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Eppur si riscalda -- and yet, it (just) heats up: Further Comments on "Quantifying hot carrier and thermal contributions in plasmonic photocatalysis"Jul 10 2019Our Comment [Sivan et al., Science 2019] (as well as its longer version [Dubi, Un, & Sivan, ArXiv 2019], and the supporting theoretical studies [Dubi and Sivan, ArXiv 2018]) on recent attempts to distinguish thermal and non-thermal ("hot carrier") contributions ... More

Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller-Plesset perturbation theorySep 02 2016We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational M{\o}ller-Plesset ... More

Reduced Dimension DVR Study of cis-trans Isomerization in the S_1 State of C_2H_2Feb 22 2011Isomerization between the cis and trans conformers of the S1 state of acetylene is studied using a reduced dimension DVR calculation. Existing DVR techniques are combined with a high accuracy potential energy surface and a kinetic energy operator derived ... More

A Szemeredi-Trotter type theorem in $\mathbb{R}^4$Mar 20 2012Jul 08 2015We show that $m$ points and $n$ two-dimensional algebraic surfaces in $\mathbb{R}^4$ can have at most $O(m^{\frac{k}{2k-1}}n^{\frac{2k-2}{2k-1}}+m+n)$ incidences, provided that the algebraic surfaces behave like pseudoflats with $k$ degrees of freedom, ... More

Addenda/Corrigenda: Fixed Points and Two-cycles of the Discrete LogarithmAug 04 2002Nov 18 2002The abstract of the original paper was as follows: We explore some questions related to one of Brizolis: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? We extend this question to ask about not ... More

An n-in-a-row GameSep 23 2012The usual $n$-in-a-row game is a positional game in which two player alternately claim points in $\bb{Z}^2$ with the winner being the first player to claim $n$ consecutive points in a line. We consider a variant of the game, suggested by Croft, where ... More

Elaborating Evaluation-Order PolymorphismApr 28 2015Sep 11 2015We classify programming languages according to evaluation order: each language fixes one evaluation order as the default, making it transparent to program in that evaluation order, and troublesome to program in the other. This paper develops a type system ... More

All about the Static Fermion Bags in the Gross-Neveu ModelMay 27 2003Sep 09 2003We review in detail the construction of {\em all} stable static fermion bags in the 1+1 dimensional Gross-Neveu model with $N$ flavors of Dirac fermions, in the large $N$ limit. In addition to the well known kink and topologically trivial solitons (which ... More

Recent Results in AdS/QCDDec 29 2008AdS/QCD is an extra-dimensional approach to modeling the light hadronic resonances in QCD. AdS/QCD models are generally successful at reproducing low-energy observables with around 10-20% accuracy, depending on the details of the model. We discuss the ... More

Relativistic Viscous Hydrodynamics for High Energy Heavy Ion CollisionsJul 29 2013It has been over a decade since the first experimental data from gold nuclei collisions at the Relativistic Heavy Ion Collider suggested hydrodynamic behavior. While early ideal hydrodynamical models were surprisingly accurate in their predictions, they ... More

Boundedness of dyadic paraproducts on matrix weighted $L^p$Sep 01 2011Sep 07 2011In this paper, we show that dyadic paraproducts $\pi_b$ with $b$ in dyadic BMO are bounded on matrix weighted $L^p(W)$ if $W$ is a matrix $\text{A}_p$ weight.

Efficient characteristic refinements for finite groupsJul 05 2016Filters were introduced by J.B. Wilson in 2013 to generalize work of Lazard with associated graded Lie rings. It holds promise in improving isomorphism tests, but the formulas introduced then were impractical for computation. Here, we provide an efficient ... More

Automorphisms of small prime power groupsMay 14 2015If $f(p, n)$ is the number of pairwise nonisomorphic groups of order $p^n$, and $g(p,n)$ is the number of groups of order $p^n$ whose automorphism group is a $p$-group, then, for $n \leq 7$, we prove that the ratio $g(p,n)/f (p,n)$ is bounded away from ... More

A discretized Severi-type theorem with applications to harmonic analysisJan 16 2018Apr 24 2018In 1901, Severi proved that if $Z$ is an irreducible hypersurface in $\mathbb{P}^4(\mathbb{C})$ that contains a three dimensional set of lines, then $Z$ is either a quadratic hypersurface or a scroll of planes. We prove a discretized version of this result ... More

Counting higher order tangencies for plane curvesJul 17 2018We prove that $n$ plane algebraic curves determine $O(n^{(k+2)/(k+1)})$ points of $k$-th order tangency. This generalizes an earlier result of Ellenberg, Solymosi, and Zahl on the number of (first order) tangencies determined by $n$ plane algebraic curves. ... More

The Large-$n_f$ Limit of the Four-Loop Splitting Functions in QCDSep 01 2017These proceedings describe a computation of the large-$n_f$ terms contributing to the QCD splitting functions at the fourth order in the strong coupling constant $\alpha_s$. Using the FORCER package for the reduction of four-loop two-point Feynman integrals, ... More

Prediction in Projection: A new paradigm in delay-coordinate reconstructionMay 18 2018Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the associated theory and heuristics are overly stringent for real-world data, however, ... More

Compatible filters for isomorphism testingMay 09 2018We provide the necessary framework to use filters in computational settings, in particular for finitely generated nilpotent groups. The main motivation for this is to take advantage of the associated graded Lie ring to make computations for isomorphism ... More

Learning Product AutomataMay 08 2017In this paper we give an optimization for active learning algorithms, applicable to learning Moore machines where the output comprises several observables. These machines can be decomposed themselves by projecting on each observable, resulting in smaller ... More

Category O and sl(k) link invariantsJan 01 2007We construct a functor valued invariant of oriented tangles on certain singular blocks of category O. Parabolic subcategories of these blocks categorify tensor products of various fundamental sl(k) representations. Projective functors restricted to these ... More

A Proposed System for Covert Communication to Distant and Broad Geographical AreasAug 20 2014Aug 23 2014A covert communication system is developed that modulates Morse code characteristics and that delivers its mes- sage economically and to geographically remote areas using radio and EchoLink. Our system allows a covert message to be sent to a receiving ... More

Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete LogarithmJan 03 2004Dec 19 2004Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The author and Pieter Moree, building on work of Zhang, Cobeli, and Zaharescu, gave heuristics for estimating the number ... More

Sharp matrix weighted strong type inequalities for the dyadic square functionJan 29 2019May 07 2019In this paper we refine the recent sparse domination of the integrated $p = 2$ matrix weighted dyadic square function by T. Hytonen, S. Petermichl, and A. Volberg to prove a pointwise sparse domination of general matrix weighted dyadic square functions. ... More

A short note on higher Mordell integralsJun 13 2019In this short note we show that techniques of Bringmann, Kaszian, and Milas hold for computing the higher Mordell integrals associated to a general family of quantum modular forms of depth two and weight one.

A proof of the refined PRV conjecture via the cyclic convolution varietyApr 25 2019In this brief note we illustrate the utility of the geometric Satake correspondence by employing the cyclic convolution variety to give a simple proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture, along with Kumar's refinement. The proof involves ... More

Random Linear Extensions of GridsFeb 22 2006A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in a linear extension ... More

Distribution of Values of Real Quadratic Zeta FunctionsOct 29 2000The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli numbers, or alternatively the values of the Riemann zeta function at odd negative ... More

A note on rich lines in truly high dimensional setsMar 05 2015Dec 26 2015We modify an argument of Hablicsek and Scherr to show that if a collection of points in $\mathbb{C}^d$ spans many $r$--rich lines, then many of these lines must lie in a common $(d-1)$--flat. This is closely related to a previous result of Dvir and Gopi. ... More

How Well Does AdS/QCD Describe QCD?Aug 03 2009Aug 05 2009AdS/QCD is an extra-dimensional approach to modeling hadronic physics, motivated by the AdS/CFT correspondence in string theory. AdS/QCD models are often more accurate than would have been expected at energies below a few GeV. We address the question ... More

Throttling for Zero Forcing and VariantsJul 18 2018Sep 19 2018Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertices that are initially blue and the number of time steps needed to color ... More

Interpretation Neutrality in the Classical Domain of Quantum TheoryNov 19 2015I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the ... More

A surgery triangle for lattice cohomologyOct 05 2008Lattice cohomology, defined by N\'emethi in (arXiv:0709.0841), is an invariant of negative definite plumbed 3-manifolds which conjecturally computes the Heegaard Floer homology HF^+. We prove a surgery exact triangle for the lattice cohomology analogous ... More

Causal programming: inference with structural causal models as finding instances of a relationMay 04 2018This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$, computes a causal ... More

The Geometry of Reduction: Model Embedding, Compound Reduction, and Overlapping State Space DomainsOct 05 2018The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another, associated with ... More

A family of vector-valued quantum modular forms of depth twoOct 02 2018We introduce and investigate an infinite family of functions which are shown to have generalised quantum modular properties. We realise their "companions" in the lower half plane both as double Eichler integrals and as non-holomorphic theta functions ... More

Reduction of Maximum Entropy Models to Hidden Markov ModelsDec 12 2012We show that maximum entropy (maxent) models can be modeled with certain kinds of HMMs, allowing us to construct maxent models with hidden variables, hidden state sequences, or other characteristics. The models can be trained using the forward-backward ... More

Efficient Algorithms for Parsing the DOP ModelApr 22 1996Excellent results have been reported for Data-Oriented Parsing (DOP) of natural language texts (Bod, 1993). Unfortunately, existing algorithms are both computationally intensive and difficult to implement. Previous algorithms are expensive due to two ... More

Salem number stretch factors and totally real fields arising from Thurston's constructionNov 17 2017In 1974, Thurston proved that, up to isotopy, every automorphism of closed orientable surface is either periodic, reducible, or pseudo-Anosov. The latter case has lead to a rich theory with applications ranging from dynamical systems to low dimensional ... More

A matrix weighted $T1$ theorem for matrix kernelled CZOs and a matrix weighted John-Nirenberg theoremAug 11 2015Jul 11 2017In this paper, we will prove a matrix weighted $T1$ theorem regarding the boundedness of certain matrix kernelled CZOs on matrix weighted $L^p(W)$ for matrix A${}_p$ weights $W$. Using some of the ideas from the proof, we will also establish a natural ... More

On the universality of the probability distribution of the product $B^{-1}X$ of random matricesApr 25 2002Feb 21 2004Consider random matrices $A$, of dimension $m\times (m+n)$, drawn from an ensemble with probability density $f(\rmtr AA^\dagger)$, with $f(x)$ a given appropriate function. Break $A = (B,X)$ into an $m\times m$ block $B$ and the complementary $m\times ... More

Schatten $p$ class commutators on the weighted Bergman space $L^2_a (\mathbb{B}_n, dv_γ)$ for $\frac{2n}{n + 1 + γ} < p < \infty$Sep 05 2011Feb 28 2012Let $P_\gamma$ be the orthogonal projection from the space $L ^2 (\mathbb{B}_n, dv_\gamma)$ to the standard weighted Bergman space $L_a ^2 (\mathbb{B}_n, dv_\gamma)$. In this paper, we characterize the Schatten $p$ class membership of the commutator $[M_f, ... More

A Comparison of Cryptography CoursesJan 03 2004The author taught two courses on cryptography, one at Duke University aimed at non-mathematics majors and one at Rose-Hulman Institute of Technology aimed at mathematics and computer science majors. Both tried to incorporate technical and societal aspects ... More

Abelian varieties over finite fields with a specified characteristic polynomial modulo lOct 29 2000May 26 2001We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a rational point of ... More

On the Wolff circular maximal functionOct 25 2011Jun 07 2013We prove sharp $L^3$ bounds for a variable coefficient generalization of the Wolff circular maximal function $M^\delta f$. For each fixed radius $r$, $M^\delta f(r)$ is the maximal average of $f$ over the $\delta$--neighborhood of a circle of radius $r$ ... More

Optimizing real-time RDF data streamsNov 16 2010The Resource Description Framework (RDF) provides a common data model for the integration of "real-time" social and sensor data streams with the Web and with each other. While there exist numerous protocols and data formats for exchanging dynamic RDF ... More

Boundedness of commutators and H${}^1$-BMO duality in the two matrix weighted settingNov 09 2015Mar 17 2016In this paper we characterize the two matrix weighted boundedness of commutators with any of the Riesz transforms (when both are matrix A${}_p$ weights) in terms of a natural two matrix weighted BMO space. Furthermore, we identify this BMO space when ... More

Spectra of Random Symmetric Hypermatrices and Random HypergraphsJul 25 2015Sep 12 2015We present progress on the problem of asymptotically describing the complex homogeneous adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy to random matrix theory that connects these spectra ... More

An algorithm for low dimensional group homologyJan 18 2009Sep 30 2009Given a finitely presented group $G$, Hopf's formula expresses the second integral homology of $G$ in terms of generators and relators. We give an algorithm that exploits Hopf's formula to estimate $H_2(G;k)$, with coefficients in a finite field k, and ... More

A causation coefficient and taxonomy of correlation/causation relationshipsAug 05 2017This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and correlation ... More

Directed path-decompositionsNov 02 2017Many of the tools developed for the theory of tree-decompositions of graphs do not work for directed graphs. In this paper we show that some of the most basic tools do work in the case where the model digraph is a directed path. Using these tools we define ... More

Inter-Theory Relations in Physics: Case Studies from Quantum Mechanics and Quantum Field TheoryFeb 21 2018The relationship that is widely presumed to hold between physical theories and their successors, in which the successors in some sense explain the success of the theories they replace, is known commonly as 'reduction.' I argue that one traditional approach ... More

Breaking the 3/2 barrier for unit distances in three dimensionsJun 16 2017Dec 24 2017We prove that every set of $n$ points in $\mathbb{R}^3$ spans $O(n^{295/197+\epsilon})$ unit distances. This is an improvement over the previous bound of $O(n^{3/2})$. A key ingredient in the proof is a new result for cutting circles in $\mathbb{R}^3$ ... More

Sharp matrix weighted weak and strong type inequalities for the dyadic square functionJan 29 2019In this paper we refine the recent sparse domination of the integrated $p = 2$ matrix weighted dyadic square function by T. Hytonen, S. Petermichl, and A. Volberg to prove a pointwise sparse domination of general matrix weighted dyadic square functions. ... More

On closed 3-braids with unknotting number oneFeb 10 2009We prove that if an alternating 3-braid knot has unknotting number one, then there must exist an unknotting crossing in any alternating diagram of it, and we enumerate such knots. The argument combines the obstruction to unknotting number one developed ... More

A spanning tree model for the Heegaard Floer homology of a branched double-coverMay 09 2008Given a diagram of a link K in S^3, we write down a Heegaard diagram for the branched-double cover Sigma(K). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of the link diagram. Using this model we make some ... More

Upper bounds for the number of primitive ray class characters with conductor below a given boundJul 09 2013We present upper bounds on certain sums which are related to Artin's primitive root conjecture and are also used in counting ray class characters.

A Covert Channel Based on Web Read-time ModulationOct 07 2014Oct 08 2014A network covert channel is created that operates by modulating the time between web resource accesses, with an 'average web user' read-time used as a reference. While the covert channel may be classified as timing based, it does not operate by changing ... More

Upper bounds on the second largest prime factor of an odd perfect numberOct 28 2018Dec 14 2018Acquaah and Konyagin showed that if $N$ is an odd perfect number where $N= p_1^{a_1}p_2^{a_2} \cdots p_k^{a_k}$ where $p_1 < p_2 \cdots < p_k$ then one must have $p_k < 3^{1/3}N^{1/3}$. Using methods similar to theirs, we show that $p_{k-1}< (2N)^{1/5}$ ... More

Moufang sets of finite Morley rank of odd typeJan 09 2014We show that for a wide class of groups of finite Morley rank the presence of a split $BN$-pair of Tits rank $1$ forces the group to be of the form $\operatorname{PSL}_2$ and the $BN$-pair to be standard. Our approach is via the theory of Moufang sets. ... More

Groups of Morley rank 4Jan 10 2014Nov 25 2014We show that any simple group of Morley rank 4 must be a bad group with no proper definable subgroups of rank larger than 1. We also give an application to groups acting on sets of Morley rank 2.

Boundary slopes of some non-Montesinos knotsJan 13 2014It is shown that there exist alternating non-Montesinos knots whose essential spanning surfaces with maximal and minimal boundary slopes are not realised by the checkerboard surfaces coming from a reduced alternating planar diagram.

Parsing Algorithms and MetricsMay 30 1996Many different metrics exist for evaluating parsing results, including Viterbi, Crossing Brackets Rate, Zero Crossing Brackets Rate, and several others. However, most parsing algorithms, including the Viterbi algorithm, attempt to optimize the same metric, ... More

Compactness of operators on generalized Fock spacesDec 25 2012Jun 03 2013For a very general class of weighted Fock spaces on $\mathbb{C}^n$, we give necessary and sufficient conditions for a Toeplitz operator with a (not necessarily positive) measure symbol to be compact. Furthermore, we show that all compact operators are ... More

An All-Sky Search for Bursts of Very High Energy Gamma Rays with HAWCJan 04 2018A new ground-based wide-field extensive air shower array known as the High-Altitude Water Cherenkov (HAWC) Observatory promises a new window to monitoring the $\sim$100 GeV gamma-ray sky with the potential for detecting a high energy spectral cutoff in ... More

Results from the first one and a half years of the HAWC GRB programJan 04 2018The High-Altitude Water Cherenkov (HAWC) Observatory is a ground-based TeV gamma-ray observatory in the state of Puebla, Mexico at an altitude of 4100 m above sea level. Its $\sim$22,000 m$^2$ instrumented area, wide field of view (2 sr), and $>$95% uptime ... More

Motivic E_{infinity} algebras and the motivic dgaDec 25 2001Jul 21 2014In this paper we define an explicit E_{infinity}-structure, i.e. a coherently homotopy associative and commutative product on chain complexes defining (integral and mod-l) motivic cohomology as well as mod -l \'etale cohomology. We also discuss several ... More

First-hit analysis of algorithms for computing quadratic irregularityNov 08 2000Nov 10 2000The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli numbers, or alternatively the values of the Riemann zeta function at odd negative ... More

Throttling for Zero Forcing and VariantsJul 18 2018Mar 13 2019Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertices that are initially blue and the number of time steps needed to color ... More

Adjacency Spectra of Random and Uniform HypergraphsJul 25 2015Jan 08 2018We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra to that of the ... More

Knot Floer Filtration Classes of Topologically Slice KnotsSep 08 2013The knot Floer complex and the concordance invariant $\varepsilon$ can be used to define a filtration on the smooth concordance group. We exhibit an ordered subset of this filtration that is isomorphic to $\mathbb{N} \times \mathbb{N}$ and consists of ... More

A matrix weighted $T1$ theorem for matrix kernelled CZOs and a matrix weighted John-Nirenberg theoremAug 11 2015In this paper, we will prove a matrix weighted $T1$ theorem regarding the boundedness of certain matrix kernelled CZOs on matrix weighted $L^p(W)$ for matrix A${}_p$ weights $W$. Using some of the ideas from the proof, we will also establish a natural ... More

ArgoNeuT, a liquid argon time projection chamber in a low energy neutrino beamOct 14 2009ArgoNeuT (Argon Neutrino Test), a NSF/DOE project at Fermilab, is the first LArTPC to go in a low energy neutrino beam and just the second LArTPC to go in a neutrino beam ever. ArgoNeuT sits just upstream of the on-axis MINOS near detector in the NuMI ... More

Structure of shocks in Burgers turbulence with Lévy noise initial dataApr 20 2012Sep 27 2012We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by L\'evy noise, or equivalently when the initial potential is a two-sided L\'evy process $\psi_0$. When $\psi_0$ is abrupt in the ... More

TikZ-Feynman: Feynman diagrams with TikZJan 20 2016TikZ-Feynman is a LaTeX package allowing Feynman diagrams to be easily generated within LaTeX with minimal user instructions and without the need of external programs. It builds upon the TikZ package and leverages the graph placement algorithms from TikZ ... More

Whittemore: An embedded domain specific language for causal programmingDec 21 2018This paper introduces Whittemore, a language for causal programming. Causal programming is based on the theory of structural causal models and consists of two primary operations: identification, which finds formulas that compute causal queries, and estimation, ... More

A Module For Boosted Dark Matter Event Generation in GENIEDec 13 2018Models that produce a flux of semi-relativistic or relativistic boosted dark matter at large neutrino detectors are well-motivated extensions beyond the minimal weakly interacting massive particle (WIMP) paradigm. Current and upcoming liquid argon time ... More

Asymptotic equidistribution and convexity for Dyson partition ranksMar 14 2019We study the Dyson rank function $N(r,t;n)$, the number of partitions with rank congruent to $r$ modulo $t$. We first show that it is monotonic in $n$, and then show that it equidistributed as $n \rightarrow \infty$. Using this result we prove a conjecture ... More

Homologically thin, non-quasi-alternating linksJun 11 2009We exhibit the first examples of links which are homologically thin but not quasi-alternating. To show that they are not quasi-alternating, we argue that none of their branched double-covers bounds a negative definite 4-manifold with non-torsion H_1. ... More

Metric Limits in Categories with a FlowJan 15 2019In topological data science, categories with a flow have become ubiquitous, including as special cases examples like persistence modules and sheaves. With the flow comes an interleaving distance, which has proven useful for applications. We give simple, ... More

On the number of total prime factors of an odd perfect numberOct 31 2018Nov 06 2018Let $N$ be an odd perfect number. Let $\omega(N)$ be the number of distinct prime factors of $N$ and let $\Omega(N)$ be the total number of prime factors of $N$. We prove that if $(3,N)=1$, then $ \frac{302}{113}\omega - \frac{286}{113} \leq \Omega. $ ... More

An improvement of an inequality of Ochem and Rao concerning odd perfect numbersJun 21 2017Oct 29 2017Let $\Omega(n)$ denote the total number of prime divisors of $n$ (counting multiplicity) and let $\omega(n)$ denote the number of distinct prime divisors of $n$. Various inequalities have been proved relating $\omega(N)$ and $\Omega(N)$ when $N$ is an ... More

Classes for Fast Maximum Entropy TrainingAug 09 2001Maximum entropy models are considered by many to be one of the most promising avenues of language modeling research. Unfortunately, long training times make maximum entropy research difficult. We present a novel speedup technique: we change the form of ... More

Parsing Inside-OutMay 19 1998The inside-outside probabilities are typically used for reestimating Probabilistic Context Free Grammars (PCFGs), just as the forward-backward probabilities are typically used for reestimating HMMs. I show several novel uses, including improving parser ... More

Invertible Toeplitz products, weighted norm inequalities, and A${}_p$ weightsSep 01 2011Feb 14 2014In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted Fock space ... More

Fredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional DerivativeFeb 11 2004Mar 18 2004We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the $n$th and $n-1$th minors, whose solution is a representation of the $n$th minor as an $n\times n$ ... More

Comparison of algorithms to calculate quadratic irregularity of prime numbersOct 29 2000In previous work, the author has extended the concept of regular and irregular primes to the setting of arbitrary totally real number fields k_{0}, using the values of the zeta function \zeta_{k_{0}} at negative integers as our ``higher Bernoulli numbers''. ... More

On the saturation conjecture for $\operatorname{Spin}(2n)$Apr 24 2018Sep 11 2018In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type $D$ (the even \emph{spin} groups: Spin$(2n)$ for $n\ge 4$ an integer), extending work ... More

Longer nilpotent series for classical unipotent subgroupsOct 29 2014Apr 24 2015In studying nilpotent groups, the lower central series and other variations can be used to construct an associated $\mathbb{Z}^+$-graded Lie ring, which is a powerful method to inspect a group. Indeed, the process can be generalized substantially by introducing ... More

A Note on Combinatorial DerivationOct 29 2012Sep 29 2014Given an infinite group $G$ and a subset $A$ of $G$ we let $\Delta(A) = {g \in G : |gA \cap A| =\infty}$ (this is sometimes called the combinatorial derivation of $A$). A subset $A$ of $G$ is called large if there exists a finite subset $F$ of $G$ such ... More

An improved bound on the number of point-surface incidences in three dimensionsApr 26 2011Sep 03 2012We show that $m$ points and $n$ smooth algebraic surfaces of bounded degree in $\mathbb{R}^3$ satisfying suitable nondegeneracy conditions can have at most $O(m^{\frac{2k}{3k-1}}n^{\frac{3k-3}{3k-1}}+m+n)$ incidences, provided that any collection of $k$ ... More

Gorenstein and Totally Reflexive OrdersApr 06 2016Apr 25 2016In this paper we study orders over Cohen-Macaulay rings. We discuss desirable properties for these orders if they are to represent NCCRs of the base rings. While some definitions have been made, we discuss an alternate definition and the non-existence ... More

An Introduction to Holographic QCD for NonspecialistsJul 18 2014Holographic QCD is an extra-dimensional approach to modeling hadrons, the bound states of the strong interactions. In holographic models, the extra spatial dimension creates a waveguide for fields, and the discrete towers of modes propagating in that ... More

Easy Monotonic Policy IterationFeb 29 2016A key problem in reinforcement learning for control with general function approximators (such as deep neural networks and other nonlinear functions) is that, for many algorithms employed in practice, updates to the policy or $Q$-function may fail to improve ... More

"'Formal' vs. 'Empirical' Approaches to Quantum-Classical Reduction"Nov 19 2015I distinguish two types of reduction within the context of quantum-classical relations, which I designate "formal" and "empirical". Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore ... More

The image of a tropical linear spaceAug 06 2018Given a tropical linear space $L \subseteq \mathbb{T}^n$ and a matrix $A \in \mathbb{T}^{m \times n}$, the image $AL$ of $L$ under $A$ is typically not a tropical linear space. We introduce a tropical linear space $\mathrm{tropim}_A(L)$, the tropical ... More

Stochastic Emergent Quantum GravityJul 18 2018We present a stochastic framework for emergent quantum gravity coupled to matter. The Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a clock relative to which dynamics may be defined, and other degrees of freedom ... More

Efficient Monte Carlo Integration Using Boosted Decision Trees and Generative Deep Neural NetworksJun 30 2017New machine learning based algorithms have been developed and tested for Monte Carlo integration based on generative Boosted Decision Trees and Deep Neural Networks. Both of these algorithms exhibit substantial improvements compared to existing algorithms ... More

Distributed Differential Privacy By SamplingJun 14 2017In this paper, we describe our approach to achieve distributed differential privacy by sampling alone. Our mechanism works in the semi-honest setting (honest-but-curious whereby aggregators attempt to peek at the data though follow the protocol). We show ... More

Rotational Period Measurement of Planet Host HD 147379Jan 05 2018The star HD 147379 was recently announced as a host of a low-mass exoplanet by Reiners et al. (2017). That announcement included a discussion of the possible detection of a periodic signal in the radial velocity observations around 21.1 days, which was ... More

Some Basic Radio System OPSEC ConsiderationsAug 03 2014This is an unscientific introduction to basic radio frequency system OPSEC aspects that I have found to be overlooked and lacking in high security system deployments that may have benefited from them.