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Parametric inference for multidimensional hypoelliptic diffusion with full observationsFeb 08 2018Multidimensional hypoelliptic diffusions arise naturally as models of neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. We build a consistent estimator of the drift and variance ... More

Towards an exact adaptive algorithm for the determinant of a rational matrixMay 31 2007In this paper we propose several strategies for the exact computation of the determinant of a rational matrix. First, we use the Chinese Remaindering Theorem and the rational reconstruction to recover the rational determinant from its modular images. ... More

Lie Bialgebra Structures for Centrally Extended Two- Dimensional Galilei Algebra and their Lie-Poisson CounterpartsOct 23 1997Jan 16 1998All bialgebra structures for centrally extended Galilei algebra are classified. The corresponding Lie-Poisson structures on centrally extended Galilei group are found.

Iterated identities and iterational depth of groupsSep 21 2014Given word on $n$ letters, we study groups which satisfiy "iterated identity" $w$, meaning that for all $x_1, \dots, x_n$ there exists $m$ such that $m$-the iteration of $w$ of Engel type, applied to $x_1, \dots, x_n$, is equal to the identity. We define ... More

Woronowicz construction of compact quantum groups for functions on permutations. Classification result for N=3Jan 28 2014We provide a classification of compact quantum groups, which can be obtained by the Woronowicz construction, when the arrays used in the twisted determinant condition are extensions of functions on permutations. General properties of such quantum groups ... More

Modeling IR SED of AGN with Spitzer and Herschel dataJan 21 2013One of the remaining open issues in the context of the analysis of Active Galactic Nuclei (AGN) is the evidence that nuclear gravitational accretion is often accompanied by a concurrent starburst (SB) activity. What is, in this picture, the role played ... More

On Orbital variety closures in sl_n. III Geometric propertiesJul 25 2005This is the third paper in the series. Here we define a few combinatorial orders on Young tableaux. The first order is obtained from induced Duflo order by the extension with the help of Vogan T_{\alpha, \beta} procedure. We call it Duflo-Vogan order. ... More

The Finite Temperature Effective Potential for Local Composite OperatorsApr 04 1997The method of the effective action for the composite operators $\Phi^2(x)$ and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field with $\lambda\Phi^4$ interaction. An expansion of the finite temperature effective potential in powers ... More

Goldstone Bosons in the Gaussian ApproximationAug 18 1995Aug 31 1995The O(N) symmetric scalar quantum field theory with \lambda\Phi^4 interaction is discussed in the Gaussian approximation. It is shown that the Goldstone theorem is fulfilled for arbitrary N.

Gaussian approximation to the condensation of the interacting Bose gasSep 29 2003The effective action formalism of quantum field theory is used to study the properties of the non-relativistic interacting Bose gas. The Gaussian approximation is formulated by calculating the effective action to the first order of the optimized expansion. ... More

Multi-particle States from the Effective Action for Local Composite Operators: Anharmonic OscillatorDec 15 1995Dec 19 1995The effective action for the local composite operator $\Phi^2(x)$ in the scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops. The effective potential ... More

Geometric construction of spinors in orthogonal modular categoriesOct 16 2002Oct 09 2003A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions ... More

Exploring the Universe with Metal-Poor StarsAug 23 2011The early chemical evolution of the Galaxy and the Universe is vital to our understanding of a host of astrophysical phenomena. Since the most metal-poor Galactic stars (with metallicities down to [Fe/H]\sim-5.5) are relics from the high-redshift Universe, ... More

An embedding resultDec 29 2013In unbounded subset $\Omega$ in $R^n$ we study the operator $u\rightarrow gu$ as an operator defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$. The functions $g$ belong to wider spaces of $L^p$ connected with the Morrey ... More

Exact Solutions to SupergravityJun 11 1996We find a general p-1-brane solution to supergravity coupled to a p+1-form field strength using the ``standard ansatz'' for the fields. In addition to the well-known elementary and solitonic p-1-brane solutions, which are the only ones preserving half ... More

String Solutions to SupergravityOct 23 1996We find the comlete solution to ten-dimensional supergravity coupled to a three-form field strength, given the ``standard ansatz" for the fields, and show that in addition to the well-known elementary and solitonic (heterotic) string solutions, one of ... More

On the determinant of hexagonal grids $H_{k,n}$Aug 31 2013Feb 15 2014We analyse the problem of singularity of graphs for hexagonal grid graphs. We introduce methods for transforming weighted graph, which do not change the determinant of adjacency matrix. We use these methods to calculate the determinant of all hexagonal ... More

Correlated radiative electron capture in ion-atom collisionsAug 30 2010Radiative double electron capture (RDEC) is a one-step process where two free (or quasi-free) target electrons are captured into a bound state of the projectile, e.g. into an empty K-shell, and the energy excess is released as a single photon. This process ... More

Kronecker limit formulas and scattering constants for Fermat curvesNov 04 2011Eisenstein series are real analytic functions which play a central role in spectral theory of the hyperbolic Laplacian. Kronecker limit formulas determine their connection to modular forms. The main result of this work is Theorem 7.2 in which a Kronecker ... More

On the numbers of 1-factors and 1-factorizations of hypergraphsMar 28 2015Dec 14 2015A hypergraph $G=(X,W)$ is called $d$-uniform if each hyperedge $w$ is a set of $d$ vertices. A 1-factor of a hypergraph $G$ is a set of hyperedges such that every vertex of the hypergraph is incident to exactly one hyperedge from the set. A 1-factorization ... More

Teichmuller geodesics that do not have a limit in PMFOct 31 2005Nov 17 2010We construct a Teichmuller geodesic which does not have a limit on the Thurston boundary of the Teichmuller space.

Lyapunov theorem for q-concave Banach spacesOct 17 2013Generalization of Lyapunov convexity theorem is proved for vector measure with values in Banach spaces with unconditional bases, which are q-concave for some $q<\infty.$

Bounded Cohomology and GeometryJan 17 2005This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class of totally ... More

A construction of a nonparametric quantum information manifoldNov 21 2005We present a construction of a Banach manifold on the set of faithful normal states of a von Neumann algebra, where the underlying Banach space is a quantum analogue of an Orlicz space. On the manifold, we introduce the exponential and mixture connections ... More

Weakly Interacting, Dilute Bose Gases in 2DJun 01 2005Jun 27 2006This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited ... More

Classification of isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$Mar 15 2015Aug 05 2015We classify isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$ and thereby reprove a result of Dorfmeister and Neher.

Harmonic Self-maps of $\mbox{SU}(3)$Dec 22 2015By constructing solutions of a singular boundary value problem we prove the existence of a countably infinite family of harmonic self-maps of $\mbox{SU}(3)$ with non-trivial, i.e. $\neq 0,\pm 1$, Brouwer degree.

Compactifying the Space of Length Functions of a Right-angled Artin GroupOct 20 2015Culler and Morgan proved that the length function of a minimal action of a group on a tree completely determines the action. As a consequence the space of minimal actions of a free group on trees, up to scaling (also known as Outer Space), embeds in infinite ... More

Representations and geometric structuresFeb 10 2016This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical legacy of Bill Thurston, held in June 2014 in Cornell. ... More

Improving LHC searches for strong EW symmetry breaking resonancesMay 18 2015Sep 05 2016Composite Higgs models generically predict the existence of heavy spin-1 resonances with the same quantum numbers as electroweak gauge bosons. The effective lagrangian description of these resonances is presented, pointing out the origin of their interactions ... More

On the numbers of 1-factors and 1-factorizations of hypergraphsMar 28 2015Dec 04 2016A 1-factor of a hypergraph $G=(X,W)$ is a set of hyperedges such that every vertex of $G$ is incident to exactly one hyperedge from the set. A 1-factorization is a partition of all hyperedges of $G$ into disjoint 1-factors. The adjacency matrix of a $d$-uniform ... More

Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitudeFeb 01 2016Following a general principle introduced by Ehrnstr\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.

Cyclic anamorphic cosmologyOct 10 2016Cyclic models of the universe have the advantage of avoiding initial conditions problems related to postulating any sort of beginning in time. To date, the only known viable examples of cyclic models have been ekpyrotic. In this paper, we show that the ... More

On $S_n$-invariant conformal blocks vector bundles of rank one on $\overline M_{0,n}$Apr 23 2014For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector bundles of conformal ... More

A minimal scale invariant axion solution to the strong CP-problemMay 30 2017Dec 07 2017We present a scale invariant extension of the Standard model allowing for the Kim-Shifman-Vainstein-Zakharov (KSVZ) axion solution of the strong CP problem in QCD. We add the minimal number of new particles and show that the Peccei-Quinn scalar might ... More

B0943+10: low-frequency study of subpulse periodicity in the Bright mode with LOFAROct 16 2017We utilise broadband sensitive LOFAR observations in 25-80 MHz frequency range to study the single-pulse emission properties of the mode-switching pulsar PSR B0943+10. We review the derivation of magnetospheric geometry, originally based on low-frequency ... More

Transversals, plexes, and multiplexes in iterated quasigroupsSep 10 2017A $d$-ary quasigroup of order $n$ is a $d$-ary operation over a set of cardinality $n$ such that the Cayley table of the operation is a $d$-dimensional latin hypercube of the same order. Given a binary quasigroup $G$, the $d$-iterated quasigroup $G^{\left[d\right]}$ ... More

Rényi relative entropies and noncommutative $L_p$-spacesSep 27 2016Jun 30 2017We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy to normal positive functionals on arbitrary von Neumann algebras, for the values $\alpha>1$. For this, we use Kosaki's definition of noncommutative $L_p$-spaces with respect to ... More

Positiveness of the permanent of 4-dimensional polystochastic matrices of order 4Jan 31 2018A nonnegative multidimensional matrix is called polystochastic if the sum of its entries over each line is equal to one. We prove that the permanent of every $4$-dimensional polystochastic matrix of order $4$ is positive.

Torsion and Linking number for a surface diffeomorphismJan 23 2018For a $\mathcal{C}^1$ diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ isotopic to the identity, we prove that for any value $l\in\mathbb{R}$ of the linking number at finite time of the orbits of two points there exists at least a point whose torsion ... More

Ranks and Symmetric Ranks of Cubic SurfacesJan 16 2018We study cubic surfaces as symmetric tensors of format $4 \times 4 \times 4$. We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The corresponding ... More

Ecology of galaxy stellar populations from optical spectroscopic surveysOct 12 2009The age and chemical composition of the stars in present-day galaxies carry important clues about their star formation processes. The latest generation of population synthesis models have allowed to derive age and stellar metallicity estimates for large ... More

Refined invariants and TQFT's from Homfly skein theoryJun 17 1998Jul 03 1998We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. ... More

On the equivalence of two expected average cost criteria for semi- Markov control processesSep 19 2013The two expected average costs used in the theory of semi-Markov control processes with a Borel state space are considered. Under some stochastic stability conditions, we prove that the two criteria are equivalent in the sense that they lead to the same ... More

Rook numbers and the normal ordering problemFeb 23 2004Jul 15 2004For an element $w$ in the Weyl algebra generated by $D$ and $U$ with relation $DU=UD+1$, the normally ordered form is $w=\sum c_{i,j}U^iD^j$. We demonstrate that the normal order coefficients $c_{i,j}$ of a word $w$ are rook numbers on a Ferrers board. ... More

Stochastic Integral with respect to Cylindrical Wiener ProcessNov 21 2005This paper is devoted to a construction of the stochastic It\^o integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the ... More

Multiple operator integrals and spectral shiftJul 02 2009Mar 06 2011Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.

Higher order spectral shift, II. Unbounded caseJan 16 2009Jul 01 2009We construct higher order spectral shift functions, which represent the remainders of Taylor-type approximations for the value of a function at a perturbed self-adjoint operator by derivatives of the function at an initial unbounded operator. In the particular ... More

On partitions of the unit interval generated by Brocot sequencesDec 27 2005Dec 15 2007Let $ p_{i, n}, i=1,..., N(n)=2^{n-1} $ be the lengths of intervals between the neighboring fractions of Brocot sequence $ F_n $. We obtain an asymptotic formula for $\sigma_{\beta}(F_n)=\sum_{i=1}^{N(n)} p_{i, n}^{\beta} $,which improves known estimates. ... More

On orbital variety closures in sl(n). II. Descendants of a Richardson orbital varietyNov 26 2003For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sl(n) orbital ... More

Comparison of quantum binary experimentsOct 21 2011Jun 21 2012A quantum binary experiment consists of a pair of density operators on a finite dimensional Hilbert space. An experiment E is called \epsilon-deficient with respect to another experiment F if, up to \epsilon, its risk functions are not worse than the ... More

Affine connections, duality and divergences for a von Neumann algebraNov 05 2003On the predual of a von Neumann algebra, we define a differentiable manifold structure and affine connections by embeddings into non-commutative L_p-spaces. Using the geometry of uniformly convex Banach spaces and duality of the L_p and L_q spaces for ... More

Base norms and discrimination of generalized quantum channelsAug 19 2013We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels ... More

Trace formulas for tuples of commuting contractionsSep 18 2013Sep 22 2013This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.

Rarefaction waves in nonlocal convection-diffusion equationsMar 29 2013Apr 16 2013We consider the "convection-diffussion" equation $u_t=J*u-u-uu_x,$ where $J$ is a probability density. We supplement this equation with step-like initial conditions and prove a convergence of corresponding solution towards a rarefaction wave, i.e. a unique ... More

Generating the Ideals Defining Unions of Schubert VarietiesMay 12 2014This note computes a Gr\"obner basis for the ideal defining a union of Schubert varieties. More precisely, it computes a Gr\"obner basis for unions of schemes given by northwest rank conditions on the space of all matrices of a fixed size. Schemes given ... More

Stellar Archaeology -- Exploring the Universe with Metal-Poor StarsJun 11 2010The abundance patterns of the most metal-poor stars in the Galactic halo and small dwarf galaxies provide us with a wealth of information about the early Universe. In particular, these old survivors allow us to study the nature of the first stars and ... More

Levi-Civita connections of flag manifoldsDec 05 2005For any flag manifold G/T we obtain an explicit expression of its Levi-Civita connection with respect to any invariant Riemannian metric.

The Effective Action for Local Composite Operators $Φ^2(x)$ and $Φ^4(x)$Jun 13 1996The generating functionals for the local composite operators, $\Phi^2(x)$ and $\Phi^4(x)$, are used to study excitations in the scalar quantum field theory with $\lambda \Phi^4$ interaction. The effective action for the composite operators is obtained ... More

Dynamical Simulations with Smeared Link Staggered FermionsNov 04 2002One of the most serious problems of the staggered fermion lattice action is flavor symmetry violation. Smeared link staggered fermions can improve flavor symmetry by an order of magnitude relative to the standard thin link action. Over the last few years ... More

Topological Susceptibility on Dynamical Staggered Fermion ConfigurationsApr 30 2001The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends quadratically on ... More

Non-Discrete Complex Hyperbolic Triangle Groups of Type (m,m,infinity)Apr 30 2010In this note we prove that a complex hyperbolic triangle group of type (m,m,infinity), i.e. a group of isometries of the complex hyperbolic plane, generated by complex reflections in three complex geodesics meeting at angles Pi/m, Pi/m and 0, is not discrete ... More

New Results from the MINOS Experiment - EPS 2011 conference proceedingsJan 17 2012The MINOS experiment is a long-baseline neutrino experiment designed to study neutrino behaviour, in particular the phenomenon of neutrino oscillations. MINOS sends the NuMI neutrino beam through two detectors, a Near Detector 1 km downstream from the ... More

Entanglement rates for bipartite open systemsMay 03 2015Aug 10 2015We provide upper bound on the maximal rate at which irreversible quantum dynamics can generate entanglement in a bipartite system. The generator of irreversible dynamics consists of a Hamiltonian and dissipative terms in Lindblad form. The relative entropy ... More

Decomposing almost complete graphs by random treesDec 01 2015Dec 07 2015An old conjecture of Ringel states that every tree with $m$ edges decomposes the complete graph $K_{2m+1}$. The best known lower bound for the order of a complete graph which admits a decomposition by every given tree with $m$ edges is $O(m^3)$. We show ... More

Bayesian Approach to Handling Informative SamplingJan 27 2015In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this research I ... More

Infinite families of harmonic self-maps of spheresJan 25 2015Oct 16 2015For each of the spheres $\mathbb{S}^{n}$, $n\geq 5$, we construct a new infinite family of harmonic self-maps, and prove that their members have Brouwer degree $\pm1$ or $\pm3$. These self-maps are obtained by solving a singular boundary value problem. ... More

Comparison of quantum channels and statistical experimentsDec 22 2015Apr 24 2016For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two ensembles obtained ... More

Whittaker functions on metaplectic covers of GL(r)May 17 2016This paper establishes a combinatorial link between different approaches to constructing Whittaker functions on a metaplectic group over a non-archimedean local field. We prove a metaplectic analogue of Tokuyama's Theorem and give a crystal description ... More

Improved gradient flow for step scaling function and scale settingJan 30 2015The gradient flow renormalized coupling offers a simple and relatively inexpensive way to calculate the step scaling function and the lattice scale, but both applications can be hindered by large lattice artifacts. Recently we introduced an empirical ... More

Spectral Stieltjes-Type Integration and Some ApplicationsNov 25 2005Mar 06 2011This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between Riemann-Stieltjes integrals associated with some classes of spectral families including, in particular, those that arise ... More

Almost Kähler 4-dimensional Lie groups with $J$-invariant Ricci tensorAug 03 2003The aim of this paper is to determine left-invariant strictly almost K\"ahler structures on 4-dimensional Lie groups $(g, J, \Omega)$ such that the Ricci tensor is $J$-invariant.

The culmination of an inverse cascade: mean flow and fluctuationsOct 25 2017Feb 01 2018Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained, and what determines them and the fluctuations around ... More

Development of novel plastic scintillators based on polyvinyltoluene for the hybrid J-PET/MR tomographOct 23 2017A novel plastic scintillator, referred to as J-PET scintillator, has been developed for the application in the digital positron emission tomography (PET). The novelty of the concept lies in application of the 2-(4-styrylphenyl)benzoxazole as a wavelength ... More

Non-classical features in general probabilistic theoriesMay 22 2017Jan 23 2018We study incompatibility of measurements and its relation to steering and nonlocality in finite dimensional general probabilistic theories (GPT). The basic idea is to represent finite collections of measurements as affine maps of a state space into a ... More

CoVaR-based portfolio selectionMar 04 2017We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions are given ... More

Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4Dec 06 2016Sep 11 2017An $n$-ary quasigroup $f$ of order $q$ is an $n$-ary operation over a set of cardinality $q$ such that the Cayley table of the operation is an $n$-dimensional latin hypercube of order $q$. A transversal in a quasigroup $f$ (or in the corresponding latin ... More

Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutionsOct 16 2017Jan 27 2018In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions ... More

Recent results from the ARIANNA neutrino experimentSep 23 2016The ARIANNA experiment is currently taking data in its pilot-phase on the Ross ice-shelf. Fully autonomous stations measure radio signals in the frequency range from 100 MHz to 1 GHz. The seven station HRA was completed in December 2014, and augmented ... More

The Malliavin derivative and compactness: application to a degenerate PDE-SDE couplingSep 06 2016Jun 29 2017Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate estimates for a ... More

Information Measures for Long-Range Correlated Sequences: the Case of the 24 Human Chromosome SequencesFeb 04 2013Sep 05 2013A new approach to estimate the Shannon entropy of a long-range correlated sequence is proposed. The entropy is written as the sum of two terms corresponding respectively to power-law (\emph{ordered}) and exponentially (\emph{disordered}) distributed blocks ... More

Sub-semi-Riemannian geometry on $H$-type groupsOct 21 2010We consider $H$(eisenberg)-type groups whose law of left translation gives rise to a bracket generating distribution of step 2. In the contrast with sub-Riemannian studies we furnish the horizontal distribution with a nondegenerate indefinite metric of ... More

Complete criterion for convex-Gaussian state detectionSep 30 2014Dec 01 2014We present a new criterion that determines whether a fermionic state is a convex combination of pure Gaussian states. This criterion is complete and characterizes the set of convex-Gaussian states from the inside. If a state passes a program it is a convex-Gaussian ... More

A Simplification of Combinatorial Link Floer HomologyMay 04 2007Jan 14 2010We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu-Ozsvath-Sarkar one.

The action of the mapping class group on maximal representationsMay 01 2006We show that the mapping class group acts properly on the space of maximal representations of the fundamental group of a closed Riemann surface into G when G = Sp(2n,R), SU(n,n), SO*(2n) or Spin(2,n).

A relation between completely bounded norms and conjugate channelsJan 11 2006We show a relation between a quantum channel $\Phi$ and its conjugate $\Phi^C$, which implies that the $p\to p$ Schatten norm of the channel is the same as the $1\to p$ completely bounded norm of the conjugate. This relation is used to give an alternative ... More

Randomization theorems for quantum channelsApr 15 2014The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum channel mapping one ... More

Quantum hypothesis testing and sufficient subalgebrasOct 22 2008Aug 02 2010We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{\rho_0,\rho_1\}$ if it contains all Bayes optimal tests of $\rho_0$ against $\rho_1$. In classical statistics, this corresponds ... More

On varieties in an orbital variety closure in semisimple Lie algebraSep 23 2004Let g be a semisimple complex Lie algebra. Let O be a nilpotent orbit in g. Fix a triangular decomposition g=n+h+n^-. An irreducible component of the intersection of O and n is called an orbital variety associated to O. It is a Lagrangian subvariety of ... More

On the center of the small quantum groupJul 13 2001Jul 25 2002Using the quantum Fourier transform F, we describe the block decomposition and multiplicative structure of a subalgebra Z + F(Z) in the center of the small quantum group u_l at a root of unity. It contains the previously known subalgebra Z, which is isomorphic ... More

Reconstructing the cosmic evolution of the chemical elementsAug 20 2014The chemical elements are created in nuclear fusion processes in the hot and dense cores of stars. The energy generated through nucleosynthesis allows stars to shine for billions of years. When these stars explode as massive supernovae, the newly made ... More

Existence of the thermodynamic limit and asymptotic behavior of some irreversible quantum dynamical systemsJul 24 2012Feb 14 2013We discuss the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. The time-dependent generator of the dynamics of the system is of the Lindblad-Kossakowski ... More

Optimized perturbation method for the propagation in the anharmonic oscillator potentialJul 17 1998The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential $\lambda x^4$ is discussed for real and imaginary time. The first order results in the imaginary time formalism provide approximations to the ... More

Lepton Flavour Violation in Supersymmetric ModelsNov 25 2003We present two recent developments on lepton flavour violation in the MSSM. 1) The supersymmetric seesaw mechanism can be realized through the exchange of heavy SU(2)_W-triplet states, rather than `right-handed' neutrinos. In this scenario the ratio of ... More

The MSW solution to the solar neutrino problem in the presence of random solar matter density perturbationsFeb 23 1996We present the evolution equation describing MSW conversion, derived in the framework of the Schr\"odinger approach, in the presence of matter density fluctuations. Then we analyse the effect of such fluctuations in the MSW scenario as a solution to the ... More

Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermionsApr 07 2010Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 ... More

Universality and Quark Masses of the Staggered Fermion ActionNov 07 2005Apr 12 2006Staggered fermions with 4 tastes are expected to describe 4-flavor QCD in the continuum limit, therefore at finite lattice spacing the staggered determinant should be equivalent to an SU(4) flavor-symmetric system up to lattice artifacts. This equivalence ... More

Fermion induced SU$(N)$ Yang-Mills TheoryNov 05 1992We investigate the gauge interaction induced by heavy fermions using both dimensional and lattice regularization. We study the condition under which heavy fermions induce a continuum gauge theory.

Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifoldsOct 21 2009Mar 11 2011We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds. ... More

Preservation of a quantum Renyi relative entropy implies existence of a recovery mapApr 11 2016Sep 23 2016It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched R\'enyi relative $\alpha$-entropy ... More