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Minimax-optimal decoding of movement goals from local field potentials using complex spectral featuresJan 29 2019We consider the problem of predicting eye movement goals from local field potentials (LFP) recorded through a multielectrode array in the macaque prefrontal cortex. The monkey is tasked with performing memory-guided saccades to one of eight targets during ... More

Power Talk for Multibus DC MicroGrids: Creating and Optimizing Communication ChannelsSep 26 2016We study a communication framework for nonlinear multibus DC MicroGrids based on a deliberate modification of the parameters of the primary control and termed power talk. We assess the case in which the information is modulated in the deviations of reference ... More

Modemless Multiple Access Communications over Powerlines for DC Microgrid ControlSep 14 2016We present a communication solution tailored specifically for DC microgrids (MGs) that exploits: (i) the communication potential residing in power electronic converters interfacing distributed generators to powerlines and (ii) the multiple access nature ... More

Distributed Proportional-Fairness Control in MicroGrids via Blockchain Smart ContractsMay 03 2017May 16 2017Residential microgrids (MGs) may host a large number of Distributed Energy Resources (DERs). The strategy that maximizes the revenue for each individual DER is the one in which the DER operates at capacity, injecting all available power into the grid. ... More

Power Talk in DC Micro Grids: Constellation Design and Error Probability PerformanceJul 09 2015Power talk is a novel concept for communication among units in a Micro Grid (MG), where information is sent by using power electronics as modems and the common bus of the MG as a communication medium. The technique is implemented by modifying the droop ... More

Anti-Jamming Strategy for Distributed Microgrid Control based on Power Talk CommunicationDec 21 2016Dec 22 2016In standard implementations of distributed secondary control for DC MicroGrids (MGs), the exchange of local measurements among neighboring control agents is enabled via off-the-shelf wireless solutions, such as IEEE 802.11. However, Denial of Service ... More

Geometric Interpretation of Theoretical Bounds for RSS-based Source Localization with Uncertain Anchor PositionsAug 23 2016The Received Signal Strength based source localization can encounter severe problems originating from uncertain information about the anchor positions in practice. The anchor positions, although commonly assumed to be precisely known prior to the source ... More

Software-Defined Microgrid Control for Resilience Against Cyber AttacksFeb 08 2018Microgrids (MGs) rely on networked control supported by off-the-shelf wireless communications. This makes them vulnerable to cyber-attacks, such as denial-of-service (DoS). In this paper, we mitigate those attacks by applying the concepts of (i) separation ... More

Secure and Robust Authentication for DC MicroGrids based on Power Talk CommunicationDec 21 2016Dec 22 2016We propose a novel framework for secure and reliable authentication of Distributed Energy Resources to the centralized secondary/tertiary control system of a DC MicroGrid (MG), networked using the IEEE 802.11 wireless interface. The key idea is to perform ... More

Secure and Resilient Low-Rate Connectivity for Smart Energy Applications through Power Talk in DC MicrogridsMar 29 2017The future smart grid is envisioned as a network of interconnected microgrids (MGs) - small-scale local power networks comprising generators, storage capacities and loads. MGs bring unprecedented modularity, efficiency, sustainability, and resilience ... More

Making the Grid Truly Smart: Autonomous System Identification in "Modemless" DC MicroGridsMar 30 2017We introduce novel framework for autonomous learning of the own configuration in direct current (DC) MicroGrids (MG) with high penetration of power electronic converters and without access to an external communication system. The framework is implemented ... More

Distributed Estimation of the Operating State of a Single-Bus DC MicroGrid without an External Communication InterfaceSep 14 2016We propose a decentralized Maximum Likelihood solution for estimating the stochastic renewable power generation and demand in single bus Direct Current (DC) MicroGrids (MGs), with high penetration of droop controlled power electronic converters. The solution ... More

Extremely Large Aperture Massive MIMO: Low Complexity Receiver ArchitecturesOct 04 2018This paper focuses on new communication paradigms arising in massive multiple-input-multiple-output systems where the antenna array at the base station is of extremely large dimension (xMaMIMO). Due to the extreme dimension of the array, xMaMIMO is characterized ... More

Non-Stationarities in Extra-Large Scale Massive MIMOMar 07 2019Massive MIMO, a key technology for increasing area spectral efficiency in cellular systems, was developed assuming moderately sized apertures. In this paper, we argue that massive MIMO systems behave differently in large-scale regimes due to spatial non-stationarity. ... More

Multiuser Communication through Power Talk in DC MicroGridsJul 21 2015Power talk is a novel concept for communication among control units in MicroGrids (MGs), carried out without a dedicated modem, but by using power electronics that interface the common bus. The information is transmitted by modulating the parameters of ... More

Power Talk: How to Modulate Data over a DC Micro Grid Bus using Power ElectronicsApr 12 2015We introduce a novel communication strategy for DC Micro Grids (MGs), termed power talk, in which the devices communicate by modulating the power levels in the DC bus. The information is transmitted by varying the parameters that the MG units use to control ... More

Wireless Access in Ultra-Reliable Low-Latency Communication (URLLC)Oct 16 2018The future connectivity landscape and, notably, the 5G wireless systems will feature Ultra-Reliable Low Latency Communication (URLLC). The coupling of high reliability and low latency requirements in URLLC use cases makes the wireless access design very ... More

Accuracy of the WKB approximation: the case of general quartic potentialMar 24 2000We analyse the accuracy of the approximate WKB quantization for the case of general one-dimensional quartic potential. In particular, we are interested in the validity of semiclassically predicted energy eigenvalues when approaching the limit $E\to \infty$, ... More

Numerical Analysis of the Anderson LocalizationSep 22 2006The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems.

Dimension dependence of the conductance distribution in the non-metallic regimesSep 17 2000Jan 18 2002We study numerically the form of the conductance distribution in the non-metallic regime for (1) weakly disordered systems which become insulating due to increase of the system length and (2) cubic d-dimensional systems, in which localization occours ... More

Metal-insulator transition in system with topological disorderNov 25 1999Nov 26 1999Metal-insulator transition in anisotropic disordered Anderson model with both topological and diagonal disorder is investigated numerically. For four sets of the model parameters we found the critical disorder and the critical exponent and prove that ... More

Notes on Leibniz thought experimentSep 03 2013Leibniz thought experiment of perception, sensing, and thinking is reconsidered. We try to understand Leibniz picture in view of our knowledge of basic neuroscience. In particular we can see how the emergence of consciousness could in principle be understood. ... More

Fano resonances in dielectric, metallic and metamaterial photonic structuresAug 27 2016We investigate numerically Fano resonances excited in periodic arrays of dielectric, metallic and left-handed cylinders. Of particular interest are Fano resonances excited in the linear array of cylin- ders. We analyze spatial distribution and symmetry ... More

Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebrasAug 31 2016Let $G=GL(m|n)$ be the general linear supergroup over an algebraically closed field $K$ of characteristic zero and let $G_{ev}=GL(m)\times GL(n)$ be its even subsupergroup. The induced supermodule $H^0_G(\lambda)$, corresponding to a dominant weight $\lambda$ ... More

Remark on representation theory of general linear groups over a non-archimedean local division algebraJan 27 2016In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the irreducible square ... More

Modeling complex points up to isotopyNov 19 2011In this paper we examine the structure of complex points of real 4-manifolds embedded into complex 3-manifolds up to isotopy. We show that there are only two types of complex points up to isotopy and as a consequence, show that any such embedding can ... More

On Stein Neighborhood Basis of Real SurfacesSep 12 2003In this paper, we show that a compact real surface embedded in a complex surface has a regular Stein neighborhood basis, provided that there are only finitely many complex points on the surface, and that they are all flat and hyperbolic. An application ... More

Circulant matrices: norm, powers, and positivityMar 26 2018Apr 23 2018In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general real circulant matrix ${\bf C}$ equals the modulus of its row/column sum. ... More

The existence and uniqueness of almost periodic and asymptotically almost periodic solutions of semilinear Cauchy inclusionsAug 08 2018The main aim of this paper is to investigate almost periodicity and asymptotic almost periodicity of abstract semilinear Cauchy inclusions of first order with (asymptotically) Stepanov almost periodic coefficients. To achieve our goal, we employ fixed ... More

Multivariate normal mixture modeling, clustering and classification with the rebmix packageJan 26 2018The rebmix package provides R functions for random univariate and multivariate finite mixture model generation, estimation, clustering and classification. The paper is focused on multivariate normal mixture models with unrestricted variance-covariance ... More

Wonderful Compactifications in Quantum Field TheoryNov 20 2014Jan 07 2016This article reviews the use of DeConcini-Procesi wonderful models in renormalization of ultraviolet divergences in position space as introduced by Bergbauer, Brunetti and Kreimer. In contrast to the exposition there we employ a slightly different approach; ... More

Definite Sums as Solutions of Linear Recurrences With Polynomial CoefficientsApr 09 2018We present an algorithm which, given a linear recurrence operator $L$ with polynomial coefficients, $m \in \mathbb{N}\setminus\{0\}$, $a_1,a_2,\ldots,a_m \in \mathbb{N}\setminus\{0\}$ and $b_1,b_2,\ldots,b_m \in \mathbb{K}$, returns a linear recurrence ... More

On extended graphical calculus for categorified quantum $sl(n)$May 22 2016We study the properties of the extended graphical calculus for categorified quantum $sl(n)$. The main results include proofs of Reidemeister 2 and Reidemeister 3-like moves involving strands corresponding to arbitrary thicknesses and arbitrary colors ... More

Numerical studies of Anderson transitionAug 10 1999We present numerical results for the statistics of $z$'s ($z$'s are defined as logarithm of eigenvalues of the transfermatrix $T^\dag T$) at the critical points of Anderson transition in 3D and 4D. The change of the density of $z$ due to the crossover ... More

Electron transport in strongly disordered structuresJun 30 2009Using the transfer matrix technique, we investigate the propagation of electron through a two dimensional disordered sample. We find that the spatial distribution of electrons is homogeneous only in the limit of weak disorder (diffusive transport regime). ... More

Absence of diffusion in certain random lattices: Numerical evidenceJul 16 2008Jul 20 2009We demonstrate, by solving numerically the time-dependent Schroedinger equation, the physical character of electron localization in a disordered two-dimensional lattice. We show, in agreement with the prediction of P. W. Anderson, that the disorder prevents ... More

Application of the Feynman-tree theorem together with BCFW recursion relationsSep 01 2016Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree ... More

Primitive vectors in induced supermodules for general linear supergroupsSep 15 2013Apr 17 2014The purpose of the paper is to derive formulas that describe the structure of the induced supermodule H^0_G(\la) for the general linear supergroup G=GL(m|n) over an algebraically closed field K of characteristic p\neq 2. Using these formulas we determine ... More

Singular shock waves in interactionsJun 13 2006n a number of papers it was shown that there are one-dimensional systems such that they contain solutions with, so called, overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction ones as well as contact discontinuities). ... More

On certain values of Kloosterman sumsMar 25 2009Apr 16 2009Let $K_{q^n}(a)$ be a Kloosterman sum over the finite field $\F_{q^n}$ of characteristic $p$. In this note so called subfield conjecture is proved in case $p>3$: if $a\ne0$ belongs to the proper subfield $\F_q$ of $\F_{q^n}$, then $K_{q^n}(a)\ne-1$. This ... More

Two simple observations on representations of metaplectic groupsSep 02 2017M. Hanzer and I. Matic have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal series representations ... More

Probability distribution of the conductance at the mobility edgeJan 26 1999Distribution of the conductance P(g) at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems. The form of the distribution is discussed. Dimension dependence of P(g) is proven. The limiting ... More

Exact solution for a diffusive nonequilibrium steady state of an open quantum chainMay 07 2010We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are ... More

Dissipative remote-state preparation in an interacting mediumOct 18 2015Jan 25 2016Standard quantum state preparation methods work by preparing a required state locally and then distributing it to a distant location by a free-space propagation. We instead study procedures of preparing a target state at a remote location in the presence ... More

Topics in quantum chaos of generic systemsMar 28 2000Mar 30 2000We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the universality classes ... More

Supersymmetric quantum mechanics based on higher excited statesNov 18 1996We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically ... More

Large-deviation statistics of a diffusive quantum spin chain and the additivity principleJan 28 2014Apr 24 2014Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative dephasing. We ... More

Anomalous nonequilibrium current fluctuations in the Heisenberg modelMay 21 2014Oct 10 2014We study fluctuation properties of a one-dimensional anisotropic Heisenberg model out of equilibrium, focusing in particular on the gapped regime. Within the open-system setting we study large-deviation properties of the spin current. Numerically evaluating ... More

On floors and ceilings of the k-Catalan arrangementNov 22 2013Nov 05 2014The set of dominant regions of the $k$-Catalan arrangement of a crystallographic root system $\Phi$ is a well-studied object enumerated by the Fu{\ss}-Catalan number $Cat^{(k)}(\Phi)$. It is natural to refine this enumeration by considering floors and ... More

Adjacency preservers on invertible hermitian matrices IIJul 10 2013Maps that preserve adjacency on the set of all invertible hermitian matrices over a finite field are characterized. It is shown that such maps form a group that is generated by the maps $A\mapsto PAP^{\ast}$, $A\mapsto A^{\sigma}$, and $A\mapsto A^{-1}$, ... More

Density-feedback control in traffic and transport far from equilibriumJun 07 2013A bottleneck situation in one-lane traffic-flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal realization ... More

Magnetization transport in spin ladders and next-nearest-neighbor chainsApr 08 2013Nov 27 2013We study magnetization transport at high temperatures in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in sectors with nonzero ... More

Entanglement of random vectorsNov 22 2006We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size and for arbitrary ... More

Combinatorial aspects of the linkage principle for general linear supergroupsSep 06 2016Let $G=GL(m|n)$ be a general linear supergroup and $G_{ev}$ be its even subsupergroup isomorphic to $GL(m)\times GL(n)$. In this paper we use the explicit description of $G_{ev}$-primitive vectors in the costandard supermodule $\nabla(\lambda)$, the largest ... More

On unitarity of some representations of classical p-adic groups IIJan 26 2017C. Jantzen has defined a correspondence which attaches to an irreducible representation of a classical $p$-adic group, a finite set of irreducible representations of classical $p$-adic groups supported in a single or in two cuspidal lines (the case of ... More

On unitarizability in the case of classical p-adic groupsSep 02 2017In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we shall give ... More

Three Characterizations of Exponential Distribution Involving Median of Sample of Size ThreeDec 08 2014In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.

The divisibility modulo 24 of Kloosterman sums on $GF(2^m)$, $m$ evenJan 18 2008Feb 16 2008In a recent work by Charpin, Helleseth, and Zinoviev Kloosterman sums $K(a)$ over a finite field $\F_{2^m}$ were evaluated modulo 24 in the case $m$ odd, and the number of those $a$ giving the same value for $K(a)$ modulo 24 was given. In this paper the ... More

Real Surfaces in Elliptic SurfacesSep 12 2003We study the structure of complex points on real surfaces, embedded into complex Elliptic surfaces. We show, for example, that any compact surface has a totally real embedding into a blow-up of a K3 surface. We also exhibit smooth disc bundles over compact ... More

Reductions of (v_3) configurationsMay 08 2005Cubic bipartite graphs with girth at least 6 correspond to symmetric combinatorial (v_3) configurations. In 1887 V. Martinetti described a simple reduction method which enables one to reduce each combinatorial (v_3) configuration to one from the infinite ... More

Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivativesAug 08 2018In the paper under review, we analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems ... More

Generalized weighted pseudo-almost periodic solutions and generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusionsAug 08 2018In this paper, we analyze the existence and uniqueness of generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusions in Banach spaces. The main results are devoted to the study of various types of weighted ... More

Causal Dynamical Triangulations in the Spincube Model of Quantum GravityJun 23 2015Jul 31 2016We study the implications of the simplicity constraint in the spincube model of quantum gravity. By relating the edge-lengths to the integer areas of triangles, the simplicity constraint imposes very strong restrictions between them, ultimately leading ... More

On Minkowski space and finite geometryOct 08 2014The main aim of this interdisciplinary paper is to characterize all maps on finite Minkowski space of arbitrary dimension $n$ that map pairs of distinct light-like events into pairs of distinct light-like events. Neither bijectivity of maps nor preservation ... More

A Polling Model with Reneging at Polling InstantsAug 01 2014In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that we consider ... More

The parallel TASEP, fixed particle number and weighted Motzkin pathsNov 11 2013In this paper the totally asymmetric exclusion process (TASEP) with parallel update on an open lattice of size $L$ is considered in the maximum-current region. A formal expression for the generating function for the weight of configurations with $N$ particles ... More

Transport in a one-dimensional isotropic Heisenberg model at high temperatureDec 12 2011Magnetization transport in a one-dimensional isotropic spin 1/2 Heisenberg model is studied. It is shown that in a nonequilibrium steady state at high temperature and constant small driving the magnetization current depends on the system length L as 1/L^{0.5}, ... More

Dephasing-induced diffusive transport in anisotropic Heisenberg modelDec 01 2009Apr 01 2010We study transport properties of anisotropic Heisenberg model in a disordered magnetic field experiencing dephasing due to external degrees of freedom. In the absence of dephasing the model can display, depending on parameter values, the whole range of ... More

Elementary epistemological features of machine intelligenceDec 04 2008Feb 09 2013Theoretical analysis of machine intelligence (MI) is useful for defining a common platform in both theoretical and applied artificial intelligence (AI). The goal of this paper is to set canonical definitions that can assist pragmatic research in both ... More

Hochschild homology of certain Soergel bimodulesOct 20 2008In this paper we compute Hochschild homology of certain Soergel bimodules. Moreover, we describe explicitly the graded bimodule maps between Soergel bimodules. This computations are motivated by the categorifications of the colored HOMFLY-PT polynomial ... More

Exact convergence times for generation of random bipartite entanglementSep 03 2008Sep 26 2008We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap of the Markov ... More

On the strong approximations of partial sums of f(nkx)Sep 27 2015We prove a strong invariance principle for the sums PN k=1 f(nkx), where f is a smooth periodic function on R and (nk)k?1 is an increasing random sequence. Our results show that in contrast to the classical Salem-Zygmund theory, the asymptotic properties ... More

Upper Bound for Critical Probability of Site Percolation on Triangular LatticeAug 21 2013In site percolation, vertices (sites) of a graph are open with probability p, and there is critical p, for which open vertices form an open path the long way across a graph, so a vertex at the origin is a part of an infinite connected open vertex set. ... More

Coexistence of diffusive and ballistic transport in a simple spin ladderFeb 22 2013We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is ... More

Calculating the probability of detecting radio signals from alien civilizationsJun 29 2007Jul 14 2007Although it might not be self-evident, it is in fact entirely possible to calculate the probability of detecting alien radio signals by understanding what types of extraterrestrial radio emissions can be expected and what properties these emissions can ... More

Homology of torus linksJun 26 2006Aug 15 2007In this paper we show that there is a cut-off in the Khovanov homology of $(2k,2kn)$-torus links, namely that the maximal homological degree of non-zero homology group of $(2k,2kn)$-torus link is $2k^2n$. Furthermore, we calculate explicitely the homology ... More

Properties of Khovanov homology for positive braid knotsNov 21 2005In this paper we solve one open problem from \cite{pat} and give some generalizations. Namely, we prove that the first homology group of positive braid knot is trivial. Also, we show that the same is true for the Khovanov-Rozansky homology \cite{kovroz} ... More

Categorification of the Dichromatic Polynomial for GraphsApr 12 2005Sep 06 2005For each graph and each positive integer $n$, we define a chain complex whose graded Euler characteristic is equal to an appropriate $n$-specialization of the dichromatic polynomial. This also gives a categorification of $n$-specializations of the Tutte ... More

Scaling of running time of quantum adiabatic algorithm for propositional satisfiabilityFeb 14 2005We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows exponentially ... More

A new cyclic sieving phenomenon for Catalan objectsJan 15 2016Feb 25 2016Based on computational experiments, Jim Propp and Vic Reiner suspected that there might exist a sequence of combinatorial objects $X_n$, each carrying a natural action of the cyclic group $C_{n-1}$ of order $n-1$ such that the triple $\left(X_n,C_{n-1},\frac{1}{[n+1]_q}{2n ... More

Fano resonances and band structure of two dimensional photonic structuresSep 18 2015We show that the frequency spectrum of two dimensional photonic crystals is strongly influenced by Fano resonances which can be excited already in the linear array of dielectric cylinders. To support this claim, we calculate the transmission of electromagnetic ... More

Comment on the paper I. M. Suslov: Finite Size Scaling from the Self Consistent Theory of LocalizationMay 03 2012In the recent paper [I.M.Suslov, JETP {\bf 114} (2012) 107] a new scaling theory of electron localization was proposed. We show that numerical data for the quasi-one dimensional Anderson model do not support predictions of this theory.

Random Matrix Theory with Non-integer Beta-parameterSep 17 2000We show that the random matrix theory with non-integer "symmetry parameter" beta describes the statistics of transport parameters of strongly disordered two dimensional systems.

Photonic crystal with left-handed componentsOct 19 2015We show that the periodic array of left-handed cylinders possesses a rich spectrum of guided modes when the negative permeability of cylinders equals exactly to minus value of permeability of embedding media. These resonances strongly influences propagation ... More

Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponentsJul 27 1999Nov 17 1999Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis ... More

Some bounds on unitary duals of classical groups - non-archimeden caseJan 27 2016In the first part of the paper we give some bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical p-adic groups. Roughly, it can show up only if the central character of the inducing ... More

Unitarizability in generalized rank three for classical p-adic groupsSep 02 2017In an earlier paper we propose an approach to the unitarizability problem in the case of classical groups over a p-adic field of characteristic zero based on cuspidal reducibility points. We have reduced earlier the unitarizability for these groups to ... More

On unitarity of some representatations of classical p-adic groups IJan 26 2017In the case of p-adic general linear groups, each irreducible representation is parabolically induced by a tensor product of irreducible representations supported by cuspidal lines. One gets in this way a parameterization of the irreducible representations ... More

$m_{n}$-Distributional chaos in Fr\' echet spacesFeb 09 2019The main aim of this paper is to introduce the concepts of $m_{n}$-distributional chaos and $\lambda$-distributional chaos for linear continuous operators and their sequences in Fr\' echet spaces ($\lambda \in (0,1]$), as well as their continuous analogues ... More

Two stable modifications of the finite section methodFeb 24 2010In this article we demonstrate and compare two modified versions of the classical finite section method for band-dominated operators in case the latter is not stable. For both methods we give explicit criteria for their applicability.

Cosine problem in EPRL/FK spinfoam modelJul 19 2013Dec 11 2013We calculate the classical limit effective action of the EPRL/FK spinfoam model of quantum gravity coupled to matter fields. By employing the standard QFT background field method adapted to the spinfoam setting, we find that the model has many different ... More

Asymptotically almost periodic and asymptotically almost automorphic vector-valued generalized functionsAug 08 2018The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the classes of asymptotically ... More

Feynman amplitudes on moduli spaces of graphsSep 02 2017Jul 24 2018This article introduces moduli spaces of coloured graphs on which Feynman amplitudes can be viewed as 'discrete' volume densities. The basic idea behind this construction is that these moduli spaces decompose into disjoint unions of open cells on which ... More

${\mathcal F}$-Hypercyclic and disjoint ${\mathcal F}$-hypercyclic properties of binary relations over topological spacesAug 08 2018In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over topological ... More

Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and normJun 14 2007Nov 21 2007Let $\F_q$ ($q=p^r$) be a finite field. In this paper the number of irreducible polynomials of degree $m$ in $\F_q[x]$ with prescribed trace and norm coefficients is calculated in certain special cases and a general bound for that number is obtained improving ... More

From Anderson to ZetaApr 28 2015Jul 15 2016For an irreducible crystallographic root system $\Phi$ and a positive integer $p$ relatively prime to the Coxeter number $h$ of $\Phi$, we give a natural bijection $\mathcal{A}$ from the set $\widetilde{W}^p$ of affine Weyl group elements with no inversions ... More

CR regular embeddings and immersions of compact orientable 4-manifolds into C3Jan 28 2015Mar 03 2015We show that a compact orientable 4-manifold M has a CR regular immersion into C3 if and only if both its first Pontryagin class and its Euler characteristic vanish, and has a CR regular embedding into C3 if and only if in addition the second Stiefel-Whitney ... More

On reducibility points beyond ends of complementary series of p-adic GL(n)Oct 17 2013Jul 09 2014In this paper we consider reducibility points beyond the ends of complementary series of general linear groups over a p-adic field, which start with Speh representations. We describe explicitly the composition series of the representations at these reducibility ... More

Exact large-deviation statistics for a nonequilibrium quantum spin chainOct 14 2013Jan 29 2014We consider a one-dimensional XX spin chain in a nonequilibrium setting with a Lindblad-type boundary driving. By calculating large deviation rate function in the thermodynamic limit, being a generalization of free energy to a nonequilibrium setting, ... More

Exact Site and Bond Percolation Probability on Lattice-like GraphsOct 01 2013I calculated the exact site and bond percolation probability on lattice-like graphs for given dimension d: site percolation probability is 1/d and bond percolation probability is 0.5(d-1)^{-1/2}