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Efficient Ladder-style DenseNets for Semantic Segmentation of Large ImagesMay 14 2019Recent progress of deep image classification models has provided great potential to improve state-of-the-art performance in related computer vision tasks. However, the transition to semantic segmentation is hampered by strict memory limitations of contemporary ... More

A Novel Georeferenced Dataset for Stereo Visual OdometryOct 01 2013In this work, we present a novel dataset for assessing the accuracy of stereo visual odometry. The dataset has been acquired by a small-baseline stereo rig mounted on the top of a moving car. The groundtruth is supplied by a consumer grade GPS device ... More

In Defense of Pre-trained ImageNet Architectures for Real-time Semantic Segmentation of Road-driving ImagesMar 20 2019Recent success of semantic segmentation approaches on demanding road driving datasets has spurred interest in many related application fields. Many of these applications involve real-time prediction on mobile platforms such as cars, drones and various ... More

Robust Semantic Segmentation with Ladder-DenseNet ModelsJun 09 2018We present semantic segmentation experiments with a model capable to perform predictions on four benchmark datasets: Cityscapes, ScanNet, WildDash and KITTI. We employ a ladder-style convolutional architecture featuring a modified DenseNet-169 model in ... More

Discriminative out-of-distribution detection for semantic segmentationAug 23 2018Oct 01 2018Most classification and segmentation datasets assume a closed-world scenario in which predictions are expressed as distribution over a predetermined set of visual classes. However, such assumption implies unavoidable and often unnoticeable failures in ... More

In Defense of Pre-trained ImageNet Architectures for Real-time Semantic Segmentation of Road-driving ImagesMar 20 2019Apr 12 2019Recent success of semantic segmentation approaches on demanding road driving datasets has spurred interest in many related application fields. Many of these applications involve real-time prediction on mobile platforms such as cars, drones and various ... More

Optimized Negative Dimensional Integration Method (NDIM) and multiloop Feynman diagram calculationFeb 27 2007Sep 09 2009We present an improved form of the integration technique known as NDIM (Negative Dimensional Integration Method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a $% \phi ^{3}\oplus \phi ^{4}$ ... More

Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams IIDec 18 2008Jun 15 2009A modular application of the integration by fractional expansion (IBFE) method for evaluating Feynman diagrams is extended to diagrams that contain loop triangle subdiagrams in their geometry. The technique is based in the replacement of this module or ... More

A Bott-Borel-Weil theorem for diagonal ind-groupsNov 10 2009We establish a theorem computing the cohomology groups of line bundles on homogeneous ind-varieties $G/B$ for diagonal ind-groups $G$. The main difficulty in proving this analog of the classical Bott-Borel-Weil theorem is in defining an appropriate analog ... More

Locally semisimple and maximal subalgebras of the finitary Lie algebras $gl(\infty)$, $sl(\infty)$, $so(\infty)$, and $sp(\infty)$Sep 15 2008We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras $\gl(\infty), \sl(\infty), \so(\infty)$, and $\sp(\infty)$. For simple finite--dimensional Lie algebras these classes of subalgebras have been described ... More

DAHA and iterated torus knotsAug 19 2014Nov 03 2014The theory of DAHA-Jones polynomials is extended from torus knots to their arbitrary iterations (for any reduced root systems and weights), which incudes the polynomiality, duality and other properties of the DAHA superpolynomials. Presumably they coincide ... More

DAHA approach to iterated torus linksSep 28 2015Nov 17 2015We extend the construction of the DAHA-Jones polynomials for any reduced root systems and DAHA-superpolynomials in type A from the iterated torus knots (our previous paper) to links, including arbitrary algebraic links. Such a passage essentially corresponds ... More

Neural networks for topology optimizationSep 27 2017In this research, we propose a deep learning based approach for speeding up the topology optimization methods. The problem we seek to solve is the layout problem. The main novelty of this work is to state the problem as an image segmentation task. We ... More

A Package of Programs for Determination of Some Classes of SubgroupoidsDec 02 2010We give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid.

Ind--varieties of generalized flags as homogeneous spaces for classical ind--groupsMar 26 2004The purpose of the present paper is twofold: to introduce the notion of a generalized flag in an infinite dimensional vector space $V$ (extending the notion of a flag of subspaces in a vector space), and to give a geometric realization of homogeneous ... More

Recursive method to obtain the parametric representation of a generic Feynman diagramAug 01 2005A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation is obtained ... More

Weight modules of direct limit Lie algebrasAug 11 1998In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras $A(\infty)$, $B(\infty)$, $C(\infty)$ and $D(\infty)$. Our main tool is the shadow ... More

Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagramsDec 18 2008Sep 02 2009We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically correspond to ... More

Programs in C++ for matrix computations in min plus algebraJun 24 2013The main purpose of this paper is to propose six programs in C++ for matrix computations and solving recurrent equations systems with entries in min plus algebra.

Sample programs in C++ for matrix computations in max plus algebraMay 17 2012The main purpose of this paper is to propose five programs in C++ for matrix computations and solving recurrent equations systems with entries in max plus algebra.

Separation between Classical and Quantum Winning Strategies for the Matching GameJul 17 2010Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required ... More

Lectures on Gaussian approximations with Malliavin calculusMar 19 2012Jun 28 2012In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the "Fourth Moment Theorem" in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution ... More

Yet another proof of the Nualart-Peccati criterionJul 16 2011Dec 16 2011In 2005, Nualart and Peccati showed that, surprisingly, the convergence in distribution of a normalized sequence of multiple Wiener-It\^o integrals towards a standard Gaussian law is equivalent to convergence of just the fourth moment to 3. Recently, ... More

NLO analysis of inclusive jet, tagged jet and di-jet production in Pb+Pb collisions at the LHCJul 28 2011We present results and predictions at next-to-leading order for the recent LHC lead-lead run at a center-of-mass energy of 2.76 TeV per nucleon-nucleon pair. Specifically, we focus on the suppression the single and double inclusive jet cross sections ... More

Testing the mechanism of QGP-induced energy lossNov 19 2005Aug 28 2006We present an analytic model of jet quenching, based on the (D)GLV energy loss formalism, to describe the system size dependence of QGP-induced parton absorption in relativistic heavy ion collisions. Numerical simulations of the transverse momentum dependence ... More

Large Angle Hadron Correlations from Medium-Induced Gluon RadiationJan 27 2005Sep 30 2005Final state medium-induced gluon radiation in ultradense nuclear matter is examined and shown to favor large angle emission when compared to vacuum bremsstrahlung due to the suppression of collinear gluons. Perturbative expression for the contribution ... More

Leading order pQCD hadron production and nuclear modification factors at RHIC and the LHCDec 07 2002Hadron production in leading order pQCD is reviewed. The shape of the single inclusive particle spectra is well described for $p_T \geq 2-3$ GeV at center of mass energies from 20 GeV to 2 TeV. The phenomenological K-factor is found to decrease systematically ... More

Galois actions on complex braid groupsFeb 26 2012We establish the faithfulness of a geometric action of the absolute Galois group of the rationals that can be defined on the discriminantal variety associated to a finite complex reflection group, and review some possible connections with the profinite ... More

Residual nilpotence for generalizations of pure braid groupsNov 23 2011It is known that the pure braid groups are residually torsion-free nilpotent. This property is however widely open for the most obvious generalizations of these groups, like pure Artin groups and like fundamental groups of hyperplane complements (even ... More

The freeness conjecture for Hecke algebras of complex reflection groups, and the case of the Hessian group G26Oct 20 2012Dec 02 2012We review the state-of-the-art concerning the freeness conjecture stated in the 1990's by Brou\'e, Malle and Rouquier for generic Hecke algebras associated to complex reflection groups, and in particular we expose in detail one of the main differences ... More

A Noncommutative Deformation of General RelativityOct 01 2003We develop a novel approach to gravity in which gravity is described by a matrix-valued symmetric two-tensor field and construct an invariant functional that reduces to the standard Einstein-Hilbert action in the commutative limit. We also introduce a ... More

Boundary Loop Models and 2D Quantum GravityMar 25 2007Aug 05 2007We study the O(n) loop model on a dynamically triangulated disk, with a new type of boundary conditions, discovered recently by Jacobsen and Saleur. The partition function of the model is that of a gas of self and mutually avoiding loops covering the ... More

Requirements Engineering Methods: A Classification Framework and Research ChallengesMar 08 2012Requirements Engineering Methods (REMs) support Requirements Engineering (RE) tasks, from elicitation, through modeling and analysis, to validation and evolution of requirements. Despite the growing interest to design, validate and teach REMs, it remains ... More

On uniform recurrence of HD0l systemsNov 08 2011Jul 17 2012We prove that the problem of deciding whether a given morphic sequence is uniformly recurrent is decidable. The proof uses decidability of HD0L periodicity problem, which was recently proved in papers of F.Durand and I.Mitrofanov.

A proof for the decidability of HD0L ultimate periodicityOct 21 2011Jul 17 2012We give a proof for the decidability of the HD0L ultimate periodicity problem.

Etingof conjecture for quantized quiver varieties II: affine quiversMay 20 2014We study the representation theory of quantizations of Gieseker moduli spaces. Namely, we prove the localization theorems for these algebras, describe their finite dimensional representations and two-sided ideals as well as their categories O in some ... More

$δ$-superderivations of semisimple Jordan superalgebrasJun 14 2011We described $\delta$-derivations and $\delta$-superderivations of simple and semisimple finite-dimensional Jordan superalgebras over algebraic closed fields with characteristic $p\neq2$. We constructed new examples of 1/2-derivations and 1/2-superderivations ... More

$δ$-superderivations of simple finite-dimensional Jordan and Lie superalgebrasOct 12 2010We introduce the concept of a $\delta$-superderivation of a superalgebra. $\delta$-Derivations of Cartan-type Lie superalgebras are treated, as well as $\delta$-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over ... More

Quantum extensions of dynamical systems and of Markov semigroupsSep 16 2015We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a recipe in order ... More

The graviton Higgs mechanismSep 25 2015The Higgs mechanism at the graviton level formulated as a Vainshtein mechanism in time domains implies that the extra-degrees of freedom become relevant depending on the direction of time (frame of reference) with respect to the preferred time direction ... More

On forced oscillations in groups of interacting nonlinear systemsAug 17 2015Sep 24 2015Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface, possibly with ... More

An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillatorMay 11 2015Mar 23 2016Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem ... More

The Vainshtein conditions: The Vainshtein mechanism in terms of Stückelberg functionsApr 02 2015Jul 14 2015Here I develop the simplest method in order to evaluate whether or not the Vainshtein mechanism can operate for a given set of parameters in a given solution. The method is based on the formulation of the mechanism in terms of the St\"uckelberg functions ... More

When is the sum of complemented subspaces complemented?Jun 26 2016We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space X to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp (in a certain ... More

The odd-order Pais-Uhlenbeck oscillatorMar 24 2016May 13 2016We consider a Hamiltonian formulation of the (2n+1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion ... More

Analytical results on the polymerisation random graph modelMar 23 2016Polymerisation of arbitrary-functional monomers is viewed as a time-continuos random graph process that limits vertex degrees by pre-defined parameters and treats the probability of new edge placement between two vertices as a function of their degrees. ... More

Artin groups and Yokonuma-Hecke algebrasJan 13 2016Apr 25 2016We attach to every Coxeter system (W,S) an extension C_W of the corresponding Iwahori-Hecke algebra. We construct a 1-parameter family of (generically surjective) morphisms from the group algebra of the corresponding Artin group onto C_W. When W is finite, ... More

Periods over Real Quadratic Number RingsNov 03 2016In this paper we construct explicitly a large class of mixed Tate periods over a real quadratic ring. The explicit objects are multiple Dedekind zeta values. We prove that over any real quadratic field K there is a cone so that the corresponding multiple ... More

Affine invariant points and new constructionsAug 23 2016In \cite{branko} Gr{\"u}nbaum asked if the set of all affine invariant points of a given convex body is equal to the set of all points invariant under every affine automorphism of the body. In \cite{ivan} we have proven the case of a body with no nontrivial ... More

Decomposition of number arrangements in the cubeDec 27 2014A subset $M \subset \textbf{R}^3$ is called a \emph{basic subset}, if for any funciton $f \colon M \to \textbf{R}$ there exist such functions $f_1; f_2; f_3 \colon \textbf{R} \to \textbf{R}$ that $f(x_1, x_2, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ for ... More

Periodic and falling-free motion of an inverted spherical pendulum with a moving pivot pointNov 06 2014Aug 10 2015For the system of an inverted spherical pendulum with friction and a periodically moving pivot point we prove the existence of at least one periodic solution with the additional property of being falling-free. The last means that the pendulum never becomes ... More

Moyennabilité à l'infini et exactitude d'un groupoïde étaleOct 29 2014We give a definition of amenability at infinity for a locally compact, $\sigma$-compact and Hausdorff etale groupoid and we study in some case the exactness of the reduced $C^*$-algebra of a such groupoid.

Erratum: Coding map for a contractive Markov systemOct 28 2014Aug 13 2015An error in the proof of Lemma 2 (ii) in [I. Werner, Math. Proc. Camb. Phil. Soc. 140(2) 333-347 (2006)], which claims the absolute continuity of dynamically defined measures (DDM), is identified. This undermines the assertion of the positivity of a DDM ... More

Studying Quantum Field TheoryNov 28 2013The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations of the quantum ... More

Minimal representations and reductive dual pairs in conformal field theoryJun 10 2010A minimal representation of a simple non-compact Lie group is obtained by ``quantizing'' the minimal nilpotent coadjoint orbit of its Lie algebra. It provides context for Roger Howe's notion of a reductive dual pair encountered recently in the description ... More

Representation theory of quantized Gieseker varieties, INov 25 2016We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite dimensional representations for all parameters and categories O for special values of parameters. We find the values of parameters, where ... More

Moment-angle manifolds, 2-truncated cubes and Massey operationsOct 27 2015Mar 11 2016We construct a family of manifolds having a nontrivial Massey $n$-product in their cohomology for any given $n$. These manifolds turn out to be smooth closed 2-connected manifolds with a compact torus $\mathbb T^m$-action called moment-angle manifolds ... More

Polynomial birth--death processes and the second conjecture of ValentDec 10 2017Dec 13 2017The conjecture of Valent about the type of Jacobi matrices with polynomially growing weights is proved.

Quark and Gluon Sivers FunctionsNov 14 2005The physics of hadron single transverse spin asymmetries is discussed. Possible measurements of both the quark and gluon Sivers functions are proposed.

Shadowing and Antishadowing in Neutrino Deep Inelastic ScatteringJul 07 2005The coherence of multiscattering quark nuclear processes leads to shadowing and antishadowing of the electromagnetic nuclear structure functions in agreement with measurements. This picture leads to substantially different antishadowing for charged and ... More

Surfactants in semiconductor heteroepitaxy: Thermodynamics and/or kinetics?Oct 27 2000The effect of surfactants on the thermodynamics and kinetics of semiconductor heteroepitaxy is briefly discussed. It is argued that the way the surfactants suppress the thermodynamic driving force for 3D islanding depends on the mechanism of exchange ... More

The Digital Flynn Effect: Complexity of Posts on Social Media Increases over TimeJul 18 2017Parents and teachers often express concern about the extensive use of social media by youngsters. Some of them see emoticons, undecipherable initialisms and loose grammar typical for social media as evidence of language degradation. In this paper, we ... More

Toric residue and combinatorial degreeSep 24 2003Jun 16 2004Consider an n-dimensional projective toric variety X defined by a convex lattice polytope P. David Cox introduced the toric residue map given by a collection of n+1 divisors Z_0,...,Z_n on X. In the case when the Z_i are T-invariant divisors whose sum ... More

Invitation to higher local fields, Part II, section 9: Local reciprocity cyclesDec 18 2000This is an introduction to noncommutative local reciprocity maps for totally ramified Galois extensions with arithmetically profinite group. These maps in general are not homomorphisms but Galois cycles; a description of their image and kernel is included. ... More

Groebner basis and the Anick resolution for U_K(sl_3^+)Mar 29 2012We compute three first steps of a minimal projective resolution for the trivial module over U_K(sl_3^+).

Groupoids, Frobenius algebras and Poisson sigma modelsJun 18 2013In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius algebras in the category ... More

On the Decomposition of the Small Diagonal of a K3 SurfaceNov 30 2016We give a new proof of the theorem of Beauville and Voisin about the decomposition of the small diagonal of a K3 surface S. Our proof is explicit and works with the embedding of S in a projective space. It is different from the one used by Beauville and ... More

Dissections of trapezoids into trapezoids homothetic to trapezoids of a given setSep 08 2017Here I present several theorems about trapezoids tilings. The first one is related to trapezoids with rational base relation, the other ones are related to those with base relation from quadratic number field.

Elementary proof of Jordan-Kronecker theoremSep 25 2011In this paper we prove the Jordan-Kronecker theorem which gives a canonical form for a pair of skew-symmetric bilinear forms on a finite-dimensional vector space over an algebraically closed field.

Group algebras of finite groups as Lie algebrasAug 30 2008We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition ... More

Twisted vector bundles on pointed nodal curvesJan 30 2004Jan 12 2005We establish a striking connection between Abramovich's and Vistoli's twisted bundles and Gieseker vector bundles. This note grew out of an attempt to understand a recent draft of Seshadri.

A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension oneNov 01 2005Oct 18 2007In this paper, we will focus - in dimension one - on the SDEs of the type dX_t=s(X_t)dB_t+b(X_t)dt where B is a fractional Brownian motion. Our principal motivation is to describe one of the simplest theory - from our point of view - allowing to study ... More

Emergence of the giant weak-component in directed random graphs with arbitrary degree distributionsJul 13 2016The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In addition we ... More

Birationally superrigid cyclic triple spacesOct 26 2004We prove the birational superrigidity and the nonrationality of a cyclic triple cover of $\mathbb{P}^{2n}$ branched over a nodal hypersurface of degree $3n$ for $n\ge 2$. In particular, the obtained result solves the problem of the birational superrigidity ... More

Double cubics and double quarticsOct 18 2004Jun 14 2005We study a double cover $\psi:X\to V\subset\mathbb{P}^{n}$ branched over a smooth divisor $R\subset V$ such that $R$ is cut on $V$ by a hypersurface of degree $2(n-\mathrm{deg}(V))$, where $n\geqslant 8$ and $V$ is a smooth hypersurface of degree 3 or ... More

Elliptic structures on weighted three-dimensional Fano hypersurfacesSep 15 2005Sep 21 2006We classify birational maps into elliptic fibrations of a general quasismooth hypersurface in $\mathbb{P}(1,a_{1},a_{2},a_{3},a_{4})$ of degree $\sum_{i=1}^{4}a_{i}$ that has terminal singularities.

Two local inequalitiesAug 04 2009Dec 05 2009We prove two local inequalities for divisors on surfaces and study their applications.

On Computation of Matrix Mittag-Leffler FunctionJun 05 2017A method for computation of the matrix Mittag-Leffler function is presented. The method is based on Jordan canonical form and implemented as a Matlab routine.

The Ekedahl Invariants for finite groupsDec 02 2013Aug 14 2015In 2009 Ekedahl introduced certain cohomological invariants of finite groups which are naturally related to the Noether Problem. We show that these invariants are trivial for every finite group in GL_3(k) and for the fifth discrete Heisenberg group H_5. ... More

Kolmogorov-Sinai entropy of a generalized Markov shiftFeb 17 2005May 30 2005In this paper we calculate Kolmogorov-Sinai entropy $h_M(S)$ of the generalized Markov shift associated with a contractive Markov system (CMS) \cite{Wer1} using the coding map constructed in \cite{Wer3}. We show that \[h_M(S)=-\sum\limits_{e\in E}\int\limits_{K_{i(e)}} ... More

Abelian localization for cyclotomic Cherednik algebrasFeb 02 2014In this paper we prove the abelian localization theorem for modules over cyclotomic Rational Cherednik algebras.

Towards multiplicities for categories O of cyclotomic rational Cherednik algebrasJul 05 2012May 22 2013Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affine parabolic category O of type A. In this paper we reduce their conjecture to some purely combinatorial conjecture. ... More

Heat Kernel Asymptotics of Zaremba Boundary Value ProblemOct 18 2001The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with non-smooth ... More

Multiplicity in difference geometryDec 04 2011We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \sigma-finite morphism between difference curves are all of the ... More

Primitive ideals in W-algebras of type AAug 21 2011Dec 04 2011In this note we classify the primitive ideals in finite W-algebras of type A.

Nonrational del Pezzo fibrationsJul 20 2004Sep 03 2007Let $X$ be a general divisor in $|3M+nL|$ on the rational scroll $\mathrm{Proj}(\oplus_{i=1}^{4}\mathcal{O}_{\mathbb{P}^{1}}(d_{i}))$, where $d_{i}$ and $n$ are integers, $M$ is the tautological line bundle, $L$ is a fibre of the natural projection to ... More

From Euler's play with infinite series to the anomalous magnetic momentApr 24 2018Oct 12 2018During a first St. Petersburg period Leonhard Euler, in his early twenties, became interested in the Basel problem: summing the series of inverse squares (posed by Pietro Mengoli in mid 17th century). In the words of Andre Weil (1989) "as with most questions ... More

On the variety of triangles for a hyper-Kaehler fourfold constructed by Debarre and VoisinJan 21 2018We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kaehler fourfold studied by Beauville and Donagi, and the hyper-Kaehler fourfold constructed by Debarre and Voisin. We exhibit an analog of the notion of "triangle" ... More

Black-Hole evaporation from the perspective of neural networksDec 10 2018We study the black-hole evaporation from the perspective of neural networks. We then analyze the evolution of the Hamiltonian, finding in this way the conditions under which the synapse connecting the neurons changes from gravitatory to inhibitory during ... More

Tilings of polygons composed of equal rectangles by similar rectanglesSep 18 2018Nov 18 2018Let a polygon be composed of equal rectangles. We find all quadratic irrationals r for which the polygon can be tiled by similar rectangles with given side ratio r.

Real multiplication curves by subfields of cyclotomic fieldsOct 09 2013In \emph{Endomorphism Algebras of Jacobians}, Ellenberg gives group theory tools to construct jacobians of curves with real multiplication. He shows the existence of curves and family of curves with real multiplication by subfields of cyclotomic fields. ... More

On self-associated sets of points in small projective spacesApr 24 2006We study moduli of ``self-associated'' sets of points in ${\bf P}^n$ for small $n$. In particular, we show that for $n=5$ a general such set arises as a hyperplane section of the Lagrangean Grassmanian $LG(5,10) \subset {\bf P}^{15}$ (this was conjectured ... More

Cramer's rules for the solution to the two-sided restricted quaternion matrix equationAug 02 2017Weighted singular value decomposition (WSVD) of a quaternion matrix and with its help determinantal representations of the quaternion weighted Moore-Penrose inverse have been derived recently by the author. In this paper, using these determinantal representations, ... More

Cramer's rule for some quaternion matrix equationsApr 25 2010Cramer's rules for some left, right and two-sided quaternion matrix equations are obtained within the framework of the theory of the column and row determinants.

On the order of vanishing of the cyclotomic p-adic L-functionMay 28 2009Aug 01 2012For a newform for Gamma_0(N) of even weight k, we prove that its attached p-adic L-function is not identically zero on the group Z_p of the p-adic units. If p >3, we prove that the order of vanishing at any p-adic integer is finite.

Lattice extensions of Hecke algebrasFeb 04 2017We investigate the extensions of the Hecke algebras of finite (complex) reflection groups by lattices of reflection subgroups that we introduced, for some of them, in our previous work on the Yokonuma-Hecke algebras and their connections with Artin groups. ... More

Face module for realizable Z-matroidsMay 16 2017Jan 17 2018In this work, we define the face module for a realizable matroid over Z. Its Hilbert series is, indeed, the expected specialization of the Grothendieck - Tutte polynomial defined by Fink and Moci. This work will appear in 'Contributions to Discrete Mathematics' ... More

"Quantization is a mystery"Jun 14 2012Expository notes which combine a historical survey of the development of quantum physics with a review of selected mathematical topics in quantization theory (addressed to students that are not complete novices in quantum mechanics). After recalling in ... More

Highest weight sl_2-categorifications I: crystalsJan 21 2012Feb 12 2012We define highest weight categorical actions of sl_2 on highest weight categories and show that basically all known examples of categorical sl_2-actions on highest weight categories (including rational and polynomial representations of general linear ... More

Symplectic four-manifolds and conformal blocksFeb 09 2003Aug 13 2004We apply ideas from conformal field theory to study symplectic four-manifolds, by using modular functors to "linearise" Lefschetz fibrations. In Chern-Simons theory this leads to the study of parabolic vector bundles of conformal blocks. Motivated by ... More