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Towards room temperature indistinguishable single-photon sources using ultra-small mode volume cavities and solid-state emittersOct 10 2017Efficient sources of indistinguishable single photons that can operate at room temperature would be highly beneficial for many applications in quantum technology. We show that the implementation of such sources is a realistic goal using solid-state emitters ... More

Interfacing microwave qubits and optical photons via spin ensemblesJan 23 2015A protocol is discussed which allows one to realize a transducer for single photons between the optical and the microwave frequency range. The transducer is a spin ensemble, where the individual emitters possess both an optical and a magnetic-dipole transition. ... More

Interfacing Superconducting Qubits and Telecom Photons via a Rare-Earth Doped CrystalFeb 21 2014Jul 25 2014We propose a scheme to couple short single photon pulses to superconducting qubits. An optical photon is first absorbed into an inhomogeneously broadened rare-earth doped crystal using controlled reversible inhomogeneous broadening. The optical excitation ... More

Electron Spin Coherences in Rare-Earth Optically Excited States for Microwave to Optical Quantum TransducersFeb 09 2018Efficient and reversible optical to microwave coherent transducers are required to enable entanglement transfer between superconducting qubits and light for quantum networks. Rare-earth-doped crystals that possess narrow optical and spin transitions are ... More

Anomalous quark-gluon chromomagnetic interaction and high energy $ρ$-meson electroproductionNov 08 2011Feb 21 2012It is shown that existence of a large anomalous chromomagnetic moment of quark induced by non-perturbative structure of QCD leads to the additional contribution to exclusive $\rho$-meson electroproduction off proton target. The significant contribution ... More

Optimal data recovery and forecasting with dummy long-horizon forecastsApr 29 2016The paper suggests a method of recovering of missing values based on optimal approximation by band-limited processes for sequences, i.e. discrete time processes, that are not necessarily band-limited. The problem is considered in the pathwise setting, ... More

On statistical indistinguishability of complete and incomplete discrete time market modelsMay 04 2015We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete ... More

A paradox of diffusion market model related with existence of winning combinations of optionsMar 19 2001We consider strategies of investments into options and diffusion market model. It is shown that there exists a correct proportion between "put" and "call" in the portfolio such that the average gain is almost always positive for a generic Black and Scholes ... More

Glueball dynamics in the hot plasmaJan 20 2016Apr 20 2016We discuss the glueball contribution to the equation of state (EoS) of hot gluon matter below and above $T_c$. It is shown that the strong changing of masses of scalar and pseudoscalar glueballs near $T_c$ plays very important role in the thermodynamics ... More

Stochastic Theory of Foreign Exchange Market DynamicsSep 29 1999A new stochastic theory of a foreign exchange markets dynamics is developed. As a result we have the new probability distribution which well describes statistical and scaling dependencies ''experimentally'' observed in foreign exchange markets in recent ... More

Pathwise estimation of the diffusion term for Cox-Ingersoll-Ross and similar processesJun 18 2015Jun 19 2015We consider estimation of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some new pathwise estimates for this coefficient and for the power ... More

Classifying Vectoids and Generalisations of OperadsMay 16 2011A new generalisation of the notion of space, called "vectoid", is suggested in this work. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated properties not used ... More

A maximization problem in tropical mathematics: a complete solution and application examplesApr 28 2013A multidimensional optimization problem is formulated in the tropical mathematics setting as to maximize a nonlinear objective function, which is defined through a multiplicative conjugate transposition operator on vectors in a finite-dimensional semimodule ... More

Solution of linear equations and inequalities in idempotent vector spacesMay 18 2013Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The approach reduces ... More

On recovering parabolic diffusions from their time-averagesSep 07 2016Oct 11 2016The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed ... More

First Order BSPDEs: examples in higher dimensionMar 22 2016May 17 2016The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations)suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman equations and allow ... More

The structure of optimal portfolio strategies for continuous time marketsMay 08 2011Apr 14 2014The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed ... More

Precision calculations for Higgs-boson production at hadron collidersSep 21 2012The next-to-next-to-leading order (NNLO) calculation of the effective Higgs gluon coupling $C_1$ for the lightest Minimal Supersymmetric Standard Model (MSSM) Higgs boson $h^0$ is presented. Selected numerical results for the total production cross section ... More

CHICOM: A code of tests for comparing unweighted and weighted histograms and two weighted histogramsMay 06 2011Oct 10 2011A self-contained Fortran-77 program for calculating test statistics to compare weighted histogram with unweighted histogram and two histograms with weighted entries is presented. The code calculates test statistics for cases of histograms with normalized ... More

Universal estimate of the gradient for parabolic equationsSep 06 2007Apr 29 2008We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient. More precisely, we found the upper limit estimate ... More

A tropical extremal problem with nonlinear objective function and linear inequality constraintsDec 26 2012We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear ... More

Predictors for time series with energy decay on higher frequenciesDec 07 2011Aug 07 2012The predictability of discrete-time processes is studied in a deterministic setting. A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies. For such processes, the prediction error can be made ... More

On the no-arbitrage market and continuity in the Hurst parameterSep 22 2015Oct 13 2015We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we ... More

Continuity of Dirac SpectraMar 26 2013It is a well-known fact that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article we extend this result to a global version. We ... More

Strong interaction effects in semileptonic B decaysOct 02 2002Strong interaction effects are addressed in connection to extracting |V_{cb}|. A comprehensive approach is described not relying on a 1/m_c expansion; it allows a percent accuracy without ad hoc assumptions about higher-order effects. An alternative to ... More

Topics in the Heavy Quark ExpansionOct 30 2000Nov 06 2000Achievements in the heavy quark theory over the last decade are reviewed, with the main emphasis put on dynamical methods which quantify nonperturbative effects via application of the Operator Product Expansion. These include the total weak decay rates ... More

Perturbative corrections to the semileptonic b-decay moments: E^\ell_{cut} dependence and running-α_s effects in the OPE approachMar 15 2004We have calculated the perturbative corrections to all the structure functions in the semileptonic decays of a heavy quark. Assuming an arbitrary gluon mass as a technical tool allowed to obtain in parallel all the BLM corrections. We report the basic ... More

On the chromomagnetic expectation value μ_G^2 and higher power corrections in heavy flavor mesonsNov 13 2001Nov 25 2001The important parameter \mu_G^2 of the heavy quark expansion is analyzed including perturbative and power corrections. It is found that \mu_G^2(2GeV) is known with a few percent accuracy. The perturbative corrections are computed and found small. A nonperturbative ... More

Universality of Fedosov's Construction for Star Products of Wick Type on Pseudo-Kähler ManilfoldsApr 02 2002Feb 06 2003In this paper we construct star products on a pseudo-K\"ahler manifold $(M,\omega,I)$ using a modification of the Fedosov method based on a different fibrewise product similar to the Wick product on $\mathbb C^n$. In a first step we show that this construction ... More

On a lower bound of the Kobayashi metricDec 17 2015It is shown that a lower bound of the Kobayashi metric of convex domains in C^n does not hold for non-convex domains.

On martingale measures and pricing for continuous bond-stock market with stochastic bondAug 03 2011Sep 30 2014This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small stochastic deviations ... More

Complete algebraic solution of multidimensional optimization problems in tropical semifieldJun 02 2017May 26 2018We consider multidimensional optimization problems that are formulated in the framework of tropical mathematics to minimize functions defined on vectors over a tropical semifield (a semiring with idempotent addition and invertible multiplication). The ... More

Methods of tropical optimization in rating alternatives based on pairwise comparisonsAug 09 2016Aug 14 2017We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when ... More

On recovering missing values for sequences in a pathwise settingApr 18 2016Sep 18 2018The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability for classes ... More

Mutual Fund Theorem for continuous time markets with random coefficientsNov 17 2009We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, ... More

Distributed Control Subject to Delays Satisfying an $\mathcal{H}_\infty$ Norm BoundFeb 07 2014Feb 10 2014This paper presents a characterization of distributed controllers subject to delay constraints induced by a strongly connected communication graph that achieve a prescribed closed loop $\mathcal{H}_\infty$ norm. Inspired by the solution to the $\mathcal{H}_2$ ... More

Floer homology of Brieskorn homology spheres: solution to Atiyah's problemJan 24 1997In this paper we answer the question posed by M.~Atiyah and give an explicit formula for Floer homology of Brieskorn homology spheres in terms of their branching sets over the 3--sphere. We further show how Floer homology is related to other invariants ... More

A multidimensional tropical optimization problem with nonlinear objective function and linear constraintsMar 03 2013Nov 03 2013We examine a multidimensional optimisation problem in the tropical mathematics setting. The problem involves the minimisation of a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear inequality ... More

Optimal replication of random vectors by ordinary integralsAug 07 2012Aug 08 2012We consider a problem of replication of random vectors by ordinary integrals in the setting when a underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral at a fixed ... More

Optimal energy storing and selling in continuous time stochastic multi-battery settingNov 04 2015May 23 2016We consider the problem of optimal energy storing and dispatching for a grid-connected energy producer with battery energy storage system (BESS). We suggests an optimal operating algorithm that helps to increase the income given limited storage capacity ... More

An algebraic approach to multidimensional minimax location problems with Chebyshev distanceNov 11 2012Minimax single facility location problems in multidimensional space with Chebyshev distance are examined within the framework of idempotent algebra. The aim of the study is twofold: first, to give a new algebraic solution to the location problems, and ... More

Bottom Quark Mass from $Υ$ Sum Rules to ${\cal O}(α_s^3)$Jun 30 2014We present the deterimination of the bottom quark mass using non-relativistic $\Upsilon$ Sum Rules at $\text{N}^3\text{LO}^*$[1]. The explicit dependence of $\overline{m}_b(\overline{m}_b)$ on the input value $\alpha_s(M_Z)$ is given for the first time. ... More

On the nature of QPO phase lags in black hole candidatesMay 03 2012Observations of quasi-periodic oscillations (QPOs) in X-ray binaries hold a key to understanding many aspects of these enigmatic systems. Complex appearance of the Fourier phase lags related to QPOs is one of the most puzzling observational effects in ... More

Optimal portfolio with unobservable market parameters and certainty equivalence principleFeb 09 2015We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather use historical ... More

Extremal properties of tropical eigenvalues and solutions to tropical optimization problemsNov 03 2013Apr 03 2014An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum ... More

A complete closed-form solution to a tropical extremal problemOct 12 2012A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two other known problems ... More

Algebraic solutions to multidimensional minimax location problems with Chebyshev distanceDec 25 2012Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The ... More

Hyperfine splitting in the bottomonium system on the lattice and in the continuumNov 16 2015The latest experimental measurements of the hyperfine splitting $E_{\rm{hfs}}=M_{\Upsilon(1 S)}-M_{\eta_b(1 S)}$ done by the Belle collaboration and the perturbative and lattice QCD predictions show a tension with the current extraction within lattice ... More

On recovering missing values in a pathwise settingApr 18 2016Apr 21 2016The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e., discrete time processes, in a pathwise setting, without using probabilistic assumptions on the ensemble. This setting targets situations where ... More

Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on a bounded domainNov 26 2014An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on bounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data are proven.

Universal estimates for parabolic equations and applications for non-linear and non-local problemsMay 08 2008We obtain some "universal" estimates for $L_2$-norm of the solution of a parabolic equation via a weighted version of $H^{-1}$-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation of the equation ... More

Cordes conditions and some alternatives for parabolic equations and discontinuous diffusionApr 29 2008The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a solution for ... More

On forward and backward SPDEs with non-local boundary conditionsJul 31 2013We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the ... More

Backward SPDEs with non-local in time and space boundary conditionsNov 07 2012Jul 31 2013We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability and regularity ... More

On almost surely periodic and almost periodic solutions of backward SPDEsAug 28 2012Jul 31 2013We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is replaced by a condition that holds almost surely and mixes the random ... More

QCD Corrections in Gamma_sl(B)Oct 30 2002Dec 31 2002Short-distance expansion of the total semileptonic B widths is reviewed for the OPE-conformable scheme employing low-scale running quark masses. The third- and fourth-order BLM corrections are given and the complete resummation of the BLM series presented. ... More

Recent Advances in Semileptonic B DecaysSep 09 2003Aspects of the OPE-based QCD theory of B decays are discussed. We have at least one nontrivial precision check of the OPE at the nonperturbative level in inclusive decays. The data suggest proximity to the `BPS' limit for B mesons. Its consequences are ... More

Two remarks on the Suita conjectureNov 24 2014It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1+\varepsilon_-}$-smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely ... More

Comparison of invariant functions on strongly pseudoconvex domainsDec 11 2012Nov 28 2014It is shown that the Carath\'eodory distance and the Lempert function are almost the same on any strongly pseudoconvex domain in $\C^n;$ in addition, if the boundary is $C^{2+\eps}$-smooth, then $\sqrt{n+1}$ times one of them almost coincides with the ... More

Invariant functions and metrics in complex analysisSep 07 2011Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$

Controlled options: derivatives with added flexibilityDec 07 2010Oct 14 2011The paper introduces a limit version of multiple stopping options such that the holder selects dynamically a weight function that control the distribution of the payments (benefits) over time. In applications for commodities and energy trading, a control ... More

On strong binomial approximation for stochastic processes and applications for financial modellingNov 04 2013Feb 06 2015This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., ... More

Algebraic solution of weighted minimax single-facility constrained location problemsOct 24 2018We consider location problems to find the optimal sites of placement of a new facility, which minimize the maximum weighted Chebyshev or rectilinear distance to existing facilities under constraints on the feasible location domain. We examine a Chebyshev ... More

Existence of Dirac Eigenvalues of higher MultiplicityApr 04 2015In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by catching the desired ... More

The Second Leaper TheoremJun 27 2017A $(p, q)$-leaper is a fairy chess piece that, from a square $a$, can move to any of the squares $a + (\pm p, \pm q)$ or $a + (\pm q, \pm p)$. Let $L$ be a $(p, q)$-leaper with $p + q$ odd and $C$ a cycle of $L$ within a $(p + q) \times (p + q)$ chessboard. ... More

Pathwise continuous time spectrum degeneracy at a single point and weak predictabilityMay 08 2017Mar 28 2018The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are predictable in some weak sense, meaning that convolution ... More

On Nyquist-Shannon Theorem with one-sided half of sampling sequenceMar 14 2016Mar 19 2016The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function can be uniquely recovered without error from a infinite two-sided sampling series taken with a sufficient frequency. This short note shows that ... More

On sub-ideal causal smoothing filtersDec 29 2010Jul 12 2011Smoothing causal linear time-invariant filters are studied for continuous time processes. The paper suggests a family of causal filters with almost exponential damping of the energy on the higher frequencies. These filters are sub-ideal meaning that a ... More

The symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domainsJul 09 2005We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.

Communication Delay Co-Design in $\mathcal{H}_2$ Distributed Control Using Atomic Norm MinimizationApr 19 2014Sep 20 2015When designing distributed controllers for large-scale systems, the actuation, sensing and communication architectures of the controller can no longer be taken as given. In particular, controllers implemented using dense architectures typically outperform ... More

On stationary solutions of two-dimensional Euler EquationJun 22 2012We study the geometry of streamlines and stability properties for steady state solutions of the Euler equations for ideal fluid.

On detecting the dependence of time seriesOct 13 2010This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires to compare ... More

A constrained tropical optimization problem: complete solution and application exampleMay 07 2013Nov 03 2013The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we follow an approach ... More

A recursive equations based representation for the $G/G/m$ queueOct 22 2012New recursive equations designed for the G/G/m queue are presented. These equations describe the queue in terms of recursions for the arrival and departure times of customers, and involve only the operations of maximum, minimum and addition.

Optimal solution of investment problems via linear parabolic equations generated by Kalman filterApr 29 2008We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. ... More

Optimal replication of random claims by ordinary integrals with applications in financeJan 03 2013Jan 04 2013By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable ... More

On prescribed change of profile for solutions of parabolic equationsMay 08 2011Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that this problem ... More

Evaluation of the mean cycle time in stochastic discrete event dynamic systemsDec 25 2012We consider stochastic discrete event dynamic systems that have time evolution represented with two-dimensional state vectors through a vector equation that is linear in terms of an idempotent semiring. The state transitions are governed by second-order ... More

The 2D Zakharov-Kuznetsov-Burgers equation on a stripApr 17 2014An initial-boundary value problem for the 2D Zakharov-Kuznetsov-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small ... More

Kawahara-Burgers equation on a stripAug 25 2014An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions ... More

Explicit solution of a tropical optimization problem with application to project schedulingMar 21 2013Nov 10 2013A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate transposition ... More

Graph-truncations of $3$-polytopesJan 15 2015In this paper we study the operation of cutting off edges of a simple $3$-polytope $P$ along the graph $\Gamma$. We give the criterion when the resulting polytope is simple and when it is flag. As a corollary we prove the analog of Eberhard's theorem ... More

A new algebraic solution to multidimensional minimax location problems with Chebyshev distanceOct 17 2012Both unconstrained and constrained minimax single facility location problems are considered in multidimensional space with Chebyshev distance. A new solution approach is proposed within the framework of idempotent algebra to reduce the problems to solving ... More

On sampling theorem with sparse decimated samplesMay 02 2016Nov 20 2016The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function is uniquely defined by infinite two-sided sampling series taken with a sufficient frequency. The paper shows that these band-limited functions ... More

The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problemsOct 29 2010The paper studies integral functionals with non-smooth functions from L_2 defined on solutions of ODEs. Some regularity is obtained in the form of estimates of L_2-norm for these functionals. This result is used for regularization of optimal control problems ... More

On the delayed stochastic integration and continuity in the Hurst parameterOct 05 2015Nov 02 2015We consider an approach to stochastic integration with respect to fractional Brownian motion with the Hurst parameter H>1/2 in the framework based on usual integral sums. We suggest a integral defined for delayed processes; this is why we call it delayed ... More

A smooth component of the fractional Brownian motion and optimal portfolio selectionSep 21 2015Oct 13 2015We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the sense that it ... More

Methods of tropical optimization in rating alternatives based on pairwise comparisonsAug 09 2016We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when ... More

Rating alternatives from pairwise comparisons by solving tropical optimization problemsApr 03 2015Nov 28 2015We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to approximate pairwise ... More

Inference of Sparse Networks with Unobserved Variables. Application to Gene Regulatory NetworksJun 01 2014Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the network is sparse ... More

QCD in beauty decays: successes and puzzlesJun 08 2004The status of the heavy quark expansion for inclusive B decays is briefly reviewed from the perspective of confronting theory with data and of extracting the heavy quark parameters. A good agreement between properly applied theory and new precision data ... More

A "BPS expansion" for B and D mesonsNov 30 2003We analyze consequences of the approximation \mu_\pi^2 -\mu_G^2 << \mu_\pi^2 (a `BPS' limit) for B and D mesons. It is shown that neglecting perturbative effects many power corrections would vanish to all orders in 1/m_Q, in particular those violating ... More

On $L_1$-distance between first exit times from two regionsMar 20 2003First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of $L_1$-distance between exit times from two regions via expectations of exit times.

Real and complex k-planes in convex hypersurfacesAug 23 2012It is shown that that the rank of the second fundamental form (resp. the Levi form) of a $\mathcal C^2$-smooth convex hypersurface $M$ in $\Bbb R^{n+1}$ (resp. $\Bbb C^{n+1}$) does not exceed an integer constant $k<n$ near a point $p\in M,$ then through ... More

Dirac Eigenvalues of higher MultiplicityJan 16 2015Let M be a closed spin manifold of dimension at least three with a fixed topological spin structure. For any Riemannian metric, we can construct the associated Dirac operator. The spectrum of this Dirac operator depends on the metric of course. In 2005, ... More

Sub-ideal causal smoothing filters for real sequencesNov 27 2014Jul 04 2015The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal smoothing ... More

Causal band-limitness and predictability criterions for one-sided sequencesAug 25 2014Sep 23 2014The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish predictability of some classes ... More

On causal band-limited mean square approximationNov 29 2011Aug 10 2012We study causal dynamic approximation of non-bandlimited processes by band-limited processes such that a part of the historical path of the underlying process is approximated in $L_2$-norm by the trace of a band-limited process. This allows to cover the ... More

On causal extrapolation of sequences with applications to forecastingAug 16 2012Feb 07 2018The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for forecasting. This ... More

Spectrum degeneracy for functions on branching lines and impact on extrapolation and samplingMay 17 2017Oct 21 2018The paper studies functions defined on continuous branching lines connected into a system. A notion of spectrum degeneracy for these functions is introduced. This degeneracy is based on the properties of the Fourier transforms for processes representing ... More