Results for "Denis Nekipelov"

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A/B Testing of AuctionsJun 02 2016For many application areas A/B testing, which partitions users of a system into an A (control) and B (treatment) group to experiment between several application designs, enables Internet companies to optimize their services to the behavioral patterns ... More
Learning and Trust in Auction MarketsMar 30 2017In this paper, we study behavior of bidders in an experimental launch of a new advertising auction platform by Zillow, as Zillow switched from negotiated contracts to using auctions in several geographically isolated markets. A unique feature of this ... More
Robust Data-Driven Guarantees in AuctionsMay 03 2015Feb 25 2016Analysis of welfare in auctions comes traditionally via one of two approaches: precise but fragile inference of the exact details of a setting from data or robust but coarse theoretical price of anarchy bounds that hold in any setting. As markets get ... More
Mechanism Design for Data ScienceApr 23 2014Jun 09 2014Good economic mechanisms depend on the preferences of participants in the mechanism. For example, the revenue-optimal auction for selling an item is parameterized by a reserve price, and the appropriate reserve price depends on how much the bidders are ... More
Econometrics for Learning AgentsMay 04 2015The main goal of this paper is to develop a theory of inference of player valuations from observed data in the generalized second price auction without relying on the Nash equilibrium assumption. Existing work in Economics on inferring agent values from ... More
Plug-in Regularized Estimation of High-Dimensional Parameters in Nonlinear Semiparametric ModelsJun 13 2018Jun 30 2018We develop a theory for estimation of a high-dimensional sparse parameter $\theta$ defined as a minimizer of a population loss function $L_D(\theta,g_0)$ which, in addition to $\theta$, depends on a, potentially infinite dimensional, nuisance parameter ... More
Dashboard Mechanisms for Online MarketplacesMay 14 2019This paper gives a theoretical model for design and analysis of mechanisms for online marketplaces where a bidding dashboard enables the bid-optimization of long-lived agents. We assume that a good allocation algorithm exists when given the true values ... More
Inference from Auction PricesFeb 19 2019Econometric inference allows an analyst to back out the values of agents in a mechanism from the rules of the mechanism and bids of the agents. This paper proposes the problem of inferring the values of agents in a mechanism from the social choice function ... More
Density Matrix Functional Theory for the Lipkin modelDec 18 2008A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the system as the two-body ... More
Stochastic Schroedinger equation from optimal observable evolutionJun 29 2006In this article, we consider a set of trial wave-functions denoted by $| Q \right>$ and an associated set of operators $A_\alpha$ which generate transformations connecting those trial states. Using variational principles, we show that we can always obtain ... More
Surveying Diffusion in Complex Geometries. An EssaySep 08 2009The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins and DNA), biological ... More
Many-Body Physics and Quantum ChaosDec 07 2007Experimental progresses in the miniaturisation of electronic devices have made routinely available in the laboratory small electronic systems, on the micron or sub-micron scale, which at low temperature are sufficiently well isolated from their environment ... More
Fukaya categories of symmetric products and bordered Heegaard-Floer homologyJan 25 2010Jul 28 2010The main goal of this paper is to discuss a symplectic interpretation of Lipshitz, Ozsvath and Thurston's bordered Heegaard-Floer homology in terms of Fukaya categories of symmetric products and Lagrangian correspondences. More specifically, we give a ... More
Asymptotics for the solutions of elliptic systems with fast oscillating coefficientsDec 04 2006May 07 2007We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense we construct ... More
Extragalactic propagation of ultrahigh energy cosmic-raysNov 14 2011In this paper we review the extragalactic propagation of ultrahigh energy cosmic-rays (UHECR). We present the different energy loss processes of protons and nuclei, and their expected influence on energy evolution of the UHECR spectrum and composition. ... More
Testing Regression Monotonicity in Econometric ModelsDec 30 2012Dec 03 2013Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical analysis. ... More
Adaptive Test of Conditional Moment InequalitiesDec 30 2011Jan 05 2012In this paper, I construct a new test of conditional moment inequalities, which is based on studentized kernel estimates of moment functions with many different values of the bandwidth parameter. The test automatically adapts to the unknown smoothness ... More
Renormalization for Lorenz maps of long monotone combinatorial typesApr 11 2012Oct 14 2013Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz ... More
Search for dark matter at high-power laser facilities : flawed luminosity calculations in QPS -- Quasi parallel scatteringNov 21 2013I point the erroneous use, in several papers published recently, of the well known expression for the luminosity of the head-on collision of two particle bunches, in a QPS -- Quasi parallel scattering -- configuration, in which the two beams are co-propagating, ... More
QCD and Hadronic Interactions with Initial-State-Radiation at B-FactoriesApr 09 2010The efforts to improve on the precision of the measurement and theoretical prediction of the anomalous magnetic moment of the muon a_mu have turned into a test of our understanding of the hadronic contribution to vacuum polarisation. I describe how recent ... More
Turbulence for (and by) amateursJul 06 2000Series of lectures on statistical turbulence written for amateurs but not experts. Elementary aspects and problems of turbulence in two and three dimensional Navier-Stokes equation are introduced. A few properties of scalar turbulence and transport phenomena ... More
(Perturbed) Conformal Field Theory Applied To 2D Disordered Systems: An IntroductionSep 25 1995We describe applications of (perturbed) conformal field theories to two-dimensional disordered systems. We present various methods of study~: (i) {\it A direct method} in which we compute the explicit disorder dependence of the correlation functions for ... More
Quantum Symmetries in 2D Massive Field TheoriesSep 30 1991We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions is shortly described. ... More
The CAPMAP Instrument and its First SeasonMay 30 2003I describe here the new CAPMAP (Cosmic Anisotropy Polarization MAPer) instrument, which performed its first season of observing between February and April 2003 from the Crawford Hill 7-meter antenna in NJ. CAPMAP is based on the design for the PIQUE instrument, ... More
The trigonometric counterpart of the Haldane Shastry ModelAug 27 1995Aug 29 1995The hierarchy of Integrable Spin Chain Hamiltonians, which are trigonometric analogs of the Haldane Shastry Model and of the associated higher conserved charges, is derived by a reduction from the trigonometric Dynamical Models of Bernard-Gaudin-Haldane-Pasquier. ... More
Compression and collisions of chirped pulses in a dense two-level mediumOct 12 2015Using numerical simulations, we study propagation of linearly-chirped optical pulses in a homogeneously broadened two-level medium. We pay attention to the three main topics -- validity of the rotating-wave approximation (RWA), pulse compression, and ... More
On the convergence of products of operator netsFeb 21 2016The generalization of the Jessen-Marcinkiewicz-Zygmund-type theorem for the abstract space with measure was obtained in current paper. Some applications to classical harmonic analysis were reviewed.
Critical current density and trapped field in HTS with asymmetric magnetization loopsNov 23 2015Applications of the extended critical state model are considered. The trapped magnetic field, the penetration field and the field dependence of the critical current density are analysed. The critical current density and the trapped field in superconducting ... More
Scalar Glueball in a Top-Down Holographic Approach to QCDMar 02 2015Identification of glueballs -- bound states of gauge bosons in Quantum Chromodynamics (QCD) -- is a very important open question in dynamics of the strong interaction. The search for the glueball ground state, carrying scalar quantum numbers, poses a ... More
Pseudodifferential extension and Todd classDec 08 2011Let M be a closed manifold. Wodzicki shows that, in the stable range, the cyclic cohomology of the associative algebra of pseudodifferential symbols of order \leq 0 is isomorphic to the homology of the cosphere bundle of M. In this article we develop ... More
Secondary invariants for Frechet algebras, quasihomomorphisms, and the residue Chern characterJun 13 2007Nov 28 2008This paper has been replaced by arXiv:0804.1042 and arXiv:0804.1048
Localization over complex-analytic groupoids and conformal renormalizationApr 24 2008Sep 16 2008We present a higher index theorem for a certain class of etale one-dimensional complex-analytic groupoids. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character of a quasihomomorphism ... More
Quasihomomorphisms and the residue Chern characterApr 07 2008Dec 18 2008We develop a general procedure, based on the renormalized eta-cochain, which allows to find local representatives of the bivariant Chern character of finitely summable quasihomomorphisms. In particular, using zeta-function renormalization we obtain a ... More
Anomalies and noncommutative index theoryMar 27 2006These are the notes of a lecture given during the summer school "Geometric and Topological Methods for Quantum Field Theory", Villa de Leyva, Colombia, july 11 - 29, 2005. We review basic facts concerning gauge anomalies and discuss the link with the ... More
The equivariant index theorem in entire cyclic cohomologyOct 13 2004Sep 16 2008Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifold M, with compact quotient. There is an assembly map which associates to any G-equivariant K-homology class on M, an element of the topological ... More
A Riemann-Roch Theorem For One-Dimensional Complex GroupoidsJan 27 2000Mar 13 2001We consider a smooth groupoid of the form \Sigma\rtimes\Gamma where \Sigma is a Riemann surface and \Gamma a discrete pseudogroup acting on \Sigma by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C_0(\Sigma)\rtimes\Gamma ... More
Conformational selection or induced fit? New insights from old principlesSep 27 2016A long standing debate in biochemistry is to determine whether the conformational changes observed during biomolecular interactions proceed through conformational selection (of preexisting isoforms) or induced fit (ligand-induced 3D reshaping). The latter ... More
On calculation of the interweight distribution of an equitable partitionFeb 28 2013Dec 26 2013We derive recursive and direct formulas for the interweight distribution of an equitable partition of a hypercube. The formulas involve a three-variable generalization of the Krawtchouk polynomials. Keywords: equitable partition; regular partition; partition ... More
Z4-linear Hadamard and extended perfect codesOct 01 2007If $N=2^k > 8$ then there exist exactly $[(k-1)/2]$ pairwise nonequivalent $Z_4$-linear Hadamard $(N,2N,N/2)$-codes and $[(k+1)/2]$ pairwise nonequivalent $Z_4$-linear extended perfect $(N,2^N/2N,4)$-codes. A recurrent construction of $Z_4$-linear Hadamard ... More
On weight distributions of perfect colorings and completely regular codesJun 30 2009May 02 2011A vertex coloring of a graph is called "perfect" if for any two colors $a$ and $b$, the number of the color-$b$ neighbors of a color-$a$ vertex $x$ does not depend on the choice of $x$, that is, depends only on $a$ and $b$ (the corresponding partition ... More
The circulation radius and critical current density in type-II superconductorsJan 21 2019Feb 04 2019A method is proposed for estimating the length scale of currents circulating in superconductors. The estimated circulation radius is used to determine the critical current density on the basis of magnetic measurements. The obtained formulas are applicable ... More
Pseudodifferential forms and supermechanicsAug 25 2003We investigate (pseudo)differential forms in the framework of supergeometry. Definitions, basic properties and Cartan calculus (DeRham differential, Lie derivative, inner product, Hodge operator) are presented; the symplectic supermechanics (even and ... More
Grassmann Electrodynamics and General RelativitySep 23 2003The aim of this paper is to present a short introduction to supergeometry on pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham differential, Lie derivative, "inner" product), metric, inner product, Killing's vector fields, Hodge ... More
The sharp estimates of all initial taylor coefficients in the Krzyz's problemApr 20 2011For each $t>0,$ up to the number $n=N(t),$ the exact estimations of all initial taylor coefficients in the class $B_t$ were found, where $B_t$ is a set of holomorphic in unit disk functions $f,$ $0<|f|<1,$ $f(0)=e^{-t}.$
The minimum volume of subspace tradesDec 08 2015A subspace bitrade of type $T_q(t,k,v)$ is a pair $(T_0,T_1)$ of two disjoint nonempty collections (trades) of $k$-dimensional subspaces of a $v$-dimensional space $F^v$ over the finite field of order $q$ such that every $t$-dimensional subspace of $V$ ... More
Approximation of quasi-stationary distributions for 1-dimensional killed diffusions with unbounded driftsMay 22 2009The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation's method of this limit, when the process is a 1-dimensional ... More
Classes de cycles en cohomologie rigideMar 20 2001We define the rigid homology. The trace morphism in rigid cohomology define by duality the cycle class in rigid homology. We verify the compatibility of this classes with rationnal equivalence and intersection theory. We deduce some formal consequences ... More
Non annulation des fonctions $L$ des formes modulaires de Hilbert en le point centralSep 29 2008Birch and Swinnerton-Dyer conjecture allows for sharp estimates on the rank of certain abelian varieties defined over $ \Q$. in the case of the jacobian of the modular curves, this problem is equivalent to the estimation of the order of vanishing at 1/2 ... More
On the rates of convergence of simulation based optimization algorithms for optimal stopping problemsSep 19 2009In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large deviation theory for ... More
On the Automorphism Groups of the Z2Z4-Linear 1-Perfect and Preparata-Like CodesJan 29 2016We consider the symmetry group of a $Z_2Z_4$-linear code with parameters of a $1$-perfect, extended $1$-perfect, or Preparata-like code. We show that, provided the code length is greater than $16$, this group consists only of symmetries that preserve ... More
On trivial zeros of Perrin-Riou's $L$-functionsJun 16 2009In the previous paper we generalized Greenberg's construction of the $\Cal L$-invariant to semistable representations. Here we prove that this construction is compatible with Perrin-Riou's theory of $p$-adic $L$-functions
A Generalization of Greenberg's $\Cal L$-invariantJun 16 2009Using the theory of $(\varphi, \Gamma)$-modules we generalizes Greenberg's construction of the $\Cal L$-invariant to semistable representations
Variations on Descents and Inversions in PermutationsApr 11 2008We study new statistics on permutations that are variations on the descent and the inversion statistics. In particular, we consider the alternating descent set of a permutation sigma = sigma_1sigma_2...sigma_n defined as the set of indices i such that ... More
The canonical pencils on Horikawa surfacesMay 26 2006Mar 02 2009We calculate the monodromies of the canonical Lefschetz pencils on a pair of homeomorphic Horikawa surfaces. We show in particular that the (pluri)canonical pencils on these surfaces have the same monodromy groups, and are related by a "partial twisting" ... More
Infinite Dimensional Geometry and Quantum Field Theory of Strings. I. Infinite Dimensional Geometry of Second Quantized Free StringMar 11 1994Sep 22 1994There are investigated several objects of an INFINITE DIMENSIONAL GEOMETRY appearing from the second quantization of a free string. The paper contains 2 chapters: 1st is devoted to the infinite dimensional geometry of flag, fundamental and $\Pi$-spaces ... More
Setting Hidden Symmetries Free by the Noncommutative Veronese MappingFeb 23 1994The short note is devoted to the setting free of hidden symmetries in Verma modules over sl(2,C) by the noncommutative Veronese mappings.
On the spectrum of two quantum layers coupled by a windowFeb 08 2007We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them. It is also ... More
Fiber sums of genus 2 Lefschetz fibrationsApr 23 2002Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.
Factorizations in SL(2,Z) and simple examples of inequivalent Stein fillingsNov 04 2013Jan 01 2014We give simple examples of elements of SL(2,Z) admitting inequivalent factorizations into products of Dehn twists. This can be interpreted in terms of inequivalent Stein fillings of a same contact 3-manifold by genus 1 Lefschetz fibrations over the disk. ... More
Symplectic maps to projective spaces and symplectic invariantsJul 21 2000After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We also show that ... More
TPC in gamma-ray astronomy above pair-creation thresholdNov 07 2012We examine the performance of a TPC as a gamma-ray telescope above the pair-creation threshold. The contributions to the photon angular resolution are studied and their dependence on energy is obtained. The effective area per detector unit mass for such ... More
Laser Wakefield Acceleration of Particle in a PlasmaMay 17 2005A review of the present situation and perspectives, in particular in the scope of a multi-Tev linear accelerator.
On The Three Point Velocity Correlation Functions in 2d Forced TurbulenceFeb 11 1999Feb 18 1999We present a simple exact formula for the three point velocity correlation functions in two dimensional turbulence which is valid on all scales and which interpolates between the direct and inverse cascade regimes. As expected, these correlation functions ... More
On Symmetries of Some Massless 2D Field TheoriesJan 06 1992We describe few aspects of the quantum symmetries of some massless two-dimensional field theories. We discuss their relations with recent proposals for the factorized scattering theories of the massless $PCM_1$ and $O(3)_{\theta=\pi}$ sigma models. We ... More
Influence of Friction on the Direct Cascade of the 2d Forced TurbulenceApr 20 1999Mar 10 2000We discuss two possible scenario for the direct cascade in two dimensional turbulent systems in presence of friction which differ by the presence or not of enstrophy dissipation in the inviscid limit.They are distinguished by the existence or not of a ... More
Holomorphic Couplings In Non-Perturbative String CompactificationsJun 30 2011In this review article we present an analysis of several aspects of four-dimensional, non-perturbative N=1 compactifications of string theory. Our study focuses on brane dynamics and their effective physics as encoded in the holomorphic couplings of the ... More
Characterization of amenability by a factorization property of the group von Neumann algebraAug 15 2011We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their article \textit{Distinguishing ... More
Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)}May 14 1997The decompositions of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)} into irreducible submodules of the Yangian algebra Y(gl(N)) are constructed. Each of the irreducible submodules admits the unique up to normalization eigenbasis of ... More
Semi-infinite wedges and the conformal limit of the fermionic Calogero-Sutherland Model with spin $\frac{1}{2}$Jan 31 1996The conformal limit over an anti-ferromagnetic vacuum of the fermionic spin $\frac{1}{2}$ Calogero-Sutherland Model is derived by using the wedge product formalism. The space of states in the conformal limit is identified with the Fock space of two complex ... More
A 15-vertex triangulation of the quaternionic projective planeMar 17 2016In 1992, Brehm and K\"uhnel constructed a 8-dimensional simplicial complex $M^8_{15}$ with 15 vertices as a candidate to be a minimal triangulation of the quaternionic projective plane. They managed to prove that it is a manifold "like a projective plane" ... More
Simply conceiving the Arrhenius law and absolute kinetic constants using the geometric distributionJul 17 2013Dec 19 2013Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent conclusions can ... More
Modeling generic aspects of ideal fibril formationSep 27 2016Many different proteins self-aggregate into insoluble fibrils growing apically by reversible addition of elementary building blocks. But beyond this common principle, the modalities of fibril formation are very disparate, with various intermediate forms ... More
On a Generalization of Alexander Polynomial for Long Virtual KnotsJun 23 2009We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by $\zeta$ meaning an analogy with $\zeta$-polynomial for virtual links. A degree of $\zeta$-polynomial estimates a virtual crossing ... More
Extensions and renormalized tracesAug 12 2009Nov 01 2009It has been shown by Nistor that given any extension of associative algebras over C, the connecting morphism in periodic cyclic homology is compatible, under the Chern-Connes character, with the index morphism in lower algebraic K-theory. The proof relies ... More
A bivariant Chern character for families of spectral triplesMar 12 2001Oct 31 2002In this paper we construct a bivariant Chern character defined on ``families of spectral triples''. Such families should be viewed as a version of unbounded Kasparov bimodules adapted to the category of bornological algebras. The Chern character then ... More
Local index theory for certain Fourier integral operators on Lie groupoidsDec 31 2013We develop a local index theory, in the sense of non-commutative geometry, for operators associated to non-proper and non-isometric actions of Lie groupoids on smooth submersions.
Chern character, Hopf algebras, and BRS cohomologyOct 23 2002We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced ... More
On the Topological Interpretation of Gravitational AnomaliesJun 05 2000We consider the mixed gravitational-Yang-Mills anomaly as the coupling between the $K$-theory and $K$-homology of a $C^*$-algebra crossed product. The index theorem of Connes-Moscovici allows to compute the Chern character of the $K$-cycle by local formulae ... More
Does a functional integral really need a Lagrangian?Dec 03 2008Nov 05 2010Path integral formulation of quantum mechanics (and also other equivalent formulations) depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this choice leads to ... More
How to Quantize Forces(?): An Academic Essay How the Strings Could Enter Classical MechanicsDec 12 2006Dec 13 2006Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or Hamiltonian ... More
Exact and approximate many-body dynamics with stochastic one-body density matrix evolutionJul 06 2004Jul 29 2005We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, $D_{ab}=| \Phi_a > < \Phi_b ... More
Large amplitude collective dynamic beyond the independent particle/quasiparticle pictureApr 07 2015In the present note, a summary of selected aspects of time-dependent mean-field theory is first recalled. This approach is optimized to describe one-body degrees of freedom. A special focus is made on how this microscopic theory can be reduced to a macroscopic ... More
Softening and melting of a vortex lattice in presence of point disorderMay 07 1998May 13 1998A phenomenological model is proposed for melting of a vortex lattice, based on screening of the elastic shear modulus by mobile or partially pinned dislocations. A first-order softening line is found and ends at a critical point beyond which the lattice ... More
Complex Multiplication Tests for Elliptic CurvesSep 26 2004We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm ... More
Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping PrincipleSep 03 2010Jul 15 2011It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in a "hard" computer-assisted proof of existence of an area-preserving ... More
Invitation to higher local fields, Part II, section 2: Adelic constructions for direct images of differentials and symbolsDec 18 2000This work introduces adelic constructions of direct images of differentials and symbols in the two-dimensional case in the relative situation. In particular, reciprocity laws for relative residues of differentials and symbols are stated and applied to ... More
The extended 1-perfect trades in small hypercubesDec 10 2015Jun 15 2017An extended $1$-perfect trade is a pair $(T_0,T_1)$ of two disjoint binary distance-$4$ even-weight codes such that the set of words at distance $1$ from $T_0$ coincides with the set of words at distance $1$ from $T_1$. Such trade is called primary if ... More
On the binary codes with parameters of doubly-shortened 1-perfect codesJul 01 2009We show that any binary $(n=2^m-3, 2^{n-m}, 3)$ code $C_1$ is a part of an equitable partition (perfect coloring) $\{C_1,C_2,C_3,C_4\}$ of the $n$-cube with the parameters $((0,1,n-1,0)(1,0,n-1,0)(1,1,n-4,2)(0,0,n-1,1))$. Now the possibility to lengthen ... More
Modular forms of weight one: Galois representations and dimensionJun 24 2009The present notes are the expanded and polished version of three lectures given in Stanford, concerning the analytic and arithmetic properties of weight one modular forms. The author tried to write them in a style accessible to non-analytically oriented ... More
Attractors of Piecewise Translation MapsAug 12 2017Piecewise Translations is a class of dynamical systems which arises from some applications in computer science, machine learning, and electrical engineering. In dimension 1 it can also be viewed as a non-invertible generalization of Interval Exchange ... More
Almost every Interval Translation Map of three intervals is finite typeMar 15 2012Aug 02 2013Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In this paper, ... More
On $Z_{2^k}$-Dual Binary CodesSep 14 2005Oct 05 2009A new generalization of the Gray map is introduced. The new generalization $\Phi: Z_{2^k}^n \to Z_{2}^{2^{k-1}n}$ is connected with the known generalized Gray map $\phi$ in the following way: if we take two dual linear $Z_{2^k}$-codes and construct binary ... More
On eigenvalues of discrete Schrödinger operators with potentials of Coulomb type decayMar 26 2002We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.
A stable classification of Lefschetz fibrationsDec 06 2004Jan 21 2005We study the classification of Lefschetz fibrations up to stabilization by fiber sum operations. We show that for each genus there is a `universal' fibration f^0_g with the property that, if two Lefschetz fibrations over S^2 have the same Euler-Poincare ... More
Graph powers and k-ordered HamiltonicityJul 28 2003It is known that if G is a connected simple graph, then G^3 is Hamiltonian (in fact, Hamilton-connected). A simple graph is k-ordered Hamiltonian if for any sequence v_1, v_2, ..., v_k of k vertices there is a Hamiltonian cycle containing these vertices ... More
Spectral estimation of the fractional order of a Lévy processJan 12 2010We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. ... More
A beginner's introduction to Fukaya categoriesJan 29 2013The goal of these notes is to give a short introduction to Fukaya categories and some of their applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co)homology and product structures. Then we introduce the Fukaya ... More
Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double coversMar 18 2008The first part of this paper is a review of the Strominger-Yau-Zaslow conjecture in various settings. In particular, we summarize how, given a pair (X,D) consisting of a Kahler manifold and an anticanonical divisor, families of special Lagrangian tori ... More
Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizationsOct 05 2004May 05 2005The topology of symplectic 4-manifolds is related to that of singular plane curves via the concept of branched covers. Thus, various classification problems concerning symplectic 4-manifolds can be reformulated as questions about singular plane curves. ... More
Linear Temporal Logic for Regular Cost FunctionsJan 07 2014May 08 2014Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is that exact ... More