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Combining Learned Lyrical Structures and Vocabulary for Improved Lyric GenerationNov 12 2018The use of language models for generating lyrics and poetry has received an increased interest in the last few years. They pose a unique challenge relative to standard natural language problems, as their ultimate purpose is reative, notions of accuracy ... More

A Comparative Analysis of Expected and Distributional Reinforcement LearningJan 30 2019Feb 21 2019Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from convergence guarantees, ... More

Distributional reinforcement learning with linear function approximationFeb 08 2019Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cram\'er distance, but ... More

Dopamine: A Research Framework for Deep Reinforcement LearningDec 14 2018Deep reinforcement learning (deep RL) research has grown significantly in recent years. A number of software offerings now exist that provide stable, comprehensive implementations for benchmarking. At the same time, recent deep RL research has become ... More

Shaping the Narrative Arc: An Information-Theoretic Approach to Collaborative DialogueJan 31 2019We consider the problem of designing an artificial agent capable of interacting with humans in collaborative dialogue to produce creative, engaging narratives. In this task, the goal is to establish universe details, and to collaborate on an interesting ... More

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theoryJun 16 2017Aug 02 2017New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined ... More

Critical phase behavior in multi-component fluid mixtures: Complete scaling analysisOct 14 2018Nov 25 2018We analyze the critical gas-liquid phase behavior of arbitrary fluid mixtures in their coexistence region. We focus on the setting relevant for polydisperse colloids, where the overall density and composition of the system are being controlled, in addition ... More

INFERNO: Inference-Aware Neural OptimisationJun 12 2018Oct 11 2018Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data. Furthermore, sometimes ... More

Termite: A System for Tunneling Through Heterogeneous DataMar 12 2019Data-driven analysis is important in virtually every modern organization. Yet, most data is underutilized because it remains locked in silos inside of organizations; large organizations have thousands of databases, and billions of files that are not integrated ... More

A Geometric Perspective on Optimal Representations for Reinforcement LearningJan 31 2019This paper proposes a new approach to representation learning based on geometric properties of the space of value functions. We study a two-part approximation of the value function: a nonlinear map from states to vectors, or representation, followed by ... More

An Atari Model Zoo for Analyzing, Visualizing, and Comparing Deep Reinforcement Learning AgentsDec 17 2018Much human and computational effort has aimed to improve how deep reinforcement learning algorithms perform on benchmarks such as the Atari Learning Environment. Comparatively less effort has focused on understanding what has been learned by such methods, ... More

Dynamics and zeta functions on conformally compact manifoldsJun 09 2011Jul 01 2011In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable ... More

On the Combination of TDDFT with Molecular Dynamics: New DevelopmentsFeb 01 2011In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we ... More

Comparative Study of the Electronic Structure of Alkaline-earth Borides (MeB2; Me=Mg, Al, Zr, Nb, and Ta) and their Normal-State ConductivityMay 14 2002By means of density functional theory the electronic structure of the MgB2 superconductor was characterised and compared with that of the related iso-structural systems: AlB2, ZrB2, NbB2, and TaB2. Using the full-potential linearized augmented plane waves ... More

Analysis of the Drift Instability Growth Rates in Non-Ideal inhomogeneous Dusty PlasmasOct 19 2004Nov 05 2004In this paper we introduce an algebraic form of the dispersion relation for a non ideal inhomogeneous dusty plasma in order to improve drastically the calculation of the drift instability growth rate. This method makes use of the multipole approximation ... More

Simulating Behaviours to face up an Emergency EvacuationJan 21 2014Computer based models describing pedestrian behavior in an emergency evacuation play a vital role in the development of active strategies that minimize the evacuation time when a closed area must be evacuated. The reference model has a hybrid structure ... More

Negative Differential Resistance and Steep Switching in Chevron Graphene Nanoribbon Field Effect TransistorsMar 17 2017Ballistic quantum transport calculations based on the non-equilbrium Green's function formalism show that field-effect transistor devices made from chevron-type graphene nanoribbons (CGNRs) could exhibit negative differential resistance with peak-to-valley ... More

Confidence Intervals for Stochastic ArithmeticJul 09 2018Sep 19 2018Quantifying errors and losses due to the use of Floating-Point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation and Uncertainty Quantification (VVUQ) process. Stochastic Arithmetic is one ... More

Measuring Masking Fault-ToleranceNov 13 2018Nov 20 2018In this paper we introduce a notion of fault-tolerance distance between labeled transition systems. Intuitively, this notion of distance measures the degree of fault-tolerance exhibited by a candidate system. In practice, there are different kinds of ... More

A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamicsDec 15 2008Apr 15 2009We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major ... More

WUVS Simulator: Detectability of spectral lines with the WSO-UV spectrographsJun 08 2017Jun 12 2017The World Space Observatory - Ultraviolet (WSO-UV) space telescope is equipped with high dispersion (55,000) spectrographs working in the 1150-3100 {\AA} spectral range. To evaluate the impact of the design on the scientific objectives of the mission, ... More

$L^p$-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operatorsMar 05 2012In this paper we prove that the generalized (in the sense of Caffarelli and Calder\'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our proofs are simpler ... More

Extracting Syntactic Patterns from DatabasesOct 31 2017Dec 06 2017Many database columns contain string or numerical data that conforms to a pattern, such as phone numbers, dates, addresses, product identifiers, and employee ids. These patterns are useful in a number of data processing applications, including understanding ... More

Cluster analysis of homicide rates in the Brazilian state of Goias from 2002 to 2014Nov 11 2018Jan 02 2019Homicide mortality is a worldwide concern and has occupied the agenda of researchers and public managers. In Brazil, homicide is the third leading cause of death in the general population and the first in the 15-39 age group. In South America, Brazil ... More

Smallify: Learning Network Size while TrainingJun 10 2018As neural networks become widely deployed in different applications and on different hardware, it has become increasingly important to optimize inference time and model size along with model accuracy. Most current techniques optimize model size, model ... More

EDGES result versus CMB and low-redshift constraints on ionization historiesApr 11 2018May 18 2018We examine the results from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES), which has recently claimed the detection of a strong absorption in the 21 cm hyperfine transition line of neutral hydrogen, at redshifts demarcating ... More

A Comparative Analysis of Expected and Distributional Reinforcement LearningJan 30 2019Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from convergence guarantees, ... More

Methods for computing state similarity in Markov Decision ProcessesJun 27 2012A popular approach to solving large probabilistic systems relies on aggregating states based on a measure of similarity. Many approaches in the literature are heuristic. A number of recent methods rely instead on metrics based on the notion of bisimulation, ... More

A Visually Plausible Grasping System for Object Manipulation and Interaction in Virtual Reality EnvironmentsMar 12 2019Interaction in virtual reality (VR) environments is essential to achieve a pleasant and immersive experience. Most of the currently existing VR applications, lack of robust object grasping and manipulation, which are the cornerstone of interactive systems. ... More

Sub-20 nm Nanopores Sculptured by a Single Nanosecond Laser PulseJun 21 2018Single-molecule based 3rd generation DNA sequencing technologies have been explored with tremendous effort, among which nanopore sequencing is considered as one of the most promising to achieve the goal of $1,000 genome project towards personalized medicine. ... More

Analytical parametrization and shape classification of anomalous HH production in the EFT approachJul 19 2016In this document we study the effect of anomalous Higgs boson couplings on non-resonant pair production of Higgs bosons ($HH$) at the LHC. We explore the space of the five parameters $\kappa_{\lambda}$, $\kappa_{t}$, $c_2$, $c_g$, and $c_{2g}$ in terms ... More

Entrenamiento de una red neuronal para el reconocimiento de imagenes de lengua de senas capturadas con sensores de profundidadMar 22 2018Due to the growth of the population with hearing problems, devices have been developed that facilitate the inclusion of deaf people in society, using technology as a communication tool, such as vision systems. Then, a solution to this problem is presented ... More

The RobotriX: An eXtremely Photorealistic and Very-Large-Scale Indoor Dataset of Sequences with Robot Trajectories and InteractionsJan 19 2019Enter the RobotriX, an extremely photorealistic indoor dataset designed to enable the application of deep learning techniques to a wide variety of robotic vision problems. The RobotriX consists of hyperrealistic indoor scenes which are explored by robot ... More

World Space Observatory-Ultraviolet: ISSIS, the imaging instrumentFeb 05 2013Jun 04 2013The Imaging and Slitless Spectroscopy Instrument (ISSIS) will be flown as part of the Science Instrumentation in the World Space Observatory-Ultraviolet (WSO-UV). ISSIS will be the first UV imager to operate in a high Earth orbit from a 2-m class space ... More

Recent Top Quark Mass Measurements from CMSDec 04 2017A variety of top quark mass measurements has been made in the recent years by the CMS Collaboration. The most recent measurements performed at 8 TeV are reported here, along with a new measurement based on data collected in 2016 at 13 TeV. The current ... More

Top mass measurements in ATLAS and CMSJan 08 2018Top quarks are produced copiously at the LHC, and a variety of related measurements has been made in the recent years by the two collaborations ATLAS and CMS. The most recent measurements of the top quark mass by the two collaborations are reported here. ... More

Phase-field approach to heterogeneous nucleationDec 20 2002We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe homogeneous as well ... More

Lagrangian surfaces with circullar ellipse of curvature in complex space formsOct 09 2002We classify the Lagrangian orientable surfaces in complex space forms with the property that the ellipse of curvature is always a circle. As a consequence, we obtain new characterizations of the Clifford torus of the complex projective plane and of the ... More

New Criteria of Generic Hyperbolicity based on Periodic PointsJun 12 2009Jun 12 2012We prove a criteria for uniform hyperbolicity based on the periodic points of the transformation. More precisely, if a mild (non uniform) hyperbolicity condition holds for the periodic points of any diffeomorphism in a residual subset of a $C^1$-open ... More

The Ergodic Closing Lemma for Nonsingular EndomorphismsJun 11 2009Jun 15 2009We prove the ergodic Closing Lemma for Nonsingular Endomorphisms.

The Ngai model of relaxation: An alternative for the study of an interacting system of small particlesJun 10 1996It is shown that the Ngai model of relaxation accounts for the main experimental results of the magnetic relaxation in an assembly of interacting fine particles.

Elastic potentials as yield surfaces for homogeneous materialsMay 31 2018This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, should be used as the basis for the plastic part of elasto-plastic constitutive models. Thus, ... More

Measurements of the top quark properties at decay with CMSJan 08 2018CMS measurements of properties related to top quark decays are discussed. The results presented regard the measurement of the W boson helicity, the investigation of anomalous couplings in the Wtb vertex, and the search for very rare decays, such as t ... More

Sub-THz and Hα activity during the preflare and main phases of a GOES class M2 eventOct 13 2011Radio and optical observations of the evolution of flare-associated phenomena have shown an initial and rapid burst at 0.4 THz only followed subsequently by a localized chromospheric heating producing an H{\alpha} brightening with later heating of the ... More

Machine learning of neuroimaging to diagnose cognitive impairment and dementia: a systematic review and comparative analysisApr 05 2018Apr 11 2018INTRODUCTION: Advanced machine learning methods might help to identify dementia risk from neuroimaging, but their accuracy to date is unclear. METHODS: We systematically reviewed the literature, 2006 to late 2016, for machine learning studies differentiating ... More

Self-organizing dynamical networks able to learn autonomouslySep 28 2018We present a model for the time evolution of network architectures based on dynamical systems. We show that the evolution of the existence of a connection in a network can be described as a stochastic non-markovian telegraphic signal (NMTS). Such signal ... More

Revisiting the atomic and molecular decomposition of the weighted Hardy spacesOct 02 2017The purpose of this article is to give another molecular decomposition for members of the weighted Hardy spacs.

Tensor and Matrix models: a one-night stand or a lifetime romance?Mar 12 2018Mar 28 2018The spectra of energy eigenstates of free tensor and matrix models are organized by Kronecker coefficients and Littlewood-Richardson numbers, respectively. Exploiting recent results in combinatorics for Kronecker coefficients, we derive a formula that ... More

The automorphism group of the $s$-stable Kneser graphsSep 30 2015Nov 23 2015For $k,s\geq2$, the $s$-stable Kneser graphs are the graphs with vertex set the $k$-subsets $S$ of $\{1,\ldots,n\}$ such that the circular distance between any two elements in $S$ is at least $s$ and two vertices are adjacent if and only if the corresponding ... More

Robust Tverberg and colorful Carathéodory results via random choiceJun 28 2016May 14 2017We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem with tolerance. In particular, we give bounds for the smallest integer $N=N(t,d,r)$ such that for any $N$ points in $R^d$, there is a partition ... More

The equivariant spectral function of an invariant elliptic operator. $L^p$-bounds, caustics, and concentration of eigenfunctionsDec 07 2015Sep 17 2017Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a compact Lie group $G$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. Using Fourier integral operator techniques, we ... More

On distance sets, box-counting and Ahlfors-regular setsMay 01 2016May 21 2017We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent $s>1$. As a corollary, we improve upon a recent result of Orponen, by showing that if $A$ is Ahlfors-regular of dimension ... More

The dimension of weakly mean porous measures: a probabilistic approachOct 07 2010Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly smaller than the dimension of the ambient space. Moreover, we give an explicit bound for the packing dimension, which is asymptotically sharp in the case ... More

Self-affine sets and the continuity of subadditive pressureSep 18 2013The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open problem, by proving ... More

Hadronic currents for $τ^-\toπ^-π^0ν_τ$ and other decays of interest in TAUOLADec 05 2011A new set of hadronic form factors, which has been implemented in TAUOLA, is described.

Young-measure solutions for multidimensional systems of conservation lawsOct 22 2018We explore Young measure solutions of systems of conservation laws through an alternative variational method that introduces a suitable, non-negative error functional to measure departure of feasible fields from being a weak solution. Young measure solutions ... More

Pulsar observations at millimetre wavelengthsJun 27 2018Detecting and studying pulsars above a few GHz in the radio band is challenging due to the typical faintness of pulsar radio emission, their steep spectra, and the lack of observatories with sufficient sensitivity operating at high frequency ranges. Despite ... More

The politics of physicists social modelsMar 03 2019I give an overview of the topic of this special issue, the applications of (statistical) physics to social sciences at large. I discuss several examples of simple social models put forward by physicists and discuss their interest. I argue that while they ... More

A lower bound for the principal eigenvalue of fully nonlinear elliptic operatorsSep 07 2017In this article we present a new technique to obtain a lower bound for the principal Dirichlet eigenvalue of a fully nonlinear elliptic operator. We ilustrate the construction of an appropriate radial function required to obtain the bound in several examples. ... More

Singular equivariant asymptotics and the momentum map. Residue formulae in equivariant cohomologyOct 07 2013Let $M$ be a smooth manifold and $G$ a compact connected Lie group acting on $M$ by isometries. In this paper, we study the equivariant cohomology of ${\bf X}=T^\ast M$, and relate it to the cohomology of the Marsden-Weinstein reduced space via certain ... More

Salem sets with no arithmetic progressionsOct 26 2015Oct 30 2015We construct Salem sets in $\mathbb{R}/\mathbb{Z}$ of any dimension (including $1$) which do not contain any arithmetic progressions of length $3$. Moreover, the sets can be taken to be Ahlfors regular if the dimension is less than $1$, and the measure ... More

Moreira's Theorem on the arithmetic sum of dynamically defined Cantor setsJul 23 2008We present a complete proof of a theorem of C.G. Moreira. Under mild checkable conditions, the theorem asserts that the Hausdorff dimension of the arithmetic sum of two dynamically defined Cantor subsets of the real line, equals either the sum of the ... More

Universal black hole stability in four dimensionsApr 10 2017Apr 24 2017We show that four-dimensional black holes become stable below certain mass when the Einstein-Hilbert action is supplemented with higher-curvature terms. We prove this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily ... More

Hadronization in tau -> K K pi nu_tau decaysSep 29 2008Hadronization in tau -> K K pi nu_tau decays is driven by both vector and axial-vector currents that we study, guided by the following principles: The 1/N_C expansion -worked out at leading order, considering only the contribution of the lightest spin ... More

Quantum DecoysAug 08 2003Mar 25 2004Alice communicates with words drawn uniformly amongst $\{\ket{j}\}_{j=1..n}$, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys $\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}$ between her messages. Such pairwise superpositions ... More

Semileptonic $τ$ decays: powerful probes of non-standard charged current weak interactionsMar 07 2019When looking for heavy ($\mathcal{O}$(few TeV)) New Physics, the most efficient way to benefit from both high and low-energy measurements simultaneously is the use of the Standard Model Effective Field Theory (SMEFT). In this talk I highlight the importance ... More

A remark on certain integral operators of fractional typeMar 09 2017We study the Hp-Lq boundedness of certain integral operators of fractional type.

Hunting Vector Bundles on $\mathbb{P}^1 \times \mathbb{P}^1$Oct 12 2017May 07 2018Boij-S\"oderberg theory concerns resolutions of graded modules over a polynomial ring over a field. Specifically Boij-S\"oderberg theory gives a description of the cone of Betti diagrams for Cohen-Macaulay modules. Eisenbud and Schreyer discovered a duality ... More

A new way to construct 1-singular Gelfand-Tsetlin modulesMar 21 2017We present a simplified way to construct the Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb C)$ related to a $1$-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic Gelfand-Tsetlin ... More

Localization of elementary systems in the theory of WignerSep 20 1999Starting from Wigner's theory of elementary systems and following a recent approach of Schroer we define certain subspaces of localized wave functions in the underlying Hilbert space with the help of the theory of modular von-Neumann algebras of Tomita ... More

Analysis on real affine G-varietiesSep 05 2003We consider the action of a real linear algebraic group $G$ on a smooth, real affine algebraic variety $M\subset \R^n$, and study the corresponding left regular $G$-representation on the Banach space $C_0(M)$ of continuous, complex valued functions on ... More

Pricing of Basket Options Using Polynomial ApproximationsApr 11 2014In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning on the remaining ... More

Pseudodifferential operators on prehomogeneous vector spacesFeb 09 2004Let $G_\C$ be a connected, linear algebraic group defined over $\R$, acting regularly on a finite dimensional vector space $V_\C$ over $\C$ with $\R$-structure $V_\R$. Assume that $V_\C$ posseses a Zariski-dense orbit, so that $(G_\C,\rho,V_\C)$ becomes ... More

Rotation Vectors for Homeomorphisms of Non-Positively Curved ManifoldsDec 30 2009Sep 12 2011Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation vectors are shown ... More

Explicit construction of effective flux functions for Riemann solutionsJan 16 2017For a family of Riemann problems for systems of conservation laws, we construct a flux function that is scalar and is capable of describing the Riemann solution of the original system.

$\mathcal A$-compact mappingsMay 29 2015Jan 25 2016For a fixed Banach operator ideal $\mathcal A$, we use the notion of $\mathcal A$-compact sets of Carl and Stephani to study $\mathcal A$-compact polynomials and $\mathcal A$-compact holomorphic mappings. Namely, those mappings $g\colon X\rightarrow Y$ ... More

Overdetermined elliptic problems in topological disksOct 27 2016We introduce a method, based on the Poincare-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs ... More

On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutionsSep 25 2016Nov 21 2018We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measures such as Bernoulli convolutions as special cases. Our main result gives ... More

On the exceptional set for absolute continuity of Bernoulli convolutionsMar 16 2013Aug 05 2013We prove that the set of exceptional $\lambda\in (1/2,1)$ such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convolutions, with the exceptional set independent of the bias. This improves ... More

Integral Field Spectroscopy and multi-wavelength imaging of the nearby spiral galaxy NGC5668: an unusual flattening in metallicity gradientMay 22 2012We present the analysis of the full bi-dimensional optical spectral cube of the nearby spiral galaxy NGC 5668, observed with the PPAK IFU at the Calar Alto observatory 3.5m telescope. We make use of broad-band imaging to provide further constraints on ... More

On black holes in higher-derivative gravitiesMar 14 2017May 07 2017We establish various general results concerning static and spherically symmetric black hole solutions of general higher-derivative extensions of Einstein gravity. We prove that the only theories susceptible of admitting solutions with $g_{tt}g_{rr}=-1$ ... More

Robust Tverberg and colorful Carathéodory results via random choiceJun 28 2016Sep 14 2016We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem that allow for arbitrary small sets of points to be removed without breaking the conclusion of the result. This improves the known bounds ... More

Equal coefficients and tolerance in coloured Tverberg partitionsApr 05 2012Apr 23 2012The coloured Tverberg theorem was conjectured by B\'ar\'any, Lov\'{a}sz and F\"uredi and asks whether for any d+1 sets (considered as colour classes) of k points each in R^d there is a partition of them into k colourful sets whose convex hulls intersect. ... More

On a variant of Tykhonov regularization in optimal control under PDEsMar 24 2018We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state constraints. In addition to exploring basic issues like existence ... More

Penrose-like inequality with angular momentum for general horizonsOct 24 2018In axially symmetric space-times it is expected that the Penrose inequality can be strengthened to include angular momentum. In a recent work [2] we have proved a weaker version of this inequality for minimal surfaces, using the monotonicity of the Geroch ... More

Natural Cohomology on $\mathbb{P}^1 \times \mathbb{P}^1$Aug 22 2018A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\mathbb{P}^1 \times \mathbb{P}^1$ with natural ... More

Shapes Characterization on Address Event Representation Using Histograms of Oriented Events and an Extended LBP ApproachFeb 09 2018Address Event Representation is a thriving technology that could change digital image processing paradigm. This paper proposes a methodology to characterize the shape of objects using the streaming of asynchronous events. A new descriptor that enhances ... More

Tverberg partitions as weak epsilon-netsNov 30 2017Jun 10 2018We prove a Tverberg-type theorem using the probabilistic method. Given $\varepsilon >0$, we find the smallest number of partitions of a set $X$ in $R^d$ into $r$ parts needed in order to induce at least one Tverberg partition on every subset of $X$ with ... More

Discrete-time quantum walks and gauge theoriesOct 30 2017A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The advantage of quantum ... More

Reeb stability and the Gromov-Hausdorff limits of leaves in compact foliationsApr 23 2013We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth instead of merely ... More

Spectral Functions of Singular OperatorsMar 28 2007Oct 28 2014The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior for certain ... More

Addendum to "Singular equivariant asymptotics and Weyl's law"Jul 20 2015Sep 01 2015Let $M$ be a closed Riemannian manifold carrying an effective and isometric action of a compact connected Lie group $G$. We derive a refined remainder estimate in the stationary phase approximation of certain oscillatory integrals on $T^\ast M \times ... More

Singular equivariant asymptotics and the moment map IIJun 12 2009This is the second of a series of papers dealing with the asymptotic behavior of certain integrals occuring in the description of the spectrum of an invariant elliptic operator on a compact Riemannian manifold carrying the action of a compact, connected ... More

Singular equivariant asymptotics and Weyl's lawJan 10 2010Aug 11 2011We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we determine the asymptotic ... More

Overlapping self-affine setsAug 16 2004We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F.Przytycki and M.Urbanski. We extend their ... More

A Modified Multifractal Formalism for a Class of Self-Similar MeasuresAug 03 2004The multifractal spectrum of a Borel measure $\mu$ in $\mathbb{R}^n$ is defined as \[ f_\mu(\alpha) = \dim_H {x:\lim_{r\to 0} \frac{\log \mu(B(x,r))}{\log r}=\alpha}. \] For self-similar measures under the open set condition the behavior of this and related ... More

Projections of self-similar and related fractals: a survey of recent developmentsJan 05 2015In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand's Theorem, and quantify the size of every ... More

Improved bounds for the dimensions of planar distance setsNov 08 2018We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than $1$, improving recent estimates of Keleti and Shmerkin, and of Liu in this regime. In particular, we ... More

Porosity, dimension, and local entropies: a surveyOct 25 2011Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will survey the various ... More

Improving the Hadronization of QCD currents in TAUOLA and PHOKHARAOct 13 2008We present our study of the hadronization structure of both vector and axial-vector currents leading to decays of the tau into two kaons and a pion. The cornerstones of our framework are the large-N_C limit of QCD, the chiral structure exhibited at low ... More