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Results for "Aaron Solomon"

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Spatio-Temporal Deep Graph InfomaxApr 12 2019Spatio-temporal graphs such as traffic networks or gene regulatory systems present challenges for the existing deep learning methods due to the complexity of structural changes over time. To address these issues, we introduce Spatio-Temporal Deep Graph ... More
Tarski's influence on computer scienceAug 15 2006Sep 27 2006The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the method of elimination ... More
Ideal Containments Under Flat ExtensionsDec 25 2015Let $\varphi : S = k[y_0,..., y_n] \to R = k[y_0,...,y_n]$ be given by $y_i \to f_i$ where $f_0,...,f_n$ is an $R$-regular sequence of homogeneous elements of the same degree. A recent paper shows for ideals, $I_\Delta \subseteq S$, of matroids, $\Delta$, ... More
Central figure-8 cross-cuts make surfaces cylindricalSep 16 2015We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and all compact intersections with planes have central symmetry, then M is a ... More
Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}Sep 18 2002The projection of a compact oriented submanifold M^{n-1} in R^{n+1} on a hyperplane P^{n} can fail to bound any region in P. We call this ``projecting to zero.'' Example: The equatorial S^1 in S^2 projects to zero in any plane containing the x_3-axis. ... More
Vectorization of Line Drawings via PolyVector FieldsJan 05 2018Sep 05 2018Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean line drawings, ... More
Tokuyama-type formulas for type BSep 01 2014Dec 15 2015We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group $\rm{Spin}_{2r+1}({\mathbb C})$, which is an analogue of the formulas of Tokuyama for Schur polynomials and ... More
Algorithms for Irrelevance-Based Partial MAPsMar 20 2013Irrelevance-based partial MAPs are useful constructs for domain-independent explanation using belief networks. We look at two definitions for such partial MAPs, and prove important properties that are useful in designing algorithms for computing them ... More
Distinct and repeated distances on a surface and incidences between points and spheresApr 06 2016In this paper we show that the number of distinct distances determined by a set of $n$ points on a constant-degree two-dimensional algebraic variety $V$ (i.e., a surface) in $\mathbb R^3$ is at least $\Omega\left(n^{7/9}/{\rm polylog} \,n\right)$. This ... More
Incidences between points on a variety and planes in R^3Mar 15 2016May 30 2017In this paper we establish an improved bound for the number of incidences between a set $P$ of $m$ points and a set $H$ of $n$ planes in $\mathbb R^3$, provided that the points lie on a two-dimensional nonlinear irreducible algebraic variety $V$ of constant ... More
Involutions, obstructions and mirror symmetryOct 16 2018Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya $A_\infty$ endomorphism algebra of such a Lagrangian is quasi-isomorphic to ... More
Hierarchical Multi-task Deep Neural Network Architecture for End-to-End DrivingFeb 09 2019A novel hierarchical Deep Neural Network (DNN) model is presented to address the task of end-to-end driving. The model consists of a master classifier network which determines the driving task required from an input stereo image and directs said image ... More
Eisenstein Series on Covers of Odd Orthogonal GroupsJan 14 2013Apr 20 2013We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the $n$-fold cover of the split odd orthogonal group $SO_{2r+1}$. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured that the $p$-power ... More
A note on Dickson polynomials of the third kind and Legendre functionsApr 16 2016Feb 15 2018The connection between Dickson polynomials of the first and second kinds, and Legendre functions is well-known. It is of great interest to know if Dickson polynomials of the $(k+1)$-th kind have any connections with Legendre functions. In this note, we ... More
Dimensions of Automorphic Representations, $L$-Functions and LiftingsApr 16 2019There are many Rankin-Selberg integrals representing Langlands $L$-functions, and it is not apparent what the limits of the Rankin-Selberg method are. The Dimension Equation is an equality satisfied by many such integrals that suggests a priority for ... More
Constant mean curvature, flux conservation, and symmetryFeb 13 2013Aug 22 2014As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the topological restrictions ... More
The Calabi homomorphism, Lagrangian paths and special LagrangiansSep 21 2012Apr 19 2013Let $\OO$ be an orbit of the group of Hamiltonian symplectomorphisms acting on the space of Lagrangian submanifolds of a symplectic manifold $(X,\omega).$ We define a functional $\CC:\OO \to \R$ for each differential form $\beta$ of middle degree satisfying ... More
A comparison of score-based methods for estimating Bayesian networks using the Kullback-Leibler divergenceSep 08 2010Dec 01 2011In this paper, we compare the performance of two methods for estimating Bayesian networks from data containing exogenous variables and random effects. The first method is fully Bayesian in which a prior distribution is placed on the exogenous variables, ... More
No skew branes on non-degenerate hyperquadricsDec 09 2004We show that non-degenerate hyperquadrics in R^{n+2} admit no skew branes. Stated more traditionally, a compact codimension-one immersed submanifold of a non-degenerate hyperquadric of euclidean space must have parallel tangent spaces at two distinct ... More
MCTS Based on Simple RegretJul 23 2012UCT, a state-of-the art algorithm for Monte Carlo tree search (MCTS) in games and Markov decision processes, is based on UCB, a sampling policy for the Multi-armed Bandit problem (MAB) that minimizes the cumulative regret. However, search differs from ... More
Doing Better Than UCT: Rational Monte Carlo Sampling in TreesAug 18 2011Jul 25 2012UCT, a state-of-the art algorithm for Monte Carlo tree sampling (MCTS), is based on UCB, a sampling policy for the Multi-armed Bandit Problem (MAB) that minimizes the accumulated regret. However, MCTS differs from MAB in that only the final choice, rather ... More
Volume analysis of supercooled water under high pressureNov 04 2016Motivated by recent experimental findings on the volume of supercooled water at high pressure [O. Mishima, J. Chem. Phys. 133, 144503 (2010)] we performed atomistic molecular dynamics simulations study of bulk water in the isothermal-isobaric ensemble. ... More
The open Gromov-Witten-Welschinger theory of blowups of the projective planeOct 15 2012We compute the Welschinger invariants of blowups of the projective plane at an arbitrary conjugation invariant configuration of points. Specifically, open analogues of the WDVV equation and Kontsevich-Manin axioms lead to a recursive algorithm that reconstructs ... More
A reverse isoperimetric inequality for J-holomorphic curvesOct 15 2012Jun 12 2014We prove that the length of the boundary of a $J$-holomorphic curve with Lagrangian boundary conditions is dominated by a constant times its area. The constant depends on the symplectic form, the almost complex structure, the Lagrangian boundary conditions ... More
J-holomorphic curves with boundary in bounded geometryNov 29 2013Oct 02 2014The fundamental properties of $J$-holomorphic maps depend on two inequalities: The gradient inequality gives a pointwise bound on the differential of a $J$-holomorphic map in terms of its energy. The cylinder inequality stipulates and quantifies the exponential ... More
Compatibility conditions on local and global spectra for $n$-mode Gaussian statesDec 15 2008Compatibility conditions between the (global) spectrum of an $n$-mode Gaussian state and the spectra of the individual modes are presented, making optimal use of beam splitter and (two-mode) squeezing transformations. An unexpected bye-product of our ... More
Verifying the Congruence Conjecture for Rubin-Stark ElementsJul 10 2008The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence is predicted ... More
Locality in the Fukaya category of a hyperkähler manifoldApr 30 2018Aug 29 2018Let $(M,I,J,K,g)$ be a hyperkahler manifold. Then the complex manifold $(M,I)$ is holomorphic symplectic. We prove that for all real $x, y,$ with $x^2 + y^2 = 1$ except countably many, any finite energy $(xJ+yK)$-holomorphic curve with boundary in a collection ... More
A Riemannian Approach to Reduced Plate, Shell, and Rod TheoriesJan 17 2012Apr 19 2013We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily ... More
Formal Verification of Self-Assembling SystemsJul 21 2010This paper introduces the theory and practice of formal verification of self-assembling systems. We interpret a well-studied abstraction of nanomolecular self assembly, the Abstract Tile Assembly Model (aTAM), into Computation Tree Logic (CTL), a temporal ... More
Self-Assembling Systems are Distributed SystemsJul 06 2009Jul 20 2011In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. We show that these graph grammars can be embedded in a graph rewriting characterization of distributed systems that was proposed by ... More
Self-Assembly of a Statistically Self-Similar FractalApr 10 2009Jul 20 2011We demonstrate existence of a tile assembly system that self-assembles the statistically self-similar Sierpinski Triangle in the Winfree-Rothemund Tile Assembly Model. This appears to be the first paper that considers self-assembly of a random fractal, ... More
Topological D-branes from DescentAug 01 2008Sep 06 2010Witten couples the open topological B-model to a holomorphic vector bundle by adding to the boundary of the worldsheet a Wilson loop for an integrable connection on the bundle. Using the descent procedure for boundary vertex operators in this context, ... More
Towards a Schubert calculus for maps from a Riemann surface to a GrassmannianMar 10 1994The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in \cite{BDW}. Also, an induction on the genus is proved, which extends the results of \cite{BDW} to a computation of ... More
The Second Parameter Problem(s)Jul 22 2013The Second Parameter (2ndP) Problem recognizes the remarkable role played by horizontal branch (HB) morphology in the development of our understanding of globular clusters, and the Galaxy, over the last 50 years. I will describe the historical development ... More
Horizontal Branch Morphology and Mass Loss in Globular ClustersSep 15 2008The connection between mass loss on the red giant branch (RGB) and horizontal branch (HB) morphology in globular clusters (GCs) has long been acknowledged but the mechanisms governing mass loss remains poorly understood from a theoretical perspective. ... More
The Spin $L$-function on $\mathrm{GSp}_6$ for Siegel modular formsJun 10 2015Jun 19 2015We give a Rankin-Selberg integral representation for the Spin (degree eight) $L$-function on $\mathrm{PGSp}_6$. The integral applies to the cuspidal automorphic representations associated to Siegel modular forms. If $\pi$ corresponds to a level one Siegel ... More
Finding local community structure in networksMar 04 2005Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community ... More
Sum of squares bounds for the total ordering principleDec 04 2018In this paper, we analyze the sum of squares hierarchy (SOS) on the total ordering principle on $n$ elements. We show that degree $\tilde{O}(\sqrt{n})$ SOS can prove the total ordering principle so in this setting SOS is considerably more powerful than ... More
Syntax and Typing for Cedille CoreNov 04 2018This document specifies a core version of the type theory implemented in the Cedille tool. Cedille is a language for dependently typed programming and computer-checked proof. Cedille can elaborate source programs down to Cedille Core, which can be checked ... More
Syntax and Semantics of CedilleJun 12 2018This document presents the syntax, classification rules, realizability semantics, and soundness theorem for Cedille, an extrinsic (i.e., Curry-style) type theory extending the Calculus of Constructions, and designed for deriving of inductive datatypes, ... More
Can Computers Create Art?Jan 13 2018May 08 2018This essay discusses whether computers, using Artificial Intelligence (AI), could create art. First, the history of technologies that automated aspects of art is surveyed, including photography and animation. In each case, there were initial fears and ... More
Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebrasOct 08 2012May 29 2013The main result here is that a simple separable C*-algebra is Z-stable (where Z denotes the Jiang-Su algebra) if (i) it has finite nuclear dimension or (ii) it is approximately subhomogeneous with slow dimension growth. This generalizes the main results ... More
Regularity for stably projectionless, simple C*-algebrasOct 06 2011Jul 17 2012This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C*-algebras: (i) Jiang-Su stability, (ii) Unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case ... More
Elliptic curves with surjective adelic Galois representationsJan 16 2009Mar 14 2010We prove useful necessary and sufficient conditions for an elliptic curve over a number field to admit a surjective adelic Galois representation. Using these conditions, we compute an example of a number field K and an elliptic curve E/K whose corresponding ... More
Variations on a theme of Runge: effective determination of integral points on certain varietiesMay 09 2008We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge's theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge's theorem ... More
The Catalan simplicial set and uniform classification of monoidal-type categoriesJul 18 2015Many monoidal-type objects are known to be classified by maps from the Catalan simplicial set $\mathbb{C}$ to various nerves of categories and higher categories. There are, for example, three different nerves of the 2-category of categories $\mathsf{Cat}$ ... More
Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth SpacesJun 27 2013Mar 18 2015There are two primary goals to this paper. In the first part of the paper we study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of the manifold. In ... More
Derivatives of Parsing Expression GrammarsMay 19 2014This paper introduces a new memoized derivative parsing algorithm for recognition of parsing expression grammars. The algorithm runs in worst case quartic time and cubic space. However, existing research suggests that due to the limited amount of backtracking ... More
Differential Privacy and the Fat-Shattering Dimension of Linear QueriesApr 19 2010Jan 19 2011In this paper, we consider the task of answering linear queries under the constraint of differential privacy. This is a general and well-studied class of queries that captures other commonly studied classes, including predicate queries and histogram queries. ... More
Smoothness of stable holonomies inside center-stable manifolds and the $C^2$ hypothesis in Pugh-Shub and Ledrappier-Young theoryAug 21 2016Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for $C^{1+\beta}$ diffeomorphisms are uniformly bi-Lipschitz and in fact $C^{1+\text{H\"older}}$. This verifies that the Pugh-Shub theory for ergodicity ... More
New Lower Bound Formulas for Multicolored Ramsey NumbersJul 27 2001We give two lower bound formulas for multicolored Ramsey numbers. These formulas improve the bounds for several small multicolored Ramsey numbers.
Conjectural relations in the tautological ring of $\bar{M}_{g,n}$Jul 08 2012We describe a very large class of conjectural relations in the tautological ring of the moduli space $\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, extending and generalizing the Faber-Zagier relations. These notes are loosely based ... More
Polynomial Form of Binary Cyclotomic PolynomialsDec 01 2018This paper presents a closed form polynomial expression for the binary cyclotomic polynomial. We contrast this against expressions for binary cyclotomic polynomials in (Lam and Leung 1996) and (Lenstra 1979).
Vojta's Inequality and Rational and Integral Points of Bounded Degree on CurvesJan 27 2006Let C in C_1xC_2 be a curve of type (d_1,d_2) in the product of the two curves C_1 and C_2. Let d be a positive integer. We prove that if a certain inequality involving d_1, d_2, d, and the genera of the curves C_1, C_2, and C is satisfied, then the set ... More
Quasideterminants and q-commuting minorsFeb 21 2006We present two new proofs of the the important q-commuting property holding among certain pairs of quantum minors of an n x n q-generic matrix. The first uses elementary quasideterminantal arithmetic; the second involves paths in an edge-weighted directed ... More
A minimal even type of the 2-adic Weil representationSep 07 2012Oct 29 2013The Weil representation is used to construct a minimal type of the two-fold central extension of $\operatorname{Sp}_{2n}(\mathbb{Q}_2)$. The corresponding Hecke algebra is shown to be isomorphic to the classical affine Hecke algebra of the split adjoint ... More
One-Parameter Families of Unit EquationsJan 27 2006We study one-parameter families of S-unit equations of the form f(t)u+g(t)v=h(t), where f, g, and h are univariate polynomials over a number field, t is an S-integer, and u and v are S-units. For many possible choices of f, g, and h, we are able to determine ... More
Interpolation of Varieties of Minimal DegreeMay 05 2016Jan 26 2017It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated through points ... More
Some applications of localization to enumerative problemsJul 13 2000A simple corollary of the localization theorem (due to the author and, independently, to Lian-Liu-Yau) is applied to several problems in enumerative geometry. New formulas for Schubert calculus on flag manifolds, due to Kong, and a new reconstruction ... More
Stable pairs and log flipsJul 01 1997This paper has two parts. In the first part, we review stable pairs and triples on curves, leading up to Thaddeus' diagram of flips and contractions starting from the blow-up of projective space along a curve embedded by a complete linear series of the ... More
Abelianization of SL(2,R) local systemsOct 20 2015The "abelianization" process introduced by Gaiotto, Hollands, Moore, and Neitzke turns $\operatorname{SL}_K \mathbb{C}$ local systems on a punctured surface into $\mathbb{C}^\times$ local systems, giving coordinates on the decorated $\operatorname{SL}_K ... More
How large should whales be?Jul 05 2012Jan 10 2013The evolution and distribution of species body sizes for terrestrial mammals is well-explained by a macroevolutionary tradeoff between short-term selective advantages and long-term extinction risks from increased species body size, unfolding above the ... More
A Bethe Ansatz for Symmetric GroupsMar 02 2010We examine the commuting elements $\theta_i=\sum_{j\neq i} \frac{s_{ij}}{z_i-z_j}$, $z_i\neq z_j$, $s_{ij}$ the transposition swapping $i$ and $j$, and we study their actions on irreducible $S_n$ representations. By applying Schur-Weyl duality to the ... More
Integral points of bounded degree on affine curvesFeb 11 2014We generalize Siegel's theorem on integral points on affine curves to integral points of bounded degree, giving a complete characterization of affine curves with infinitely many integral points of degree d or less over some number field. Generalizing ... More
Rational preimages in families of dynamical systemsSep 28 2011Given a rational function of degree at least two defined over a number field k, we study the cardinality of the set of rational iterated preimages. We prove bounds for the cardinality of this set as the rational function varies in certain families. Our ... More
The Structure of E6Nov 21 2007Dec 20 2007We present the subalgebra structure of sl(3,O), a particular real form of E6 chosen for its relevance to particle physics through the connection between its associated Lie group SL(3,O) and generalized Lorentz groups. Given the complications related to ... More
Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebrasApr 18 2013Feb 22 2014We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of simple modules ... More
Zero-sum Analogues of van der Waerden's Theorem on Arithmetic ProgressionsFeb 09 2018Let $r$ and $k$ be positive integers with $r \mid k$. Denote by $w_{\mathrm{\mathfrak{z}}}(k;r)$ the minimum integer such that every coloring $\chi:[1,w_{\mathrm{\mathfrak{z}}}(k;r)] \rightarrow \{0,1,\dots,r-1\}$ admits a $k$-term arithmetic progression ... More
Zero-sum Generalized Schur NumbersFeb 09 2018Let $r$ and $k$ be positive integers with $r \mid k$. Denote by $S_{\mathrm{\mathfrak{z}}}(k;r)$ the minimum integer $n$ such that every coloring $\chi:[1,n] \rightarrow \{0,1,\dots,r-1\}$ admits a solution to $\sum_{i=1}^{k-1} x_i = x_k$ with $\sum_{i=1}^{k} ... More
The Cuntz semigroup of continuous functions into certain simple C*-algebrasJul 17 2010Dec 17 2010This paper contains computations of the Cuntz semigroup of separable C*-algebras of the form C_0(X,A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murray-von Neumann semigroups of C(K,A) ... More
The Dimensions of Integral Points and Holomorphic Curves on the Complements of HyperplanesJan 27 2006In this article we completely determine the possible dimensions of integral points and holomorphic curves on the complement of a union of hyperplanes in projective space. Our main theorems generalize a result of Evertse and Gyory, who determined when ... More
Linear forms in logarithms and integral points on higher-dimensional varietiesMar 18 2013We apply inequalities from the theory of linear forms in logarithms to deduce effective results on S-integral points on certain higher-dimensional varieties when the cardinality of S is sufficiently small. These results may be viewed as a higher-dimensional ... More
Generalizations of Siegel's and Picard's TheoremsMar 30 2005We prove new theorems which are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from $\mathbb{C}$ to affine curves. These include results on integral points over ... More
Deterministic Partially Dynamic Single Source Shortest Paths in Weighted GraphsMay 29 2017In this paper we consider the decremental single-source shortest paths (SSSP) problem, where given a graph $G$ and a source node $s$ the goal is to maintain shortest distances between $s$ and all other nodes in $G$ under a sequence of online adversarial ... More
Polynomial eigenvalue bounds from companion formsJan 15 2017Feb 21 2017We show how $\ell$-ifications, which are companion forms of matrix polynomials, namely, lower order matrix polynomials with the same eigenvalues as a given complex square matrix polynomial, can be used in combination with other recent results to produce ... More
Using symmetry to count rational curvesMar 16 2001Mar 19 2001An analogy is drawn between recent work with Kley (math.AG/0007082) and the WDVV equations. That is, both are regarded as symmetries of generating functions with coefficients that "count" rational curves on a complex projective manifold. It is shown how ... More
Another way to enumerate rational curves with torus actionsMay 25 1999Aug 25 1999A new proof of the mirror conjecture for Fano and Calabi-Yau complete intersections in P^n is given, using only the circle action on the graph space. The proof applies to projective bundles as well, with applications to "linear" relative Calabi-Yau's ... More
Quantum Schubert CalculusOct 24 1994May 29 1997This paper works out the versions of the classical Giambelli and Pieri formulas in the context of quantum cohomology of a complex Grassmannian.
The exterior square $L$-function on $\mathrm{GU}(2,2)$May 10 2015In this paper we give Rankin-Selberg integrals for the quasisplit unitary group on four variables, $\mathrm{GU}(2,2)$, and a closely-related quasisplit form of $\mathrm{GSpin}_6$. First, we give a two-variable Rankin-Selberg integral on $\mathrm{GU}(2,2)$. ... More
Blind Analysis in Particle PhysicsDec 17 2003A review of the blind analysis technique, as used in particle physics measurements, is presented. The history of blind analyses in physics is briefly discussed. Next the dangers of "experimenter's bias" and the advantages of a blind analysis are described. ... More
Zeros of random linear combinations of entire functions with complex Gaussian coefficientsMay 22 2016Aug 05 2016We study zero distribution of random linear combinations of the form $$P_n(z)=\sum_{j=0}^n\eta_jf_j(z),$$ in any Jordan region $\Omega \subset \mathbb C$. The basis functions $f_j$ are entire functions that are real-valued on the real line, and $\eta_0,\dots,\eta_n$ ... More
Limitations on Cloning in Classical MechanicsOct 28 2010Dec 28 2011In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive ... More
A Note on Amortized Space ComplexityNov 21 2016In this note, we show that while almost all functions require exponential size branching programs to compute, for all functions $f$ there is a branching program computing a large number of copies of $f$ which has linear size per copy of $f$. We then discuss ... More
Asymptotic stability of $N$-solitons in the cubic NLS equationMar 07 2016Jul 21 2016In this article we consider the Cauchy problem for the cubic focusing nonlinear Schr\"o\-dinger (NLS) equation on the line with initial datum close to a particular $N$-soliton. Using inverse scattering and the $\bar{\partial}$ method we establish the ... More
On the p-adic Second Main TheoremMar 17 2013We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections are transverse. ... More
G$_{2}$-Manifolds and M-Theory CompactificationsOct 30 2018Oct 31 2018The mathematical features of a string theory compactification determine the physics of the effective four-dimensional theory. For this reason, understanding the mathematical structure of the possible compactification spaces is of profound importance. ... More
On the Approximation Resistance of Balanced Linear Threshold FunctionsJul 12 2018Dec 13 2018In this paper, we show that there exists a balanced linear threshold function (LTF) which is unique games hard to approximate, refuting a conjecture of Austrin, Benabbas, and Magen. We also show that the almost monarchy predicate on k variables is approximable ... More
Long-time asymptotics for the Massive Thirring modelJul 02 2018We consider the massive Thirring model and establish pointwise long-time behavior of its solutions in weighted Sobolev spaces. For soliton-free initial data we can show that the solution converges to a linear solution modulo a phase correction caused ... More
The Fourier expansion of modular forms on quaternionic exceptional groupsApr 19 2018Jun 27 2018Suppose that $G$ is a simple adjoint reductive group over $\mathbf{Q}$, with an exceptional Dynkin type, and with $G(\mathbf{R})$ quaternionic (in the sense of Gross-Wallach). Then there is a notion of modular forms for $G$, anchored on the so-called ... More
An almost-linear time algorithm for uniform random spanning tree generationNov 17 2017We give an $m^{1+o(1)}\beta^{o(1)}$-time algorithm for generating a uniformly random spanning tree in an undirected, weighted graph with max-to-min weight ratio $\beta$. We also give an $m^{1+o(1)}\epsilon^{-o(1)}$-time algorithm for generating a random ... More
Unramified Godement-Jacquet theory for the spin similitude groupApr 19 2017Apr 19 2018Suppose $F$ is a non-archimedean local field. The classical Godement-Jacquet theory is that one can use Schwartz-Bruhat functions on $n \times n$ matrices $M_n(F)$ to define the local standard $L$-functions on $\mathrm{GL}_n$. The purpose of this partly ... More
On the frequency and severity of interstate warsJan 15 2019Lewis Fry Richardson argued that the frequency and severity of deadly conflicts of all kinds, from homicides to interstate wars and everything in between, followed universal statistical patterns: their frequency followed a simple Poisson arrival process ... More
A non-boundary nef divisor on $\bar{M}_{0,12}$Dec 23 2011We describe a nef divisor $D_P$ on $\bar{M}_{0,12}$ that is not numerically equivalent to an effective sum of boundary divisors.
Internally Perfect MatroidsOct 15 2015Feb 22 2016In 1977 Stanley proved that the $h$-vector of a matroid is an $\mathcal{O}$-sequence and conjectured that it is a pure $\mathcal{O}$-sequence. In the subsequent years the validity of this conjecture has been shown for a variety of classes of matroids, ... More
Eigenvalue bounds for matrix polynomials in generalized basesFeb 28 2016May 28 2016We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.
Cauchy-like and Pellet-like results for polynomialsJun 21 2015Jan 01 2016We obtain several Cauchy-like and Pellet-like results for the zeros of a general complex polynomial by considering similarity transformations of the squared companion matrix and the reformulation of the zeros of a scalar polynomial as the eigenvalues ... More
A quaternionic Saito-Kurokawa lift and cusp forms on $G_2$Apr 23 2019We consider a special theta lift $\theta(f)$ from cuspidal Siegel modular forms $f$ on $\mathrm{Sp}_4$ to "modular forms" $\theta(f)$ on $\mathrm{SO}(4,4)$. This lift can be considered an analogue of the Saito-Kurokawa lift, where now the image of the ... More
NSym into Q_{\infty} is not a Hopf MapOct 28 2004Nov 10 2004There is a natural algebra map (in fact, embedding) from the noncommutative symmetric functions NSym to the quadratic algebra Q_{\infty} of pseudoroots of polynomials. In this note, I show that it is not a coalgebra map. Hence, the Hopf algebra structure ... More
First passage time and stochastic resonance of excitable systemsSep 25 2016We study noise induced thermally activated barrier crossing of a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a spatially uniform temperature. The viscous friction is considered to decrease exponentially ... More