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An isomorphism between branched and geometric rough pathsDec 05 2017Apr 27 2018We exhibit an explicit natural isomorphism between spaces of branched and geometric rough paths. This provides a multi-level generalisation of the isomorphism of Lejay-Victoir (2006) as well as a canonical version of the It\^o-Stratonovich correction ... More

Persistence paths and signature features in topological data analysisJun 01 2018Dec 12 2018We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra ... More

Random walks and Lévy processes as rough pathsOct 30 2015Apr 26 2017We consider random walks and L\'evy processes in a homogeneous group $G$. For all $p > 0$, we completely characterise (almost) all $G$-valued L\'evy processes whose sample paths have finite $p$-variation, and give sufficient conditions under which a sequence ... More

Characteristic functions of measures on geometric rough pathsJul 12 2013Nov 09 2014We define a characteristic function for probability measures on the signatures of geometric rough paths. We apply our results to determine uniqueness of random variables based on their expected signature, and prove a method of moments for weak convergence ... More

A Primer on the Signature Method in Machine LearningMar 11 2016In these notes, we wish to provide an introduction to the signature method, focusing on its basic theoretical properties and recent numerical applications. The notes are split into two parts. The first part focuses on the definition and fundamental properties ... More

Signature moments to characterize laws of stochastic processesOct 25 2018The normalized sequence of moments characterizes the law of any finite-dimensional random variable. We prove an analogous result for path-valued random variables, that is stochastic processes, by using the normalized sequence of signature moments. We ... More

A support and density theorem for Markovian rough pathsJan 11 2017Jun 01 2018We establish two results concerning a class of geometric rough paths $\mathbf{X}$ which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for $\mathbf{X}$ in $\alpha$-H\"older rough path topology ... More

Characteristic functions of measures on geometric rough pathsJul 12 2013May 18 2017We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially solving the analogue ... More

Constructing supersingular elliptic curves with a given endomorphism ringJan 29 2013Oct 23 2014Let O be a maximal order in the quaternion algebra B_p over Q ramified at p and infinity. The paper is about the computational problem: Construct a supersingular elliptic curve E over F_p such that End(E) = O. We present an algorithm that solves this ... More

Canonical RDEs and general semimartingales as rough pathsApr 26 2017Apr 26 2018In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. A new metric is exhibited in which ... More

On the Number of Facets of Polytopes Representing Comparative Probability OrdersMar 21 2011Fine and Gill (1973) introduced the geometric representation for those comparative probability orders on n atoms that have an underlying probability measure. In this representation every such comparative probability order is represented by a region of ... More

Superdiffusive limits for deterministic fast-slow dynamical systemsJul 10 2019We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times Y$ of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)}) v(y_k)\;,\quad y_{k+1} = f(y_k)\;, \end{cases} \] where $\alpha\in(1,2)$. ... More

Renormalising SPDEs in regularity structuresNov 28 2017May 20 2019The formalism recently introduced in arXiv:1610.08468 allows one to assign a regularity structure, as well as a corresponding "renormalisation group", to any subcritical system of semilinear stochastic PDEs. Under very mild additional assumptions, it ... More

Deterministic homogenization for discrete-time fast-slow systems under optimal moment assumptionsMar 25 2019We consider discrete-time fast-slow systems of the form $$ X^{(n)}_{k+1} = X^{(n)}_k + n^{-1}a_n(X_k^{(n)},Y_k^{(n)}) + n^{-1/2}b_n(X_k^{(n)},Y_k^{(n)})\;, \quad Y_{k+1}^{(n)} = T_nY_k^{(n)}\;.$$ We give conditions under which the dynamics of the slow ... More

Multiscale systems, homogenization, and rough pathsDec 04 2017Mar 25 2019In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey ... More

A Computationally Efficient Limited Memory CMA-ES for Large Scale OptimizationApr 21 2014We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical optimization of non-linear, ... More

Small cancellation groups and translation numbersNov 04 1996In this paper we prove that C(4)-T(4)-P, C(3)-T(6)-P and C(6)-P small cancellation groups are translation dis crete in the strongest possible sense and that in these groups for any $g$ and any $n$ there is an algorithm deciding whether or not the equation ... More

Fermionic T-duality and U-duality in type II supergravityDec 08 2011Jan 01 2012This thesis deals with the two duality symmetries of N=2 D=10 supergravity theories that are descendant from the full superstring theory: fermionic T-duality and U-duality. The fermionic T-duality transformation is applied to the D-brane and pp-wave solutions ... More

Spin system trajectory analysis under optimal control pulsesDec 18 2012Several methods are proposed for the analysis, visualization and interpretation of high-dimensional spin system trajectories produced by quantum mechanical simulations. It is noted that expectation values of specific observables in large spin systems ... More

On Epsilon-Nets, Distance Oracles, and Metric EmbeddingsJun 19 2012We give two new applications of an observation from \cite{ADFGW11}. The first is an almost linear sized constant time data structure for reporting very large distances in undirected graphs. The second is a generic transformation of results about $\ell_1$-embeddability ... More

Rationality of an $S_6$-invariant quartic $3$-foldOct 01 2015Jan 13 2016We complete the study of rationality problem for hypersurfaces $X_t\subset\p^4$ of degree $4$ invariant under the action of the symmetric group $S_6$.

On some Fano--Enriques threefoldsOct 02 2008Aug 12 2009We give a classification of Fano threefolds $X$ with canonical Gorenstein singularities such that $X$ possess a regular involution, which acts freely on some smooth surface in $|-K_X|$, and the linear system $|-K_X|$ gives a morphism which is not an embedding. ... More

On polarized K3 surfaces of genus 33Feb 09 2011Jul 19 2016We prove that the moduli space of smooth primitively polarized $\mathrm{K3}$ surfaces of genus 33 is unirational.

On Fano threefolds with canonical Gorenstein singularitiesMay 26 2008We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.

Covering spheres with spheresMay 31 2006Given a sphere of radius $r>1$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a ... More

Higgs boson parity. Discussion of the experimentJul 26 2015Nov 04 2015Recently CMS and ATLAS announced that they have measured the Higgs boson parity. In fact, these results allow to define parity for a small class of models only. For the majority of models the used approach provides no information about Higgs parity.

Fluctuation-dissipation theorem and models of learningFeb 12 2004Oct 26 2004Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian learners perform ... More

Time to Quantify FalsifiabilityJun 02 2015Here we argue that the notion of falsifiability, a key concept in defining a valid scientific theory, can be quantified using Bayesian Model Selection, which is a standard tool in modern statistics. This relates falsifiability to the quantitative version ... More

Inference of entropies of discrete random variables with unknown cardinalitiesJul 02 2002We examine the recently introduced NSB estimator of entropies of severely undersampled discrete variables and devise a procedure for calculating the involved integrals. We discover that the output of the estimator has a well defined limit for large cardinalities ... More

Combinatorics of affine birational mapsMar 12 2013Feb 29 2016The main object of study of the present paper is the group $\au_n$ of \emph{unimodular automorphisms} of $\com^n$. Taking $\au_n$ as a working example, our intention was to develop an approach (or rather an edifice) which allows one to prove, for instance, ... More

Quasi-algebraic geometry of curves I. Riemann-Roch theorem and JacobianOct 10 1997We discuss an analogue of Riemann-Roch theorem for curves with an infinite number of handles. We represent such a curve X by its Shottki model, which is an open subset U of CP^{1} with infinite union of circles as a boundary. An appropriate bundle on ... More

Continuity Equation in the Presence of a Non-local potential in Non-Commutative Phase-SpaceFeb 19 2019We studied the continuity equation in the presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore we examined the influence of the phase-space ... More

Characterizing Arithmetic Read-Once FormulaeAug 08 2014An \emph{arithmetic read-once formula} (ROF for short) is a formula (i.e. a tree of computation) in which the operations are $\{+,\times\}$ and such that every input variable labels at most one leaf. We give a simple characterization of such formulae. ... More

Analytical Description of a Luminescent Solar Concentrator DeviceMar 09 2019Analytical solution for the optical efficiency of a luminescent solar concentrator is presented. Due to a large number of input parameters and their complex effect on the device efficiency numerical simulations have been previously used for this purpose. ... More

Counterfactual Graphical Models for Longitudinal Mediation Analysis with Unobserved ConfoundingMay 01 2012Mar 04 2013Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social ... More

The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groupsJan 10 2002Mar 03 2002We show that if $H$ is a quasiconvex subgroup of infinite index in a non-elementary hyperbolic group $G$ then the Schreier coset graph $X$ for $G$ relative to $H$ is non-amenable (that is, $X$ has positive Cheeger constant). We present some corollaries ... More

A novel method based on the Tikhonov functional for non-negative solution of a system of linear equations with non-negative coefficientsJul 28 2013We propose a novel method for a solution of a system of linear equations with the non-negativity condition. The method is based on the Tikhonov functional and has better accuracy and stability than other well-known algorithms.

A remark on mapping tori of free group endomorphismsAug 23 2002We observe that the results of Feighn-Handel and Geoghegan-Mihalik-Sapir-Wise about coherence and Hopficity of mapping tori of injective endomorphisms of free groups extend to non-injective endomorphisms.

Ducks on the torus: existence and uniquenessOct 10 2009We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually ... More

Tropical geometry and correspondence theorems via toric stacksJan 10 2010Jul 11 2011In this paper we generalize correspondence theorems of Mikhalkin and Nishinou-Siebert providing a correspondence between algebraic and parameterized tropical curves. We also give a description of a canonical tropicalization procedure for algebraic curves ... More

Relations among characteristic classes of manifold bundlesOct 25 2013Jul 18 2016We study relations among characteristic classes of smooth manifold bundles with highly-connected fibers. For bundles with fiber the connected sum of $g$ copies of a product of spheres $S^d \times S^d$ and an odd $d$, we find numerous algebraic relations ... More

Equimultiplicity in Hilbert-Kunz theoryAug 26 2016Apr 16 2017This paper develops a theory of equimultiplicity for Hilbert-Kunz multiplicity and uses it to study the behavior of Hilbert-Kunz multiplicity on the Brenner- Monsky hypersurface. A number of applications follows, in particular we show that Hilbert-Kunz ... More

On the anti-Yetter-Drinfeld module-contramodule correspondenceApr 21 2017We study a functor from anti-Yetter Drinfeld modules to contramodules in the case of a Hopf algebra $H$. Some byproducts of this investigation are the establishment of sufficient conditions for this functor to be an equivalence, verification that the ... More

Curves of infinite genus I Riemann--Roch theorem for small degreeFeb 07 2002The most useful and interesting line bundles over algebraic curves of a very high genus have the ratio \delta of the degree to the genus close to half-integer values, usually \delta \approx 0, \delta \approx 1/2, or \delta \approx 1; the numeric properties ... More

Geometic vertex operatorsMay 21 1998Sep 27 2002Vertex operators, being families of birational transformations of infinite-dimensional algebraic ``varieties'' M, act on appropriate line bundles on M. However, they act on (meromorphic) sections only as_partial operators_: they are defined on a subspace ... More

Error Bound for Compound Wishart MatricesFeb 23 2014Mar 12 2014In this paper we consider non-asymptotic behavior of the real compound Wishart matrices that generalize the classical real Wishart distribution. In particular, we consider matrices of the form 1/nXBX', where X consists of real centered Gaussian elements ... More

Diagonalization-free implementation of spin relaxation theory for large spin systemsNov 30 2010The Liouville space spin relaxation theory equations are reformulated in such a way as to avoid the computationally expensive Hamiltonian diagonalization step, replacing it by numerical evaluation of the integrals in the generalized cumulant expansion. ... More

An example of a reducible Severi varietyNov 24 2013Dec 25 2013We construct a positive-dimensional, reducible Severi variety on a toric surface.

On Severi varieties on Hirzebruch surfacesJul 31 2006In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.

Detecting quasiconvexity: algorithmic aspectsJun 27 1995The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$. This provides ... More

Limiting distribution of visits of sereval rotations to shrinking intervalsMay 10 2010We show that given $n$ normalized intervals on the unit circle, the numbers of visits of $d$ random rotations to these intervals have a joint limiting distribution as lengths of trajectories tend to infinity. If $d$ then tends to infinity, then the numbers ... More

A Generalization of a Result of Hardy and LittlewoodSep 18 2007Nov 08 2011In this note we study the growth of \sum_{m=1}^M\frac1{\|m\alpha\|} as a function of M for different classes of \alpha\in[0,1). Hardy and Littlewood showed that for numbers of bounded type, the sum is \simeq M\log M. We give a very simple proof for it. ... More

Common information revisitedApr 16 2011Jun 18 2012One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$ and $y$ measures ... More

Fano threefolds with canonical Gorenstein singularities and big degreeAug 12 2009Nov 19 2014We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.

One base point free theorem for weak log Fano threefoldsJun 02 2009Feb 01 2010Let $(X,D)$ be log canonical pair such $\dim X = 3$ and the divisor $-(K_X + D)$ is nef and big. For a special class of such $(X,D)$'s we prove that the linear system $|-n(K_{X}+D)|$ is free for $n \gg 0$.

Gain control in molecular information processing: Lessons from neuroscienceAug 03 2011Statistical properties of environments experienced by biological signaling systems in the real world change, which necessitate adaptive responses to achieve high fidelity information transmission. One form of such adaptive response is gain control. Here ... More

A New Algorithm for Two-Stage Group TestingJan 20 2019Group testing is a well-known search problem that consists in detecting of $s$ defective members of a set of $t$ samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all defective elements ... More

On semicontinuity of multiplicities in familiesFeb 20 2019The paper investigates the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities in families of ideals. It is shown that Hilbert-Samuel multiplicity is upper semicontinuous almost generally and that Hilbert-Kunz multiplicity is upper semicontinuous ... More

The Phase-Space Noncommutativity Effect on the Large and Small Wavefunction Components Approach at Dirac EquationAug 03 2014Sep 16 2018By the large and small wave-function components approach we achieved the nonrela-tivistic limit of the Dirac equation in interaction with an electromagnetic potential in noncommutative phase-space, and we tested the effect of the phase-space noncommutativity ... More

On semicontinuity of multiplicities in familiesFeb 20 2019Feb 22 2019The paper investigates the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities in families of ideals. It is shown that Hilbert-Samuel multiplicity is upper semicontinuous almost generally and that Hilbert-Kunz multiplicity is upper semicontinuous ... More

On Severi varieties and Moduli spaces of curves in arbitrary characteristicSep 06 2004Apr 26 2006This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

Convex and star-shaped sets associated with stable distributionsJul 02 2007Mar 22 2008It is known that each symmetric stable distribution in $R^d$ is related to a norm on $R^d$ that makes $R^d$ embeddable in $L_p([0,1])$. In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to a convex set ... More

Sequences modulo one: convergence of local statisticsOct 16 2014We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in $\mathbb R^2$ and on the sequence $\sqrt n\bmod1 $.

Enumeration of rational curves with cross-ratio constraintsSep 24 2015Oct 21 2016In this paper we prove the algebraic-tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor, the map has prescribed ... More

Musings on generic-case complexityMay 13 2015We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.

Some invariance properties of cyclic cohomology with coefficientsNov 04 2016In this paper, we further explore the conceptual approach to cyclic cohomology with coefficients. In particular we give a derived version of the definition with better invariance properties. We show that the new definition agrees with the old under certain ... More

Sphericity of a real hypersurface via projective geometryOct 12 2015Jun 26 2016In this work, we obtain an unexpected geometric characterization of sphericity of a real-analytic Levi-nondegenerate hypersurface $M\subset\mathbb C^{2}$. We prove that $M$ is spherical if and only if its Segre\,(-Webster) varieties satisfy an elementary ... More

On Zariski's theorem in positive characteristicMar 16 2011Jan 19 2012In the current paper we show that the dimension of a family $V$ of irreducible reduced curves in a given ample linear system on a toric surface $S$ over an algebraically closed field is bounded from above by $-K_S.C+p_g(C)-1$, where $C$ denotes a general ... More

Diffusion-limited aggregation with jumps and flightsJan 03 2006The paper suggests a generalisation of the diffusion-limited aggregation (DLA) based on using a general stochastic process to control particle movements before sticking to a growing cluster. This leads to models with variable characteristics that can ... More

Currents on free groupsDec 07 2004Sep 19 2005We study the properties of geodesic currents on free groups, particularly the "intersection form" that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces.

An example of a non-quasiconvex subgroup of a word hyperbolic group with exotic limit setJun 29 1995We construct an example of a torsion free freely indecomposable finitely presented non-quasiconvex subgroup $H$ of a word hyperbolic group $G$ such that the limit set of $H$ is not the limit set of a quasiconvex subgroup of $G$. In particular, this gives ... More

On AdS_4 x CP^3 T-dualityNov 03 2010Nov 09 2010We give a supergravity treatment of the set of bosonic and fermionic T-dualities in the AdS_4 x CP^3 background. We consider T-dualities along three flat AdS_4 directions, three complexified isometries of CP^3, and six fermionic T-dualities. Concentrating ... More

Triple Higgs coupling in the most general 2HDM at SM-like scenarioOct 28 2015Oct 12 2016We consider the triple Higgs coupling for $h(125)$ Higgs boson within the most general 2HDM. At moderate values of parameters of model, allowing by modern data, noticeable deviation of this coupling from its SM value is improbable. This deviation can ... More

Information theory and adaptationNov 24 2010In this Chapter, we ask questions (1) What is the right way to measure the quality of information processing in a biological system? and (2) What can real-life organisms do in order to improve their performance in information-processing tasks? We then ... More

Analytical solution for optimal squeezing of wave packet of a trapped quantum particleApr 17 2008Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final state is presented ... More

Nonlinear wave equation, nonlinear Riemann problem, and the twistor transform of Veronese websJun 04 2000Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave ... More

Modal logics of finite direct powers of $ω$ have the finite model propertyMar 11 2019Let $(\omega^n,\preceq)$ be the direct power of $n$ instances of $(\omega,\leq)$, natural numbers with the standard ordering, $(\omega^n,\prec)$ the direct power of $n$ instances of $(\omega,<)$. We show that for all finite $n$, the modal logics of $(\omega^n,\preceq)$ ... More

Generic-case complexity of Whitehead's algorithm, revisitedMar 17 2019In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$ are "strictly ... More

On some integral transforms of Coulomb functions related to three-dimensional proper Lorentz groupApr 07 2019Considering the relationship between two bases in representation space of the three-dimensional proper Lorentz group, we derive some formulas with integrals involving Coulomb wave functions, which can be considered as Fourier, Mellin, $K$-Bessel, Hankel ... More

Importance of Copying Mechanism for News Headline GenerationApr 25 2019News headline generation is an essential problem of text summarization because it is constrained, well-defined, and is still hard to solve. Models with a limited vocabulary can not solve it well, as new named entities can appear regularly in the news ... More

Bases of schurian antisymmetric coherent configurations and isomorphism test for schurian tournamentsAug 29 2011It is known that for any permutation group $G$ of odd order one can find a subset of the permuted set whose stabilizer in $G$ is trivial, and if $G$ is primitive, then also a base of size at most 3. Both of these results are generalized to the coherent ... More

The geometry of relative Cayley graphs for subgroups of hyperbolic groupsJan 07 2002Jan 09 2002We show that if H is a quasiconvex subgroup of a hyperbolic group G then the relative Cayley graph Y (also known as the Schreier coset graph) for G/H is Gromov-hyperbolic. We also observe that in this situation if G is torsion-free and non-elementary ... More

Charged Compact Stars in $f(\mathcal{G})$ GravitySep 15 2018This work is devoted to investigate some of the interior configuration of static anisotropic spherical stellar charged structures in the regime of $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the Gauss Bonnet invariant. The structure of particular ... More

Expansions for solutions of the Schlesinger equation at a singular pointDec 10 2012A local behavior of solutions of the Schlesinger equation is studied. We obtain expansions for this solutions, which converge in some neighborhood of a singular point. As a corollary the similar result for the sixth Painlev\'e equation was obtained. In ... More

Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. BellSep 13 2016May 02 2017In \cite{Ka14} we produced an algorithm for deciding whether or not an element $\phi\in Out(F_N)$ is an iwip ("fully irreducible") automorphism. At several points that algorithm was rather inefficient as it involved some general enumeration procedures ... More

On purely loxodromic actionsApr 20 2015Jul 07 2015We construct an example of an isometric action of $F(a,b)$ on a $\delta$-hyperbolic graph $Y$, such that this action is acylindrical, purely loxodromic, has asymptotic translation lengths of nontrivial elements of $F(a,b)$ separated away from $0$, has ... More

One (more) line on the most Ancient Algorithm in HistoryAug 23 2018We give a new simple and short ("one-line") analysis for the runtime of the well-known Euclidean Algorithm. While very short simple, the obtained upper bound in near-optimal.

Upper semi-continuity of the Hilbert-Kunz multiplicityJul 24 2014We prove that the Hilbert-Kunz multiplicity is upper semi-continuous in F-finite rings and algebras of essentially finite type over an excellent local ring.

Generic-case complexity of Whitehead's algorithm, revisitedMar 17 2019Mar 21 2019In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$ are "strictly ... More

Free Will - A road less travelled in quantum informationFeb 16 2016Conway and Kochen's Free Will Theory is examined as an important foundational element in a new area of activity in computer science - developing protocols for quantum computing

Kronecker webs, bihamiltonian structures, and the method of argument translationAug 09 1999Mar 27 2000We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call a {\em Kronecker web}. We describe two functors between Kronecker webs and integrable ... More

Fermionic T-duality in massive type IIA supergravity on AdS_{10-k} x M_kDec 28 2015Fermionic T-duality transformation is studied for the N=1 supersymmetric solutions of massive type IIA supergravity with the metric AdS_{10-k} x M_k for k=3 and 5. We derive the Killing spinors of these backgrounds and use them as an input for the fermionic ... More

Frobenius map and the $p$-adic Gamma functionJun 02 2010In this note we study the relationship between the power series expansion of the Dwork exponential and the Mahler expansion of the $p$-adic Gamma function. We exploit this relationship to prove that certain quantities that appeared in our previous computations ... More

Natural Neutrino Dark EnergySep 04 2010A new class of neutrino dark energy models is presented. The new models are characterized by the lack of exotic particles or couplings that violate the standard model symmetry. It is shown that these models lead to several concrete predictions for the ... More

LM-CMA: an Alternative to L-BFGS for Large Scale Black-box OptimizationNov 01 2015The limited memory BFGS method (L-BFGS) of Liu and Nocedal (1989) is often considered to be the method of choice for continuous optimization when first- and/or second- order information is available. However, the use of L-BFGS can be complicated in a ... More

Enumeration of rational curves with cross-ratio constraintsSep 24 2015In this paper we prove the algebraic-tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor, the map has prescribed ... More

Deep learning for detection of bird vocalisationsSep 25 2016This work focuses on reliable detection of bird sound emissions as recorded in the open field. Acoustic detection of avian sounds can be used for the automatized monitoring of multiple bird taxa and querying in long-term recordings for species of interest ... More

Chemically Induced Dynamic Nuclear Polarization of 19F NucleiApr 19 2006Apr 27 2011This study explores, both theoretically and experimentally, the photochemically induced dynamic nuclear polarization (photo-CIDNP) of 19F nuclei, the associated spin relaxation, cross-relaxation and cross-correlation effects, as well as potential applications ... More

Effective bisector estimate with application to Apollonian circle packingsApr 24 2012Let \Gamma<\PSL(2,\C) be a geometrically finite non-elementary discrete subgroup, and let its critical exponent \delta\ be greater than 1. We use representation theory of \PSL(2,\C) to prove an effective bisector counting theorem for \Gamma, which allows ... More

On endomorphisms of hypersurfacesOct 15 2015For any prime $p\ge 5$, we show that generic hypersurface $X_p\subset\mathbb{P}^p$ defined over $\mathbb{Q}$ admits a non-trivial rational dominant self-map of degree $>1$, defined over $\bar{\mathbb{Q}}$. A simple arithmetic application of this fact ... More