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Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphsJul 07 2006Jun 21 2012In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are ... More

A formula for the Jacobian of a genus one curve of arbitrary degreeOct 14 2015We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree $n \le 4$ to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree $n$, an $n \times n$ alternating matrix of ... More

Invariant theory for the elliptic normal quintic, I. Twists of X(5)Oct 16 2011A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant theory of such models. We use it to explain how we found our algorithm for ... More

Design of a magnetically actuated flapping wing contrivanceMar 18 2019Unmanned micro aerial vehicle research is an active area of development due to the vast potential applications. Prior work towards realizing flapping flight has achieved some success however they have relied heavily upon the use of rotary electric motors. ... More

Quasi-isometries and rigidity of solvable groupsNov 27 2005Jul 07 2006In this note, we announce the first results on quasi-isometric rigidity of non-nilpotent polycyclic groups. In particular, we prove that any group quasi-isometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in Sol. We prove ... More

Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groupsJun 07 2007Jun 21 2012In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].

The Hessian of a genus one curveOct 12 2006Nov 30 2010We continue our development of the invariant theory of genus one curves with the aim of computing certain twists of the universal family of elliptic curves parametrised by the modular curve X(n) for n = 2,3,4,5. Our construction makes use of a covariant ... More

The invariants of a genus one curveOct 10 2006It was first pointed out by Weil that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n = 2,3,4 were already known to the nineteenth centuary invariant theorists. We have ... More

Thermodynamics of statistical inference by cellsMay 15 2014Oct 06 2014The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on statistical estimation ... More

Proceedings FM-09 Workshop on Formal Methods for AerospaceMar 28 2010The main workshop objective was to promote a holistic view and interdisciplinary methods for design, verification and co-ordination of aerospace systems, by combining formal methods with techniques from control engineering and artificial intelligence. ... More

Hyperpolygons and Hitchin systemsOct 23 2014We study the hyperk\"ahler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperk\"ahler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these spaces for all ... More

On the Enlargement by Prüfer Objects of the Cluster Category of type $A_\infty$Nov 18 2014Feb 25 2016In a paper by Holm and Jorgensen, the cluster category $\mathscr{D}$ of type $A_\infty$, with Auslander-Reiten quiver $\mathbb{Z} A_\infty$, is introduced. Slices in the Auslander-Reiten quiver of $\mathscr{D}$ give rise to direct systems; the homotopy ... More

Entropic stability beyond partial hyperbolicityMar 14 2011We analyze a class of deformations of Anosov diffeomorphisms: these $C^0$-small, but $C^1$-macroscopic deformations break the topological conjugacy class but leave the high entropy dynamics unchanged. More precisely, there is a partial conjugacy between ... More

Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topologyMay 07 2014On the torus of dimension $2$, $3$, or $4$, we show that the subset of diffeomorphisms with trivial centralizer in the $C^1$ topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to ... More

Visibility of 4-covers of elliptic curvesJan 26 2017Feb 08 2017Let $C$ be a $4$-cover of an elliptic curve $E$, written as a quadric intersection in $\mathbb{P}^3$. Let $E'$ be another elliptic curve with $4$-torsion isomorphic to that of $E$. We show how to write down the $4$-cover $C'$ of $E'$ with the property ... More

A Caldero-Chapoton map depending on a torsion classOct 26 2015Feb 25 2016Frieze patterns of integers were studied by Conway and Coxeter. Let $\mathscr{C}$ be the cluster category of Dynkin type $A_n$. Indecomposables in $\mathscr{C}$ correspond to diagonals in an $(n+3)$-gon. Work done by Caldero and Chapoton showed that the ... More

Some minimisation algorithms in arithmetic invariant theoryMar 06 2017We extend the work of Cremona, Fisher and Stoll on minimising genus one curves of degrees 2,3,4,5, to some of the other representations associated to genus one curves, as studied by Bhargava and Ho. Specifically we describe algorithms for minimising bidegree ... 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

Isometry Structures on Vector BundlesMay 19 2016Oct 10 2016In this paper, we prove that total space of every vector bundle with the base manifold on which the canonical isometric action acts freely, also carries a principal bundle structure. We also obtain another principal bundle based on the total space of ... More

Long-time existence for Yang-Mills flowOct 11 2016We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region. ... More

Generating Sequences With Recurrent Neural NetworksAug 04 2013Jun 05 2014This paper shows how Long Short-term Memory recurrent neural networks can be used to generate complex sequences with long-range structure, simply by predicting one data point at a time. The approach is demonstrated for text (where the data are discrete) ... More

Shear viscosity of CFT plasma at finite couplingApr 19 2008May 29 2008We present evidence for the universality of the shear viscosity of conformal gauge theory plasmas beyond infinite coupling. We comment of subtleties of computing the shear viscosity in effective models of gauge/gravity correspondence rather than in string ... More

The Dirichlet Series for the Exterior Square $L$-function on GL(n)Sep 26 2009We present an elementary derivation of the Jacquet-Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients $A(m_1,...,m_{n-1})$.

The X-ray Power Spectral Density Function of the Seyfert Active Galactic Nucleus NGC 7469Oct 15 2010We present the broadband X-ray power spectral density function (PSD) of the X-ray-luminous Seyfert 1.2 NGC 7469, measured from Rossi X-ray Timing Explorer monitoring data and two XMM-Newton observations. We find significant evidence for a turnover in ... More

Black hole spectra in holography: consequences for equilibration of dual gauge theoriesJan 19 2015May 07 2015For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented ... More

Higgs PhysicsDec 14 2014With the discovery of the Higgs, we have access to a plethora of new physical processes that allow us to further test the SM and beyond. We show a convenient way to parametrize these physics using an effective theory for Higgs couplings, discussing the ... More

Boson Sampling is Robust to Small Errors in the Network MatrixDec 08 2014We demonstrate the robustness of BosonSampling to imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix $\tilde{U}$ that is within $\epsilon$ of the desired matrix $U$ ... More

1D accretion discs around eccentric planets: observable near-infrared variabilityNov 04 2014Dec 29 2014I present the results of 1D models of circumplanetary discs around planets on eccentric orbits. I use a classical viscous heating model to calculate emission fluxes at the wavelengths targeted by the NIRCam instrument on JWST, and compare the variability ... More

AdS boson stars in string theoryOct 28 2015Boson stars are stationary soliton-like gravitational configurations supported by a complex scalar field charged under the global $U(1)$ symmetry. We discuss properties of boson stars in type IIB supergravity approximation to string theory. A notable ... More

Classical Liouville Theory and the Microscopic Interpretation of Black Hole EntropyMar 18 2004In this paper we will give a general introduction to the role of conformal symmetry in the microscopic interpretation of black hole entropy and then compute the entropy of a Schwarzschild black hole by finding a classical central charge of the Virasoro ... More

The Quantum Hall effect, Skyrmions and AnomaliesAug 19 1998We discuss the properties of Skyrmions in the Fractional Quantum Hall effect (FQHE). We begin with a brief description of the Chern-Simons-Landau-Ginzburg description of the FQHE, which provides the framework in which to understand a new derivation of ... More

Effect of dipolar moments in domain sizes of lipid bilayers and monolayersNov 18 2006Dec 14 2006Lipid domains are found in systems such as multi-component bilayer membranes and single component monolayers at the air-water interface. It was shown by Andelman et al. (Comptes Rendus 301, 675 (1985)) and McConnell et al. (Phys. Chem. {\bf 91}, 6417 ... More

Plasmon decay and thermal transport from spin-charge coupling in generic Luttinger liquidsDec 20 2014We discuss the violation of spin-charge separation in generic nonlinear Luttinger liquids and investigate its effect on the relaxation and thermal transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We identify basic scattering ... More

Transport theory of superconductors with singular interaction correctionsMay 01 2010We study effects of strong fluctuations on the transport properties of superconductors near the classical critical point. In this regime conductivity is set by the delicate interplay of two competing effects. The first is that strong electron-electron ... More

Interaction corrections to tunneling conductance in ballistic superconductorsApr 19 2009Feb 08 2010It is known that in the two-dimensional disordered superconductors electron-electron interactions in the Cooper channel lead to the negative logarithmic in temperature correction to the tunneling conductance above the critical temperature. Physically ... More

On (Non)Supermodularity of Average Control EnergySep 27 2016Oct 05 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

Stochastic selection processesNov 17 2015We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been studied on a case-by-case ... More

Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over pathsNov 14 2014Jun 11 2015Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak measurements of the ... More

Interpolation and embeddings of weighted tent spacesSep 18 2015Feb 09 2016Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on $X$ we identify ... More

Fell bundles over groupoidsJul 21 1996The author provides some definitions and structural results about Fell bundles, defined as C^*-algebra bundles over topological groupoids. Such bundles are a mutual generalization of semi-direct products of groups with C^*-algebras and C^*-algebra bundles ... More

Disjoint $n$-amalgamation and pseudofinite countably categorical theoriesOct 13 2015Disjoint $n$-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this paper, we show that if a countably categorical theory $T$ admits an expansion ... More

Compact groups and absolute extensorsAug 15 1999We discuss compact Hausdorff groups from the point of view of the general theory of absolute extensors. In particular, we characterize the class of simple, connected and simply connected compact Lie groups as AE(2)-groups the third homotopy group of which ... More

A volume-based approach to the multiplicative ergodic theorem on Banach spacesFeb 23 2015Dec 07 2015A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the Lyapunov exponents ... More

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part II: The Degenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part I: The Nondegenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More

Factorization of a Matrix Differential Operator Using Functions in its KernelSep 17 2015Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a straight-forward generalization ... More

Factor equivalence of Galois modules and regulator constantsSep 17 2012Jun 21 2013We compare two approaches to the study of Galois module structures: on the one hand factor equivalence, a technique that has been used by Fr\"ohlich and others to investigate the Galois module structure of rings of integers of number fields and of their ... More

Admissibility in Positive LogicsOct 27 2016The paper studies admissibility of multiple-conclusion rules in the positive logics. Using modification of a method used by M.~Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility in positive logics is equivalent ... More

The Alexander module of a trigonal curve. IIFeb 17 2012Sep 19 2012We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.

Plane sextics with a type $\mathbf{E}_6$ singular pointJul 27 2009Jan 25 2010We give a classification up to equisingular deformation and compute the fundamental groups of maximizing plane sextics with a type $\mathbf{E}_6$ singular point.

Zariski $k$-plets via dessins d'enfantsOct 01 2007Apr 17 2008We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.

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

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

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

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

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

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

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

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

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

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 $\Phi_m$.

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

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

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

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

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.

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

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

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

Duality symmetry in high energy scatteringAug 17 2009Dec 15 2009We discuss the duality symmetry of the linear(BFKL) and the non-linear(BK) high energy evolutions in the multicolor limit. We show that the usual color dipole picture is dual to the forward reggeized gluon formulation. The presented analysis is also generalized ... More

Fast Algorithms for Distributed Optimization and Hypothesis Testing: A TutorialSep 13 2016Oct 06 2016We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent linear-time algorithm ... More

Can Turing machine be curious about its Turing test results? Three informal lectures on physics of intelligenceJun 27 2016What is the nature of curiosity? Is there any scientific way to understand the origin of this mysterious force that drives the behavior of even the stupidest naturally intelligent systems and is completely absent in their smartest artificial analogs? ... More

On the entropy of a noisy functionAug 06 2015Jun 22 2016Let $0 < \epsilon < 1/2$ be a noise parameter, and let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$. We upper bound the entropy of $T_{\epsilon} f$ by the average ... More

Monte Carlo Renormalization Group calculation in $λφ^4_3$Sep 23 1997We start by discussing some theoretical issues of renormalization group transformations and Monte Carlo renormalization group technique. A method to compute the anomalous dimension is proposed and investigated. As an application, we find excellent values ... More

On Eling-Oz formula for the holographic bulk viscosityMar 19 2011May 09 2011Recently Eling and Oz [1] proposed a simple formula for the bulk viscosity of holographic plasma. They argued that the formula is valid in the high temperature (near-conformal) regime, but is expected to break down at low temperatures. We point out that ... More

Hydrodynamics of the cascading plasmaMar 20 2009Jun 03 2009The cascading gauge theory of Klebanov et.al realizes a soluble example of gauge/string correspondence in a non-conformal setting. Such a gauge theory has a strong coupling scale Lambda, below which it confines with a chiral symmetry breaking. A holographic ... More

Shear viscosity of boost invariant plasma at finite couplingJan 29 2008Mar 04 2008We discuss string theory alpha' corrections in the dual description of the expanding boost invariant N=4 supersymmetric Yang-Mills plasma at strong coupling. We compute finite 't Hooft coupling corrections to the shear viscosity and find that it disagrees ... More

A holographic perspective on Gubser-Mitra conjectureJul 28 2005Oct 17 2005We point out an elementary thermodynamics fact that whenever the specific heat of a system is negative, the speed of sound in such a media is imaginary. The latter observation presents a proof of Gubser-Mitra conjecture on the relation between dynamical ... More

Comments on fractional instantons in N=2 gauge theoriesJan 10 2001Jun 18 2001N=1^* gauge theories are believed to have fractional instanton contributions in the confining vacua. D3 brane probe computations in gravitation dual of large-N N=2^* gauge theories point to the absence of such contributions in the low energy gauge dynamics. ... More

Relaxation time of non-conformal plasmaAug 03 2009Nov 27 2009We study effective relaxation time of viscous hydrodynamics of strongly coupled non-conformal gauge theory plasma using gauge theory/string theory correspondence. We compute leading corrections to the conformal plasma relaxation time from the relevant ... More

Efficient subgraph-based sampling of Ising-type models with frustrationSep 13 2014Here is proposed a general subgraph-based method for efficiently sampling certain graphical models, typically using subgraphs of a fixed treewidth, and also a related method for finding minimum energy (ground) states. In the case of models with frustration, ... More

A Maximal Extension of the Best-Known Bounds for the Furstenberg-Sárközy TheoremDec 06 2016We show that if $h\in \mathbb{Z}[x]$ is a polynomial of degree $k \geq 2$ such that $h(\mathbb{N})$ contains a multiple of $q$ for every $q\in \mathbb{N}$, known as an $\textit{intersective polynomial}$, then any subset of $\{1,2,\dots,N\}$ with no nonzero ... More

Logarithmic CFT on the Boundary and the World-SheetSep 12 2000The correspondences between logarithmic operators in the CFTs on the boundary of AdS_3 and on the world-sheet and dipole fields in the bulk are studied using the free field formulation of the SL(2,C)/SU(2) WZNW model. We find that logarithmic operators ... More