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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

A Simple Condition for Bounded DisplacementNov 07 2011Jul 11 2016We study separated nets that correspond to substitution tilings of the Euclidean space. We give a simple condition, in terms of the eigenvalues and eigenspaces of the substitution matrix, to know whether the separated net is a bounded displacement of ... 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

Optical Generation of Excitonic Valley Coherence in Monolayer WSe2Mar 21 2013Due to degeneracies arising from crystal symmetries, it is possible for electron states at band edges ("valleys") to have additional spin-like quantum numbers. An important question is whether coherent manipulation can be performed on such valley pseudospins, ... More

A note on Dickson polynomials of the third kind and Legendre functionsApr 16 2016Apr 14 2019In this paper, we show that the Dickson polynomials of the third kind satisfy a nonhomogeneous second order linear ordinary differential equation whose general solution contains Legendre functions.

Wasserstein Coresets for Lipschitz CostsMay 18 2018Sparsification is becoming more and more relevant with the proliferation of huge data sets. Coresets are a principled way to construct representative weighted subsets of a data set that have matching performance with the full data set for specific problems. ... 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

Quasiperiodic infinite words : multi-scale case and dynamical propertiesMar 14 2006An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not sufficient to imply ... More

Incidences between points and lines on two- and three-dimensional varietiesSep 28 2016Let $P$ be a set of $m$ points and $L$ a set of $n$ lines in $\mathbb R^4$, such that the points of $P$ lie on an algebraic three-dimensional surface of degree $D$ that does not contain hyperplane or quadric components, and no 2-flat contains more than ... 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

Efficient collinear third-harmonic generation in a single two-dimensional nonlinear photonic crystalSep 03 2003We propose novel multi-phase-matched process that starts with generation of a pair of symmetric second-harmonic waves. Each of them interacts again with the fundamental wave to produce two constructively interfering third harmonic waves collinear to the ... 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

Can quantum wormholes set $Lam$ 0Apr 08 1993We find the quantum analogues of Carlini-Mijic wormholes and consider their application to the cosmological constant problem. In a simple model with $\Lambda$ only we differ with the results of Strominger.

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

Cohomology Groups of Deformations of Line Bundles on Complex ToriAug 12 2009Aug 29 2009The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations ... 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

Deep Closest Point: Learning Representations for Point Cloud RegistrationMay 08 2019Point cloud registration is a key problem for computer vision applied to robotics, medical imaging, and other applications. This problem involves finding a rigid transformation from one point cloud into another so that they align. Iterative Closest Point ... More

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

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

Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by σ = (1 2 ... n) and τ = (1 2)Jul 09 2013Jul 06 2017The symmetric group is generated by {\sigma} = (1 2 ... n) and {\tau} = (1 2). We answer an open problem of Nijenhuis and Wilf by constructing a Hamilton path in the directed Cayley graph for all n, and a Hamilton cycle for odd n.

Aesthetics of Neural Network ArtMar 13 2019This paper proposes a way to understand neural network artworks as juxtapositions of natural image cues. It is hypothesized that images with unusual combinations of realistic visual cues are interesting, and, neural models trained to model natural images ... More

Simplified Parsing Expression DerivativesAug 27 2018This paper presents a new derivative parsing algorithm for parsing expression grammars; this new algorithm is both simpler and faster than the existing parsing expression derivative algorithm presented by Moss. This new algorithm improves on the worst-case ... More

Lecture Notes on Rectifiable Reifenberg for MeasuresDec 18 2018These series of notes serve as an introduction to some of both the classical and modern techniques in Reifenberg theory. At its heart, Reifenberg theory is about studying general sets or measures which can be, in one sense or another, approximated on ... More

Generalized boundary strata classesApr 16 2018We describe a generalization of the usual boundary strata classes in the Chow ring of $\overline{\mathcal{M}}_{g,n}$. The generalized boundary strata classes additively span a subring of the tautological ring. We describe a multiplication law satisfied ... More

On the Curved Geometry of Accelerated OptimizationDec 11 2018In this work we propose a differential geometric motivation for Nesterov's accelerated gradient method (AGM) for strongly-convex problems. By considering the optimization procedure as occurring on a Riemannian manifold with a natural structure, The AGM ... More

Pain and Spontaneous ThoughtApr 10 2017Pain is among the most salient of experiences while also, curiously, being among the most malleable. A large body of research has revealed that a multitude of explicit strategies can be used to effectively alter the attention-demanding quality of acute ... 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

Global existence for the derivative NLS equation in the presence of solitonsMar 31 2017Aug 05 2017We prove the existence of global solutions to the DNLS equation with initial data in a large subset of $H^2(\mathbb R)\cap H^{1,1}(\mathbb R)$ containing a neighborhood of all solitons. We use the inverse scattering transform method, which was recently ... More

Sum of squares lower bounds from symmetry and a good storyNov 30 2017Dec 14 2018In this paper, we develop machinery which makes it much easier to prove sum of squares lower bounds when the problem is symmetric under permutations of $[1,n]$ and the unsatisfiability of our problem comes from integrality arguments, i.e. arguments that ... 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

Exciton Dissociation and Charge Separation at Donor-Acceptor Interfaces from Quantum-Classical Dynamics SimulationsJun 03 2019In organic photovoltaic (OPV) systems, exciton dissociation and ultrafast charge separation at donor-acceptor heterojunctions both play a key role in controlling the efficiency of the conversion of excitation energy into free charge carriers. In this ... More

Implications of the Higgs Boson and the LHC for the MSSMMar 05 2013These lectures were presented at the TASI 2012 summer school to a mixture of graduate students in particle theory and cosmology. They serve as an elementary introduction to the Minimal Supersymmetric Standard Model (MSSM) and discuss the implications ... 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

Difference Ramsey Numbers and Issai NumbersApr 05 1999We present a recursive algorithm for finding good lower bounds for the classical Ramsey numbers. Using notions from this algorithm we then give some results for generalized Schur numbers, which we call Issai numbers.

Permutations Containing and Avoiding 123 and 132 PatternsMar 29 1999We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern equals (n-2)2^(n-3). We then give a bijection onto the set of permutations which avoid 123-patterns and have exactly one 132-pattern. Finally, we show that ... 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

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

Equilateral sets in the $\ell_1$ sum of Euclidean spacesNov 12 2018Let $E^n$ denote the (real) $n$-dimensional Euclidean space. It is not known whether an equilateral set in the $\ell_1$ sum of $E^a$ and $E^b$, denoted here as $E^a \oplus_1 E^b$, has maximum size at least $\dim(E^a \oplus_1 E^b) + 1 = a + b + 1$ for ... More

Proof of Stasinski and Voll's Hyperoctahedral Group ConjectureAug 29 2014Apr 16 2018In a recent paper, Stasinski and Voll introduced a length-like statistic on hyperoctahedral groups and conjectured a product formula for this statistic's signed distribution over arbitrary quotients. Stasinski and Voll proved this conjecture for a few ... 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

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

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

A unifying framework for generalizations of the Enestrom-Kakeya theoremNov 27 2017Feb 04 2018The classical Enestrom-Kakeya theorem establishes upper and lower bounds on the zeros of a polynomial with positive coefficients that are explicit functions of those coefficients. We establish a unifying framework that incorporates this theorem and several ... 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

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

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

Facial structure of the cone of nonnegative ternary quarticsOct 24 2011In this work we will discuss the facial structure of the cone of nonnegative ternary quartics with real coefficients. We will establish an equivalence relation on the set of all faces, which preserves certain properties like dimension or the number of ... 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

A measure of quantum correlations that lies between entanglement and discordOct 30 2018When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally ... 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).

Dark Matter in the Finely Tuned Minimal Supersymmetric Standard ModelJun 13 2004Jul 08 2004We explore dark matter in the Finely Tuned Minimal Supersymmetric Standard model recently proposed by Arkani-Hamed and Dimopoulos. Relative to the MSSM, there are fewer particles at freeze-out, so the calculation of the relic abundance simplifies. Similarly, ... 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.

Quantum- and Quasi-Plucker CoordinatesJun 03 2004Jan 04 2006We demonstrate a passage from the "quasi-Plucker coordinates" of Gelfand and Retakh, to the quantum Plucker coordinates built from q-generic matrices. In the process, we rediscover the defining relations of the quantum Grassmannian of Taft and Towber ... More

Ideal class groups and torsion in Picard groups of varietiesMay 09 2008We give a new general technique for constructing and counting number fields with an ideal class group of nontrivial m-rank. Our results can be viewed as providing a way of specializing the Picard group of a variety V over $\mathbb{Q}$ to obtain class ... 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

Superalgebra in Characteristic 2Apr 03 2018Following the work of Siddharth Venkatesh, we study the category $\textbf{sVec}_2$. This category is a proposed candidate for the category of supervector spaces over fields of characteristic $2$ (as the ordinary notion of a supervector space does not ... More

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

K-theoretic characterization of C*-algebras with approximately inner flipMay 04 2015May 13 2015It is determined exactly which classifiable C*-algebras have approximately inner flip. The answer includes a number of C*-algebras with torsion in their K-theory, and a number of C*-algebras that are self-absorbing but not strongly self-absorbing.

Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by σ = (1 2 ... n) and τ = (1 2)Jul 09 2013Oct 27 2013The symmetric group is generated by {\sigma} = (1 2 ... n) and {\tau} = (1 2). We answer an open problem of Nijenhuis and Wilf by constructing a Hamilton path in the directed Cayley graph for all n, and a Hamilton cycle for odd n.

Analytical formulations of Peer-to-Peer Connection EfficiencyFeb 13 2003Use of Peer-to-Peer (P2P) service networks introduces a new communication paradigm because peers are both clients and servers and so each peer may provide/request services to/from other peers. Empirical studies of P2P networks have been undertaken and ... 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

Ordinal Conditional Functions for Nearly Counterfactual RevisionMar 31 2016We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in this context ... 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 Time Lower Bound for Multiple Nucleation on a SurfaceFeb 14 2009Aug 04 2009Majumder, Reif and Sahu have presented a stochastic model of reversible, error-permitting, two-dimensional tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time. One open question ... More

Self-Assembly as Graph Grammar as Distributed SystemFeb 14 2009Jul 20 2011In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. It turns out that these graph grammars are a "dual notion" of a graph rewriting characterization of distributed systems that was proposed ... 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

ALPSII Status ReportJun 21 2019ALPS II is a light shining through a wall style experiment that will use optical cavities to resonantly enhance the coupling between photons and axion-like particles in the mass range below 0.1 meV. In the last year there has been significant experimental ... More

Flag varieties for the Yangian Y(gl_n)Jan 04 2006We show that the Yangian Yn over gl_n possesses some features of the ring of regular functions on GL_n. In particular, we use the theory of quasideterminants to construct noncommutative flags associated to Yn. In so doing, a class of comodule algebras ... More

Search for Dilepton Resonances with the ATLAS Detector and Run 2 DataJun 19 2019A search for resonances in the dielectron and dimuon mass spectra from 250 GeV to 6 TeV is presented. The data were recorded during Run 2 of the LHC by the ATLAS experiment using proton-proton ($pp$) collisions with a center-of-mass energy of $\sqrt{s} ... More

Implementation of Pellet's theoremOct 08 2012Pellet's theorem determines when the zeros of a polynomial can be separated into two regions, based on the presence or absence of positive roots of an auxiliary polynomial, but does not provide a method to verify its conditions or to compute the roots ... More

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 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.

A Programming Language Oriented Approach to ComputabilityFeb 10 2014The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's (aspiring) computer ... More

MESA Isochrones and Stellar Tracks (MIST) 0: Methods for the construction of stellar isochronesJan 20 2016I describe a method to transform a set of stellar evolution tracks onto a uniform basis and then interpolate within that basis to construct stellar isochrones. The method accommodates a broad range of stellar types, from substellar objects to high-mass ... More

An Application of a Log Version of the Kodaira Vanishing Theorem to Embedded Projective VarietiesJul 01 1997Given an embedded smooth projective variety Y in CP^n, we show how the existence of a hypersurface with high multiplicity along Y, but of relatively low degree and log canonical near Y implies vanishing of higher cohomology for certain twists of powers ... More

Comment on Yu et al., "High Quality Binary Protein Interaction Map of the Yeast Interactome Network." Science 322, 104 (2008)Jan 05 2009We test the claim by Yu et al. -- presented in Science 322, 104 (2008) -- that the degree distribution of the yeast (Saccharomyces cerevisiae) protein-interaction network is best approximated by a power law. Yu et al. consider three versions of this network. ... More

Distributions of $n$th Powers in Finite FieldsOct 25 2016In this paper, we first find the distribution of nth power residues modulo a prime $p$ by analyzing sums involving Dirichlet characters. We then extend this method to characterize the distribution of powers in arbitrary finite fields.

New Results From BABARDec 15 2001The BABAR experiment at the PEP-II asymmetric B factory at SLAC has collected a large sample of data at the $\Upsilon(4S)$ resonance. I will summarize BABAR's new results on CP violation, B mixing and lifetimes, and a selection of rare B decays. In particular, ... More

Memory Consistency Conditions for Self-Assembly ProgrammingSep 15 2009Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correction. We address both questions, by reducing ... More

Distributed Agreement in Tile Self-AssemblyFeb 20 2009Jul 16 2010Laboratory investigations have shown that a formal theory of fault-tolerance will be essential to harness nanoscale self-assembly as a medium of computation. Several researchers have voiced an intuition that self-assembly phenomena are related to the ... More

A Note on Support in Triangulated CategoriesApr 24 2008In this note, I define a notion of a compactly supported object in a triangulated category. I prove a number of propositions relating this to traditional notions of support and give an application to the theory of derived Morita equivalence. I also discuss ... More