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Hyper-lithographyAug 09 2016The future success of integrated circuits (IC) technology relies on the continuing miniaturization of the feature size, allowing more components per chip and higher speed. Extreme anisotropy opens new opportunities for spatial pattern compression from ... More

M$^2$I: Channel Modeling for Metamaterial-Enhanced Magnetic Induction CommunicationsJul 17 2014Apr 04 2016Magnetic Induction (MI) communication technique has shown great potentials in complex and RF-challenging environments, such as underground and underwater, due to its advantage over EM wave-based techniques in penetrating lossy medium. However, the transmission ... More

Optically tunable topological photonic crystalJan 30 2019Topological photonic insulators pave the way toward efficient integrated photonic devices with minimized scattering losses. Optical properties of the majority of topological structures proposed to date are fixed by design such that no changes to their ... More

Continuous supersymmetric transformation for photonic designJan 25 2019We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve their propagation ... More

Supersymmetric microring laser arraysFeb 08 2019Coherent combination of emission power from an array of coupled semiconductor lasers operating on the same chip is of fundamental and technological importance. In general, the nonlinear competition among the array supermodes can entail incoherence and ... More

Variable Focus Nonlinear Lens via Transformation OpticsApr 17 2012We propose a structure consisting of nonlinear core and graded-index shell that can be switched from a concentrator squeezing light into the core to a variable focus lens by varying the intensity of incident light.

Dynamics of large femtosecond filament arrays: possibilities, limitations, and trade-offsDec 09 2015Stable propagation of large, multifilament arrays over long distances in air paves new ways for microwave-radiation manipulation. Although, the dynamics of a single or a few filaments was discussed in some of the previous studies, we show that the stability ... More

Phase transition in multimode nonlinear parity-time-symmetric waveguide couplersSep 11 2015Parity-time-symmetric ($\mathcal{PT}$-symmetric) optical waveguide couplers have become a key component for integrated optics. They offer new possibilities for fast, ultracompact, configurable, all-optical signal processing. Here, we study nonlinear properties ... More

Gaussian Beams in Near-Zero Transition MetamaterialsAug 01 2012We theoretically and numerically investigate the phenomenon of resonant field enhancement of Gaussian beams in two types of transition metamaterials: with a positive-zero-negative index profile and with a positive-zero-positive index profile and demonstrate ... More

Meta-$\mathcal{PT}$ Symmetry in Asymmetric Directional CouplersDec 21 2015Despite the benefits that directional coupler based parity-time symmetric systems may offer to the field of integrated optics, the realization of such couplers relies on rather strict design constraints on the waveguide parameters. Here, we investigate ... More

Nonlinear parity-time-symmetric transition in finite-size optical couplersSep 11 2015Parity-time-symmetric ($\mathcal{PT}$-symmetric) optical waveguide couplers offer a great potential for future applications in integrated optics. Studies of nonlinear $\mathcal{PT}$-symmetric couplers present new possibilities for ultracompact configurable ... More

Optical Bistability in Nonlinear Optical Coupler with Negative Index ChannelMay 02 2007May 05 2007We discuss a novel kind of nonlinear coupler with one channel filled with a negative index material (NIM). The opposite directionality of the phase velocity and the energy flow in the NIM channel facilitates an effective feedback mechanism that leads ... More

Experimental Demonstration of Non-Resonant Hyperlens in the Visible RangeDec 07 2014A metamaterial hyperlens offers a unique solution to overcome the diffraction limit by transforming evanescent waves responsible for imaging subwavelength features of an object into propagating waves. However, the first realizations of optical hyperlenses ... More

Modulation instability of structured-light beams in negative-index metamaterialsJan 13 2016Jan 15 2016One of the most fundamental properties of isotropic negative-index metamaterials, namely opposite directionality of the Poynting vector and the wavevector, enable many novel linear and nonlinear regimes of light-matter interactions. Here, we predict distinct ... More

Necklace Beam Generation in Nonlinear Colloidal Engineered MediaOct 21 2015Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum ... More

Inhomogeneous All-Dielectric Magnetic MetamaterialsJul 23 2015Anomalous field enhancement accompanied by resonant absorption phenomenon was originally discussed in the context of plasma physics and in applications related to radio-communications between the ground and spacecraft returning to Earth. Indeed, there ... More

Orbital angular momentum beam instabilities in engineered nonlinear colloidal mediaSep 17 2017In this letter, we experimentally demonstrate the evolution of the optical vortex beams of different topological charges propagating in engineered nano-colloidal suspension of negative polarizability with saturable nonlinearities. Due to the high power ... More

High-Efficiency All-Dielectric Metasurfaces for Ultra-Compact Beam Manipulation in Transmission ModeJul 22 2015Jul 25 2015Metasurfaces are two-dimensional optical structures enabling complete control of the amplitude, phase, and polarization of light. Unlike plasmonic metasurfaces, planar silicon structures facilitate high transmission, low losses and compatibility with ... More

From Positive- to Negative-Index Materials: Transitional PhenomenaDec 31 2007Apr 08 2008Electromagnetic field propagation through a transition layer between the positive-index and negative-index materials with linearly changing dielectric permittivity and magnetic permeability was investigated. It is shown that at oblique incidence, the ... More

Free-Space Nonlinear Beam Combining Towards FilamentationSep 02 2016Multi-filamentation opens new degrees of freedom for manipulating electromagnetic waves in air. However, without control, multiple filament interactions, including attraction, repulsion or fusion often result in formation of complex disordered filament ... More

Electromagnetic Enhancement in Lossy Optical Transition MetamaterialsMay 03 2010We investigate the effect of anomalous field enhancement in metamaterials where the effective refractive index gradually changes from positive to negative values, i.e. transition metamaterials. We demonstrate that considerable field enhancement can be ... More

Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theoremJan 20 2015We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the first Noether ... More

Resonant interaction of optical pulses with plasmonic oscillations in metal nanoparticlesOct 30 2005We derive envelope equations which generate the Maxwell-Lorentz model and describe the interaction of optical pulses with plasmonic oscillations in metal nanoparticle composites. A family of solitary wave solutions is found which is analogous to self-induced ... More

Noether's theorem for higher-order variational problems of Herglotz typeJul 21 2015We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation, transversality conditions, a DuBois-Reymond necessary optimality condition ... More

Higher-order variational problems of Herglotz type with time delayMar 13 2016Apr 27 2016We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Main results are higher-order Euler-Lagrange and DuBois-Reymond necessary optimality conditions as well as a higher-order Noether type ... More

Noether currents for higher-order variational problems of Herglotz type with time delayApr 01 2017We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such generalized variational problems, which are particularly useful in the search ... More

Inverse scattering on the line for the matrix Sturm-Liouville equationDec 19 2015The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.

Metamaterial all-optical switching based on resonance mode coupling in dielectric meta-atomsDec 10 2014All-optical switching based on optical nonlinearity must undergo complex processes of light-mater interaction in atom and electron scale, so a relative high power and long response time is required, that construct main bottlenecks in all-optical technology. ... More

An inverse problem for the differential operator on the graph with a cycle with different orders on different edgesSep 20 2013Jan 12 2014We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive procedure for the ... More

Spectral synthesis for the differentiation operator in the Schwartz spaceJan 07 2016We consider the spectral synthesis problem for the differentiation operator D=d/dt in the Schwartz space E(a;b) and the dual problem of local description for closed submodules in a special module of entire functions.

High frequency asymptotics of global vibrations in a problem with concentrated massApr 16 2008We consider an elastic system containing a small region where the density is very much higher then elsewhere. Such system possesses two types of eigenvibrations, which are local and global vibrations. Complete asymptotic expansions of global eigenvibrations ... More

Loops on polyhedral products and diagonal arrangementsJan 19 2009In this paper we establish a connection between the loop space homology of the generalization of wedge defined by a simplicial complex K (so called polyhedral product) and the homology of certain diagonal arrangements associated with K. We illustrate ... More

Constrained energy problems with external fields for infinite dimensional vector measuresOct 11 2010We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from above, satisfy ... More

Constrained energy problems with external fieldsJan 25 2010Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set, satisfy certain normalizing ... More

Necessary and sufficient conditions for the solvability of the Gauss variational problem for infinite dimensional vector measuresJul 03 2012We continue our investigation of the Gauss variational problem for infinite dimensional vector measures associated with a condenser $(A_i)_{i\in I}$. It has been shown in Potential Anal., DOI:10.1007/s11118-012-9279-8 that, if some of the plates (say ... More

Equilibrium problems for infinite dimensional vector potentials with external fieldsNov 04 2009The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying certain normalizing ... More

Lightlike foliations on Lorentzian manifolds with weakly irreducible holonomy algebraJun 06 2005We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one lightlike hypersurface. ... More

An inverse problem for the non-self-adjoint matrix Sturm-Liouville operatorJul 14 2014The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient ... More

Special Partial GraphsMay 31 2013The attempts to prove the Four Color Problem last for long years. A little hope arises that the properties of the minimal partial triangulations will be very useful for the solution of the Four Color Problem. That is why the material of this paper is ... More

K-theory of locally finite graph $C^*$-algebrasJul 22 2010Apr 24 2013We calculate the K-theory of the Cuntz-Krieger algebra ${\cal O}_E$ associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic ... More

The non-perturbative BRST quartet mechanism in Landau gauge QCD: Ghost-gluon and ghost-quark bound statesJan 22 2013The non-perturbative BRST quartet mechanism in infrared Landau gauge QCD is presented. It is demonstrated that positivity violation for transverse gluons allows to identify the gluon's non-perturbative BRST quartet. To describe the respective BRST-daughter ... More

Features of ghost-gluon and ghost-quark bound states related to BRST quartetsFeb 14 2011Jun 26 2011The BRST quartet mechanism in infrared Landau gauge QCD is investigated. Based on the observed positivity violation for transverse gluons $A_{\mathrm {tr}}$ the field content of the non-perturbative BRST quartet generated by $A_{\mathrm {tr}}$ is derived. ... More

Non-Perturbative Instabilities as a Solution of the Cosmological Moduli ProblemJul 12 2005It is widely accepted that moduli in the mass range 10eV - $10^4$GeV which start to oscillate with an amplitude of the order of the Planck scale either jeopardize successful predictions of nucleosynthesis or overclose the Universe. It is shown that the ... More

Quantum Action Principle for Covariant Systems. Bosonic stringMar 01 2011A new form of covariant quantum theory based on a quantum version of the action principle is considered for the case of a free bosonic string. The central idea of the new approach is to delay conditions of stationarity of the classical action with respect ... More

Extremes of multidimensional stationary Gaussian random fieldsOct 10 2016May 11 2018Let $\{X(\mathbf{t}):\mathbf{t}=(t_1, t_2, \ldots, t_d)\in[0,\infty)^d\}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function $r$ satisfying conditions $r(\mathbf{t})<1$ for every ... More

Kleinian orbifolds uniformized by RP groups with an elliptic and a hyperbolic generatorMar 31 2009We consider non-elementary Kleinian groups \Gamma, without invariant plane, generated by an elliptic and a hyperbolic element with their axes lying in one plane. We find presentations and a complete list of orbifolds uniformized by such \Gamma.

On the principal impossibility to prove P=NPNov 15 2012The material of the article is devoted to the most complicated and interesting problem -- a problem of P = NP?. This research was presented to mathematical community in Hyderabad during International Congress of Mathematicians. But there it was published ... More

The Tits alternative for non-spherical Pride groupsJul 21 2006Mar 16 2007Pride groups, or ``groups given by presentations in which each defining relator involves at most two types of generators'', include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations. We show that ... More

On Perfect Codes in the Johnson GraphApr 29 2010In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n,w). We present combinatorial and number theory techniques to provide necessary conditions for existence of such codes and reduce the range of parameters in which ... More

Enumerative Coding for Grassmannian SpaceNov 17 2009Aug 28 2010The Grassmannian space $\Gr$ is the set of all $k-$dimensional subspaces of the vector space~\smash{$\F_q^n$}. Recently, codes in the Grassmannian have found an application in network coding. The main goal of this paper is to present efficient enumerative ... More

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theoriesNov 03 2015A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here ... More

On recovering Sturm-Liouville differential operators with deviating argumentFeb 07 2018We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their spectra. We establish ... More

A Converting of the Directed GraphsOct 18 2012The presented material continues the previous article (arxiv:1007.1059) and also is devoted to the equivalent conversion between the graphs. The examining of the transformation of the vertex graphs into the edge graphs (together with the opposite transformation) ... More

Low and high frequency approximations to eigenvibrations of string with double contrastsApr 16 2008Sep 13 2009We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density ... More

A short proof of Grünbaum's Conjecture about affine invariant pointsFeb 21 2016Let us denote by $\mathcal K_n$ the hyperspace of all convex bodies of $\mathbb R^n$ equipped with the Hausdorff distance topology. An affine invariant point $p$ is a continuous and Aff(n)-equivariant map $p:\mathcal K_n\to \mathbb R^n$, where Aff(n) ... More

Mean-Set Attack: Cryptanalysis of Sibert et al. Authentication ProtocolJun 24 2010We analyze the Sibert et al. group-based (Feige-Fiat-Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge. In addition, we provide experimental evidence that our approach is practical and can succeed even ... More

Extremes of multidimensional stationary Gaussian random fieldsOct 10 2016Let $\{X(\mathbf{t}):\mathbf{t}=(t_1, t_2, \ldots, t_d)\in[0,\infty)^d\}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function $r$ satisfying conditions $r(\mathbf{t})<1$ for every ... More

Limit theory for planar Gilbert tessellationsApr 30 2010A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing ... More

Goodness-of-fit tests based on sup-functionals of weighted empirical processesJun 02 2014Apr 01 2016A large class of goodness-of-fit test statistics based on sup-functionals of weighted empirical processes is proposed and studied. The weight functions employed are Erd\H{o}s-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian bridge. Based ... More

Quantum Action Principle in Relativistic MechanicsDec 07 2008A quantum version of the action principle is considered in the case of a free relativistic particle. The classical limit of the quantum action is obtained.

Asymptotics of the order statistics for a process with a regenerative structureJul 05 2017Sep 14 2017In the paper, a regenerative process $\{X_n:n\in\mathbb{N}\}$ with finite mean cycle length is considered. For~$M_n^{(q)}$ denoting the $q$-th largest value in $\{X_k : 1\leqslant k \leqslant n\}$, we prove that \begin{equation*} \sup_{x\in\mathbb{R}} ... More

Cumulative-Separable CodesMay 10 2010q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are considered. The relation between different codes from this class is demonstrated. Improved boundaries of ... More

Equivariant absolute extensor property on hyperspaces of convex setsJan 12 2014Feb 07 2014Let G be a compact group acting on a Banach space L by means of linear isometries. The action of G on L induces a natural continuous action on cc(L), the hyperspace of all compact convex subsets of L endowed with the Hausdorff metric topology. The main ... More

On the Quantum Creation of Matter in the Expanding UniverseMay 09 2011Quantum Action Principle which has been used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics \cite{GLL} is applied to quantum cosmology. The quantum creation of matter in a minisuperspace model with one homogeneous ... More

On maxima of stationary fieldsOct 10 2018Oct 15 2018Let $\{X_{\mathbf{n}} : \mathbf{n}\in\mathbb{Z}^d\}$ be a weakly dependent stationary field with maxima $M_{A} := \sup\{X_{\mathbf{i}} : \mathbf{i}\in A\}$ for finite $A\subset\mathbb{Z}^d$ and $M_{\mathbf{n}} := \sup\{X_{\mathbf{i}} : \mathbf{1} \leq ... More

An inverse problem for Sturm-Liouville operators on trees with partial information given on the potentialsNov 15 2017We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse problem, which ... More

Exact conservation laws for truncated gyrokinetic Vlasov-Poisson equationsJun 28 2013The purpose of the current work is adapting the results of the Noether method derivation of momentum transport equation for the gyrokinetic Vlasov-Poisson system to numerical implementations. In particular, we are considering the delta-f truncated Gyrokinetic ... More

The impurity problem in a bilayer system of dipolesJun 24 2013Nov 17 2013We consider a bilayer geometry where a single impurity moves in a two-dimensional plane and is coupled, via dipolar interactions, to a two-dimensional system of fermions residing in the second layer. Dipoles in both layers point in the same direction ... More

Electron-phonon coupling in a two-dimensional inhomogeneous electron gas: consequences for surface spectral propertiesAug 27 2007Aug 12 2008We investigate the coupling of an inhomogeneous electron system to phonons. The properties of an electronic system composed of a mixture of microscopic ordered and disordered islands are changed fundamentally by a phonon mode. In high-Tc cuprates, such ... More

Homology of non-$k$-overlapping discsMar 04 2014In this paper we describe the homology and cohomology of some natural bimodules over the little discs operad, whose components are configurations of non-$k$-overlapping discs. At the end we briefly explain how this algebraic structure intervenes in the ... More

Graphs of relations and Hilbert seriesJan 19 2008We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n-1)/2 relations for n less or ... More

A Variant of the Gröbner Basis Algorithm for Computing Hilbert BasesMar 25 2013Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field given as a matrix ... More

Near Earth Object 2012XJ112 as a source of bright bolides of achondritic natureFeb 03 2014We analyze the likely link between the recently discovered Near Earth Object 2012XJ112 and a bright fireball observed over the south of Spain on December 27, 2012. The bolide, with an absolute magnitude of -9 +- 1, was simultaneously imaged during the ... More

Some asymptotic expansions for a semilinear reaction-diffusion problem in a sectorFeb 05 2009Sep 27 2009A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have multiple solutions. ... More

Universal Gröbner Bases for Binary Linear CodesApr 04 2013Each linear code can be described by a code ideal given as the sum of a toric ideal and a non-prime ideal. In this way, several concepts from the theory of toric ideals can be translated into the setting of code ideals. It will be shown that after adjusting ... More

Graver Bases and Universal Gröbner Bases for Linear CodesJan 24 2014May 07 2014Two correspondences have been provided that associate any linear code over a finite field with a binomial ideal. In this paper, algorithms for computing their Graver bases and universal Gr\"obner bases are given. To this end, a connection between these ... More

An infinite family of locally X graphs based on incidence geometriesNov 28 2018A graph ${\mathcal G}$ is locally X if the graphs induced on the neighbours of every vertex of ${\mathcal G}$ are isomorphic to the graph $X$. We prove that the infinite family of incidence graphs of the $r$-rank incidence geometries, $\Gamma(KG(n,k),r)$, ... More

Raman study of magnetic excitations and magneto-elastic coupling in alpha-SrCr2O4Apr 01 2014Feb 09 2015Using Raman spectroscopy, we investigate the lattice phonons, magnetic excitations, and magneto-elastic coupling in the distorted triangular-lattice Heisenberg antiferromagnet alpha-SrCr2O4, which develops helical magnetic order below 43 K. Temperature ... More

Exponentiality of first passage times of continuous time Markov chainsMay 26 2011Oct 24 2013Let $(X,\p_x)$ be a continuous time Markov chain with finite or countable state space $S$ and let $T$ be its first passage time in a subset $D$ of $S$. It is well known that if $\mu$ is a quasi-stationary distribution relatively to $T$, then this time ... More

Constructions of High-Rate MSR Codes over Small FieldsMay 05 2015Jan 28 2016A novel technique for construction of minimum storage regenerating (MSR) codes is presented. Based on this technique, three explicit constructions of MSR codes are given. The first two constructions provide access-optimal MSR codes, with two and three ... More

Blaschke addition and convex polyhedraFeb 16 2005This is an extended version of a talk on October 4, 2004 at the research seminar ``Differential geometry and applications'' (headed by Academician A. T. Fomenko) at Moscow State University. The paper contains an overview of available (but far from well-known) ... More

Ion Condensation onto Ribozyme is Site-Specific and Fold-DependentFeb 15 2019The highly charged RNA molecules, with each phosphate carrying a single negative charge, cannot fold into well-defined architectures with tertiary interactions, in the absence of ions. For ribozymes, divalent cations are known to be more efficient than ... More

Human and Machine Judgements for Russian Semantic RelatednessAug 31 2017Semantic relatedness of terms represents similarity of meaning by a numerical score. On the one hand, humans easily make judgments about semantic relatedness. On the other hand, this kind of information is useful in language processing systems. While ... More

Maltese cross coupling to cold atoms in free spaceFeb 08 2019We demonstrate a novel geometry for strong coupling of light and matter in free space, i.e., without the use of optical cavities. Guided by optical metrology tools, we use a manual pick-and-place technique to precisely and stably position four high numerical ... More

Modelling movement for collective adaptive systems with CARMAJul 08 2016Space and movement through space play an important role in many collective adaptive systems (CAS). CAS consist of multiple components interacting to achieve some goal in a system or environment that can change over time. When these components operate ... More

On a Probabilistic Interpretation of Relativistic Quantum MechanicsDec 08 2010A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After that, quantum dynamics ... More

Extreme points and geometric aspects of compact convex sets in asymmetric normed spacesApr 02 2014Inspired in the theorem of Krein-Milamn, we investigate the existence of extreme points in compact convex subsets of asymmetric normed spaces. We focus our attention in the finite dimensional case, giving a geometric description of all compact convex ... More

On the cohomology of highly connected covers of finite complexesJul 07 2006Relying on the computation of the Andre-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra.

Common envelope events with low-mass giants: understanding the transition to the slow spiral-inJun 15 2016Jul 08 2016We present a three-dimensional (3D) study of common envelope events (CEEs) to provide a foundation for future one-dimensional (1D) methods to model the self-regulated phase of a CEE. The considered CEEs with a low-mass red giant end with one of three ... More

Magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $β$-Li$_2$IrO$_3$Jan 03 2018Mar 02 2018We present a theoretical study of the static and dynamical properties of the Kitaev magnet $\beta$-Li$_2$IrO$_3$ based on the minimal $J$-$K$-$\Gamma$ model. We argue that the incommensurate magnetic order of $\beta$-Li$_2$IrO$_3$ can be qualitatively ... More

Quantum Action Principle in Relativistic Mechanics (II)Oct 19 2010Quantum Action Principle formulated earlier is used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics. In this new approach the probability "flows" in the Minkowsky space being dependent on an inner time parameter ... More

Two-Time Quantum MechanicsMar 14 2010A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.

Majorana representations of spin and an alternative solution of the Kitaev honeycomb modelJan 29 2018Based on the Dirac spinor representation of the SO(4) group, we discuss the relationship between three types of representation of spin in terms of Majorana fermions, namely the Kitaev representation, the SO(3) representation and the SO(4) chiral representation. ... More

A polling system whose stability region depends on a whole distribution of service timesMay 28 2012We present an example of a single-server polling system with two queues and an adaptive service policy where the stability region depends on the expected values of all the primitives and also on a certain exponential moment of the service-time distribution ... More

A partial inverse problem for the Sturm-Liouville operator on the graph with a loopNov 15 2017The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some additional data. We ... More

Quantifying word salad: The structural randomness of verbal reports produced during First Episode Psychosis predicts negative symptoms and Schizophrenia diagnosis 6 months laterOct 26 2016Background: The precise quantification of negative symptoms is necessary to improve differential diagnosis and prognosis prediction in Schizophrenia. In chronic psychotic patients, the representation of verbal reports as word graphs provides automated ... More

Minimal energy problems for strongly singular Riesz kernelsFeb 27 2016We study minimal energy problems for strongly singular Riesz kernels on a manifold. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such problems by switching to Hadamard's partie ... More

Weak turbulence in two-dimensional magnetohydrodynamicsDec 04 2012A weak wave turbulence theory is developed for two-dimensional (2D) magnetohydrodynamics (MHD). We derive and analyze the kinetic equation describing the three-wave interactions of pseudo-Alfv\'en waves. Our analysis is greatly helped by the fortunate ... More

Quantifying word salad: The structural randomness of verbal reports predicts negative symptoms and Schizophrenia diagnosis 6 months laterOct 26 2016Oct 30 2016Background: The precise quantification of negative symptoms is necessary to improve differential diagnosis and prognosis prediction in Schizophrenia. In chronic psychotic patients, the representation of verbal reports as word graphs provides automated ... More

The stability of the higher topological complexity of real projective spaces: an approach to their immersion dimensionSep 24 2016The $s$-th higher topological complexity of a space $X$, $TC_s(X)$, can be estimated from above by homotopical methods, and from below by homological methods. We give a thorough analysis of the gap between such estimates when $X=RP^m$, the real projective ... More