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Standardized drought indices: A novel uni- and multivariate approachAug 26 2015As drought is among the natural hazards which affects people and economies worldwide and often results in huge monetary losses sophisticated methods for drought monitoring and decision making are needed. Several different approaches to quantify drought ... More

Modelling extremes using approximate Bayesian ComputationNov 05 2014By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With a focus on ... More

Recurrent Dropout without Memory LossMar 16 2016Aug 05 2016This paper presents a novel approach to recurrent neural network (RNN) regularization. Differently from the widely adopted dropout method, which is applied to \textit{forward} connections of feed-forward architectures or RNNs, we propose to drop neurons ... More

R-vine Models for Spatial Time Series with an Application to Daily Mean TemperatureMar 14 2014We introduce an extension of R-vine copula models for the purpose of spatial dependency modeling and model based prediction at unobserved locations. The newly derived spatial R-vine model combines the flexibility of vine copulas with the classical geostatistical ... More

Autoconvolution for Unsupervised Feature LearningJun 02 2016In visual recognition tasks, supervised learning shows excellent performance. On the other hand, unsupervised learning exploits cheap unlabeled data and can help to solve the same tasks more efficiently. We show that the recursive autoconvolutional operator, ... More

Spatial composite likelihood inference using local C-vinesJul 03 2014We present a vine copula based composite likelihood approach to model spatial dependencies, which allows to perform prediction at arbitrary locations. This approach combines established methods to model (spatial) dependencies. On the one hand the geostatistical ... More

Asymptotically hyperbolic normalized Ricci flow and rotational symmetryJun 22 2015Sep 27 2016We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time ... More

Asymptotically hyperbolic normalized Ricci flow and rotational symmetryJun 22 2015Dec 05 2018We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time ... More

Pricing Weather Derivatives for Extreme EventsSep 19 2011We consider pricing weather derivatives for use as protection against weather extremes. The method described utilizes results from spatial statistics and extreme value theory to first model extremes in the weather as a max-stable process, and then use ... More

Approximate Bayesian Computing for Spatial ExtremesSep 19 2011Dec 13 2011Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this ... More

Recursive Autoconvolution for Unsupervised Learning of Convolutional Neural NetworksJun 02 2016Mar 26 2017In visual recognition tasks, such as image classification, unsupervised learning exploits cheap unlabeled data and can help to solve these tasks more efficiently. We show that the recursive autoconvolution operator, adopted from physics, boosts existing ... More

A novel variable-distance antenna test range and high spatial resolution corroboration of the inverse square law for 433.5 MHz radiationAug 23 2015Oct 28 2015A novel, low-budget, open-air, slant-geometry antenna test range for UHF radiation is presented. It was designed primarily to facilitate variation of the distance between emitter and receiver antennas, but has also the potential for adaptation to simultaneous ... More

Time Evolution of Entropy in Gravitational CollapseNov 05 2008Apr 29 2009We study the time evolution of the entropy of a collapsing spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. domain wall and radiation) and induced radiation alone during the ... More

Galilean-Invariant XEFTMar 16 2015XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly ... More

On three third order mock theta functions and Hecke-type double sumsAug 07 2012We obtain four Hecke-type double sums for three of Ramanujan's third order mock theta functions. We discuss how these four are related to the new mock theta functions of Andrews' work on $q$-orthogonal polynomials and Bringmann, Hikami, and Lovejoy's ... More

Combinatorial methods of character enumeration for the unitriangular groupDec 10 2010Jul 22 2011Let $\UT_n(q)$ denote the group of unipotent $n\times n$ upper triangular matrices over a field with $q$ elements. The degrees of the complex irreducible characters of $\UT_n(q)$ are precisely the integers $q^e$ with $0\leq e\leq \lfloor \frac{n}{2} \rfloor ... More

Laboratory Experiments on Wave TurbulenceJan 05 2010This review paper is devoted to a presentation of recent progress in wave turbulence. I first present the context and state of the art of this field of research both experimentally and theoretically. I then focus on the case of wave turbulence on the ... More

Bacterial hydrodynamicsSep 07 2015Bacteria predate plants and animals by billions of years. Today, they are the world's smallest cells yet they represent the bulk of the world's biomass, and the main reservoir of nutrients for higher organisms. Most bacteria can move on their own, and ... More

Life around the scallop theoremNov 12 2010Locomotion on small scales is dominated by the effects of viscous forces and, as a result, is subject to strong physical and mathematical constraints. Following Purcell's statement of the scallop theorem which delimitates the types of swimmer designs ... More

Life at high Deborah numberApr 28 2009In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by ... More

Mathematical Properties of Dynamic Systems and the Foundations of Quantum TheoryJun 11 2011Oct 18 2016While it is widely acknowledged that quantum theory is strange, and that the world view it implies is elusive, there is considerably less consensus as to why this is the case. This article will explore the possibility that the theory is opaque because ... More

Relating F-Signature and F-Splitting Ratio of Pairs Using Left-DerivativesJun 19 2012Nov 27 2012We first relate an approximate $n^{th}$-order left derivative of $s(R, f^t)$ at the F-pure threshold $c$ to the F-splitting ratio $r_F(R, f^c)$. Next, we apply the methods developed by Monsky and Teixeira in their investigation of syzygy gaps and $p$-fractals ... More

Upper oriented chromatic number of undirected graphs and oriented colorings of product graphsMay 17 2010The oriented chromatic number of an oriented graph $\vec G$ is the minimum order of an oriented graph $\vev H$ such that $\vec G$ admits a homomorphism to $\vev H$. The oriented chromatic number of an undirected graph $G$ is then the greatest oriented ... More

On-off intermittency over an extended range of control parameterDec 01 2011Apr 23 2012We propose a simple phenomenological model exhibiting on-off intermittency over an extended range of control parameter. We find that the distribution of the 'off' periods has as a power-law tail with an exponent varying continuously between -1 and -2, ... More

Real space analysis of inherent structuresOct 21 2004Jul 26 2005We study a generalization of the one-dimensional disordered Potts model, which exhibits glassy properties at low temperature. The real space properties of inherent structures visited dynamically are analyzed through a decomposition into domains over which ... More

An exactly solvable dissipative transport modelSep 28 2005Feb 01 2006We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, ... More

Inner density waves: The need for two-dimensional spectroscopyFeb 28 2002In this paper, I emphasize the need for integral field spectroscopy in the study of density waves (bars, spirals, m=1 modes) in the centre of galaxies. I illustrate this by focusing on the complex and time dependent structures revealed by such techniques. ... More

Is the black hole in NGC1277 really over-massive?May 15 2013A claim has been made by van den Bosch et al. (2012) that NGC1277 hosts an over-massive BH with a mass larger than half its spheroid mass. We revisit this claim by examining the predictions from dynamical realisations based on new MGE models of NGC1277. ... More

Extragalactic science at very high spectral resolutionSep 27 2004I briefly mention a few possible applications of very high spectral resolution spectroscopy with CRIRES to the study of nearby galaxies. This includes the fields of AGN, dynamically cold systems, super stellar and emission line clusters, and a more speculative ... More

The Formation of Massive Stars by Accretion Through Trapped Hypercompact HII RegionsSep 04 2003Jul 29 2004The formation of massive stars may take place at relatively low accretion rates over a long period of time if the accretion can continue past the onset of core hydrogen ignition. The accretion may continue despite the formation of an ionized HII region ... More

Hierarchical configurations for cross-correlation interferometers with many elementsSep 04 2012Array configurations built on a hierarchy of simple elements have excellent properties for cross-correlation imaging interferometers including a smooth distribution of measured Fourier components, high angular resolution, low side lobes, and compact array ... More

Quotient Stacks and String OrbifoldsMar 01 2001Oct 15 2001In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather are literally ... More

Sudakov Effects in Higgs Production at the LHCMay 21 1997We discuss the resummation of Sudakov effects in a cross section from the viewpoint of its underlying factorization near the edge of phase space. We perform the resummation of Sudakov threshold logarithms in Higgs (Standard Model and Minimal Supersymmetric ... More

On Programs and GenomesOct 24 2011We outline the global control architecture of genomes. A theory of genomic control information is presented. The concept of a developmental control network called a cene (for control gene) is introduced. We distinguish parts-genes from control genes or ... More

Binary Disruption by Massive Black Holes in Globular ClustersJan 16 2005Mar 21 2005A massive (~10^2-10^4 Msun) black hole at the center of a globular cluster will tidally disrupt binaries that pass sufficiently close. Such an encounter results in the capture of one binary component by the black hole and ejection of the other star. A ... More

Detectability of Planck-Scale-Induced Blurring with Gamma-Ray BurstsJan 15 2015Microscopic fluctuations inherent to the fuzziness of spacetime at the Planck scale might accumulate in wavefronts propagating a cosmological distance and lead to noticeable blurring in an image of a pointlike source. Distant quasars viewed in the optical ... More

Are High-Redshift Quasars Blurry?Oct 13 2006It has been suggested that the fuzzy nature of spacetime at the Planck scale may cause lightwaves to lose phase coherence, and if severe enough this could blur images of distant point-like sources sufficiently that they do not form an Airy pattern at ... More

Deeply virtual Compton scattering off nucleiSep 16 2008Sep 24 2008Deeply virtual Compton scattering (DVCS) is the golden exclusive channel for the study of the partonic structure of hadrons, within the universal framework of generalized parton distributions (GPDs). This paper presents the aim and general ideas of the ... More

Fundamental Groups of Random Clique ComplexesJul 20 2012Feb 18 2013Clique complexes of Erd\H{o}s-R\'{e}nyi random graphs with edge probability between $n^{-{1\over 3}}$ and $n^{-{1\over 2}}$ are shown to be aas not simply connected. This entails showing that a connected two dimensional simplicial complex for which every ... More

Weak amenability is stable under graph productsNov 15 2015Apr 05 2016Weak amenability of discrete groups was introduced by Haagerup and co-authors in the 1980's. It is an approximation property known to be stable under direct products and free products. In this paper we show that graph products of weakly amenable discrete ... More

On the degree-wise coherence of FI_G-modulesJun 14 2016In this work we study a kind of coherence condition on FI_G-modules, which generalizes the usual notion of finite generation. We prove that a module is coherent, in the appropriate sense, if and only if its generators, as well as its torsion, appears ... More

Uniform Transformation of Non-Separable Probability DistributionsAug 16 2016A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher dimensions, or non-separable ... More

A Tale of Two Turing MachinesOct 28 2016Two Turing Machines may be able to answer questions about each other that they cannot answer about themselves.

Olivier Chesneau's work on low mass starsDec 09 2015During his too short career, Olivier Chesneau pioneered the study of the circumstellar environments of low mass evolved stars using very high angular resolution techniques. He applied state of the art high angular resolution techniques, such as optical ... More

Classical and Quantum Equations of Motion of an n-dimesional BTZ Black HoleOct 17 2015We investigate the gravitational collapse of a non-rotating $n$-dimensional BTZ black hole in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass of a "spherically" symmetric domain wall, ... More

Mathematical Properties of Dynamic Systems and the Foundations of Quantum TheoryJun 11 2011Nov 04 2016While it is widely acknowledged that quantum theory is strange, and that the world view it implies is elusive, there is considerably less consensus as to why this is the case. This article will explore the possibility that the theory is opaque because ... More

Hörmander's solution of the $\bar\partial$ -equation with compact supportApr 16 2016This work is a complement of the study on H\"ormander's solution of the $\bar\partial$ equation initialised by H. Hedenmalm. Let $\varphi$ be a strictly plurisubharmonic function of class C 2 in C n, let $c_\varphi(z)$ be the smallest eigenvalue of $i\partial\bar\partial\varphi$ ... More

On the $L^{r}$ Hodge theory in complete non compact riemannian manifoldsJun 27 2015Sep 13 2016We study solutions for the Hodge laplace equation $\Delta u=\omega $ on $p$ forms with $\displaystyle L^{r}$ estimates for $r>1$. Our main hypothesis is that $\Delta $ has a spectral gap in $\displaystyle L^{2}.$ We use this to get {\sl non classical} ... More

Local Borcherds Products for Unitary GroupsMay 06 2016For a discrete subgroup of an indefinite unitary group $U(1,n+1)$, $n\geq 1$, consider the attached modular variety. Using local Borcherds products, we study Heegner divisors in the local Picard group over a boundary component of a compactification of ... More

Strong forms of self-duality for Hopf monoids in speciesDec 17 2013Nov 20 2015A vector species is a functor from the category of finite sets with bijections to vector spaces (over a fixed field); informally, one can view this as a sequence of $S_n$-modules. A Hopf monoid (in the category of vector species) consists of a vector ... More

Local density of states of the one-dimensional spinless fermion modelNov 28 2011Jan 12 2012We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbor hopping t>0 and interaction V in its Luttinger liquid phase -2t < V <= 2t. The bulk density of states and the local density of states ... More

Constructing Reducible Brill-Noether CurvesMar 07 2016Apr 15 2016It was recently determined exactly through how many general points a nondegenerate curve with nonspecial hyperplane section can pass. This gives rise to a method of constructing reducible curves $C_1 \cup_\Gamma C_2 \to \mathbb{P}^r$ with general nodes: ... More

Nanomaterials : a review of the definitions, applications, health effects. How to implement secure development Nanomatériaux : une revue des définitions, des applications, des effets sanitaires et des moyens à mettre en oeuvre pour un développement sécurisé ... MoreJun 11 2011Nanomaterials are an active area of research but also an economic sector in full expansion which addresses many applications domains. For instance, french production for the most common nanomaterials (such as silica, titanium dioxide, carbon black) is ... More

Constructing Reducible Brill--Noether CurvesMar 07 2016Sep 18 2018It was recently determined exactly through how many general points a nondegenerate curve with nonspecial hyperplane section can pass. This gives rise to a method of constructing reducible curves $C_1 \cup_\Gamma C_2 \to \mathbb{P}^r$ with general nodes: ... More

Astronomy from Coast to Coast to CoastJan 08 2018Canada is a triangle-shaped country, roughly speaking. We all know that the Atlantic Ocean is at its eastern corner in the Maritimes, and off the west coast of British Columbia is the Pacific Ocean. The Arctic Ocean, however, makes up the bulk of Canada's ... More

Living with technologyMar 12 2018Our use of IT has, broadly speaking, until recently evolved around work-oriented tasks. This is or, indeed, has been changing. IT has moved beyond the workplace and into leisure, entertainment, games and our homes. It has in short moved into our everyday ... More

Critère pour l'intégralité des coefficients de Taylor des applications miroirDec 18 2009We give a necessary and sufficient condition for the integrality of the Taylor coefficients of mirror maps at the origin. By mirror maps, we mean formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are particular solutions of certain ... More

A Division Algorithm Approach to $p$-Adic Sylvester ExpansionsAug 06 2015A method of constructing finite $p$-adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci-Sylvester (greedy) algorithm by iterating a $p$-adic division algorithm. The method extends to irrational $p$-adics ... More

Computing a Data DividendMay 06 2019Jun 27 2019Quality data is a fundamental contributor to success in statistics and machine learning. If a statistical assessment or machine learning leads to decisions that create value, data contributors may want a share of that value. This paper presents methods ... More

BSEA-1 - A Stream Cipher Backdooring TechniqueMar 26 2019Recent years have shown that more than ever governments and intelligence agencies try to control and bypass the cryptographic means used for the protection of data. Backdooring encryption algorithms is considered as the best way to enforce cryptographic ... More

Probability of Error for Detecting a Change in a Parameter, Total Variation of the Posterior Distribution, and Bayesian Fisher InformationJan 31 2019The van Trees inequality relates the Ensemble Mean Squared Error of an estimator to a Bayesian version of the Fisher Information. The Ziv-Zakai inequality relates the Ensemble Mean Squared Error of an estimator to the Minimum Probability of Error for ... More

A symplectic refinement of shifted Hecke insertionJan 21 2019Mar 20 2019Buch, Kresch, Shimozono, Tamvakis, and Yong defined Hecke insertion to formulate a combinatorial rule for the expansion of the stable Grothendieck polynomials $G_\pi$ indexed by permutations in the basis of stable Grothendieck polynomials $G_\lambda$ ... More

Representation of signals as series of orthogonal functionsNov 18 2018This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for 2D signals. ... More

Trend without hiccups: a Kalman filter approachJul 13 2018Have you ever felt miserable because of a sudden whipsaw in the price that triggered an unfortunate trade? In an attempt to remove this noise, technical analysts have used various types of moving averages (simple, exponential, adaptive one or using Nyquist ... More

Coordinates of R[x,y]: Constructions and classificationsJun 26 2012Let R be a PID. We construct and classify all coordinates of R[x,y] of the form p_2y+Q_2(p_1x+Q_1(y)) with p_1 and p_2 in qt(R) and Q_1 and Q_2 in qt(R)[y]. From this construction (with R=K[z]) we obtain non tame automorphisms s of K[x,y,z] (where K is ... More

A differential Chevalley theoremOct 30 2008We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a differential scheme under ... More

Ramanujan's radial limits and mixed mock modular bilateral $q$-hypergeometric seriesSep 17 2013Jun 20 2014Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsom, Ono, and Rhoades for mock theta functions. Here we see that the author's previous work on the dual nature of Appell--Lerch sums ... More

Two binomial coefficient conjecturesFeb 07 2011Much is known about binomial coefficients where primes are concerned, but considerably less is known regarding prime powers and composites. This paper provides two conjectures in these directions, one about counting binomial coefficients modulo 16 and ... More

A power matrix approach to the Witt algebra and Loewner equationsJul 09 2009The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of power matrices, ... More

Factoriality of q-Gaussian von Neumann algebrasNov 24 2003Apr 21 2010We prove that the von Neumann algebras generated by $n$ $q$-Gaussian elements, are factors for $n\ge 2$.

A Poincaré-Birkhoff-Witt criterion for Koszul operadsSep 14 2007Nov 12 2008The aim of this article is to give a criterion, generalizing the criterion introduced by Priddy for algebras, to verify that an operad is Koszul. We define the notion of a Poincare-Birkhoff-Witt basis in the context of operads. Then we show that an operad ... More

Large deviations and support results for nonlinear Schrodinger equations with additive noise and applicationsJun 18 2004Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrodinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored space wise. The solutions ... More

Constructing Reducible Brill--Noether Curves IINov 07 2017Sep 18 2018In this paper, we study maps from reducible curves $f : C \cup_\Gamma D \to \mathbb{P}^r$. We restrict our attention to two cases: first, when $f|_D$ factors through a hyperplane $H$ and $f|_C$ is transverse to $H$; and second, when $r = 3$. Degeneration ... More

On the Singular Structure of Graph HypersurfacesApr 29 2010Mar 09 2011We show that the singular loci of graph hypersurfaces correspond set-theoretically to their rank loci. The proof holds for all configuration hypersurfaces and depends only on linear algebra. To make the conclusion for the second graph hypersurface, we ... More

Singular Moduli of Shimura CurvesNov 27 2007Mar 15 2008The $j$-function acts as a parametrization of the classical modular curve. Its values at complex multiplication (CM) points are called singular moduli and are algebraic integers. A Shimura curve is a generalization of the modular curve and, if the Shimura ... More

On the Tits building of paramodular groupsMay 17 2004We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally ... More

Local Borcherds Products for Unitary GroupsMay 06 2016Aug 22 2017For a discrete subgroup of an indefinite unitary group $U(1,n+1)$, $n\geq 1$, consider the attached modular variety. Using local Borcherds products, we study Heegner divisors in the local Picard group over a boundary component the compactified variety. ... More

The central support of the Plancherel measure of an affine Hecke algebraOct 15 2013We give conceptual proofs of certain basic properties of the arrangement of shifted root hyperplanes associated to a root system and a Weyl group invariant real valued parameter function on the root system. The method is based on the role of this shifted ... More

Affine Hecke algebras and the conjectures of Hiraga, Ichino and IkedaJul 26 2018Jul 27 2018Hiraga, Ichino and Ikeda have conjectured an explicit expression for the Plancherel density of the group of points of a reductive group defined over a local field $F$, in terms of local Langlands parameters. In these lectures we shall present a proof ... More

Connecting Sharpe ratio and Student t-statistic, and beyondAug 02 2018May 14 2019Sharpe ratio is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the excess return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected ... More

The Dynamical Degrees of a MappingOct 08 2011Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees $\delta_p(f)$, $1\le p\le {\rm dim}(X)$. We give the definition of the dynamical degrees show how they are computed in certain ... More

Formalism for Relative Gromov-Witten InvariantsJul 15 2005We develop a formalism for relative Gromov-Witten invariants of Li that is analogous to the Symplectic Field Theory of Eliashberg, Givental, and Hofer. This formalism allows us to express natural degeneration formulae in terms of generating functions ... More

A proof of the polycirculant conjectureJun 30 2005This paper presents a solution of the polycirculant conjecture which states that every vertex-transitive graph G has an automorphism that permutes the vertices in cycles of the same length. This is done by identifying vertex-transitive graphs as coset ... More

Lifting Tropical Curves in Space and Linear Systems on GraphsSep 09 2010Aug 20 2011Tropicalization is a procedure for associating a polyhedral complex in Euclidean space to a subvariety of an algebraic torus. We study the question of which graphs arise from tropicalizing algebraic curves. By using Baker's specialization of linear systems ... More

An Andreotti-Grauert theorem with $L^r$ estimatesMar 04 2012Apr 16 2014By a theorem of Andreotti and Grauert if $\omega $ is a $(p,q)$ current, $q < n,$ in a Stein manifold $\displaystyle \Omega,\ \bar \partial $ closed and with compact support, then there is a solution $u$ to $\bar \partial u=\omega $ still with compact ... More

The raising steps method. Applications to the $\bar \partial $ equation in Stein manifoldsDec 30 2013Jan 09 2014In order to get estimates on the solutions of the equation $\bar \partial u=\omega $ on Stein manifold, we introduce a new method the "raising steps method", to get global results from local ones. In particular it allows us to transfer results form open ... More

Estimates $ L^{r}-L^{s}$ for solutions of the $\bar \partial $ equation in strictly pseudo convex domains in ${\mathbb{C}}^{n}.$Dec 26 2013Jan 24 2014We prove estimates for solutions of the $\bar \partial u=\omega $ equation in a strictly pseudo convex domain $ \Omega $ in ${\mathbb{C}}^{n}.$ For instance if the $ (p,q)$ current $\omega $ has its coefficients in $L^{r}(\Omega )$ with $1\leq r<2(n+1)$ ... More

Irreducible Local Systems on Nilpotent OrbitsOct 24 2016Let $G$ be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit $\mathcal O$ through a ... More

Lorentzian Cobordisms, Compact Horizons and the Generic ConditionJun 24 2014We consider the problem of determining which conditions are necessary for cobordisms to admit Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without a smoothness hypothesis necessary in the original ... More

A Concise Resolution to the Two Envelope ParadoxFeb 18 2012Aug 24 2012In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically, a subjective ... More

The Semiotic MachineSep 02 2008A semiotic model of the user interface in human-computer interaction. Algorithmic sign, semotics, algorithmic art.

The Stock Market as a Game: An Agent Based Approach to Trading in StocksSep 02 2008Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" ... More

Quantum Computing Simulation Optimizations and Operational Errors on Various 2-qubit Multiplier CircuitsAug 15 2002Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates. Additionally, ... More

How to Grow an Organism Inside-Out: Evolution of an internal skeleton from an external skeleton in bilateral organismsJul 16 2012An intriguing unanswered question about the evolution of bilateral animals with internal skeletons is how an internal skeleton evolved in the first place. Computational modeling of the development of bilateral symmetric organisms suggests an answer to ... More

On cyclic CAT(0) domains of discontinuityJun 01 2010Let $X$ be a CAT(0) space, and $G$ a discrete cyclic group of isometries of $X$. We investigate the domain of discontinuity for the action of $G$ on the boundary $\partial X$.

A Density Matrix-based Algorithm for Solving Eigenvalue ProblemsJan 17 2009A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, ... More

Generalized Representation Stability and FI_d-modulesJun 08 2016Oct 04 2016In this note we consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FI_d-modules exhibit behaviors in the spirit of Church-Farb representation ... More

Semi-supervised clustering methodsJul 01 2013Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning that there is ... More

Time Evolution of Entropy of a Charged Domain Wall during Gravitational CollapseFeb 11 2010We study the time evolution of the entropy of a collapsing charged spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. charged domain wall and radiation) and induced radiation ... More

Ramanujan's $_{1}ψ_1$ summation, Hecke-type double sums, and Appell-Lerch sumsAug 07 2012We use a specialization of Ramanujan's ${}_1\psi_1$ summation to give a new proof of a recent formula of Hickerson and Mortenson which expands a special family of Hecke-type double sums in terms of Appell-Lerch sums and theta functions.