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Achieving Connectivity Between Wide Areas Through Self-Organising Robot Swarm Using Embodied EvolutionJul 12 2018Abruptions to the communication infrastructure happens occasionally, where manual dedicated personnel will go out to fix the interruptions, restoring communication abilities. However, sometimes this can be dangerous to the personnel carrying out the task, ... More

Towards autonomous ocean observing systems using Miniature Underwater Gliders with UAV deployment and recovery capabilitiesFeb 08 2019This paper presents preliminary results towards the development of an autonomous ocean observing system using Miniature Underwater Gliders (MUGs) that can operate with the support of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vessels (USVs) ... More

Coulomb drag in quantum circuitsSep 09 2008Oct 22 2008We study drag effect in a system of two electrically isolated quantum point contacts (QPC), coupled by Coulomb interactions. Drag current exhibits maxima as a function of QPC gate voltages when the latter are tuned to the transitions between quantized ... More

Keldysh technique and non-linear sigma-model: basic principles and applicationsJan 23 2009Apr 27 2009The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic ... More

Coulomb drag at zero temperatureOct 08 2007We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is inversely proportional to the third power of the dimensionless sheet ... More

Keldysh Ginzburg-Landau action of fluctuating superconductorsJun 19 2007Sep 24 2007We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent ... More

Ocean gravitational-modes in transient neutron starsNov 30 2015The neutron star ocean is a plasma of ions and electrons that extends from the base of the neutron star's envelope to a depth where the plasma crystallizes into a solid crust. During an accretion outburst in an X-ray transient, material accumulates in ... More

The spectral norm error of the naive Nystrom extensionOct 24 2011The naive Nystrom extension forms a low-rank approximation to a positive-semidefinite matrix by uniformly randomly sampling from its columns. This paper provides the first relative-error bound on the spectral norm error incurred in this process. This ... More

Special relativity as classical kinematics of a particle with the upper bound on its speed. Part II. The general Lorentz transforrmation and the generalized velocity composition theoremMay 09 2014The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics without employing ... More

A Short Note on Mapping CylindersJun 06 2012Jul 13 2012Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.

Extending and Characterizing Quantum Magic GamesSep 18 2012The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations cannot do so, a phenomenon dubbed "quantum pseudo-telepathy". ... More

A Grauert Type Theorem and Extension of Matrices with Entries in H^{\infty}Dec 15 2001In the paper we prove an extension theorem for matrices with entries in H^{\infty}(U) for U being a Riemann surface of a special type. One of the main components of the proof is a Grauert type theorem for "holomorphic" vector bundles defined over maximal ... More

Resolving disagreement for eta/s in a CFT plasma at finite couplingMay 17 2008The ratio of shear viscosity to entropy density in a strongly coupled CFT plasma can be computed using the AdS/CFT correspondence either from equilibrium correlation functions or from the Janik-Peschanski dual of the boost invariant plasma expansion. ... More

N=2* hydrodynamicsJun 23 2004Using gauge theory /string theory correspondence certain universal aspects of the strongly coupled four dimensional gauge theory hydrodynamics were established in hep-th/0311175. The analysis were performed in the framework of ``membrane paradigm'' approach ... More

Localization and holography in N=2 gauge theoriesApr 20 2013Sep 18 2013We compare exact results from Pestun's localization of SU(N) N=2^* gauge theory on S^4 with available holographic models. While localization can explain the Coulomb branch vacuum of the holographic Pilch-Warner flow, it disagrees with the holographic ... More

Quantum phase transitions in cascading gauge theoryAug 30 2011We study a ground state of N=1 supersymmetric SU(K+P) x SU(K) cascading gauge theory of Klebanov et.al [1,2] on R x S^3 at zero temperature. A radius of S^3 sets a compactification scale mu. An interplay between mu and the strong coupling scale Lambda ... More

On SUGRA description of boost-invariant conformal plasma at strong couplingMar 24 2008Mar 26 2008We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. ... More

Bulk viscosity of gauge theory plasma at strong couplingAug 27 2007Sep 01 2007We propose a lower bound on bulk viscosity of strongly coupled gauge theory plasmas. Using explicit example of the N=2^* gauge theory plasma we show that the bulk viscosity remains finite at a critical point with a divergent specific heat. We present ... More

Transport properties of cascading gauge theoriesSep 12 2005Cascading gauge theories of Klebanov et.al. provide a model within a framework of gauge theory/string theory duality for a four dimensional non-conformal gauge theory with a spontaneously generated mass scale. Using the dual supergravity description we ... More

On effective action of string theory flux compactificationsDec 07 2003Feb 12 2004We discuss four dimensional effective actions of string theory flux compactifications. These effective actions describe four dimensional gravity coupled to overall Kahler modulus of the compactification manifold. We demonstrate the agreement between ten ... More

On the thermodynamic instability of LSTJul 12 2001Jul 20 2001The high energy thermodynamics of Little String Theory (LST) is known to be unstable. An unresolved question is whether the corresponding instability in LST holographic dual is of stringy or supergravity origin. We study UV thermodynamics of a large metric ... More

New type scalar fields for cosmic accelerationJun 07 2006We present a model where a non-conventional scalar field may act like dark energy leading to cosmic acceleration. The latter is driven by an appropriate field configuration, which result in an effective cosmological constant. The potential role of such ... More

Levels of Distribution and the Affine SieveJun 05 2014This article is an expanded version of the author's lecture in the Basic Notions Seminar at Harvard, September 2013. Our goal is a brief and introductory exposition of aspects of two topics in sieve theory which have received attention recently: (1) the ... More

Volumes of line bundlesNov 26 2002Dec 10 2003This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,

A Direct Sampler for G-Wishart VariatesApr 04 2013The G-Wishart distribution is the conjugate prior for precision matrices that encode the conditional independencies of a Gaussian graphical model. While the distribution has received considerable attention, posterior inference has proven computationally ... More

Z-set unknotting in uncountable products of realsFeb 08 2011We prove a version of $Z$-set unknotting theorem for uncountable products of real numbers.

Generalized varieties of sums of powersJan 09 2014Let $X\subset\mathbb{P}^{N}$ be an irreducible, non-degenerate variety. The generalized variety of sums of powers $VSP_H^X(h)$ of $X$ is the closure in the Hilbert scheme $Hilb_{h}(X)$ of the locus parametrizing collections of points $\{x_{1},...,x_{h}\}$ ... More

A fast analysis-based discrete Hankel transform using asymptotic expansionsJan 07 2015May 20 2015A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order $0$ as well as evaluating Schl\"{o}milch and Fourier--Bessel expansions in $\mathcal{O}(N(\log N)^2/\log\!\log N)$ operations. The algorithm is based ... More

Nested Bethe Ansatz and Finite Dimensional Canonical Commutation RelationsApr 24 2000Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed ... More

Spectral Difference Equations Satisfied by KP Soliton WavefunctionsNov 11 1998The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these translational ... More

Bispectrality of $N$-Component KP Wave Functions: A Study in Non-CommutativityMay 11 2015Nov 01 2015A wave function of the $N$-component KP Hierarchy with continuous flows determined by an invertible matrix $H$ is constructed from the choice of an $MN$-dimensional space of finitely-supported vector distributions. This wave function is shown to be an ... More

Grassmannians, Nonlinear Wave Equations and Generalized Schur FunctionsNov 11 1998Feb 26 1999A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear partial differential ... More

Bispectral KP Solutions and Linearization of Calogero-Moser Particle SystemsDec 14 1994Dec 15 1994A new construction using finite dimensional dual grassmannians is developed to study rational and soliton solutions of the KP hierarchy. In the rational case, properties of the tau function which are equivalent to bispectrality of the associated wave ... More

Ocean g-modes on transient neutron starsNov 30 2015Nov 17 2016The neutron star ocean is a plasma of ions and electrons that extends from the base of the neutron star's envelope to a depth where the plasma crystallizes into a solid crust. During an accretion outburst in an X-ray transient, material accumulates in ... More

Schwarz triangle mappings and Teichmüller curves: abelian square-tiled surfacesMar 13 2012Oct 17 2012We consider normal covers of CP^1 with abelian deck group, branched over at most four points. Families of such covers yield arithmetic Teichm\"uller curves, whose period mapping may be described geometrically in terms of Schwarz triangle mappings. These ... More

Ground state of a large number of particles on a frozen topographyJan 25 2006Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical ... More

Exponential concentration of cover timesJul 29 2014We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding-Lee-Peres and Ding. The estimate is asymptotically sharp as the ratio of hitting time to cover time goes to zero. ... More

Crossover in the local density of states of mesoscopic SNS junctionsMay 05 2008Andreev levels deplete energy states above the superconductive gap, which leads to the peculiar nonmonotonous crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions. This effect is especially pronounced ... More

KP Solitons are BispectralSep 07 1998It is by now well known that the wave functions of rational solutions to the KP hierarchy which can be achieved as limits of the pure $n$-soliton solutions satisfy an eigenvalue equation for ordinary differential operators in the spectral parameter. This ... More

The Non-Axiomatizability of O-MinimalityMar 13 2012Mar 29 2012Fix a language L extending the language of real closed fields by at least one new predicate or function symbol. Call an L-structure R pseudo-o-minimal if it is (elementarily equivalent to) an ultraproduct of o-minimal structures. We show that for any ... More

The effect of stock market indexing on corporate tax avoidanceSep 01 2015Membership in the Russell 1000 and 2000 Indices is based on a ranking of market capitalization in May. Each index is separately value weighted such that firms just inside the Russell 2000 are comparable in size to firms just outside (i.e. at the bottom ... More

The Cosmological ConstantNov 23 2012Contrary to popular mythology, Einstein did not invent the cosmological constant just in order construct his model universe. He discussed it earlier in "The Foundations of General Relativity" in connection with the proper structure of the source-free ... More

A Note on Optimality of Quantum Circuits over Metaplectic BasisJun 07 2016Jun 09 2016Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate $R=|0\rangle \langle 0| + |1\rangle \langle 1| - |2\rangle \langle 2|$. It is arguably, a ternary basis with the simplest ... More

Applications of Thin OrbitsJun 20 2016This text is based on a series of three expository lectures on a variety of topics related to "thin orbits," as delivered at Durham University's Easter School on "Dynamics and Analytic Number Theory" in April 2014. The first lecture reviews closed geodesics ... More

Tensor networks for dynamic spacetimesNov 18 2016Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary ... More

The Bertini involutionDec 05 2012We summarize and extend E. Moody's results on the explicit equations related to the Bertini involution.

On the Local Theory of Billiards in PolygonsMay 06 2014A periodic trajectory on a polygonal billiard table is stable if it persists under any sufficiently small perturbation of the table. It is a standard result that a periodic trajectory on an $n$-gon gives rise in a natural way to a closed path on an $n$-punctured ... More

Physics and Chemistry of Purcell's AlignmentJan 17 1995Paramagnetic alignment of suprathermally rotating grains is discussed in view of recent progress in understanding subtle processes taking place over grain surface. It is shown that in typical ISM conditions, grains with surfaces of amorphous H$_{2}$O ... More

Vacuum Instability in Topologically Massive Gauge TheoryAug 12 1998We find the critical charge for a topologically massive gauge theory for any gauge group, generalising our earlier result for SU(2). The relation between critical charges in TMGT, singular vectors in the WZNW model and logarithmic CFT is investigated. ... More

A New Definition of the Steenrod Operations in Algebraic GeometryMay 09 2008The Steenrod operations (mod p) in Chow theory are defined for any prime p for a quasi-projective scheme, without appealing to the results of any domain but Milnor's K-theory. The new definition also gives a direct formula that depends only on the scheme ... More

Transcendental lattice of an extremal elliptic surfaceJul 10 2009Oct 01 2009We develop an algorithm computing the transcendental lattice and the Mordell--Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces

Irreducible $p$-local compact groups I. The structure of $p$-local compact groups of rank $1$Dec 18 2013Jan 23 2014Let $p$ be a fixed prime number. The main purpose of this paper is to introduce the notion of \textit{irreducible} $p$-local compact group, which provides a first reduction towards a classification of all $p$-local compact groups. In order to test this ... More

Outer automorphism groups of some ergodic equivalence relationsDec 17 2003Let R a be countable ergodic equivalence relation of type II_1 on a standard probability space (X,m). The group Out(R) of outer automorphisms of R consists of all invertible Borel measure preserving maps of the space which map R-classes to R-classes modulo ... More

A divisorial valuation with irrational volumeJun 21 2002In this paper we present a divisorial valuation with irrational volume using an algebro-geometric construction.

On certain Cuntz-Pimsner algebrasAug 29 2001Let $A$ be a separable unital C*-algebra and let $\pi : A \ra \Lc(\Hf)$ be a faithful representation of $A$ on a separable Hilbert space $\Hf$ such that $\pi(A) \cap \Kc(\Hf) = \{0 \}$. We show that $\Oc_E$, the Cuntz-Pimsner algebra associated to the ... More

Plane sextics with a type $\bold E_8$ singular pointFeb 13 2009We construct explicit geometric models for and compute the fundamental groups of all plane sextics with simple singularities only and with at least one type $\bold E_8$ singular point. In particular, we discover four new sextics with nonabelian fundamental ... More

Classical Zariski pairsJul 10 2009We compute the fundamental groups of all irreducible plane sextics constituting classical Zariski pairs

On H-closed paratopological groupsMar 28 2010A Hausdorff paratopological group G is H-closed if G is closed in each Hausdorff paratopological group containing G. We obtain criteria of H-closedness for some classes of abelian paratopological groups. In particular, for topological groups.

Universal C*-algebra of real rank zeroNov 26 1999Apr 16 2000It is well-known that every commutative separable unital C*-algebra of real rank zero is a quotient of the C*-algebra of all compex continous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing that the class ... More

Uncountable direct systems and a characterization of non-separable projective $C^{\ast}$-algebrasAug 15 1999We introduce the concept of a direct $C_{\omega}^{\ast}$-system and show that every non-separable unital $C^{\ast}$-algebra is the limit of essentially unique direct $C_{\omega}^{\ast}$-system. This result is then applied to the problem of characterization ... More

On the biregular geometry of Fulton-MacPherson configuration spacesMar 22 2016Let $X[n]$ be the Fulton-MacPherson configuration space of $n$ ordered points on a smooth projective variety $X$. We prove that if either $n\neq 2$ or $\dim(X)\geq 2$, then the connected component of the identity of $Aut(X[n])$ is isomorphic to the connected ... More

Positivity on subvarieties and vanishing of higher cohomologyDec 06 2010We study the relationship between positivity of line bundles restricted to complete intersection subvarieties and the vanishing of higher cohomology groups. Based on this connection we prove generalizations of the vanishing theorems of Kawamata-Viehweg ... More

Maximum screening fields of superconducting multilayer structuresJan 07 2015It is shown that a multilayer comprised of alternating thin superconducting and insulating layers on a thick substrate can fully screen the applied magnetic field exceeding the superheating fields $H_s$ of both the superconducting layers and the substrate, ... More

Lines generate the Picard groups of certain Fermat surfacesMay 14 2013Jun 05 2014We answer a question of T.Shioda and show that, for any positive integer $m$ prime to 6, the Picard group of the Fermat surface $\Phi_m$ is generated by the classes of lines contained in $\Phi_m$.

On the biregular geometry of the Fulton-MacPherson compactificationMar 22 2016Oct 11 2017Let $X[n]$ be the Fulton-MacPherson compactification of the configuration space of $n$ ordered points on a smooth projective variety $X$. We prove that if either $n\neq 2$ or $\dim(X)\geq 2$, then the connected component of the identity of $Aut(X[n])$ ... More

Finite approximations of $p$-local compact groupsMar 30 2015Dec 08 2015We show that the classifying space of a $p$-local compact group is approximated by a telescope of classifying spaces of $p$-local finite groups. This result has numerous implications, like a Stable Elements Theorem for $p$-local compact groups, or the ... More

The binomial ideal of the intersection axiom for conditional probabilitiesFeb 09 2009Dec 04 2009The binomial ideal associated with the intersection axiom of conditional probability is shown to be radical and is expressed as intersection of toric prime ideals. This resolves a conjecture in algebraic statistics due to Cartwright and Engstr\"om.

Congruence classes of large configurations in vector spaces over finite fieldsJan 28 2019Bennett, Hart, Iosevich, Pakianathan, and Rudnev found an exponent $s<d$ such that any set $E\subset \mathbb{F}_q^d$ with $|E|\gtrsim q^s$ determines $\gtrsim q^{\binom{k+1}{2}}$ congruence classes of $(k+1)$-point configurations for $k\leq d$. Because ... More

Topological AE(0)-groupsJan 04 2000We investigate topological AE(0) -groups class of which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of an universal AE(0) -group of a given weight as well as the existence of an universal ... More

From Apollonius To Zaremba: Local-Global Phenomena in Thin OrbitsAug 27 2012We discuss a number of naturally arising problems in arithmetic, culled from completely unrelated sources, which turn out to have a common formulation involving "thin" orbits. These include the local-global problem for integral Apollonian gaskets and ... More

Rational Growth in Virtually Abelian GroupsAug 20 2018We show that any subgroup of a finitely generated virtually abelian group $G$ grows rationally relative to $G$, that the set of right cosets of any subgroup of $G$ grows rationally, and that the set of conjugacy classes of $G$ grows rationally. These ... More

Oka's conjecture on irreducible plane sexticsJan 24 2007Apr 17 2008We partially prove and partially disprove Oka's conjecture on the fundamental group/Alexander polynomial of an irreducible plane sextic. Among other results, we enumerate all irreducible sextics with simple singularities admitting dihedral coverings and ... More

Topological characterization of torus groupsAug 15 1999Topological characterization of torus groups is given.

Complemented subspaces of products of Banach spacesFeb 28 2000We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.

On (Non)Supermodularity of Average Control EnergySep 27 2016Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims ... More

A model-insensitive determination of First-hitting-time densities with Application to Equity default-swapsFeb 12 2010Mar 29 2010Equity default-swaps pay the holder a fixed amount of money when the underlying spot level touches a (far-down) barrier during the life of the instrument. While most pricing models give reasonable results when the barrier lies within the range of liquidly ... More

Critical phenomena in N=4 SYM plasmaMay 05 2010Strongly coupled N=4 supersymmetric Yang-Mills plasma at finite temperature and chemical potential for an R-symmetry charge undergoes a second order phase transition. We demonstrate that this phase transition is of the mean field theory type. We explicitly ... More

Gauge theories on hyperbolic spaces and dual wormhole instabilitiesFeb 21 2004Jul 26 2004We study supergravity duals of strongly coupled four dimensional gauge theories formulated on compact quotients of hyperbolic spaces. The resulting background geometries are represented by Euclidean wormholes, which complicates establishing the precise ... More

Compactifications of the N=2^* flowFeb 14 2003In hep-th/0004063 Pilch and Warner (PW) constructed N=2 supersymmetric RG flow corresponding to the mass deformation of the N=4 SU(N) Yang-Mills theory. In this paper we present exact deformations of PW flow when the gauge theory 3-space is compactified ... More

Finite temperature resolution of the Klebanov-Tseytlin singularityNov 16 2000Feb 19 2001Naked singularities in the gravitational backgrounds dual to gauge theories can be hidden behind the black hole horizon. We present an exact black hole solution in the Klebanov-Tseytlin geometry [hep-th/0002159]. Our solution realizes Maldacena dual of ... More

Violation of the holographic bulk viscosity boundOct 01 2011Motivated by gauge theory/string theory correspondence, a lower bound on the bulk viscosity of strongly coupled gauge theory plasma was proposed in arXiv:0708.3459. We consider strongly coupled N=4 supersymmetric Yang-Mills plasma compactified on a two-manifold ... More

Chiral symmetry breaking in cascading gauge theory plasmaDec 10 2010Nov 12 2013N=1 supersymmetric SU(K+P)xSU(K) cascading gauge theory of Klebanov et.al [1,2] undergoes a first-order finite temperature confinement/deconfinement phase transition at T_c=0.6141111(3) Lambda, where Lambda is the strong coupling scale of the theory. ... More

On universality of stress-energy tensor correlation functions in supergravityAug 11 2004Jan 21 2005Using the Minkowski space AdS/CFT prescription we explicitly compute in the low-energy limit the two-point correlation function of the boundary stress-energy tensor in a large class of type IIB supergravity backgrounds with a regular translationally invariant ... More

Gauge/string correspondence in curved spaceNov 15 2002Jan 08 2003We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this gauge theory ... More

A Conical Tear Drop as a Vacuum-Energy Drain for the Solution of the Cosmological Constant ProblemJun 02 2004Feb 01 2005We propose a partial solution to the cosmological constant problem by using the simple observation that a three-brane in a six-dimensional bulk is flat. A model is presented in which Standard Model vacuum energy is always absorbed by the transverse space. ... More

Relativistic Superluminal NeutrinosSep 28 2011Oct 13 2011We present a possible solution to the reported OPERA anomaly for the speed of neutrinos, based on the idea that it is a local effect caused by a scalar field sourced by the earth. The coupling of the scalar to neutrinos effectively changes the background ... More

Universality of small black hole instability in AdS/CFTSep 25 2015$AdS_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\cal V}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black ... More

Eigenvalue Clustering, Control Energy, and Logarithmic CapacityNov 01 2015Apr 23 2016We prove two bounds showing that if the eigenvalues of a matrix are clustered in a region of the complex plane then the corresponding discrete-time linear system requires significant energy to control. A curious feature of one of our bounds is that the ... More

The "Most informative boolean function" conjecture holds for high noiseOct 29 2015We prove the "Most informative boolean function" conjecture of Courtade and Kumar for high noise $\epsilon \ge 1/2 - \delta$, for some absolute constant $\delta > 0$. Namely, if $X$ is uniformly distributed in $\{0,1\}^n$ and $Y$ is obtained by flipping ... More

The Debris Disk Fraction for M-dwarfs in Nearby, Young, Moving GroupsJan 25 2016I present the first substantial work to measure the fraction of debris disks for M-dwarfs in nearby moving groups (MGs). Utilising the $AllWISE$ IR catalog, 17 out of 151 MG members are found with an IR photometric excess indicative of disk structure. ... More

A Meta-Logic of Inference Rules: SyntaxNov 27 2014This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the ... More

Z(N) wall junctions: Monopole fossils in hot QCDFeb 27 2001We point out that the effective action of hot Yang--Mills theories has semi-classical solutions, which are naturally identified with monopole world lines, ``frozen'' into the short imaginary time dimension. The solutions look like wall junctions: lines ... More

n-Schur Functions and Determinants on an Infinite GrassmannianNov 11 1998A set of functions is defined which is indexed by a positive integer $n$ and partitions of integers. The case $n=1$ reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the frame bundle ... More

Description of Black Hole Microstates by Means of a Free Affine-Scalar FieldMay 13 2004In this article we will investigate the origin of central extensions in the Poisson algebra of charges, which arise in the dimensionally reduced theories describing black holes. We will see that the equations of motion and constraints arising from the ... More

Evolution of cooperation and communication skills as a consequence of environment fluctuationsSep 22 2006Dynamics of a social population is analyzed taking into account some physical constraints on individual behavior and decision making abilities. The model, based on Evolutionary Game Theory, predicts that a population has to pass through a series of different ... More

Aspects of Classical Descriptive Set TheoryAug 28 2013This report consists of two parts. The first part is a brief exposition of classical descriptive set theory. This part introduces some fundamental concepts, motivations and results from the classical theory and ends with a section on the important result ... More

All-orders wormhole vertex operators from the Wheeler-deWitt equationJan 29 1992Jan 30 1992We discuss the calculation of semi-classical wormhole vertex operators from wave functions which satisfy the Wheeler-deWitt equation and momentum constraints, together with certain `wormhole boundary conditions'. We consider a massless minimally coupled ... More

The field of definition of affine invariant submanifolds of the moduli space of abelian differentialsOct 17 2012Apr 03 2014The field of definition of an affine invariant submanifold M is the smallest subfield of the reals such that M can be defined in local period coordinates by linear equations with coefficients in this field. We show that the field of definition is equal ... More

Sums of Adjoint OrbitsOct 09 2009Mar 26 2011Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow ... More

The Tits Alternative: An Elementary ExpositionOct 09 2009Nov 25 2009This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.