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Results for "Eric Erhardt"

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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
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
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
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
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
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
Propulsion in a viscoelastic fluidMar 21 2007Flagella beating in complex fluids are significantly influenced by viscoelastic stresses. Relevant examples include the ciliary transport of respiratory airway mucus and the motion of spermatozoa in the mucus-filled female reproductive tract. We consider ... More
Enhanced diffusion by reciprocal swimmingMar 31 2011Purcell's scallop theorem states that swimmers deforming their shapes in a time-reversible manner ("reciprocal" motion) cannot swim. Using numerical simulations and theoretical calculations we show here that in a fluctuating environment, reciprocal swimmers ... More
Domain-Specific Modeling and Code Generation for Cross-Platform Multi-Device Mobile AppsSep 10 2015Nowadays, mobile devices constitute the most common computing device. This new computing model has brought intense competition among hardware and software providers who are continuously introducing increasingly powerful mobile devices and innovative OSs ... More
Energy Dissipation and Transport in Nanoscale DevicesMar 22 2010Understanding energy dissipation and transport in nanoscale structures is of great importance for the design of energy-efficient circuits and energy-conversion systems. This is also a rich domain for fundamental discoveries at the intersection of electron, ... More
Some Advances in Transformation-Based Part of Speech TaggingJun 02 1994Most recent research in trainable part of speech taggers has explored stochastic tagging. While these taggers obtain high accuracy, linguistic information is captured indirectly, typically in tens of thousands of lexical and contextual probabilities. ... More
Time dependent particle production and particle number in cosmological de Sitter spaceFeb 19 2014In this paper we consider the occupation number of induced quasi-particles produced during a time-dependent process using three-different methods: Instantaneous diagonalization, Bogolyubov transformation between two different vacua, and the Unruh-de Witt ... More
Quantum Mechanical Effects in Gravitational CollapseJan 12 2010In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\"odinger formalism. The Functional Schr\"odinger formalism allows ... More
Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via SymmetrizationNov 10 2014We consider a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques, we establish existence, convexity and symmetry of minimizers ... More
Analytical results for a Fokker-Planck equation in the small noise limitFeb 11 2005We present analytical results for the lowest cumulants of a stochastic process described by a Fokker-Planck equation with nonlinear drift. We show that, in the limit of small fluctuations, the mean, the variance and the covariance of the process can be ... More
A Note on Injectivity of Frobenius on Local Cohomology of HypersurfacesFeb 11 2015Let $k$ be a field of characteristic $p > 0$ such that $[k:k^p] < \infty$ and let $f \in R = k[x_0, ..., x_n]$ be homogeneous of degree $d$. We obtain a sharp bound on the degrees in which the Frobenius action on $H^n_\mathfrak{m}(R/fR)$ can be injective ... More
Bimodality and Latent Heat of Gold NucleiFeb 17 2010Peripheral collisions give access to a set of events where hot quasi-projectile (QP) sources are produced exploring a large range of excitation energy. In this range evaporation and multifragmentation are both observed for a similar charge/size of the ... More
Entropic aging and extreme value statisticsApr 09 2010Jul 08 2010Entropic aging consists in a progressive slowing down of the low-temperature dynamics of a glassy system due to the rarefaction of downwards directions on the energy landscape, as lower and lower energy levels are reached. A prototypical model exhibiting ... More
M/L in individual galaxiesOct 27 2006Nov 02 2006In this short report, I briefly review, illustrate and discuss various techniques (e.g., X ray halos, lensing, kinematics) used to derive mass (hence M/L) profiles of individual galaxies.
Gas and stellar 2D kinematics in early-type galaxiesOct 01 1999We have obtained integral field spectroscopy of a small sample of early-type galaxies to study the kinematical coupling between the stellar and gaseous components in their central regions.
The origin of sigma-drops: mapping stellar kinematics and populations in spiralsOct 27 2006The link between nuclear activity and the host galaxy remains elusive. It seems now clear that the galactic environment is not the key, and that there is no significant apparent difference in terms of the presence of bars/spirals between active and non-active ... More
String Orbifolds and Quotient StacksFeb 28 2001Oct 15 2001In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling definitions, and ... More
Stacks and D-Brane BundlesFeb 27 2001Apr 03 2001In this paper we describe explicitly how the twisted ``bundles'' on a D-brane worldvolume in the presence of a nontrivial B field, can be understood in terms of sheaves on stacks. We also take this opportunity to provide the physics community with a readable ... More
The formation of massive stars: accretion, disks and the development of hypercompact HII regionsMar 31 2006Jun 15 2007The hypothesis that massive stars form by accretion can be investigated by simple analytical calculations that describe the effect that the formation of a massive star has on its own accretion flow. Within a simple accretion model that includes angular ... More
Top quark in theorySep 18 2008I review how the top quark is embedded in the Standard Model and some its proposed extensions, and how it manifests itself in various hadron collider signals.
Top Quark production dynamicsAug 04 2003I discuss various aspects of the dynamics of top quark production both via the strong interaction (pair production) and via the charged current weak interaction (single top production).
NLO Calculations for Charm Production in DISDec 15 1999I present a short overview of the NLO QCD calculations available for deep-inelastic production of heavy quarks.
What are little worlds made of? Stellar abundances and the building blocks of planetsFeb 24 2015If the photospheres of solar-type stars represent the composition of circumstellar disks from which any planets formed, spectroscopic determinations of stellar elemental abundances offer information on the composition of those planets, including smaller, ... More
Computer Art in the Former Soviet BlocSep 02 2008Documents early computer art in the Soviet bloc and describes Marxist art theory.
Agent Models of Political InteractionsSep 02 2008Looks at state interactions from an agent based AI perspective to see state interactions as an example of emergent intelligent behavior. Exposes basic principles of game theory.
PhysmaticsJun 17 2005Public lecture given at The Fields Institute, June 2, 2005.
Solitons and Helices: The Search for a Math-Physics BridgeAug 24 1994We present evidence for an undiscovered link between N=2 supersymmetric quantum field theories and the mathematical theory of helices of coherent sheaves. We give a thorough review for nonspecialists of both the mathematics and physics involved, and invite ... More
Topological Orbifold Models and Quantum Cohomology RingsNov 25 1992We discuss the toplogical sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of ${\bf CP}^1$ ... More
A Developmental Network Theory of Gynandromorphs, Sexual Dimorphism and Species FormationDec 21 2012Gynandromorphs are creatures where at least two different body sections are a different sex. Bilateral gynandromorphs are half male and half female. Here we develop a theory of gynandromorph ontogeny based on developmental control networks. The theory ... More
Cancer Networks: A general theoretical and computational framework for understanding cancerOct 26 2011We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms. Cancer networks ... More
The inner environment of protoplanetary disks with near infrared spectro-interferometrySep 17 2009In this paper, I review how optical spectro-interferometry has become a particularly well suited technique to study the close environment of young stars, by spatially resolving both their IR continuum and line emission regions. I summarize in which ways ... More
Reconstructing Metric Trees from Order Information on Triples is NP CompleteMar 04 2006We show that reconstructing a tree from order information on triples is NP-hard. This is in contrast to the case for ultra-metrics and for subtree information on quadruples which are both known to allow polynomial time reconstruction.
Physics perspectives at JLab with a polarized positron beamFeb 12 2014Polarized positron beams are in some respect mandatory complements to polarized electron beams. The advent of the PEPPo concept for polarized positron production opens the possibility for the developement at the Jefferson Laboratory of a continuous polarized ... More
Lusztig's Canonical Quotient and Generalized DualityApr 16 2001We present a new characterization of Lusztig's canonical quotient group. We also define a duality map: to a pair consisting of a nilpotent orbit and a conjugacy class in its fundamental group, the map assigns a nilpotent orbit in the Langlands dual Lie ... More
Cluster Origin of Triple Star HD 188753 and its PlanetSep 16 2005Oct 26 2005The recent discovery by M. Konacki of a ``hot Jupiter'' in the hierarchical triple star system HD 188753 challenges established theories of giant-planet formation. If the orbital geometry of the triple has not changed since the birth of the planet, then ... More
Criterion for the integrality of the Taylor coefficients of mirror maps in several variablesAug 22 2011We give a necessary and sufficient condition for the integrality of the Taylor coefficients at the origin of formal power series $q_i({\mathbf z})=z_i\exp(G_i({\mathbf z})/F({\mathbf z}))$, with ${\mathbf z}=(z_1,...,z_d)$ and where $F({\mathbf z})$ and ... More
Weakest Preconditions and Cumulative Subgoal Fulfillment: A ComparisonApr 24 2012We contrast the use of weakest preconditions for the correct construction of procedures with the cumulative subgoal fulfillment (CSF) approach. An example of Cohen and Monin is used for this purpose. The CSF construction process is demonstrated.
Matroid theory for algebraic geometersSep 11 2014This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be representable. ... More
A non-abelian analogue of Whitney's 2-isomorphism theoremAug 09 2012Sep 10 2012We give a non-abelian analogue of Whitney's 2-isomorphism theorem for graphs. Whitney's theorem states that the cycle space determines a graph up to 2-isomorphism. Instead of considering the cycle space of a graph which is an abelian object, we consider ... More
Perturbative Wilsonian Formalism for Noncommutative Gauge Theories in the Matrix RepresentationMay 07 2003We study the perturbative approach to the Wilsonian integration of noncommutative gauge theories in the matrix representation. We begin by motivating the study of noncommutative gauge theories and reviewing the matrix formulation. We then systematically ... More
UV-IR mixing and the quantum consistency of noncommutative gauge theoriesNov 08 2002We study the quantum mechanical consistency of noncommutative gauge theories by perturbatively analyzing the Wilsonian quantum effective action in the matrix formulation. In the process of integrating out UV states, we find new divergences having dual ... More
Towards a Theoretical Understanding of the XYZ Mesons from QCDDec 14 2015The XYZ mesons are mesons that contain a heavy quark and antiquark but have properties that seem to require additional constituents. Some of them are electrically charged, so they must be tetraquark mesons whose additional constituents are a light quark ... More
The Polyakov, Nambu and Jona-Lasinio model and its applications to describe the sub-nuclear particlesOct 27 2015To study the high energy nuclear physics and the associated phenomenon, as the QGP/hadronic matter phase transition, the Nambu and Jona-Lasinio model (NJL) appears as an interesting alternative to the Quantum Chromodynamics, which is not solvable at the ... More
Interpolating sequences and Carleson measures in the Hardy-Sobolev spaces of the ball in $C^n$Sep 07 2015In this work we study Hardy Sobolev spaces in the ball of $C^n$ with respect to interpolating sequences and Carleson measures. We compare them with the classical Hardy spaces of the ball and we stress analogies and differences.
The raising steps method. Applications to the $\displaystyle L^{r}$ Hodge theory in a compact riemannian manifoldJun 01 2015Let $X$ be a smooth manifold and $\displaystyle \Omega $ a domain in $\displaystyle X.$ The Raising Steps Method allows to get from local results on solutions $u$ of equation $ Du=\omega $ global ones in $ \Omega .$ It was introduced in~\cite{AmarSt13} ... More
Statistical Mechanics and Quantum Fields on FractalsOct 25 2012Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the corresponding absence ... More
Ground-state phase diagram of a half-filled one-dimensional extended Hubbard modelApr 11 2002Sep 29 2002The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion, and hopping t. A critical line V_c(U) approximately equal to U/2 separates ... More
Dynamical density-matrix renormalization-group methodMar 25 2002I present a density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems. The method is based on an exact variational principle for dynamical correlation ... More
Mott-Peierls Transition in the extended Peierls-Hubbard modelNov 25 1997The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density matrix renormalization group method. Results show that the ground state evolves from a Mott-Peierls insulator with a correlation gap at half-filling ... More
Bijective counting of involutive Baxter permutationsOct 19 2010Oct 28 2011We enumerate bijectively the family of involutive Baxter permutations according to various parameters; in particular we obtain an elementary proof that the number of involutive Baxter permutations of size $2n$ with no fixed points is $\frac{3\cdot 2^{n-1}}{(n+1)(n+2)}\binom{2n}{n}$, ... More
Helium Compton Form Factor Measurements at CLASJun 30 2013The distribution of the parton content of nuclei, as encoded via the generalized parton distributions (GPDs), can be accessed via the deeply virtual Compton scattering (DVCS) process contributing to the cross section for leptoproduction of real photons. ... More
Single Deep Counterfactual Regret MinimizationJan 22 2019Feb 10 2019Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games. However, CFR's reliance on full game-tree traversals limits its scalability. For this reason, the game's ... More
Quenched asymptotics for interacting diffusions on inhomogeneous random graphsNov 22 2018The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi case was considered. ... More
The Expected Order of a Random Unitary MatrixSep 01 2006Let M=M(n,q) be the average of the orders of the elements in the finite unitary group U(n,q). The asymptotic estimate log(M)=nlog(q)-log(n) +o(log n) is proved.
Conformal invariants associated with quadratic differentialsAug 02 2016Z. Nehari developed a general technique for obtaining inequalities for conformal maps and domain functions from contour integrals and the Dirichlet principle. Given a harmonic function with singularity on a domain $R$, it associates a monotonic functional ... More
The Kodaira dimension of Siegel modular varieties of genus 3 or higherMay 18 2004We consider the moduli space $A_{pol}(n)$ of (non-principally) polarised abelian varieties of genus $g\geq3$ with coprime polarisation and full level-$n$ structure. Based upon the analysis of the Tits building in math/0405321, we give an explicit lower ... More
Interpolation for Restricted Tangent Bundles of General CurvesNov 13 2015May 19 2016Let (C, p_1, p_2, \ldots, p_n) be a general marked curve of genus g, and q_1, q_2, ..., q_n \in P^r be a general collection of points. We determine when there exists a nondegenerate degree d map f : C \to P^r so that f(p_i) = q_i for all i. This is a ... More
Line-Bundles on Stacks of Relative MapsJul 15 2005This paper provides some technical results needed in "Formalism for Relative Gromov-Witten Invariants." We study line-bundles on the moduli stacks of relative stable and rubber maps that are used to define relative Gromov-Witten invariants in the sense ... More
Pluriharmonic MorphismsAug 10 1996Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we characterise pluriharmonic ... More
On the Translation Invariance of Wavelet SubspacesSep 22 1999An examination of the translation invariance of $V_0$ under dyadic rationals is presented, generating a new equivalence relation on the collection of wavelets. The equivalence classes under this relation are completely characterized in terms of the support ... More
Spectral transfer morphisms for unipotent affine Hecke algebrasOct 29 2013Oct 11 2015In this paper we will give a complete classification of the spectral transfer morphisms between the unipotent affine Hecke algebras of the various inner forms of a given quasi-split absolutely simple algebraic group, defined over a non-archimidean local ... More
The Geometry of Sampling on Unions of LatticesAug 26 2003In this short note we show two results concerning sampling translation invariant subspaces of $\ltwod$ on unions of lattices. The first result shows that the sampling transform on a union of lattices is a constant times an isometry if and only if the ... More
Crystal Combinatorics and Geometric SatakeOct 22 2017This is an REU paper written for the University of Chicago REU, summer 2017. The main purpose of this note is to collect some of the many combinatorial models for MV cycles that exist in the literature. In particular, we will investigate MV polytopes, ... More
Partial regularity for the steady hyperdissipative fractional Navier-Stokes equationsMar 21 2018We extend the Caffarelli-Kohn-Nirenberg type partial regularity theory for the steady $5$-dimensional fractional Navier-Stokes equations with external force to the hyperdissipative setting. In our argument we use the methods of Colombo-De Lellis-Massaccesi ... More
Counting unrooted maps using tree-decompositionJan 06 2006We present a new method to count unrooted maps on the sphere up to orientation-preserving homeomorphisms. The principle, called tree-decomposition, is to deform a map into an arborescent structure whose nodes are occupied by constrained maps. Tree-decomposition ... More
Invertible dynamics on blow-ups of P^kNov 04 2014We discuss automorphisms and pseudo-automorphisms on blowups of complex projective space with an eye to finding ones with interesting dynamical behavior.
Borcherds Products for U(1,1)Feb 21 2013Jun 21 2013The Borcherds lift for indefinite unitary groups, previously constructed by the author, is examined here in greater detail for the special case of the group U(1,1). The inputs for the lifting in this case are weakly holomorphic modular forms of weight ... More
On linear extension for interpolating sequencesOct 10 2006Title: On linear extension for interpolating sequences. Author: Eric Amar Abstract: Let A be a uniform algebra on the compact space X and $\sigma $ a probability measure on X. We define the Hardy spaces $H^{p}(\sigma)$ and the $H^{p}(\sigma)$ interpolating ... More
Orthogonal Frames of TranslatesOct 10 2003Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have ... More
Berkovich log discrepancies in positive characteristicNov 08 2017Jul 21 2018We introduce and study a log discrepancy function on the space of semivaluations centered on schemes in positive characteristic that shares many properties with the analogue in characteristic zero. Strong $F$-regularity and sharp $F$-purity of Cartier ... More
The von Neumann algebra generated by t-gaussiansJan 23 2006We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently close to 1, ... More
A weak notion of strict pseudo-convexity. Applications and examplesJun 10 2009Mar 04 2016Let $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly pseudo-convex points on ... More
Division Algebra Cyclicity in Prime Degree over a p-Adic CurveFeb 04 2014We reprove two results of Saltman, Theorem 5.1 and Corollary 5.2 of [Sa07]: If F is the function field of a smooth p-adic curve and D is an F-division algebra of prime degree l\neq p, then D is Z/l-cyclic, and that if D is an F-division algebra of prime ... More
Exit from a basin of attraction for stochastic weakly damped nonlinear Schrödinger equationsFeb 16 2006We consider weakly damped nonlinear Schr\"odinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero is an asymptotically ... More
Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noiseDec 16 2004Uniform large deviations for the laws of the paths of the solutions of the stochastic nonlinear Schrodinger equation when the noise converges to zero are presented. The noise is a real multiplicative Gaussian noise. It is white in time and colored in ... More
Steady-State Behavior of Some Load Balancing Mechanisms in Cloud Storage SystemsJan 06 2018In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We consider a system of $n$ servers storing files using a Maximum Distance Separable code (cf. \cite{li2016mean}). Specifically, each file ... More
Genus two 3-manifolds are built from handle number one piecesNov 06 1998Dec 31 2001Let M be a closed, irreducible, genus two 3-manifold, and F a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in M. Then each component manifold M_i of M-F has handle number at most one, i.e. admits a Heegaard ... More
Computing a Data DividendMay 06 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
Categorical Equivalence and the Renormalization GroupMar 07 2019In this article we review how categorical equivalences are realized by renormalization group flow in physical realizations of stacks, derived categories, and derived schemes. We begin by reviewing the physical realization of sigma models on stacks, as ... More
The Maximal Rank Conjecture for Sections of CurvesAug 14 2012Sep 18 2018Let be a general curve of genus g embedded via a general linear series of degree d in P^r. The well-known Maximal Rank Conjecture asserts that the restriction maps H^0(O_{P^r}(m)) \to H^0(O_C(m) are of maximal rank; if known, this conjecture would determine ... More
Convergence of Taylor Series of real normed division algebrasSep 17 2018Apr 24 2019We propose a new way to compute the radius of convergence for Quaternionic hyperholomorphic functions and for Octonion analytic functions. We extend the theorem of Cauchy Hadamard and the theorem of Abel on convergence of series to Quaternionic analysis ... More
Degenerations of Curves in Projective Space and the Maximal Rank ConjectureSep 16 2018In this note, we give an overview of a new technique for studying Brill--Noether curves in projective space via degeneration. In particular, we give a roadmap to the proof of the Maximal Rank Conjecture.
Spectral Distribution in the Eigenvalues Sequence of Products of g-Toeplitz StructuresMay 02 2019Starting from the definition of an $n\times n$ $g$-Toeplitz matrix, $T_{n,g}(u)=\left[\widehat{u}_{r-gs}\right]_{r,s=0}^{n-1},$ where $g$ is a given nonnegative parameter, $\{\widehat{u}_{k}\}$ is the sequence of Fourier coefficients of the Lebesgue integrable ... More
Differentials over differential fieldsJan 18 2007Given an algebra $A$ over a differential field $K$, we study derivations on $A$ that are compatible with the derivation on $K$. There is a universal object, which is a twisted version of the usual module of differentials, and we establish some of its ... More
PERSEUS Technology: New Trends in Information and Communication SecurityDec 30 2010Using cryptography to protect information and communication has bacically two major drawbacks. First, the specific entropy profile of encrypted data makes their detection very easy. Second, the use of cryptography can be more or less regulated, not to ... More
Deep Convolutional Neural Networks as Generic Feature ExtractorsOct 06 2017Recognizing objects in natural images is an intricate problem involving multiple conflicting objectives. Deep convolutional neural networks, trained on large datasets, achieve convincing results and are currently the state-of-the-art approach for this ... 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