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Coulomb Drag and Magnetotransport in Graphene Double LayersJun 13 2012We review the fabrication and key transport properties of graphene double layers, consisting of two graphene monolayers placed in close proximity, independently contacted, and separated by an ultra-thin dielectric. We outline a simple band structure model ... More

Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers at $ν=0$ in High Magnetic FieldsFeb 01 2011Jul 04 2011We investigate the transverse electric field ($E$) dependence of the $\nu$=0 quantum Hall state (QHS) in dual-gated graphene bilayers in high magnetic fields. The longitudinal resistivity ($\rho_{xx}$) measured at $\nu$=0 shows an insulating behavior ... More

Tunable $Γ- K$ Valley Populations in Hole-Doped Trilayer WSe$_2$Jan 10 2018We present a combined experimental and theoretical study of valley populations in the valence bands of trilayer WSe$_2$. Shubnikov$-$de Haas oscillations show that trilayer holes populate two distinct subbands associated with the $K$ and $\Gamma$ valleys, ... More

Dielectric Thickness Dependence of Carrier Mobility in Graphene with HfO2 Top DielectricOct 05 2010We investigate the carrier mobility in mono- and bi-layer graphene with a top HfO2 dielectric, as a function of the HfO2 film thickness and temperature. The results show that the carrier mobility decreases during the deposition of the first 2-4 nm of ... More

DFT Simulations of Inter-Graphene-Layer Coupling with Rotationally Misaligned hBN Tunnel Barriers in Graphene/hBN/Graphene Tunnel FETsOct 07 2016Van der Waal's heterostrucutures allow for novel devices such as two-dimensional-to-two-dimensional tunnel devices, exemplified by interlayer tunnel FETs. These devices employ channel/tunnel-barrier/channel geometries. However, during layer-by-layer exfoliation ... More

Lateral Spin Injection in Germanium NanowiresMar 19 2010Aug 24 2010Electrical injection of spin-polarized electrons into a semiconductor, large spin diffusion length, and an integration friendly platform are desirable ingredients for spin-based devices. Here we demonstrate lateral spin injection and detection in germanium ... More

Interaction and disorder in bilayer counterflow transport at filling factor oneApr 05 2005We study high mobility, interacting GaAs bilayer hole systems exhibiting counterflow superfluid transport at total filling factor $\nu=1$. As the density of the two layers is reduced, making the bilayer more interacting, the counterflow Hall resistivity ... More

Invertible families of sets of bounded degreeSep 16 1994Let H = (H,V) be a hypergraph with edge set H and vertex set V. Then hypergraph H is invertible iff there exists a permutation pi of V such that for all E belongs to H(edges) intersection of(pi(E) and E)=0. H is invertibility critical if H is not invertible ... More

Scaling Properties of Ge-SixGe1-x Core-Shell Nanowire Field Effect TransistorsDec 09 2009We demonstrate the fabrication of high-performance Ge-SixGe1-x core-shell nanowire field-effect transistors with highly doped source and drain, and systematically investigate their scaling properties. Highly doped source and drain regions are realized ... More

Interlayer Exciton Laser with Extended Spatial Coherence in an Atomically-Thin HeterostructureJan 03 2019Two-dimensional semiconductors have emerged as a new class of materials for nanophotonics for their strong exciton-photon interaction and flexibility for engineering and integration. Taking advantage of these properties, we engineer an efficient lasing ... More

Atomistic simulation of the electronic states of adatoms in monolayer MoS2May 30 2013Mar 26 2014Using an ab initio density functional theory (DFT) based electronic structure method, we study the effects of adatoms on the electronic properties of monolayer transition metal dichalcogenide (TMD) Molybdenum-disulfide (MoS2). We consider the 1st (Li, ... More

Giant Frictional Drag in Double Bilayer Graphene HeterostructuresMar 02 2016We study the frictional drag between carriers in two bilayer graphene flakes separated by a 2 $-$ 5 nm thick hexagonal boron nitride dielectric. At temperatures ($T$) lower than $\sim$ 10 K, we observe a large anomalous negative drag emerging predominantly ... More

From Exceptional Field Theory to Heterotic Double Field Theory via K3Dec 06 2016In this paper we show how to obtain the heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the $\mathrm{SL}(5)$ exceptional field theory and show that when the extended space contains a generalised ... More

Minimality and nonergodicity on a family of flat surfaces in genus 3Jan 03 2008We prove that a certain family of flat surfaces in genus 3 does not fulfill Veech's Dichotomy. These flat surfaces provide uncountably many minimal but nonergodic directions. The conditions on this family are a combinatorical one and an irrationality ... More

Advances in Artificial Intelligence: Deep Intentions, Shallow AchievementsMay 18 2015Over the past decade, AI has made a remarkable progress due to recently revived Deep Learning technology. Deep Learning enables to process large amounts of data using simplified neuron networks that simulate the way in which the brain works. At the same ... More

You want to survive the data deluge: Be careful, Computational Intelligence will not serve you as a rescue boatJul 20 2016We are at the dawn of a new era, where advances in computer power, broadband communication and digital sensor technologies have led to an unprecedented flood of data inundating our surrounding. It is generally believed that means such as Computational ... More

The physical and circuit-theoretic significance of the Memristor : Full versionFeb 07 2016Feb 10 2016It is observed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence of the voltage and current state variables, associated by their electrodynamics sense with ... More

Dualising consistent truncationsDec 30 2015We use exceptional field theory to establish a duality between certain consistent 7-dimensional truncations with maximal SUSY from IIA to IIB. We use this technique to obtain new consistent truncations of IIB on $S^3$ and $H^{p,q}$ and also give a no-go ... More

Beyond traditional Curvature-Dimension I: new model spaces for isoperimetric and concentration inequalities in negative dimensionSep 14 2014Aug 03 2015We study the isoperimetric, functional and concentration properties of $n$-dimensional weighted Riemannian manifolds satisfying the Curvature-Dimension condition, when the generalized dimension $N$ is negative, and more generally, is in the range $N \in ... More

Cognitive Surveillance: Why does it never appear among the AVSS Conferences topics?Jun 22 2014Video Surveillance is a fast evolving field of research and development (R&D) driven by the urgent need for public security and safety (due to the growing threats of terrorism, vandalism, and anti-social behavior). Traditionally, surveillance systems ... More

Cognitive Robotics: for never was a story of more woe than thisJan 08 2014Jul 19 2014We are now on the verge of the next technical revolution - robots are going to invade our lives. However, to interact with humans or to be incorporated into a human "collective" robots have to be provided with some human-like cognitive abilities. What ... More

A Proof of Bobkov's Spectral Bound For Convex Domains via Gaussian Fitting and Free Energy EstimationFeb 05 2012We obtain a new proof of Bobkov's lower bound on the first positive eigenvalue of the (negative) Neumann Laplacian (or equivalently, the Cheeger constant) on a bounded convex domain $K$ in Euclidean space. Our proof avoids employing the localization method ... More

An approximate analytical (structural) superposition in terms of two, or more, "alfa"-circuits of the same topology: Pt. 2 - the "internal circuit mechanism"Apr 26 2010Apr 27 2010This is the second part, after [1], of the research devoted to analysis of 1-ports composed of similar conductors ("f-circuits") described by the characteristic i = f(v) of a polynomial type. This analysis is performed by means of the power-law "alfa"-circuits" ... More

When you talk about "Information processing" what actually do you have in mind?Dec 19 2012"Information Processing" is a recently launched buzzword whose meaning is vague and obscure even for the majority of its users. The reason for this is the lack of a suitable definition for the term "information". In my attempt to amend this bizarre situation, ... More

Unveiling the mystery of visual information processing in human brainJul 02 2008It is generally accepted that human vision is an extremely powerful information processing system that facilitates our interaction with the surrounding world. However, despite extended and extensive research efforts, which encompass many exploration fields, ... More

Modeling Visual Information Processing in Brain: A Computer Vision Point of View and ApproachAug 07 2007We live in the Information Age, and information has become a critically important component of our life. The success of the Internet made huge amounts of it easily available and accessible to everyone. To keep the flow of this information manageable, ... More

A comment on the low-dimensional Busemann-Petty problemDec 10 2005The generalized Busemann-Petty problem asks whether centrally-symmetric convex bodies having larger volume of all m-dimensional sections necessarily have larger volume. When m>3 this is known to be false, but the cases m=2,3 are still open. In those cases, ... More

Generalized Intersection BodiesDec 02 2005Apr 28 2006We study the structures of two types of generalizations of intersection-bodies and the problem of whether they are in fact equivalent. Intersection-bodies were introduced by Lutwak and played a key role in the solution of the Busemann-Petty problem. A ... More

Searching for image information content, its discovery, extraction, and representationMay 02 2005Image information content is known to be a complicated and controvercial problem. This paper posits a new image information content definition. Following the theory of Solomonoff-Kolmogorov-Chaitin's complexity, we define image information content as ... More

Switched systems and the logical foundation of circuit theoryDec 15 2008Switched (singular) systems become very common, which requires some revision of the conceptual basis of system theory.

On the concept of switching nonlinearity (a comment on "Switching control of linear systems for generating chaos" by X. Liu, K-L. Teo, H. Zhang and G. Chen)Mar 21 2008Mar 22 2008It is explained and stressed that the chaotic states in [1] are obtained by means of nonlinear switching.

On the role of Convexity in Isoperimetry, Spectral-Gap and ConcentrationDec 26 2007Dec 24 2008We show that for convex domains in Euclidean space, Cheeger's isoperimetric inequality, spectral gap of the Neumann Laplacian, exponential concentration of Lipschitz functions, and the a-priori weakest requirement that Lipschitz functions have \emph{arbitrarily ... More

Notes on the connectivity of Cayley coset digraphsNov 10 1994Hamidoune's connectivity results for hierarchical Cayley digraphs are extended to Cayley coset digraphs and thus to arbitrary vertex transitive digraphs. It is shown that if a Cayley coset digraph can be hierarchically decomposed in a certain way, then ... More

Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter ConditionAug 23 2011Aug 29 2012We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a probability measure, whose generalized Ricci curvature is bounded from below (possibly negatively), and generalized dimension and diameter of the convex support are ... More

Spectral Estimates, Contractions and HypercontractivityAug 03 2015Jul 14 2016Sharp comparison theorems are derived for all eigenvalues of the (weighted) Laplacian, for various classes of weighted-manifolds (i.e. Riemannian manifolds endowed with a smooth positive density). Examples include Euclidean space endowed with strongly ... More

Advances in Computational Biology: A Real Boost or a Wishful ThinkingMay 18 2015Computational biology is on the verge of a paradigm shift in its research practice - from a data-based (computational) paradigm to an information-based (cognitive) paradigm. As in the other research fields, this transition is impeded by lack of a right ... More

Harmonic Measures on the Sphere via Curvature-DimensionMay 16 2015We show that the family of probability measures on the $n$-dimensional unit sphere, having density proportional to: \[ S^n \ni y \mapsto \frac{1}{|y - x|^{n+\alpha}}, \] satisfies the Curvature-Dimension condition $CD(n-1-\frac{n+\alpha}{4},-\alpha)$, ... More

Advances in Artificial Intelligence: Are you sure, we are on the right track?Feb 17 2015Over the past decade, AI has made a remarkable progress. It is agreed that this is due to the recently revived Deep Learning technology. Deep Learning enables to process large amounts of data using simplified neuron networks that simulate the way in which ... More

The Spatial Structure of Transnational Human ActivityJan 23 2015Recent studies have shown that the spatial structures of animal displacements and local-scale human motion follow L\'{e}vy flights. Whether transnational human activity (THA) also exhibits such a pattern has however not been thoroughly examined as yet. ... More

Not only a lack of right definitions: Arguments for a shift in information-processing paradigmSep 01 2010Machine Consciousness and Machine Intelligence are not simply new buzzwords that occupy our imagination. Over the last decades, we witness an unprecedented rise in attempts to create machines with human-like features and capabilities. However, despite ... More

Higher dimensional conformal metrics from PDEs and Null Surface Formulation of GRNov 14 2011May 31 2012We analyze the relationship between $n$-dimensional conformal metrics and a certain class of partial differential equations (PDEs) that are in duality with the eikonal equation. In particular, we extend the Null Surface Formulation of General Relativity ... More

The nonlinear-by-switching systems (a heuristic discussion of some basic singular systems)Jan 23 2008Jan 24 2008Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly switching, systems. ... More

Generating Static Black Holes in Higher Dimensional Space-TimesOct 30 2003Nov 06 2003In this article we extend to higher dimensional space-times a recent theorem proved by Salgado which characterizes a three-parameter family of static and spherically symmetric solutions to the Einstein Field Equations. As it happens in four dimensions, ... More

I'm sorry to say, but your understanding of image processing fundamentals is absolutely wrongAug 01 2008The ongoing discussion whether modern vision systems have to be viewed as visually-enabled cognitive systems or cognitively-enabled vision systems is groundless, because perceptual and cognitive faculties of vision are separate components of human (and ... More

Generalized Intersection Bodies are not EquivalentJan 26 2007Feb 04 2007In 2000, A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied by the author in [http://www.arxiv.org/math.MG/0512058], ... More

A remark on two duality relationsMar 19 2006Jun 17 2006We remark that an easy combination of two known results yields a positive answer, up to log(n) terms, to a duality conjecture that goes back to Pietsch. In particular, we show that for any two symmetric convex bodies K,T in R^n, denoting by N(K,T) the ... More

Paving the Way for Image Understanding: A New Kind of Image Decomposition is DesiredJul 22 2005In this paper we present an unconventional image segmentation approach which is devised to meet the requirements of image understanding and pattern recognition tasks. Generally image understanding assumes interplay of two sub-processes: image information ... More

D-branes on some one- and two-parameter Calabi-Yau hypersurfacesDec 21 1999Feb 10 2000D-branes on one-parameter Calabi-Yau spaces and two-parameter K3-fibered Calabi-Yau manifolds are analyzed from both the Gepner model point of view and the geometric perspective. We compute part of the spectrum of the boundary states and comment on the ... More

On the role of Convexity in Functional and Isoperimetric InequalitiesApr 03 2008Dec 24 2008This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity assumptions (e.g. ... More

Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivityOct 20 2018Non-transversal intersection of the free and fixed boundary is shown to hold and a classification of blow-up solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the mean-field ... More

Lower bounds for identifying subset members with subset queriesNov 03 1994An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs in areas such ... More

Analytic Continuation of Hypergeometric Functions in the Resonant CaseFeb 03 2016We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant ... More

On the confinement of semiflexible chains under torsionDec 27 2012The effect of a finite torque on semiflexible polymers in a confined environment is investigated. It is shown how a new lengthscale appears in the strongly confined limit. The influence of a torque on the extension of biopolymers in nanochannels is also ... More

Let us first agree on what the term "semantics" means: An unorthodox approach to an age-old debateJan 01 2012Traditionally, semantics has been seen as a feature of human language. The advent of the information era has led to its widespread redefinition as an information feature. Contrary to this praxis, I define semantics as a special kind of information. Revitalizing ... More

An approximate analytical (structural) superposition in terms of two, or more, "alfa"-circuits of the same topology: Pt.1 - description of the superpositionApr 23 2010Apr 26 2010One-ports named "f-circuits", composed of similar conductors described by a monotonic polynomial, or quasi-polynomial (i.e. with positive but not necessarily integer, powers) characteristic i = f(v) are studied, focusing on the algebraic map f --> F. ... More

Free boundary regularity in the optimal partial transport problemOct 11 2012Mar 19 2013In the optimal partial transport problem, one is asked to transport a fraction $0<m \leq \min\{||f||_{L^1}, ||g||_{L^1}\}$ of the mass of $f=f \chi_\Omega$ onto $g=g\chi_\Lambda$ while minimizing a transportation cost. If $f$ and $g$ are bounded away ... More

The "psychological map of the brain", as a personal information card (file), - a project for the student of the 21st centuryJan 17 2011Jan 19 2011We suggest a procedure that is relevant both to electronic performance and human psychology, so that the creative logic and the respect for human nature appear in a good agreement. The idea is to create an electronic card containing basic information ... More

On the mathematical representation of nonlinearityJul 07 2008Oct 24 2008The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more "constructive", is considered supported by arguments related to: the axiomatization of system theory, ... More

In Quest of Image Semantics: Are We Looking for It Under the Right Lamppost?Sep 02 2006In the last years we witness a dramatic growth of research focused on semantic image understanding. Indeed, without understanding image content successful accomplishment of any image-processing task is simply incredible. Up to the recent times, the ultimate ... More

A converse to Maz'ya's inequality for capacities under curvature lower boundMar 27 2009We survey some classical inequalities due to Maz'ya relating isocapacitary inequalities with their functional and isoperimetric counterparts in a measure-metric space setting, and extend Maz'ya's lower bound for the $q$-capacity ($q>1$) in terms of the ... More

Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower BoundFeb 09 2009Dec 01 2009It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the measure ... More

Does a Plane Imitate a Bird? Does Computer Vision Have to Follow Biological Paradigms?Nov 04 2005We posit a new paradigm for image information processing. For the last 25 years, this task was usually approached in the frame of Treisman's two-stage paradigm [1]. The latter supposes an unsupervised, bottom-up directed process of preliminary information ... More

7-dimensional ${\cal N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field TheoryDec 06 2016We show how to construct seven-dimensional half-maximally supersymmetric consistent truncations of 11-/10-dimensional SUGRA using $\mathrm{SL}(5)$ exceptional field theory. Such truncations are defined on generalised $\mathrm{SU}(2)$-structure manifolds ... More

Generalized degrees and densities for families of setsNov 08 1994Let F be a family of subsets of {1,2,...,n}. The width-degree of an element x in at least one member of F is the width of the family {U in F | x in U}. If F has maximum width-degree at most k, then F is locally k-wide. Bounds on the size of locally k-wide ... More

Autoequivalences of twisted K3 surfacesNov 02 2017Jan 31 2019Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a given Hodge isometry ... More

Strong Aharonov-Bohm oscillations in GaAs two-dimensional holesDec 27 2006Mar 07 2007We measured Aharonov-Bohm resistance oscillations in a shallow two-dimensional GaAs hole ring structure, defined by local anodic surface oxidation. The amplitude of the oscillations is about 10% of the ring resistance, the strongest seen in a hole system. ... More

Zeeman splitting of interacting two-dimensional electrons with two effective massesJun 05 2006Jun 06 2006We have realized an AlAs two-dimensional electron system in which electrons occupy conduction-band valleys with different Fermi contours and effective masses. In the quantum Hall regime, we observe both resistivity spikes and persistent gaps at crossings ... More

Shubnikov-de Haas oscillations of high mobility holes in monolayer and bilayer WSe$_2$: Landau level degeneracy, effective mass, and negative compressibilityFeb 02 2016We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, ... More

Highly Valley-Polarized Singlet and Triplet Interlayer Excitons in van der Waals HeterostructureJan 01 2019Jan 31 2019Two-dimensional semiconductors feature valleytronics phenomena due to locking of the spin and momentum valley of the electrons. However, the valley polarization is intrinsically limited in monolayer crystals by the fast intervalley electron-hole exchange. ... More

Silicon-based Infrared Metamaterials with Ultra-Sharp Fano ResonancesSep 25 2013Metamaterials and meta-surfaces represent a remarkably versatile platform for light manipulation, biological and chemical sensing, nonlinear optics, and even spaser lasing. Many of these applications rely on the resonant nature of metamaterials, which ... More

Realization of a High Mobility Dual-gated Graphene Field Effect Transistor with Al2O3 DielectricJan 19 2009Sep 12 2009We fabricate and characterize dual-gated graphene field-effect transistors (FETs) using Al2O3 as top-gate dielectric. We use a thin Al film as a nucleation layer to enable the atomic layer deposition of Al2O3. Our devices show mobility values of over ... More

Chemical Potential and Quantum Hall Ferromagnetism in Bilayer GrapheneJan 03 2014Jul 07 2014Bilayer graphene has a unique electronic structure influenced by a complex interplay between various degrees of freedom. We probe its chemical potential using double bilayer graphene heterostructures, separated by a hexagonal boron nitride dielectric. ... More

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin SystemsFeb 23 2012We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates ... More

Graphical NewtonAug 05 2015Apr 25 2016Computing the Newton step for a generic function $f: \mathbb{R}^N \rightarrow \mathbb{R}$ takes $O(N^{3})$ flops. In this paper, we explore avenues for reducing this bound, when the computational structure of $f$ is known beforehand. It is shown that ... More

Entire approximations for a class of truncated and odd functionsSep 06 2013We solve the problem of finding optimal entire approximations of prescribed exponential type (unrestricted, majorant and minorant) for a class of truncated and odd functions with a shifted exponential subordination, minimizing the $L^1(\R)$-error. The ... More

Extremal functions in de Branges and Euclidean spaces IIAug 10 2015This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of Beurling and ... More

Competition between Kondo screening and quantum Hall edge reconstructionOct 20 2015We report on a Kondo correlated quantum dot connected to two-dimensional leads where we demonstrate the renormalization of the g-factor in the pure Zeeman case i.e, for magnetic fields parallel to the plane of the quantum dot. For the same system we study ... More

Extremal problems in de Branges spaces: the case of truncated and odd functionsDec 02 2014In this paper we find extremal one-sided approximations of exponential type for a class of truncated and odd functions with a certain exponential subordination. These approximations optimize the $L^1(\mathbb{R}, |E(x)|^{-2}dx)$-error, where $E$ is an ... More

Dualising consistent IIA / IIB truncationsOct 12 2015Dec 10 2015We use exceptional field theory to establish a duality between certain consistent 7-dimensional truncations with maximal SUSY from IIA to IIB. We use this technique to obtain new consistent truncations of IIB on $S^3$ and $H^{p,q}$ and work out the explicit ... More

Obstructions to regularity in the classical Monge problemNov 22 2013We provide counterexamples to regularity of optimal maps in the classical Monge problem under various assumptions on the initial data. Our construction is based on a variant of the counterexample in \cite{LSW} to Lipschitz regularity of the monotone optimal ... More

Método de BPHZ para Pontos de Lifshitz m-Axiais AnisotrópicosMar 08 2014In this work we investigate the critical behavior of physical systems with competing interactions that present points Lifshitz m-axial. For this study we used the techniques of Quantum Field Theory with Massive Scalar interactions of type {\lambda}{\phi}^4 ... More

A Unifying Framework for Linearly Solvable ControlFeb 14 2012Recent work has led to the development of an elegant theory of Linearly Solvable Markov Decision Processes (LMDPs) and related Path-Integral Control Problems. Traditionally, MDPs have been formulated using stochastic policies and a control cost based ... More

Moduli Stabilization in Toroidal Type IIB OrientifoldsDec 22 2005We discuss the first step in the moduli stabilization program a la KKLT for a general class of resolved toroidal type IIB orientifolds. In particular, we discuss their geometry, the topology of the divisors relevant for the D3-brane instantons which can ... More

An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodiesMar 28 2007Nov 21 2007We prove an isoperimetric inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by ... More

Robust dynamical decoupling with bounded controlsAug 09 2002We propose a general procedure for implementing dynamical decoupling without requiring arbitrarily strong, impulsive control actions. This is accomplished by designing continuous decoupling propagators according to Eulerian paths in the decoupling group ... More

Nonbinary Quantum Stabilizer CodesMay 01 2000We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over $GF_{4}$ and binary quantum codes to one between selforthogonal codes ... More

LP Mixed Data Science : Outline of TheoryNov 04 2013Nov 06 2013This article presents the theoretical foundation of a new frontier of research-`LP Mixed Data Science'-that simultaneously extends and integrates the practice of traditional and novel statistical methods for nonparametric exploratory data modeling, and ... More

United Statistical Algorithm, Small and Big Data: Future OF StatisticianAug 02 2013This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small Data and Big ... More

LP Approach to Statistical ModelingMay 11 2014We present an approach to statistical data modeling and exploratory data analysis called `LP Statistical Data Science.' It aims to generalize and unify traditional and novel statistical measures, methods, and exploratory tools. This article outlines fundamental ... More

Derivative bounds for fractional maximal functionsOct 10 2015Jan 18 2016In this paper we study the regularity properties of fractional maximal operators acting on $BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.

Hypothesis testing of scientific Monte Carlo calculationsJan 05 2018The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. ... More

Non-transversal intersection of free and fixed boundary for fully nonlinear elliptic operators in two dimensionsMay 09 2015In the study of classical obstacle problems, it is well known that in many configurations the free boundary intersects the fixed boundary tangentially. The arguments involved in producing results of this type rely on the linear structure of the operator. ... More

Bounding $S_n(t)$ on the Riemann hypothesisFeb 14 2017Let $S(t) = \tfrac{1}{\pi} \arg \zeta (\frac12 + it)$ be the argument of the Riemann zeta-function at the point $\tfrac12 + it$. For $n \geq 1$ and $t>0$ define its iterates \begin{equation*} S_n(t) = \int_0^t S_{n-1}(\tau) \,{\rm d}\tau\, + \delta_n\,, ... More

Maximal Invariants Over Symmetric ConesJan 02 2012In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered eigenvalues ... More

Extremal functions in de Branges and Euclidean spacesJun 20 2014In this work we obtain optimal majorants and minorants of exponential type for a wide class of radial functions on $\mathbb{R}^N$. These extremal functions minimize the $L^1(\mathbb{R}^N, |x|^{2\nu + 2 - N}dx)$-distance to the original function, where ... More

Emergence of Topologically Protected Helical States in Minimally Twisted Bilayer GrapheneFeb 08 2018Bilayer graphene samples in which inversion symmetry is broken have quantum valley Hall ground states that support counterpropogating topologically protected helical (TPH) edge states localized along domain walls between AB and BA stacking regions. Moreover, ... More

Coarsening in one dimension: invariant and asymptotic statesMay 29 2015Dec 02 2015We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential rate and the ... More

A strictly-functorial and small dg-enhancement of the derived category of perfect complexesFeb 23 2015Let k be a field. We construct a strictly-functorial presheaf of small dg-categories over k on the category of k-schemes of finite type, which gives dg-enhancements of the derived categories of perfect complexes.

Sharper lower and upper bounds for the gaussian rank of a graphJun 18 2014Aug 04 2014An open problem in graphical Gaussian models is to determine the smallest number of observations needed to guarantee the existence of the maximum likelihood estimator of the covariance matrix with probability one. In this paper we formalize a closely ... More

On the stability of the polygonal isoperimetric inequalityFeb 18 2014We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a ... More