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Pushing the Limits of Exoplanet Discovery via Direct Imaging with Deep LearningApr 12 2019Further advances in exoplanet detection and characterisation require sampling a diverse population of extrasolar planets. One technique to detect these distant worlds is through the direct detection of their thermal emission. The so-called direct imaging ... More

Critical Scaling Properties at the Superfluid Transition of $^4$He in AerogelMar 30 2006Dec 04 2006We study the superfluid transition of $^4$He in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by ... More

Suppression of Quantum Corrections by Classical BackgroundsJan 13 2014May 22 2014We use heat-kernel techniques in order to compute the one-loop effective action in the cubic Galileon theory for a background that realizes the Vainshtein mechanism. We find that the UV divergences are suppressed relative to the predictions of standard ... More

N$^3$LO approximate results for top-quark differential cross sections and forward-backward asymmetryJun 12 2015I present a calculation of approximate N$^3$LO corrections from NNLL soft-gluon resummation for differential distributions in top-antitop pair production in hadronic collisions. Soft-gluon corrections are the dominant contribution to top-quark production ... More

An elementary approach to the option pricing problemOct 20 2015Apr 06 2016Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair price of European ... More

Holomorphic extendability in $\mathbf C^n$ as a rare phenomenonNov 16 2016Dec 01 2016We consider various notions of holomorphic extendability of complex valued functions defined on subsets of $\mathbf C^n$, including one-sided extendability. We show that in the relevant function spaces, these phenomena of holomorphic extendability are ... More

Criticality and Transport in Magnetized Holographic SystemsDec 02 2018In this master's thesis the Einstein-Maxwell-Dilaton theory is used to model the dynamics of 2+1-dimensional, strongly coupled, large-$N$ quantum field theories with intrinsic T-violation, at finite density and temperature, in the presence of a magnetic ... More

Kernels of L-functions and shifted convolutionsNov 21 2016We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Brown's technique to ... More

Mass Concentration Phenomenon for the Quintic Nonlinear Schrödinger Equation in One DimensionMar 29 2006We consider the $L^{2}$-critical quintic focusing nonlinear Schr\"odinger equation (NLS) on ${\bf R}$. It is well known that $H^{1}$ solutions of the aforementioned equation blow up in finite time. In higher dimensions, for $H^{1}$ spherically symmetric ... More

On the inverse of the sum of two sectorial operatorsJul 03 2012Jul 02 2013We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of operator valued $H^\infty$-calculus is sufficient for maximal regularity of ... More

Preserving closedness of operators under summationJul 12 2013May 20 2014We give a sufficient condition for the sum of two closed operators to be closed. In particular, we study the sum of two sectorial operators with the sum of their sectoriality angles greater than $\pi$. We show that if one of the operators admits bounded ... More

Onto Interpolation for the Dirichlet Space and for $W^{1,2}(\mathbb{D})$Jul 21 2018Nov 14 2018We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of capacity of some condensers. The same condition in fact characterizes all onto interpolating sequences for $ W^{1,2}(\mathbb{D}) ... More

Infinitesimal Extensions of P^1 and their Hilbert SchemesOct 08 2001In order to calculate the multiplicity of an isolated rational curve C in a local complete intersection variety X, i.e. the length of the Hilbert scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X. This is equivalent ... More

Heinz-Kato inequality in Banach spacesNov 12 2018We show a Heinz-Kato inequality in Banach spaces for sectorial operators having bounded imaginary powers.

Continuous spectrum or measurable reducibility for quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$Nov 30 2015We continue our study of the local theory for quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $G=SU(2)$, over a rotation satisfying a Diophantine condition and satisfying a closeness-to-constants condition, by proving a dichotomy between measurable ... More

Automorphisms of smooth canonically polarized surfaces in characteristic 2Aug 06 2014Aug 14 2014This paper investigates the structure of the automorphism scheme of a smooth canonically polarized surface $X$ defined over an algebraically closed field of characteristic 2. In particular it is investigated when Aut(X) is not smooth. This is a situation ... More

Fast mean-reversion asymptotics for large portfolios of stochastic volatility modelsNov 21 2018We consider a large portfolio limit where the asset prices evolve according certain stochastic volatility models with default upon hitting a lower barrier. When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit ... More

Neural network-based modelling of unresolved stresses in a turbulent reacting flow with mean shearApr 17 2019Data-driven methods for modelling purposes in fluid mechanics are a promising alternative given the continuous increase of both computational power and data-storage capabilities. Highly non-linear flows including turbulence and reaction are challenging ... More

Eccentricity generation in hierarchical triple systems with non-coplanar and initially circular orbitsAug 23 2014In a previous paper, we developed a technique for estimating the inner eccentricity in coplanar hierarchical triple systems on initially circular orbits, with comparable masses and with well separated components, based on an expansion of the rate of change ... More

Holomorphic extendability in $\mathbf C^n$ as a rare phenomenonNov 16 2016We consider various notions of holomorphic extendability of complex valued functions defined on subsets of $\mathbf C^n$, including one-sided extendability. We show that in the relevant function spaces, these phenomena of holomorphic extendability are ... More

Landesman-Laser Conditions and Quasilinear Elliptic ProblemsMar 21 2003In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami $(PS)$ condition. ... More

On the evolution of random graphs on spaces of negative curvatureMay 14 2012In this work, we study a family of random geometric graphs on hyperbolic spaces. In this setting, N points are chosen randomly on a hyperbolic space and any two of them are joined by an edge with probability that depends on their hyperbolic distance, ... More

Local Rigidity of Diophantine translations in higher dimensional toriDec 16 2016Dec 28 2016We prove a theorem asserting that, given a Diophantine rotation $\alpha $ in a torus $\T ^{d} \equiv \R ^{d} / \Z ^{d}$, any perturbation, small enough in the $C^{\infty}$ topology, that does not destroy all orbits with rotation vector $\alpha$ is actually ... More

Invariant Distributions and local theory of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$}Jul 17 2014Sep 30 2014We prove local genericity of Distributional Unique Ergodicity (DUE) for certain classes of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$, extending and/or refining some preceding results in the field. The proof is based on a more careful analysis ... More

Differentiable Rigidity for quasiperiodic cocycles in compact Lie groupsJul 17 2014Sep 08 2014We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove differentiable ... More

On Neumann superlinear elliptic problemsApr 01 2003In this paper we are going to show the existence of a nontrivial solution to the following model problem, \begin{equation*} \left\{\begin{array}{lll} -\Delta (u) = 2uln(1+u^2)+\frac{|u|^2}{1+u^2}2u+u(sin(u)-cos(u)) \mbox{a.e. on } \Omega \frac{\partial ... More

Expanding solutions of quasilinear parabolic equationsDec 25 2017We decompose locally in time maximal $L^{q}$-regular solutions of abstract quasilinear parabolic equations as a sum of a smooth term and an arbitrary small$-$with respect to the maximal $L^{q}$-regularity space norm$-$remainder. In view of this observation, ... More

Three dimensional divisorial extremal neighborhoodsAug 31 2003Sep 18 2003Revised version. Proper credits added. In this paper we study divisorial extremal neighborhoods f:Y-->X, such that X is a cAn type three dimensional terminal singularity, and C=f(E) is a smooth curve, where E is the f-exceptional divisor. We view a divisorial ... More

Families of D-minimal models and applications to 3-fold divisorial contractionsOct 03 2002Apr 27 2005Let X/T be a one parameter family of canonical 3-folds and let D be a Weil divisor on it flat over T. We study the problem of when the D_t-minimal models of X_t form a family and we obtain conditions for this to happen. As an application of this we classify ... More

First order deformations of schemes with normal crossing singularitiesJul 18 2010We describe the sheaf T^1(X) of first order deformations of a reduced scheme with normal crossing singularities. In particular, we obtain a formula for T^1(X) in a suitable log resolution of X.

Vector fields and moduli of canonically polarized surfaces in positive characteristicOct 09 2017Oct 17 2017This paper investigates the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the moduli problem ... More

Smoothings of Fano varieties with normal crossing singularitiesMay 04 2010Jul 07 2013This paper obtains criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. The difference with the original version is that the theory of logarithmic structures ... More

Extensions of the Laurent Decomposition and the spaces $A^p(Ω)$May 26 2016We generalize the classical Laurent decomposition in the setting of domains $\Omega\subseteq \mathbb C$ bounded by Jordan curves. This leads us to study the Fr\'echet spaces $A^p(\Omega)$, and their relation to the spaces $C^p(\partial \Omega)$. In the ... More

Quotients of schemes by $α_p$ or $μ_p$ actions in characteristic p>0Dec 26 2014Aug 31 2015This paper studies schemes X defined over a field of characteristic p>0 which admit a nontrivial $\alpha_p$ or $\mu_p$ action. In particular, the structure of the quotient map $X \rightarrow Y$ is investigated. Information on local properties of the quotient ... More

Automorphisms of smooth canonically polarized surfaces in positive characteristicJun 29 2015This paper investigates the geometry of a smooth canonically polarized surface $X$ defined over an algebraically closed field of characteristic $p>0$ in the case when the automorphism scheme of $X$ is not smooth. This is a situation that appears only ... More

Smoothings of Fano schemes with normal crossing singularities of dimension at most threeJul 21 2009We study the deformation theory of a Fano variety X with normal crossing singularities of dimension at most three. We obtain a formula for the sheaf T^1(X) of first order deformations of X in a suitable log resolution of X and its singular locus Z and ... More

Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groupsMay 18 2015In this m\'emoire we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will prove that $C^{\infty}$ reducible cocycles are dense in the $C^{\infty}$ ... More

The Cauchy problem for the semilinear quintic Schrödinger equation in one dimension,the defocusing caseDec 20 2002Aug 05 2009This paper has been withdrawn by the author

Theoretical results for top-quark cross sections and distributionsSep 23 2016I present new results and updates for total cross sections and differential distributions in top-antitop pair and single-top production. Soft-gluon corrections are added to exact fixed-order results to provide the best predictions at approximate N$^3$LO ... More

Theoretical results for electroweak-boson and single-top productionJun 12 2015I present results from recent high-order calculations for the production of electroweak bosons and top quarks. In particular, I discuss $W$ and $Z$ boson production at large transverse momentum, single-top production, and FCNC top production. Theoretical ... More

Generating and evaluating application-specific hardware extensionsMar 28 2014Modern platform-based design involves the application-specific extension of embedded processors to fit customer requirements. To accomplish this task, the possibilities offered by recent custom/extensible processors for tuning their instruction set and ... More

A little quantum help for cosmic censorship and a step beyond all thatDec 12 2013Feb 19 2014The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop ... More

Geometry of the Frenkel-Kac-Segal cocycleApr 12 1994We present an analysis of the cocycle appearing in the vertex operator representation of simply-laced, affine, Kac-Moody algebras. We prove that it can be described in the context of $R$-commutative geometry, where $R$ is a Yang-Baxter operator, as a ... More

Comments on the Gribov AmbiguityMay 20 1993We discuss the existence of Gribov ambiguities in $SU(m)\times U(1)$ gauge theories over the $n-$spheres. We achieve our goal by showing that there is exactly one conjugacy class of groups of gauge transformations for the theories given above. This implies ... More

Mixed Variational InferenceJan 15 2019The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies. Variational approaches ... More

Terminal 3-fold divisorial contractions of a surface to a curve, IOct 06 2001Let C be a smooth curve on an index 1 terminal 3-fold. We investigate the existence of extremal terminal divisorial contractions Y-->X that contract an irreducible surface E to C. We consider cases in respect to the singularities of the general hypersurface ... More

Combinatorial proofs of Infinite versions of the Hales-Jewett theoremNov 08 2012We provide new and purely combinatorial proofs of two infinite extensions of the Hales--Jewett theorem. The first one is due to T. Carlson and S. Simpson and the second one is due T. Carlson. Both concern infinite increasing sequences of finite alphabets. ... More

A scattering approach to a surface with hyperbolic cuspOct 14 2016Apr 17 2018Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and $Y=[1,\infty)\times S^{1}$. We consider a family of complete surfaces arising by endowing $X\cup_{S^{1}}Y$ with a parameter dependent Riemannian metric, such that the restriction of ... More

Existence result for a Neumann problemMar 19 2003In this paper we are going to show the existence of a nontrivial solution to the following model problem, $\{\begin{array}{lll} - \Delta (u) = 2uln(1+u^2)+\frac{|u|^2}{1+u^2}2u+usin(u) {a.e. on} \Omega \frac{\partial u}{\partial \eta} = 0 {a.e. on} \partial ... More

A novel approach to construct numerical methods for stochastic differential equationsMar 07 2013Mar 13 2013In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.

Conic manifolds under the Yamabe flowJul 11 2018We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we show well posedness of the short time solution in the $L^q$-setting. Moreover, we give a picture of the ... More

Complex powers for cone differential operators and the heat equation on manifolds with conical singularitiesFeb 01 2017Apr 17 2018We obtain left and right continuous embeddings for the domains of the complex powers of sectorial $\mathbb{B}$-elliptic cone differential operators. We apply this result to the heat equation on manifolds with conical singularities and provide asymptotic ... More

Adaptive mesh reconstruction: Total Variation BoundAug 30 2009We consider 3-point numerical schemes for scalar Conservation Laws, that are oscillatory either to their dispersive or anti-diffusive nature. Oscillations are responsible for the increase of the Total Variation (TV); a bound on which is crucial for the ... More

On construction of boundary preserving numerical schemesJan 28 2016Feb 15 2016Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.

SFA Referee Allocation SchemeAug 28 2014For many sports, the allocation of officials to matches is performed manually and is a very time consuming procedure. For the Scottish Football Association (SFA), the allocation of referees and other officials to matches is governed by a number of rules ... More

High-order threshold corrections for top-pair and single-top productionSep 25 2015I present results for high-order corrections from threshold resummation to cross sections and differential distributions in top-antitop pair production and in single-top production. I show aN$^3$LO results for the total $t{\bar t}$ cross section as well ... More

N$^3$LO calculations for top-quark differential cross sections near partonic thresholdSep 08 2015I present calculations of approximate corrections from NNLL soft-gluon resummation for total and differential cross sections in top-antitop pair production and single-top production in hadronic collisions. I show that soft-gluon corrections from partonic ... More

A scattering approach to a surface with hyperbolic cuspOct 14 2016Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and $Y=[1,\infty)\times S^{1}$. We consider a family of complete surfaces arising by endowing $X\cup_{S^{1}}Y$ with a parameter dependent Riemannian metric, such that the restriction of ... More

Doubling and Desingularization Constructions for Minimal SurfacesDec 28 2010In the first part of the paper we discuss the current status of the application of the gluing methodology to doubling and desingularization constructions for minimal surfaces in Riemannian three-manifolds. In particular a doubling construction for equatorial ... More

Smoothings of schemes with non-isolated singularitiesAug 04 2008Aug 24 2009In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain ... More

Percolation on sparse random graphs with given degree sequenceMar 09 2007We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards we focus on ... More

Cohomological rigidity and the Anosov-Katok constructionNov 07 2017Nov 12 2018We provide a general argument for the failure of Anosov-Katok-like constructions (as in \cite{AFKo2015} and \cite{NKInvDist}) to produce Cohomologically Rigid diffeomorphisms in manifolds other than tori. A $C^{\infty }$ smooth diffeomorphism $f $ of ... More

Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groupsMar 05 2019Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in $\mathbb{T}^{d} \times G$, $G$ a compact Lie group, over a Diophantine rotation. We then prove that if this rotation ... More

Ergodic Theorems for discrete Markov chainsJul 27 2017Jul 31 2017Let $X_n$ be a discrete time Markov chain with state space $S$ (countably infinite, in general) and initial probability distribution $\mu^{(0)} = (P(X_0=i_1),P(X_0=i_2),\cdots,)$. What is the probability of choosing in random some $k \in \mathbb{N}$ with ... More

3-fold divisorial extremal neighborhoods over cE7 and cE6 Compound DuVal singularitiesMar 28 2007Jan 17 2008Let X be the germ of a Gorenstein 3-fold singularity and C a smooth curve through it such that the general hyperplane section S of X containing D is DuVal of type E6 or E7. In this paper we obtain criteria for the existence of a terminal divisorial extremal ... More

Q-Gorenstein deformations of non-normal surfacesApr 11 2005Nov 06 2007Revised Version. An example of a locally smoothable stable surface that does not have a global smoothing has been added.

Closedness and invertibility for the sum of two closed operatorsFeb 14 2016May 03 2018We show a Kalton-Weis type theorem for the general case of non-commuting operators. More precisely, we consider sums of two possibly non-commuting linear operators defined in a Banach space such that one of the operators admits a bounded $H^\infty$-calculus, ... More

Light Propagation and Large-Scale InhomogeneitiesMar 22 2007Feb 17 2010We consider the effect on the propagation of light of inhomogeneities with sizes of order 10 Mpc or larger. The Universe is approximated through a variation of the Swiss-cheese model. The spherical inhomogeneities are void-like, with central underdensities ... More

Zero Temperature Glass Transition in the Two-Dimensional Gauge Glass ModelDec 02 2003Mar 05 2004We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite size scaling behavior, ... More

Optimal PMU Placement Using Nonlinear ProgrammingJul 19 2015Aug 22 2015Phasor Measurement Units (PMUs) are essential measuring devices for monitoring, control and protection of power systems. The objective of the optimal PMU placement (OPP) problem is to minimize the number of PMUs and select the bus locations to make a ... More

Effective cosmological equations of induced f(R) gravityJun 23 2010Oct 21 2010We expand the study of generalized brane cosmologies by allowing for an $f(\tilde{\cal R})$ gravity term on the brane, with $\tilde{\cal R}$ the curvature scalar derived from the induced metric. We also include arbitrary matter components on the brane ... More

HetNets and Massive MIMO: Modeling, Potential Gains, and Performance AnalysisSep 19 2013We consider a heterogeneous cellular network (HetNet) where a macrocell tier with a large antenna array base station (BS) is overlaid with a dense tier of small cells (SCs). We investigate the potential benefits of incorporating a massive MIMO BS in a ... More

On the preservation of unitarity during black hole evolution and information extraction from its interiorJan 02 2012May 22 2012For more than 30 years the discovery that black holes radiate like black bodies of specific temperature has triggered a multitude of puzzling questions concerning their nature and the fate of information that goes down the black hole during its lifetime. ... More

A new approach to information loss (no) problem for Black HolesSep 26 2010Jan 02 2012The discovery that black holes emit thermal type radiation changed radically our perception of their behavior. Until then, their interior was considered as causally disconnected from the rest of the universe, so any kind of information, that went down ... More

On the Ergodic Capacity of Underlay Cognitive Dual-Hop AF Relayed Systems under Non-Identical Generalized-K Fading ChannelsAug 31 2015The ergodic capacity of underlay cognitive (secondary) dual-hop relaying systems is analytically investigated. Specifically, the amplify-and-forward transmission protocol is considered, while the received signals undergo multipath fading and shadowing ... More

Beauty and Charm Production in Fixed Target ExperimentsMay 21 2004We present calculations of NNLO threshold corrections for beauty and charm production in pi- p and pp interactions at fixed-target experiments.

Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP LoadsMay 27 2016This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye or delta ZIP loads has a unique solution over a region that can be explicitly calculated from the network ... More

Maximum Principles for Vectorial Approximate Minimizers of Nonconvex FunctionalsSep 09 2008Dec 09 2011We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing ... More

Labeling Topics with Images using Neural NetworksAug 01 2016Topics generated by topic models are usually represented by lists of $t$ terms or alternatively using short phrases and images. The current state-of-the-art work on labeling topics using images selects images by re-ranking a small set of candidates for ... More

A Guide to Flat Direction Analysis in Anomalous U(1) ModelsDec 03 1997We suggest a systematic procedure to study D- and F-flat directions in a large class of models with an anomalous U(1). This class of models is characterized by the existence of a vacuum that breaks all Abelian gauge symmetries connecting the observable ... More

Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularitiesAug 24 2017We study the porous medium equation on manifolds with conical singularities. Given strictly positive initial values, we show that the solution exists in the maximal $L^{q}$-regularity space for all times and is instantaneously smooth in space and time, ... More

Performance Analysis of a Cooperative Wireless Network with Adaptive Relays: A Network-Level StudyOct 12 2017Oct 19 2017In this work, we investigate the stability region, the throughput performance, and the queueing delay of an asymmetric relay-assisted cooperative random access wireless network with multipacket reception (MPR) capabilities. We consider a network of $N$ ... More

An optimal adaptive wavelet method for First Order System Least SquaresNov 16 2017In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are ... More

A flexible multidimensional rectangular mesh administration and refinement technique with application in cancer invasion modelsJun 19 2017We present a mesh-structure data administration technique for the bookkeeping of adaptive mesh refinement, in particular h-refinement, of rectangular parallelepiped meshes. Our technique is a unified approach for 1-, 2- and 3D domains, that can be extended ... More

On the Solution of Gauss Circle Problem Conjecture (Revised)Dec 31 2015We give a proof of a mean value asymptotic formula for the number of representations of an integer as sum of two squares known as the Gauss circle problem.

Global Smoothing for the Periodic KdV EvolutionMar 22 2011Mar 29 2011The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for $H^s$ initial data, $s>-1/2$, and for any $s_1<\min(3s+1,s+1)$, the difference of the nonlinear and linear evolutions is in $H^{s_1}$ for all times, ... More

The one-dimensional Keller-Segel model with fractional diffusion of cellsJun 24 2009We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel ... More

On homeomorphisms and $C^{1}$ mapsApr 27 2018Our purpose in this article is first, following [8], to prove that if $\alpha $, $\beta $ are any points of the open unit disc $D(0;1)$ in the complex plane ${\bf C}$ and $r$, $s$ are any positive real numbers such that ${\overline{D}}( \alpha ;r) \subseteq ... More

Existence and maximal $L^{p}$-regularity of solutions for the porous medium equation on manifolds with conical singularitiesApr 20 2015We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness and maximal $L^{p}$-regularity of a short time solution. In particular, we obtain information on the short time asymptotics of the solution near ... More

Iterated Integrals and higher order automorphic formsMar 17 2008Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's theory, we prove ... More

Variational inequalitiesFeb 17 2015If $- \infty < \alpha < \beta < \infty $ and $f \in C^{3} \left( [ \alpha , \beta ] \times {\bf R}^{2} , {\bf R} \right) $ is bounded, while $y \in C^{2} \left( [ \alpha , \beta ] , {\bf R} \right) $ solves the typical one-dimensional problem of the calculus ... More

On condition numbers of polynomial eigenvalue problems with nonsingular leading coefficientsJul 22 2009In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition numbers of eigenvalues ... More

The Evolution of the Mixing RateJan 17 2007In this paper we present a study of the mixing time of a random walk on the largest component of a supercritical random graph, also known as the giant component. We identify local obstructions that slow down the random walk, when the average degree d ... More

On pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arraysJan 11 2019The group of almost Riordan arrays contains the group of Riordan arrays as a subgroup. In this note, we exhibit examples of pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arrays.

Fixed point free homeomorphisms of the complex planeAug 09 2016Our purpose in this article is to prove that the group $H({\bf C})$ of homeomorphisms of the complex plane ${\bf C}$ is a metric group equipped with the metric induced by uniform convergence of homeomorphisms and their inverses on compacts and the set ... More

Design space exploration tools for the ByoRISC configurable processor familyMar 26 2014In this paper, the ByoRISC (Build your own RISC) configurable application-specific instruction-set processor (ASIP) family is presented. ByoRISCs, as vendor-independent cores, provide extensive architectural parameters over a baseline processor, which ... More

Throughput of a Cognitive Radio Network under Congestion Constraints: A Network-Level StudyJan 29 2015Jun 12 2015In this paper we analyze a cognitive radio network with one primary and one secondary transmitter, in which the primary transmitter has bursty arrivals while the secondary node is assumed to be saturated (i.e. always has a packet waiting to be transmitted). ... More

Constructing higher-order hydrodynamics: The third orderJul 09 2015Mar 18 2016Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy ... More

BMN Operators for N=1 Superconformal Yang-Mills Theories and Associated String BackgroundsDec 10 2002Jun 16 2003We study a class of near-BPS operators for a complex 2-parameter family of N=1 superconformal Yang-Mills theories that can be obtained by a Leigh-Strassler deformation of N=4 SYM theory. We identify these operators in the large N and large R-charge limit ... More

The Muckenhoupt $A_\infty$ class as a metric space and continuity of weighted estimatesJul 05 2011We show how the $A_\infty$ class of weights can be considered as a metric space. As far as we know this is the first time that a metric d is considered on this set. We use this metric to generalize the results obtained in [9]. Namely, we show that for ... More