Results for "Niko Tratnik"
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Generalized cut method for computing the edge-Wiener indexFeb 08 2019The edge-Wiener index of a connected graph $G$ is defined as the Wiener index of the line graph of $G$. In this paper it is shown that the edge-Wiener index of an edge-weighted graph can be computed in terms of the Wiener index, the edge-Wiener index, ... More The edge-Hosoya polynomial of benzenoid chainsDec 15 2017The Hosoya polynomial is a well known vertex-distance based polynomial, closely correlated to the Wiener index and the hyper-Wiener index, which are widely used molecular-structure descriptors. In the present paper we consider the edge version of the ... More Resonantly Equivalent Catacondensed Even Ring SystemsJan 24 2019In this paper we generalize the binary coding procedure of perfect matchings from catacondensed benzenoid graphs to catacondensed even ring systems (also called cers). Next, we study cers with isomorphic resonance graphs. For this purpose, we define resonantly ... More On the Clar Number of Benzenoid GraphsSep 13 2017A Clar set of a benzenoid graph $B$ is a maximum set of independent alternating hexagons over all perfect matchings of $B$. The Clar number of $B$, denoted by ${\rm Cl}(B)$, is the number of hexagons in a Clar set for $B$. In this paper, we first prove ... More The Wiener polarity index of benzenoid systems and nanotubesNov 09 2017In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry, materials engineering, ... More On the Steiner hyper-Wiener index of a graphOct 20 2017May 15 2018In this paper, we study the Steiner hyper-Wiener index of a graph, which is obtained from the standard hyper-Wiener index by replacing the classical graph distance with the Steiner distance. It is shown how this index is related to the Steiner Hosoya ... More Resonance Graphs and Perfect Matchings of Graphs on SurfacesOct 02 2017Let $G$ be a graph embedded in a surface and let $\mathcal F$ be a set of even faces of $G$ (faces bounded by a cycle of even length). The resonance graph of $G$ with respect to $\mathcal F$, denoted by $R(G;\mathcal F)$, is a graph such that its vertex ... More The Graovac-Pisanski Index of Armchair NanotubesApr 27 2017The Graovac-Pisanski index, which is also called the modified Wiener index, considers the symmetries and the distances in molecular graphs. Carbon nanotubes are molecules made of carbon with a cylindrical structure possessing unusual valuable properties. ... More Predicting Melting Points by the Graovac-Pisanski IndexSep 05 2017Theoretical molecular descriptors alias topological indices are a convenient means for expressing in a numerical form the chemical structure encoded in a molecular graph. The structure descriptors derived from molecular graphs are widely used in Quantitative ... More Almost additive entropyJan 06 2014We explore consequences of a hyperbolic metric induced by the composition property of the Harvda-Charvat/Dar\'{o}czy/Cressie-Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter \ $q\approx ... More Tsallis entropy and hyperbolicityAug 28 2013Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we examine consequences ... More Escort distributions and Tsallis entropyJun 22 2012We present an argument justifying the origin of the escort distributions used in calculations involving the Tsallis entropy. We rely on an induced hyperbolic Riemannian metric reflecting the generalized composition property of the Tsallis entropy. The ... More Weak Chaos from Tsallis EntropyApr 26 2011Nov 29 2012We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument relies on properties ... More Rate of parity violation from measure concentrationDec 04 2007We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. ... More The EM algorithm and the Laplace ApproximationJan 24 2014The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the ... More Magnetoresistance through spin polarized p-statesOct 24 2002Jul 23 2003We present a theoretical study of the ballistic magnetoresistance in Ni contacts using first-principles, atomistic electronic-structure calculations. In particular we investigate the role of defects in the contact region in order to explain the recently ... More Evaluations of Ramanujan Continued FractionsDec 24 2009In this paper we present experimental ways of evaluating Ramanujan`s quantities which as someone can see are related with algebraic numbers. The good thing with algebraic numbers is that can be found in a closed form, from there approximations, using ... More Algebraic Equations Solved with Jacobi Elliptic FunctionsJul 01 2013Mar 27 2014In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic singular modulus $k$. ... More On the Gauss Circle ProblemOct 21 2014Dec 18 2014We analyze the double series of Bessel functions given by Ramanujan. Using a very simple lemma we establish the uniform convergence of these series. By this we address to the Gauss circle problem. Multiple ergodic averages for three polynomials and applicationsJun 22 2006Aug 25 2007We find the smallest characteristic factor and a limit formula for the multiple ergodic averages associated to any family of three polynomials and polynomial families of the form $\{l_1p,l_2p,...,l_kp\}$. We then derive several multiple recurrence results ... More Tutorial for Bayesian forensic likelihood ratioApr 12 2013In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced. Such LRs are necessarily ... More Generative, Fully Bayesian, Gaussian, Openset Pattern ClassifierJul 23 2013Jul 24 2013This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class covariance, which is ... More Groups, non-additive entropy and phase transitionsApr 01 2014We investigate the possibility of discrete groups furnishing a kinematic framework for systems whose thermodynamic behaviour may be given by non-additive entropies. Relying on the well-known result of the growth rate of balls of nilpotent groups, we see ... More Diophantine equations coming from binomial near-collisionsJan 12 2019Feb 25 2019In this paper we solve the Diophantine equation $\binom{m}{l}-\binom{n}{k}=d$ (where m,n are positive integers unknowns) when (k,l)=(3,6) for various values of d and when (k,l)=(8,2) and d=1. As a byproduct of our results we will obtain that (k,l)-near ... More On the Representation of Involutive Jamesian FunctionsJun 20 2017Sep 09 2017Involutive Jamesian Functions are functions aimed to predict the outcome of an athletic competition. They were introduced in 1981 by Bill James, but until recently little was known regarding their form. Using methods from quasigroup theory we are able ... More Generalized Elliptic Integrals and ApplicationsApr 04 2013Jun 22 2013We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals. On Generalized Integrals and Ramanujan-Jacobi Special FunctionsSep 25 2013Nov 15 2015In this article we consider new generalized functions for evaluating integrals and roots of functions. The construction of these generalized functions is based on Rogers-Ramanujan continued fraction, the Ramanujan-Dedekind eta, the elliptic singular modulus ... More Convexity and the "Pythagorean" metric of space(-time)Jun 06 2016We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic ... More Entropies from coarse-graining: convex polytopes vs. ellipsoidsJul 16 2015We examine the Boltzmann/Gibbs/Shannon $\mathcal{S}_{BGS}$ and the non-additive Havrda-Charv\'{a}t / Dar\'{o}czy/Cressie-Read/Tsallis \ $\mathcal{S}_q$ \ and the Kaniadakis $\kappa$-entropy \ $\mathcal{S}_\kappa$ \ from the viewpoint of coarse-graining, ... More Extensive limit of a non-extensive entanglement entropyMar 21 2014An important calculation has been that of the (von Neumann) entanglement entropy of the ground state of 1-dimensional lattice models at criticality and of their massive perturbations. This entropy turned out to be, generally, non-extensive. It was noticed, ... More Asymptotic cones and quantum gravitySep 23 2013Asymptotic cones are structures that encode how a metric space appears when seen from far away. We discuss their meaning and potential significance for quantum gravity. The geodesic rule and the spectrum of the vacuumJun 30 2006We analyze the consequences of a recent argument justifying the validity of the "geodesic rule" which can be used to determine the density of global topological defects. We derive a formula that provides a rough estimate of the number of string-like defects ... More Entropy and curvature variations from effective potentialsApr 22 2005By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy $S$ of a finite-dimensional system around a non-degenerate critical point of its potential energy $V$. We compare $S$ with the entropy of ... More Tsallis entropy composition and the Heisenberg groupJan 01 2013We present an embedding of the Tsallis entropy into the 3-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition ... More A stochastic derivation of the geodesic ruleFeb 09 2006We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field $\phi$ in each causally connected volume. As these volumes collide and coalescence, $\phi$ evolves by performing a random walk ... More Algebra and calculus for Tsallis thermostatisticsJul 03 2005We construct generalized additions and multiplications, forming fields, and division algebras inspired by the Tsallis thermo-statistics. We also construct derivations and integrations in this spirit. These operations do not reduce to the naively expected ... More Lagrangian immersions in the product of Lorentzian two manifoldMar 03 2014Mar 26 2014For Lorentzian 2-manifolds $(\Sigma_1,g_1)$ and $(\Sigma_2,g_2)$ we consider the two product para-K\"ahler structures $(G^{\epsilon},J,\Omega^{\epsilon})$ defined on the product four manifold $\Sigma_1\times\Sigma_2$, with $\epsilon=\pm 1$. We show that ... More Optimal Infinity-Quasiconformal ImmersionsJun 26 2012Jul 18 2014For a Hamiltonian $K \in C^2(\mathbb{R}^{N \times n})$ and a map $u:\Omega \subseteq \mathbb{R}^n \longrightarrow \mathbb{R}^N$, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,\Omega) \ :=\ \big\|K(Du)\big\|_{L^\infty(\Omega)} . ... More On 4-fold covering movesFeb 19 2003Jan 22 2004We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two local moves suffice. ... More Representability of Aut_F and End_FJan 05 2003Recently N. Nitsure showed that for a coherent sheaf F on a noetherian scheme the automorphism functor Aut_F is representable if and only if F is locally free. Here we remove the noetherian hypothesis and show that the same result holds for the endomorphism ... More On Algebraic FunctionsMay 05 2013Mar 27 2014In this note we consider functions with Moebius-periodic rational coefficients. These functions under some conditions take algebraic values and can be recovered by theta functions and the Dedekind eta function. Special cases are the elliptic singular ... More The general solution of Schrodigers differential equationOct 31 2009In this note we solve theoretically the Schrodingers differential equation using results based on our previous work which concern semigroup operators. Our method does not use eigenvectors or eigenvalues and the solution depends only from the selected ... More Approximation of Sums of PrimesMar 27 2009In this work we consider sums of primes that converging very slow. We set as a base, a reformulation of analytic prime number theorem and we use the values of Riemann Zeta function for the approximation. We also give the truncation error of these approximations ... More A joint analysis of the Drake equation and the Fermi paradoxJan 27 2013Feb 26 2013I propose a unified framework for a joint analysis of the Drake equation and the Fermi paradox, which enables a simultaneous, quantitative study of both of them. The analysis is based on a simplified form of the Drake equation and on a fairly simple scheme ... More Ricci curvature, isoperimetry and a non-additive entropyFeb 18 2015Mar 17 2015Searching for the dynamical foundations of the Havrda-Charv\'{a}t/Dar\'{o}czy/Cressie-Read/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an $N$-Ricci curvature or a Bakry-\'{E}mery-Ricci ... More Nilpotence and the generalized uncertainty principle(s)Mar 11 2013Oct 09 2013We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, "deformations" of Lie algebras. We briefly comment on formal aspects related to the well-posedness of one of ... More Vanishing largest Lyapunov exponent and Tsallis entropyMar 13 2012Jul 11 2013We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity ... More Tsallis entropy induced metrics and CAT(k) spacesNov 20 2011Feb 06 2012Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set \ $\mathbb{R}^n_q$ \ induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a "hyperbolic analogue" of the ... More Geometric variations of the Boltzmann entropyApr 22 2008We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation ... More The role of Star Formation in the evolution of spiral galaxiesJan 27 2000Spiral galaxies offer a unique opportunity to study the role of star formation in galaxy evolution and to test various theoretical star formation schemes. I review some recent relevant work on the evolution of spiral galaxies. Detailed models are used ... More