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Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometryJun 14 2005We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood ... More

On the Onsager-Machlup functional for the Brownian motion on the Heisenberg groupAug 24 2019Given a stochastic process, the problem of finding the corresponding Onsager-Machlup functional is well known in probability theory, and it has been intensively studied over the last fifty years. For a stochastic process taking values in a Riemannian ... More

Coupling in the Heisenberg group and its applications to gradient estimatesOct 20 2016Nov 25 2017We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling such as estimates on the coupling rate, and upper and lower bounds on the ... More

Singular perturbations of Ornstein-Uhlenbeck processes: integral estimates and Girsanov densitiesJan 02 2018Apr 10 2019We consider a perturbation of an infinite-dimensional Ornstein--Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts $F_0$. The only further assumption on $F_0$ is that it is bounded by a radially symmetric ... More

Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentialsJul 06 2019This paper studies convergence to equilibrium for second-order Langevin dynamics under general growth conditions on the potential. Although we are principally motivated by the case when the potential is singular, e.g. when the dynamics has repulsive forces ... More

An application of a functional inequality to quasi-invariance in infinite dimensionsFeb 03 2016One way to interpret smoothness of a measure in infinite dimensions is quasi-invariance of the measure under a class of transformations. Usually such settings lack a reference measure such as the Lebesgue or Haar measure, and therefore we can not use ... More

Heat Kernel Analysis on Infinite-Dimensional Heisenberg GroupsMay 12 2008We introduce a class of non-commutative Heisenberg like infinite dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the corresponding heat kernel ... More

Diffeomorphisms of the circle and Brownian motions on an infinite-dimensional symplectic groupFeb 14 2008An embedding of the group $\Diff(S^{1})$ of orientation preserving diffeomorphims of the unit circle $S^1$ into an infinite-dimensional symplectic group, $\Sp(\infty)$, is studied. The authors prove that this embedding is not surjective. A Brownian motion ... More

Sub-Laplacians on sub-Riemannian manifoldsNov 29 2014We consider different sub-Laplacians on a sub-Riemannian manifold $M$. Namely, we compare different natural choices for such operators, and give conditions under which they coincide. One of these operators is a sub-Laplacian we constructed previously ... More

Lévy Processes in a Step 3 Nilpotent Lie GroupJul 02 2012Jul 03 2012The infinitesimal generators of L\'evy processes in Euclidean space are pseudo-differential operators with symbols given by the L\'evy-Khintchine formula. This classical analysis relies heavily on Fourier analysis which in the case when the state space ... More

Hypoelliptic heat kernel on nilpotent Lie groupsMay 15 2015Feb 03 2016The starting point of our analysis is an old idea of writing an eigenfunction expansion for a heat kernel considered in the case of a hypoelliptic heat kernel on a nilpotent Lie group $G$. One of the ingredients of this approach is the generalized Fourier ... More

Weak Convergence to Brownian Motion on Sub-Riemannian ManifoldsMar 02 2014Oct 06 2014This paper considers a classical question of approximation of Brownian motion by a random walk in the setting of a sub-Riemannian manifold $M$. To construct such a random walk we first address several issues related to the degeneracy of such a manifold. ... More

A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groupsJun 10 2011Nov 15 2011Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure which is formally ... More

Square integrable holomorphic functions on infinite-dimensional Heisenberg type groupsSep 29 2008We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure $\mu$ on these groups ... More

Harnack inequalities in infinite dimensionsSep 07 2012Sep 24 2012We consider the Harnack inequality for harmonic functions with respect to three types of infinite dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails ... More

Integrated Harnack inequalities on Lie groupsNov 28 2007Aug 01 2008We show that the logarithmic derivatives of the convolution heat kernels on a uni-modular Lie group are exponentially integrable. This result is then used to prove an "integrated" Harnack inequality for these heat kernels. It is shown that this integrated ... More

Singular perturbations of Ornstein-Uhlenbeck processes: integral estimates and Girsanov densitiesJan 02 2018Oct 25 2018We consider a perturbation of an infinite-dimensional Ornstein--Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts $F_0$. The only further assumption on $F_0$ is that it is bounded by a radially symmetric ... More

Integration by parts and quasi-invariance for the horizontal Wiener measure on a foliated compact manifoldJul 11 2017Sep 20 2018We prove several versions of Driver's integration by parts formula for the horizontal Wiener measure on a totally geodesic Riemannian foliation and prove that the horizontal Wiener measure has a quasi-invariance property with respect to flows generated ... More

On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifoldsSep 19 2018Oct 18 2018In this note we show how results in \cite{BaudoinBonnefont2016, BaudoinGarofalo2013, CoulhonJiangKoskelaSikora2017} yield the Cheng-Yau estimate on two classes of sub-Riemannian manifolds: Carnot groups and sub-Riemannian manifolds satisfying a generalized ... More

Integration by parts and quasi-invariance for the horizontal Wiener measure on a foliated compact manifoldJul 11 2017Jun 07 2019We prove several versions of Driver's integration by parts formula for the horizontal Wiener measure on a totally geodesic Riemannian foliation and prove that the horizontal Wiener measure has a quasi-invariance property with respect to flows generated ... More

Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groupsAug 07 2011We study heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg-like Lie groups. In particular, we show that Cameron-Martin type quasi-invariance results hold in this subelliptic setting and give $L^p$-estimates for the Radon-Nikodym derivatives. ... More

Coupling in the Heisenberg group and its applications to gradient estimatesOct 20 2016We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling such as estimates on the coupling rate, and upper and lower bounds on the ... More

Gradient Bounds for Kolmogorov Type DiffusionsMar 04 2018We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized $\Gamma$-calculus techniques. The advantages and ... More

Gradient Bounds for Kolmogorov Type DiffusionsMar 04 2018Mar 18 2019We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized $\Gamma$-calculus techniques. The advantages and ... More

Left-invariant geometries on $\mathrm{SU}(2)$ are uniformly doublingAug 09 2017Jun 12 2018A classical aspect of Riemannian geometry is the study of estimates that hold uniformly over some class of metrics. The best known examples are eigenvalue bounds under curvature assumptions. In this paper, we study the family of all left-invariant geometries ... More

Dimension-independent Harnack inequalities for subordinated semigroupsApr 18 2010Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the Bakry-Emery curvature condition, the subordinate semigroup with power $\alpha$ satisfies a dimension-free Harnack ... More

Equivalence of the Brownian and energy representationsNov 23 2015We consider two unitary representations of the infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by quasi-invariance of the Wiener measure, and the second representation is the energy representation. ... More

Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck typeMar 08 2005We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i x_i b_i(x) \frac{\del f}{\del x_i}(x).$$ We prove existence and uniqueness of solutions to the martingale problem ... More

Riemannian geometry of ${\rm Diff}(S^1)/S^1$ and representations of the Virasoro algebraOct 28 2005Nov 19 2005The main result of the paper is a computation of the Ricci curvature of $\DS/S^1$. Unlike earlier results on the subject, we do not use the K\"{a}hler structure symmetries to compute the Ricci curvature, but rather rely on classical finite-dimensional ... More

Realization and Extension of Abstract Operation Contracts for Program LogicJan 18 2015For engineering software with formal correctness proofs it is crucial that proofs can be efficiently reused in case the software or its specification is changed. Unfortunately, in reality even slight changes in the code or its specification often result ... More

Numerical methods for checking the regularity of subdivision schemesFeb 10 2012In this paper, motivated by applications in computer graphics and animation, we study the numerical methods for checking $C^k-$regularity of vector multivariate subdivision schemes with dilation 2I. These numerical methods arise from the joint spectral ... More

Weyl denominator identity for finite-dimensional Lie superalgebrasMay 08 2009Jul 26 2010Weyl denominator identity for finite-dimensional Lie superalgebras, conjectured by V.~Kac and M.~Wakimoto in 1994, is proven.

Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter numberNov 30 2009Weyl denominator identity for the affinization of a basic Lie superalgebra with a non-zero Killing form was formulated by Kac and Wakimoto and was proven by them in defect one case. In this paper we prove this identity.

A Multiquadratic Field Generalization of Artin's ConjectureFeb 15 2012Sep 08 2014We prove that (under the assumption of the generalized Riemann hypothesis) a totally real multiquadratic number field $K$ has a positive density of primes $p \in \mathbb{Z}$ for which the image of the unit group $(\mathcal{O}_K)^{\times})$ in $(\mathcal{O}_K/p\mathcal{O}_K)^{\times})$ ... More

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedomMar 29 2009We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$. The well known Morales-Ramis theorem ... More

Collider Experiment: Strings, Branes and Extra DimensionsMay 12 2003May 18 2003Selected topics showcasing the exploration for new physics using colliders; presented at TASI 2001.

Are bottom PDFs needed at the LHC?Jul 21 2014Processes involving bottom quarks play a crucial role in the LHC phenomenology, from flavour physics to Higgs characterisation and as a window to new physics, appearing both as signals and irreducible background in BSM searches. These processes can be ... More

NNLO analysis of the LHC W lepton charge asymmetry dataOct 11 2011The reweighting method presented in earlier publications is applied for incorporating the LHC W lepton asymmetry data published in 2010 into the NNPDF2.1 NNLO analysis. We confirm the result of the NLO analysis which indicated that these data reduce PDF ... More

Time-dependent modelling of PKS 2155-304 in a low stateSep 12 2014We apply both leptonic and leptohadronic emission scenarios for modelling the multiwavelength photon spectra and the observed variability in the optical, X-ray, and TeV gamma-ray energy bands of blazar PKS 2155-304 while being in a low state between 25 ... More

Boundedness of derivatives and anti-derivatives of holomorphic functions as a rare phenomenonNov 16 2016In this article we prove a general result which in particular suggests that, on a simply connected domain in C, all the derivatives and anti-derivatives of the generic holomorphic function are unbounded. A similar result holds for the operator of partial ... More

The Higgs System in and Beyond the Standard ModelJan 28 2014After the discovery of the Higgs boson particle on the 4th of July of 2012 at the Large Hadron Collider, sited at the european CERN laboratory, we are entering in a fascinating period for Particle Physics where both theorists and experimentalists are ... More

A Radon-Nikodym theorem for completely multi-positive linear maps and applicationsOct 04 2005052<p type="texpara" tag="Body Text" et="abstract" >A completely $n$ -positive linear map from a locally $C^{\ast}$-algebra $A$ to another locally $C^{\ast}$-algebra $B $is an $n\times n$ matrix whose elements are continuous linear maps from $A$ to $B$ ... More

On Hilbert modules over locally C*-algebras IIAug 02 2005In this paper we study the unitary equivalence between Hilbert modules over a locally C*-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally C*-algebra and show that a Hilbert module over a Frechet ... More

Edge Universality for Orthogonal Ensembles of Random MatricesDec 17 2008We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of \cite{S:08} on the representation of the reproducing ... More

Crossed products of locally C*-algebrasDec 06 2005The crossed products of locally C*-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C*-algebra is proved.

The (g-2)_mu data and the lightest Higgs boson in 2HDM(II)Dec 07 2001Dec 09 2001The present limits on the lightest Higgs boson in 2HDM (II) in light of the new E821 measurement of g-2 for the muon are discussed.

ECFA-Summary: Higgs, gamma-gamma and e-gamma physicsDec 24 2003Recent results obtained within ECFA/DESY and ECFA Study by the Higgs and gamma gamma /e gamma physics working groups are presented.

The new (g-2) for muon measurement and limits on the light Higgs bosons in 2HDM (II)Mar 20 2001Oct 01 2001We discuss how new data for a_{mu}= (g-2)_{mu}/2 improve constraints on new physics. Using two types of estimations of a_{mu}^{had} (Davier & H"{o}cker (case A) and Jegerlehner2000 (case B)) we evaluate 95% CL intervals for a new contribution, which can ... More

The Structure of the Photon in Hard Hadronic ProcessesDec 24 1997The concept of the structure of the photon is discussed and the progress in the measurement of various structure functions of the photon as well of parton distributions in the photon is shortly reviewed.

Status of 2HDM with a Light Higgs ParticleDec 24 1996Present data do not rule out the light neutral Higgs particle h or A with mass below 40--50 GeV in the framework of the general 2HDM ("Model II"). The status of this model in a light of existing LEP I data and a potential of the new muon experiment (g-2), ... More

The $\mathrm{GL}_4$ Rapoport-Zink SpaceNov 05 2018We give a description of the $\mathrm{GL}_4$ Rapoport-Zink space, including the connected components, irreducible components, intersection behavior of the irreducible components, and Ekedahl-Oort stratification. As an application of this, we also give ... More

Renewal processes with costs and rewardsApr 22 2014We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the elementary renewal ... More

Handling temporality of clinical events with application to Adverse Drug Event detection in Electronic Health Records: A scoping reviewApr 09 2019The increased adoption of Electronic Health Records(EHRs) has brought changes to the way the patient care is carried out. The rich heterogeneous and temporal data space stored in EHRs can be leveraged by machine learning models to capture the underlying ... More

Continued Fraction Expansions of Matrix EigenvectorsOct 11 2008We examine various properties of the continued fraction expansions of matrix eigenvector slopes of matrices from the SL(2, Z) group. We calculate the average period length, maximum period length, average period sum, maximum period sum and the distributions ... More

A cancellation-free formula for the Schur elements of the Ariki-Koike algebraJan 07 2011Schur elements play a powerful role in the representation theory of symmetric algebras. In the case of the Ariki-Koike algebra, Schur elements are Laurent polynomials whose factors determine when Specht modules are projective irreducible and whether the ... More

Role of input atomic data in spectroscopic analyses of the Sun and metal-poor starsApr 08 2011Analysis of high-resolution stellar spectra relies heavily upon atomic data. These include energy levels, wavelengths, cross-sections for various types of interactions between particles and photons, such as photoionization and collision induced transitions. ... More

Ionization balance of Ti in the photospheres of the Sun and four late-type starsJan 04 2011In this paper we investigate statistical equilibrium of Ti in the atmospheres of late-type stars. The Ti I/Ti II level populations are computed with available experimental atomic data, except for photoionization and collision induced transition rates, ... More

The prime spectrum of a quantum Bruhat cell translateJul 08 1997Jul 10 1997The prime spectra of two families of algebras, $S^w$ and $\check{S}^w$, $w\in W,$ indexed by the Weyl group $W$ of a semisimple finitely dimensional are studied. The algebras $S^w$ have been introduced by A.~Joseph; they are $q$-analogues of the algebras ... More

The Two-Peak Model of LS I +61303: Radio Spectral Index AnalysisSep 10 2010The most puzzling aspect of the radio emission from LSI+61303 is that the large periodic radio outburst, with period equal to the orbital one, occurs very displaced from periastron passage, nearly at apoastron. In 1992, Taylor, one of the discoverers ... More

The 1D parabolic-parabolic Patlak-Keller-Segel model of chemotaxis: the particular integrable case and soliton solutionApr 27 2015Sep 28 2016In this paper we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears ... More

Spectroscopic studies of star forming regionsDec 14 2006This paper reviews the results of studies of star forming regions, carried out at the Konkoly Observatory in the last two decades. The studies involved distance determination of star-forming dark clouds, search for candidate pre-main sequence stars, and ... More

SUSY@LHC.CERN.CHJan 01 2008I discuss the program of work towards discoveries at the LHC, and I include seeds for orientation and navigation in the parameter space given the foreseen multitude of excesses at startup.

Towards the NNPDF3.0 parton set for the second LHC runJul 11 2014The full exploitation of the increasingly precise LHC measurements is essential in order to reduce the uncertainty of theoretical predictions at hadron colliders. The NNPDF2.3 fit was the first PDF determination including the effect of the early LHC data. ... More

Universality classes for the "ricepile" model with absorbing propertiesSep 10 1999The absorbing "ricepile" model with stochastic toppling rules has been numerically studied. Local limited, local unlimited, nonlocal limited and nonlocal unlimited versions of the absorbing model have been investigated. Transport properties and different ... More

The role of hadronic cascades in GRB models of efficient neutrino productionMay 29 2014We investigate the effects of hadronic cascades on the gamma-ray burst (GRB) prompt emission spectra in scenarios of efficient neutrino production. By assuming a fiducial GRB spectrum and a power-law proton distribution extending to ultra-high energies, ... More

Invariant algebraic curves for Liénard dynamical systems revisitedMar 21 2018Apr 20 2018A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of irreducible invariant algebraic curves for Li\'{e}nard dynamical systems $x_t=y$, $y_t=-g(x)y-f(x)$ with $\text{deg} ... More

Closure properties of predicates recognized by deterministic and non-deterministic asynchronous automataOct 14 2010Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous ... More

On multipliers of Hilbert modules over locally C*-algebrasJul 08 2007In this paper, we investigate the structure of the multiplier module of a Hilbert module over a locally C*-algebra and the relationship between the set of all adjointable operators from a Hilbert A-module E to a Hilbert A-module F and the set of all adjointable ... More

A Radon-Nikodym theorem for completely n-positive linear maps on pro-C*-algebras and its applicationsJan 09 2007The order relation on the set of completely n-positive linear maps from a pro-C*-algebra A to L(H), the C*-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each completely n-positive ... More

Late-type Stars in the Inner GalaxyJul 27 2004Asymptotic Giant Branch (AGB) stars are good tracers of the Galactic structure. They are bright in the infrared and can therefore be detected even in the most obscured regions of the Galaxy. Maser emission from their circumstellar envelopes can be detected ... More

Bounding dimension of ambient space by density for mean curvature flowMar 01 2005For an ancient solution of the mean curvature flow, we show that each time slice M_t is contained in an affine subspace with dimension bounded in terms of the density and the dimension of the evolving submanifold. Recall that an ancient solution is a ... More

Covariant completely positive linear maps between locally C*-algebrasSep 05 2006We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel'fand,Naimark,Segal) construction for completely positive linear maps between locally $C^{*}$-algebras. As an application of this construction, we show that a covariant completely positive ... More

The dual of the James Tree space is asymptotically uniformly convexApr 26 2000The dual of the James Tree space is asymptotically uniformly convex.

On the Ghost Centre of Lie SuperalgebrasOct 21 1999We define a notion of ghost centre of a Lie superalgebra g=g_0+g_1 which is a sum of invariants with respect to the usual adjoint action (centre) and invariants with respect to a twisted adjoint action (``anticentre''). We calculate the anticentre in ... More

"Boring formal methods" or "Sherlock Holmes deduction methods"?Dec 06 2016This paper provides an overview of common challenges in teaching of logic and formal methods to Computer Science and IT students. We discuss our experiences from the course IN3050: Applied Logic in Engineering, introduced as a "logic for everybody" elective ... More

Generalization of the "Stark unit" for abelian L-functions with multiple zerosDec 14 2008For an abelian extension of number fields we show that the Stark conjecture for all Artin L-functions with zero of order r is equivalent to existence of a special element in the rational span of the r-th exterior power of the Galois module of units of ... More

A non-increasing Lindley-type equationApr 22 2014In this paper we study the Lindley-type equation $W=\max\{0, B - A - W\}$. Its main characteristic is that it is a non-increasing monotone function in its main argument $W$. Our main goal is to derive a closed-form expression of the steady-state distribution ... More

Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensionsMay 14 2014Dec 20 2016This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness ... More

On the cyclotomic Hecke algebras of complex reflection groupsOct 03 2007Following the definition of Rouquier for the "families of characters" of a Weyl group and its generalization to the case of complex reflection groups, already appeared in the works of Broue-Kim and Malle-Rouquier, we show that these "families" depend ... More

Degree and valuation of the Schur elements of cyclotomic Hecke algebrasFeb 28 2008Aug 12 2008Following the generalization of the notion of families of characters, defined by Lusztig for Weyl groups, to the case of complex reflection groups, thanks to the definition given by Rouquier, we show that the degree and the valuation of the Schur elements ... More

Examples of cyclic polynomially bounded operators that are not similar to contractions, IIMar 09 2018May 15 2018The question if polynomially bounded operator is similar to a contraction was posed by Halmos and was answered in the negative by Pisier. His counterexample is an operator of infinite multiplicity, while all its restrictions on invariant subspaces of ... More

Strongly typical representations of the basic classical Lie superalgebrasSep 20 2000The category of representations with a strongly typical central character of a basic classical Lie superalgebra is proven to be equivalent to the category of representations of its even part corresponding to an appropriate central character. For a Lie ... More

Hermitian Structures and Compatible Connections on A-bundlesOct 15 1998A-manifolds and A-bundles are manifolds and vector bundles modelled on a projective finitely generated module over a topological algebra A. In this paper we investigate the conditions under which an A-bundle is provided with an A-valued hermitian structure ... More

On a generic Verma module at the critical level over affine Lie superalgebrasApr 12 2005Jan 23 2007We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra not of the type A(2k,2l)^{(4)}. We obtain the character formula for a simple module with a generic highest weight ... More

Introduction to Astrophysics of MicroquasarsJun 29 2005The Astrophysics of microquasars - galactic miniatures of the far distant quasars - has become one of the most active fields of modern Astronomy in recent years. Here I review the astronomical methods used for the investigation of these objects, from ... More

Human Factors of Formal MethodsApr 29 2014This paper provides a brief introduction to the work that aims to apply the achievements within the area of engineering psychology to the area of formal methods, focusing on the specification phase of a system development process.

On rational blow-downs in Heegaard-Floer homologySep 29 2007Motivated by a result of L.P. Roberts on rational blow-downs in Heegaard-Floer homology, we study such operations along 3-manifolds that arise as branched double covers of $S^{3}$ along several non-alternating, slice knots.

Network model of human languageSep 19 2007The phenomenon of human language is widely studied from various points of view. It is interesting not only for social scientists, antropologists or philosophers, but also for those, interesting in the network dynamics. In several recent papers word web, ... More

Random networks with preferential growth and vertex deathSep 23 2015A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is connected to an existing ... More

On Euler characteristics of Selmer groups for abelian varieties over global function fieldsDec 07 2015Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell\neq p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Sel_A(K)_\ell$.

Variance of $\mathcal{B}$-free integers in short intervalsDec 01 2015We prove some new statements on the distribution of $\mathcal{B}$-free numbers in short intervals. In particular, we show an asymptotic result for the variance of the number of $\mathcal{B}$-free integers in random short intervals which are, in some sense, ... More

Asymptotic shape in a continuum growth modelSep 23 2015A continuum growth model is introduced. The state at time $t$, $S_t$, is a subset of $\mathbb{R}^d$ and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs somewhere in ... More

Painlevé analysis for two 1D parabolic-parabolic models of chemotaxis; some travelling wave solutionsJul 01 2016In this paper we study the Painlev\'e analysis for two models of chemotaxis. We find that in some cases the reductions of these models in terms of travelling wave variable allow exact analytical solutions.

LLFR: A Lanczos-Based Latent Factor Recommender for Big Data ScenariosJun 14 2016The purpose if this master's thesis is to study and develop a new algorithmic framework for Collaborative Filtering to produce recommendations in the top-N recommendation problem. Thus, we propose Lanczos Latent Factor Recommender (LLFR); a novel "big ... More

Spatio-temporal features of FocusSTOct 25 2016In this technical report we summarise the spatio-temporal features and present the core operators of FocusST specification framework. We present the general idea of these operators, using a Steam Boiler System example to illustrate how the specification ... More

Weak Convergence of Sequential Empirical Processes under Weak DependenceNov 14 2017Oct 30 2018The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness assumption on ... More

Isocurvature, non-gaussianity and the curvaton modelApr 07 2008Recent analyses of the statistical distribution of the temperature anisotropies in the CMB do not rule out the possibility that there is a large non-gaussian contribution to the primordial power spectrum. This fact motivates the re-analysis of the curvaton ... More

Shuffle bialgebrasMar 14 2007Dec 12 2008The goal of our work is to study the spaces of primitive elements of the Hopf algebras associated to the permutaedra and the associaedra. We introduce the notion of shuffle and preshuffle bialgebras, and compute the subpaces of primitive elements associated ... More

On Morita equivalence of group actions on locally C*-algebrasMay 25 2007We extend to the context of locally C*-algebras a result of F. Combes [Proc. London Math. Soc. 49(1984), 289-306].

Photon and its hadronic interactionDec 24 2003A short overview of basics aspects of hadronic interaction of the photon is presented.