cssi/SciSciGPT-SciSciNet huggingface dataset:
Connecting discrete particle mechanics to continuum granular micromechanics: Anisotropic continuum properties under compaction

Abstract A systematic and mechanistic connection between granular materials’ macroscopic and grain level behaviors is developed for monodisperse systems of spherical elastic particles under die compaction. The Granular Micromechanics Approach (GMA) with static assumption is used to derive the stiffness tensor of transversely isotropic materials, from the average behavior of particle-particle interactions in all different directions at the microscale. Two particle-scale directional density distribution functions, namely the directional distribution of a combined mechano-geometrical property and the directional distribution of a purely geometrical property, are proposed and parametrized by five independent parameters. Five independent components of the symmetrized tangent stiffness tensor are also determined from discrete particle mechanics (PMA) calculations of nine perturbations around points of the loading path. Finally, optimal values for these five GMA parameters were obtained by minimizing the error between PMA calculations and GMA closed-form predictions of stiffness tensor during the compaction process. The results show that GMA with static assumption is effective at capturing the anisotropic evolution of microstructure during loading, even without describing contacts independently but rather accounting for them in an average sense.
Bockstein basis and resolution theorems in extension theory

Abstract We prove a generalization of the Edwards–Walsh Resolution Theorem: Theorem Let G be an abelian group with P G = P , where P G = { p ∈ P : Z ( p ) ∈ Bockstein basis σ ( G ) } . Let n ∈ N and let K be a connected CW-complex with π n ( K ) ≅ G , π k ( K ) ≅ 0 for 0 ⩽ k n . Then for every compact metrizable space X with XτK (i.e., with K an absolute extensor for X), there exists a compact metrizable space Z and a surjective map π : Z → X such that (a) π is cell-like, (b) dim Z ⩽ n , and (c) ZτK.
On the k-planar local crossing number

Abstract Given a fixed positive integer k , the k -planar local crossing number of a graph G , denoted by LCR k ( G ) , is the minimum positive integer L such that G can be decomposed into k subgraphs, each of which can be drawn in a plane such that no edge is crossed more than L times. In this note, we show that under certain natural restrictions, the ratio LCR k ( G ) ∕ LCR 1 ( G ) is of order 1 ∕ k 2 , which is analogous to the result of Pach et al. (2018) for the k -planar crossing number CR k ( G ) (defined as the minimum positive integer C for which there is a k -planar drawing of G with C total edge crossings). As a corollary of our proof we show that, under similar restrictions, one may obtain a k -planar drawing of G with both the total number of edge crossings as well as the maximum number of times any edge is crossed essentially matching the best known bounds. Our proof relies on the crossing number inequality and several probabilistic tools such as concentration of measure and the Lovasz local lemma.
Identifiability of Large Phylogenetic Mixture Models

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. Such models are of increasing interest for data analysis, as they can capture the variety of evolutionary processes that may be occurring across long sequences of DNA or proteins. The fundamental question of whether parameters of such a model are identifiable is difficult to address, due to the complexity of the parameterization. Identifiability is, however, essential to their use for statistical inference.
Batched Stochastic Bayesian Optimization via Combinatorial Constraints Design

In many high-throughput experimental design settings, such as those common in biochemical engineering, batched queries are often more cost effective than one-by-one sequential queries. Furthermore, it is often not possible to directly choose items to query. Instead, the experimenter specifies a set of constraints that generates a library of possible items, which are then selected stochastically. Motivated by these considerations, we investigate \emph{Batched Stochastic Bayesian Optimization} (BSBO), a novel Bayesian optimization scheme for choosing the constraints in order to guide exploration towards items with greater utility. We focus on \emph{site-saturation mutagenesis}, a prototypical setting of BSBO in biochemical engineering, and propose a natural objective function for this problem. Importantly, we show that our objective function can be efficiently decomposed as a difference of submodular functions (DS), which allows us to employ DS optimization tools to greedily identify sets of constraints that increase the likelihood of finding items with high utility. Our experimental results show that our algorithm outperforms common heuristics on both synthetic and two real protein datasets.
Phase Retrieval Meets Statistical Learning Theory: A Flexible Convex Relaxation

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP) in methods such as PhaseLift and compete with recently developed non-convex techniques for phase retrieval. We relax the quadratic equations for phaseless measurements to inequality constraints each of which representing a symmetric "slab". Through a simple convex program, our proposed estimator finds an extreme point of the intersection of these slabs that is best aligned with a given anchor vector. We characterize geometric conditions that certify success of the proposed estimator. Furthermore, using classic results in statistical learning theory, we show that for random measurements the geometric certificates hold with high probability at an optimal sample complexity. Phase transition of our estimator is evaluated through simulations. Our numerical experiments also suggest that the proposed method can solve phase retrieval problems with coded diffraction measurements as well.
Algorithm-hardware co-optimization of the memristor-based framework for solving SOCP and homogeneous QCQP problems

A memristor crossbar, which is constructed with memristor devices, has the unique ability to change and memorize the state of each of its memristor elements. It also has other highly desirable features such as high density, low power operation and excellent scalability. Hence the memristor crossbar technology can potentially be utilized for developing low-complexity and high-scalability solution frameworks for solving a large class of convex optimization problems, which involve extensive matrix operations and have critical applications in multiple disciplines. This paper, as the first attempt towards this direction, proposes a novel memristor crossbar-based framework for solving two important convex optimization problems, i.e., second-order cone programming (SOCP) and homogeneous quadratically constrained quadratic programming (QCQP) problems. In this paper, the alternating direction method of multipliers (ADMM) is adopted. It splits the SOCP and homogeneous QCQP problems into sub-problems that involve the solution of linear systems, which could be effectively solved using the memristor crossbar in O(1) time complexity. The proposed algorithm is an iterative procedure that iterates a constant number of times. Therefore, algorithms to solve SOCP and homogeneous QCQP problems have pseudo-O(N) complexity, which is a significant reduction compared to the state-of-the-art software solvers (O(N3.5)-O(N4)).
Features for Multi-target Multi-camera Tracking and Re-identification

Multi-Target Multi-Camera Tracking (MTMCT) tracks many people through video taken from several cameras. Person Re-Identification (Re-ID) retrieves from a gallery images of people similar to a person query image. We learn good features for both MTMCT and Re-ID with a convolutional neural network. Our contributions include an adaptive weighted triplet loss for training and a new technique for hard-identity mining. Our method outperforms the state of the art both on the DukeMTMC benchmarks for tracking, and on the Market-1501 and DukeMTMC-ReID benchmarks for Re-ID. We examine the correlation between good Re-ID and good MTMCT scores, and perform ablation studies to elucidate the contributions of the main components of our system. Code is available1.
Homologically thin, non-quasi-alternating links

We exhibit the first examples of links which are homologically thin but not quasi-alternating. To show that they are not quasi-alternating, we argue that none of their branched double-covers bounds a negative definite 4-manifold with non-torsion $H_1$. Using this method, we also complete the determination of the quasi-alternating pretzel links.
PART-PRODUCTS OF S-RESTRICTED INTEGER COMPOSITIONS

If S is a cofinite set of positive integers, an "S-restricted composition of n" is a sequence of elements of S, denoted →λ = (λ1, λ2, ... ), whose sum is n. For uniform random S-restricted compositions, the random variable B(→λ) = πi λi is asymptotically lognormal. (A precise statement of the theorem includes an error term to bound the rate of convergence.) The proof is based upon a combinatorial technique for decomposing a composition into a sequence of smaller compositions.
Higgs inflation, seesaw physics and fermion dark matter

Abstract We present an inflationary model in which the Standard Model Higgs doublet field with non-minimal coupling to gravity drives inflation, and the effective Higgs potential is stabilized by new physics which includes a dark matter particle and right-handed neutrinos for the seesaw mechanism. All of the new particles are fermions, so that the Higgs doublet is the unique inflaton candidate. With central values for the masses of the top quark and the Higgs boson, the renormalization group improved Higgs potential is employed to yield the scalar spectral index n s ≃ 0.968 , the tensor-to-scalar ratio r ≃ 0.003 , and the running of the spectral index α = d n s / d ln ⁡ k ≃ − 5.2 × 10 − 4 for the number of e-folds N 0 = 60 ( n s ≃ 0.962 , r ≃ 0.004 , and α ≃ − 7.5 × 10 − 4 for N 0 = 50 ). The fairly low value of r ≃ 0.003 predicted in this class of models means that the ongoing space and land based experiments are not expected to observe gravity waves generated during inflation.
Condition (K) for inverse semigroups and the ideal structure of their $C^*$-algebras

Abstract Inspired by results for graph C ⁎ -algebras, we investigate connections between the ideal structure of an inverse semigroup S and that of its tight C ⁎ -algebra by relating ideals in S to certain open invariant sets in the associated tight groupoid. We also develop analogues of Conditions (L) and (K) for inverse semigroups, which are related to certain congruences on S. We finish with applications to the inverse semigroups of self-similar graph actions and some relevant comments on the authors' earlier uniqueness theorems for inverse semigroups.
FINITE TRIGONOMETRIC CHARACTER SUMS VIA DISCRETE FOURIER ANALYSIS

We prove several old and new theorems about finite sums involving characters and trigonometric functions. These sums can be traced back to theta function identities from Ramanujan's notebooks and were first systematically studied by Berndt and Zaharescu where their proofs involved complex contour integration. We show how to prove most of Berndt–Zaharescu's and some new identities by elementary methods of discrete Fourier analysis.
Weak equivalence to Bernoulli shifts for some algebraic actions

Namely, we prove that if $G$ is a countable, discrete group and $f\in M_{n}(\Z(G))$ is invertible on $\ell^{2}(G)^{\oplus n},$ but $f$ is not invertible in $M_{n}(\Z(G))$, then the measure-preserving action of $G$ on $X_{f}$ equipped with the Haar measure is weakly equivalent to a Bernoulli action. We shall in fact prove this weak equivalence in the case that $f$ has a "formal inverse in $\ell^{2}$".
Towards a Holistic Integration of Spreadsheets with Databases: A Scalable Storage Engine for Presentational Data Management

Spreadsheet software is the tool of choice for interactive ad-hoc data management, with adoption by billions of users. However, spreadsheets are not scalable, unlike database systems. On the other hand, database systems, while highly scalable, do not support interactivity as a first-class primitive. We are developing DataSpread, to holistically integrate spreadsheets as a front-end interface with databases as a back-end datastore, providing scalability to spreadsheets, and interactivity to databases, an integration we term presentational data management (PDM). In this paper, we make the first step towards this vision for relational databases: developing a storage engine for PDM, studying how to flexibly represent spreadsheet data within a relational database and how to support and maintain access by position. We first conduct an extensive survey of spreadsheet use to motivate our functional requirements for a storage engine for PDM. We develop a natural set of mechanisms for flexibly representing spreadsheet data and demonstrate that identifying the optimal representation is NP-Hard; however, we develop an efficient approach to identify the optimal representation from an important and intuitive subclass of representations. We extend our mechanisms with positional access mechanisms that don't suffer from cascading update issues, leading to constant time access and modification performance. We evaluate these representations on a workload of typical spreadsheets and spreadsheet operations, providing up to 50% reduction in storage, and up to 50% reduction in formula evaluation time.
The avalanche principle and negative curvature

We use the geometric structure of the hyperbolic upper half plane to provide a new proof of the Avalanche Principle introduced by M. Goldstein and W. Schlag in the context of $$\mathrm {SL}_{2}({\mathbb {R}})$$ matrices. This approach allows to interpret and extend this result to arbitrary $$\text {CAT}(-1)$$ metric spaces. Through the proof, we deduce a polygonal Schur theorem for these spaces.
Selection of input primitives for the generalized label correcting method

The generalized label correcting method is an efficient search-based approach to trajectory optimization. It relies on a finite set of piecewise constant control primitives that are concatenated into candidate control signals. This paper investigates the principled selection of this set of control primitives. Emphasis is placed on a particularly challenging input space geometry, the n-dimensional sphere. We propose using controls which minimize a generalized energy function and discuss the optimization technique used to obtain these control primitives. A numerical experiment is presented showing a factor of two improvement in running time when using the optimized control primitives over a random sampling strategy.
End-to-end ASR-free keyword search from speech

End-to-end (E2E) systems have achieved competitive results compared to conventional hybrid hidden Markov model (HMM)-deep neural network based automatic speech recognition (ASR) systems. Such E2E systems are attractive due to the lack of dependence on alignments between input acoustic and output grapheme or HMM state sequence during training. This paper explores the design of an ASR-free end-to-end system for text query-based keyword search (KWS) from speech trained with minimal supervision. Our E2E KWS system consists of three sub-systems. The first sub-system is a recurrent neural network (RNN)-based acoustic auto-encoder trained to reconstruct the audio through a finite-dimensional representation. The second sub-system is a character-level RNN language model using embeddings learned from a convolutional neural network. Since the acoustic and text query embeddings occupy different representation spaces, they are input to a third feed-forward neural network that predicts whether the query occurs in the acoustic utterance or not. This E2E ASR-free KWS system performs respectably despite lacking a conventional ASR system and trains much faster.
Some methods for heterogeneous treatment effect estimation in high dimensions

When devising a course of treatment for a patient, doctors often have little quantitative evidence on which to base their decisions, beyond their medical education and published clinical trials. Stanford Health Care alone has millions of electronic medical records that are only just recently being leveraged to inform better treatment recommendations. These data present a unique challenge because they are high dimensional and observational. Our goal is to make personalized treatment recommendations based on the outcomes for past patients similar to a new patient. We propose and analyze 3 methods for estimating heterogeneous treatment effects using observational data. Our methods perform well in simulations using a wide variety of treatment effect functions, and we present results of applying the 2 most promising methods to data from The SPRINT Data Analysis Challenge, from a large randomized trial of a treatment for high blood pressure.
Adversarial Machine Learning at Scale

Adversarial examples are malicious inputs designed to fool machine learning models. They often transfer from one model to another, allowing attackers to mount black box attacks without knowledge of the target model's parameters. Adversarial training is the process of explicitly training a model on adversarial examples, in order to make it more robust to attack or to reduce its test error on clean inputs. So far, adversarial training has primarily been applied to small problems. In this research, we apply adversarial training to ImageNet. Our contributions include: (1) recommendations for how to succesfully scale adversarial training to large models and datasets, (2) the observation that adversarial training confers robustness to single-step attack methods, (3) the finding that multi-step attack methods are somewhat less transferable than single-step attack methods, so single-step attacks are the best for mounting black-box attacks, and (4) resolution of a "label leaking" effect that causes adversarially trained models to perform better on adversarial examples than on clean examples, because the adversarial example construction process uses the true label and the model can learn to exploit regularities in the construction process.
Jet Correlations from PHENIX: Low-pT to High-pT

PHENIX has measured many different two-particle azimuthal correlations in several different colliding systems, beam energies, $p_{T}$ windows, etc. The initial striking results from the first full energy Au+Au run have been confirmed, i.e. the observation of away-side suppression at intermediate $p_{T}$ and the shape modification at low $p_{T}$. With the new high-statistics data these results have been extended to further explore the physics resulting in these modified correlations. In this contribution we present a wide variety of correlation results at high-$p_{T}$ ($>$ 5 GeV/c) and at low $p_{T}$ ($\sim$ 1-4 GeV/c). We discuss the implication of these data on energy loss models and on the possibilities of determining medium properties from these correlations.
Exact solution of plane Poiseuille flow in a channel filled with a porous medium

In this paper I have presented an analytical solution to the problem of plane Poiseuille flow in a channel filled with a porous medium Nield et al have expressed it in terms of elliptic integrals I express it in an equivalent but a more conventional form in terms of Weierstrass elliptic function I also present the R code to plot the velocity profile and compute the flux
An LMI Based Stability Margin Analysis for Active PV Power Control of Distribution Networks with Time-Invariant Delays

High penetration of photovoltaic (PV) generators can lead to voltage issues in distribution networks. Various approaches including the real power control through PV inverters have been proposed to address voltage issues. However, among different control strategies, communication delays are inevitably involved and they need to be carefully considered in the control loop. Those delays can significantly deteriorate the system performance with undesired voltage quality, and may also cause system instability. In this paper, according to the inverter based active power control strategy, a linearized state space model with communication delay is presented. A delay dependent stability criterion using linear matrix inequality (LMI) approach is used to rigorously obtain the delay margins based on different system parameters. The method can handle multiple PVs in the distribution network as well.
A New Lower Bound on Guard Placement for Wireless Localization

The problem of wireless localization introduced in [EGS07] asks to place a set of fixed localizers (guards) in the plane so as to enable mobile communication devices to prove that they are inside or outside a secure region, defined by the interior of a polygon P . The guards are equipped with directional transmitters that can broadcast a key within a fixed angular range. The polygon P is virtual in the sense that it does not block broadcasts. A mobile device (henceforth, a point in the plane) determines whether it is inside or outside P from a monotone Boolean formula composed from the broadcasts using AND(·) and OR(+) operations only. The restriction to monotone formulas is particularly relevant to localization, which is more reliable when relying on the presence instead of the absence of broadcast keys. The primary goal is to minimize the number of guards. Solutions for convex and orthogonal polygons were established [EGS07], but for general polygons, a considerable gap between a lower bound of dn/2e and an upper bound of n − 2 guards remains to be closed. See also [O’R07]. This work is related to a number of interesting problems on art galleries and floodlights mentioned in [EGS07]. In this paper we establish a lower bound of b2n/3c−1 guards for polygons in general position, for the case in which the placement of guards is restricted to polygon vertices (vertex guards). A vertex guard that broadcasts over the full internal or external angle at that vertex is called natural. Natural guards alone do not suffice to localize a region [EGS07], so non-natural guards must be employed as well. In [EGS07], the authors use vertex guards only, and leave open the question of whether general guards (i.e, guards placed at arbitrary points) are more efficient. We answer their question positively by establishing a solution with n/2 general guards for a polygon that requires no fewer than 2n/3 − 1 vertex guards for localization.
A symmetry breaking transition in the edge/triangle network model

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp transition between two phases with different symmetries, analogous to the transition between a fluid and a crystalline solid.
WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS

For a group G , a weak Cayley table isomorphism is a bijection f : G → G such that f ( g 1 g 2 ) is conjugate to f ( g 1 ) f ( g 2 ) for all g 1 , g 2 ∈ G . The set of all weak Cayley table isomorphisms forms a group ( G ) that is the group of symmetries of the weak Cayley table of G . We determine ( G ) for each of the 17 wallpaper groups G , and for some other crystallographic groups.
Examples of Descent up to Nilpotence

We give a survey of the ideas of descent and nilpotence, beginning with the theory of thick subcategories. We focus on examples arising from chromatic homotopy theory (such as Rognes’ Galois extensions) and from group actions, as well as a few examples in algebra. These ideas provide tools for studying certain invariants of tensor-triangulated categories.
Iterative Amortized Inference.

Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a learned model, inference is amortized over data examples and therefore more computationally efficient. However, standard inference models are restricted to direct mappings from data to approximate posterior estimates. The failure of these models to reach fully optimized approximate posterior estimates results in an amortization gap. We aim toward closing this gap by proposing iterative inference models, which learn to perform inference optimization through repeatedly encoding gradients. Our approach generalizes standard inference models in VAEs and provides insight into several empirical findings, including top-down inference techniques. We demonstrate the inference optimization capabilities of iterative inference models and show that they outperform standard inference models on several benchmark data sets of images and text.
Online matrix completion and online robust PCA

“To be considered for an 2015 IEEE Jack Keil Wolf ISIT Student Paper Award.” This work studies two interrelated problems - online robust PCA (RPCA) and online matrix completion (MC). Both problems assume that an accurate estimate of the low-dimensional subspace from which the first true data vector is generated is available. We develop a practical modification of a recently proposed algorithm to solve both problems; and we obtain correctness results for the proposed algorithms under mild assumptions.
Deep Object-Centric Representations for Generalizable Robot Learning

Robotic manipulation in complex open-world scenarios requires both reliable physical manipulation skills and effective and generalizable perception. In this paper, we propose using an object-centric prior and a semantic feature space for the perception system of a learned policy. We devise an object-level attentional mechanism that can be used to determine relevant objects from a few trajectories or demonstrations, and then immediately incorporate those objects into a learned policy. A task-independent attention locates possible objects in the scene, and a task-specific attention identifies which objects are predictive of the trajectories. The scope of the task-specific attention is easily adjusted by showing demonstrations with distractor objects or with diverse relevant objects. Our results indicate that this approach exhibits good generalization across object instances using very few samples, and can be used to learn a variety of manipulation tasks using reinforcement learning.
An Application of ASP Theories of Intentions to Understanding Restaurant Scenarios: Insights and Narrative Corpus

This paper presents a practical application of Answer Set Programming to the understanding of narratives about restaurants. While this task was investigated in depth by Erik Mueller, exceptional scenarios remained a serious challenge for his script-based story comprehension system. We present a methodology that remedies this issue by modeling characters in a restaurant episode as intentional agents. We focus especially on the refinement of certain components of this methodology in order to increase coverage and performance. We present a restaurant story corpus that we created to design and evaluate our methodology.
On differential polynomial rings over locally nilpotent rings

Let δ be a derivation of a locally nilpotent ring R. Then the differential polynomial ring R[X; δ] cannot be mapped onto a ring with a non-zero idempotent. This answers a recent question by Greenfeld, Smoktunowicz and Ziembowski.
Lattice stability for atomistic chains modeled by local approximations of the embedded atom method

Abstract The nucleation and motion of lattice defects such as dislocations and cracks can occur when the configuration loses stability at a critical strain. Thus, the accurate approximation of critical strains for lattice instability is a key criterion for predictive computational modeling of material deformation. Coarse-grained continuum approximations of atomistic models are needed to compute the long-range elastic interaction of defects with surfaces. In this paper, we present a comparison of the lattice stability for atomistic chains modeled by the embedded atom method (EAM) with their approximation by local Cauchy-Born models. The volume-based Cauchy-Born strain-energy density is given by the energy-density for a homogeneously strained lattice and is the typical strain energy density used by continuum models to coarse-grain the atomistic energy of a lattice [13] . The reconstruction-based Cauchy-Born model uses linear (and bilinear) extrapolation of local atoms (usually nearest-neighbor atoms in the reference lattice) to approximate the positions of nonlocal atoms and thus approximates a nonlocal atomistic site energy by a local atomistic site energy [18] , [5] . The reconstruction-based Cauchy-Born site energy has been proposed to accurately transition between an atomistic model used in the neighborhood of a defect and the coarse-grained volume-based local model. We find that both the volume-based local model and the reconstruction-based local model can give O (1) errors for the critical strain when the embedding energy density is nonlinear. In the physical case of a strictly convex embedding energy density, the critical strain predicted by the volume-based model is always equal to or larger than that predicted by the atomistic model ( Theorem 5.1 ), but the critical strain for reconstruction-based models can be either larger, equal, or smaller than that predicted by the atomistic model ( Theorem 5.2 ). If we further restrict our model to nearest-neighbor interactions, then the critical strain for the atomistic and reconstruction-based Cauchy-Born models are equal ( Corollary 4.1 , Corollary 4.2 ), but the critical strain for the volume-based Cauchy-Born model is O (1) larger ( Theorem 4.3 ). We thus expect that reconstruction-based models are more accurate than volume-based models near lattice instabilities if nearest-neighbor interactions dominate, but we note that it is not known how to coarse-grain reconstruction-based models in three space dimensions.
Shape and Spatially-Varying Reflectance Estimation from Virtual Exemplars

This paper addresses the problem of estimating the shape of objects that exhibit spatially-varying reflectance. We assume that multiple images of the object are obtained under a fixed view-point and varying illumination, i.e., the setting of photometric stereo. At the core of our techniques is the assumption that the BRDF at each pixel lies in the non-negative span of a known BRDF dictionary. This assumption enables a per-pixel surface normal and BRDF estimation framework that is computationally tractable and requires no initialization in spite of the underlying problem being non-convex. Our estimation framework first solves for the surface normal at each pixel using a variant of example-based photometric stereo. We design an efficient multi-scale search strategy for estimating the surface normal and subsequently, refine this estimate using a gradient descent procedure. Given the surface normal estimate, we solve for the spatially-varying BRDF by constraining the BRDF at each pixel to be in the span of the BRDF dictionary; here, we use additional priors to further regularize the solution. A hallmark of our approach is that it does not require iterative optimization techniques nor the need for careful initialization, both of which are endemic to most state-of-the-art techniques. We showcase the performance of our technique on a wide range of simulated and real scenes where we outperform competing methods.
A non-Markovian model of rill erosion

We introduce a new model for rill erosion. We start with a network similar to that in the Discrete Web [7, 11] and instantiate a dynamics which makes the process highly non-Markovian. The behavior of nodes in the streams is similar to the behavior of Polya urns with time-dependent input. In this paper we use a combination of rigorous arguments and simulation results to show that the model exhibits many properties of rill erosion; in particular, nodes which are deeper in the network tend to switch less quickly.
Central moments-based cascaded lattice Boltzmann method for thermal convective flows in three-dimensions

Abstract Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal energy transport equation represented as a convection-diffusion equation (CDE) for the temperature field. In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. In this approach, the fluid motion is solved by another 3D cascaded LB model from prior work. Owing to the differences in the number of collision invariants to represent the dynamics of flow and the transport of the temperature field, the structure of the collision operator for the 3D cascaded LB formulation for the CDE is found to be markedly different from that for the NSE. The new 3D cascaded (LB) models for thermal convective flows are validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity enclosure at different Rayleigh numbers against prior numerical benchmark solutions. Results show good quantitative agreement of the profiles of the flow and thermal fields, and the magnitudes of the peak convection velocities as well as the heat transfer rates given in terms of the Nusselt number
Properties of knots preserved by cabling

We examine geometric properties of a knot J that are unchanged by taking a (p,q)-cable K of J. Specifically, we relate w(K) to w(J), where w(K) is the width of K in the sense of Gabai. We use this information to demonstrate that thin position is a minimal bridge position of J if and only if the same is true for K, and more generally we show that any thin position of K is an "obvious" cabling of a thin position of J. We conclude by proving that J is meridionally small (mp-small) if and only if K is meridionally small (mp-small), and if J is mp-small and every non-minimal bridge position of J is stabilized, then the same is true for K.
Are Slepian-Wolf rates necessary for distributed parameter estimation?

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Slepian-Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian-Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator (MVUE) that has the same performance as that of the optimal estimator in the centralized case while requiring information rates less than the conditions required in the Slepian-Wolf rate region.
Classical Kloosterman sums: Representation theory, magic squares, and Ramanujan multigraphs

Abstract We consider a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of “magical” combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.
Yamabe flow: Steady solitons and Type II singularities

Abstract We study the convergence of complete non-compact conformally flat solutions to the Yamabe flow to Yamabe steady solitons. We also prove the existence of Type II singularities which develop at either a finite time T or as t → + ∞ .
Slightly improved sum-product estimates in fields of prime order

Let $\mathbb{F}_p$ be the field of residue classes modulo a prime number $p$ and let $A$ be a nonempty subset of $\mathbb{F}_p$. In this paper we show that if $|A|\preceq p^{0.5}$, then \[ \max\{|A\pm A|,|AA|\}\succeq|A|^{13/12};\] if $|A|\succeq p^{0.5}$, then \[ \max\{|A\pm A|,|AA|\}\succapprox \min\{|A|^{13/12}(\frac{|A|}{p^{0.5}})^{1/12},|A|(\frac{p}{|A|})^{1/11}\}.\] These results slightly improve the estimates of Bourgain-Garaev and Shen. Sum-product estimates on different sets are also considered.
Critical Points of Strichartz Functional

We study a pair of infinite dimensional dynamical systems naturally associated with the study of minimizing/maximizing functions for the Strichartz inequalities for the Schrodinger equation. One sy...
Degeneracy of triality-symmetric morphisms

We define a new symmetry for morphisms of vector bundles, called triality symmetry, and compute Chern class formulas for the degeneracy loci of such morphisms. In an appendix, we show how to canonically associate an octonion algebra bundle to any rank 2 vector bundle.
A Polynomial Invariant and Duality for Triangulations

The Tutte polynomial ${T}_G(X,Y)$ of a graph $G$ is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs $G$, $T_G(X,Y) = {T}_{G^*}(Y,X)$ where $G^*$ denotes the dual graph. We examine this property from the perspective of manifold topology, formulating polynomial invariants for higher-dimensional simplicial complexes. Polynomial duality for triangulations of a sphere follows as a consequence of Alexander duality. The main goal of this paper is to introduce and begin the study of a more general $4$-variable polynomial for triangulations and handle decompositions of orientable manifolds. Polynomial duality in this case is a consequence of Poincare duality on manifolds. In dimension 2 these invariants specialize to the well-known polynomial invariants of ribbon graphs defined by B. Bollobas and O. Riordan. Examples and specific evaluations of the polynomials are discussed.
Robust Deep Reinforcement Learning with Adversarial Attacks

This paper proposes adversarial attacks for Reinforcement Learning (RL). These attacks are then leveraged during training to improve the robustness of RL within robust control framework. We show that this adversarial training of DRL algorithms like Deep Double Q learning and Deep Deterministic Policy Gradients leads to significant increase in robustness to parameter variations for RL benchmarks such as Mountain Car and Hopper environment. Full paper is available at (https://arxiv.org/abs/1712.03632)[32]
Finding Balance: Split Graphs and Related Classes

A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following interesting counting fact: unlabeled, unbalanced split graphs on $n$ vertices can be placed into a bijection with all unlabeled split graphs on $n-1$ or fewer vertices. In this paper we translate these concepts and the theorem to different combinatorial settings: minimal set covers, bipartite graphs with a distinguished block and posets of height one.
Linear extensions of orders invariant under abelian group actions

Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under $G$ extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder <= on the powerset PX invariant under G and such that if A is a proper subset of B, then A<B (i.e., A<=B but not B<=A).
The reflection distance between zigzag persistence modules

By invoking the reflection functors introduced by Bernstein et al. (Russ Math Surv 28(2):17–32, 1973), in this paper we define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the $$\ell ^1$$ -bottleneck distance between their respective persistence diagrams.
Computational Modeling of the Photon Transport, Tissue Heating, and Cytochrome C Oxidase Absorption during Transcranial Near-Infrared Stimulation

Transcranial near-infrared stimulation (tNIRS) has been proposed as a tool to modulate cortical excitability. However, the underlying mechanisms are not clear where the heating effects on the brain tissue needs investigation due to increased near-infrared (NIR) absorption by water and fat. Moreover, the risk of localized heating of tissues (including the skin) during optical stimulation of the brain tissue is a concern. The challenge in estimating localized tissue heating is due to the light interaction with the tissues’ constituents, which is dependent on the combination ratio of the scattering and absorption properties of the constituent. Here, apart from tissue heating that can modulate the cortical excitability (“photothermal effects”); the other mechanism reported in the literature is the stimulation of the mitochondria in the cells which are active in the adenosine triphosphate (ATP) synthesis. In the mitochondrial respiratory chain, Complex IV, also known as the cytochrome c oxidase (CCO), is the unit four with three copper atoms. The absorption peaks of CCO are in the visible (420–450 nm and 600–700 nm) and the near-infrared (760–980 nm) spectral regions, which have been shown to be promising for low-level light therapy (LLLT), also known as “photobiomodulation”. While much higher CCO absorption peaks in the visible spectrum can be used for the photobiomodulation of the skin, 810 nm has been proposed for the non-invasive brain stimulation (using tNIRS) due to the optical window in the NIR spectral region. In this article, we applied a computational approach to delineate the “photothermal effects” from the “photobiomodulation”, i.e., to estimate the amount of light absorbed individually by each chromophore in the brain tissue (with constant scattering) and the related tissue heating. Photon migration simulations were performed for motor cortex tNIRS based on a prior work that used a 500 mW cm−2 light source placed on the scalp. We simulated photon migration at 630 nm and 700 nm (red spectral region) and 810 nm (near-infrared spectral region). We found a temperature increase in the scalp below 0.25 °C and a minimal temperature increase in the gray matter less than 0.04 °C at 810 nm. Similar heating was found for 630 nm and 700 nm used for LLLT, so photothermal effects are postulated to be unlikely in the brain tissue.
Two-magnon bound states in the Kitaev model in a [111] field

It is now well established that the Kitaev honeycomb model in a magnetic field along the [111] direction harbors an intermediate gapless quantum spin liquid (QSL) phase sandwiched between a gapped non-Abelian QSL at low fields $Hl{H}_{c1}$ and a partially polarized phase at high fields $Hg{H}_{c2}$. Here, we analyze the low-field and high-field phases and phase transitions in terms of single- and two-magnon excitations using exact diagonalization and density matrix renormalization group methods. We find that the energy to create a bound state of two-magnon ${\mathrm{\ensuremath{\Delta}}}_{p}$ becomes lower than the energy to create a single spin flip ${\mathrm{\ensuremath{\Delta}}}_{s}$ near ${H}_{c2}$. In the entire Kitaev spin liquid, ${\mathrm{\ensuremath{\Delta}}}_{p}l{\mathrm{\ensuremath{\Delta}}}_{s}$ and both gaps vanish at ${H}_{c2}$. We make testable predictions for magnon pairing that could be observable in Raman scattering measurements on Kitaev QSL candidate materials.
Leveraging Just a Few Keywords for Fine-Grained Aspect Detection Through Weakly Supervised Co-Training.

User-generated reviews can be decomposed into fine-grained segments (e.g., sentences, clauses), each evaluating a different aspect of the principal entity (e.g., price, quality, appearance). Automatically detecting these aspects can be useful for both users and downstream opinion mining applications. Current supervised approaches for learning aspect classifiers require many fine-grained aspect labels, which are labor-intensive to obtain. And, unfortunately, unsupervised topic models often fail to capture the aspects of interest. In this work, we consider weakly supervised approaches for training aspect classifiers that only require the user to provide a small set of seed words (i.e., weakly positive indicators) for the aspects of interest. First, we show that current weakly supervised approaches fail to leverage the predictive power of seed words for aspect detection. Next, we propose a student-teacher approach that effectively leverages seed words in a bag-of-words classifier (teacher); in turn, we use the teacher to train a second model (student) that is potentially more powerful (e.g., a neural network that uses pre-trained word embeddings). Finally, we show that iterative co-training can be used to cope with noisy seed words, leading to both improved teacher and student models. Our proposed approach consistently outperforms previous weakly supervised approaches (by 14.1 absolute F1 points on average) in six different domains of product reviews and six multilingual datasets of restaurant reviews.
Decentralization in Bitcoin and Ethereum Networks

Blockchain-based cryptocurrencies have demonstrated how to securely implement traditionally centralized systems, such as currencies, in a decentralized fashion. However, there have been few measurement studies on the level of decentralization they achieve in practice. We present a measurement study on various decentralization metrics of two of the leading cryptocurrencies with the largest market capitalization and user base, Bitcoin and Ethereum. We investigate the extent of decentralization by measuring the network resources of nodes and the interconnection among them, the protocol requirements affecting the operation of nodes, and the robustness of the two systems against attacks. In particular, we adapted existing internet measurement techniques and used the Falcon Relay Network as a novel measurement tool to obtain our data. We discovered that neither Bitcoin nor Ethereum has strictly better properties than the other. We also provide concrete suggestions for improving both systems.
Construction of Milnorian representations

We prove a partial converse to the main theorem of the author’s previous paper Proper affine actions: a sufficient criterion (submitted; available at arXiv:1612.08942). More precisely, let G be a semisimple real Lie group with a representation $$\rho $$ on a finite-dimensional real vector space V, that does not satisfy the criterion from the previous paper. Assuming that $$\rho $$ is irreducible and under some additional assumptions on G and $$\rho $$, we then prove that there does not exist a group of affine transformations acting properly discontinuously on V whose linear part is Zariski-dense in $$\rho (G)$$.