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1
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The uncertainty relation expressed by means of a new entropic function

100%
Majerník V.
Open Physics
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2008
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vol. 6
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issue 2
363-371
EN
In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.
2
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Labyrinthine pathways towards supercycle attractors in unimodal maps

76%
Moyano L., Silva D., Robledo A.
Open Physics
|
2009
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vol. 7
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issue 3
591-600
EN
As an important preceding step for the demonstration of an uncharacteristic (q-deformed) statisticalmechanical structure in the dynamics of the Feigenbaum attractor we uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the pre-images of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated with the family of supercycles. iv) This map is given in closed form by the same kind of q-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is final-stage ultra-fast dynamics towards the attractor, with a sensitivity to initial conditions which decreases as an exponential of an exponential of time. We discuss the relevance of these properties to the comprehension of the discrete scale-invariance features, and to the identification of the statistical-mechanical framework present at the period-doubling transition to chaos. This is the first of three studies (the other two are quoted in the text) which together lead to a definite conclusion about the applicability of q-statistics to the dynamics associated to the Feigenbaum attractor.
3
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How people react to a deadline: time distribution of conference registrations and fee payments

76%
Alfi V., Gabrielli A., Pietronero L.
Open Physics
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2009
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vol. 7
|
issue 3
483-489
EN
In this paper we present two simple mathematical models to describe human behavior in reaction to deadlines. When a real commitment (e.g. money) is involved, as in the case of a payment deadline, the expected reaction is to postpone it as close as possible to the deadline to minimize the risk of loosing the value. For low risk commitments this tendency is still present but expected to be looser. In order to test these predictions in a quantitative way, we performed data analysis for the total number of registrations and fee payments vs. time for the recent scientific conference “Statphys 23”, comparing it with the data of another conference in order to recover universal features. Two related models respectively for registrations (weak engagement) and fee payment (strong engagement) are then introduced which are able to explain in a simple way both behaviors, and which show an excellent agreement with real data.
4
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A mathematical structure for the generalization of conventional algebra

76%
Kaabouchi A., Nivanen L., Wang Q., Badiali J., Méhauté A.
Open Physics
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2009
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vol. 7
|
issue 3
549-554
EN
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate an algebra in which the conventional algebraic rules are generalized.
5
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Comprehensive Analyses of Gaussian Graphical Model under Different Biological Networks

76%
Dokuzoğlu D., Purutçuoğlu V.
Acta Physica Polonica A
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2017
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vol. 132
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issue 3
1106-1111
EN
Naturally, genes interact with each other by forming a complicated network and the relationship between groups of genes can be shown by different functions as gene networks. Recently, there has been a growing concern in uncovering these complex structures from gene expression data by modeling them mathematically. The Gaussian graphical model is one of the very popular parametric approaches for modelling the underlying types of biochemical systems. In this study, we evaluate the performance of this probabilistic model via different criteria, from the change in dimension of the systems to the change in the distribution of the data. Hereby, we generate high dimensional simulated datasets via copulas and apply them in Gaussian graphical model to compare sensitivity, specificity, F-measure and various other accuracy measures. We also assess its performance under real datasets. We consider that such comprehensive analyses can be helpful for assessing the limitation of this common model and for developing alternative approaches, to overcome its disadvantages.
6
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Instability transitions and ensemble equivalence in diffusive flow

64%
Ha M.
Open Physics
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2009
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vol. 7
|
issue 3
575-583
EN
We investigate the critical behavior of one-dimensional (1D) stochastic flow with competing nonlocal and local hopping events, in context of the totally asymmetric simple exclusion process (TASEP) with a defect site in a 1D closed chain. The defect site can effectively generate various boundary conditions, controlling the total number of particles in the system. Both open and periodic-like setups exhibit dynamic instability transitions from a populated finite density phase to an empty road (ER) phase as the nonlocal hopping rate increases. In the stationary populated phase, strong clustering promoted by nonlocal skids drives such transitions and determines their scaling properties. By static and dynamic simulations, we locate such transition points, and discuss their nature and scaling properties. In the open TASEP variant, we numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current, while it is first order in the regime where the bulk controls the current. Since it is well known that such transitions are absent in the periodic TASEP variant, we compare our results in the open setup with those in the periodic-like setup, and discuss the issue of the ensemble equivalence. Finally, the same discussion is extended to the symmetric cases.
7
Content available remote

q-Gaussian approximants mimic non-extensive statistical-mechanical expectation for many-body probabilistic model with long-range correlations

64%
Thistleton W., Marsh J., Nelson K., Tsallis C.
Open Physics
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2009
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vol. 7
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issue 3
387-394
EN
We study a strictly scale-invariant probabilistic N-body model with symmetric, uniform, identically distributed random variables. Correlations are induced through a transformation of a multivariate Gaussian distribution with covariance matrix decaying out from the unit diagonal, as ρ/r α for r =1, 2, ..., N-1, where r indicates displacement from the diagonal and where 0 ⩽ ρ ⩽ 1 and α ⩾ 0. We show numerically that the sum of the N dependent random variables is well modeled by a compact support q-Gaussian distribution. In the particular case of α = 0 we obtain q = (1-5/3 ρ) / (1- ρ), a result validated analytically in a recent paper by Hilhorst and Schehr. Our present results with these q-Gaussian approximants precisely mimic the behavior expected in the frame of non-extensive statistical mechanics. The fact that the N → ∞ limiting distributions are not exactly, but only approximately, q-Gaussians suggests that the present system is not exactly, but only approximately, q-independent in the sense of the q-generalized central limit theorem of Umarov, Steinberg and Tsallis. Short range interaction (α > 1) and long range interactions (α < 1) are discussed. Fitted parameters are obtained via a Method of Moments approach. Simple mechanisms which lead to the production of q-Gaussians, such as mixing, are discussed.
8
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Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

64%
Lundow P., Markström K.
Open Physics
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2009
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vol. 7
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issue 3
490-502
EN
In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to e.g. the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of e.g. latent heat and critical temperature, as well as the micro-canonical properties of interest.
9
Content available remote

Generalized binomial distribution in photon statistics

64%
Ilyin A.
Open Physics
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2015
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vol. 13
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issue 1
EN
The photon-number distribution between two parts of a given volume is found for an arbitrary photon statistics. This problem is related to the interaction of a light beam with a macroscopic device, for example a diaphragm, that separates the photon flux into two parts with known probabilities. To solve this problem, a Generalized Binomial Distribution (GBD) is derived that is applicable to an arbitrary photon statistics satisfying probability convolution equations. It is shown that if photons obey Poisson statistics then the GBD is reduced to the ordinary binomial distribution, whereas in the case of Bose- Einstein statistics the GBD is reduced to the Polya distribution. In this case, the photon spatial distribution depends on the phase-space volume occupied by the photons. This result involves a photon bunching effect, or collective behavior of photons that sharply differs from the behavior of classical particles. It is shown that the photon bunching effect looks similar to the quantum interference effect.
10
Content available remote

Stochastic dynamics and mean field approach in a system of three interacting species

64%
Valenti D., Spagnolo B.
|
EN
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied, by using Lotka-Volterra equations. A correlated dichotomous noise acts on the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of the three species. After analyzing the time behaviour of the three species in a single site, we consider a two-dimensional spatial domain, applying a mean field approach and obtaining the time behaviour of the first and second order moments for different multiplicative noise intensities. We find noise-induced oscillations of the three species with an anticorrelated behaviour of the two preys. Finally, we compare our results with those obtained by using a coupled map lattice (CML) model, finding a good qualitative agreement. However, some quantitative discrepancies appear, that can be explained as follows: i) different stationary values occur in the two approaches; ii) in the mean field formalism the interaction between sites is extended to the whole spatial domain, conversely in the CML model the species interaction is restricted to the nearest neighbors; iii) the dynamics of the CML model is faster since an unitary time step is considered.
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