Estimation and comparison of signed symmetric covariation coefficient and generalized association parameter for alpha-stable dependence modeling

Accepté à Communications in Statistics - Theory and methodsInternational audienceIn this paper we study the estimators of two measures of dependence: the signed symmetric covariation coefficient proposed by Garel and Kodia and the generalized association parameter put forward by Paulauskas. In the sub-Gaussian case, the signed symmetric covariation coefficient and the generalized association parameter coincide. The estimator of the signed symmetric covariation coefficient proposed here is based on fractional lower-order moments. The estimator of the generalized association parameter is based on estimation of a stable spectral measure. We investigate the relative performance of these estimators by comparing results from simulations

Structural and ultrametric properties of twenty(L-alanine)

We study local energy minima of twenty(L-alanine). The minima are generated using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo simulations, with subsequent minimization. We find that the lower-energy configurations are $\alpha$-helices for a wide range of dielectric constant values $(\epsilon = 1,10,80),$ and that there is no noticeable difference between the distribution of energy minima in $\phi \psi$ space for different values of $\epsilon .$ Ultrametricity tests show that lower-energy $(\alpha$ -helical) $\epsilon =1$ configurations form a set which is ultrametric to a certain degree, providing evidence for the presence of fine structure among those minima. We put forward a heuristic argument for this fine structure. We also find evidence for ultrametricity of a different kind among $\epsilon =10$ and $\epsilon =80$ energy minima. We analyze the distribution of lengths of $\alpha$-helical portions among the minimized configurations and find a persistence phenomenon for the $\epsilon =1$ ones, in qualitative agreement with previous studies of critical lengths. Email contact: [email protected]: Saclay-T93/025 Email: [email protected]

Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of length $L$, we analyse the statistics of the weights $w_L(\vec r)$ of the last monomer as follows. We numerically compute the probability distributions $P_1(w)$ of the maximal weight $w_L^{max}= max_{\vec r} [w_L(\vec r)]$, the probability distribution $\Pi(Y_2)$ of the parameter $Y_2(L)= \sum_{\vec r} w_L^2(\vec r)$ as well as the average values of the higher order moments $Y_k(L)= \sum_{\vec r} w_L^k(\vec r)$. We find that there exists a temperature $T_{gap}<T_c$ such that (i) for $T<T_{gap}$, the distributions $P_1(w)$ and $\Pi(Y_2)$ present the characteristic Derrida-Flyvbjerg singularities at $w=1/n$ and $Y_2=1/n$ for $n=1,2..$. In particular, there exists a temperature-dependent exponent $\mu(T)$ that governs the main singularities $P_1(w) \sim (1-w)^{\mu(T)-1}$ and $\Pi(Y_2) \sim (1-Y_2)^{\mu(T)-1}$ as well as the power-law decay of the moments $\bar{Y_k(i)} \sim 1/k^{\mu(T)}$. The exponent $\mu(T)$ grows from the value $\mu(T=0)=0$ up to $\mu(T_{gap}) \sim 2$. (ii) for $T_{gap}<T<T_c$, the distribution $P_1(w)$ vanishes at some value $w_0(T)<1$, and accordingly the moments $\bar{Y_k(i)}$ decay exponentially as $(w_0(T))^k$ in $k$. The histograms of spatial correlations also display Derrida-Flyvbjerg singularities for $T<T_{gap}$. Both below and above $T_{gap}$, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

Numerical study of the disordered Poland-Scheraga model of DNA denaturation

We numerically study the binary disordered Poland-Scheraga model of DNA denaturation, in the regime where the pure model displays a first order transition (loop exponent $c=2.15>2$). We use a Fixman-Freire scheme for the entropy of loops and consider chain length up to $N=4 \cdot 10^5$, with averages over $10^4$ samples. We present in parallel the results of various observables for two boundary conditions, namely bound-bound (bb) and bound-unbound (bu), because they present very different finite-size behaviors, both in the pure case and in the disordered case. Our main conclusion is that the transition remains first order in the disordered case: in the (bu) case, the disorder averaged energy and contact densities present crossings for different values of $N$ without rescaling. In addition, we obtain that these disorder averaged observables do not satisfy finite size scaling, as a consequence of strong sample to sample fluctuations of the pseudo-critical temperature. For a given sample, we propose a procedure to identify its pseudo-critical temperature, and show that this sample then obeys first order transition finite size scaling behavior. Finally, we obtain that the disorder averaged critical loop distribution is still governed by $P(l) \sim 1/l^c$ in the regime $l \ll N$, as in the pure case.Comment: 12 pages, 13 figures. Revised versio

Statistics of low energy excitations for the directed polymer in a 1+d1+d random medium (d=1,2,3d=1,2,3)

We consider a directed polymer of length $L$ in a random medium of space dimension $d=1,2,3$. The statistics of low energy excitations as a function of their size $l$ is numerically evaluated. These excitations can be divided into bulk and boundary excitations, with respective densities $\rho^{bulk}_L(E=0,l)$ and $\rho^{boundary}_L(E=0,l)$. We find that both densities follow the scaling behavior $\rho^{bulk,boundary}_L(E=0,l) = L^{-1-\theta_d} R^{bulk,boundary}(x=l/L)$, where $\theta_d$ is the exponent governing the energy fluctuations at zero temperature (with the well-known exact value $\theta_1=1/3$ in one dimension). In the limit $x=l/L \to 0$, both scaling functions $R^{bulk}(x)$ and $R^{boundary}(x)$ behave as $R^{bulk,boundary}(x) \sim x^{-1-\theta_d}$, leading to the droplet power law $\rho^{bulk,boundary}_L(E=0,l)\sim l^{-1-\theta_d}$ in the regime $1 \ll l \ll L$. Beyond their common singularity near $x \to 0$, the two scaling functions $R^{bulk,boundary}(x)$ are very different : whereas $R^{bulk}(x)$ decays monotonically for $0<x<1$, the function $R^{boundary}(x)$ first decays for $0<x<x_{min}$, then grows for $x_{min}<x<1$, and finally presents a power law singularity $R^{boundary}(x)\sim (1-x)^{-\sigma_d}$ near $x \to 1$. The density of excitations of length $l=L$ accordingly decays as $\rho^{boundary}_L(E=0,l=L)\sim L^{- \lambda_d}$ where $\lambda_d=1+\theta_d-\sigma_d$. We obtain $\lambda_1 \simeq 0.67$, $\lambda_2 \simeq 0.53$ and $\lambda_3 \simeq 0.39$, suggesting the possible relation $\lambda_d= 2 \theta_d$.Comment: 15 pages, 25 figure

THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder

Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of the local order parameter $\rho(r)$ scale with a set $x(q)$ of non-trivial exponents $x(q) \neq q x(1)$. In this paper, we revisit these ideas to incorporate more recent findings: (i) whenever a multifractal measure $w(r)$ normalized over space $\sum_r w(r)=1$ occurs in a random system, it is crucial to distinguish between the typical values and the disorder averaged values of the generalized moments $Y_q =\sum_r w^q(r)$, since they may scale with different generalized dimensions $D(q)$ and $\tilde D(q)$ (ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E {\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces a lack of self-averaging at critical points for thermodynamic observables, in particular for the order parameter. After this general discussion valid for any random critical point, we apply these ideas to random polymer models that can be studied numerically for large sizes and good statistics over the samples. We study the bidimensional wetting or the Poland-Scheraga DNA model with loop exponent $c=1.5$ (marginal disorder) and $c=1.75$ (relevant disorder). Finally, we argue that the presence of finite Griffiths ordered clusters at criticality determines the asymptotic value $x(q \to \infty) =d$ and the minimal value $\alpha_{min}=D(q \to \infty)=d-x(1)$ of the typical multifractal spectrum $f(\alpha)$.Comment: 17 pages, 20 figure

Sequence randomness and polymer collapse transitions

Contrary to expectations based on Harris' criterion, chain disorder with frustration can modify the universality class of scaling at the theta transition of heteropolymers. This is shown for a model with random two-body potentials in 2D on the basis of exact enumeration and accurate Monte Carlo results. When frustration grows beyond a certain finite threshold, the temperature below which disorder becomes relevant coincides with the theta one and scaling exponents definitely start deviating from those valid for homopolymers.Comment: 4 pages, 4 eps figure

The Theoretical Astrophysical Observatory: Cloud-Based Mock Galaxy Catalogues

We introduce the Theoretical Astrophysical Observatory (TAO), an online virtual laboratory that houses mock observations of galaxy survey data. Such mocks have become an integral part of the modern analysis pipeline. However, building them requires an expert knowledge of galaxy modelling and simulation techniques, significant investment in software development, and access to high performance computing. These requirements make it difficult for a small research team or individual to quickly build a mock catalogue suited to their needs. To address this TAO offers access to multiple cosmological simulations and semi-analytic galaxy formation models from an intuitive and clean web interface. Results can be funnelled through science modules and sent to a dedicated supercomputer for further processing and manipulation. These modules include the ability to (1) construct custom observer light-cones from the simulation data cubes; (2) generate the stellar emission from star formation histories, apply dust extinction, and compute absolute and/or apparent magnitudes; and (3) produce mock images of the sky. All of TAO's features can be accessed without any programming requirements. The modular nature of TAO opens it up for further expansion in the future.Comment: 17 pages, 11 figures, 2 tables; accepted for publication in ApJS. The Theoretical Astrophysical Observatory (TAO) is now open to the public at https://tao.asvo.org.au/. New simulations, models and tools will be added as they become available. Contact [email protected] if you have data you would like to make public through TAO. Feedback and suggestions are very welcom

Semi-Analytic Galaxy Evolution (SAGE): Model Calibration and Basic Results

This paper describes a new publicly available codebase for modelling galaxy formation in a cosmological context, the "Semi-Analytic Galaxy Evolution" model, or SAGE for short. SAGE is a significant update to that used in Croton et al. (2006) and has been rebuilt to be modular and customisable. The model will run on any N-body simulation whose trees are organised in a supported format and contain a minimum set of basic halo properties. In this work we present the baryonic prescriptions implemented in SAGE to describe the formation and evolution of galaxies, and their calibration for three N-body simulations: Millennium, Bolshoi, and GiggleZ. Updated physics include: gas accretion, ejection due to feedback, and reincorporation via the galactic fountain; a new gas cooling--radio mode active galactic nucleus (AGN) heating cycle; AGN feedback in the quasar mode; a new treatment of gas in satellite galaxies; and galaxy mergers, disruption, and the build-up of intra-cluster stars. Throughout, we show the results of a common default parameterization on each simulation, with a focus on the local galaxy population.Comment: 15 pages, 9 figures, accepted for publication in ApJS. SAGE is a publicly available codebase for modelling galaxy formation in a cosmological context, available at https://github.com/darrencroton/sage Questions and comments can be sent to Darren Croton: [email protected]