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List-Decodable Linear RegressionMay 14 2019May 15 2019We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample $\{ (x_i,y_i)\}_{i \leq ... More

Learning Neural Networks with Two Nonlinear Layers in Polynomial TimeSep 18 2017Apr 20 2018We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the algorithm succeeds ... More

Moment-Matching PolynomialsJan 04 2013We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem and deviate significantly ... More

Eigenvalue Decay Implies Polynomial-Time Learnability for Neural NetworksAug 11 2017We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal assumptions ... More

Threshold graphs, shifted complexes, and graphical complexesMar 04 2007We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the independent set, neighborhood, and dominance complexes. We present a number ... More

Learning One Convolutional Layer with Overlapping PatchesFeb 07 2018We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches. Additionally, our algorithm requires only mild conditions on the underlying distribution. ... More

Chip-firing and energy minimization on M-matricesMar 07 2014Nov 21 2014We consider chip-firing dynamics defined by arbitrary M-matrices. M-matrices generalize graph Laplacians and were shown by Gabrielov to yield avalanche finite systems. Building on the work of Baker and Shokrieh, we extend the concept of energy minimizing ... More

Flow-firing processesFeb 06 2019We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted ... More

Shifted set families, degree sequences, and plethysmOct 26 2006Jan 10 2008We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. The first part collects for the first time in one place, various implications such as: Threshold implies Uniquely Realizable implies Degree-Maximal ... More

Bounding the Sensitivity of Polynomial Threshold FunctionsSep 28 2009Nov 09 2009We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of polynomial threshold functions. More specifically, for a Boolean function f on n variables equal to the sign of a real, multivariate polynomial of total degree ... More

An Invariance Principle for PolytopesDec 24 2009Sep 12 2012Let X be randomly chosen from {-1,1}^n, and let Y be randomly chosen from the standard spherical Gaussian on R^n. For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that |Pr [X belongs to P] - Pr [Y belongs to ... More

Preserving Randomness for Adaptive AlgorithmsNov 02 2016We introduce the concept of a randomness steward, a tool for saving random bits when executing a randomized estimation algorithm $\mathsf{Est}$ on many adaptively chosen inputs. For each execution, the chosen input to $\mathsf{Est}$ remains hidden from ... More

Toward Attribute Efficient Learning AlgorithmsNov 27 2003We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time $n^{\tilde{O}(k^{1/3})}$. ... More

Polynomial-Time Approximation Schemes for Knapsack and Related Counting Problems using Branching ProgramsAug 18 2010We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm produces a (1 ... More

List-Decodable Linear RegressionMay 14 2019We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample $\{ (x_i,y_i)\}_{i \leq ... More

Directed rooted forests in higher dimensionDec 24 2015Nov 18 2016For a graph G, the generating function of rooted forests, counted by the number of connected components, can be expressed in terms of the eigenvalues of the graph Laplacian. We generalize this result from graphs to cell complexes of arbitrary dimension. ... More

Scheduling ProblemsJan 13 2014Dec 02 2015We introduce the notion of a scheduling problem which is a boolean function $S$ over atomic formulas of the form $x_i \leq x_j$. Considering the $x_i$ as jobs to be performed, an integer assignment satisfying $S$ schedules the jobs subject to the constraints ... More

Projection volumes of hyperplane arrangementsJan 28 2010We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones is given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this held ... More

Exact MAP Inference by Avoiding Fractional VerticesMar 08 2017Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open question is to ... More

Submodular Functions Are Noise StableJun 02 2011Jun 13 2011We show that all non-negative submodular functions have high {\em noise-stability}. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on $\{-1,1\}^n$ (for any constant accuracy parameter ... More

Reliably Learning the ReLU in Polynomial TimeNov 30 2016We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $\mathbf{x} \mapsto \max(0, \mathbf{w} \cdot \mathbf{x})$ with $\mathbf{w} \in \mathbb{S}^{n-1}$. Our algorithm works in the ... More

Sparse Polynomial Learning and Graph SketchingFeb 17 2014Nov 07 2014Let $f:\{-1,1\}^n$ be a polynomial with at most $s$ non-zero real coefficients. We give an algorithm for exactly reconstructing f given random examples from the uniform distribution on $\{-1,1\}^n$ that runs in time polynomial in $n$ and $2s$ and succeeds ... More

Learning Ising Models with Independent FailuresFeb 13 2019We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the essentially optimal ... More

Coxeter arrangements in three dimensionsJan 24 2015Let ${\mathcal A}$ be a finite real linear hyperplane arrangement in three dimensions. Suppose further that all the regions of ${\mathcal A}$ are isometric. We prove that ${\mathcal A}$ is necessarily a Coxeter arrangement. As it is well known that the ... More

Chip firing on Dynkin diagrams and McKay quiversJan 25 2016Feb 27 2016Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for finite subgroups ... More

The Positive Bergman Complex of an Oriented MatroidJun 07 2004We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive Bergman complex is defined so that given a linear ideal I with associated ... More

On the topology of no $k$-equal spacesJul 31 2017We consider the topology of real no $k$-equal spaces via the theory of cellular spanning trees. Our main theorem proves that the rank of the $(k-2)$-dimensional homology of the no $k$-equal subspace of $\mathbb{R}$ is equal to the number of facets in ... More

Cuts and flows of cell complexesJun 27 2012Sep 30 2014We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension the theory ... More

Relations on Generalized Degree SequencesJun 25 2008Jan 23 2009We study degree sequences for simplicial posets and polyhedral complexes, generalizing the well-studied graphical degree sequences. Here we extend the more common generalization of vertex-to-facet degree sequences by considering arbitrary face-to-flag ... More

Simplicial and Cellular TreesJun 22 2015Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed first by Bolker, ... More

Cellular spanning trees and Laplacians of cubical complexesAug 13 2009May 05 2010We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms of the eigenvalues of its cellular Laplacian operators, generalizing a previous result for simplicial complexes. As an application, we obtain explicit formulas for ... More

Simplicial matrix-tree theoremsFeb 19 2008Aug 21 2008We generalize the definition and enumeration of spanning trees from the setting of graphs to that of arbitrary-dimensional simplicial complexes $\Delta$, extending an idea due to G. Kalai. We prove a simplicial version of the Matrix-Tree Theorem that ... More

Chip-firing on general invertible matricesAug 18 2015We propose a generalization of the graphical chip-firing model allowing for the redistribution dynamics to be governed by any invertible integer matrix while maintaining the long term critical, superstable, and energy minimizing behavior of the classical ... More

The Bergman complex of a matroid and phylogenetic treesNov 21 2003May 04 2005We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural subdivision of the Bergman complex of M is a geometric realization of the ... More

On the connectivity of spaces of three-dimensional tilingsFeb 02 2017Mar 24 2017We consider domino tilings of three-dimensional cubiculated manifolds with or without boundary, including subsets of Euclidean space and three-dimensional tori. In particular, we are interested in the connected components of the space of tilings of such ... More

A Geometric Interpretation of the Characteristic Polynomial of Reflection ArrangementsJun 11 2009We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of type $A_n$, $B_n$, and $D_n$, the coefficients of the characteristic polynomial of the reflection arrangement are proportional ... More

Directed Rooted Forests in Higher DimensionDec 24 2015Feb 23 2016For a graph G, the generating function of rooted forests, counted by the number of connected components, can be expressed in terms of the eigenvalues of the graph Laplacian. We generalize this result from graphs to cell complexes of arbitrary dimension. ... More

Rigorous derivation of the mean field Green functions of the two-band Hubbard model of superconductivityApr 05 2007The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the Hubbard operator ... More

The boundary layer problem in Bayesian adaptive quadratureSep 25 2006The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer, is the first ... More

Finiteness of the Hopping Induced Energy Corrections in CupratesMar 09 2009The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in cuprates, ... More

Reliable operations on oscillatory functionsMay 14 1999Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors ... More

Signature of Fermi surface jumps in positron spectroscopy dataAug 05 1999A subtractionless method for solving Fermi surface sheets ({\tt FSS}), from measured $n$-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron-electron annihilation radiation ({\tt 2D-ACAR}) technique, ... More

Mean field solutions to singlet hopping and superconducting pairing within a two-band Hubbard modelSep 25 2006The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation ... More

A Cheeger-Type Inequality on Simplicial ComplexesSep 23 2012Oct 26 2012In this paper, we consider a variation on Cheeger numbers related to the coboundary expanders recently defined by Dotterer and Kahle. A Cheeger-type inequality is proved, which is similar to a result on graphs due to Fan Chung. This inequality is then ... More

Desargues maps and the Hirota-Miwa equationJun 04 2009Sep 28 2009We study the Desargues maps $\phi:\ZZ^N\to\PP^M$, which generate lattices whose points are collinear with all their nearest (in positive directions) neighbours. The multidimensional compatibility of the map is equivalent to the Desargues theorem and its ... More

Geometric algebra and quadrilateral latticesJan 03 2008Motivated by the fundamental results of the geometric algebra we study quadrilateral lattices in projective spaces over division rings. After giving the noncommutative discrete Darboux equations we discuss differences and similarities with the commutative ... More

Geometric discretization of the Koenigs netsMar 07 2002Apr 26 2002We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs ... More

Holomorphic Curves and Toda SystemsJul 03 1995Jul 04 1995Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in real, complex ... More

Asymptotically periodic L^2 minimizers in strongly segregating diblock copolymersJan 07 2009Using the delta correction to the standard free energy \cite{bc} in the elastic setting with a quadratic foundation term and some parameters, we introduce a one dimension only model for strong segregation in diblock copolymers, whose sharp interface periodic ... More

Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x)Nov 11 1997We show that every $\mu$-constant family of isolated hypersurface singularities of type f(x) + tg(x), where t is a parameter, is topologically trivial. In the proof we construct explicitely a vector field trivializing the family. The proof uses only the ... More

Blow-analytic retraction onto the central fibreJan 26 1997Let X be a complex analytic space and let f:X -> C be a proper complex analytic function with nonsingular generic fibres. By adapting the blowanalytic methods of Kuo we construct a retraction of a neighbourhood of the central fibre f^{-1}(0) onto f^{-1}(0). ... More

Distinct Distances: Open Problems and Current BoundsJun 08 2014May 19 2015We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.

Additivity of the ideal of microscopic setsMay 25 2015A set $M\subset\mathbb{R}$ is microscopic if for each $\varepsilon>0$ there is a sequence of intervals $(J_n)_{n\in\omega}$ covering $M$ and such that $|J_n|\leq \varepsilon^{n+1}$ for each $n\in\omega$. We show that there is a microscopic set which cannot ... More

YSO Jets and Molecular Outflows: Tracing the History of Star FormationApr 29 1998Collimated outflows from Young Stellar Objects (YSOs) can be seen as tracers of the accretion powered systems which drive them. In this paper I review some theoretical and observational aspects of YSO outflows through the prism of questions relating to ... More

Towards a Synthesis of Core-Collapse Supernova TheoryJun 06 1996New insights into the mechanism and character of core--collapse supernova explosions are transforming the approach of theorists to their subject. The universal realization that the direct hydrodynamic mechanism does not work and that a variety of hydrodynamic ... More

Poincare Duality and Spin^c Structures for Noncommutative ManifoldsJul 13 2001We prove a noncompact Serre-Swan theorem characterising modules which are sections of vector bundles not necessarily trivial at infinity. We then identify the endomorphism algebras of the resulting modules. The endomorphism results continue to hold for ... More

Universality of multiplicity distribution in proton-proton and electron-positron collisionsJul 06 2015It is argued that the multiplicity distribution in proton-proton ($pp$) collisions, which is often parameterized by the negative binomial distribution, results from the multiplicity distribution measured in electron-positron ($e^{+}e^{-}$) collisions, ... More

Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakesApr 13 2016Jun 21 2016Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic ... More

The concept of duality for automata over a changing alphabet and generation of a free group by such automataJul 26 2016In the paper, we deal with the notion of an automaton over a changing alphabet, which generalizes the concept of a Mealy-type automaton. We modify the methods based on the idea of a dual automaton and its action used by B. Steinberg et al. (2011) and ... More

Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group TheoryJun 16 2016We investigate the properties of parity-time symmetric periodic photonic structures using Heesh-Shubnikov group theory. Classical group theory cannot be used to categorize the symmetry of the eigenmodes because the time-inversion operator is antiunitary. ... More

On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spacesOct 08 20164-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which ... More

Generic freeness in frame bundle prolongations of $C^\infty$ actionsMay 20 2016Let a real Lie group $G$ act on a $C^\infty$ real manifold~$M$. Assume that the action is $C^\infty$ and that every nontrivial element of~$G$ has a nowhere dense fixpoint set in $M$. We show that, in some higher order frame bundle $F$ of~$M$, there exist ... More

Rapidity and Centrality Dependence of Proton and Anti-proton Production from Au+Au Collisions at sqrt(sNN) = 130GeVJun 20 2003We report on the rapidity and centrality dependence of proton and anti-proton transverse mass distributions from Au+Au collisions at sqrt(sNN) = 130GeV as measured by the STAR experiment at RHIC. Our results are from the rapidity and transverse momentum ... More

Strange anti-particle to particle ratios at mid-rapidity in sqrt(s_NN)= 130 GeV Au+Au CollisionsNov 22 2002Jul 15 2003Values of the ratios in the mid-rapidity yields of anti-Lambda/Lambda = 0.71 +/- 0.01(stat.) +/- 0.04(sys.), anti-Xi+/Xi- = 0.83 +/- 0.04(stat.) +/- 0.05 (sys.), anti-Omega+/Omega- = 0.95 +/- 0.15(stat) +/- 0.05(sys.) and K+/K- 1.092 +/- 0.023(combined) ... More

Search for the decay K_L-> pi^0 nu nubarJun 08 1998Jun 10 1998We report on a search for the rare decay K_L -> pi^0 nu nubar in the KTeV experiment at Fermilab. We searched for two-photon events whose kinematics were consistent with an isolated pi^0 coming from the decay K_L -> pi^0 nu nubar. One candidate event ... More

Semi-Adequate Closed Braids and VolumeJun 28 2014May 22 2015In this paper, we show that the volumes for a family of A-adequate closed braids can be bounded above and below in terms of the twist number, the number of braid strings, and a quantity that can be read from the combinatorics of a given closed braid diagram. ... More

Efficient, Differentially Private Point EstimatorsSep 27 2008Differential privacy is a recent notion of privacy for statistical databases that provides rigorous, meaningful confidentiality guarantees, even in the presence of an attacker with access to arbitrary side information. We show that for a large class of ... More

Pseudo-goldstone higgs from five dimensionsOct 22 2007Oct 27 2007I discuss radiative generation of the higgs potential in 5D models of gauge-higgs unification.

Lambda-Free Logical FrameworksApr 11 2008Nov 18 2008We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it ... More

The Generic Critical Behaviour for 2D Polymer CollapseOct 30 2015Dec 01 2015The nature of the theta point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur (DS) for an exactly solvable model. We use a ... More

Searches for Long-lived Particles at the Tevatron ColliderFeb 07 2008Several searches for long-lived particles have been performed using data from p-pbar collisions from Run II at the Tevatron. In most cases, new analysis techniques have been developed to carry out each search and/or estimate the backgrounds. These searches ... More

Young Physicists' ForumOct 15 2001The Young Physicists' Forum was an opportunity for the younger members of the particle-physics community to gather at Snowmass 2001 and to study and debate major issues that face the field over the next twenty years. Discussions were organized around ... More

Central charges, S-duality and massive vacua of N=1* super Yang-MillsJun 07 2006Aug 02 2006We provide a simple derivation of the extremal values of the superpotential in massive vacua of N=1* SYM, making use of the required modular weight for the central charge of BPS walls interpolating between these vacua. This modular weight descends from ... More

Asymptotic behaviour of fast diffusions on graphsJan 07 2019We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincar\'e (2012) 13(6): 1501-1510 and Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327, and obtain asymptotic ... More

Branched diagrams and the Ozsváth-Szabó spectral sequenceOct 09 2015We present a fresh set of Heegaard multidiagrams which clarify the Ozsv\'ath-Szab\'o spectral sequence from the Khovanov homology of a link to the Heegaard Floer homology of its branched double cover. The spectral sequence constructed from these diagrams ... More

Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fieldsAug 23 2011Let $ F$ be an imaginary quadratic field and $\mathcal{O}$ its ring of integers. Let $ \mathfrak{n} \subset \mathcal{O} $ be a non-zero ideal and let $ p> 5$ be a rational inert prime in $F$ and coprime with $\mathfrak{n}$. Let $ V$ be an irreducible ... More

The Next U.S. Astronomy Decadal SurveyAug 01 2017The U.S. astronomy decadal surveys have been models for advice to government on how to apportion resources to optimise the scientific return on national investments in facilities and manpower. The U.S. is now gearing up to conduct its 2020 survey and ... More

Decay to zero of matrix coefficients at Adjoint infinityJun 08 2006We prove that if a unitary representation of a connected Lie group has the property that no nonozero vector is fixed by any nontrival normal connected subgroup, then the matrix coefficients decay to zero at Adjoint-infinity.

The geometry of points on quantum projectivizationsMar 02 2009Suppose $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal. We study the geometry of the functor $\Gamma_{n}$ ... More

Bondary-connectivity via graph theoryNov 12 2007Sep 27 2011We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of $\Z^d$, where "connectedness" and "boundary" are understood with respect to various graphs on the vertices of $\Z^d$. We provide ... More

Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI modelFeb 21 2011We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study possible MPS-based ... More

The Galois action on geometric lattices and the mod-$\ell$ I/OMOct 29 2015Feb 05 2018This paper studies the Galois action on a special lattice of geometric origin, which is related to mod-$\ell$ abelian-by-central quotients of geometric fundamental groups of varieties. As a consequence, we formulate and prove the mod-$\ell$ abelian-by-central ... More

Reconstructing function fields from rational quotients of mod-$\ell$ Galois groupsAug 22 2014Oct 29 2015In this paper, we develop the main step in the global theory for the mod-$\ell$ analogue of Bogomolov's program in birational anabelian geometry for higher-dimensional function fields over algebraically closed fields. More precisely, we show how to reconstruct ... More

Categoricity and covering spacesDec 10 2014This thesis develops some of the basic model theory of covers of algebraic curves. In particular, an equivalence between the good model-theoretic behaviour of the modular j-function, and the openness of certain Galois representations in the Tate-modules ... More

The Real Chevalley InvolutionMar 08 2012Feb 13 2014We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate ... More

Auditory information loss in real-world listening environmentsFeb 20 2019Whether animal or speech communication, environmental sounds, or music -- all sounds carry some information. Sound sources are embedded in acoustic environments that contain any number of additional sources that emit sounds that reach the listener's ears ... More

Asymptotic Solutions of Polynomial Equations with Exp-Log CoefficientsApr 15 2019We present an algorithm for computing asymptotic approximations of roots of polynomials with exp-log function coefficients. The real and imaginary parts of the approximations are given as explicit exp-log expressions. We provide a method for deciding ... More

A Brief History of the Co-evolution of Supernova Theory with Neutrino PhysicsDec 13 2018The histories of core-collapse supernova theory and of neutrino physics have paralleled one another for more than seventy years. Almost every development in neutrino physics necessitated modifications in supernova models. What has emerged is a complex ... More

Bernoulli property for homogeneous systemsDec 07 2018Let $G$ be a semisimple Lie group with Haar measure $\mu$ and let $\Gamma$ be an irreducible lattice in $G$. For $g\in G$, we consider left translation $L_g$ acting on $(G\backslash\Gamma,\mu)$. We show that if $L_g$ is $K$ (which is equivalent to positive ... More

Generalizations of the Burns-Hale TheoremNov 26 2018The Burns-Hale theorem states that a group G is left-orderable if and only if G is locally projectable onto the class of left-orderable groups. Similar results have appeared in the literature in the case of UPP groups and Conradian left-orderable groups, ... More

Improved Photometric Classification of Supernovae using Deep LearningOct 15 2018We present improved photometric supernovae classification using deep recurrent neural networks. The main improvements over previous work are (i) the introduction of a time gate in the recurrent cell that uses the observational time as an input; (ii) greatly ... More

A new reduction strategy for special negative sectors of planar two-loop integrals without Laporta algorithmDec 13 2018In planar two-loop integrals there is a dedicated sector such that when its index is zero, the two-loop integral decomposes into the product of two one-loop integrals. We show an alternative reduction strategy for these sectors when their index is negative ... More

Flat chains in banach spacesNov 13 2004We generalize the notion of flat chains with arbitrary coefficient groups to Banach spaces and prove a sequential compactness result. We also remove the restriction that a flat chain have finite mass in order for its support to exist.

Algebras with two multiplications and their cumulantsMar 25 2018Cumulants are a notion that comes from the classical probability theory, they are an alternative to a notion of moments. We adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication structures. We present ... More

Multivariable spectral multipliers and quasielliptic operatorsJul 28 2008We study multivariable spectral multipliers $F(L_1,L_2)$ acting on Cartesian product of ambient spaces of two self-adjoint operators $L_1$ and $L_2$. We prove that if $F$ satisfies H\"ormander type differentiability condition then the operator $F(L_1,L_2)$ ... More

Eigenvalues of Toeplitz Operators on the Annulus and Neil AlgebraMar 13 2013Aug 27 2013By working with all collection of all the Sarason Hilbert Hardy spaces for the annulus algebra an improvement to the results of Aryana and Clancey on eigenvalues of self adjoint Toeplitz operators on an annulus is obtained. The ideas are applied to Toeplitz ... More

Commuting-Liftable Subgroups of Galois Groups IIAug 02 2012Jan 23 2015Let $n$ denote either a positive integer or $\infty$, let $\ell$ be a fixed prime and let $K$ be a field of characteristic different from $\ell$. In the presence of sufficiently many roots of unity in $K$, we show how to recover some of the inertia/decomposition ... More

Simple Irreducible Subgroups of Exceptional Algebraic GroupsOct 09 2013Oct 10 2014A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible subgroups of exceptional algebraic groups $G$ which are connected, closed and simple of rank ... More

Spin Structure of the Proton from Polarized Inclusive Deep-Inelastic Muon-Proton ScatteringFeb 12 1997We have measured the spin-dependent structure function $g_1^p$ in inclusive deep-inelastic scattering of polarized muons off polarized protons, in the kinematic range $0.003 < x < 0.7$ and $1 GeV^2 < Q^2 < 60 GeV^2$. A next-to-leading order QCD analysis ... More

The Ozsváth-Szabó spectral sequence and combinatorial link homologyOct 09 2015Jul 13 2017The Khovanov homology of a link in $S^3$ and the Heegaard Floer homology of its branched double cover are related through a spectral sequence constructed by Ozsv\'ath and Szab\'o. This spectral sequence has topological applications but is difficult to ... More