On the resonance eigenstates of an open quantum baker map

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, $|z_{min}|\leq |z|\leq |z_{max}|$. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius $r$. We prove that, if the moduli converge to $r=|z_{max}|$, then the sequence of eigenstates converges to a fixed phase space measure $\rho_{max}$. The same holds for sequences with eigenvalue moduli converging to $|z_{min}|$, with a different limit measure $\rho_{min}$. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius $|z_{min}|< r < |z_{max}|$, we identify families of eigenstates with precise self-similar properties.Comment: 32 pages, 2 figure

Microbiological characteristics of subgingival microbiota in adult periodontitis, localized juvenile periodontitis and rapidly progressive periodontitis subjects

Objective To describe the prevalence of the cultivable subgingival microbiota in periodontal diseases and to draw attention to the polymicrobial nature of periodontic infections.Methods The study population consisted of 95 patients, 51 females and 44 males, aged 14-62 years. Twenty-nine patients exhibited adult periodontitis (AP), six localized juvenile periodontitis (LJP), and 60 rapidly progressive periodontitis (RPP). Two to four pooled bacterial samples were obtained from each patient. Samples were collected with sterile paper points from the deepest periodontal pockets. The samples were cultured under anaerobic and microaerophilic conditions using selective and non-selective media. Isolates were characterized to species level by conventional biochemical tests and by a commercial rapid test system.Results Prevotella intermedia and Capnocytophaga spp. were the most frequently detected microorganisms in all diagnostic groups. Porphyromonas gingivalis and Peptostreptococcus micros were found more frequently in AP and RPP patients, while Actinohacillus actinomycetemcomitans and Eikenella corrodens were associated with AP, LJP and RPP patients. The other bacterial species, including Actinomyces spp., Streptococcus spp. and Euhacterium spp., were detected at different levels in the three disease groups.Conclusions The data show the complexity of the subgingival microbiota associated with different periodontal disease groups, indicating that the detection frequency and levels of recovery of some periodontal pathogens are different in teeth affected by different forms of periodontal disease

Coarse Grained Liouville Dynamics of piecewise linear discontinuous maps

We compute the spectrum of the classical and quantum mechanical coarse-grained propagators for a piecewise linear discontinuous map. We analyze the quantum - classical correspondence and the evolution of the spectrum with increasing resolution. Our results are compared to the ones obtained for a mixed system.Comment: 11 pages, 8 figure

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Spectral problems in open quantum chaos

This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic. We will focus on the distribution of quantum resonances, and the structure of the corresponding metastable states. Our study includes the toy model of open quantum maps, as well as the recent quantum monodromy operator method.Comment: Compared with the previous version, misprints and typos have been corrected, and the bibliography update

Dissipation time and decay of correlations

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the opposite, it is fast for a large class of exponentially mixing systems which include uniformly expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Fractal Weyl law for Linux Kernel Architecture

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be $\nu \approx 0.63$ that corresponds to the fractal dimension of the network $d \approx 1.2$. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension $d<2$.Comment: RevTex 6 pages, 7 figs, linked to arXiv:1003.5455[cs.SE]. Research at http://www.quantware.ups-tlse.fr/, Improved version, changed forma