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Assigning a classifying space to a fusion system up to $F$-isomorphismApr 28 2011Mar 09 2015Complementary to the Inventiones work of Benson, Grodal, Henke we give criteria for a space to have cohomology $F$-isomorphic in the sense of Quillen to the stable elements. Moreover we extend results about group models for fusion systems to fusion systems ... More

Analyzing Business Process Anomalies Using AutoencodersMar 03 2018Businesses are naturally interested in detecting anomalies in their internal processes, because these can be indicators for fraud and inefficiencies. Within the domain of business intelligence, classic anomaly detection is not very frequently researched. ... More

BINet: Multi-perspective Business Process Anomaly ClassificationFeb 08 2019In this paper, we introduce BINet, a neural network architecture for real-time multi-perspective anomaly detection in business process event logs. BINet is designed to handle both the control flow and the data perspective of a business process. Additionally, ... More

A few examples of $p$-good and $p$-bad classifying spacesNov 27 2014May 23 2016We give examples of spaces which are good and bad at different primes in the sense of Bousfield and Kan in any arbitrary combination and investigate which impact the existence of a Sylow $p$-subgroup has on the homotopy type on the classifying space and ... More

On the cohomology of the free loop space of a complex projective spaceOct 30 2011Let $\Lambda (\mathbb{C}P^n)$ denote the free loop space of the complex projective space $\mathbb{C}P^n$, i. e. $\mathbb{C}P^n$ is the projective space of the vector space $\mathbb{C}^{n+1}$ of dimension $n+1$ over the complex numbers $\mathbb{C}$ and ... More

Group models for fusion systemsApr 12 2011Nov 13 2013We study group models for fusion systems and construct homology decompositions for the models of Robinson and Leary-Stancu type.

Loop homology of spheres and complex projective spacesApr 27 2011Nov 14 2011In his Inventiones paper, Ziller (Invent. Math: 1-22, 1977) computed the integral homology as a graded abelian group of the free loop space of compact, globally symmetric spaces of rank 1. Chas and Sullivan (String Topology, 1999)showed that the homology ... More

Assigning a classifying space to a fusion system up to F-isomorphismApr 28 2011Oct 20 2016Complementary to and in extension of the Inventiones work of Benson, Grodal, Henke [Group cohomology and control of p-fusion, Invent. Math. 197 (2014), 491-507] we give criteria for a space to have cohomology (strongly) F-isomorphic in the sense of Quillen ... More

Homology decompositions and groups inducing fusion systemsMar 30 2011We relate the construction of groups which realize saturated fusion systems and signaliser functors with homology decompositions of p-local finite groups. We prove that the cohomology ring of Robinson's construction is in some precise sense very close ... More

The Free Loop Space Homology of $(n-1)$-connected $2n$-manifoldsJul 10 2012Apr 22 2016Our goal in this paper is to compute the integral free loop space homology of $(n-1)$-connected $2n$-manifolds $M$, $n\geq 2$. We do this when $n\neq 2,4,8$, or when $n\neq 2$ and $\tilde H^*(M)$ has trivial cup product squares, though the techniques ... More

Signalizer functors for group models, existence of classifying spaces and applications to the fundamental groupMay 17 2011Jul 21 2014We solve the seventh problem of Oliver's list [M.\ Aschbacher, R.\ Kessar, B.\ Oliver, \textit{Fusion systems in algebra and topology}, LMS Lecture Note Series: 31, Cambridge University Press, 2011] via an explicit signalizer functor construction in the ... More

Loop space homology associated to the mod 2 Dickson invariantsJan 20 2010Mar 31 2011The spaces BG_2 and BDI(4) have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces one has for q odd the classifying spaces of the finite groups BG_2(q)and the exotic family ... More

Spectral classification of Pleiades brown dwarf candidatesOct 19 2011We report on the results of the spectroscopy of 10 objects previously classified as brown dwarf candidates via RIJHK colors by Eisenbeiss et al. (2009), who performed deep imaging observations on a 0.4 sq.deg. field at the edge of the Pleiades. We describe ... More

Generalization of an Upper Bound on the Number of Nodes Needed to Achieve Linear SeparabilityFeb 10 2018An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on the number of ... More

Refining Parameters of the XO-5 Planetary System with High-Precision Transit PhotometryMar 07 2011Studies of transiting extrasolar planets offer an unique opportunity to get to know the internal structure of those worlds. The transiting exoplanet XO-5 b was found to have an anomalously high Safronov number and surface gravity. Our aim was to refine ... More

A lucky imaging multiplicity study of exoplanet host starsFeb 21 2012To understand the influence of additional wide stellar companions on planet formation, it is necessary to determine the fraction of multiple stellar systems amongst the known extrasolar planet population. We target recently discovered radial velocity ... More

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)Oct 13 2009We construct full exceptional collections of vector bundles on the Lagrangian Grassmannians LG(4,8) and LG(5,10).

Cauchy independent measures and super-additivity of analytic capacityNov 12 2012We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition ... More

Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjectureMar 27 2011Apr 21 2011Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties that are enough ... More

Reachability in Higher-Order-CountersJun 05 2013Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those ... More

Paramagnetic tunneling state concept of the low-temperature magnetic anomalies of multicomponent insulating glassesMar 17 2006A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. ... More

Exceptional collections on isotropic GrassmanniansOct 25 2011Sep 13 2015We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the ... More

On multi-dimensional sampling and interpolationApr 02 2013The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above (from ... More

String center of mass operator and its effect on BRST cohomologyNov 15 1995We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended ... More

Homological projective duality for quadricsFeb 26 2019Mar 01 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019Mar 01 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

An ICT-Based Real-Time Surveillance System for Controlling Dengue in Sri LankaMay 16 2014Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by law is a passive ... More

Approximation of discrete functions and size of spectrumApr 02 2013Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$, then measure($S$)$\geq ... More

Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formulaOct 01 1998In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained ... More

Discrete Translates in $L^2(R)$Dec 02 2016A set $\Lambda\subset R$ is called $p$-spectral, if there is a function $\varphi\in L^p(R)$ whose $\Lambda$-translates $\{\varphi(t-\lambda),\lambda\in\Lambda\}$ span $L^p(R)$. We prove that exponentially small non-zero perturbations of the integers are ... More

$L^2-$interpolation with error and size of spectraJun 18 2008Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density ... More

Homological projective duality for quadricsFeb 26 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Categorical joinsMar 31 2018Feb 26 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Fast gradient descent method for convex optimization problems with an oracle that generates a $(δ,L)$-model of a function in a requested pointNov 07 2017Feb 02 2019In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast gradient descent ... More

Moments of random sums and Robbins' problem of optimal stoppingJul 17 2011Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense ... More

Scattering theory and Banach space valued singular integralsNov 28 2012We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy ... More

Governing Singularities of Schubert VarietiesMar 12 2006Jun 29 2006We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, ... More

Diagonalization of the Finite Hilbert Transform on two adjacent intervalsNov 06 2015We study the interior problem of tomography. The starting point is the Gelfand-Graev formula, which converts the tomographic data into the finite Hilbert transform (FHT) of an unknown function $f$ along a collection of lines. Pick one such line, call ... More

Subtle Characteristic ClassesJan 26 2014We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the powers of the fundamental ideal of the Witt ring, contain the Arason invariant ... More

Magnetic susceptibility of the quark condensate via holographyFeb 11 2009Jan 13 2010We discuss the holographic derivation of the magnetic susceptibility of the quark condensate. It is found that the susceptibility emerges upon the account of the Chern-Simons term in the holographic action. We demonstrate that Vainshtein's relation is ... More

On Beurling's sampling theorem in $\R^n$Jun 03 2011We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.

Regenerative compositions in the case of slow variation: A renewal theory approachSep 27 2011Sep 01 2012A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and Marynych (2010) ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Mild and viscosity solutions to quasilinear parabolic path-dependent PDEsNov 24 2016We study and compare two different concepts for weak solutions to quasilinear parabolic path-dependent partial differential equations (PPDEs). The first concept is that of a mild solution as it appears, e.g., in the Laplace functionals of historical superprocesses. ... More

Discrete Translates in Function SpacesDec 02 2016Mar 16 2017We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This result remains true ... More

Paramagnetic tunneling state concept of the magnetic anomalies of amorphous insulatorsSep 05 2005A generalized tunneling model of insulating glasses is formulated, considering tunneling states to be paramagnetic centers of spin 1/2. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of ... More

Derived categories of cyclic covers and their branch divisorsNov 07 2014Dec 17 2015Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$ and $\mathrm{D^b}(Z)$ ... More

Spherical structures on torus knots and linksAug 02 2010Jul 07 2011The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found ... More

Evaluation of the Einstein's strength of difference schemes for some chemical reaction-diffusion equationsMar 10 2018In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical reaction-diffusion ... More

On the Duality between Sampling and InterpolationDec 04 2015We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

When is a Schubert variety Gorenstein?Sep 25 2004Nov 21 2005A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. ... More

A Gröbner basis for Kazhdan-Lusztig idealsSep 03 2009Nov 11 2011Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. ... More

Neutrino energy quantization in rotating mediumSep 30 2008Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle ... More

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop LevelSep 20 2007In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, ... More

Discrete Uniqueness Sets for Functions with Spectral GapsSep 15 2016It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces ... More

Categorical joinsMar 31 2018Mar 01 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016Oct 25 2017We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Exponential-Uniform Identities Related to RecordsJun 05 2012We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate distributional identities ... More

Automatic Kolmogorov complexity, normality and finite state dimension revisitedJan 31 2017Jul 02 2019It is well known that normality can be described as incompressibility via finite automata. Still the statement and the proof of this result as given by Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not follow the standard ... More

Spectral perturbation theory and the two weights problemJun 08 2013The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs ... More

Yet again on polynomial convergence for SDEs with a gradient-type driftJun 28 2017Jul 23 2017Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.

Mild and viscosity solutions to semilinear parabolic path-dependent PDEsNov 24 2016Nov 14 2018We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The ... More

Lambda-coalescents with dust componentFeb 06 2011We consider the lambda-coalescent processes with positive frequency of singleton clusters. The class in focus covers, for instance, the beta$(a,b)$-coalescents with $a>1$. We show that some large-sample properties of these processes can be derived by ... More

The Bernoulli sieve: an overviewMay 31 2010The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the residual allocation model or stick-breaking. We give ... More

Limit theorems for the number of occupied boxes in the Bernoulli sieveJan 27 2010The Bernoulli sieve is a version of the classical `balls-in-boxes' occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative renewal process, also known as the residual allocation model or stick-breaking. ... More

A generalization of the Erdős-Turán law for the order of random permutationApr 26 2011May 03 2012We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on $n$ integers. Under certain assumptions ... More

Proving existence results in martingale theory using a subsequence principleMay 11 2012May 29 2012New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local martingale. ... More

Improved AGN light curve analysis with the z-transformed discrete correlation functionFeb 06 2013The cross-correlation function (CCF) is commonly employed in the study of AGN, where it is used to probe the structure of the broad line region by line reverberation, to study the continuum emission mechanism by correlating multi-waveband light curves ... More

Reflection arrangements and ribbon representationsAug 06 2011Nov 16 2011Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a Specht module. ... More

Differential posets have strict rank growth: a conjecture of StanleyFeb 14 2012We establish strict growth for the rank function of an r-differential poset. We do so by exploiting the representation theoretic techniques developed by Reiner and the author for studying related Smith forms.

Külshammer ideals of algebras of quaternion typeMay 25 2016May 27 2016For a symmetric algebra A over a field K of characteristic p \textgreater{} 0 K{\"u}lshammer constructed a descending sequence of ideals of the centre of A. If K is perfect this sequence was shown to be an invariant under derived equivalence and for algebraically ... More

Projected generalized free energies for non-equilibrium statesSep 04 2013We develop a systematic procedure to approximate generalized free energy in out of equilibrium stochastic systems. The procedure only requires knowledge of the averages of macroscopic observables and uses quasi-equilibrium distribution to this task. As ... More

Charmed Meson Decays and QCD Sum RulesJun 25 2003The current status of the QCD sum rule predictions for charmed mesons is overviewed.

Upper bounds on $f_D$ and $f_{D_s}$ from two-point correlation function in QCDDec 19 2008Feb 11 2009The correlation function of two pseudoscalar charmed quark currents with a positive hadronic spectral density is employed to obtain upper bounds on the decay constants of $D$ and $D_s$ mesons. Including all known terms of the operator-product-expansion ... More

Perfect fluids coupled to inhomogeneities in the late UniverseJan 08 2016We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such scales, the Universe is highly inhomogeneous and is filled with inhomogeneities in the form of galaxies and the groups of galaxies. We also suggest ... More

Ramanujan Complexes and High Dimensional ExpandersJan 06 2013Jan 14 2013Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last three decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various efforts made ... More

Universal scaling of resolution with photon number in superresolution fluorescence microscopySep 20 2012Oct 09 2012Superresolution fluorescence microscopy techniques beat the diffraction limit, enabling ultra-high resolution imaging in biological physics and nanoscience. In all cases that have been studied experimentally, the resolution scales inversely with the square ... More

Integrable structures of dispersionless systems and differential geometrySep 28 2016We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbons-Tsarev systems associated to moduli space of algebraic curves of arbitrary ... More

Arrows of time and the beginning of the universeMay 16 2013May 29 2013I examine two cosmological scenarios in which the thermodynamic arrow of time points in opposite directions in the asymptotic past and future. The first scenario, suggested by Aguirre and Gratton, assumes that the two asymptotic regions are separated ... More

Perspectives in cosmologyAug 05 2009The "new standard cosmology", based on the theory of inflation, has very impressive observational support. I review some outstanding problems of the new cosmology and the global view of the universe -- the multiverse -- that it suggests. I focus in particular ... More

The vacuum energy crisisMay 09 2006The smallness of the vacuum energy density and its near coincidence with the average matter density of the universe are naturally explained by anthropic selection. An alternative explanation, based on the cyclic model of Steinhardt and Turok, does not ... More

Probabilities in the landscapeFeb 27 2006Mar 15 2006I review recent progress in defining probability distributions in the inflationary multiverse.

Cosmological constant problems and their solutionsJun 11 2001Jun 21 2001There are now two cosmological constant problems: (i) why the vacuum energy is so small and (ii) why it comes to dominate at about the epoch of galaxy formation. Anthropic selection appears to be the only approach that can naturally resolve both problems. ... More

Calorimeter-Based Triggers at the ATLAS Detector for Searches for Supersymmetry in Zero-Lepton Final StatesMay 22 2012This thesis consists of three closely related parts. An analysis of data recorded by the ATLAS detector in 2010 in proton-proton collisions at a center-of-mass energy of 7 TeV with an integrated luminosity of 33.4/pb is performed, searching for supersymmetric ... More

Homological stability for unlinked Euclidean circles in $R^3$Oct 31 2013Dec 05 2013We prove a homological stability theorem for unlinked Euclidean circles in $R^3$ and use a theorem of Hatcher and Brendle to deduce homological stability for unlinked embedded circles. We discuss generalizations to unlinked Euclidean spheres with additional ... More

Computational approaches to many-body dynamics of unstable nuclear systemsDec 19 2014The goal of this presentation is to highlight various computational techniques used to study dynamics of quantum many-body systems. We examine the projection and variable phase methods being applied to multi-channel problems of scattering and tunneling; ... More

Applications of Continuum Shell ModelMay 16 2006The nuclear many-body problem at the limits of stability is considered in the framework of the Continuum Shell Model that allows a unified description of intrinsic structure and reactions. Technical details behind the method are highlighted and practical ... More

Random Partitions and the Quantum Benjamin-Ono HierarchyAug 12 2015Nov 23 2015Jack measures $M_V (\varepsilon_2, \varepsilon_1)$ on partitions $\lambda$ are discrete stochastic processes occurring naturally in the study of continuum circular $\beta$-ensembles in generic background potentials $V$ and arbitrary values $\beta$ of ... More

Localizing to submanifolds in uniformly finite homologyFeb 10 2016Given a non-compact Riemannian manifold M and a submanifold N of codimension q, we will construct under certain assumptions on both M and N a localization map in uniformly finite homology. Investigating the continuity of the localization map for certain ... More

Geometry of Cyclic Quotients, I: Knotted Totally Geodesic Submanifolds in Positively Curved SpheresOct 16 1994We prove that there exists a metric of positive curvature in a three-sphere which admits a given torus knot as a closed geodesic.We also sketch a construction of a metric in a four sphere, very likely of positive curvature, which admits a totally geodesic ... More

Quadratic Equations in Groups from the Global Geometry ViewpointJul 21 1994I use harmonic maps and minimal surfaces to study quadratic equations in groups.

Rationality of secondary classesJul 19 1994We prove the Bloch conjecture : $ c_2(E) \in H^4_\cald (X,\bbz(2))$ is torsion for holomorphic rank two vector bundles $E$ with an integrable connection over a complex projective variety $X$. We prove also the rationality of the Chern-Simons invariant ... More

Pricing of basket options IIApr 05 2014We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case. Observe that implementations of polynomial and spline approximation in ... More

Linear perturbations of black holes: stability, quasi-normal modes and tailsMar 20 2009May 26 2009Black holes have their proper oscillations, which are called the quasi-normal modes. The proper oscillations of astrophysical black holes can be observed in the nearest future with the help of gravitational wave detectors. Quasi-normal modes are also ... More

Massive scalar field quasi-normal modes of higher dimensional black holesJul 28 2006Sep 15 2006We study quasinormal spectrum of massive scalar field in the $D$-dimensional black hole background. We found the qualitatively different dependence on the field mass of the fundamental modes for $D\geq6$. The behaviour of higher modes is qualitatively ... More

Computation of Eigenvalues, Spectral Zeta Functions and Zeta-Determinants on Hyperbolic SurfacesApr 10 2016Sep 08 2016These are lecture notes from a series of three lectures given at the summer school "Geometric and Computational Spectral Theory" in Montreal in June 2015. The aim of the lecture was to explain the mathematical theory behind computations of eigenvalues ... More

Description of sound as a self-consistent field in continuous media, analogous to a superconducting state. Theoretical explanation of the experimental Fletcher-Munson curvesJun 22 2015Sep 14 2015We introduce a description of sound waves using the phonon field equivalent to a 4 dimensional second-rank tensor of distortion similar to electromagnetic waves, which are described by a 4-vector of the electromagnetic field. The exact wave solutions ... More

First-Order Logic on Higher-Order Nested Pushdown TreesFeb 09 2012We introduce a new hierarchy of higher-order nested pushdown trees generalising Alur et al.'s concept of nested pushdown trees. Nested pushdown trees are useful representations of control flows in the verification of programs with recursive calls of first-order ... More

A Turning Band Approach to Kernel Convolution for Arbitrary SurfacesSep 05 2015One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However, points on the arbitrary ... More