Kullback-Leibler and Renormalized Entropy: Applications to EEGs of Epilepsy Patients

Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods.Comment: 15 pages, 4 Postscript figures. Submitted to Phys. Rev. E, 199

Tachyon fields with effects of quantum matter in an Anti-de Sitter Universe

We consider an Anti-de Sitter universe filled by quantum conformal matter with the contribution from the usual tachyon and a perfect fluid. The model represents the combination of a trace-anomaly annihilated and a tachyon driven Anti-de Sitter universe. The influence exerted by the quantum effects and by the tachyon on the AdS space is studied. The radius corresponding to this universe is calculated and the effect of the tachyon potential is discussed, in particular, concerning to the possibility to get an accelerated scale factor for the proposed model (implying an accelerated expansion of the AdS type of universe). Fulfillment of the cosmological energy conditions in the model is also investigatedComment: 14 Latex pages, no figure

Vanishing Cosmological Constant in Modified Gauss-Bonnet Gravity with Conformal Anomaly

We consider dark energy cosmology in a de Sitter universe filled with quantum conformal matter. Our model represents a Gauss-Bonnet model of gravity with contributions from quantum effects. To the General Relativity action an arbitrary function of the GB invariant, f(G), is added, and taking into account quantum effects from matter the cosmological constant is studied. For the considered model the conditions for a vanishing cosmological constant are considered. Creation of a de Sitter universe by quantum effects in a GB modified gravity is discussed.Comment: 8 pages latex, 1 figure. To appear in Int. J. Mod. Phys.

A Tale of Two Animats: What does it take to have goals?

What does it take for a system, biological or not, to have goals? Here, this question is approached in the context of in silico artificial evolution. By examining the informational and causal properties of artificial organisms ('animats') controlled by small, adaptive neural networks (Markov Brains), this essay discusses necessary requirements for intrinsic information, autonomy, and meaning. The focus lies on comparing two types of Markov Brains that evolved in the same simple environment: one with purely feedforward connections between its elements, the other with an integrated set of elements that causally constrain each other. While both types of brains 'process' information about their environment and are equally fit, only the integrated one forms a causally autonomous entity above a background of external influences. This suggests that to assess whether goals are meaningful for a system itself, it is important to understand what the system is, rather than what it does.Comment: This article is a contribution to the FQXi 2016-2017 essay contest "Wandering Towards a Goal

Crossover between the Dense Electron-Hole Phase and the BCS Excitonic Phase in Quantum Dots

Second order perturbation theory and a Lipkin-Nogami scheme combined with an exact Monte Carlo projection after variation are applied to compute the ground-state energy of $6\le N\le 210$ electron-hole pairs confined in a parabolic two-dimensional quantum dot. The energy shows nice scaling properties as N or the confinement strength is varied. A crossover from the high-density electron-hole phase to the BCS excitonic phase is found at a density which is roughly four times the close-packing density of excitons.Comment: Improved variational and projection calculations. 17 pages, 3 ps figures. Accepted for publication in Int. J. Mod. Phys.

Analytic results for NN particles with 1/r21/r^2 interaction in two dimensions and an external magnetic field

The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a $(2N-4)$-dimensional problem which is independent of $B$ and $\omega_0$. An exact, infinite set of relative mode excitations are obtained for any $N$. The $N=3$ problem reduces to that of a ficticious particle in a two-dimensional, non-linear potential of strength $\beta$, subject to a ficticious magnetic field $B_{\rm fic}\propto J$, the relative angular momentum.Comment: To appear in Physical Review Letters (in press). RevTeX file. Two figures available from [email protected] or [email protected]

Interplay between excitation kinetics and reaction-center dynamics in purple bacteria

Photosynthesis is arguably the fundamental process of Life, since it enables energy from the Sun to enter the food-chain on Earth. It is a remarkable non-equilibrium process in which photons are converted to many-body excitations which traverse a complex biomolecular membrane, getting captured and fueling chemical reactions within a reaction-center in order to produce nutrients. The precise nature of these dynamical processes -- which lie at the interface between quantum and classical behaviour, and involve both noise and coordination -- are still being explored. Here we focus on a striking recent empirical finding concerning an illumination-driven transition in the biomolecular membrane architecture of {\it Rsp. Photometricum} purple bacteria. Using stochastic realisations to describe a hopping rate model for excitation transfer, we show numerically and analytically that this surprising shift in preferred architectures can be traced to the interplay between the excitation kinetics and the reaction center dynamics. The net effect is that the bacteria profit from efficient metabolism at low illumination intensities while using dissipation to avoid an oversupply of energy at high illumination intensities.Comment: 21 pages, 13 figures, accepted for publication in New Journal of Physic