Sparse Inpainting and Isotropy

Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide analytic computations and simulations of inpainted maps for a Gaussian isotropic model of CMB data, suggesting that the resulting angular trispectrum may exhibit small but non-negligible deviations from isotropy.Comment: 18 pages, 6 figures. v3: matches version published in JCAP; formatting changes and single typo correction only. Code available from http://zuserver2.star.ucl.ac.uk/~smf/code.htm

Abstract polymer models with general pair interactions

A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of the BEG model with infinite range interactions, decaying polynomially as $1/r^{d+\lambda}$ with $\lambda>0$, is studied.Comment: 19 pages. Corrected statement for the stability condition (2.3) and modified section 3.1 of the proof of theorem 1 consistently with (2.3). Added a reference and modified a sentence at the end of sec. 2.

Avaliação de diferentes pré-tratamentos do inóculo para produção de H2 por bactérias anaeróbias

A produção de biohidrogênio através do processo de fermentação anaeróbia tem recebido grande destaque nos últimos tempos. O enriquecimento do inóculo através de pré-tratamento elimina e/ou inibi micro-organismos consumidores de H2 não formadores de esporo e favorece a seleção de micro-organismos produtores de H2, dentre os quais se destacam os micro-organismos do gênero Clostridium. Os efeitos dos diferentes pré-tratamentos do inóculo (ácido, alcalino e térmico) sobre o desempenho das comunidades bacterianas responsáveis pela produção de H2 foram avaliados através dos níveis de expressão das hidrogenases de Clostridium associados aos rendimentos máximos de H2 obtidos. O pré-tratamento térmico apresentou o maior rendimento de H2 (4,62 mol de H2/mol de sacarose) e o maior nível de expressão das hidrogenases, 64 vezes superior ao do inóculo in natura, em 72 h de fermentação. Elevados rendimentos de H2 também foram obtidos pelos inóculos com pré-tratamento alcalino (3,93 mol de H2/mol de sacarose) e ácido (3,85 mol de H2/mol de sacarose) em diferentes tempos, 48 e 120 h, respectivamente. A razão dos ácidos acético e butírico (HAc/HBu) auxiliou na avaliação do desempenho das comunidades bacterianas produtoras de H2

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes

Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The analysis of the fractional version (of order $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ with real sign-varying density is constructed and some of its properties examined. The equation of vibrations of plates is considered and the case of circular vibrating disks $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure

Action research and democracy

This contribution explores the relationship between research and learning democracy. Action research is seen as being compatible with the orientation of educational and social work research towards social justice and democracy. Nevertheless, the history of action research is characterized by a tension between democracy and social engineering. In the social-engineering approach, action research is conceptualized as a process of innovation aimed at a specific Bildungsideal. In a democratic approach action research is seen as research based on cooperation between research and practice. However, the notion of democratic action research as opposed to social engineering action research needs to be theorized. So called democratic action research involving the implementation by the researcher of democracy as a model and as a preset goal, reduces cooperation and participation into instruments to reach this goal, and becomes a type of social engineering in itself. We argue that the relationship between action research and democracy is in the acknowledgment of the political dimension of participation: ‘a democratic relationship in which both sides exercise power and shared control over decision-making as well as interpretation’. This implies an open research design and methodology able to understand democracy as a learning process and an ongoing experiment

Order in glassy systems

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.Comment: Typos corrected, clarifications adde