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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

Bees with attitude: the effect of gusts on flight dynamicsFeb 10 2018Flight is a complicated task at small scales in part due to the ubiquitous unsteady air which contains it. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping ... More

Higher descents on an elliptic curve with a rational 2-torsion pointSep 10 2015Let $E$ be an elliptic curve over a number field $K$. Descent calculations on $E$ can be used to find upper bounds for the rank of the Mordell-Weil group, and to compute covering curves that assist in the search for generators of this group. The general ... More

Deformations of group actionsJul 24 2004Jul 16 2006Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We also describe ... 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].

Added costs of insect-scale flapping flight in unsteady airflowsOct 28 2016The aerial environment in the operating domain of small-scale natural and artificial flapping wing fliers is highly complex, unsteady and generally turbulent. Considering flapping flight in an unsteady wind environment with a periodically varying lateral ... 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

First cohomology and local rigidity of group actionsMay 24 2005Feb 22 2013There is an error in the proof of Proposition 3.7. Proposition 3.7 is needed for the proof of the main theorem.

Groups acting on manifolds: around the Zimmer programSep 28 2008Dec 05 2008This paper is a survey on the {\em Zimmer program}. In it's broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are $(1)$ to put in context the original questions and conjectures ... More

Local Rigidity of group actions: Past, Present, FutureJul 21 2005Apr 20 2007This survey aims to cover the motivation for and history of the study of local rigidity of group actions. There is a particularly detailed discussion of recent results, including outlines of some proofs. The article ends with a large number of conjectures ... More

First cohomology, rigidity and deformations of isometric group actionsNov 05 2004Feb 22 2013There is an error in the proof of Theorem 1.1 that invalidates proofs of other theorems. Theorem 1.5 is unaffected.

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

When is a group action determined by its orbit structure?Mar 19 2003We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group $\Gamma$ on a topological manifold where the fixed sets for ... More

A Spherical Harmonic Approach to Redshift Distortion: Implications for $Ω$ and the Power SpectrumSep 20 1993We examine the nature of galaxy clustering in redshift space using a method based on an expansion of the galaxian density field in Spherical Harmonics and linear theory. We derive a compact and self-consistent expression for the distortion when applied ... More

Local solubility and height bounds for coverings of elliptic curvesMar 25 2011We study genus one curves that arise as 2-, 3- and 4-coverings of elliptic curves. We describe efficient algorithms for testing local solubility and modify the classical formulae for the covering maps so that they work in all characteristics. These ingredients ... 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

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

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

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

On The Validity of the Streaming Model for the Redshift-Space Correlation Function in the Linear RegimeDec 20 1994The relation between the galaxy correlation function in real and redshift-space is derived in the linear regime by an appropriate averaging of the joint probability distribution of density and velocity. The derivation recovers the familiar linear theory ... More

robumeta: An R-package for robust variance estimation in meta-analysisMar 07 2015Meta-regression models are commonly used to synthesize and compare effect sizes. Unfortunately, traditional meta-regression methods are ill-equipped to handle the complex and often unknown correlations among non-independent effect sizes. Robust variance ... More

Intrinsic ergodicity for certain nonhyperbolic robustly transitive systemsMar 21 2009Apr 11 2009We show that a class of robustly transitive diffeomorphisms originally described by Ma\~{n}\'{e} are intrinsically ergodic. More precisely we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic, but nevertheless have constant entropy ... More

Local rigidity of affine actions of higher rank groups and latticesAug 16 2004Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $\Gamma<J$ be a lattice. We prove a very general local rigidity result about actions of $J$ or $\Gamma$. This shows that almost all so-called "standard actions" are ... 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

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.

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

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.

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

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

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

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

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.

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

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

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

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

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

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 $\Phi_m$.

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

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

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.

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

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

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 $A(m_1,...,m_{n-1})$.

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

Elliptic curves with p-Selmer growth for all pApr 05 2012Jun 21 2013It is known, that for every elliptic curve over Q there exists a quadratic extension in which the rank does not go up. For a large class of elliptic curves, the same is known with the rank replaced by the 2-Selmer group. We show, however, that there exists ... 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

On Factoring an Operator Using Elements of its KernelNov 25 2015A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the derivation $\partial$ ... More

From rational billiards to dynamics on moduli spacesApr 30 2015Jul 26 2015This short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, ... More

Schwarz triangle mappings and Teichmüller curves: the Veech-Ward-Bouw-Möller curvesMar 13 2012Jan 24 2013We study a family of Teichm\"uller curves T(n,m) constructed by Bouw and M\"oller, and previously by Veech and Ward in the cases n=2,3. We simplify the proof that T(n,m) is a Teichm\"uller curve, avoiding the use M\"oller's characterization of Teichm\"uller ... 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

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

Hurwitz equivalence of braid monodromies and extremal elliptic surfacesNov 02 2009We discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group $\Gamma$ and use it to construct exponentially large families of not Hurwitz equivalent simple braid monodromy factorizations of the same element. ... 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.

Mean Curvature Motion of Graphs with Constant Contact Angle and Moving BoundariesMay 29 2008We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic ... More

Lattice games without rational strategiesJun 09 2011We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional lattice game ... More

Tropical cycles and Chow polytopesJan 26 2010May 28 2010The Chow polytope of an algebraic cycle in a torus depends only on its tropicalisation. Generalising this, we associate a Chow polytope to any abstract tropical variety in a tropicalised toric variety. Several significant polyhedra associated to tropical ... More

Characteristic formulas over intermediate logicsAug 13 2012We expand the notion of characteristic formula to infinite finitely presentable subdirectly irreducible algebras. We prove that there is a continuum of varieties of Heyting algebras containing infinite finitely presentable subdirectly irreducible algebras. ... More

A Jensen Inequality for a Family of Analytic FunctionsNov 30 2001We improve an estimate (obtained in "A.Brudnyi, Small amplitude limit cycles and the distribution of zeros of families of analytic functions, Ann. of Math. 154 (2) (2001), 227-243") for the average number of limit cycles of a planar polynomial vector ... More

Inverse problems for the number of maximal independent setsNov 18 2011We study the following inverse graph-theoretic problem: how many vertices should a graph have given that it has a specified value of some parameter. We obtain asymptotic for the minimal number of vertices of the graph with the given number $n$ of maximal ... More

Recent Advances in Charm PhysicsSep 16 2002New results from charm experiments have led to renewed interest in this physics. The charm sector is now seen as a powerful tool to search for new physics and to advance our understanding of the standard model. We owe much of this progress to the combination ... More

Decidable models of small theoriesApr 06 2015Nov 23 2015Many counterexamples are known in the class of small theories due to Goncharov and Millar. The prime model of a decidable small theory is not necessarily decidable. The saturated model of a hereditarily decidable small theory is not necessarily decidable. ... More

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

Exponents and Almost Periodic OrbitsAug 01 1999We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Cech cohomology group of the closure of the image of the map. We show that this group generalizes the subgroup ... More