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

Areas of triangles and SL_2 actions in finite ringsJun 11 2019In Euclidean space, one can use the dot product to give a formula for the area of a triangle in terms of the coordinates of each vertex. Since this formula involves only addition, subtraction, and multiplication, it can be used as a definition of area ... More

Natural Language Processing with Small Feed-Forward NetworksAug 01 2017We show that small and shallow feed-forward neural networks can achieve near state-of-the-art results on a range of unstructured and structured language processing tasks while being considerably cheaper in memory and computational requirements than deep ... More

Doubly slice odd pretzel knotsApr 29 2019Jun 07 2019We prove that an odd pretzel knot is doubly slice if it has $2n+1$ twist parameters consisting of $n+1$ copies of $a$ and $n$ copies of $-a$ for some odd integer $a$. Combined with the work of Issa and McCoy, it follows that these are the only doubly ... More

Band Number and the Double Slice GenusJan 22 2019We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound is based on ... More

Connectedness and Hamiltonicity of graphs on vertex coloringsJul 19 2015Given a graph $H$, let $G^j_k(H)$ be the graph whose vertices are the proper $k$-colorings of $H$, with edges joining two colorings if $H$ contains a connected subgraph on at most $j$ vertices that includes all vertices where the colorings differ. Properties ... More

Dirichlet Spectrum and Heat ContentMay 09 2002Let $M$ be a complete Riemannian manifold and $D\subset M$ a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet spectrum of $D$ and ... More

Heat content determines planar trianglesJul 12 2016We prove that heat content determines planar triangles.

List rankings and on-line list rankings of graphsJan 15 2014A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number of $G$, also ... More

Using Simulated Annealing to Calculate the Trembles of Trembling Hand PerfectionSep 10 2003Within the literature on non-cooperative game theory, there have been a number of attempts to propose logorithms which will compute Nash equilibria. Rather than derive a new algorithm, this paper shows that the family of algorithms known as Markov chain ... More

Finding Traitors in Secure Networks Using Byzantine AgreementsAug 19 2003Feb 05 2006Secure networks rely upon players to maintain security and reliability. However not every player can be assumed to have total loyalty and one must use methods to uncover traitors in such networks. We use the original concept of the Byzantine Generals ... More

On clique immersions in line graphsSep 17 2019We prove that if $L(G)$ immerses $K_t$ then $L(mG)$ immerses $K_{mt}$, where $mG$ is the graph obtained from $G$ by replacing each edge in $G$ with a parallel edge of multiplicity $m$. This implies that when $G$ is a simple graph, $L(mG)$ satisfies a ... 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

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

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

The list chromatic index of simple graphs whose odd cycles intersect in at most one edgeJul 21 2015Nov 18 2017We study the class of simple graphs $\mathcal{G}^*$ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in $\mathcal{G}^*$ and prove that every $G \in \mathcal{G}^*$ satisfies ... More

Matrix roots of imprimitive irreducible nonnegative matricesJul 16 2014Jun 03 2015Using matrix function theory, Perron-Frobenius theory, combinatorial matrix theory, and elementary number theory, we characterize, classify, and describe in terms of the Jordan canonical form the matrix pth-roots of imprimitive irreducible nonnegative ... More

Mean field convergence of a model of multiple TCP connections through a buffer implementing REDMar 14 2006RED (Random Early Detection) has been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows by dropping or marking packets with a probability that increases with ... More

Jordan chains of $h$-cyclic matricesJul 16 2014Feb 24 2015Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative imprimitive irreducible ... More

ALMA observations of the nearby AGB star L$_{\rm 2}$ Puppis. II. Gas disk properties derived from $^{\rm 12}$CO and $^{\rm13}$CO $J=$3$-$2 emissionMar 14 2018The circumstellar environment of the AGB star L$_{\rm 2}$ Puppis was observed with ALMA in cycle 3, with a resolution of $15 \times 18 \rm\ mas$. The molecular emission shows a differentially rotating disk, inclined to a nearly edge-on position. In the ... 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

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

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

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

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

Lines in supersingular quarticsApr 20 2016We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the ... 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

A note on compact-like semitopological groupsJul 25 2019The note contains a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is presented a semiregular semitopological group $G$ which is not $T_3$. We show that each weakly ... More

Bose-Einstein condensation of light in a cavityJan 02 2014Apr 01 2014The paper considers Bose-Einstein condensation (BEC) of light in a cavity with medium. In the framework of two-level model we show the effect of gaseous medium on the critical temperature of light condensation in the system. Transition of the system to ... 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

The DarkSide Program at LNGSSep 14 2011DarkSide is a direct detection dark matter program based on two phase time projection chambers with depleted argon targets. The DarkSide detectors are designed, using novel low background techniques and active shielding, to be capable of demonstrating ... 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

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

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.

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

Regulator constants of integral representations of finite groupsMar 30 2017Dec 22 2018Let G be a finite group and p be a prime. We investigate isomorphism invariants of $\mathbb{Z}_{p}[G]$-lattices whose extension of scalars to $\mathbb{Q}_p$ is self-dual, called regulator constants. These were originally introduced by Dokchitser--Dokchitser ... 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

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.

Tritangents to smooth sextic curvesSep 12 2019We prove that a smooth plane sextic curve can have at most 72 tritangents, whereas a smooth real sextic may have at most 66 real tritangents.

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.

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

X-ray Properties of SPT Selected Galaxy Clusters at 0.2<z<1.5 Observed with XMM-NewtonJul 06 2018Nov 29 2018We present measurements of the X-ray observables of the intra-cluster medium (ICM), including luminosity $L_X$, ICM mass $M_{ICM}$, emission-weighted mean temperature $T_X$, and integrated pressure $Y_X$, that are derived from XMM-Newton X-ray observations ... 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

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

Diffusion Processes in Turbulent Magnetic FieldsJul 04 2007Jul 05 2007We study of the effect of turbulence on diffusion processes within magnetized medium. While we exemplify our treatment with heat transfer processes, our results are quite general and are applicable to different processes, e.g. diffusion of heavy elements. ... 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

Optimal phase measurements with pure Gaussian statesSep 02 2005Feb 08 2006We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive ... More

Fast Algorithms for Distributed Optimization and Hypothesis Testing: A TutorialSep 13 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

Introduction into "Local Correlation Modelling"Sep 18 2009Sep 22 2009In this paper we provide evidence that financial option markets for equity indices give rise to non-trivial dependency structures between its constituents. Thus, if the individual constituent distributions of an equity index are inferred from the single-stock ... 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

Computable randomness and monotonicitySep 25 2015We show that $z\in\R^n$ is computably random if and only if every computable monotone function on $\R^n$ is differentiable at $z$.

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

Inelastic quantum tunneling through disordered potential barrierJul 19 2004Jul 20 2004The effect of inelastic scattering on quantum tunneling through a rectangular potential barrier, of length $L$, containing randomly distributed impurities, is considered. It is shown that, despite the fact that the inelastic transition probability $\mathcal{T}_{\mathrm{inelastic}}$ ... More

Magnetoconductivity of low-dimensional disordered conductors at the onset of the superconducting transitionMar 13 2009Jun 24 2009Magnetoconductivity of the disordered two- and three-dimensional superconductors is addressed at the onset of superconducting transition. In this regime transport is dominated by the fluctuation effects and we account for the interaction corrections coming ... 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

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

On the theoretical RF field limits of multilayer coating structures of superconducting resonator cavitiesSep 22 2013This Comment addresses theoretical field limits for superconducting-insulating (S-I) thin films multilayers discussed by S. Posen, G. Catelani, M. Liepe, J. Sethna, and M. Transtrum [1]. It is shown that their criticism of the SIS multilayer approach ... More

Long-time existence for Yang-Mills flowOct 11 2016Mar 22 2019We 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

Central limit theorems via Stein's method for randomized experiments under interferenceApr 09 2018Mar 06 2019We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson estimator is ... More

Three-dimensional flow in cavity with elevated helicity driven by parallel wallsApr 02 2017Jul 13 2018The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow yet having simple single-block cubical geometry of computational domain. ... More

A new measure of asymmetry of binary wordsApr 08 2010A binary word is symmetric if it is a palindrome or an antipalindrome. We define a new measure of asymmetry of a binary word equal to the minimal number of letters of the word whose deleting from the word yields a symmetric word and obtain upper and lower ... More

On the palindromic decomposition of binary wordsApr 08 2010We prove a precise formula for the minimal number K(n) such that every binary word of length $n$ can be divided into K(n) palindromes. Also we estimate the average number $\ol K(n)$ of palindromes composing a random binary word of the length n.

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

Periodic Billiards in Isosceles TrianglesJun 28 2013Jul 01 2013Any periodic trajectory on an isosceles triangle gives rise to a periodic trajectory on a right triangle obtained by identifying the halves of the original triangle. We examine the relationship between periodic trajectories on isosceles triangles and ... More

Hereditarily Structurally Complete Superintuitionistic Deductive SystemsNov 15 2016The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of hereditary structurality ... 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

Bispectrality of KP SolitonsJun 04 1998It is by now well known that the wave functions of rational solutions to the KP hierarchy (those which can be achieved as limits of the pure n-soliton solutions) satisfy an additional eigenvalue equation for ordinary differential operators in the spectral ... More

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

On the Artal--Carmona--Cogolludo constructionJan 10 2013Jun 06 2014We derive explicit defining equations for a number of irreducible maximizing plane sextics with double singular points only. For most real curves, we also compute the fundamental group of the complement; all groups found are abelian. As a by-product, ... More

Dihedral coverings of trigonal curvesMay 06 2010We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve~$D$ with a singular point of multiplicity $(\deg D-3)$.

Plane sextics via dessins d'enfantsDec 17 2008Oct 01 2009We develop a geometric approach to the study of plane sextics with a triple singular point. As an application, we give an explicit geometric description of all irreducible maximal sextics with a type $\bold E_7$ singular point and compute their fundamental ... More

On the half-space theorem for minimal surfaces in Heisenberg spaceJun 18 2012Nov 02 2015We propose a simple proof of the vertical half-space theorem for Heisenberg space.

On Setting of Heat-and-Mass Transfer Problems under Directed CrystallizationAug 11 2011So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems describing the free ... More

Numerical homotopy continuation for control and online identification of nonlinear systems: the survey of selected resultsJan 26 2013The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine) nonlinear systems are ... More

The Negative Cycle Vectors of Signed Complete GraphsDec 30 2015A signed graph is a graph where the edges are assigned labels of either "$+$" or "$-$". The sign of a cycle in the graph is the product of the signs of its edges. We equip each signed complete graph with a vector whose entries are the number of negative ... More

Stochastic Backpropagation through Mixture Density DistributionsJul 19 2016The ability to backpropagate stochastic gradients through continuous latent distributions has been crucial to the emergence of variational autoencoders and stochastic gradient variational Bayes. The key ingredient is an unbiased and low-variance way of ... More

The Local-Global Principle for Integral Soddy Sphere PackingsAug 27 2012Fix an integral Soddy sphere packing P. Let K be the set of all curvatures in P. A number n is called represented if n is in K, that is, if there is a sphere in P with curvature equal to n. A number n is called admissible if it is everywhere locally represented, ... More