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First Steps Towards an Imprecise Poisson ProcessMay 14 2019Jun 04 2019The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here consider a rate ... More

First Steps Towards an Imprecise Poisson ProcessMay 14 2019The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here consider a rate ... More

Computing Inferences for Large-Scale Continuous-Time Markov Chains by Combining Lumping with ImprecisionApr 03 2018May 31 2018If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain is usually ... More

Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error BoundsFeb 23 2017Oct 10 2018Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there ... More

An Imprecise Probabilistic Estimator for the Transition Rate Matrix of a Continuous-Time Markov ChainApr 04 2018Jul 11 2018We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions ... More

Imprecise Markov Models for Scalable and Robust Performance Evaluation of Flexi-Grid Spectrum Allocation PoliciesJan 17 2018Apr 27 2018The possibility of flexibly assigning spectrum resources with channels of different sizes greatly improves the spectral efficiency of optical networks, but can also lead to unwanted spectrum fragmentation.We study this problem in a scenario where traffic ... 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

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

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

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

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

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

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

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

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

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

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

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

Algorithm of Ensemble Pulsar TimeAug 09 2006An algorithm of the ensemble pulsar time based on the Wiener filtration method has been constructed. This algorithm has allowed the separation of the contributions of an atomic clock and a pulsar itself to the post-fit pulsar timing residuals. The method ... 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

Converting Reconfigurable Petri Nets to MaudeSep 30 2014Nov 12 2014Model checking is an important aim of the theoretical computer science. It enables the verification of a model with a set of properties such as liveness, deadlock or safety. One of the typical modelling techniques are Petri nets they are well understood ... 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

Cuspidal representations which are not strongly cuspidalOct 16 2007We give a description of all the cuspidal representations of $\mathrm{GL}_4(\mathfrak{o}_2)$, where $\mathfrak{o}_2$ is a finite ring coming from the ring of integers in a local field, modulo the square of its maximal ideal $\mathfrak{p}$. This shows ... More

Growing supermassive black holes: sub-grid modelling and intermediate-scale processesSep 24 2012The sheer range of scales in the Universe makes it impossible to model all at once. It is necessary, therefore, when conducting numerical experiments, that we employ sub-resolution prescriptions that can represent the scales we are unable to model directly. ... 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

Structure of Kahler groups, I: second cohomologyMar 02 1999We prove the Carlson-Toledo conjecture (for all Kahler groups which do not have property T of Kazhdan).We deduce a conjecture of Goldman-Donaldson for all 3-manifold groups which are rich in the sense of [Re2].

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

The OCDF diagram. A metamodel for object-oriented systems visual designDec 12 2014We present a metamodel for modeling control and data flows on subclass scales in object-oriented systems. UML Profiles were used as a representation mean and a complete metamodel definition was provided with an example of a diagram application.

I.M.Gelfand and his seminar -- a presenceMay 04 2015Feb 16 2016These are reminiscences of I.M.Gelfand's mathematical seminar of 1970s-1980s. The essay will appear in the March 2016 issue of Notices of the AMS.

A-infinity algebras associated with elliptic curves and Eisenstein-Kronecker seriesApr 26 2016May 20 2016We compute the A-infinity structure on the self-Ext algebra of the vector bundle $G$ over an elliptic curve of the form $G=\bigoplus_{i=1}^r P_i\oplus \bigoplus_{j=1}^s L_j$, where $(P_i)$ and $(L_j)$ are line bundles of degrees 0 and 1, respectively. ... More

Hitchin Functionals and Nonspontaneous Supersymmetry BreakingSep 08 2008A new mechanism of supersymmetry breaking involving a dynamical parameter is introduced. It is independent of particle phenomenology and gauge groups. An explicit realization of this mechanism takes place in Type II superstring compactifications which ... More

Theory OverviewOct 25 2016We set the scene for theoretical issues in charm physics that were discussed at CHARM 2016 in Bologna. In particular we emphasize the importance of improving our understanding of standard model contributions to numerous charm observables and we discuss ... More

On the mechanism of generation of the Kelvin-Helmholtz instabilityJan 20 2016Mechanism of the Kelvin-Helmholtz instability based on the Kutta-Zhoukovsky theorem is considered. The mechanism itself generates the velocity shear, thereby redistributing the flow energy which drives the instability.

Spatial geometry of charged rotating and non-rotating rings in rotating and non-rotating framesFeb 05 2016Spatial geometry of charged thin rotating and non-rotating rings in a rotating frame is investigated. It is shown, on an example of interaction between a charged probe and two positive charged non-rotating and negative charged rotating rings that the ... More

Poisson structures and birational morphisms associated with bundles on elliptic curvesDec 19 1997In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study birational morphisms ... More

Probing Brain Oxygenation with Near Infrared spectroscopy, the Role of Carbon Dioxide and Blood PressureOct 18 2015The fundamentals of near infrared spectroscopy (NIRS) are reviewed. Among the major factors controlling the cerebral blood flow (CBF), the effect of PaCO2 is peculiar in that it violates autoregulatory CBF mechanisms and allows to explore the full range ... More

Symmetry Reduction and Exact Solutions in Twisted Noncommutative GravityAug 04 2009We review the noncommutative gravity of Wess et al. and discuss its physical applications. We define noncommutative symmetry reduction and construct deformed symmetric solutions of the noncommutative Einstein equations. We apply our framework to find ... More

Module parallel transports in fuzzy gauge theoryJan 23 2012Sep 19 2013In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct for every derivation ... More

Optimized Mission Planning for Planetary Exploration RoversNov 01 2015The exploration of planetary surfaces is predominately unmanned, calling for a landing vehicle and an autonomous and/or teleoperated rover. Artificial intelligence and machine learning techniques can be leveraged for better mission planning. This paper ... More

On homogeneous hypersurfaces in ${\mathbb C}^3$Oct 24 2016We consider a family $M_t^n$, with $n\ge 2$, $t>1$, of real hypersurfaces in a complex affine $n$-dimensional quadric arising in connection with the classification of homogeneous compact simply-connected real-analytic hypersurfaces in ${\mathbb C}^n$ ... More

Quantum Integrable Model of an Arrangement of HyperplanesJan 25 2010Mar 28 2011The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted arrangement of affine ... More

Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin ModelJul 30 2004Oct 11 2004We show that the Shapovalov norm of a Bethe vector in the Gaudin model is equal to the Hessian of the logarithm of the corresponding master function at the corresponding isolated critical point. We show that different Bethe vectors are orthogonal. These ... More

Translation of the C.J. Malmstén's paper De integralibus quibusdam definitis, seriebusque infinitisSep 16 2013We translate the paper De Integralibus quibusdam definitis, seriebusque infinitis

Local inequalities for plurisubharmonic functionsMar 01 1999The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of polynomial, algebraic ... More

Feynman integral for functional Schrödinger equationsSep 26 2002We consider functional Schr\"{o}dinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock models. An infinite-dimensional ... More

Algorithmically detecting the bridge number of hyperbolic knotsOct 05 2007Mar 27 2012We exhibit an algorithm to determine the bridge number of a hyperbolic knot in the 3-sphere. The proof uses adaptations of almost normal surface theory for compact surfaces with boundary in ideally triangulated knot exteriors.

A first look at Bottomonium melting via a stochastic potentialDec 11 2013Feb 23 2015We investigate the phenomenon of Bottomonium melting in a thermal quark-gluon plasma using three-dimensional stochastic simulations based on the concept of open-quantum systems. In this non-relativistic framework, introduced in [Phys.Rev. D85 (2012) 105011], ... More

Improved Maximum Entropy Analysis with an Extended Search SpaceOct 28 2011Jan 07 2013The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD ... More

Spaces of quasi-maps into the flag varieties and their applicationsMar 18 2006Mar 22 2006Given a projective variety X and a smooth projective curve C one may consider the moduli space of maps C --> X. This space admits certain compactification whose points are called quasi-maps. In the last decade it has been discovered that in the case when ... More

SQCD, Superconducting Gaps and Cyclic RG FlowsFeb 20 2012We consider the relation between the \Omega -deformed N=2 SQCD with the single deformation parameter and integrable models of the BCS-like superconductivity. It is argued that the vortex string worldsheet theory is related to the Russian Doll(RD) model ... More

Total positivity, Grassmannians, and networksSep 27 2006The aim of this paper is to discuss a relationship between total positivity and planar directed networks. We show that the inverse boundary problem for these networks is naturally linked with the study of the totally nonnegative Grassmannian. We investigate ... More

A simple polynomial time algorithm to approximate the permanent within a simply exponential factorApr 09 1997We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of $n$ positive semidefinite $n \times n$ matrices within a factor $2^{O(n)}$. Consequently, the algorithm allows us to approximate in randomized polynomial ... More