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PRM-RL: Long-range Robotic Navigation Tasks by Combining Reinforcement Learning and Sampling-based PlanningOct 11 2017May 16 2018We present PRM-RL, a hierarchical method for long-range navigation task completion that combines sampling based path planning with reinforcement learning (RL). The RL agents learn short-range, point-to-point navigation policies that capture robot dynamics ... More

Long Range Neural Navigation Policies for the Real WorldMar 23 2019Learned Neural Network based policies have shown promising results for robot navigation. However, most of these approaches fall short of being used on a real robot -- they require extensive training in environments, most of which do not simulate the visuals ... More

Visual Representations for Semantic Target Driven NavigationMay 15 2018What is a good visual representation for autonomous agents? We address this question in the context of semantic visual navigation, which is the problem of a robot finding its way through a complex environment to a target object, e.g. go to the refrigerator. ... More

Learning Navigation Behaviors End-to-End with AutoRLSep 26 2018Feb 01 2019We learn end-to-end point-to-point and path-following navigation behaviors that avoid moving obstacles. These policies receive noisy lidar observations and output robot linear and angular velocities. The policies are trained in small, static environments ... More

Visual Representations for Semantic Target Driven NavigationMay 15 2018Jul 02 2019What is a good visual representation for autonomous agents? We address this question in the context of semantic visual navigation, which is the problem of a robot finding its way through a complex environment to a target object, e.g. go to the refrigerator. ... More

Visual Representations for Semantic Target Driven NavigationMay 15 2018Mar 10 2019What is a good visual representation for autonomous agents? We address this question in the context of semantic visual navigation, which is the problem of a robot finding its way through a complex environment to a target object, e.g. go to the refrigerator. ... More

FollowNet: Robot Navigation by Following Natural Language Directions with Deep Reinforcement LearningMay 16 2018Understanding and following directions provided by humans can enable robots to navigate effectively in unknown situations. We present FollowNet, an end-to-end differentiable neural architecture for learning multi-modal navigation policies. FollowNet maps ... More

RL-RRT: Kinodynamic Motion Planning via Learning Reachability Estimators from RL PoliciesJul 10 2019This paper addresses two challenges facing sampling-based kinodynamic motion planning: a way to identify good candidate states for local transitions and the subsequent computationally intractable steering between these candidate states. Through the combination ... More

RL-RRT: Kinodynamic Motion Planning via Learning Reachability Estimators from RL PoliciesJul 10 2019Jul 12 2019This paper addresses two challenges facing sampling-based kinodynamic motion planning: a way to identify good candidate states for local transitions and the subsequent computationally intractable steering between these candidate states. Through the combination ... More

On the role of time in perceptual decision makingFeb 10 2015According to the dominant view, time in perceptual decision making is used for integrating new sensory evidence. Based on a probabilistic framework, we investigated the alternative hypothesis that time is used for gradually refining an internal estimate ... More

Long-Range Indoor Navigation with PRM-RLFeb 25 2019Long-range indoor navigation requires guiding robots with noisy sensors and controls through cluttered environments along paths that span a variety of buildings. We achieve this with PRM-RL, a hierarchical robot navigation method in which reinforcement ... More

Co-jumping of Treasury Yield Curve RatesMay 04 2019We study the role of co-jumps in the interest rate futures markets. To disentangle continuous part of quadratic covariation from co-jumps, we localize the co-jumps precisely through wavelet coefficients and identify statistically significant ones. Using ... More

Kovalevski exponents and integrability properties in class A homogeneous cosmological modelsOct 18 2002Qualitative approach to homogeneous anisotropic Bianchi class A models in terms of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the Kovalevski Exponents according to Adler - van Moerbecke method we discuss how algebraic ... More

Neutrino Oscillations in Strong Gravitational FieldsJan 05 2012Neutrinos do oscillate, which up to our best knowledge implies that they are massive particles. As such, neutrinos should interact with gravitational fields. As their masses are tiny, the gravitational fields must be extremely strong. In this paper we ... More

A frequentist two-sample test based on Bayesian model selectionApr 14 2011Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to verify. In such conditions, ... More

Recommendation systems with quantum k-NN and Grover's algorithms for data processingDec 12 2018In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In addition to the ... More

QCD Corrections to Inclusive Distributions of Leptons in Decays of Polarised Heavy QuarksOct 20 1994Compact analytic expressions have been obtained for the first order perturbative QCD corrections to the inclusive spectra of the leptons in the semileptonic decays of polarised heavy quarks. Charmed and beautiful $\Lambda$ baryons from $Z^0$ decays can ... More

Onset of Deconfinement and Critical Point - Future Ion Program at the CERN SPSDec 21 2005A new experimental program to study hadron production in collisions of nuclei at the CERN SPS is presented. The program will focus on measurements of fluctuations and long correlations with the aim to identify properties of the onset of deconfinement ... More

Quark Gluon Plasma in a+a Collisions at CERN SPSJun 04 1998A brief review of a history of data collection and interpretation of the results on high energy A+A collisions is presented. Basic assumptions and main results of a statistical model of the early stage of the A+A collisions are discussed. It is concluded ... More

A Method to Study `Chemical' Fluctuations in Nucleus--Nucleus CollisionsDec 13 1997Nov 24 1998A method to study event--by--event fluctuations of the `chemical' (particle type) composition of the final state of high energy collisions is proposed.}

Pion and Strangeness Production as Signals of QCD Phase TransitionJan 24 1997Feb 19 1997It is shown that data on pion and strangeness production in central nucleus-nucleus collisions are consistent with the hypothesis of a Quark Gluon Plasma formation between 15 A GeV/c (BNL AGS) and 160 A GeV/c (CERN SPS) collision energies. The experimental ... More

Radiation Processes in BlazarsAug 28 1997We present an overview of the current theoretical models attempting to describe the structure and radiative processes operating in blazars and discuss the observational constraints that these models must confront.

Relativity theory of clocks and rulersNov 25 2002Special Relativity (SR) kinematics is derived from very intuitive assumptions. Contrary to standard Einstein's derivation, no light signal is used in the construction nor it is assumed to exist. Instead we postulate the existence of two equivalence classes ... More

On Bell's theorem, quantum communication, and entanglement detectionNov 25 2008(A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and ``free will''. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of ... More

Hadronic jet models todayNov 03 2010The matter content of relativistic jets in AGNs is dominated by a mixture of protons, electrons, and positrons. During dissipative events these particles tap a significant portion of the internal and/or kinetic energy of the jet and convert it into electromagnetic ... More

Multivariate Gauss-Lucas TheoremsMar 29 2012A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

Some heuristics on the gaps between consecutive primesFeb 02 2011May 05 2011We propose the formula for the number of pairs of consecutive primes $p_n, p_{n+1}<x$ separated by gap $d=p_{n+1}-p_n$ expressed directly by the number of all primes $<x$, i.e. by $\pi(x)$. As the application of this formula we formulate 7 conjectures, ... More

A Note on the Andrica ConjectureOct 19 2010We derive heuristically the approximate formula for the difference $\sqrt{p_{n+1}} - \sqrt{p_n}$, where $p_n$ is the n-th prime. We find perfect agreement between this formula and the available data from the list of maximal gaps between consecutive primes. ... More

Evidence in favor of the Baez-Duarte criterion for the Riemann HypothesisMay 17 2006Nov 05 2008We present formulae allowing calculation of numerical values of the numbers $c_k$ appearing in the Baez-Duarte criterion for the Riemann Hypothesis for arbitrary large $k$. We present plots of $c_k$ for $k \in (1, 10^9)$.

Swapping space for time: An alternative to time-domain interferometryAug 09 2018Dec 08 2018Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as ... More

Limit cycles that do not comprise steady states of reactorsJun 05 2017It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank reactors coupled with mass recycle loop was tested numerically. The above-mentioned ... More

Semi-supervised Multitask Learning for Sequence LabelingApr 24 2017We propose a sequence labeling framework with a secondary training objective, learning to predict surrounding words for every word in the dataset. This language modeling objective incentivises the system to learn general-purpose patterns of semantic and ... More

Angular momentum, mass and charge inequalities for black holes in Einstein-Maxwell gravity with dark matter sectorJan 26 2017Feb 18 2017Angular momentum and mass-charge inequalities for axisymmetric maximal time-symmetric initial data in Einstein-Maxwell gravity with dark matter sector were derived. The dark matter sector is mimicked by another U(1)-gauge field coupled to the ordinary ... More

Uniqueness of dilaton Melvin-Schwarzschild solutionJan 25 2016We show that the dilaton Melvin-Schwarzschild black hole is the only asymptotically dilaton Melvin static axisymmetric solution of Einstein-Maxwell dilaton equations of motion.

Uniqueness of photon sphere for Einstein-Maxwell-dilaton black holes with arbitrary coupling constantFeb 10 2016The uniqueness of static asymptotically flat photon sphere for static black hole solution in Einstein-Maxwell-dilaton theory with arbitrary coupling constant was proposed. Using the conformal positive energy theorem we show that the dilaton sphere subject ... More

A critical point theorem on a closed ball and some applications to boundary value problemsMar 23 2015We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.

Anonymous On-line Communication Between Program AnalysesNov 08 2015We propose a light-weight client-server model of communication between program analyses. Clients are individual analyses and the server mediates their communication. A client cannot see properties of any other and the communication is anonymous. There ... More

Easyprove: a tool for teaching precise reasoningJul 14 2015Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often chaotically written) ... More

Will a physicist prove the Riemann Hypothesis?Oct 05 2014Dec 01 2015In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix Theory, relation ... More

A necessary and sufficient condition for local controllability around closed orbitsDec 15 2013In this paper we give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.

Positive Opetopes with Contractions form a Test CategoryDec 16 2017Jan 09 2018We show that the category of positive opetopes with contraction morphisms, i.e. all face maps and some degeneracies, forms a test category. The category of positive opetopic sets pOpeSet can be defined as a full subcategory of the category of polygraphs ... More

Approximation of convex bodies by polytopes with respect to minimal width and diameterMar 29 2017Denote by ${\mathcal K}^d$ the family of convex bodies in $E^d$ and by $w(C)$ the minimal width of $C \in {\mathcal K}^d$. We ask for the greatest number $\Lambda_n ({\mathcal K}^d)$ such that every $C \in {\mathcal K}^d$ contains a polytope $P$ with ... More

Improving the upper bound on the length of the shortest reset wordsFeb 17 2017Mar 29 2018We improve the best known upper bound on the length of the shortest reset words of synchronizing automata. The new bound is slightly better than $114 n^3 / 685 + O(n^2)$. The \v{C}ern\'y conjecture states that $(n-1)^2$ is an upper bound. So far, the ... More

EW baryogenesis via DMNov 08 2016We discuss the impact of a swifter cosmological expansion induced by modified cosmological history of the universe on scenarios realising electroweak baryogenesis. We detail the possible experimental bounds one can place on such cosmological modification ... More

Why is Helfenstein's claim about equichordal points false?Feb 08 2012This article explains why a paper by Heinz G. Helfenstein entitled "Ovals with equichordal points", published in J.London Math.Soc.31, 54-57, 1956, is incorrect. We point out a computational error which renders his conclusions invalid. More importantly, ... More

Characterization of compact monotonically ($ω$)-monolithic spaces using system of retractionsJan 29 2014We prove that a compact space is monotonically Sokolov if and only if it is monotonically $\omega$-monolithic. This gives answers to several questions of R. Rojas-Hernandez and V. V. Tkachuk.

Separable reduction theorems by the method of elementary submodelsJan 08 2011Mar 17 2011We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to a special ... More

On the scaling of the chemical distance in long-range percolation modelsApr 26 2003Apr 06 2005We consider the (unoriented) long-range percolation on Z^d in dimensions d\ge1, where distinct sites x,y\in Z^d get connected with probability p_{xy}\in[0,1]. Assuming p_{xy}=|x-y|^{-s+o(1)} as |x-y|\to\infty, where s>0 and |\cdot| is a norm distance ... More

Multitopes are the same as principal ordered face structuresOct 28 2007Jun 16 2008We show that the category of principal ordered face structures is equivalent to the category of multitopes. We show that the category of principal ordered face structures is equivalent to the category of multitopes. On the way we introduce the notion ... More

Soft QCD measurements at LHCFeb 08 2018Results from recent soft QCD measurements by LHC experiments ALICE, ATLAS, CMS, LHCb, LHCf and TOTEM are reported. The measurements include total, elastic and inelastic cross sections, inclusive and identified particle spectra, underlying event and hadronic ... More

Optimal probabilistic measurement of phaseJul 11 2013When measuring phase of quantum states of light, the optimal single-shot measurement implements projection on the un-physical phase states. If we want to improve the precision further we need to accept a reduced probability of success, either by implementing ... More

Simultaneous projectional skeletonsMay 07 2013We prove the existence of a simultaneous projectional skeleton for certain subspaces of $\mathcal{C}(K)$ spaces. This generalizes a result on simultaneous projectional resolutions of identity proved by M. Valdivia. We collect some consequences of this ... More

Top Quark Pair Production in the Threshold RegionDec 17 1995Recent results on production and decays of polarized top quarks are reviewed. Top quark pair production in $e^+e^-$ annihilation is considered near energy threshold. For longitudinally polarized electrons the produced top quarks and antiquarks are highly ... More

Pion and Strangeness PuzzlesJun 28 1996Jul 08 1996The dependence of pion and strangeness production on the number of participant nucleons and collision energy is discussed for central A+A collisions. A possible interpretation of the experimental results assuming transition to QGP is sketched within a ... More

Differences between Quark and Gluon jets as seen at LEPOct 31 2001The differences between quark and gluon jets are studied using LEP results on jet widths, scale dependent multiplicities, ratios of multiplicities, slopes and curvatures and fragmentation functions. It is emphasized that the observed differences stem ... More

All tight multipartite Bell correlation inequalities for three dichotomic observables per observerNov 08 2006A derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and three possible local settings. The procedure can be extended straightforwardly to multiparty correlations.

Bell Theorem for Nonclassical Part of Quantum Teleportation ProcessDec 07 1999The quantum teleportation process is composed of a joint measurement performed upon two subsystems A and B (uncorrelated), followed by a unitary transformation (parameters of which depend on the outcome of the measurement) performed upon a third subsystem ... More

Nearest neighbor spacing distribution of prime numbers and quantum chaosDec 16 2012Jan 07 2014We give heuristic arguments and computer results to support the hypothesis that, after appropriate rescaling, the statistics of spacings between adjacent prime numbers follows the Poisson distribution. The scaling transformation removes the oscillations ... More

Failed attempt to disproof the Riemann HypothesisOct 08 2009In this paper we are going to describe the results of the computer experiment, which in principle can rule out the Riemann Hypothesis. We use the sequence $c_k$ appearing in the \BD criterion for the RH. Namely we calculate $c_{100000}$ with thousand ... More

50 Years of Neutrino PhysicsDec 10 2010Some important topics from history of neutrino physics over the last fifty years are discussed. History of neutrinos is older, at 4th December 2010 it will be eightieth anniversary of the "neutrino birth". In that day W. Pauli wrote the famous letter ... More

Effective chain complexes for twisted productsSep 06 2012Nov 14 2012In the paper weak sufficient conditions for the reduction of the chain complex of a twisted product to a free finitely generated chain complex are found.

Lightest Higgs boson masses in the R-parity violating supersymmetryJan 04 2012The first results on the searches of the Higgs boson appeared this Summer from the LHC and Tevatron groups, and has been recently backed up by the ATLAS and CMS experiments taking data at CERN's LHC. Even though the excitement that this particle has been ... More

Constraining an R-parity violating supergravity model with the Higgs induced Majorana neutrino magnetic momentsJan 04 2012It is well known, that R-parity violating supersymmetric models predict a non-zero magnetic moment for neutrinos. In this work we study the Majorana neutrino transition magnetic moments within an RpV modified minimal supergravity model. Specifically, ... More

The formal theory of monoidal monadsDec 02 2010We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg-Moore algebras for an oplax monoidal monad, we always have a natural monoidal structures. ... More

Known Galactic field Blazhko starsOct 26 2012Nov 20 2012A list of known Galactic field stars exhibiting Blazhko effect containing 242 stars is presented. All the entries including their designations, positions, pulsation, and Blazhko periods were collected from the available literature. The actual values of ... More

Temporal Leggett-Garg-Bell inequalities for sequential multi-time actions in quantum information processing, and a re-definition of Macroscopic RealismSep 09 2010The usual formulation of Macrorealism is recast to make this notion fully concurrent with the basic ideas behind classical physics. The assumption of non-invasiveness of measurements is dropped. Instead, it is assumed that the current state of the system ... More

Dark energy as a manifestation of nontrivial arithmeticApr 20 2016Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, $\mathbb{R}_+^4$ and $(-L/2,L/2)^4$, are considered where different types of arithmetic ... More

Modelling and tuning in top quark physicsJan 15 2019In this proceedings I discuss the general strategy and impact of tuning Monte-Carlo event generators for physics processes involving top quarks. Special emphasis is put on disinguishing the different usages of event generators in the experiments and the ... More

A proof of convergence of multi-class logistic regression networkMar 29 2019This paper revisits the special type of a neural network known under two names. In the statistics and machine learning community it is known as a multi-class logistic regression neural network. In the neural network community, it is simply the soft-max ... More

6+infinity new expressions for the Euler-Mascheroni constantApr 16 2019In the first part we present results of four ``experimental'' determinations of the Euler-Mascheroni constant $\gamma$. Next we give new formulas expressing the $\gamma$ constant in terms of the Ramanujan-Soldner constant $\mu$. Employing the cosine integral ... More

On some mathematical model of turbulent flow with intensive selfmixingJul 27 2011Paper contains description of a new non laminar mathematical model of turbulent flow. Equations of the model are given and main conservation laws for this model are proven.

Application of spherical convex bodies to Wulff shapeMar 11 2019Apr 13 2019We present some relationships between the diameter, width and thickness of a reduced convex body on the $d$-dimensional sphere. We apply the obtained properties to recognize if a Wulff shape in the Euclidean $d$-space is self-dual.

Some Remarks on the Distribution of twin PrimesMay 25 2001The computer data up to $2^{44}\approx 1.76\times 10^{13}$ on the gaps between consecutive twins is presented. The simple derivation of the heuristic formula describing computer results contained in the recent papers by P.F.Kelly and T.Pilling \cite{Kelly1}, ... More

Multidegrees of tame automorphisms of C^nMar 07 2011Apr 08 2011Let F=(F_1,...,F_n):C^n --> C^n be a polynomial mapping. By the multidegree of the mapping F we mean mdeg F=(deg F_1,...,deg F_n), an element of N^n. The aim of this paper is to study the following problem (especially for n=3): for which sequence (d_1,...,d_n) ... More

Tame automorphisms of C^3 with multidegree of the form (p_1,p_2,d_3)Apr 08 2009Let d_3 >= p_2 > p_1 >= 3 be integers such that p_1,p_2 are prime numbers. In this paper we show that the sequence (p_1,p_2,d_3) is the multidegree of some tame automorphisms of C^3 if and only if d_3 is in p_1*N+p_2*N, i.e. if and only if d_3 is a linear ... More

Negative moments of the gaps between consecutive primesMay 13 2018Jun 06 2018We derive heuristically approximate formulas for the negative $k$--moments $M_{-k}(x)$ of the gaps between consecutive primes$<x $ represented directly by $\pi(x)$ --- the number of primes up to $x$. In particular we propose an analytical formula for ... More

On completion of a linearly independent set to a basis with shifts of a fixed vectorMay 27 2019Let $\mathbb{F}$ be an infinite field. Let $n$ be a positive integer and let $1\leq d\leq n$. Let $\vec{f}_1, \vec{f}_2, \ldots, \vec{f}_{d-1} \in \mathbb{F}^{n}$ be $d-1$ linearly independent vectors. Let $\vec{x}=(x_1,x_2,\ldots,x_{d},0,0,\ldots,0)\in\mathbb{F}^{n}$, ... More

On the moments of the gaps between consecutive primesMay 30 2017We derive heuristically formula for the $k$--moments $M_k(x)$ of the gaps between consecutive primes$<x $ represented directly by $x$$\pi(x)$ --- the number of primes up to: $M_k(x)= \Gamma(k+1)x^k/\pi^{k-1}(x)+\mathcal{O}(x)$, We illustrate obtained ... More

Neutron Stars: Formation and StructureJan 24 1998A short introduction is given to astrophysics of neutron stars and to physics of dense matter in neutron stars. Observed properties of astrophysical objects containing neutron stars are discussed. Current scenarios regarding formation and evolution of ... More

Onset of Deconfinement and Critical Point: NA49 and NA61/SHINE at the CERN SPSJan 31 2008This paper is dedicated to the memory of Jozsef Zimanyi one of the founders of the experiment NA49 at the CERN SPS. Firstly, the paper summarizes the main results of NA49 concerning observation of the onset of deconfinement in central Pb+Pb collisions ... More

Mechanical Stretching of Proteins: Calmodulin and TitinDec 16 2004Mechanical unfolding of several domains of calmodulin and titin is studied using a Go-like model with a realistic contact map and Lennard-Jones contact interactions. It is shown that this simple model captures the experimentally observed difference between ... More

On the Paradoxical Book of BellMay 03 2006Jan 22 2015This is an essay-review on a recently re-issued book of John Bell "Speakable and Unspeakable in Quantum Mechanics". The discussion concentrates around the Bell Theorem, its assumptions, consequences and frequent overinterpretations.

Violations of Local Realism in the Innsbruck GHZ ExperimentNov 05 1998It is shown that a careful analysis of the `wrong' events (those not present in the usual formulations of the GHZ argument), which are a necessary feature of the tests of local realism involving independent sources, permits one to show that there is no ... More

Coupling Gravity and the Standard Model: a Conformal ApproachOct 30 1996In 1992 Professor Ryszard R\c{a}czka started to work on formulation of a version of the Standard Model conformally coupled with gravity. Being his student I had got the honour to participate in those researches. The conformally invariant Higgs-Free Model ... More

Status of the Exclusive MSSM Higgs production at LHC after the Run IOct 14 2013We investigate the prospects for Central Exclusive Diffractive (CED) production of MSSM Higgs bosons at the LHC using forward proton detectors (FPD) proposed to be installed 220 m and 420 m from ATLAS and CMS detectors. We summarize the situation after ... More

From p+p to Pb+Pb Collisions: Wounded Nucleon versus Statistical ModelsJun 25 2013Jul 08 2013System size dependence of hadron production properties is discussed within the Wounded Nucleon Model and the Statistical Model in the grand canonical, canonical and micro-canonical formulations. Similarities and differences between predictions of the ... More

Regularization just by quantization -- a new approach to the old problem of infinities in quantum field theory (Draft of lecture notes)Sep 16 2012May 08 2013This is the current form of lecture notes on my approach to field quantization. I explain on a simple scalar-field model the physical motivation and show some preliminary applications (field produced by a pointlike charge, the vacuum-to-vacuum loop diagram, ... More

Compact Symbolic Execution (technical report)Jan 29 2012We present a generalisation of King's symbolic execution technique called compact symbolic execution. It is based on a concept of templates: a template is a declarative parametric description of such a program part, generating paths in symbolic execution ... More

Numerical evidence in favor of the Arenstorf formulaJun 05 2004The formula $\lim_{N\to\infty}\sum_{p<N,p,p+2 both prime} \log(p)\log(p+2) = C_2$ is tested on the computer up to $N=2^{40}\approx 1.1\times 10^{12}$ and very good agreement is found.

Computer experiments with Mersenne primesDec 11 2011We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated geometrical means of ... More

Two arguments that the nontrivial zeros of the Riemann zeta function are irrationalFeb 22 2010Feb 28 2010We have used the first 2600 nontrivial zeros gamma_l of the Riemann zeta function calculated with 1000 digits accuracy and developed them into the continued fractions. We calculated the geometrical means of the denominators of these continued fractions ... More

Weighted Approach to General Entropy FunctionMay 14 2013The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under reasonable ... More

Improved approximation for 3-dimensional matching via bounded pathwidth local searchApr 04 2013Aug 20 2013One of the most natural optimization problems is the k-Set Packing problem, where given a family of sets of size at most k one should select a maximum size subfamily of pairwise disjoint sets. A special case of 3-Set Packing is the well known 3-Dimensional ... More

Generalized Plonka Sums and ProductsOct 28 2012We give an abstract categorical treatment of Plonka sums and products using lax and oplax morphisms of monads. Plonka sums were originally defined as operations on algebras of regular theories. Their arities are sup-semilattices. It turns out that even ... More

Approximate Dynamic Programming By Minimizing Distributionally Robust BoundsMay 08 2012May 21 2012Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by ... More

Recent results from NA61/SHINEDec 13 2014This paper briefly presents the NA61/SHINE facility at the CERN SPS and its measurements motivated by physics of strong interactions, neutrinos and cosmic rays.

Status of High-Energy Neutrino AstronomyNov 17 2014With the recent discovery of high-energy neutrinos of extra-terrestrial origin by the IceCube neutrino observatory, neutrino-astronomy is entering a new era. This review will cover currently operating open water/ice neutrino telescopes, the latest evidence ... More

Bright Blazhko RRab Lyrae stars observed by ASAS and the SuperWASP surveysFeb 13 2014Period study of 321 fundamental mode galactic field RR Lyrae type stars (RRab), which had appropriate data in ASAS and SuperWASP surveys, brighter than 12.5 mag in maximum light was performed. We found 100 stars to be definitely modulated. In 25 cases, ... More

Doubly Heavy Tetraquarks and BaryonsJan 16 2014During the last three years strong experimental evidence from $B$ and charm factories has been accumulating for the existence of exotic hadronic quarkonia, narrow resonances which cannot be made from a quark and an antiquark. Their masses and decay modes ... More

Time travel in a space-time ring resonatorMay 30 2018Feb 12 2019A ring resonator can be treated as a universal model of a looped dynamics in a Hilbert space. A particular example of a loop occurs in the problem of time travel in space-times whose topologies allow for closed timelike curves (CTCs). I generalize the ... More