Results for "Wiktor Walasik"

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Plasmon-soliton waves in planar slot waveguides: I. ModelingJun 24 2015Jun 29 2015We present two complementary models to study stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. The considered nonlinearity is of focusing Kerr ... More
Plasmon-soliton waves in planar slot waveguides: II. Results for stationary waves and stability analysisJun 26 2015Jun 29 2015We describe the results of the two methods we developed to calculate the stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. These two methods are ... More
Stationary plasmon-soliton waves in metal-dielectric nonlinear planar structures: modeling and propertiesNov 28 2013Dec 02 2013We present three complementary methods to study stationary nonlinear solutions in one-dimensional nonlinear metal-dielectric structures. Two of them use an approximate treatment of the Kerr type nonlinear term taking into account only the leading electric ... 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
Symmetric metal slot waveguides with nonlinear dielectric core: bifurcations, size effects, and higher order modesMay 09 2014We study the nonlinear waves propagating in metal slot waveguides with a Kerr-type dielectric core. We develop two independent semi-analytical models to describe the properties of such waveguides. Using those models we compute the dispersion curves for ... 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
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
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
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
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
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
Characterizations of some free random variables by properties of conditional moments of third degree polynomialsNov 18 2012We investigate Laha-Lukacs properties of noncommutative random variables (processes). We prove that some families of free Meixner distributions can be characterized by the conditional moments of polynomial functions of degree 3. We also show that this ... More
A Characterization of the Normal Distribution by the Independence of a Pair of Random VectorsJan 01 2016Kagan and Shalaevski 1967 have shown that if the random variables $X_1,\dots,X_n$ are independent and identically distributed and the distribution of $\sum_{i=1}^n(X_i+a_i)^2$ $a_i\in \mathbb{R}$ depends only on $\sum_{i=1}^na_i^2$ , then each $X_i$ follows ... More
Sparse, complex-valued representations of natural sounds learned with phase and amplitude continuity priorsDec 17 2013Feb 18 2014Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns phase invariant ... More
Efficient coding of spectrotemporal binaural sounds leads to emergence of the auditory space representationNov 04 2013Feb 19 2014To date a number of studies have shown that receptive field shapes of early sensory neurons can be reproduced by optimizing coding efficiency of natural stimulus ensembles. A still unresolved question is whether the efficient coding hypothesis explains ... More
New characterization of two-state normal distributionJan 01 2014In this article we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional expectation ... More
On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systemsSep 28 2008This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the ... 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
Natural statistics of binaural soundsFeb 19 2014Mar 01 2014Binaural sound localization is usually considered a discrimination task, where interaural time (ITD) and level (ILD) disparities at pure frequency channels are utilized to identify a position of a sound source. In natural conditions binaural circuits ... More
Sample Variance in Free ProbabilityJul 22 2016Aug 03 2016Let $X_1, X_2,\dots, X_n$ denote i.i.d.~centered standard normal random variables, then the law of the sample variance $Q_n=\sum_{i=1}^n(X_i-\bar{X})^2$ is the $\chi^2$-distribution with $n-1$ degrees of freedom. It is an open problem in classical probability ... More
Coxeter Groups, Ruins, and Weighted $L^2$-cohomologyFeb 14 2016Given a Coxeter system $(W,S)$ and a multiparameter $\mathbf{q}$ of real numbers indexed by $S$, one can define the weighted $L^2$-cohomology groups and associate to them a nonnegative real number called the weighted $L^2$-Betti number. We show that for ... More
Sample Variance in Free ProbabilityJul 22 2016Oct 21 2016Let $X_1, X_2,\dots, X_n$ denote i.i.d.~centered standard normal random variables, then the law of the sample variance $Q_n=\sum_{i=1}^n(X_i-\bar{X})^2$ is the $\chi^2$-distribution with $n-1$ degrees of freedom. It is an open problem in classical probability ... More
The weighted Singer conjecture for Coxeter groups in dimensions three and fourMar 09 2015Given a Coxeter system $(W,S)$ there is a contractible simplicial complex $\Sigma$ called the Davis complex on which $W$ acts properly and cocompactly. In an article of Dymara, the weighted $L^2$-(co)homology groups of $\Sigma$ were defined, and in an ... More
The Four-Vertex Theorem, The Evolute, and The Decomposition of PolygonsJun 12 2009Jun 15 2009The Four-Vertex Theorem has been of interest ever since a discrete version appeared in 1813 due to Cauchy. Up until now, there have been many different versions of this theorem, both for discrete cases and smooth cases. In 2004, an approach relating the ... More
Polygon Vertex Extremality and Decomposition of PolygonsApr 11 2010In this paper, we show that if we decompose a polygon into two smaller polygons, then by comparing the number of extremal vertices in the original polygon versus the sum of the two smaller polygons, we can gain at most two globally extremal vertices in ... More
The fattened Davis complex and weighted $L^2$-(co)homology of Coxeter groupsFeb 26 2015Associated to a Coxeter system $(W,S)$ there is a contractible simplicial complex $\Sigma$ called the Davis complex on which $W$ acts properly and cocompactly by reflections. Given a positive real multiparameter $\mathbf{q}$, one can define the weighted ... More
Derivation, interpretation, and analog modelling of fractional variable order derivative definitionApr 18 2013The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical scheme for a ... More
Using Machine Learning to Enhance Vehicles Traffic in ATN (PRT) SystemsDec 16 2017This paper discusses new techniques to enhance Automated Transit Networks (ATN, previously called Personal Rapid Transit - PRT) based on Artificial Intelligence tools. The main direction is improvement of the cooperation of autonomous modules that use ... More
The $e$-vector of a simplicial complexJun 13 2018We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, $\Delta$, and we introduce the $e$-vector of $\Delta$, which relates to the coefficients of the exponential Hilbert ... More
Noncommutative probability of type DSep 05 2016Jan 01 2017We construct a deformed Fock space and a Brownian motion coming from Coxeter groups of type D. The construction is analogous to that of the $q$-Fock space (of type A) and the $(\alpha,q)$-Fock space (of type B).
Convolution, subordination and characterization problems in noncommutative probabilityApr 18 2015Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations in free probability to random variables with unbounded support. Using ... More
Noncommutative probability of type DSep 05 2016We construct a deformed Fock space and a Brownian motion coming from Coxeter groups of type D. The construction is analogous to that of the $q$-Fock space (of type A) and the $(\alpha,q)$-Fock space (of type B).
Fock space associated to Coxeter group of type BNov 28 2014In this article we construct a generalized Gaussian process coming from Coxeter groups of type B. It is given by creation and annihilation operators on an $(\alpha,q)$-Fock space, which satisfy the commutation relation $$ b_{\alpha,q}(x)b_{\alpha,q}^\ast(y)-qb_{\alpha,q}^\ast(y)b_{\alpha,q}(x)=\langle ... More
Accurate autocorrelation modeling substantially improves fMRI reliabilityNov 27 2017Sep 06 2018Given the recent controversies in some neuroimaging statistical methods, we compare the most frequently used functional Magnetic Resonance Imaging (fMRI) analysis packages: AFNI, FSL and SPM, with regard to temporal autocorrelation modeling. This process, ... More
Cooperation of Multiple Autonomous Robots and Analysis of their Swarm BehaviorDec 28 2018In this paper, we extended previous studies of cooperating autonomous robots to include situations when environmental changes and changes in the number of robots in the swarm can affect the efficiency to execute tasks assigned to the swarm of robots. ... More
Improving Resilience of Autonomous Moving Platforms by Real Time Analysis of Their CooperationMay 11 2017Environmental changes, failures, collisions or even terrorist attacks can cause serious malfunctions of the delivery systems. We have presented a novel approach improving resilience of Autonomous Moving Platforms AMPs. The approach is based on multi-level ... More
Quantitive and sociological analysis of blog networksJun 07 2005This paper examines the emerging phenomenon of blogging, using three different Polish blogging services as the base of the research. Authors show that blog networks are sharing their characteristics with complex networks gamma coefficients, small worlds, ... More
The new computer program for three dimensional relativistic hydrodynamical modelJan 30 2006Feb 09 2006An effective computer program for three dimensional relativistic hydrodynamical model has been developed. It implements a new approach to the early hot phase of relativistic heavy-ion collisions. The computer program simulates time-space evolution of ... More
Additive colorings of planar graphsFeb 03 2012Feb 06 2012An \emph{additive coloring} of a graph $G$ is an assignment of positive integers $\{1,2,...,k\}$ to the vertices of $G$ such that for every two adjacent vertices the sums of numbers assigned to their neighbors are different. The minimum number $k$ for ... More
Quasi-Linear-Time Algorithm for Longest Common Circular FactorJan 31 2019We introduce the Longest Common Circular Factor (LCCF) problem in which, given strings $S$ and $T$ of length $n$, we are to compute the longest factor of $S$ whose cyclic shift occurs as a factor of $T$. It is a new similarity measure, an extension of ... More
Magnetic anisotropy of epitaxial (Ga,Mn)As on (113)A GaAsFeb 02 2010Feb 08 2010The temperature dependence of magnetic anisotropy in (113)A (Ga,Mn)As layers grown by molecular beam epitaxy is studied by means of superconducting quantum interference device (SQUID) magnetometry as well as by ferromagnetic resonance (FMR) and magnetooptical ... More
Magnetization dynamics down to zero field in dilute (Cd,Mn)Te quantum wellsOct 17 2008The evolution of the magnetization in (Cd,Mn)Te quantum wells after a short pulse of magnetic field was determined from the giant Zeeman shift of spectroscopic lines. The dynamics in absence of magnetic field was found to be up to three orders of magnitude ... More
Structural and paramagnetic properties of dilute Ga1-xMnxNDec 21 2009Jul 21 2011Systematic investigations of the structural and magnetic properties of single crystal (Ga,Mn)N films grown by metal organic vapor phase epitaxy are presented. High resolution transmission electron microscopy, synchrotron x-ray diffraction, and extended ... More
GaMnN epitaxial films with high magnetizationMay 15 2012May 17 2012We report on the fabrication of pseudomorphic wurtzite GaMnN grown on GaN with Mn concentrations up to 10% using molecular beam epitaxy. According to Rutherford backscattering the Mn ions are mainly at the Ga-substitutional positions, and they are homogeneously ... More
Comprehensive evaluation of statistical speech waveform synthesisNov 15 2018Dec 11 2018Statistical TTS systems that directly predict the speech waveform have recently reported improvements in synthesis quality. This investigation evaluates Amazon's statistical speech waveform synthesis (SSWS) system. An in-depth evaluation of SSWS is conducted ... More
Human Tissues Investigation Using PALS TechniqueNov 13 2017Samples of uterine leiomyomatis and normal tissues taken from patients after surgery were investigated using the Positron Annihilation Lifetime Spectroscopy (PALS). Significant differences in all PALS parameters between normal and diseased tissues were ... More
Manipulating Mn--Mg$_k$ cation complexes to control the charge- and spin-state of Mn in GaNNov 13 2013Owing to the variety of possible charge and spin states and to the different ways of coupling to the environment, paramagnetic centres in wide band-gap semiconductors and insulators exhibit a strikingly rich spectrum of properties and functionalities, ... More