cssi/SciSciGPT-SciSciNet huggingface dataset:
Phase retrieval from power spectra of masked signals

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein have found limited success. One alternative is to create redundancy in the measurement process by illuminating the signal multiple times, distorting the signal each time with a different mask. Despite several recent advances in phase retrieval, the community has yet to construct an ensemble of masks which uniquely determines all signals and admits an efficient reconstruction algorithm. In this paper, we leverage the recently proposed polarization method to construct such an ensemble. First, we construct four explicit masks which enable polarization recovery of any signal with non-vanishing Fourier transform, and then we construct Θ(logM ) random masks which, with high probability, simultaneously enable polarization recovery of any signal whatsoever. We also present numerical simulations to illustrate the stability of the polarization method in this setting. In comparison to a state-of-the-art phase retrieval algorithm known as PhaseLift, we find that polarization is much faster with comparable stability.
When is a fourfold Massey product defined

We define a new invariant in the homology of a differential graded algebra. This invariant is the obstruction to defining a fourfold Massey product.
Solving Visual Madlibs with Multiple Cues

This paper focuses on answering fill-in-the-blank style multiple choice questions from the Visual Madlibs dataset. Previous approaches to Visual Question Answering (VQA) have mainly used generic image features from networks trained on the ImageNet dataset, despite the wide scope of questions. In contrast, our approach employs features derived from networks trained for specialized tasks of scene classification, person activity prediction, and person and object attribute prediction. We also present a method for selecting sub-regions of an image that are relevant for evaluating the appropriateness of a putative answer. Visual features are computed both from the whole image and from local regions, while sentences are mapped to a common space using a simple normalized canonical correlation analysis (CCA) model. Our results show a significant improvement over the previous state of the art, and indicate that answering different question types benefits from examining a variety of image cues and carefully choosing informative image sub-regions.
Chebyshev approximation and higher order derivatives of Lyapunov functions for estimating the domain of attraction

Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor expansion is not always satisfactory. This paper provides solvable ways for estimating the DA via Chebyshev approximation. Firstly, for Chebyshev approximation without the remainder, higher order derivatives of Lyapunov functions are used for estimating the DA, and the largest estimate is obtained by solving a generalized eigenvalue problem. Moreover, for Chebyshev approximation with the remainder, an uncertain polynomial system is reformulated, and a condition is proposed for ensuring the convergence to the largest estimate with a selected Lyapunov function. Numerical examples demonstrate that both accuracy and efficiency are improved compared to Taylor approximation.
Optimal transient growth in thin-interface internal solitary waves

The dynamics of perturbations to large-amplitude internal solitary waves (ISWs) in two-layered flows with thin interfaces is analysed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct–adjoint iterations of the Navier–Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin–Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough ) of potentially unstable Richardson number, . They propagate through the base wave as coherent packets whose total energy gain increases rapidly with . The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local Wentzel–Kramers–Brillouin (WKB) approximation for spatially growing Kelvin–Helmholtz (K–H) waves through the zone. The WKB approach is able to capture properties (e.g. carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K–H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave. Two-dimensional numerical calculations of the nonlinear evolution of optimal disturbance packets leads to the generation of large-amplitude K–H billows that can emerge on the leading face of the wave and that break down into turbulence in the lee of the wave. The nonlinear calculations are used to derive a slowly varying model of ISW decay due to repeated encounters with optimal or free wave packets. Field observations of unstable ISW by Moum et al. (J. Phys. Oceanogr., vol. 33 (10), 2003, pp. 2093–2112) are consistent with excitation by optimal disturbances.
Exact duals and short certificates of infeasibility and weak infeasibility in conic linear programming

In conic linear programming—in contrast to linear programming—the Lagrange dual is not an exact dual: it may not attain its optimal value, or there may be a positive duality gap. The corresponding Farkas’ lemma is also not exact (it does not always prove infeasibility). We describe exact duals, and certificates of infeasibility and weak infeasibility for conic LPs which are nearly as simple as the Lagrange dual, but do not rely on any constraint qualification. Some of our exact duals generalize the SDP duals of Ramana, and Klep and Schweighofer to the context of general conic LPs. Some of our infeasibility certificates generalize the row echelon form of a linear system of equations: they consist of a small, trivially infeasible subsystem obtained by elementary row operations. We prove analogous results for weakly infeasible systems. We obtain some fundamental geometric corollaries: an exact characterization of when the linear image of a closed convex cone is closed, and an exact characterization of nice cones. Our infeasibility certificates provide algorithms to generate all infeasible conic LPs over several important classes of cones; and all weakly infeasible SDPs in a natural class. Using these algorithms we generate a public domain library of infeasible and weakly infeasible SDPs. The status of our instances can be verified by inspection in exact arithmetic, but they turn out to be challenging for commercial and research codes.
A Fast Eddy-current Non Destructive Testing Finite Element Solver in Steam Generator

In this paper we present an advanced numerical method to simulate a real life challenging industrial problem that consists of the non-destructive testing in steam generators. We develop a finite element technique that handles the big data numerical set of systems arising when a discretization of the eddy-current equation in three dimensional space is made. Using a high performance technique, our method becomes fully efficient. We provide numerical simulations using the software Freefem++ which has a powerful tool to handle finite element method and parallel computing. We show that our technique speeds up the simulation with a good efficiency factor.
Horizontal and vertical mutation fans

We introduce diagrams for m-cluster categories which we call “horizontal” and “vertical” mutation fans. These are analogous to the mutation fans (also known as “semi-invariant pictures” or “scattering diagrams”) for the standard (m = 1) cluster case, which are dual to the poset of finitely generated torsion classes. The purpose of these diagrams is to visualize mutations and analogues of maximal green sequences in the m-cluster category with special emphasis on the c-vectors (the “brick” labels).
Singular Riemannian flows and characteristic numbers

Let M be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on M to a small tubular neighborhood of each connected component of its singular stratum is foliated diffeomorphic to an isometric flow on the same neighborhood. We then prove a formula that computes characteristic numbers of M as the sum of residues associated with the infinitesimal foliation at the components of the singular stratum of the flow.
What is the force on a magnetic dipole

This paper will be of interest to physics graduate students and faculty. We show that attempts to modify the force on a magnetic dipole by introducing either hidden momentum or internal forces are not correct. The standard textbook result is correct even in the presence of time dependent electromagnetic fields.
Successive Standardization of Rectangular Arrays.

In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization) that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an iteration begins with operations on columns: first subtract the mean of each column; then divide by its standard deviation. The iteration continues with the same two operations done successively for rows. These four operations applied in sequence completes one iteration. One then iterates again, and again, and again, ... In [1] it was argued that if arrays are made up of real numbers, then the set for which convergence of these successive iterations fails has Lebesgue measure 0. The limiting array has row and column means 0, row and column standard deviations 1. A basic result on convergence given in [1] is true, though the argument in [1] is faulty. The result is stated in the form of a theorem here, and the argument for the theorem is correct. Moreover, many graphics given in [1] suggest that except for a set of entries of any array with Lebesgue measure 0, convergence is very rapid, eventually exponentially fast in the number of iterations. Because we learned this set of rules from Bradley Efron, we call it “Efron’s algorithm”. More importantly, the rapidity of convergence is illustrated by numerical examples.
Design of Multifunctional Soft Doming Actuator for Soft Machines

Bilayer bending based soft actuators are widely utilized in soft robotics for locomotion and object gripping. However, studies on soft actuators based on bilayer doming remain largely unexplored despite the often-observed dome-like shapes in undersea animals such as jellyfish and octopus suction cup. Here, based on the simplified model of bending-induced doming of circular bilayer plates with mismatched deformation, we explore the design of soft doming actuator upon pneumatic actuation and its implications in design of multifunctional soft machines. The bilayer actuator is composed of patterned embedded pneumatic channel on top for radial expansion and a solid elastomeric layer on bottom for strain-limiting. We show that both the cavity volume and bending angle at the rim of the actuated dome can be controlled by tuning the height gradient of the pneumatic channel along the radial direction. We demonstrate its potential multifunctional applications in swimming, adhesion, and gripping, including high efficient jellyfish-inspired underwater soft robots with locomotion speed of 84 cm/min and rotation-based soft grippers with low energy cost by harnessing the large rim bending angle, as well as octopus-inspired soft adhesion actuators with strong and switchable adhesion force of over 10 N by utilizing the large cavity volume.
Exact Simultaneous Recovery of Locations and Structure from Known Orientations and Corrupted Point Correspondences

Let $$t_1,\ldots ,t_{n_l} \in {\mathbb {R}}^d$$ and $$p_1,\ldots ,p_{n_s} \in {\mathbb {R}}^d$$ and consider the bipartite location recovery problem: given a subset of pairwise direction observations $$\{(t_i - p_j) / \Vert t_i - p_j\Vert _2\}_{i,j \in [n_\ell ] \times [n_\text {s}]}$$ , where a constant fraction of these observations are arbitrarily corrupted, find $$\{t_i\}_{i \in [n_\ell ]}$$ and $$\{p_j\}_{j \in [n_\text {s}]}$$ up to a global translation and scale. This task arises in the Structure from Motion problem from computer vision, which consists of recovering the three-dimensional structure of a scene from photographs at unknown vantage points. We study the recently introduced ShapeFit algorithm as a method for solving this bipartite location recovery problem. In this case, ShapeFit consists of a simple convex program over $$d(n_l + n_s)$$ real variables. We prove that this program recovers a set of $$n_l+n_s$$ i.i.d. Gaussian locations exactly and with high probability if the observations are given by a bipartite Erdős–Renyi graph, d is large enough, and provided that at most a constant fraction of observations involving any particular location are adversarially corrupted. This recovery theorem is based on a set of deterministic conditions that we prove are sufficient for exact recovery. Finally, we propose a modified pipeline for the Structure for Motion problem, based on this bipartite location recovery problem.
Methods for parametrizing varieties of Lie algebras

Abstract A real n-dimensional anticommutative nonassociative algebra is represented by an element of ∧ 2 ( R n ) ⁎ ⊗ R n . For each μ ∈ ∧ 2 ( R n ) ⁎ ⊗ R n , there is a unique subset Λ ⊆ { ( i , j , k ) : 1 ≤ i j ≤ n , 1 ≤ k ≤ n } so that the structure constant μ i j k with i j is nonzero if and only if ( i , j , k ) ∈ Λ . The set of all μ ∈ ∧ 2 ( R n ) ⁎ ⊗ R n with subset Λ is denoted S Λ ( R ) ; these sets stratify ∧ 2 ( R n ) ⁎ ⊗ R n . We describe how to smoothly parametrize the Lie algebras in S Λ ( R ) up to isomorphism, for Λ satisfying certain frequently seen hypotheses.
Asymptotics for the level set equation near a maximum

We give asymptotics for the level set equation for mean curvature flow on a convex domain near the point where it attains a maximum. It is known that solutions are not necessarily $C^3,$ and we recover this result and construct non-smooth solutions which are $C^3.$ We also construct solutions having prescribed behavior near the maximum. We do this by analyzing the asymptotics for rescaled mean curvature flow converging to a stationary sphere.
Existence, uniqueness and removable singularities for nonlinear partial differential equations in geometry

This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.
Hydra: Leveraging functional slicing for efficient distributed SDN controllers

The conventional approach to scaling Software-Defined Networking (SDN) controllers today is to partition switches based on network topology, with each partition being controlled by a single physical controller, running all SDN applications. However, topological partitioning is limited by the fact that (i) performance of latency-sensitive (e.g., monitoring) SDN applications associated with a given partition may be impacted by co-located compute-intensive (e.g., route computation) applications; (ii) simultaneously achieving low convergence time and response times might be challenging; and (iii) communication between instances of an application across partitions may increase latencies. To tackle these issues, in this paper, we explore functional slicing, a complementary approach to scaling, where multiple SDN applications belonging to the same topological partition may be placed in physically distinct servers. We present Hydra, a framework for distributed SDN controllers based on functional slicing. Hydra chooses partitions based on convergence time as the primary metric, but places application instances across partitions in a manner that keeps response times low while considering communication between applications of a partition, and instances of an application across partitions. Evaluations using the Floodlight controller show the importance and effectiveness of Hydra in simultaneously keeping convergence times on failures small, while sustaining higher throughput per partition and ensuring responsiveness to latency sensitive applications.
Learning transformations for clustering and classification

A low-rank transformation learning framework for subspace clustering and classification is proposed here. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature to partition such high-dimensional data into clusters corresponding to their underlying low-dimensional subspaces. Low-dimensional intrinsic structures are often violated for real-world observations, as they can be corrupted by errors or deviate from ideal models. We propose to address this by learning a linear transformation on subspaces using nuclear norm as the modeling and optimization criteria. The learned linear transformation restores a low-rank structure for data from the same subspace, and, at the same time, forces a maximally separated structure for data from different subspaces. In this way, we reduce variations within the subspaces, and increase separation between the subspaces for a more robust subspace clustering. This proposed learned robust subspace clustering framework significantly enhances the performance of existing subspace clustering methods. Basic theoretical results presented here help to further support the underlying framework. To exploit the low-rank structures of the transformed subspaces, we further introduce a fast subspace clustering technique, which efficiently combines robust PCA with sparse modeling. When class labels are present at the training stage, we show this low-rank transformation framework also significantly enhances classification performance. Extensive experiments using public data sets are presented, showing that the proposed approach significantly outperforms state-of-the-art methods for subspace clustering and classification. The learned low cost transform is also applicable to other classification frameworks.
Control function instrumental variable estimation of nonlinear causal effect models

The instrumental variable method consistently estimates the effect of a treatment when there is unmeasured confounding and a valid instrumental variable. A valid instrumental variable is a variable that is independent of unmeasured confounders and affects the treatment but does not have a direct effect on the outcome beyond its effect on the treatment. Two commonly used estimators for using an instrumental variable to estimate a treatment effect are the two stage least squares estimator and the control function estimator. For linear causal effect models, these two estimators are equivalent, but for nonlinear causal effect models, the estimators are different. We provide a systematic comparison of these two estimators for nonlinear causal effect models and develop an approach to combing the two estimators that generally performs better than either one alone. We show that the control function estimator is a two stage least squares estimator with an augmented set of instrumental variables. If these augmented instrumental variables are valid, then the control function estimator can be much more efficient than usual two stage least squares without the augmented instrumental variables while if the augmented instrumental variables are not valid, then the control function estimator may be inconsistent while the usual two stage least squares remains consistent. We apply the Hausman test to test whether the augmented instrumental variables are valid and construct a pretest estimator based on this test. The pretest estimator is shown to work well in a simulation study. An application to the effect of exposure to violence on time preference is considered.
LedgerGuard: Improving Blockchain Ledger Dependability

The rise of crypto-currencies has spawned great interest in their underlying technology, namely, Blockchain. The central component in a Blockchain is a shared distributed ledger. A ledger comprises series of blocks, which in turns contains a series of transactions. An identical copy of the ledger is stored on all nodes in a blockchain network. Maintaining ledger integrity and security is one of the crucial design aspects of any blockchain platform. Thus, there are typically built-in validation mechanisms leveraging cryptography to ensure the validity of incoming blocks before committing them into the ledger. However, a blockchain node may run over an extended period of time, during which the blocks on the disk can may become corrupted due to software or hardware failures, or due to malicious activity. This paper proposes LedgerGuard, a tool to maintain ledger integrity by detecting corrupted blocks and recovering these blocks by synchronizing with rest of the network. The experimental implementation of LedgerGuard is based on Hyperledger Fabric, which is a popular open source permissioned blockchain platform.
Mirror symmetry for P^2 and tropical geometry

Abstract This paper explores the relationship between mirror symmetry for P 2 , at the level of big quantum cohomology, and tropical geometry. The mirror of P 2 is typically taken to be ( ( C × ) 2 , W ) , where W is a Landau–Ginzburg potential of the form x + y + 1 / x y . The complex moduli space of the mirror is the universal unfolding of W, and oscillatory integrals produce a Frobenius manifold structure on this universal unfolding. We show that W can be deformed by counting Maslov index two tropical disks, and the natural parameters appearing in this deformation are then the flat coordinates on the moduli space. Furthermore, the oscillatory integrals are shown to read off directly tropical curve counts from the potential. Thus we show in fact that mirror symmetry for P 2 is equivalent in a strong sense to tropical curve counting formulas, including tropical formulas for gravitational descendent invariants.
An application of liaison theory to the Eisenbud–Green–Harris conjecture

Abstract In this paper, we apply liaison theory to the Eisenbud–Green–Harris conjecture and prove that the conjecture holds for a certain subclass of homogeneous ideals in the linkage class of a complete intersection ideal. In the case of three variables, we prove that the conjecture holds for Gorenstein ideals.
Modal makeup of transmission eigenchannels

The wide range of transmission eigenvalues and correlation frequencies of the transmission eigenchannels is explained in terms of the transmission matrices of the modes of the random medium.
Efficient Visual Coding: From Retina To V2

The human visual system has a hierarchical structure consisting of layers of processing, such as the retina, V1, V2, etc. Understanding the functional roles of these visual processing layers would help to integrate the psychophysiological and neurophysiological models into a consistent theory of human vision, and would also provide insights to computer vision research. One classical theory of the early visual pathway hypothesizes that it serves to capture the statistical structure of the visual inputs by efficiently coding the visual information in its outputs. Until recently, most computational models following this theory have focused upon explaining the receptive field properties of one or two visual layers. Recent work in deep networks has eliminated this concern, however, there is till the retinal layer to consider. Here we improve on a previously-described hierarchical model Recursive ICA (RICA) [1] which starts with PCA, followed by a layer of sparse coding or ICA, followed by a component-wise nonlinearity derived from considerations of the variable distributions expected by ICA. This process is then repeated. In this work, we improve on this model by using a new version of sparse PCA (sPCA), which results in biologically-plausible receptive fields for both the sPCA and ICA/sparse coding. When applied to natural image patches, our model learns visual features exhibiting the receptive field properties of retinal ganglion cells/lateral geniculate nucleus (LGN) cells, V1 simple cells, V1 complex cells, and V2 cells. Our work provides predictions for experimental neuroscience studies. For example, our result suggests that a previous neurophysiological study improperly discarded some of their recorded neurons; we predict that their discarded neurons capture the shape contour of objects.
Online Forecasting Matrix Factorization

We consider the problem of forecasting a high-dimensional time series that can be modeled as matrices where each column denotes a measurement and use low-rank matrix factorization for predicting future values or imputing missing ones. We define and analyze our problem in the online setting in which the data arrive as a stream and only a single pass is allowed. We present and analyze new matrix factorization techniques that can learn low-dimensional embeddings effectively in an online manner. Based on these embeddings, we derive a recursive minimum mean square error estimator based on an autoregressive model. Experiments with two real datasets of tens of millions of measurements show the benefits of the proposed approach.
Vector Bundles and Gromov–Hausdorff Distance

We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov–Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our ideas with simple specific examples involving vector bundles on the circle, the two-torus, the two-sphere, and finite metric spaces. Our topic is motivated by statements concerning “monopole bundles” over matrix algebras in the literature of theoretical high-energy physics.
THE ALEXANDER AND JONES POLYNOMIALS THROUGH REPRESENTATIONS OF ROOK ALGEBRAS

In the 1920's Artin defined the braid group, Bn, in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most important knot invariants, can be described completely using the braid group. There has been a recent growth of interest in other diagrammatic algebras, whose elements have a similar topological flavor to the braid group. These have wide ranging applications in areas including representation theory and quantum computation. We consider representations of the braid group when passed through another diagrammatic algebra, the planar rook algebra. By studying traces of these matrices, we recover both the Jones and Alexander polynomials.
DRAT-based Bit-Vector Proofs in CVC4

Many state-of-the-art Satisfiability Modulo Theories (SMT) solvers for the theory of fixed-size bit-vectors employ an approach called bit-blasting, where a given formula is translated into a Boolean satisfiability (SAT) problem and delegated to a SAT solver. Consequently, producing bit-vector proofs in an SMT solver requires incorporating SAT proofs into its proof infrastructure. In this paper, we describe three approaches for integrating DRAT proofs generated by an off-the-shelf SAT solver into the proof infrastructure of the SMT solver CVC4 and explore their strengths and weaknesses. We implemented all three approaches using CryptoMiniSat as the SAT back-end for its bit-blasting engine and evaluated performance in terms of proof-production and proof-checking.
The Nonlinear Heat Equation on Dense Graphs and Graph Limits

The continuum limit of coupled dynamical systems is an approximate procedure, by which the dynamical problem on a sequence of large graphs is replaced by an evolution integral equation on a continuous spatial domain. While this method has been widely used in the analysis of pattern formation in nonlocally coupled networks, its mathematical basis remained little understood. In this paper, we use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before. Specifically, for dynamical networks on convergent sequences of simple and weighted graphs, we prove convergence of solutions of the initial-value problems for discrete models to those of the limiting continuous equations. In addition, for sequences of simple graphs converging to \0, 1\-valued graphons, it is shown that the convergence r...
Moonshine for all finite groups

In recent literature, moonshine has been explored for some groups beyond the Monster, for example the sporadic O’Nan and Thompson groups. This collection of examples may suggest that moonshine is a rare phenomenon, but a fundamental and largely unexplored question is how general the correspondence is between modular forms and finite groups. For every finite group G, we give constructions of infinitely many graded infinite-dimensional $$\mathbb {C}[G]$$ -modules where the McKay–Thompson series for a conjugacy class [g] is a weakly holomorphic modular function properly on $$\varGamma _0({{\mathrm{ord}}}(g))$$ . As there are only finitely many normalized Hauptmoduln, groups whose McKay–Thompson series are normalized Hauptmoduln are rare, but not as rare as one might naively expect. We give bounds on the powers of primes dividing the order of groups which have normalized Hauptmoduln of level $${{\mathrm{ord}}}(g)$$ as the graded trace functions for any conjugacy class [g], and completely classify the finite abelian groups with this property. In particular, these include $$(\mathbb {Z}/ 5 \mathbb {Z})^5$$ and $$(\mathbb {Z}/ 7 \mathbb {Z})^4$$ , which are not subgroups of the Monster.
Direct splitting method for the Baum–Connes conjecture

Abstract We develop a new method for studying the Baum–Connes conjecture, which we call the direct splitting method. We introduce what we call property (γ) for G-equivariant Kasparov cycles. We show that the existence of a G-equivariant Kasparov cycle with property (γ) implies the split-injectivity of the assembly map μ A G for any separable G- C ⁎ -algebra A. We also show that if such a cycle exists, the assembly map μ A G is an isomorphism if and only if the cycle acts as the identity on the right-hand side group K ⁎ ( A ⋊ r G ) of the Baum–Connes conjecture. In a separate paper, with J. Brodzki, E. Guentner and N. Higson, we use this method to give a finite-dimensional proof of the Baum–Connes conjecture for groups which act properly and co-compactly on a finite-dimensional CAT(0)-cubical space.
Single bunch transverse instability in a circular accelerator with chromaticity and space charge

The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly on the bunch model but they are rather sensitive to the wake shape. In particular, space charge effects are investigated in the paper and it is shown that their influence depends on sign of wake field enhancing the bunch stability if the wake is negative. The resistive wall wake is considered in detail including a comparison of single and collective effects. A comparison of the results with earlier publications is carried out.
Ramsey numbers of degenerate graphs

A graph is d-degenerate if all its subgraphs have a vertex of degree at most d. We prove that there exists a constant c such that for all natural numbers d and r, every d-degenerate graph G of chromatic number r has Ramsey number at most 2 d2 cr |V (G)|. This solves a conjecture of Burr and Erdýos from 1973.
EDML: a method for learning parameters in Bayesian networks

We propose a method called EDML for learning MAP parameters in binary Bayesian networks under incomplete data. The method assumes Beta priors and can be used to learn maximum likelihood parameters when the priors are uninformative. EDML exhibits interesting behaviors, especially when compared to EM. We introduce EDML, explain its origin, and study some of its properties both analytically and empirically.
Regularity of the Level Set Flow

We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C1 manifold with cylindrical singularities.© 2017 Wiley Periodicals, Inc.
A SUPPLEMENT TO MY PAPER ON REAL AND COMPLEX OPERATOR IDEALS

Abstract We show that the main problem left open in [2] can be solved using the Banach spaces Zα recently constructed by Kalton [1]. This gives an example of a complex operator ideal that has no real analogue. It thus shows the richer structure of complex operator ideals compared with the real ones.
Intuitionism and the liar paradox

Abstract The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the contradiction. This leads to a general resolution of the classical semantic paradoxes. This paper is an expanded version of parts of Weaver [10]
Mined semantic analysis: A new concept space model for semantic representation of textual data

Mined Semantic Analysis (MSA) is a novel concept space model which employs unsupervised learning to generate semantic representations of text. MSA represents textual structures (terms, phrases, documents) as a Bag of Concepts (BoC) where concepts are derived from concept rich encyclopedic corpora. Traditional concept space models exploit only target corpus content to construct the concept space. MSA, alternatively, uncovers implicit relations between concepts by mining for their associations (e.g., mining Wikipedia's “See also” link graph). We evaluate MSA's performance on benchmark datasets for measuring semantic relatedness of words and sentences. Empirical results show competitive performance of MSA compared to prior state-of-the-art methods. Additionally, we introduce the first analytical study to examine statistical significance of results reported by different semantic relatedness methods. Our study shows that, the nuances of results across top performing methods could be statistically insignificant. The study positions MSA as one of state-of-the-art methods for measuring semantic relatedness, besides the inherent interpretability and simplicity of the generated semantic representation.
Domain and range symmetries of operator fractional Brownian fields

Abstract An operator fractional Brownian field (OFBF) is a Gaussian, stationary increment R n -valued random field on R m that satisfies the operator self-similarity property { X ( c E t ) } t ∈ R m = L { c H X ( t ) } t ∈ R m , c > 0 , for two matrix exponents ( E , H ). In this paper, we characterize the domain and range symmetries of OFBF, respectively, as maximal groups with respect to equivalence classes generated by orbits and, based on a new anisotropic polar-harmonizable representation of OFBF, as intersections of centralizers. We also describe the sets of possible pairs of domain and range symmetry groups in dimensions ( m , 1 ) and ( 2 , 2 ).
The impact of surface area, volume, curvature, and Lennard–Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.
Rich component analysis

In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might have one set of molecular observations and one set of physiological observations on the same group of individuals, and we want to quantify molecular patterns that are uncorrelated with physiology. Despite being a common problem, this is highly challenging when the correlations come from complex distributions. In this paper, we develop the general framework of Rich Component Analysis (RCA) to model settings where the observations from different views are driven by different sets of latent components, and each component can be a complex, high-dimensional distribution. We introduce algorithms based on cumulant extraction that provably learn each of the components without having to model the other components. We show how to integrate RCA with stochastic gradient descent into a meta-algorithm for learning general models, and demonstrate substantial improvement in accuracy on several synthetic and real datasets in both supervised and unsupervised tasks. Our method makes it possible to learn latent variable models when we don't have samples from the true model but only samples after complex perturbations.
Evaluation of small elements of the eigenvectors of certain symmetric tridiagonal matrices with high relative accuracy

Abstract Evaluation of the eigenvectors of symmetric tridiagonal matrices is one of the most basic tasks in numerical linear algebra. It is a widely known fact that, in the case of well separated eigenvalues, the eigenvectors can be evaluated with high relative accuracy. Nevertheless, in general, each coordinate of the eigenvector is evaluated with only high absolute accuracy. In particular, those coordinates whose magnitude is below the machine precision are not expected to be evaluated with any accuracy whatsoever. It turns out that, under certain conditions, frequently encountered in applications, small (e.g. 10 − 50 ) coordinates of eigenvectors of symmetric tridiagonal matrices can be evaluated with high relative accuracy. In this paper, we investigate such conditions, carry out the analysis, and describe the resulting numerical schemes. While our schemes can be viewed as a modification of already existing (and well known) numerical algorithms, the related error analysis appears to be new. Our results are illustrated via several numerical examples.
Distributed Maximum Likelihood Using Dynamic Average Consensus

This paper presents the formulation and analysis of a novel distributed maximum likelihood algorithm that utilizes a first-order optimization scheme. The proposed approach utilizes a static average consensus algorithm to reach agreement on the initial condition to the iterative optimization scheme and a dynamic average consensus algorithm to reach agreement on the gradient direction. The current distributed algorithm is guaranteed to exponentially recover the performance of the centralized algorithm. Though the current formulation focuses on maximum likelihood algorithm built on first-order methods, it can be easily extended to higher order methods. Numerical simulations validate the theoretical contributions of the paper.
A finer Tate duality theorem for local Galois symbols

Abstract Let K be a finite extension of Q p . Let A, B be abelian varieties over K with good reduction. For any integer m ≥ 1 , we consider the Galois symbol K ( K ; A , B ) / m → H 2 ( K , A [ m ] ⊗ B [ m ] ) , where K ( K ; A , B ) is the Somekawa K-group attached to A , B . This map is a generalization of the Galois symbol K 2 M ( K ) / m → H 2 ( K , μ m ⊗ 2 ) of the Bloch–Kato conjecture, where K 2 M ( K ) is the Milnor K-group of K. In this paper we give a geometric description of the image of this generalized Galois symbol by looking at the Tate duality pairing H 2 ( K , A [ m ] ⊗ B [ m ] ) × Hom G K ( A [ m ] , B ⋆ [ m ] ) → Z / m , where B ⋆ is the dual abelian variety of B. Under this perfect pairing we compute the exact annihilator of the image of the Galois symbol in terms of an object of integral p-adic Hodge theory. In this way we generalize a result of Tate for H 1 . Moreover, our result has applications to zero cycles on abelian varieties.
STAR REDUCIBLE COXETER GROUPS

We define ``star reducible'' Coxeter groups to be those Coxeter groups for which every fully commutative element (in the sense of Stembridge) is equivalent to a product of commuting generators by a sequence of length-decreasing star operations (in the sense of Lusztig). We show that the Kazhdan--Lusztig bases of these groups have a nice projection property to the Temperley--Lieb type quotient, and furthermore that the images of the basis elements $C'_w$ (for fully commutative $w$) in the quotient have structure constants in ${\Bbb Z}^{\geq 0}[v, v^{-1}]$. We also classify the star reducible Coxeter groups and show that they form nine infinite families (types $A_n$, $B_n$, $D_n$, $E_n$, $F_n$, $H_n$, affine $A_{n-1}$ for $n$ odd, affine $C_{n-1}$ for $n$ even, and the case where the Coxeter graph is complete), with two exceptional cases (of ranks 6 and 7). This paper is the sequel to math.QA/0509362.
Information-theoretic analysis of generalization capability of learning algorithms

We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems, and give theoretical guidelines for striking the right balance between data fit and generalization by controlling the input-output mutual information. We propose a number of methods for this purpose, among which are algorithms that regularize the ERM algorithm with relative entropy or with random noise. Our work extends and leads to nontrivial improvements on the recent results of Russo and Zou.
SIGNATURE PAIRS FOR GROUP-INVARIANT HERMITIAN POLYNOMIALS

We study the signature pair for certain group-invariant Hermitian polynomials arising in CR geometry. In particular, we determine the signature pair for the finite subgroups of SU(2). We introduce the asymptotic positivity ratio and compute it for cyclic subgroups of U(2). We calculate the signature pair for dihedral subgroups of U(2).
Quality-Driven Resource Allocation for Full-Duplex Delay-Constrained Wireless Video Transmissions

In this paper, wireless video transmission over full-duplex channels under total bandwidth and minimum required quality constraints is studied. In order to provide the desired performance levels to the end-users in real-time video transmissions, quality of service requirements such as statistical delay constraints are also considered. Effective capacity is used as the throughput metric in the presence of such statistical delay constraints since deterministic delay bounds are difficult to guarantee due to the time-varying nature of wireless fading channels. A communication scenario with multiple pairs of users in which different users have different delay requirements is addressed. Following characterizations from the rate-distortion theory, a logarithmic model of the quality-rate relation is used for predicting the quality of the reconstructed video in terms of the peak signal-to-noise ratio at the receiver side. Since the optimization problem is not concave or convex, the optimal bandwidth and power allocation policies that maximize the weighted sum video quality subject to total bandwidth, maximum transmission power level and minimum required quality constraints are derived by using monotonic optimization theory.
Reinforcing Adversarial Robustness using Model Confidence Induced by Adversarial Training

In this paper we study leveraging confidence information induced by adversarial training to reinforce adversarial robustness of a given adversarially trained model. A natural measure of confidence is $\|F({\bf x})\|_\infty$ (i.e. how confident $F$ is about its prediction?). We start by analyzing an adversarial training formulation proposed by Madry et al.. We demonstrate that, under a variety of instantiations, an only somewhat good solution to their objective induces confidence to be a discriminator, which can distinguish between right and wrong model predictions in a neighborhood of a point sampled from the underlying distribution. Based on this, we propose Highly Confident Near Neighbor (${\tt HCNN}$), a framework that combines confidence information and nearest neighbor search, to reinforce adversarial robustness of a base model. We give algorithms in this framework and perform a detailed empirical study. We report encouraging experimental results that support our analysis, and also discuss problems we observed with existing adversarial training.