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A Categorification of the Vandermonde DeterminantNov 20 2018Nov 26 2018In the spirit of Bar Natan's construction of Khovanov homology, we give a categorification of the Vandermonde determinant. Given a sequence of positive integers $\vec{x}=(x_1,...,x_n)$, we construct a commutative diagram in the shape of the Bruhat order ... More

Torsion in thin regions of Khovanov homologyMar 13 2019In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to only contain $\mathbb{Z}_2$ torsion. In this paper, we ... More

Length scale for the onset of Fickian diffusion in supercooled liquidsSep 16 2004Jan 25 2005The interplay between self-diffusion and excitation lines in space-time was recently studied in kinetically constrained models to explain the breakdown of the Stokes-Einstein law in supercooled liquids. Here, we further examine this interplay and its ... More

Coburn's Lemma and the Finite Section Method for Random Jacobi OperatorsMay 19 2015Sep 23 2015We study the spectra and pseudospectra of finite and infinite tridiagonal random matrices, in the case where each of the diagonals varies over a separate compact set, say $U,V,W\subset\mathbb{C}$. Such matrices are sometimes termed stochastic Toeplitz ... More

Spectrum of a Feinberg-Zee Random Hopping MatrixOct 04 2011Dec 23 2011This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general ... More

On Symmetries of the Feinberg-Zee Random Hopping MatrixSep 02 2015Nov 27 2016In this paper we study the spectrum $\Sigma$ of the infinite Feinberg-Zee random hopping matrix, a tridiagonal matrix with zeros on the main diagonal and random $\pm 1$'s on the first sub- and super-diagonals; the study of this non-selfadjoint random ... 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

From fifty years ago, the birth of modern liquid-state scienceSep 15 2016The story told in this autobiographical perspective begins fifty years ago at the 1967 Gordon Research Conference on the Physics and Chemistry of Liquids. It traces developments in liquid-state science from that time, including contributions from the ... More

Corresponding States of Structural Glass FormersNov 15 2008Nov 25 2008The variation with respect to temperature T of transport properties of 58 fragile structural glass forming liquids (68 data sets in total) are analyzed and shown to exhibit a remarkable degree of universality. In particular, super-Arrhenius behaviors ... More

On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and OperatorsJul 01 2011May 13 2013In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E.B.Davies ... More

Illusions of phase coexistence: Comments on "Metastable liquid-liquid transition ..." by J. C. Palmer et al., Nature 510, 385 (2014)Jul 25 2014Aug 20 2014The recent paper cited above claims that a molecular simulation of one specific model of supercooled water establishes a stable interface separating two metastable liquid phases, which would imply the existence of metastable two-liquid criticality for ... More

Causes and Consequences of genetic background effects illuminated by integrative genomic analysisSep 02 2013Feb 01 2014The phenotypic consequences of individual mutations are modulated by the wild type genetic background in which they occur.Although such background dependence is widely observed, we do not know whether general patterns across species and traits exist, ... 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

Characteristic Formulas 50 Years Later (An Algebraic Account)Jul 22 2014The Jankov (characteristic) formulas were introduced by V.Jankov fifty tears ago in 1963. Nowadays the Jankov (or frame) formulas are used in virtually every branch of propositional logic: intermediate, modal, fuzzy, relevant, many-valued, etc. All these ... More

New Algorithms for Solving Tropical Linear SystemsSep 20 2013The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is known, although ... 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

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

Gromov's measure equivalence and rigidity of higher rank latticesNov 01 1999In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the ... 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

The Reasonable Effectiveness of Mathematics in the Physical SciencesDec 24 2012Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is discovered; Logicism ... 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

Multilinear Superhedging of Lookback OptionsOct 04 2018In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their ... More

Super-Replication of the Best Pairs Trade in HindsightOct 04 2018Oct 17 2018For a market with $m$ assets and $T$ discrete trading sessions, Ordentlich and Cover (1998) found that the `Cost of Achieving the Best Rebalancing Rule in Hindsight' is $p(T,m)=\sum\limits_{n_1+\cdot\cdot\cdot+n_m=T}\binom{T}{n_1,...,n_m}(n_1/T)^{n_1}\cdot\cdot\cdot(n_m/T)^{n_m}$. ... More

Reflection identities of harmonic sums of weight fourSep 12 2018We consider the reflection identities for harmonic sums at weight four. We decompose a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or positive values of the argument. ... More

Uhlenbeck compactness for Yang-Mills flow in higher dimensionsDec 28 2018Feb 08 2019This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension $n \geq 4,$ including rectifiability of the singular set.

Genus From Sandpile Torsor AlgorithmApr 20 2018Previous work by Chan-Church-Grochow and Baker-Wang showed that the structure of the output of the rotor routing or Bernardi process can be used to distinguish a planar ribbon graph from a nonplanar ribbon graph. Here, we show that the structure of the ... More

Discriminants and Quasi-symmetryNov 24 2017This paper gives a geometric interpretation of the notion of quasi-symmetric representation and uses this to show that the discriminant locus associated to such a representation is a hyperplane arrangement. Moreover, we identify this hyperplane arrangement, ... More

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

Poisson--Dirichlet distribution for random Belyi surfacesJan 19 2005Nov 21 2006Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying ... 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

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

Linear Flows on $κ$-SolenoidsJun 24 1999Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.

Information Rates and post-FEC BER Prediction in Optical Fiber CommunicationsNov 28 2016Information-theoretic metrics to analyze optical fiber communications systems with binary and nonbinary soft-decision FEC are reviewed. The numerical evaluation of these metrics in both simulations and experiments is also discussed. Ready-to-use closed-form ... More

Asymptotic cohomological functions on projective varietiesJan 27 2005In this paper we define certain analogues of the volume of a divisor - called asymptotic cohomological functions - and investigate their behaviour on the Neron--Severi space. We establish that asymptotic cohomological functions are invariant with respect ... 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.

On the unit distance problemSep 23 2017The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known bound is $Cn^{\frac{4}{3}}$. ... More

On the Picard group of a Delsarte surfaceJul 01 2013We suggest an algorithm computing, in some cases, an explicit generating set for the N\'eron--Severi lattice of a Delsarte surface.

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.

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

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

Pseudocompact paratopological groups that are topologicalJun 08 2014We obtain necessary and sufficient conditions when a pseudocompact paratopological group is topological. (2-)pseudocompact and countably compact paratopological groups that are not topological are constructed. It is proved that each 2-pseudocompact paratopological ... More

Tent spaces over metric measure spaces under doubling and related assumptionsMay 10 2013Sep 25 2013In this article, we define the Coifman-Meyer-Stein tent spaces $T^{p,q,\alpha}(X)$ associated with an arbitrary metric measure space $(X,d,\mu)$ under minimal geometric assumptions. While gradually strengthening our geometric assumptions, we prove duality, ... More

Portfolio Optimization Under UncertaintyAug 11 2009Sep 21 2009Classical mean-variance portfolio theory tells us how to construct a portfolio of assets which has the greatest expected return for a given level of return volatility. Utility theory then allows an investor to choose the point along this efficient frontier ... More

Ł-Axiomatizability in intermediate and normal modal logicsJul 22 2014A set $F$ of formulas is complete relative to a given class of logics, if every logic from this class can be axiomatized by formulas from $F$. A set of formulas $F$ is {\L}-complete relative to a given class of logics, if every logic of this class can ... More

Effective Action of the Baryonic Branch in String Theory Flux ThroatsMay 07 2014Sep 12 2014We discuss consistent truncations of type IIB supergravity on resolved warped deformed conifolds with fluxes. These actions represent the gravitational duals to the baryonic branch deformation of the Klebanov-Strassler cascading gauge theory. As an application, ... More

On jet quenching parameters in strongly coupled non-conformal gauge theoriesMay 18 2006Aug 02 2006Recently Liu, Rajagopal and Wiedemann (LRW) [hep-ph/0605178] proposed a first principle, nonperturbative quantum field theoretic definition of ``jet quenching parameter'' \hat{q} used in models of medium-induced radiative parton energy loss in nucleus-nucleus ... More

Higher derivative corrections to near-extremal black holes in type IIB supergravityApr 24 2006Jun 08 2006We discuss string theory alpha' corrections to charged near-extremal black 3-branes/black holes in type IIB supergravity. We find that supersymmetric global AdS_5 x S^5 geometry is not corrected to leading order in alpha', while charged or non-extremal ... More

Inflation on the resolved warped deformed conifoldJan 01 2006Aug 10 2006Braneworld inflation on the resolved warped deformed conifold is represented by the dynamics of a D3-brane probe with the world volume of a brane spanning the large dimensions of the observable Universe. This model was recently proposed as a string theory ... More

Coarse-graining 1/2 BPS geometries of type IIB supergravitySep 26 2004Recently Lin, Lunin and Maldacena (LLM) (hep-th/0409174) explicitly mapped 1/2 BPS excitations of type IIB supergravity on AdS_5 x S^5 into free fermion configurations. We discuss thermal coarse-gaining of LLM geometries by explicitly mapping the corresponding ... More

Gauge/gravity correspondence in accelerating universeMar 06 2002Apr 16 2002We discuss time-dependent backgrounds of type IIB supergravity realizing gravitation duals of gauge theories formulated in de Sitter space-time as a tool of embedding de Sitter in a supergravity. We show that only the gravitational duals to non-conformal ... More

Instantons and singularities in the Yang-Mills flowFeb 13 2014Oct 11 2016Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the flow ... More

Continuous homomorphisms of Arens-Michael algebrasAug 15 1999Feb 19 2000It is shown that every continuous homomorphism of Arens-Michael algebras can be obtained as the limit of a morphism of certain projective systems consisting of Fr\'{e}chet algebras. Based on this we prove that a complemented subalgebra of an uncountable ... More

The Automorphisms group of \bar{M}_{g,n}Oct 07 2011Let \bar{\mathcal{M}}_{g,n}$ be the moduli stack parametrizing Deligne-Mumford stable n-pointed genus g curves and let \bar{M}_{g,n} be its coarse moduli space: the Deligne-Mumford compactification of the moduli space of n-pointed genus g smooth curves. ... More

Linear Time Average Consensus on Fixed Graphs and Implications for Decentralized Optimization and Multi-Agent ControlNov 15 2014May 23 2016We describe a protocol for the average consensus problem on any fixed undirected graph whose convergence time scales linearly in the total number nodes $n$. The protocol is completely distributed, with the exception of requiring all nodes to know the ... More

Multiple Conclusion Rules in Logics with the Disjunction PropertySep 02 2015We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible ... More

Recent Results From CLEO-cMay 23 2005This paper describes recent preliminary results from the CLEO-c experiment using an initial ~60 pb^-1 sample of data collected in e^+e^- collisions at a center of mass energy around the mass of the psi(3770). A first measurement of the branching fraction ... More

Orbit equivalence rigidityNov 01 1999Consider a countable group Gamma acting ergodically by measure preserving transformations on a probability space (X,mu), and let R_Gamma be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there exist group ... More

An asymptotic result concerning a question of WilfNov 11 2011Let $\Lambda$ be a numerical semigroup with embedding dimension $e(\Lambda)$. Define $c(\Lambda)$ to be one plus the largest integer not in $\Lambda$, and define $c'(\Lambda)$ to be the number of elements in $\Lambda$ less than $c(\Lambda)$. It was asked ... More

A multivariate CLT in Wasserstein distance with near optimal convergence rateFeb 17 2016Let $X_1, \ldots , X_n$ be i.i.d. random vectors in $\mathbb{R}^d$ with $\|X_1\| \le \beta$. Then, we show that $\frac{1}{\sqrt{n}}(X_1 + \ldots + X_n)$ converges to a Gaussian in Wasserstein-2 distance at a rate of $O\left(\frac{\sqrt{d} \beta \log n}{\sqrt{n}} ... More

Long-time existence for Yang-Mills flowOct 11 2016Nov 09 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

Adaptive Computation Time for Recurrent Neural NetworksMar 29 2016Apr 18 2016This paper introduces Adaptive Computation Time (ACT), an algorithm that allows recurrent neural networks to learn how many computational steps to take between receiving an input and emitting an output. ACT requires minimal changes to the network architecture, ... More

A Simulation of Oblivious Multi-Head One-Way Finite Automata by Real-Time Cellular AutomataDec 03 2010In this paper, we present the simulation of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head one-way finite automata and is characterized by having its heads moving only forward, ... More

On irreducible sextics with non-abelian fundamental groupNov 20 2007We calculate the fundamental groups $\pi=\pi_1(P^2\setminus B)$ for all irreducible plane sextics $B\subset\P^2$ with simple singularities for which $\pi$ is known to admit a dihedral quotient $D_{10}$. All groups found are shown to be finite, two of ... More

An upper bound on $\ell_q$ norms of noisy functionsSep 25 2018Let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$ and let $q \ge 1$. We upper bound the $\ell_q$ norm of $T_{\epsilon} f$ by the average $\ell_q$ norm of conditional ... More

Mixing in 3-D Cavity by Moving Cavity WallsJul 13 2018The mixing in this enclosure is investigated numerically using 3-D flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for several representative scenarios of moving cavity walls: ... More

Reflection identities of harmonic sums up to weight threeAug 28 2018We discuss reflections identities of harmonic sums up to weight three. The need for this kind of identities emerges in analysis of the general structure of eigenvalue of the BFKL equation. The reflection identities decompose a product of two harmonic ... More

Functoriality of motivic lifts of the canonical constructionDec 20 2018Let (G,X) be a Shimura datum and K a neat open compact subgroup of $G(\mathbb{A}_f)$. Under mild hypothesis on (G,X), the canonical construction associates a variation of Hodge structure on $\textrm{Sh}_K(G,X)(\mathbb{C})$ to a representation of G. It ... More

Diagrammatic State Sums for 2D Pin-Minus TQFTsNov 30 2018The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a ... More

Non-conformal holographic Gauss-Bonnet hydrodynamicsJan 18 2018Jan 26 2018We study hydrodynamics of four-dimensional non-conformal holographic plasma with non-equal central charges $c\ne a$ at the ultraviolet fixed point. We compute equation of state, the speed of sound waves, transport coefficients (shear and bulk viscosities), ... More

Analytical Approach for Calculating Chemotaxis Sensitivity FunctionFeb 13 2017We consider the chemotaxis problem for a one-dimensional system. To analyze the interaction of bacteria and attractant we use a modified Keller-Segel model which accounts attractant absorption. To describe the system we use the chemotaxis sensitivity ... More

Mean Curvature Motion of Triple Junctions of Graphs in Two DimensionsSep 03 2008We consider a system of three surfaces, graphs over a bounded domain in ${\mathbb R}^2$, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to $2\pi/3$.) For ... More

The existence problem for Steiner networks in strictly convex domainsJun 03 2008We consider the existence problem for `Steiner networks' (trivalent graphs with 120 degree angles at each junction) in strictly convex domains, with `Neumann' boundary conditions (orthogonal intersection with the domain boundary.) For each of the three ... More

Sarkozy's Theorem for P-Intersective PolynomialsNov 28 2011Feb 01 2015We define a necessary and sufficient condition on a polynomial $h\in \mathbb{Z}[x]$ to guarantee that every set of natural numbers of positive upper density contains a nonzero difference of the form $h(p)$ for some prime $p$. Moreover, we establish a ... More

Flows on solenoids are generically not almost periodicJun 22 1999The space of non-singular flows on any given solenoid is shown to contain a generic subset consisting of flows that are not almost periodic. Whether this result carries over to Hamiltonian flows remains an open question.

Simplicity of twists of abelian varietiesDec 11 2013We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.

Towards the generalized Shapiro and Shapiro conjectureJul 13 2008We find a new, asymptotically better, bound $g\le\frac14d^2+O(d)$ on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except $g=0$ (the original conjecture).

Regular Orbital Measures on Lie AlgebrasFeb 11 2009Let H be a regular element of an irreducible Lie Algebra g, and let mu be the orbital measure supported on the Adjoint orbit of H. We show that the k-th power of the Fourier transform of mu is in L^2(g) if and only if k > dim g/(dim g-rank g).

On the Center Problem for Ordinary Differential EquationsJan 28 2003Nov 17 2003The classical Center-Focus problem posed by H. Poincare in 1880's asks about the classification of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point (which is called a center). ... More

Smooth models of singular $K3$-surfacesAug 24 2016Jun 20 2017We show that the classical Fermat quartic has exactly three smooth spatial models. As a generalization, we give a classification of smooth spatial (as well as some other) models of singular $K3$-surfaces of small discriminant. As a by-product, we observe ... More

Projective spaces in Fermat varietiesDec 19 2015We give a brief systematic overview of a few results concerning the N\'eron--Severi lattices of Fermat varieties and Delsarte surfaces.

Distinguishing extension numbers for $\mathbf R^n$ and $S^n$Aug 25 2014In the setting of a group $\Gamma$ acting faithfully on a set $X$, a $k$-coloring $c: X\rightarrow \{1, 2, ..., k\}$ is called $\Gamma$-distinguishing if the only element of $\Gamma$ that fixes $c$ is the identity element. The distinguishing number $D_\Gamma(X)$ ... More

On the birational geometry of spaces of complete forms II: skew-formsMar 23 2018Jun 10 2018Moduli spaces of complete skew-forms are compactifications of spaces of skew-symmetric linear maps of maximal rank on a fixed vector space, where the added boundary divisor is simple normal crossing. In this paper we compute their effective, nef and movable ... More

On the birational geometry of spaces of complete forms I: collineations and quadricsMar 24 2018Mar 31 2018Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics from the point ... More

Limits of conformal images and conformal images of limits for planar random curvesOct 12 2018Consider a chordal random curve model on a planar graph, in the scaling limit when a fine-mesh graph approximates a simply-connected planar domain. The well-known precompactness conditions of Kemppainen and Smirnov show that certain "crossing estimates" ... More

Projective Algebras and Primitive Subquasivarieties in Varieties with Factor CongruencesJul 07 2017Aug 10 2017We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its homomorphic ... More

Cover's Rebalancing Option With Discrete Hindsight OptimizationMar 03 2019We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set ... More

On direct summands of homological functors on length categoriesMay 08 2013Dec 27 2014We show that direct summands of certain additive functors arising as bifunctors with a fixed argument in an abelian category are again of that form whenever the fixed argument has finite length or, more generally, satisfies the descending chain condition ... More