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Asymptotic Hilbert Polynomial and a bound for Waldschmidt constantsNov 24 2015In the paper we give an upper bound for the Waldschmidt constants of the wide class of ideals. This generalizes the result obtained by Dumnicki, Harbourne, Szemberg and Tutaj-Gasinska, Adv. Math. 2014. Our bound is given by a root of a suitable derivative ... More

Symbolic powers of planar point configurationsMay 27 2012We study initial degrees of symbolic powers of ideals of arbitrary finite sets of points in the projective plane over an algebraically closed field of characteristic zero. We show, how bounds on the growth of these degrees determine the geometry of the ... More

Symbolic powers of planar point configurations IIApr 21 2015We study initial sequences of various configurations of planar points. We answer several questions asked in our previous paper (Symbolic powers of planar point configurations), and we extend our considerations to the asymptotic setting of Waldschmidt ... More

Local effectivity in projective spacesFeb 23 2018In this note we introduce a Waldschmidt decomposition of divisors which might be viewed as a generalization of Zariski decomposition based on the effectivity rather than the nefness of divisors. As an immediate application we prove a recursive formula ... More

Regularity and non-emptyness of linear systems in $\mathbb P^n$Feb 07 2008The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general position. To ... More

Linear systems in P^3 with low degrees and low multiplicitiesOct 12 2008We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the cases that have not been completed in a paper by E. Ballico and M.C. Brambilla. ... More

Containments of symbolic powers of ideals of generic points in $\PP^3$Dec 04 2012We show that the Conjecture of Harbourne and Huneke, $I^{(Nr-(N-1))} \subset M^{(r-1)(N-1)}I^{r}$ holds for ideals of generic (simple) points in $\PP^3$. As a result, for such ideals we prove the following bounds, which can be recognized as generalizations ... More

Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10Apr 08 2008In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$, 8, 9, 10, i.e. systems of curves of given degree passing through points in general position with multiplicities at least $m,...,m,m_0$, ... More

Symbolic powers of ideals of generic points in P^3May 02 2011B. Harbourne and C. Huneke conjectured that for any ideal $I$ of fat points in $P^N$ its $r$-th symbolic power $I^{(r)}$ should be contained in $M^{(N-1)r}I^r$, where $M$ denotes the homogeneous maximal ideal in the ring of coordinates of $P^N$. We show ... More

Linear subspaces, symbolic powers and Nagata type conjecturesJul 05 2012Sep 30 2012Prompted by results of Guardo, Van Tuyl and the second author for lines in projective 3 space, we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r dimensional planes in projective ... More

Special homogeneous linear systems on Hirzebruch surfacesJul 22 2009The Segre-Gimigliano-Harbourne-Hirschowitz Conjecture can be naturally formulated for Hirzebruch surfaces F_n. We show that this Conjecture holds for imposed base points of equal multiplicity bounded by 8.

Special homogeneous linear systems on Hirzebruch surfaces - algorithmic issuesNov 07 2009We present algorithms used in the computational part of the article "Special homogeneous linear systems on Hirzebruch surfaces".

Reduction method for linear systems of plane curves with base fat pointsJun 28 2006In the paper we develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne Conjecture holds for systems with base points of equal multiplicity bounded ... More

Expected term bases for generic multivariate Hermite interpolationMar 30 2005The main goal of the paper is to find an effective estimation for the minimal number of generic points in $\mathbb K^2$ for which the basis for Hermite interpolation consists of the first $\ell$ terms (with respect to total degree ordering). As a result ... More

Lower bounds for Waldschmidt constants of generic lines in $\mathbb{P}^3$ and a Chudnovsky-type theoremMar 06 2018The Waldschmidt constant $\alphahat(I)$ of a radical ideal $I$ in the coordinate ring of $\PP^N$ measures (asymptotically) the degree of a hypersurface passing through the set defined by $I$ in $\PP^N$. Nagata's approach to the 14th Hilbert Problem was ... More

Symbolic generic initial systems of star configurationsJan 19 2014The purpose of this note is to describe limiting shapes (as introduced by Mayes) of symbolic generic initial systems of star configurations in projective spaces over a field of characteristic 0.

Resurgences for ideals of special point configurations in ${\bf P}^N$ coming from hyperplane arrangementsApr 19 2014Symbolic powers of ideals have attracted interest in commutative algebra and algebraic geometry for many years, with a notable recent focus on containment relations between symbolic powers and ordinary powers. Several invariants have been introduced and ... More

New effective bounds on the dimension of a linear system in $\mathbb P^2$May 10 2005Jul 09 2005The main goal of this paper is to present an algorithm bounding the dimension of a linear system of curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Hirschowitz--Harbourne Conjecture when the ... More

A containment result in $\mathbb{P}^n$ and the Chudnovsky conjectureMar 11 2016In the paper we prove the containment $I^{(nm)}\subset M^{(n-1)m}I^m$, for a radical ideal $I$ of $s$ general points in $\mathbb{P}^n$, where $s\geq 2^n$. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least $2^n$ ... More

Points fattening on P^1 x P^1 and symbolic powers of bi-homogeneous idealsApr 21 2013We study symbolic powers of bi-homogeneous ideals of points in the Cartesian product of two projective lines and extend to this setting results on the effect of points fattening obtained by Bocci, Chiantini and Dumnicki, Szemberg, Tutaj-Gasi\'nska. We ... More

A containment result in $\mathbb{P}^n$ and the Chudnovsky conjectureMar 11 2016Nov 25 2016In the paper we prove the containment $I^{(nm)}\subset M^{(n-1)m}I^m$, for a radical ideal $I$ of $s$ general points in $\mathbb{P}^n$, where $s\geq 2^n$. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least $2^n$ ... More

A vanishing theorem and symbolic powers of planar point idealsFeb 04 2013The purpose of this note is twofold. We present first a vanishing theorem for families of linear series with base ideal being a fat points ideal. We apply then this result in order to give a partial proof of a conjecture raised by Bocci, Harbourne and ... More

Asymptotic Hilbert Polynomial and limiting shapesJul 02 2014The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of P^n. M. Mustata and S. Mayes established a connection between volumes of complements of limiting ... More

Counterexamples to the $I^{(3)} \subset I^2$ containmentJan 30 2013Apr 21 2015We show that in general the third symbolic power of a radical ideal of points in the complex projective plane is not contained in the second usual power of that ideal. This answers in negative a question asked by Huneke and generalized by Harbourne.

On absolute linear Harbourne constantsJul 15 2015Jan 13 2016In the present note we study absolute linear Harbourne constants. These are invariants which were introduced in order to relate the lower bounds on the selfintersection of negative curves on birationally equivalent surfaces to the complexity of the birational ... More

Very general monomial valuations of $\mathbb{P}^2$ and a Nagata type conjectureDec 19 2013Feb 05 2016It is well known that multi-point Seshadri constants for a small number $s$ of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for $s\geq 9$ points. Tackling the problem in the language ... More

Seshadri constants via Okounkov functions and the Segre-Harbourne-Gimigliano-Hirschowitz ConjectureMar 31 2013In this note we relate the SHGH Conjecture to the rationality of one-point Seshadri constants on blow ups of the projective plane, and explain how rationality of Seshadri constants can be tested with the help of functions on Newton--Okounkov bodies.

A matrixwise approach to unexpected hypersurfacesJul 10 2019The aim of this note is to give a generalization of some results concerning unexpected hypersurfaces. Unexpected hypersurfaces occur when the actual dimension of the space of forms satisfying certain vanishing data is positive and the imposed vanishing ... More

Parameter estimation in the presence of the most general Gaussian dissipative reservoirSep 11 2016We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both ... More

Finding Traps in Non-linear Spin ArraysNov 18 2009Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear structure. While ... More

Perfect State Transfer without State Initialization and Remote CollaborationFeb 06 2009May 09 2013We present a perfect state transfer protocol via a qubit chain with the evolution governed by the $xx$ Hamiltonian. In contrast to the recent protocol announced in [Phys. Rev. Lett. {\bf 101}, 230502 (2008)], our method does not demand any remote-cooperated ... More

One-Qubit and Two-Qubit Codes in Noisy State TransferMay 04 2009Quantum state transfer is a procedure, which allows to exchange quantum information between stationary qubit systems. It is anticipated that the transfer will find applications in solid-state quantum computing. In this contribution, we discuss the effects ... More

Parameter estimation in the presence of the most general Gaussian dissipative reservoirSep 11 2016Jan 16 2017We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both ... More

On quantum interferometric measurements of temperatureDec 17 2014Sep 14 2015We provide a detailed description of the quantum interferometric thermometer, which is a device that estimates the temperature of a sample from the measurements of the optical phase. For the first time, we rigorously analyze the operation of such a device ... More

On the Sylvester-Gallai theorem for conicsNov 10 2014In the present note we give a new proof of a result due to Wiseman and Wilson which establishes an analogue of the Sylvester-Gallai theorem valid for curves of degree two. The main ingredients of the proof come from algebraic geometry. Specifically, we ... More

The planar Ising model and total positivityJun 20 2016Jun 29 2016A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph $G$. Let $a_1,\dots,a_k,b_k,\dots,b_1$ be ... More

Homomorphism reconfiguration via homotopyAug 12 2014We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring throughout. ... More

Transitivity vs. Intransitivity in decision making process. (An example in quantum game theory)Jan 12 2009Feb 01 2009We compare two different ways of quantization a simple sequential game Cat's Dilemma in the context of the debate on intransitive and transitive preferences. This kind of analysis can have essential meaning for the research on the artificial intelligence ... More

Nonuniqueness of gravity-induced fermion interaction in the Einstein-Cartan theoryNov 12 2008Dec 12 2008The problem of nonuniqueness of minimal coupling procedure for Einstein--Cartan (EC) gravity with matter is investigated. It is shown that the predictions of the theory of gravity with fermionic matter can radically change if the freedom of addition of ... More

Twisted Rindler space-timesApr 22 2010The (linearized) noncommutative Rindler space-times associated with canonical, Lie-algebraic and quadratic twist-deformed Minkowski spaces are provided. The corresponding deformed Hawking spectra detected by Rindler observers are derived as well.

Monogamy of entanglement as a necessary and sufficient condition for safe QKD in any physical theoryMay 15 2007We show that the monogamy of entanglement is a sufficient phenomenon in every physical theory, if the quantum key distribution is to be safe on the grounds of such theory. To do so we present the QKD protocol that is safe in any physical theory under ... More

Approximation of analytic sets with proper projection by algebraic setsMay 12 2009Let $X$ be an analytic subset of $U\times C^n$ of pure dimension $k$ such that the projection of $X$ onto $U$ is a proper mapping, where $U$ is a Runge domain in $C^k$. We show that $X$ can be approximated by algebraic sets.

Heisenberg chains cannot mirror a stateSep 02 2008Nov 27 2008Faithful exchange of quantum information can in future become a key part of many computational algorithms. Some Authors suggest to use chains of mutually coupled spins as channels for quantum communication. One can divide these proposals into the groups ... More

Contour integrals as $Ad$-invariant functions on the fundamental groupJul 11 2005We introduce a general approach to contour integrals. It covers usual Abelian integrals, the higher order Melnikov integrals and the generalized Abelian integrals. We prove that the generating function always satisfies a linear differential equation of ... More

A dichotomy for Borel functionsOct 08 2008The dichotomy discovered by Solecki in \cite{Sol} states that any Baire class 1 function is either $\sigma$-continuous or "includes" the Pawlikowski function $P$. The aim of this paper is to give an argument which is simpler than the original proof of ... More

A note on ccc forcingsSep 23 2008The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc $\sigma$-ideal I any I-positive Borel set contains modulo I an I-positive closed set?

Parallel Prefix Algorithms for the Registration of Arbitrarily Long Electron Micrograph SeriesDec 07 2017Recent advances in the technology of transmission electron microscopy have allowed for a more precise visualization of materials and physical processes, such as metal oxidation. Nevertheless, the quality of information is limited by the damage caused ... More

Forcing, games and families of closed setsOct 13 2009We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For definable ($\mathbf{\Pi}^1_1$ on $\mathbf{\Sigma}^1_1) $\sigma$-ideals we show ... More

Approximation of maps into spheres by piecewise-regular maps of class C^kAug 21 2018Dec 13 2018The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.

Faster Than Light CommunicationNov 04 1999Nov 16 1999This paper has been withdrawn by the author, due a crucial error in the main idea.

A model of morphogen transport IINov 28 2014Apr 07 2015A model of morphogen transport consisting of two evolutionary PDEs of reaction-diffusion type and three ODEs posed on a rectangular domain is analysed. We prove that the problem is globally well-posed and that the corresponding solutions converge, as ... More

Affine strict polynomial functors and formalityNov 13 2014We introduce the notion of affine strict polynomial functor. We show how this concept helps to understand homological behavior of the operation of Frobenius twist in the category of strict polynomial functors over a field of positive characteristic. We ... More

The planar Ising model and total positivityJun 20 2016Dec 29 2016A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph $G$. Let $a_1,\dots,a_k,b_k,\dots,b_1$ be ... More

Line arrangements with the maximal number of triple pointsJun 25 2014The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We give precise conditions on ground fields F over which such extremal configurations ... More

Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-timesJan 10 2011The time-dependent spectra of disc area operator for twisted acceleration-enlarged Newton-Hooke space-times are derived. It is demonstrated that the corresponding area quanta are expanding or oscillating in time.

Generalized Dirac bracket and the role of the Poincaré symmetry in the program of canonical quantization of fields 2Nov 12 2010In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the quantization of electrodynamics, ... More

Deformation of nonrelativistic space-time and forces noticed by noninertial observerJul 27 2010We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph], we recall ... More

Ellipsoids of U(3) modelNov 19 2009Nov 25 2009The Cartan model of SO(3)/SO(2) matrices is applied to reduce of rotational degrees of freedom on coadjoint orbits of u^*(3) Poisson algebra. The seven--dimensional Poisson algebra u_SO(3) obtained by SO(3) reduction of u^*(3) algebra is found and canonical ... More

Generalized Dirac bracket and the role of the Poincaré symmetry in the program of canonical quantization of fields 1Oct 27 2010Nov 12 2010An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be consistently replaced ... More

Local approximation of the solutions of algebraic equationsMar 27 2008A method of local approximation of holomorphic solutions of algebraic equations is discussed

Quantum Wire as Open SystemNov 15 2007May 02 2008The faithful exchange of quantum information will soon become one of the challenges of the emerging quantum information technology. One of the possible solutions is to transfer a superposition through a chain of properly coupled spins. Such a system is ... More

Quasi-Quantum Model of PotentizationNov 23 2009Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during the decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist ... More

Investigation of astrophysical phenomena in short time scales with "Pi of the Sky" apparatusOct 07 2008In this thesis the data analysis designed by author for the "Pi of the Sky" experiment is presented. The data analysis consists of data reduction and specific algorithms for identification of short time scale astrophysical processes. The algorithms have ... More

Approximation of sets defined by polynomials with holomorphic coefficientsDec 18 2007Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to a_1,...,a_s ... More

Analysis of Implementation Hierocrypt-3 algorithm (and its comparison to Camellia algorithm) using ALTERA devicesDec 17 2003Alghoritms: HIEROCRYPT-3, CAMELLIA and ANUBIS, GRAND CRU, NOEKEON, NUSH, Q, RC6, SAFER++128, SC2000, SHACAL were requested for the submission of block ciphers (high level block cipher) to NESSIE (New European Schemes for Signatures, Integrity, and Encryption) ... More

Error correction in quantum cryptography based on artificial neural networksOct 01 2018Intensive work on quantum computing has increased interest in quantum cryptography in recent years. Although this technique is characterized by a very high level of security, there are still challenges that limit the widespread use of quantum key distribution. ... More

Classical conformal blocks from TBA for the elliptic Calogero-Moser systemFeb 26 2011Jun 22 2011The so-called Poghossian identities connecting the toric and spherical blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain expressions for the classical ... More

Charge-density-wave phases of the generalized t-V modelNov 22 2015Apr 27 2016The one-dimensional extended t-V model of fermions on a lattice is a model with repulsive interactions of finite range that exhibits a transition between a Luttinger liquid conducting phase and a Mott insulating phase. It is known that by tailoring the ... More

Integral expression for a topological charge in the Faddeev-Niemi non-linear sigma modelNov 08 2013We have introduced Faddeev-Niemi type variables for static SU(3) Yang-Mills theory. The variables suggest that a non-linear sigma model whose sigma fields take values in SU(3)/(U(1)xU(1)) and SU(3)/(SU(2)xU(1)) may be relevant to infrared limit of the ... More

Generalized twist deformations of Poincare and Galilei quantum groupsFeb 20 2015The three quantum groups dual to the generalized twist deformed Poincare Hopf algebras are provided with use of FRT procedure. Their Galilean counterparts are obtained by nonrelativistic contraction scheme.

Twist deformation of l-conformal Galilei Hopf algebraJul 03 2013The six Abelian twist-deformations of l-conformal Galilei Hopf algebra are considered. The corresponding twisted space-times are derived as well.

Two-particle system in Coulomb potential for twist-deformed space-timeJul 11 2018In this article, we define two-particle system in Coulomb potential for twist-deformed space-time with spatial directions commuting to time-dependent function $f_{\kappa_a}({t})$. Particularly, we provide the proper Hamiltonian function and further, we ... More

Formal Semantics of Architectural Decision ModelsJul 08 2018A software architecture is the result of multiple decisions made by a software architect. These decisions are called architectural decisions, as they bring solutions to architectural problems. Relations between decisions can be captured in architectural ... More

The Henon-Heiles system defined on canonically deformed space-timeOct 25 2016In this article we provide canonically deformed classical Henon-Heiles system. Further we demonstrate that for proper value of deformation parameter $\theta$ there appears chaos in the model.

Towards Optimal Sorting of 16 ElementsAug 03 2011One of the fundamental problem in the theory of sorting is to find the pessimistic number of comparisons sufficient to sort a given number of elements. Currently 16 is the lowest number of elements for which we do not know the exact value. We know that ... More

Search for η-->e+e- decay with the WASA experimentJan 25 2013Nowadays the field of searching for a new physics became a very interesting subject in a light meson decays due to a recent results from KTeV collaboration which found the 3.3\sigma\ disagreement between Standard Model theory and their results of \pi ... More

Irregular Labellings of Circulant GraphsNov 01 2011We investigate the \textit{irregularity strength} ($s(G)$) and \textit{total vertex irregularity strength} ($tvs(G)$) of circulant graphs $Ci_n(1,2,...,k)$ and prove that $tvs(Ci_n(1,2,...,k))=\lceil\frac{n+2k}{2k+1}\rceil$, while $s(Ci_n(1,2,...,k))=\lceil\frac{n+2k-1}{2k}\rceil$ ... More

Stars, Dust, and the Growth of UV-Selected Sub-L* Galaxies at Redshift z~2Aug 25 2011[Abridged] This work concerns very faint (R_lim=28 AB mag; M_(stars, lim) ~ 10^8 Msun), UV-selected sub-L* BX galaxies at z~2.3. Stellar masses, dust content, and dust-corrected SFRs are constrained using broadband SED fitting, giving insights into the ... More

Noncommutative Sprott systems and their jerk dynamicsJun 21 2018In this article we provide the noncommutative Sprott models. We demonstrate, that effectively, each of them is described by system of three complex, ordinary and nonlinear differential equations. Apart of that, we find for such modified models the corresponding ... More

Continuous frames and the Kadison-Singer problemFeb 01 2018In this paper we survey a recent progress on continuous frames inspired by the solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava. We present an extension of Lyapunov's theorem for discrete frames due to Akemann and Weaver and ... More

Analysis of experimental uncertainties in the R-correlation measurement in the decay of free neutronsJun 29 2004Sep 07 2004The experiment aiming at the simultaneous determination of the two transversal polarisation components of electrons emitted in the decay of free, polarised neutrons is in progress at the Paul Scherrer Institute (Villigen, Switzerland). The non-zero value ... More

Completeness of the isomorphism problem for separable C*-algebrasJun 05 2013Jul 13 2013We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation. This means ... More

The fermionic observable in the Ising model and the inverse Kac-Ward operatorMar 12 2013Apr 30 2015We show that the critical Kac-Ward operator on isoradial graphs acts in a certain sense as the operator of s-holomorphicity, and we identify the fermionic observable for the spin Ising model as the inverse of this operator. This result is partially a ... More

Derived Kan extension for strict polynomial functorsJun 16 2011Nov 08 2014We investigate fundamental properties of adjoint functors to the precomposition functor in the category of strict polynomial functors.

On Serre functor in the category of strict polynomial functorsMar 19 2016We introduce and study a Serre functor in the category ${\cal P}_d$ of strict polynomial functors over a field of positive characteristic. By using it we obtain the Poincar\'e duality formula for Ext--groups from [C3] in elementary way. We also show that ... More

Circle patterns and critical Ising modelsDec 23 2017A circle pattern is an embedding of a planar graph in which each face is inscribed in a circle. We define and prove magnetic criticality of a new family of Ising models on planar graphs whose dual is a circle pattern. Our construction includes as a special ... More

Rabi-resonant behavior of periodically-driven correlated fermion systemsApr 11 2019Fermi-Hubbard system with a periodically-modulated interaction has been recently shown to resonantly absorb energy at series of drive frequencies. In the present work, with the help of static perturbation theory we argue that driving couples to Hubbard ... More

Information and the arrow of timeJan 16 2011Apr 16 2012This paper is a discussion about the relationship between time and information. We argue that the direction of arrow of time is related to the directivity of information copying that occurs in Nature.

An Optimal Lower Bound for Buffer Management in Multi-Queue SwitchesJul 09 2010Aug 14 2012In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets ... More

Minimum energy required to copy one bit of informationApr 27 2010May 14 2010In this paper, we calculate energy required to copy one bit of useful information in the presence of thermal noise. For this purpose, we consider a quantum system capable of storing one bit of classical information, which is initially in a mixed state ... More

Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violationsJul 22 2009Sep 21 2010We show that monogamy of Bell's inequality violations, which is strictly weaker condition than no-signaling is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results ... More

BiosupersymmetryJun 11 2009The growth of biological systems described by the Gompertz and West-Brown-Enquist functions is considered in the framework of the space-like supersymmetric quantum mechanics. It has been shown that the supersymmetric effect of a fermion-boson conversion ... More

On the choice of coupling procedure for the Poincaré gauge theory of gravityFeb 25 2009Mar 25 2009The gauge approach to the theory of gravity has been widely discussed as an alternative to standard general relativity. The Poincar{\'e} group, as a symmetry group of all relativistic theories in the absence of gravitation, constitutes the most natural ... More

Measurement of Delta G/G from high transverse momentum hadron pairs in COMPASSSep 10 2008The new COMPASS Delta G/G result obtained from high transverse momentum hadron pairs in the Q^2>1 GeV^2 region is presented. Comparing to the previous analysis in this region the statistical error of Delta G/G is reduced by a factor 3 to 0.10. A weighted ... More

Quantum Entanglement in Some Physical SystemsOct 09 2007The summary of the Author's results on Bell inequalities and macroscopic entanglement.

On the Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other SciencesJun 25 2007Comment on "Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences" by P. Castorina, P. P. Delsanto and C. Guiot, Phys. Rev. Lett. {\bf 96}, 188701 (2006) is presented. It has been proved that the West-like ... More

Superfast Algorithms and the Halting Problem in Geometric AlgebraNov 05 2006A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are exploited to obtain ... More

Strategy in Ulam's Game and Tree Code Give Error-Resistant ProtocolsOct 18 2004We present a new approach to construction of protocols which are proof against communication errors. The construction is based on a generalization of the well known Ulam's game. We show equivalence between winning strategies in this game and robust protocols ... More

Finite arithmetic subgroups of GL_nMar 23 1998We discuss the following conjecture of Kitaoka: if a finite subgroup $G$ of $GL_{n}(O_{K})$ is invariant under the action of $Gal(K/\Bbb Q)$ then it is contained in $GL_{n}(K^{ab})$. Here $O_{K}$ is the ring of integers in a finite, Galois extension $K$ ... More

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More