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One-loop corrections to three-body leptonic chargino decaysOct 09 2007Oct 17 2007We calculate full one-loop corrections to the genuine three-body decays of the light chargino \chi_1^\pm to \chi^0_1 l^\pm \nu in the Minimal Supersymmetric Standard Model. We find that the corrections to the decay width can be of the order of a few percent. ... More

CP violation in the chargino/neutralino sector of the MSSMApr 03 2008The CP-violating effects in the neutralino sector of the MSSM can be observed in event-counting type experiments, i.e. without the need of exploiting variables sensitive to beam or neutralino polarization. On the other hand, such CP-odd effects in the ... More

Light stops emerging in WW cross section measurements?Mar 22 2013Aug 12 2013Recent ATLAS and CMS measurements show a slight excess in the WW cross section measurement. While still consistent with the Standard Model within 1-2 sigma, the excess could be also a first hint of physics beyond the Standard Model. We argue that this ... More

Constraining compressed supersymmetry using leptonic signaturesJun 28 2012We study the impact of the multi-lepton searches at the LHC on supersymmetric models with compressed mass spectra. For such models the acceptances of the usual search strategies are significantly reduced due to requirement of large effective mass and ... More

Refining light stop exclusion limits with $W^+W^-$ cross sectionsMay 20 2015Sep 16 2015If light supersymmetric top (stop) quarks are produced at the LHC and decay via on- or off-shell $W$-bosons they can be expected to contribute to a precision $W^+W^-$ cross section measurement. Using the latest results of the CMS experiment, we revisit ... More

DeepXS: Fast approximation of MSSM electroweak cross sections at NLOOct 18 2018Jun 04 2019We present a deep learning solution to the prediction of particle production cross sections over a complicated, high-dimensional parameter space. We demonstrate the applicability by providing state-of-the-art predictions for the production of charginos ... More

CP violation in chargino production in e+e- collisionsOct 17 2007We present the analysis of CP-violating effects in non-diagonal chargino pair production in e+e- collisions. These effects appear only at the one-loop level. We show that CP-odd asymmetries in chargino production are sensitive to the phases of mu and ... More

Long-lived bino and wino in supersymmetry with heavy scalars and higgsinosJun 29 2015Oct 30 2015We point out that there is a parameter region in supersymmetry with heavy scalars and higgsinos, in which the heavier of bino and wino becomes long-lived as a consequence of the heavy higgsinos. In this region these electroweak gaugino sectors are secluded ... More

CP-violation in SUSY cascades at the LHCSep 01 2010We study the potential to observe CP-violating effects in SUSY cascade decay chains at the LHC. Asymmetries composed by triple products of momenta of the final state particles are sensitive to CP-violating effects. Due to large boosts that dilute the ... More

Neutralinos betray their singlino nature at the ILCJun 30 2014It is one of the most challenging tasks at the Large Hadron Collider and at a future Linear Collider not only to observe physics beyond the Standard Model, but to clearly identify the underlying new physics model. In this paper we concentrate on the distinction ... More

Tau-Sneutrino NLSP and Multilepton Signatures at the LHCMay 27 2010Oct 28 2010In models with gravitino as the lightest supersymmetric particle(LSP), the next to lightest supersymmetric particle (NLSP) can have a long lifetime and appear stable in collider experiments. We study the leptonic signatures of such a scenario with tau-sneutrino ... More

Proton decay testing low energy SUSYJul 20 2017We show that gauge coupling unification in SUSY models can make a non-trivial interconnection between collider and proton decay experiments. Under the assumption of precise gauge coupling unification in the MSSM, the low energy SUSY spectrum and the unification ... More

Can R-parity violation hide vanilla supersymmetry at the LHC?Sep 25 2012Jan 17 2013Current experimental constraints on a large parameter space in supersymmetric models rely on the large missing energy signature. This is usually provided by the lightest neutralino which stability is ensured by the R-parity. However, if the R-parity is ... More

Early spin determination at the LHC?Feb 01 2011Apr 03 2011If signals of new physics are discovered at the LHC it will be crucial to determine the spin structure of the new model. We discuss a method that can help to address this question with a low integrated luminosity, L=1 fb^-1, at sqrt{s}=14 TeV. Based on ... More

Momentum reconstruction at the LHC for probing CP-violation in the stop sectorAug 12 2010Jul 21 2011We study the potential to observe CP-violating effects in SUSY stop cascade decay chains at the LHC. Asymmetries composed by triple products of momenta of the final state particles are sensitive to CP-violating effects. Due to large boosts that dilute ... More

Towards Measuring the Stop Mixing Angle at the LHCSep 17 2009Jan 06 2011We address the question of how to determine the stop mixing angle and its CP-violating phase at the LHC. As an observable we discuss ratios of branching ratios for different decay modes of the light stop ~t_1 to charginos and neutralinos. These observables ... More

Gravitino vs Neutralino LSP at the LHCMay 14 2019Using the latest LHC data, we analyse and compare the lower limits on the masses of gluinos and the lightest stop in two natural supersymmetric motivated scenarios: one with a neutralino being the lightest supersymmetric particle (LSP) and the other one ... More

`Stop' that ambulance! New physics at the LHC?Jun 03 2014Dec 01 2014A number of LHC searches now display intriguing excesses. Most prominently, the measurement of the $W^+W^-$ cross-section has been consistently $\sim 20\%$ higher than the theoretical prediction across both ATLAS and CMS for both 7 and 8 TeV runs. More ... More

A new approach to gauge coupling unification and proton decayFeb 16 2019May 07 2019An analytical formalism, including RG running at two loop order, is used to link the supersymmetric and GUT spectra in any GUT model in which the three gauge couplings unify. In each specific GUT model, one can then fully explore the interplay between ... More

A new approach to gauge coupling unification and proton decayFeb 16 2019A novel analytical formalism is proposed, linking the supersymmetric and GUT spectra in any GUT model in which the three gauge couplings unify. In each specific GUT model, one can then fully explore the interplay between the pattern of supersymmetry breaking ... More

Polarization-independent CP-odd Observable in e^+e^- Chargino Production at One LoopSep 21 2007We discuss CP violation in the process e^+e^- \to \tilde\chi^+_i\tilde\chi^-_j with unpolarized beams. When the scalars are heavy, the box-diagram results constitute a major part of the full result. However, there are situations when the vertex and self-energy ... More

Model-independent combination of diphoton constraints at 750 GeVDec 21 2015Apr 27 2016Motivated by the recent diphoton excess reported by both the ATLAS and CMS collaborations, we provide a model-independent combination of diphoton results obtained at $\sqrt{s}=8$ and 13 TeV at the LHC. We consider resonant s-channel production of a spin-0 ... More

Towards discrimination of MSSM and NMSSM scenarios at collidersApr 03 2014One of the challenging tasks at future experiments is the clear identification of the underlying new physics model. In this study we concentrate on the distinction between different supersymmetric models, the MSSM and the NMSSM, exploring the gaugino/higgsino ... More

A framework to create customised LHC analyses within CheckMATEMar 03 2015Jun 02 2015Checkmate is a framework that allows the user to conveniently test simulated BSM physics events against current LHC data in order to derive exclusion limits. For this purpose, the data runs through a detector simulation and is then processed by a user ... More

Implications of light charginos for Higgs observables, LHC searches and dark matterMay 14 2013A rather high Higgs mass, m_h = 126 GeV, suggests that at least a part of the supersymmetric spectrum of the MSSM may live beyond O(1TeV) and hence inaccessible to the LHC. However, there are theoretical and phenomenological reasons supporting a possibility ... More

Reducing the fine-tuning of gauge-mediated SUSY breakingFeb 22 2016Aug 30 2016Despite their appealing features, models with gauge-mediated supersymmetry breaking (GMSB) typically present a high degree of fine-tuning, due to the initial absence of the top trilinear scalar couplings, $A_t=0$. In this paper, we carefully evaluate ... More

The BSM-AI project: SUSY-AI - Generalizing LHC limits on Supersymmetry with Machine LearningMay 09 2016Jun 22 2016A key research question at the Large Hadron Collider (LHC) is the test of models of new physics. Testing if a particular parameter set of such a model is excluded by LHC data is a challenge: It requires the time consuming generation of scattering events, ... More

Natural SUSY: Now or Never?Jun 21 2016As we anticipate the first results of the 2016 run, we assess the discovery potential of the LHC to `natural supersymmetry'. To begin with, we explore the region of the model parameter space that can be excluded with various centre-of-mass energies (13 ... More

MSSM parameter determination via chargino production at the LC: NLO correctionsAug 07 2012Very precise measurements of masses and cross sections, with errors of <1%, are expected to be achievable with a future linear collider. Such an accuracy gives sensitivity at the level of quantum corrections, which therefore must be incorporated in order ... More

DeepXS: Fast approximation of MSSM electroweak cross sections at NLOOct 18 2018We present a deep and active learning solution to the prediction of particle production cross sections over a complicated, high-dimensional parameter space. We demonstrate the applicability by providing state-of-the-art predictions for the production ... More

CheckMATE 2: From the model to the limitNov 29 2016Feb 28 2017We present the latest developments to the CheckMATE program that allows models of new physics to be easily tested against the recent LHC data. To achieve this goal, the core of CheckMATE now contains over 60 LHC analyses of which 12 are from the 13 TeV ... More

One-loop effects on MSSM parameter determination via chargino production at the LCNov 15 2012Mar 20 2013At a future linear collider, very precise measurements, typically with errors of <1%, are expected to be achievable. Such an accuracy yields sensitivity to quantum corrections, which therefore must be incorporated into theoretical calculations in order ... More

CheckMATE 2: From the model to the limitNov 29 2016We present the latest developments to the CheckMATE program that allows models of new physics to be easily tested against the recent LHC data. To achieve this goal, the core of CheckMATE now contains over 60 LHC analyses of which 12 are from the 13 TeV ... More

The BSM-AI project: SUSY-AI - Generalizing LHC limits on Supersymmetry with Machine LearningMay 09 2016Apr 26 2017A key research question at the Large Hadron Collider (LHC) is the test of models of new physics. Testing if a particular parameter set of such a model is excluded by LHC data is a challenge: It requires the time consuming generation of scattering events, ... More

Confronting dark matter with the diphoton excess from a parent resonance decayMar 14 2016A diphoton excess with an invariant mass of about 750 GeV has been recently reported by both ATLAS and CMS experiments at LHC. While the simplest interpretation requires the resonant production of a 750 GeV (pseudo)scalar, here we consider an alternative ... More

Tackling light higgsinos at the ILCJul 12 2013Dec 10 2013In supersymmetric extensions of the Standard Model, higgsino-like charginos and neutralinos are preferred to have masses of the order of the electroweak scale by naturalness arguments. Such light $\widetilde{\chi}^0_1$, $\widetilde{\chi}^0_2$ and $\widetilde{\chi}^{\pm}_1$ ... More

Characterizing Invisible Electroweak Particles through Single-Photon Processes at High Energy $e^+e^-$ CollidersMar 30 2015We explore the scenarios where the only accessible new states at the electroweak scale consist of a pair of color-singlet electroweak particles, whose masses are degenerate at the tree level and split only by electroweak symmetry breaking at the loop ... More

What is a Natural SUSY scenario?Jul 25 2014Jul 06 2015The idea of "Natural SUSY", understood as a supersymmetric scenario where the fine-tuning is as mild as possible, is a reasonable guide to explore supersymmetric phenomenology. In this paper, we re-examine this issue in the context of the MSSM including ... More

Measurement of CP Violation in the MSSM Neutralino Sector with the ILDJan 25 2012Supersymmetric models provide many new complex phases which lead to CP violating effects in collider experiments. As an example, CP-sensitive triple product asymmetries in neutralino production and subsequent leptonic two-body decays are studied within ... More

Prospects for natural SUSYJun 21 2016Dec 14 2016As we anticipate the first results of the 2016 run, we assess the discovery potential of the LHC to `natural supersymmetry'. To begin with, we explore the region of the model parameter space that can be excluded with various centre-of-mass energies (13 ... More

Complementarity of Resonant Scalar, Vector-Like Quark and Superpartner Searches in Elucidating New PhenomenaAug 03 2016Aug 29 2016The elucidation of the nature of new phenomena requires a multi-pronged approach to understand the essential physics that underlies it. As an example, we study the simplified model containing a new scalar singlet accompanied by vector-like quarks, as ... More

Bounded confidence model: addressed information maintain diversity of opinionsJan 11 2011Dec 15 2011A community of agents is subject to a stream of messages, which are represented as points on a plane of issues. Messages are sent by media and by agents themselves. Messages from media shape the public opinion. They are unbiased, i.e. positive and negative ... More

Paradox of integration---Cellular automata approachJun 02 2019We discuss the self-deprecating strategy introduced by Peter Blau as one of stages of the process of social integration. Recently we have introduced a two-dimensional space of status, real and surface one ($A$ and $B$), and we have demonstrated that with ... More

Black-Litterman model with intuitionistic fuzzy posterior returnJan 03 2016The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. ... More

Multiplied configurations characterized by their closed substructuresMar 11 2012We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled "Multiplied configurations, ... More

Anderson localization of a Rydberg electron along a classical orbitMar 24 2017May 12 2017Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum suppression of classical ... More

Mental ability and common sense in an artificial societyMar 24 2014We read newspapers and watch TV every day. There are many issues and many controversies. Since media are free, we can hear arguments from every possible side. How do we decide what is wrong or right? The first condition to accept a message is to understand ... More

Multiplied configurations, series induced by quasi difference setsMar 16 2012Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of another configuration. ... More

On the strong law of large numbers for dependent subgaussian random variablesJul 11 2016Let $\sigma>0$ and $p>1$. We call a random variable $X$ to be {\it $\sigma$-subgaussian of rank $p$} if $\ln\mathbb{E}\exp(sX)\le \sigma^ps^p/p$. When $p=2$ we have exactly the subgaussian case. Let $(X_n)$ be a sequence of $\sigma_n$-subgaussian random ... More

The effect of inhomogeneities on the distance to the last scattering surface and the accuracy of the CMB analysisJan 17 2011The standard analysis of the CMB data assumes that the distance to the last scattering surface can be calculated using the distance-redshift relation as in the Friedmann model. However, in the inhomogeneous universe, even if <\delta\rho> =0, the distance ... More

From chemical freezeout to critical conditions in heavy ion collisionsJun 23 2004Jun 24 2004We compare the statistical thermodynamics of hadron resonance gas with recent LGT results at finite chemical potential. We argue that for $T\leq T_c$ the equation of state derived from Monte--Carlo simulations of two quark--flavor QCD at finite chemical ... More

Polarization of synchrotron emission from relativistic reconfinement shocksJan 26 2009We study the polarization properties of relativistic reconfinement shocks with chaotic magnetic fields. Using our hydrodynamical model of their structure, we calculate synthetic polarization maps, longitudinal polarization profiles and discuss the spatially ... More

Decoupling, lepton flavour violation and leptogenesisMay 10 2005Several classes of neutrino mass models, which can naturally account for hierarchical masses and the bi-large pattern of neutrino mixing, are constructed from a bottom-up perspective based on the idea of decoupling of one right-chiral neutrino from the ... More

Saturation effects in QCD from linear transport equationSep 09 2010We show that the GBW saturation model provides an exact solution to the one-dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the ... More

Derivation of the relativistic momentum and relativistic equation of motion from Newton's second law and Minkowskian space-time geometrySep 17 2013Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion $\vec{F}=d\vec{p}/dt$, where ... More

A way to discover Maxwell's equations theoreticallyAug 23 2013The Coulomb force, established in the rest frame of a source-charge $Q$, when transformed to a new frame moving with a velocity $\vec{V}$ has a form $\vec{F}= q\vec{{E}} + q\vec{v} \times \vec{{B}}$, where $\vec{{E}}=\vec{E}'_\parallel + \gamma\vec{E}'_\perp ... More

Dissipation Efficiency of Reconfinement Shocks in Relativistic JetsOct 31 2011We calculate the dissipation efficiency of relativistic reconfinement shocks. Building on previous work (Nalewajko & Sikora 2009), we consider different distributions of the external pressure. The average dissipation efficiency epsilon_diss is a function ... More

A Note on Several Meteorological Topics Related to Polar RegionsAug 18 2011Analysis of the meteorology of Polar Regions is fundamental to the process of understanding the global climatology of the Earth and Earth-like planets. The nature of air circulation in a polar vortex is of preliminary importance. I have show that the ... More

Polarization swings from curved trajectories of the emitting regionsAug 27 2012We present a model of polarization swings in blazars from axially symmetric blobs propagating on curved trajectories. If the minimum inclination of the velocity vector to the line of sight is smaller than Gamma^{-1}, the polarization angle maximum rotation ... More

Nonlinear extension of the CCFM equationJun 06 2012In order to study such effects like parton saturation in final states at the LHC one of the approaches is to combine physics of the BK and the CCFM evolution equations. We report on recently obtained resummed form of the BK equation and nonlinear extension ... More

Some aspects of final states and QCD evolution equationsNov 16 2012In order to study such effects like parton saturation in final states at the LHC one of the approaches is to combine physics of the BK and the CCFM evolution equations. We report on recently obtained resummed form of the BK equation and nonlinear extension ... More

Definable topological dynamicsFeb 17 2016For a group $G$ definable in a first order structure $M$ we develop basic topological dynamics in the category of definable $G$-flows. In particular, we give a description of the universal definable $G$-ambit and of the semigroup operation on it. We find ... More

The Laplace Motion in Phylogenetic Comparative MethodsMar 06 2014The majority of current phylogenetic comparative methods assume that the stochastic evolutionary process is homogeneous over the phylogeny or offer relaxations of this in rather limited and usually parameter expensive ways. Here we make a preliminary ... More

Origin of the thermodynamic time arrow demonstrated in a realistic statistical systemSep 19 2013Emergence of one-time-direction macroscopic evolution of a classical system of two mixed gases having different temperatures is derived and explained. The analysis performed at the microscopic level, where the time-symmetric laws of mechanics govern the ... More

Fluctuation Relations in Stochastic ThermodynamicsAug 07 2013Fluctuation relations are identities, holding in non-equilibrium systems, that have attracted a lot of interest in the last 20 years. This is a series of 4 lectures discussing various aspects of such relations for stochastic equations modeling non-equilibrium ... More

Random iteration and projection methodJul 23 2013We show that under suitable conditions a random orbit generated by a system of nonexpansive maps recovers an invariant set via its omega-limit. In particular, this explains what happens to the Kaczmarz--von Neumann projection algorithm in the infeasible ... More

Finite nuclear mass corrections to electric and magnetic interactions in diatomic moleculesNov 25 2009In order to interpret precise measurements of molecular properties the finite nuclear mass corrections to the Born-Oppenheimer approximation have to be accounted for. It is shown that they can be obtained systematically in the perturbative approach. The ... More

Two-center two-electron integrals with exponential functionsMay 11 2009Sep 29 2009We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single negative power ... More

Correlated exponential functions in high precision calculations for diatomic moleculesSep 06 2012Nov 29 2012Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation ... More

Cobordisms with chronologies and a generalisation of the Khovanov complexApr 06 2010There are two categorifications of the Jones polynomial: "even" discovered by M.Khovanov in 1999 and "odd" dicovered by P.Ozsvath, J.Rasmussen and Z.Szabo in 2007. The first one can be fully constructed in the category of cobordisms (strictly: in the ... More

Fast approximation of solutions of SDE's with oblique reflection on an orthantDec 02 2008We consider the discrete "fast" penalization scheme for SDE's driven by general semimartingale on orthant $\mathbb{R}_{+}^{d}$ with oblique reflection.

Explicitly correlated wavefunctions of the ground state and the lowest quintuplet state of the carbon atomMar 14 2019Mar 16 2019Variational, nonrelativisitic energies have been calculated for the ground state ($^3P_g$) and the lowest quintuplet state ($^5S_u$) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated Gaussian (ECG) ... More

Cosmological backreaction within the Szekeres model and emergence of spatial curvatureApr 10 2017Jun 13 2017This paper discusses the phenomenon of backreaction within the Szekeres model. Cosmological backreaction describes how the mean global evolution of the Universe deviates from the Friedmannian evolution. The analysis is based on models of a single cosmological ... More

Square root of gerbe holonomy and invariants of time-reversal-symmetric topological insulatorsFeb 20 2017The Feynman amplitudes with the two-dimensional Wess-Zumino action functional have a geometric interpretation as bundle gerbe holonomy. We present details of the construction of a distinguished square root of such holonomy and of a related 3d-index and ... More

Production of four-jets in single- and double-parton scattering within high-energy factorizationJan 02 2017Feb 24 2017We report on a first study of 4-jet production in a high energy factorization (HEF) framework \cite{Kutak:2016mik,Kutak:2016ukc}. We include and discuss contributions from both single-parton scattering (SPS) and double-parton scattering (DPS) and compare ... More

Parallel multiple selection by regular samplingNov 17 2016Nov 18 2016In this paper we present a deterministic parallel algorithm solving the multiple selection problem in congested clique model. In this problem for given set of elements S and a set of ranks $K = \{k_1 , k_2 , ..., k_r \}$ we are asking for the $k_i$-th ... More

Applying Relativistic Reconnection to Blazar JetsSep 06 2016Rapid and luminous flares of non-thermal radiation observed in blazars require an efficient mechanism of energy dissipation and particle acceleration in relativistic active galactic nuclei (AGN) jets. Particle acceleration in relativistic magnetic reconnection ... More

Building an Internet Radio System with Interdisciplinary factored system for automatic content recommendationApr 01 2016Automatic systems for music content recommendation have assumed a new role in recent years. These systems have transformed from being just a convenient, standalone tool into an inseparable element of modern living. In addition, not only do these systems ... More

Impact of overlapping resonances on magnetoassociation of cold molecules in tight trapsFeb 19 2016Sep 21 2016Overlapping Feshbach resonances are commonly observed in experiments with ultracold atoms and can influence the molecule production process. We derive an effective approach to describe magnetoassociation in an external trap in the presence of multiple ... More

On norms in some class of exponential type Orlicz spaces of random variablesSep 09 2017Feb 26 2019A new characteristics of the exponential type Orlicz spaces generated by some exponential functions is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with the Luxemburg norms. On the ... More

Emergence of spatial curvatureJul 06 2017Aug 31 2017This paper investigates the phenomenon of emergence of spatial curvature. This phenomenon is absent in the Standard Cosmological Model, which has a flat and fixed spatial curvature (small perturbations are considered in the Standard Cosmological Model ... More

Selected Methods for non-Gaussian Data AnalysisNov 23 2018Feb 08 2019The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the case of univariate ... More

Analytical Representations of Divisors of IntegersFeb 25 2017Mar 26 2017Certain analytical expressions which "feel" the divisors of natural numbers are investigated. We show that these expressions encode to some extent the well-known algorithm of the sieve of Eratosthenes. Most part of the text is written in pedagogical style, ... More

Adelic Maass spaces on U(2,2)Jun 19 2007Generalizing the results of Kojima, Gritsenko and Krieg, we define an adelic version of the Maass space for hermitian modular forms of weight k regarded as functions on adelic points of the quasi-split unitary group U(2,2) associated with an imaginary ... More

On return rate implied by behavioural present valueFeb 03 2013The future value of a security is described as a random variable. Distribution of this random variable is the formal image of risk uncertainty. On the other side, any present value is defined as a value equivalent to the given future value. This equivalence ... More

Fejer's approximation of continuous functions of unitary operatorsMar 08 2014This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary operator we give a ... More

Simulating an infinite mean waiting timeJul 23 2019We consider a hybrid method to simulate the return time to the initial state in a critical-case birth--death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach ... More

Effects of uniform acceleration on quantum states and vacuum entanglement in relativistic quantum informationAug 16 2019In this thesis we focus on the influence of uniform acceleration on quantum states and their properties, as well as on quantum entanglement contained in the vacuum. First, we analyze a quantum clock measuring time in terms of the decay of an unstable ... More

Option pricing in constant elasticity of variance model with liquidity costsSep 21 2014Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The Goal of this ... More

Spaces of directed paths on pre-cubical setsMay 26 2016The spaces of directed paths on the geometric realizations of pre-cubical sets, called also $\square$--sets, can be interpreted as the spaces of possible executions of Higher Dimensional Automata, which are models for concurrent computations. In this ... More

Directed path spaces via discrete vector fieldsAug 07 2017Let $K$ be an arbitrary semi-cubical set that can be embedded in a standard cube. Using Discrete Morse Theory, we construct a CW-complex that is homotopy equivalent to the space $\vec{P}(K)_v^w$ of directed paths between two given vertices $v,w$ of $K$. ... More

Recurrence for smooth curves in the moduli space and application to the billiard flow on nibbled ellipsesApr 29 2019In view of classical results of Masur and Veech almost every element in the moduli space of compact translation surfaces is recurrent. In this paper we focus on the problem of recurrence for elements of smooth curves in the moduli space. We give an effective ... More

Density of mild mixing property for vertical flows of Abelian differentialsMar 19 2009We prove that if $g\geq 2$ then the set of all Abelian differentials $(M,\omega)$ for which the vertical flow is mildly mixing is dense in every stratum of the moduli space $\mathcal{H}_g$. The proof is based on a sufficient condition for special flows ... More

A rank-based selection with cardinal payoffs and a cost of choiceDec 18 2008A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables $X_1,X_2,...,X_n$ from a uniform distribution on $[0; 1]$, are observed sequentially by the grader. He has to ... More

Cramér transform of Rademacher seriesAug 12 2014Nov 14 2014A variational formula for the Cram\'er transform of series of weighted, independent symmetric Bernoulli random variables (Rademacher series) is given.

On $k$-transitive closures of directed pathsDec 23 2014In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.

Maass spaces on U(2,2) and the Bloch-Kato conjecture for the symmetric square motive of a modular formNov 08 2011Let K be an imaginary quadratic field of discriminant -D_K<0. We introduce a notion of an adelic Maass space S_{k, -k/2}^M for automorphic forms on the quasi-split unitary group U(2,2) associated with K and prove that it is stable under the action of ... More

Definable topological dynamicsFeb 17 2016Mar 24 2017For a group $G$ definable in a first order structure $M$ we develop basic topological dynamics in the category of definable $G$-flows. In particular, we give a description of the universal definable $G$-ambit and of the semigroup operation on it. We find ... More

Entropy and Optimization of PortfoliosAug 01 2014We briefly review the approach to optimization of portfolios according to the theory of Markowitz and propose a further modification that can improve the outcome of the optimization process. The modification takes account of the entropic contribution ... More

Non-resonant driving of H atom with broken time-reversal symmetryMay 15 2000The dynamics of atomic hydrogen placed in a static electric field and illuminated by elliptically polarized microwaves is studied in the range of small field amplitudes where perturbation calculations are applicable. For a general configuration of the ... More