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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

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

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

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

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

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

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

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

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

The NMSSM lives: with the 750 GeV diphoton excessFeb 24 2016Apr 26 2016We propose an NMSSM scenario that can explain the excess in the diphoton spectrum at 750 GeV recently observed by ATLAS and CMS. We show that in a certain limit with a very light pseudoscalar one can reproduce the experimental results without invoking ... 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

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

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

Comments on: Antarctic Automatic Weather Station Program: 30 Years of Polar ObservationsMay 08 2013Recently Lazzara et al. (2012) presented a review of the technical and scientific progress in deployment, data collection and analysis of the Automated Weather Stations (AWS) in the Antarctic. In the subsection entitled Science Applications using AWS ... More

The Dynamics of Sex Ratio Evolution: From the Gene Perspective to Multilevel SelectionApr 19 2013Mar 02 2014The new dynamical game theoretic model of sex ratio evolution emphasizes the role of males as passive carriers of sex ratio genes. This shows inconsistency between population genetic models of sex ratio evolution and classical strategic models. In this ... More

Probing QCD chiral cross over transition in heavy ion collisions with fluctuationsJul 11 2012We argue that by measuring higher moments of the net proton number fluctuations in heavy ion collisions (HIC) one can probe the QCD chiral cross over transition experimentally. We discuss the properties of fluctuations of the net baryon number in the ... More

Forward physics hard processes and saturation: theory and phenomenology reviewDec 19 2011Selected aspects of the theory and phenomenology of production of forward jets at the LHC and RHIC are overviewed. In the theory part we discuss basics of frameworks originating from the BFKL dynamics while in the phenomenology part we present results ... More

A necessary condition for characteristic zero universal deformation rings of finite group representationsJul 15 2014We prove the following result related to the inverse problem for universal deformation rings of group representations: Given a finite field k, denote by W(k) the ring of Witt vectors over k and by K the field of fractions of W(k). If a complete noetherian ... More

Non-linear evolution equation for gluon density at large values of coupling constantJun 23 2014The recently proposed nonlinear evolution equation \cite{Kutak:2013hda} for unintegrated gluon densities valid for large values of the QCD coupling constant $\bar{\alpha} _s$ is presented. In particular we outline its derivation, numerical solution and ... More

Gluon saturation and entropy production in proton proton collisionsMar 18 2011Sep 29 2011We study properties of high energy factorisable gluon densities focusing on saturation effects. In particular we show that the property of saturation of unintegrated gluon density allows for introduction of thermodynamical entropy associated with production ... More

Accurate Born-Oppenheimer potential for HeH+Mar 18 2012We demonstrate high accuracy calculations for the HeH$^+$ molecule using newly developed analytic formulas for two-center two-electron integrals with exponential functions. The Born-Oppenheimer potential for the ground electronic $^1\Sigma^+$ state is ... More

Nuclear vector polarizability correction to hyperfine splittingJun 25 2007The interaction of orbital electrons with the charge and magnetic moment of the nucleus polarizes it, and the detailed description requires a careful treatment of the nuclear vector polarizability. We present a complete and closed form expression for ... More

Nuclear structure corrections in muonic deuteriumFeb 16 2011Mar 15 2011The muonic hydrogen experiment measuring the $2P-2S$ transition energy [R. Pohl {\em et al.}, Nature {\bf 466}, 213 (2010)] is significantly discrepant with theoretical predictions based on quantum electrodynamics. A possible approach to resolve this ... More

Born-Oppenheimer potential for H$_2$Jul 02 2010Sep 27 2010The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small distances James-Coolidge ... More

Studies of the Triple Pomeron Vertex in Perturbative QCD and Its Applications in PhenomenologyMar 06 2007We study the properties of the Triple Pomeron Vertex in the perturbative QCD using the twist expansion method. Such analysis allows us to find the momenta configurations preferred by the vertex. When the momentum transfer is zero, the dominant contribution ... More

Doped Spin Ladder: Zhang-Rice Singlets or Rung-centred Holes?Jan 17 2007We formulate charge transfer model for a single doped spin ladder, relevant for the intrinsically doped plane of coupled spin ladders in Sr$_{3}$Ca$_{11}$Cu$_{24}$O$_{41}$. Assuming the presence of the experimentally observed charge order in the system ... More

Polaron in the t-J Models with Three-Site Terms: the SU(2) and the Ising CasesJan 07 2009We compare the role of the three-site terms added to the t-J models in the SU(2) and the Ising cases in the extremely low doping regime, i.e. when a single hole added to the strongly interacting half-filled system becomes a polaron. We show that in the ... More

Degenerate minimal see-saw and leptogenesisJan 27 2004Feb 04 2004We analyze the most general version of the supersymmetric minimal see-saw model with only two right-chiral neutrinos which are degenerate in masses at the scale of Grand Unification. We study the renormalization effects that give rise to non-zero CP asymmetries ... More

Testing Distribution Identity EfficientlyOct 16 2009We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution on the same ... More

Universal formats for nonlinear dynamical systemsJan 15 1998It is demonstrated that very general nonlinear dynamical systems covering all cases arising in practice can be brought down to rate equations of chemical kinetics

Tail estimates of series of independent random variablesFeb 23 2015Variational formulas for tail estimates (rate functions) of series of independent random variables are given.

Explicitly correlated wavefunctions of the ground state and the lowest quintuplet state of carbon atomMar 14 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

Hard scale dependent gluon density, saturation and forward-forward dijet production at the LHCSep 12 2014Mar 27 2015We propose a method to introduce Sudakov effects to the unintegrated gluon density promoting it to be hard scale dependent. The advantage of the approach is that it guarantees that the gluon density is positive definite and that the Sudakov effects cancel ... More

Quark mass anomalous dimension and $Λ_{\overline{\textrm{MS}}}$ from the twisted mass Dirac operator spectrumNov 14 2013Jul 29 2014We investigate whether it is possible to extract the quark mass anomalous dimension and its scale dependence from the spectrum of the twisted mass Dirac operator in Lattice QCD. The answer to this question appears to be positive, provided that one goes ... More

Pencils of lines in generalized Laguerre spacesMar 30 2012In the paper we characterize subspaces and pencils of lines of generalized (and multidimensional) Laguerre spaces and we consider definability of the structure of "conic" pencils in the Grassmann space of 1-subspaces. We also study definability of the ... More

Differentiable functions on modules and the equation $grad(w)=Mgrad(v)$Jul 19 2016Let $A$ be a finite-dimensional, commutative algebra over $\mathbb{R}$ or $\mathbb{C}$. The notion of $A$-differentiable functions on $A$ is extended to the notion of $A$-differentiable functions on a finitely generated $A$-module $B$. Let $U$ be an open, ... More

Polynomial growth of the derivative for diffeomorphisms on toriMay 06 2002We consider area--preserving diffeomorphisms on tori with zero entropy. We classify ergodic area--preserving diffeomorphisms of the 3--torus for which the sequence $\{Df^n\}_{n\in{\Bbb N}}$ has polynomial growth. Roughly speaking, the main theorem says ... More

Effective method of computing Li's coefficients and their propertiesFeb 11 2004Jun 02 2004In this paper we present an effective method for computing certain real coefficients $\lambda_{n}$ which appear in a criterion for the Riemann hypothesis proved by Xian-Jin Li. With the use of this method a sequence of over three-thousand $\lambda_{n}$'s ... More

Behavioural present valueFeb 03 2013Impact of chosen behavioural factors on imprecision of present value is discussed here. The formal model of behavioural present value is offered as a result of this discussion. Behavioural present value is described here by fuzzy set. These considerations ... More

Simplified non-Navier-Stokes model of turbulent flow and its first numerical realization in D2Jul 27 2011This paper contains information about numerical realization of the model of turbulent flow proposed by Marek Burnat (see ARXIV: M.Burnat "On some mathematical model of turbulent flow with intensive selfmixing"). As an example the numerical experiment ... More

Limit distribution of the quartet balance index for Aldous's b>=0-modelMar 06 2018Nov 21 2018This paper builds up on T. Martinez-Coronado, A. Mir, F. Rossello and G. Valiente's work "A balance index for phylogenetic trees based on quartets", introducing a new balance index for trees. We show here that this balance index, in the case of Aldous's ... 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

Top Quark Physics at The Tevatron: Results and ProspectsJun 23 2004Measurements of the top quark mass and the t-tbar and single top production cross sections, obtained by CDF and D0 Collaboration at the Tevatron, are presented. The methodology of the CDF and D0 analyses and their underlying assumptions are summarized. ... More

The brightest gamma-ray flares of blazarsNov 01 2012Dec 27 2012I present a systematic study of gamma-ray flares in blazars. For this purpose, I propose a very simple and practical definition of a flare as a period of time, associated with a given flux peak, during which the flux is above half of the peak flux. I ... More

Computational indeterminism in complex models of social systemsAug 25 2012We argue that complex models with many parameters do not allow to infer about cause and effect.

Resummation in nonlinear equation for high energy factorizable gluon density and its extension to include coherenceJun 25 2012Nov 16 2012Motivated by forthcoming p-Pb experiments at Large Hadron Collider which require both knowledge of gluon densities accounting for saturation and for processes at a wide range of $p_t$ we study basic momentum space evolution equations of high energy QCD ... More

Hierarchy of Frustrations as Supplementary Indices in Complex System Dynamics, Applied to the U.S. IntermarketApr 12 2013Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S. Intermarket is chosen ... More

Comments on the Regional Climate Variability Driven by Foehn Winds in the McMurdo Dry Valleys, AntarcticaAug 21 2013Sep 03 2013The main objection to Speirs, McGowan, Steinhoff and Bromwich [Int. J. Climatol. 33: 945-958] work arises from the lack of analyses of the probability distribution functions of underlying processes leading to wind formation of which velocities are measured ... More

"ATLAS Overview and Main Results"May 20 2013May 24 2013An overview of the ATLAS experiment, its physics program and a selection of the most important results, based on the data taken in pp collisions at energies of 7 and 8 TeV in 2011 and 2012, respectively, is presented. The question of possible changes ... More

$α^4$ Ry corrections to singlet states of heliumJul 07 2006Corrections of order $\alpha^4$Ry are calculated for the singlet states $1^1S_0$ and $2^1S_0$ of the helium atom. The result for $1^1S_0$ state is in slight disagreement with that of Korobov and Yelkhovsky in [Phys. Rev. Lett. {\bf 87}, 193003 (2001)]. ... More

Higher-order effective Hamiltonian for light atomic systemsNov 18 2004We present the derivation of the effective higher-order Hamiltonian, which gives $m \alpha^6$ contribution to energy levels of an arbitrary light atom. The derivation is based on the Foldy-Wouthuysen transformation of the one-particle Dirac Hamiltonian ... More

A Central Limit Theorem for Punctuated EquilibriumFeb 16 2016May 11 2016Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated - the phenotype can jump. Such a jump can especially occur ... More

On the strong law of large numbers for $\varphi$-subgaussian random variablesJul 11 2016Oct 01 2016For $p\ge 1$ let $\varphi_p(x)=x^2/2$ if $|x|\le 1$ and $\varphi_p(x)=1/p|x|^p-1/p+1/2$ if $|x|>1$. For a random variable $\xi$ let $\tau_{\varphi_p}(\xi)$ denote $\inf\{a\ge 0:\;\forall_{\lambda\in\mathbb{R}}\; \ln\mathbb{E}\exp(\lambda\xi)\le\varphi_p(a\lambda)\}$; ... More

Stirring two grains of sandOct 05 2014Consider two unit balls in a $d$-dimensional flat torus with edge length $r$, for $d\geq 2$. The balls do not move by themselves but they are pushed by a Brownian motion. The balls never intersect---they reflect if they touch. It is proved that the joint ... More

Penney's game between many playersDec 17 2012May 04 2014We recall a combinatorial derivation of the functions generating probability of winnings for each of many participants of the Penney's game and show a generalization of the Conway's formula to this case.

On cocycles with values in the group SU(2)Feb 15 2000In this paper we introduce the notion of degree for $C^1$-cocycles over irrational rotations on the circle with values in the group SU(2). It is shown that if a $C^1$-cocycle $\phi:S^1\to SU(2)$ over an irrational rotation by $\alpha$ has nonzero degree, ... More

On nodal lines of Neumann eigenfunctionsMar 02 2002We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain. The technique is based on the `mirror coupling' of reflected Brownian motions.

On some generalization of the Möbius configurationOct 03 2013Apr 15 2014The M\"obius $(8_4)$ configuration is generalized in a purely combinatorial approach. We consider $(2n_n)$ configurations ${\goth M}_{(n,\varphi)}$ depending on a permutation $\varphi$ in the symmetric group $S_n$. Classes of non-isomorphic configurations ... More

Norms of sub-exponential random vectorsMar 31 2018Dec 06 2018We discuss various forms of the Luxemburg norm in spaces of random vectors with coordinates belonging to the classical Orlicz spaces of exponential type. We prove equivalent relations between some kinds of these forms. We also show when the so-called ... More

Multi-variate Quickest Detection of Significant Change ProcessNov 18 2011The paper deals with a mathematical model of a surveillance system based on a net of sensors. The signals acquired by each node of the net are Markovian process, have two different transition probabilities, which depends on the presence or absence of ... More

A general inequality for packings of boxesApr 20 2018Keller packings and tilings of boxes are investigated. Certain general inequality measuring a complexity of such systems is proved. A straightforward application to the unit cube tilings is given.

Báez-Duarte's Criterion for the Riemann Hypothesis and Rice's IntegralsMar 30 2006Apr 01 2006Criterion for the Riemann hypothesis found by B\'{a}ez-Duarte involves certain real coefficients $c_{k\text{}}$defined as alternating binomial sums. These coefficients can be effectively investigated using N\"{o}% rlund-Rice's integrals. Their behavior ... More

Congruences among modular forms on U(2,2) and the Bloch-Kato conjectureOct 12 2007Let k be a positive integer divisible by 4, l>k a prime, and f an elliptic cuspidal eigenform of weight k-1, level 4, and non-trivial character. Let \rho_f be the l-adic Galois representation attached to f. In this paper we provide evidence for the Bloch-Kato ... More

Helly's theorem for systolic complexesMay 20 2014We prove the analogue of Helly's theorem for systolic complexes. Namely, we show that 7-systolic complexes have Helly dimension less or equal to 1, whereas 6-systolic complexes have Helly dimension bounded from the above by 2.

On execution spaces of PV-programsFeb 16 2015Semaphores were introduced by Dijkstra as a tool for modeling concurrency in computer programs. In this paper we provide a formal definition of PV-programs, i.e. programs using semaphores, their state spaces and execution spaces. The main goal of this ... More

The phylogenetic effective sample size and jumpsSep 18 2018The phylogenetic effective sample size is a parameter that has as its goal the quantification of the amount of independent signal in a phylogenetically correlated sample. It was studied for Brownian motion and Ornstein-Uhlenbeck models of trait evolution. ... More

Weak lensing and the Dyer-Roeder approximationNov 17 2010The distance-redshift relation plays an important role in cosmology. In the standard approach to cosmology it is assumed that this relation is the same as in the homogeneous universe. As the real universe is not homogeneous there are several methods to ... More

Nonlinear dynamical systems and classical orthogonal polynomialsJan 14 1998It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schr\"odinger ... More