on the surface, as well as the average amount of time it spends in the disc during each visit. This includes the case where the center of the disc is a cone point.
A central limit theorem for a new statistic on permutations

This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving central limit theorems more generally. It gives us an opportunity to acknowledge the work of our teacher and friend B. V. Rao.
Can recursive neural tensor networks learn logical reasoning

Recursive neural network models and their accompanying vector representations for words have seen success in an array of increasingly semantically sophisticated tasks, but almost nothing is known about their ability to accurately capture the aspects of linguistic meaning that are necessary for interpretation or reasoning. To evaluate this, I train a recursive model on a new corpus of constructed examples of logical reasoning in short sentences, like the inference of some animal walks from some dog walks or some cat walks, given that dogs and cats are animals. This model learns representations that generalize well to new types of reasoning pattern in all but a few cases, a result which is promising for the ability of learned representation models to capture logical reasoning.
Coordination and Control of Multiple Climbing Robots in Transport of Heavy Loads through Extreme Terrain.

The discovery of ice deposits in the permanently shadowed craters of the lunar North and South Pole Moon presents an important opportunity for In-Situ Resource Utilization. These ice deposits maybe the source for sustaining a lunar base or for enabling an interplanetary refueling station. These ice deposits also preserve a unique record of the geology and environment of their hosts, both in terms of impact history and the supply of volatile compounds, and so are of immense scientific interest. To date, these ice deposits have been studied indirectly and by remote active radar, but they need to be analyzed in-situ by robotic systems that can study the depths of the deposits, their purity and composition. However, these shadowed craters never see sunlight and are one of the coldest places in the solar system. NASA JPL proposed use of solar reflectors mounted on crater rims to project sunlight into the crater depths for use by ground robots. The solar reflectors would heat the crater base and vehicles positioned at the base sufficiently to survive the cold-temperatures. Our approach analyzes part of the logistics of the approach, with teams of robots climbing up and down to the crater to access the ice deposits. The mission will require robots to climb down extreme environments and carry large structures, including instruments and communication devices.
Rouquier complexes are functorial over braid cobordisms

Using the diagrammatic calculus for Soergel bimodules developed by B. Elias and M. Khovanov, we show that Rouquier complexes are functorial over braid cobordisms. We explicitly describe the chain maps which correspond to movie move generators.
Exploiting dual connectivity in heterogeneous cellular networks

We consider network utility maximization problems over heterogeneous cellular networks (HetNets) that permit dual connectivity. Dual connectivity (DC) is a feature that targets emerging practical HetNet deployments that will comprise of non-ideal (higher latency) connections between transmission nodes, and has been recently introduced to the LTE-Advanced standard. DC allows for a user to be simultaneously served by a macro node as well as one other (typically micro or pico) node and requires relatively coarser level coordination among serving nodes. For such a DC enabled HetNet we comprehensively analyze the problem of determining an optimal user association that maximizes the weighted sum rate system utility subject to per-user rate constraints, over all feasible associations. Here, in any feasible association each user can be associated with (i.e., configured to receive data from) any one macro node (in a given set of macro nodes) and any one pico node that lies in the chosen macro node's coverage area. We show that, remarkably, this problem can be cast as a non-monotone submodular set function maximization problem, which allows us to construct a constant-factor approximation algorithm. We then consider the proportional fairness (PF) system utility and characterize the PF optimal resource allocation. This enables us to construct an efficient algorithm to determine an association that is optimal up-to an additive constant. We then validate the performance of our algorithms via numerical results.
Dileptons and Photons at RHIC

Electromagnetic emission in the form of photons or dileptons provide important information on the onset and evolution of a heavy ion collision at ultrarelativistic energies. We briefly summarize the theoretical assessments of the thermalized electromagnetic emissivities from a hot partonic and hadronic medium, and compare them to current experiments at collider energies.
Adversarial Examples for Evaluating Reading Comprehension Systems

Standard accuracy metrics indicate that reading comprehension systems are making rapid progress, but the extent to which these systems truly understand language remains unclear. To reward systems with real language understanding abilities, we propose an adversarial evaluation scheme for the Stanford Question Answering Dataset (SQuAD). Our method tests whether systems can answer questions about paragraphs that contain adversarially inserted sentences, which are automatically generated to distract computer systems without changing the correct answer or misleading humans. In this adversarial setting, the accuracy of sixteen published models drops from an average of 75% F1 score to 36%; when the adversary is allowed to add ungrammatical sequences of words, average accuracy on four models decreases further to 7%. We hope our insights will motivate the development of new models that understand language more precisely.
Proof of a conjecture of Stanley–Zanello

Abstract We prove that the number of partitions of an integer into at most b distinct parts of size at most n forms a unimodal sequence for n sufficiently large with respect to b. This resolves a recent conjecture of Stanley and Zanello.
Phase transition in the sample complexity of likelihood-based phylogeny inference

Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which is perhaps the most widely used in phylogenetic practice because of its superior empirical accuracy. At the theoretical level, except for its consistency, that is, the guarantee of eventual correct reconstruction as the size of the input data grows, much remains to be understood about the statistical properties of maximum likelihood in this context. In particular, the best bounds on the sample complexity or sequence-length requirement of maximum likelihood, that is, the amount of data required for correct reconstruction, are exponential in the number, n, of tips—far from known lower bounds based on information-theoretic arguments. Here we close the gap by proving a new upper bound on the sequence-length requirement of maximum likelihood that matches up to constants the known lower bound for some standard models of evolution. More specifically, for the r-state symmetric model of sequence evolution on a binary phylogeny with bounded edge lengths, we show that the sequence-length requirement behaves logarithmically in n when the expected amount of mutation per edge is below what is known as the Kesten-Stigum threshold. In general, the sequence-length requirement is polynomial in n. Our results imply moreover that the maximum likelihood estimator can be computed efficiently on randomly generated data provided sequences are as above. Our main technical contribution, which may be of independent interest, relates the total variation distance between the leaf state distributions of two trees with a notion of combinatorial distance between the trees. In words we show in a precise quantitative manner that the more different two evolutionary trees are, the easier it is to distinguish their output.
Multivariate Bayesian structural time series model

This paper deals with inference and prediction for multiple correlated time series, where one also has the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for time series, we use Bayesian tools for model fitting, prediction and feature selection, thus extending some recent works along these lines for the univariate case. The Bayesian paradigm in this multivariate setting helps the model avoid overfitting, as well as captures correlations among multiple target time series with various state components. The model provides needed flexibility in selecting a different set of components and available predictors for each target series. The cyclical component in the model can handle large variations in the short term, which may be caused by external shocks. Extensive simulations were run to investigate properties such as estimation accuracy and performance in forecasting. This was followed by an empirical study with one-step-ahead prediction on the max log return of a portfolio of stocks that involve four leading financial institutions. Both the simulation studies and the extensive empirical study confirm that this multivariate model outperforms three other benchmark models, viz. a model that treats each target series as independent, the autoregressive integrated moving average model with regression (ARIMAX), and the multivariate ARIMAX (MARIMAX) model.
Sparse Beltrami Coefficients, Integral Means of Conformal Mappings and the Feynman-Kac Formula

In this note, we give an estimate for the dimension of the image of the unit circle under a quasiconformal mapping whose dilatation has small support. We also prove an analogous estimate for the rate of growth of a solution of a second-order parabolic equation given by the Feynman-Kac formula with a sparsely supported potential and introduce a dictionary between the two settings.
Multiaccess Communication via a Broadcast Approach Adapted to the Multiuser Channel

A broadcast strategy for multiple access communication over slowly fading channels is introduced, in which the channel state information is known to only the receiver. In this strategy, the transmitters split their information streams into multiple independent information streams, each adapted to a specific actual channel realization. The major distinction between the proposed strategy and the existing ones is that in the existing approaches, each transmitter adapts its transmission strategy only to the fading process of its direct channel to the receiver, hence, directly adopting a single-user strategy previously designed for the single-user channels. However, the contribution of each user to a network-wide measure (e.g., sum-rate capacity) depends not only on the user’s direct channel to the receiver, but also on the qualities of other channels. Driven by this premise, this paper proposes an alternative broadcast strategy in which the transmitters adapt their transmissions to the combined states resulting from all users’ channels. This leads to generating a larger number of information streams by each transmitter and adopting a different decoding strategy by the receiver. An achievable rate region and an outer bound that capture the tradeoff among the rates of different information layers are established, and it is shown that the achievable rate region subsumes the existing known capacity regions obtained based on adapting the broadcast approach to the single-user channels.
Polynomial-time approximation for nonconvex optimization problems with an L1-constraint

Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that nonconvex optimization problems with an L1-constraint can be approximately solved in polynomial time. We first show that nonlinear integer programs with an L1-constraint can be solved in a number of oracle steps that is polynomial in the dimension of the decision variable, for each fixed radius of the L1-constraint. When specialized to polynomial integer programs, our result shows that such problems have a time complexity that is polynomial in simultaneously both the dimension of the decision variables and number of constraints, for each fixed radius of the L1-constraint. We prove this result using a geometric argument that leverages ideas from stochastic process theory and from the theory of convex bodies in high-dimensional spaces. We conclude by providing an additive polynomial time approximation scheme (PTAS) for continuous optimization of Lipschitz functions subject to Lipschitz constraints intersected with an L1-constraint, and we sketch a generalization to mixed-integer optimization.
Solving Conic Systems via Projection and Rescaling

We propose a simple projection and rescaling algorithm to solve the feasibility problem $$\begin{aligned} \text { find } x \in L \cap \Omega , \end{aligned}$$ where L and \(\Omega \) are respectively a linear subspace and the interior of a symmetric cone in a finite-dimensional vector space V. This projection and rescaling algorithm is inspired by previous work on rescaled versions of the perceptron algorithm and by Chubanov’s projection-based method for linear feasibility problems. As in these predecessors, each main iteration of our algorithm contains two steps: a basic procedure and a rescaling step. When \(L \cap \Omega \ne \emptyset \), the projection and rescaling algorithm finds a point \(x \in L \cap \Omega \) in at most \(\mathcal {O}(\log (1/\delta (L \cap \Omega )))\) iterations, where \(\delta (L \cap \Omega ) \in (0,1]\) is a measure of the most interior point in \(L \cap \Omega \). The ideal value \(\delta (L\cap \Omega ) = 1\) is attained when \(L \cap \Omega \) contains the center of the symmetric cone \(\Omega \). We describe several possible implementations for the basic procedure including a perceptron scheme and a smooth perceptron scheme. The perceptron scheme requires \(\mathcal {O}(r^4)\) perceptron updates and the smooth perceptron scheme requires \(\mathcal {O}(r^2)\) smooth perceptron updates, where r stands for the Jordan algebra rank of V.
Resilient operation of transportation networks via variable speed limits

In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current particle densities. The density on each link has first order dynamics driven by the difference of its incoming and outgoing flows. A link irreversibly fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities do not necessarily help in preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. Our main result shows that systemic failures under feasible external inflows can always be averted through a proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it is much easier in practice to adjust the speed limits than to build more physical capacity or to alter routing decisions that are determined by social behavior.