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1.
We introduce here the q-Laplace transform as a new weapon in Tsallis’ arsenal, discussing its main properties and analyzing some examples. The q-Gaussian instance receives special consideration. Also, we derive the q-partition function from the q-Laplace transform. 相似文献
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We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q-Gaussian distributions and the q-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed q-entropy is attained, in both cases, by a generalized q-Gaussian distribution. This complements the fact that the q-Gaussians maximize the q-entropies subject to a moment constraint, and yields new variational characterizations of the generalizedq-Gaussians. We show that the generalized Fisher information naturally pop up in the expression of the time derivative of the q-entropies, for distributions satisfying a certain nonlinear heat equation. This result includes as a particular case the classical de Bruijn identity. Then we study further properties of the generalized Fisher information and of their minimization. We show that, though non additive, the generalized Fisher information of a combined system is upper bounded. In the case of mixing, we show that the generalized Fisher information is convex for q≥1. Finally, we show that the minimization of the generalized Fisher information subject to moment constraints satisfies a Legendre structure analog to the Legendre structure of thermodynamics. 相似文献
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We consider a single Abelian Higgs vortex on a surface Σ whose Gaussian curvature K is small relative to the size of the vortex, and analyse vortex motion by using geodesics on the moduli space of static solutions. The moduli space is Σ with a modified metric, and we propose that this metric has a universal expansion, in terms of K and its derivatives, around the initial metric on Σ. Using an integral expression for the Kähler potential on the moduli space, we calculate the leading coefficients of this expansion numerically, and find some evidence for their universality. The expansion agrees to first order with the metric resulting from the Ricci flow starting from the initial metric on Σ, but differs at higher order. We compare the vortex motion with the motion of a point particle along geodesics of Σ. Relative to a particle geodesic, the vortex experiences an additional force, which to leading order is proportional to the gradient of K. This force is analogous to the self-force on bodies of finite size that occurs in gravitational motion. 相似文献
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We discuss the modification of the Kapteyn multiplicative process using the q-product of Borges [E.P. Borges, A possible deformed algebra and calculus inspired in nonextensive thermostatistics, Physica A 340 (2004) 95]. Depending on the value of the index q a generalisation of the log-Normal distribution is yielded. Namely, the distribution increases the tail for small (when q<1) or large (when q>1) values of the variable upon analysis. The usual log-Normal distribution is retrieved when q=1, which corresponds to the traditional Kapteyn multiplicative process. The main statistical features of this distribution as well as related random number generators and tables of quantiles of the Kolmogorov–Smirnov distance are presented. Finally, we illustrate the validity of this scenario by describing a set of variables of biological and financial origin. 相似文献
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The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics . Starting from the q-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length. 相似文献
8.
We investigate the geometry of the moduli space of N vortices on line bundles over a closed Riemann surface Σ of genus g>1, in the little explored situation where 1≤N<g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ. For N=1, we show that the metric on the moduli space converges to a natural Bergman metric on Σ. When N>1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics. 相似文献
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The nonextensive parameter for nonequilibrium electron gas of the plasma in an electromagnetic field is studied. We exactly obtained an expression of the q-parameter based on Boltzmann kinetic theories for plasmas, where Coulombian interactions and Lorentz forces play dominant roles. We show that the q-parameter different from unity is related by an equation to temperature gradient, electric field strength, magnetic induction as well as overall bulk velocity of the gas. The effect of the magnetic field on the q-parameter depends on the overall bulk velocity. Thus the q-parameter for the electron gas in an electromagnetic field represents the nonequilibrium nature or nonisothermal configurations of the plasma with electromagnetic interactions. 相似文献
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Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q-generalized thermostatistical formalism, is characterized by a parameter q and in the limit q→1 reduces to the standard, linear Schrödinger equation. The q-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1 limit the q-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations. 相似文献
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A micro-level agent-based model of innovation diffusion was developed that explicitly combines (a) an individual’s perception of the advantages or relative utility derived from adoption, and (b) social influence from members of the individual’s social network. The micro-model was used to simulate macro-level diffusion patterns emerging from different configurations of micro-model parameters. Micro-level simulation results matched very closely the adoption patterns predicted by the widely-used Bass macro-level model (Bass, 1969 [1]). For a portion of the p−q domain, results from micro-simulations were consistent with aggregate-level adoption patterns reported in the literature. Induced Bass macro-level parameters p and q responded to changes in micro-parameters: (1) p increased with the number of innovators and with the rate at which innovators are introduced; (2) q increased with the probability of rewiring in small-world networks, as the characteristic path length decreases; and (3) an increase in the overall perceived utility of an innovation caused a corresponding increase in induced p and q values. Understanding micro to macro linkages can inform the design and assessment of marketing interventions on micro-variables–or processes related to them–to enhance adoption of future products or technologies. 相似文献
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We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order q, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2 or 3. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-q entropy for 1≤q≤2 or 3≤q≤4, which also contains the multi-qubit polygamy inequality as a special case. 相似文献
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We study the enumerative significance of the s-pointed genus zero Gromov–Witten invariant on a homogeneous space X. For that, we give an interpretation in terms of rational curves on X. 相似文献
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We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador” nodes and l of each ambassador’s descendants where m and l are random variables selected from any choice of distributions pl and qm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l, the power-law exponent is (2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically. 相似文献
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A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
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Community detection is a very important problem in social network analysis. Classical clustering approach, K-means, has been shown to be very efficient to detect communities in networks. However, K-means is quite sensitive to the initial centroids or seeds, especially when it is used to detect communities. To solve this problem, in this study, we propose an efficient algorithm K-rank, which selects the top-K nodes with the highest rank centrality as the initial seeds, and updates these seeds by using an iterative technique like K-means. Then we extend K-rank to partition directed, weighted networks, and to detect overlapping communities. The empirical study on synthetic and real networks show that K-rank is robust and better than the state-of-the-art algorithms including K-means, BGLL, LPA, infomap and OSLOM. 相似文献
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Suppose that the sphere Sn has initially a homogeneous distribution of mass and let G be the Lie group of orientation preserving projective diffeomorphisms of Sn. A projective motion of the sphere, that is, a smooth curve in G, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sn and, more generally, examples of subgroups H of G such that a force free motion initially tangent to H remains in H for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=SOn+1). The main tool is a Riemannian metric on G, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy. 相似文献
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A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞ and infinite equation of state parameter, w→∞. During evolution it subsequently passes through the stiff fluid era, q=2, w=1, the radiation dominated era, q=1, w=1/3 and the matter dominated era, q=1/2, w=0. Finally, deceleration halts, q=0, w=−1/3, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1, w→−1. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1) the model. 相似文献
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We use Beck's quasi-additivity of Tsallis entropies for n independent subsystems to show that like the case of n=2, the entropic index q approaches 1 by increasing system size. Then, we will generalize that concept to correlated subsystems to find that in the case of correlated subsystems, when system size increases, q also approaches a value corresponding to the additive case. 相似文献
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In this paper, the dynamics of opinion formation is investigated based on a BA (Barabási–Albert) scale-free network, using a majority–minority rule governed by parameter q. As the value of q is smoothly varied, a phase transition occurs between an ordered phase and a disordered one. By performing extensive Monte Carlo simulations, we show that the phase transition is dependent on the system size, as well as on m, the number of edges added at each time step during the growth of the BA scaling network. Additionally, some theoretical analysis is given based on mean-field theory, by neglecting fluctuations and correlations. It is observed that the theoretical results coincide with results from simulations, especially for very large m. 相似文献