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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

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

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

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.

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

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

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

Supercharge optical arraysSep 15 2018Oct 06 2018We introduce the notion of a supercharge optical array synthesized according to supersymmetric charge operators. Starting from an arbitrary array, mathematical supersymmetry transformation can be used systematically to create a zero-energy physical state ... 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

Trajectories and orbital angular momentum of necklace beams in nonlinear colloidal suspensionsMar 28 2017Recently, we have predicted that the modulation instability of optical vortex solitons propagating in nonlinear colloidal suspensions with exponential saturable nonlinearity leads to formation of necklace beams (NBs) [S.~Z.~Silahli, W.~Walasik and N.~M.~Litchinitser, ... 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

Reconfigurable Topological Photonic CrystalJun 16 2017Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically ... 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

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

Supersymmetry-guided method for mode selection and optimization in coupled systemsJun 05 2018Single-mode operation of coupled systems such as optical-fiber bundles, lattices of photonic waveguides, or laser arrays requires an efficient method to suppress unwanted super-modes. Here, we propose a systematic supersymmetry-based approach to selectively ... 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

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

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

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

On asymptotic normality of U-statistic of a stationary absolutely regular sequence in a triangular array schemeApr 14 2019Apr 16 2019Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents the sufficient conditions for the asymptotic normality (for $n\to\infty$ and common ... 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

Experimental demonstration of valley-Hall topological photonic crystal at telecommunication wavelengthsDec 20 2017May 18 2018Photonic topological insulators provide unprecedented possibilities to eliminate scattering losses and improve the efficiency of optical communication systems. Despite significant theoretical efforts, the experimental demonstration of an integrated photonic ... 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

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

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

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

Supersymmetric microring laser arraysFeb 08 2019Feb 28 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

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

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

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

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.

Reconfiguring structured light beams using nonlinear metasurfacesMay 18 2018Ultra-compact, low-loss, fast, and reconfigurable optical components, enabling manipulation of light by light, could open numerous opportunities for controlling light on the nanoscale. Nanostructured all-dielectric metasurfaces have been shown to enable ... More

Fast approaches for Bayesian estimation of size of hard-to-reach populations using Network Scale-upApr 12 2018The Network scale-up method is commonly used to overcome difficulties in estimating the size of hard-to-reach populations. The method uses indirect information based on social network of each participant taken from the general population, but in some ... More

Cartesian approach for constrained mechanical systemsNov 14 2010In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential equations in ... More

Cartesian approach for constrained mechanical system with three degree of freedomFeb 16 2009In the history of mechanics, there have been two points of view for studying mechanical systems: The Newtonian and the Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential equations ... 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

Direct and inverse spectral problems for a class of non-selfadjoint band matricesApr 19 2013The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The obtained results ... More

Micro and Macro Fractals generated by multi-valued dynamical systemsApr 28 2013Given a multi-valued function $\Phi$ on a topological space $X$ we study the properties of its fixed fractal, which is defined as the closure of the orbit $\Phi^\omega(Fix(\Phi))=\bigcup_{n\in\omega}\Phi^n(Fix(\Phi))$ of the set $Fix(\Phi)=\{x\in X:x\in\Phi(x)\}$ ... 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.

Two-generator Kleinian orbifoldsJun 02 2006We give a complete list of orbifolds uniformised by discrete non-elementary two-generator subgroups of PSL(2,C) without invariant plane whose generators and their commutator have real traces.

On asymptotic efficiency of multivariate version of Spearman's rhoJun 05 2009A multivariate version of Spearman's rho for testing independence is considered. Its asymptotic efficiency is calculated under a general distribution model specified by the dependence function. The efficiency comparison study that involves other multivariate ... More

Comparing Techniques for Aggregating Interrelated Replications in Software EngineeringJul 18 2018Jul 29 2018Context: Researchers from different groups and institutions are collaborating towards the construction of groups of interrelated replications. Applying unsuitable techniques to aggregate interrelated replications' results may impact the reliability of ... 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

Effective masses for Laplacians on periodic graphsFeb 10 2015May 03 2015We consider Laplacians on periodic both discrete and metric equilateral graphs. Their spectrum consists of an absolutely continuous part (which is a union of non-degenerate spectral bands) and flat bands, i.e., eigenvalues of infinite multiplicity. We ... More

On the solution of the Graph Isomorphism Problem Part 1Jul 07 2010The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the help of the effective ... More

Maximising Bernoulli measures and dimension gaps for countable branched systemsFeb 21 2018Kifer, Peres, and Weiss proved that there exists $c_0>0,$ such that $\dim \mu\leq 1-c_0$ for any probability measure $\mu$ which makes the digits of the continued fraction expansion i.i.d. random variables. In this paper we prove that amongst this class ... More

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

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

Melting of charge order in the low-temperature state of an electronic ferroelectricMay 29 2019Strong electronic interactions can drive a system into a state with a symmetry breaking. Lattice frustration or competing interactions tend to prevent a symmetry breaking, leading to quantum disordered phases. In spin systems frustration can produce a ... More

Quadratic automaton algebras and intermediate growthMay 28 2017Nov 21 2017We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its ideal of relations does not possess a finite Gr\"obner basis with respect ... More

Three dimensional Sklyanin algebras and Groebner basesJan 04 2016Aug 27 2016We consider a Sklyanin algebra S with 3 generators, which is the quadratic algebra over a field k with three generators x,y,z given by three relations pxy+qyx+rzz=0, pyz+qzy+rxx=0 and pzx+qxz+ryy=0, where p,q,r are parameters from the fileld k. This class ... More

Finite dimensional semigroup quadratic algebras with minimal number of relationsApr 11 2011Aug 04 2011A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra ... More

Error analysis for a fractional-derivative parabolic problem on quasi-graded meshes using barrier functionsMay 17 2019May 21 2019An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple and general numerical-stability ... 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

Harmonic analysis on spherical homogeneous spaces with solvable stabilizerJun 06 2011Sep 07 2012For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over ... More

A fuzzy-set theoretical framework for computing exit rates of rare events in potential-driven diffusion processesAug 02 2017This article is about molecular simulation. However, the theoretical results apply for general overdamped Langevin dynamics simulations. Molecular simulation is often used for determining the stability of a complex (e.g., ligand-receptor). The stability ... More

Adaptive variable selection in nonparametric sparse additive modelsAug 26 2015We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset L_2([0,1]^d)$ and ... More

An extremal problem with applications to testing multivariate independenceDec 03 2010Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this paper, we study a class of extremal problems that is closely connected to the problem of testing ... 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

Chaotic Dynamics of Stellar Spin Driven by Planets Undergoing Lidov-Kozai Oscillations: Resonances and Origin of ChaosNov 04 2014Many exoplanetary systems containing hot Jupiters are found to possess significant misalignment between the spin axis of the host star and the planet's orbital angular momentum axis. A possible channel for producing such misaligned hot Jupiters involves ... More

Rewriting systems and the multiplicative structure in the cohomology of $π_1(Σ_{g_1}\times\cdots\timesΣ_{g_n})$ with twisted $\mathbb{Z}$-coefficientsJul 24 2019Let $\pi_g$ stand for the fundamental group of the closed orientable surface $\Sigma_g$ of genus $g$. We use a finite complete rewriting system for $\pi_g$ in order to produce an explicit contracting homotopy for the standard minimal $\pi_g$-free resolution ... 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

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

Dynamical Bonding Driving Mixed Valency in a Metal BorideMar 26 2019Samarium hexaboride is an anomaly, having many exotic and seemingly mutually incompatible properties. It was proposed to be a mixed-valent semiconductor, and later - a topological Kondo insulator, and yet has a Fermi surface despite being an insulator. ... More

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

Moving Beyond the Mean: Analyzing Variance in Software Engineering ExperimentsJul 18 2018Sep 05 2018Software Engineering (SE) experiments are traditionally analyzed with statistical tests (e.g., t-tests, ANOVAs, etc.) that assume equally spread data across treatments (i.e., the homogeneity of variances assumption). Differences across treatments' variances ... More

A New Class of X-Ray Tails of Early-Type Galaxies and Subclusters in Galaxy Clusters - Slingshot Tails vs Ram Pressure Stripped TailsMar 01 2019We show that there is a new class of gas tails - slingshot tails - which form as a subhalo (i.e. a subcluster or early-type cluster galaxy) moves away from the cluster center towards the apocenter of its orbit. These tails can point perpendicular or even ... More

The conjugacy problem for two by two matrices over polynomial ringsJan 19 2008We give an effective solution of the conjugacy problem for two by two matrices over the polynomial ring in one variable over a finite field.

Collective spin dynamics of Z2 vortex crystals in triangular Kitaev-Heisenberg antiferromagnetsMay 21 2019Jul 09 2019We show that the mesoscopic incommensurate $\mathbb{Z}_2$ vortex crystals proposed for layered triangular anisotropic magnets can be most saliently identified by two distinctive signatures in dynamical spin response experiments: The presence of pseudo-Goldstone ... More

Local compactness in right bounded asymmetric normed spacesFeb 13 2017We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some results found ... 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.

Dimensions of equilibrium measures on a class of planar self-affine setsJun 21 2017Jul 23 2018We study equilibrium measures (K\"aenm\"aki measures) supported on self-affine sets generated by a finite collection of diagonal and anti-diagonal matrices acting on the plane and satisfying the strong separation property. Our main result is that such ... More

Clicks and Cliques. Exploring the Soul of the CommunityOct 09 2017In the paper we analyze 26 communities across the United States with the objective to understand what attaches people to their community and how this attachment differs among communities. How different are attached people from unattached? What attaches ... More

Effect of an Optical Negative Index Thin Film on Optical BistabilityJul 20 2006We investigate nonlinear transmission in a layered structure consisting of a slab of positive index material (PIM) with Kerr-type nonlinearity and a sub-wavelength layer of linear negative index material (NIM) sandwiched between semi-infinite linear dielectrics. ... More

Cellular approximations of p-local compact groupsJun 15 2017Let A be the classifying space of an abelian p-torsion group. We compute A-cellular approximations (in the sense of Chach\'olski and Farjoun) of classifying spaces of p-local compact groups, with special emphasis in the cases which arise from honest compact ... More

Relating Postnikov pieces with the Krull filtration: A spin-off of Serre's theoremJul 07 2005We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra ... More

Postnikov pieces and BZ/p-homotopy theorySep 21 2004We present a constructive method to compute the cellularization with respect to K(Z/p, m) for any integer m > 0 of a large class of H-spaces, namely all those which have a finite number of non-trivial K(Z/p, m)-homotopy groups (the pointed mapping space ... More

Quadrature rules for $L^1$-weighted norms of orthogonal polynomialsJul 09 2014In this paper we obtain $L^1$-weighted norms of classical orthogonal polynomials (Hermite, Laguerre and Jacobi polynomials) in terms of the zeros of these orthogonal polynomials; these expressions are usually known as quadrature rules. In particular these ... 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

Source Code Optimization using Equivalent MutantsMar 26 2018Jul 02 2018A mutant is a program obtained by syntactically modifying a program's source code; an equivalent mutant is a mutant, which is functionally equivalent to the original program. Mutants are primarily used in \emph{mutation testing}, and when deriving a test ... More

On affinely closed homogeneous spacesJun 24 2004Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corollary, a description of affine G-algebras with finitely generated invariant ... More

Differences of Harmonic Numbers and the $abc$-ConjectureAug 02 2017Our main source of inspiration was a talk by Hendrik Lenstra on harmonic numbers, which are numbers whose only prime factors are two or three. Gersonides proved 675 years ago that one can be written as a difference of harmonic numbers in only four ways: ... More

Discovery of a superhard iron tetraboride superconductorApr 18 2013Single crystals of novel orthorhombic (space group Pnnm) iron tetraboride FeB4 were synthesised at pressures above 8 GPa and high temperatures. Magnetic susceptibility measurements demonstrated bulk superconductivity below 2.9 K. The putative isotope ... More

Norm Monitoring under Partial Action ObservabilityMay 15 2015Apr 21 2016In the context of using norms for controlling multi-agent systems, a vitally important question that has not yet been addressed in the literature is the development of mechanisms for monitoring norm compliance under partial action observability. This ... More

RUSSE: The First Workshop on Russian Semantic SimilarityMar 15 2018The paper gives an overview of the Russian Semantic Similarity Evaluation (RUSSE) shared task held in conjunction with the Dialogue 2015 conference. There exist a lot of comparative studies on semantic similarity, yet no analysis of such measures was ... More

Nonlinear combining of multiple laser beams in Kerr mediumOct 08 2015We consider combining of multiple laser beams into a single near diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. The beams with the total power above critical are combined in the near field and then propagated in the Kerr medium. ... More

Implicit Contextual Integrity in Online Social NetworksFeb 09 2015Jul 06 2015Many real incidents demonstrate that users of Online Social Networks need mechanisms that help them manage their interactions by increasing the awareness of the different contexts that coexist in Online Social Networks and preventing them from exchanging ... More

Nonlinear combining of laser beamsApr 03 2014We propose to combine multiple laser beams into a single diffraction-limited beam by the beam self-focusing (collapse) in the Kerr medium. The beams with the total power above critical are first combined in the near field and then propagated in the optical ... More

Resolving Multi-party Privacy Conflicts in Social MediaJul 16 2015Feb 22 2016Items shared through Social Media may affect more than one user's privacy --- e.g., photos that depict multiple users, comments that mention multiple users, events in which multiple users are invited, etc. The lack of multi-party privacy management support ... More

Toward defeating diffraction and randomness for laser beam propagation in turbulent atmosphereNov 08 2017A large distance propagation in turbulent atmosphere results in disintegration of laser beam into speckles. We find that the most intense speckle approximately preserves both the Gaussian shape and the diameter of the initial collimated beam while loosing ... More

Reconstructing surface triangulations by their intersection matricesFeb 24 2014The intersection matrix of a finite simplicial complex has as each of its entries the rank of the intersection of its respective simplices. We prove that such matrix defines the triangulation of a closed connected surface up to isomorphism.

Cellular replication limits in the Luria-Delbrück mutation modelNov 14 2015Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbr\"uck model assumed that cells are intrinsically capable of dividing an unlimited number of times. This assumption however, is not true for human somatic ... More

Non-Gaussian Statistics of Multiple FilamentationMay 15 2010We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of ... More

The box dimensions of exceptional self-affine sets in $\mathbb{R}^3$Jul 17 2019We study the box dimensions of self-affine sets in $\mathbb{R}^3$ which are generated by a finite collection of generalised permutation matrices. We obtain bounds for the dimensions which hold with very minimal assumptions and give rise to sharp results ... More

Distributed Estimation of a Parametric Field: Algorithms and Performance AnalysisOct 28 2013Oct 23 2014This paper presents a distributed estimator for a deterministic parametric physical field sensed by a homogeneous sensor network and develops a new transformed expression for the Cramer-Rao lower bound (CRLB) on the variance of distributed estimates. ... More

Distributed Estimation of a Parametric Field Using Sparse Noisy DataSep 20 2012The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes its observation ... More