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Proportional Approval Voting, Harmonic k-median, and Negative AssociationApr 07 2017Mar 12 2018We study a generic framework that provides a unified view on two important classes of problems: (i) extensions of the k-median problem where clients are interested in having multiple facilities in their vicinity (e.g., due to the fact that, with some ... More

Supersoft X-ray emission from a white dwarf binary not powered by nuclear fusionJul 03 2019Supersoft X-ray sources are stellar objects which emit X-rays with temperatures of about 1 million Kelvin and luminosities well in excess of what can be produced by stellar coronae. It has generally been presumed that the objects in this class are binary ... More

No large population of unbound or wide-orbit Jupiter-mass planetsJul 24 2017Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale ... More

FPT Approximation Schemes for Maximizing Submodular FunctionsOct 01 2015We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to select a subset ... More

Proportional RankingsDec 05 2016In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that cohesive groups of ... More

What Do We Elect Committees For? A Voting Committee Model for Multi-Winner RulesNov 21 2016We present a new model that describes the process of electing a group of representatives (e.g., a parliament) for a group of voters. In this model, called the voting committee model, the elected group of representatives runs a number of ballots to make ... More

Proportionality Degree of Multiwinner RulesOct 20 2018We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size $k$; the goal ... More

Mixed Integer Programming with Convex/Concave Constraints: Fixed-Parameter Tractability and Applications to Multicovering and VotingSep 08 2017Nov 20 2017A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating non-decreasing piecewise ... More

Two Stars Two Ways: Confirming a Microlensing Binary Lens Solution with a Spectroscopic Measurement of the OrbitJun 04 2015Light curves of microlensing events involving stellar binaries and planetary systems can provide information about the orbital elements of the system due to orbital modulations of the caustic structure. Accurately measuring the orbit in either the stellar ... More

Optimal Survey Strategies and Predicted Planet Yields for the Korean Microlensing Telescope NetworkJun 09 2014The Korean Microlensing Telescope Network (KMTNet) will consist of three 1.6m telescopes each with a 4 deg^{2} field of view (FoV) and will be dedicated to monitoring the Galactic Bulge to detect exoplanets via gravitational microlensing. KMTNet's combination ... More

The countable Telescope Conjecture for module categoriesJan 25 2008May 16 2008By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A, B) is of finite type." We prove a modification of this ... More

Singular compactness and definability for $Σ$-cotorsion and Gorenstein modulesApr 24 2018May 25 2018We introduce a general version of singular compactness theorem which makes it possible to show that being a $\Sigma$-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed along the way, ... More

OGLE-III Microlensing Events and the Structure of the Galactic BulgeMay 13 2014Jan 07 2015We present and study the largest and the most comprehensive catalog of microlensing events ever constructed. The sample of standard microlensing events comprises 3718 unique events from years 2001--2009, with 1409 not detected before in real-time by the ... More

Final Release of the OGLE Collection of Cepheids and RR Lyrae Stars in the Magellanic System. The Outer RegionsJul 03 2019We present the final release of the OGLE collection of classical pulsators (Cepheids and RR Lyr stars) in the Large and Small Magellanic Clouds. The sky coverage has been increased from 670 to 765 square degrees compared to the previous edition of the ... More

OGLE-2018-BLG-0532Lb: Cold Neptune With Possible Jovian SiblingMay 15 2019We report the discovery of the planet OGLE-2018-BLG-0532Lb, with very obvious signatures in the light curve that lead to an estimate of the planet-host mass ratio $q=M_{\rm planet}/M_{\rm host}\simeq 1\times10^{-4}$. Although there are no obvious systematic ... More

Measuring switching processes in financial markets with the Mean-Variance spin glass approachMar 13 2015In this article we use the Mean-Variance Model in order to measure the current market state. In our study we take the approach of detecting the overall alignment of portfolios in the spin picture. The projection to the ground-states enables us to use ... More

A feasible interpolation for random resolutionApr 22 2016Sep 11 2016Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo ... More

Topologies induced by group actionsDec 01 2014We introduce some canonical topologies induced by actions of topological groups on groups and rings. For $H$ being a group [or a ring] and $G$ a topological group acting on $H$ as automorphisms, we describe the finest group [ring] topology on $H$ under ... More

New examples of small Polish structuresJun 23 2012We answer some questions from a paper of Krupi\'nski by giving suitable examples of small Polish structures. First, we present a class of small Polish group structures without generic elements. Next, we construct a first example of a small non-zero-dimensional ... More

Reducible Quantum Electrodynamics. I. The Quantum Dimension of the Electromagnetic FieldMay 30 2015In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the Canonical Commutation ... More

Generalized thermostatistics and mean-field theoryNov 20 2002Sep 30 2003The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized thermostatistics. ... More

Generalised thermostatistics using hyperensemblesSep 03 2007The hyperensembles, introduced by Crooks in a context of non-equilibrium statistical physics, are considered here as a tool for systems in equilibrium. Simple examples like the ideal gas, the mean-field model, and the Ising interaction on small square ... More

Rigorous results in non-extensive thermodynamicsAug 25 1999This paper studies quantum systems with a finite number of degrees of freedom in the context of non-extensive thermodynamics. A trial density matrix, obtained by heuristic methods, is proved to be the equilibrium density matrix. If the entropic parameter ... More

Granular Collapse as a Percolation TransitionMay 18 1999Sep 17 1999Inelastic collapse is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a transition between a state containing small collapsed clusters ... More

On Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems: A New Approach Based on Wick's TheoremJul 25 1994A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect to the hybridization ... More

Self-Consistent Strong-Coupling-Perturbation Theory for the Anderson Model, Based on Wicks TheoremAug 12 1996A strong-coupling-perturbation theory around the Atomic Limit of the Anderson model with large $U$ for a localized $f$-orbital coupled to a conduction-electron band is presented. Although an auxiliary-particle representation is {\em not} used, application ... More

Symmetry Tests within the Standard Model and Beyond from Nuclear Muon CaptureSep 17 1998Precision measurements in nuclear muon capture on the proton and $^3$He allow for tests of the Standard Model for the strong and electroweak interactions, complementary to those achieved in high energy experiments. The present situation and future prospects ... More

Strangeness and Quark--Gluon PlasmaDec 21 2011I review the foundational motivation which led us to the ultra relativistic heavy ion collision research at SPS, RHIC and now LHC: the quantum vacuum structure; the deconfined nature of quark-gluon plasma (QGP) phase filling the Universe for the first ... More

Massless particles on supergroups and AdS3 x S3 supergravityFeb 01 2011Jun 27 2011Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the ... More

Models for ModulesFeb 09 2012Sep 14 2012We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral discretization ... More

A note on causality in the bulk and stability on the boundaryAug 06 2003Oct 06 2003By carefully analyzing the radial part of the wave-equation for a scalar field in AdS, we show that for a particular range of boundary conditions on the scalar field, the radial spectrum contains a bound state. Using the AdS/CFT correspondence, we interpret ... More

Exploration PotentialSep 16 2016Sep 28 2016We introduce exploration potential, a quantity for that measures how much a reinforcement learning agent has explored its environment class. In contrast to information gain, exploration potential takes the problem's reward structure into account. This ... More

Recent Developments in Superstring PhenomenologyMay 20 1992Recent developments in superstring phenomenology are summarized on a non-technical level. (Talk presented at the XXVIIth Rencontre de Moriond on Electroweak Interactions and Unified Theories.)

Differential Equations in Special Kahler GeometryAug 21 1992Sep 09 1992The structure of differential equations as they appear in special \K\ geometry of $N=2$ supergravity and $(2,2)$ vacua of the heterotic string is summarized. Their use for computing couplings in the low energy effective Lagrangians of string compactifications ... More

Rescaling limits of complex rational mapsNov 14 2012We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space.It is shown that any given sequence of maps of degree $d \ge 2$ has at most $2d-2$ dynamically distinct rescaling limits which ... More

Frobenius Manifolds from Yang-Mills InstantonsOct 29 1997We present an elementary self-contained account of semisimple Frobenius manifolds in three dimensions, and exhibit a new family of explicit examples. These examples are constructed from Yang-Mills instantons with a certain symmetry.

Spin gauge symmetry in the action principle for classical relativistic particlesJan 20 2015We suggest that the physically irrelevant choice of a representative worldline of a relativistic spinning particle should correspond to a gauge symmetry in an action approach. Using a canonical formalism in special relativity, we identify a (first-class) ... More

How to See the Chiral Structure of QCD Vacuum in Low Energy $π-π$ ScatteringOct 17 1995Precise measurement of the $\pi\pi$-phase shift $\delta^0_0(E)$ at very low energies would provide, for the first time, the experimental evidence in favour of or against the existence of a large quark condensate in the QCD vacuum, which is standardly ... More

Jacob's ladders and properties of complete additivity and complete multiplicativity in the set of reverse iterated integrals (energies)Sep 02 2014New class of integral identities concerning constraints on behavior of the Riemann's zeta function on the critical line is introduced in this paper. Namely, we have obtained new kind of $\sigma$-additivity and $\sigma$-multiplicativity in the class of ... More

Jacob's ladders, heterogeneous quadrature formulae, big asymmetry and related formulae for the Riemann zeta-functionJan 13 2014In this paper we obtain as our main result new class of formulae expressing correlation integrals of the third-order in $Z$ on disconnected sets $\mathring{G}_1(x),\mathring{G}_2(y)$ by means of an autocorrelative sum of the second order in $Z$. Moreover, ... More

New consequences of the Riemann-Siegel formula and a law of asymptotic equality of signum-areas of $Z(t)$ functionDec 17 2013In this paper we obtain the first mean-value theorems for the function $Z(t)$ on some disconnected sets. Next, we obtain a geometric law that controls chaotic behavior of the graph of the function $Z(t)$. This paper is the English version of the papers ... More

Jacob's ladders, their iterations and the new class of integrals connected with parts of the Hardy-Littlewood integral of the function $|ζ(1/2+it)|^2$Sep 21 2012In this paper we introduce the iterations of the Jacob's ladder and the new type of integral containing certain product of the factors $|\zeta|^2$ corresponding to the components of some disconnected set of the critical line. Next, we obtain an asymptotic ... More

Jacob's ladders and certain asymptotic multiplicative formula for the function $|\zf|^2$Jan 16 2012In this paper it is proved that a mean-value of the product of some factors $|\zeta|^2$ is asymptotically equal to the product of the mean-values of $\zeta|^2$, and this holds true for every fixed number of the factors.

On the order of the Titchmarsh's sum in the theory of the Riemann zeta-function and on the biquadratic effect in the information theoryDec 27 2011We obtain in this paper the solution of the classical problem on the order of the Titchmarsh's sum (1934). Simultaneously, we obtain a connection of this problem and the Kotelnikoff-Whittaker-Nyquist's theorem from the information theory.

The validity of the analog of the Riemann hypothesis for some parts of $ζ(s)$ and the new formula for $π(x)$Sep 05 2011An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the solutions of the ... More

Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integralJul 02 2009The elementary geometric properties of Jacob's ladders lead to a class of new asymptotic formulae for short and microscopic parts of the Hardy-Littlewood integral. This class of asymptotic formulae cannot be obtained by methods of Balasubramanian, Heath-Brown ... More

On some properties of Riemann zeta function on critical lineOct 04 2007The aim of this paper is to show further results following those published in [5], and to relate the Riemann zeta function to the relativistic cosmology.

Jacob's ladders and multiplicative algebra of reversely iterated integrals (energies) on the critical lineJun 13 2014Certain completely logarithmic formula for a set of reversely iterated integrals (energies) is proved in this paper. Namely, in this case we have that integral powers of $\ln T$ are contained on input as well as on output of corresponding integrals (energies). ... More

Riemann hypothesis and the arc length of the Riemann $Z(t)$-curveApr 07 2014On Riemann hypothesis it is proved in this paper that the arc length of the Riemann $Z$-curve is asymptotically equal to the double sum of local maxima of the function $Z(t)$ on corresponding segment. This paper is English remake of our paper \cite{9}, ... More

Jacob's ladders and some generalizations of certain Ramachandra's inequalityAug 01 2013In this paper we obtain some essential generalizations of certain Ramachandra's inequality, i. e. we obtain new lower estimates for the energies of some complicated signals generated by the Riemann zeta-function on the critical line.

Jacob's ladders, conjugate integrals, external mean-values and other properties of a multiply $π(T)$-autocorrelation of the function $|\zf|^2$Feb 15 2013Feb 18 2013In this paper we obtain a new class of transformation formulae (without an explicit presence of a derivative) for the integrals containing products of factors $|\zf|^2$ with respect to two components of a disconnected set on the critical line.

Jacob's ladders and the $\tilde{Z}^2$-transformation of the orthogonal system of trigonometric functionsJul 01 2010Oct 29 2010It is shown in this paper that there is a continuum set of orthogonal systems relative to the weight function $\tilde{Z}^2(t)$. The corresponding integrals cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.

Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integralJun 03 2009Feb 04 2010The elementary geometric properties of the Jacob's ladders \cite{7} lead to a class of new formulae for short parts of the Hardy-Littlewood integral. This class of formulae cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.

Jacob's ladders and the almost exact asymptotic representation of the Hardy-Littlewood integralJan 26 2009In this paper we introduce a nonlinear integral equation such that the system of global solution to this equation represents a class of a very narrow beam at $T\to\infty$ (an analogue to the laser beam) and this sheaf of solutions leads to an almost-exact ... More

Steady-State Flow-Force Compensation in a Hydraulic Spool ValveDec 04 2013A high-speed jet flowing inside of a partially-open hydraulic valve is accompanied by a reaction force, also referred to as flow force. The nature of this force has remained a mystery despite an extensive research effort spanning many decades. The momentum ... More

Convergence to consensus in multiagent systems and the lengths of inter-communication intervalsJan 14 2011Apr 20 2011A theorem on (partial) convergence to consensus of multiagent systems is presented. It is proven with tools studying the convergence properties of products of row stochastic matrices with positive diagonals which are infinite to the left. Thus, it can ... More

Cold Electroweak BaryogenesisSep 01 2004We present arguments that the CKM CP-violation in the standard model may be sufficient for the generation of the baryon asymmetry, if the electroweak transition in the early universe was of the cold, tachyonic, type after electroweak-scale inflation. ... More

Numerical study of plasmon properties in the SU(2)-Higgs modelAug 29 1997We discuss an explorative computation of real time autocorrelation functions, in the classical approximation. The results for the `plasmon' frequencies and damping rates appear compatible with the divergencies expected from perturbation theory.

The Evolution of GalaxiesAug 07 2007The evolution of galaxies results from a combination of internal and external processes. The star formation is an internal process transforming cold and dense cores of molecular clouds to stars. It may be triggered internally by expanding shells, or externally, ... More

Galaxy Collisions, Gas Stripping and Star Formation in the Evolution of GalaxiesDec 23 2004A review of gravitational and hydrodynamical processes during formation of clusters and evolution of galaxies is given. Early, at the advent of N-body computer simulations, the importance of tidal fields in galaxy encounters has been recognized. Orbits ... More

Special Riemannian geometries and the Magic Square of Lie algebrasOct 12 2008We investigate nonintegrable Riemannian geometries modelled after certain symmetric spaces related to the Freudenthal-Tits Magic Square. The collection of four such structures found by Nurowski is extended by further eight. A focus is given to those admitting ... More

Calculation of QCD loops using tree-level matrix elementsMay 17 2010The possibility of treating colour in one-loop amplitude calculations alike the other quantum numbers is briefly discussed for semi-numerical algorithms based on generalized unitarity and parametric integration techniques. Numerical results are presented ... More

CDT as a scaling limit of matrix modelsMay 09 2011It is shown that generalized CDT, the two-dimensional theory of quantum gravity, constructed as a scaling limit from so-called causal dynamical triangulations, can be obtained from a cubic matrix model. It involves taking a new scaling limit of matrix ... More

An analytic method for bounding $ψ(x)$Nov 06 2015In this paper we present an analytic altorithm which calculates almost sharp bounds for the normalized error term $(t-\psi(t))/\sqrt{t}$ for $t\leq x$ in expected run time $O(x^{1/2+\varepsilon})$ for every $\varepsilon>0$. The method has been implemented ... More

Cortical composition hierarchy driven by spine proportion economical maximization or wire volume minimizationOct 28 2015The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites ... More

SUSY with R-symmetry: confronting EW precision observables and LHC constraintsOct 22 2015After motivation and short presentation of the minimal supersymmetric model with R-symmetry (MRSSM), we address the question of accomodating the measured Higgs boson mass in accordance with electroweak precision observables and LHC constraints.

Reducible Quantum Electrodynamics. II. The charged states of the vacuumOct 09 2015May 28 2016An explicit construction is given of field operators satisfying the free Dirac equation. The quantum expectation of these field operators forms a spinor which satisfies the original Dirac equation. The current operators are defined as pair correlation ... More

Homogeneous rank one perturbationsNov 11 2016A holomorphic family of closed operators with a rank one perturbation given by the function $x^{\frac{m}{2}}$ is studied. The operators can be used in a toy model of renormalization group.

Contour curves and isophotes on rational ruled surfacesSep 26 2016The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some fixed vector. ... More

A feasible interpolation for random resolutionApr 22 2016Oct 19 2016Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo ... More

X-rays from magnetic intermediate mass Ap/Bp starsJan 19 2016The X-ray emission of magnetic intermediate mass Ap/Bp stars is reviewed and put into context of intrinsic as well as extrinsic hypotheses for its origin. New X-ray observations of Ap/Bp stars are presented and combined with an updated analysis of the ... More

Jacob's ladders, interactions between $ζ$-oscillating systems and $ζ$-analogue of an elementary trigonometric identitySep 29 2016In our previous papers, we have introduced within the theory of the Riemann zeta function the following notions: Jacob's ladders, oscillating systems, $\zeta$-factorization, metamorphoses, \dots In this paper we obtain $\zeta$-analogue of an elementary ... More

Reflection Scan: an Off-Path Attack on TCPJan 10 2012Jan 24 2012The paper demonstrates how traffic load of a shared packet queue can be exploited as a side channel through which protected information leaks to an off-path attacker. The attacker sends to a victim a sequence of identical spoofed segments. The victim ... More

Representations and isomorphism identities for infinitely divisible processesJul 26 2016Jul 27 2016We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with random translations. ... More

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approachMar 12 2019Apr 15 2019Recent theoretical and experimental studies have shown significance of the phenomenon of quantum information scrambling (i.e. a spread of quantum information over a systems degrees of freedom) for problems encountered in high-energy physics, quantum information, ... More

Partial correlation hypersurfaces in Gaussian graphical modelsJun 01 2018Sep 21 2018We derive a combinatorial sufficient condition for a partial correlation hypersurface in the parameter space of a directed Gaussian graphical model to be nonsingular, and speculate on whether this condition can be used in algorithms for learning the graph. ... More

A poset classifying non-commutative term ordersJan 10 2002We study a certain poset on the free monoid on a countable alphabet. This poset is determined by the fact that its total extensions are precisely the standard term orders. We also investigate the poset classifying degree-compatible standard term orders, ... More

Modularity, Atomicity and States in Archimedean Lattice Effect AlgebrasJan 08 2010Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there exists an $(o)$-continuous ... More

The Bousso entropy bound in selfgravitating gas of massless particlesFeb 20 2007Jul 12 2008The Bousso entropy bound is investigated in a static spherically symmetric spacetime filled with an ideal gas of massless bosons or fermions. Especially lightsheets generated by spheres are considered. Statistical description of the gas is given. Conditions ... More

An equivalence between Frobenius algebras and Calabi-Yau categoriesSep 21 2016Jul 25 2017We show that the bigroupoid of separable symmetric Frobenius algebras over an algebraically closed field and the bigroupoid of finitely semi-simple Calabi-Yau categories are equivalent. To this end, we construct a trace on the category of finitely-generated ... More

Morse Homology for the Yang-Mills Gradient FlowMar 04 2011Oct 26 2015We use the Yang-Mills gradient flow on the space of connections over a closed Riemann surface to construct a Morse-Bott chain complex. The chain groups are generated by Yang-Mills connections. The boundary operator is defined by counting the elements ... More

Homotopy- and Cohomology Groups of Kan ComplexesAug 01 2016This article shows several new methods for proofs on Kan complexes while using them to give a compact introduction to the homotopy groups of these complexes. Then more advanced objects are studied starting with homology and the Hurewicz homomorphism. ... More

Construction of operator product expansion coefficients via consistency conditionsJun 30 2009In this thesis an iterative scheme for the construction of operator product expansion (OPE) coefficients is applied to determine low order coefficients in perturbation theory for a specific toy model. We use the approach to quantum field theory proposed ... More

Varieties defined by natural transformationsApr 10 2009We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free algebras in the varieties ... More

An explicit Skorokhod embedding for functionals of Markovian excursionsSep 23 2005We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of Markovian excursions. Our setting allows to solve the Skorokhod embedding problem, in particular, for diffusions and their ... More

Stably Newton non-degenerate singularitiesJun 02 2014Jan 28 2015We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. The answer is negative. The easiest example can be given in characteristic $p$: the function $x^p$ is not stably equivalent ... More

A feasible interpolation for random resolutionApr 22 2016Feb 01 2017Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo ... More

On the computational complexity of finding hard tautologiesDec 08 2012Jul 18 2013It is well-known (cf. K.-Pudl\'ak 1989) that a polynomial time algorithm finding tautologies hard for a propositional proof system $P$ exists iff $P$ is not optimal. Such an algorithm takes $1^{(k)}$ and outputs a tautology $\tau_k$ of size at least $k$ ... More

Uniform measures and convolution on topological groupsAug 06 2006May 14 2010Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on an arbitrary ... More

Varieties of pairs of nilpotent matrices annihilating each otherNov 19 2002Nov 18 2003We classify the irreducible components of the varieties V(n,a,b) of pairs (A,B) of matrices of size n such that AB = BA = 0 and A^a = B^b = 0.

MATLAB Implementation of C1 finite elements: Bogner-Fox-Schmit rectangleMay 22 2019Rahman and Valdman (2013) introduced a new vectorized way to assemble finite element matrices. We utilize underlying vectorization concepts and extend MATLAB codes to implementation of Bogner-Fox-Schmit C1 rectangular elements in 2D. Our focus is on the ... More

A lightweight BFT consensus protocol for blockchainsMar 27 2019Jun 14 2019We present a general consensus framework that allows to easily introduce a customizable Byzantine fault tolerant consensus algorithm to an existing (delegated) proof-of-stake blockchain. We prove the safety of the protocol under the assumption that less ... More

Non-classical correlations in reducible Quantum ElectrodynamicsDec 26 2018The question is discussed whether the momentum of a photon has a quantum uncertainty or whether it is a classical quantity. The latter assumption is the main characteristic of reducible Quantum Electrodynamics (rQED). Recent experiments in Quantum Optics ... More

Non-embeddable 1-convex manifoldsSep 27 2012Nov 11 2013We show that every small resolution of a three-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve ... More

On Wagoner complexesMar 11 2009May 04 2010Wagoner complexes are simplicial complexes associated to groups of Kac-Moody type. They admit interesting homotopy groups which are related to integral group homology if the root datum is of 2-spherical type. We give a general definition of Wagoner complexes, ... More

Percolation in the hyperbolic space: non-uniqueness phase and fibrous clustersApr 13 2015In this thesis, I am going to consider Bernoulli percolation on graphs admitting vertex-transitive actions of groups of isometries of d-dimensional hyperbolic spaces H^d. In the first chapter, I give an overview concerning percolation and its terminology. ... More

Small maximal spaces of non-invertible matricesJul 14 2004A vector space A of matrices is called rank-critical if any vector space that properly contains A has a strictly higher generic rank. I present a sufficient condition for A to be rank-critical, and apply this condition to prove that certain Lie algebra ... More

Cauchy filters from Pelant's gamesOct 07 2013The language of finite games is used to rephrase Pelant's proof of his result: The separable modification of the complete metric space $C([0,\omega_1])$ is not complete.

Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functionsNov 13 2002We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical function on such a set corresponds to a function on the simplicial complex with ... More

The ring of arithmetical functions with unitary convolution: Divisorial and topological propertiesJan 10 2002We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical functions with ... More