Nonparametric Hierarchical Clustering of Functional Data

In this paper, we deal with the problem of curves clustering. We propose a nonparametric method which partitions the curves into clusters and discretizes the dimensions of the curve points into intervals. The cross-product of these partitions forms a data-grid which is obtained using a Bayesian model selection approach while making no assumptions regarding the curves. Finally, a post-processing technique, aiming at reducing the number of clusters in order to improve the interpretability of the clustering, is proposed. It consists in optimally merging the clusters step by step, which corresponds to an agglomerative hierarchical classification whose dissimilarity measure is the variation of the criterion. Interestingly this measure is none other than the sum of the Kullback-Leibler divergences between clusters distributions before and after the merges. The practical interest of the approach for functional data exploratory analysis is presented and compared with an alternative approach on an artificial and a real world data set

Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach

One-dimensional thermodynamic instabilities are phase transitions not prohibited by Landau's argument, because the energy of the domain wall (DW) which separates the two phases is infinite. Whether they actually occur in a given system of particles must be demonstrated on a case-by-case basis by examining the (non-) analyticity properties of the corresponding transfer integral (TI) equation. The present note deals with the generic Peyrard-Bishop model of DNA denaturation. In the absence of exact statements about the spectrum of the singular TI equation, I use Gauss-Hermite quadratures to achieve a single-parameter-controlled approach to rounding effects; this allows me to employ finite-size scaling concepts in order to demonstrate that a phase transition occurs and to derive the critical exponents.Comment: 5 pages, 6 figures, subm. to Phys. Rev.

Electrodynamics with radiation reaction

The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.Comment: 5 page

Simulations of metastable decay in two- and three-dimensional models with microscopic dynamics

We present a brief analysis of the crossover phase diagram for the decay of a metastable phase in a simple dynamic lattice-gas model of a two-phase system. We illustrate the nucleation-theoretical analysis with dynamic Monte Carlo simulations of a kinetic Ising lattice gas on square and cubic lattices. We predict several regimes in which the metastable lifetime has different functional forms, and provide estimates for the crossovers between the different regimes. In the multidroplet regime, the Kolmogorov-Johnson-Mehl-Avrami theory for the time dependence of the order-parameter decay and the two-point density correlation function allows extraction of both the order parameter in the metastable phase and the interfacial velocity from the simulation data.Comment: 14 pages, 4 figures, submitted to J. Non-Crystalline Solids, conference proceeding for IXth International Conference on the Physics of Non-Crystalline Solids, October, 199

Monte Carlo Calculations for Liquid 4^4He at Negative Pressure

A Quadratic Diffusion Monte Carlo method has been used to obtain the equation of state of liquid $^4$He including the negative pressure region down to the spinodal point. The atomic interaction used is a renewed version (HFD-B(HE)) of the Aziz potential, which reproduces quite accurately the features of the experimental equation of state. The spinodal pressure has been calculated and the behavior of the sound velociy around the spinodal density has been analyzed.Comment: 10 pages, RevTex 3.0, with 4 PostScript figures include

Tidal Dwarf Galaxies at Intermediate Redshifts

We present the first attempt at measuring the production rate of tidal dwarf galaxies (TDGs) and estimating their contribution to the overall dwarf population. Using HST/ACS deep imaging data from GOODS and GEMS surveys in conjunction with photometric redshifts from COMBO-17 survey, we performed a morphological analysis for a sample of merging/interacting galaxies in the Extended Chandra Deep Field South and identified tidal dwarf candidates in the rest-frame optical bands. We estimated a production rate about 1.4 {\times} 10^{-5} per Gyr per comoving volume for long-lived TDGs with stellar mass 3 {\times} 10^{8-9} solar mass at 0.5<z<1.1. Together with galaxy merger rates and TDG survival rate from the literature, our results suggest that only a marginal fraction (less than 10%) of dwarf galaxies in the local universe could be tidally-originated. TDGs in our sample are on average bluer than their host galaxies in the optical. Stellar population modelling of optical to near-infrared spectral energy distributions (SEDs) for two TDGs favors a burst component with age 400/200 Myr and stellar mass 40%/26% of the total, indicating that a young stellar population newly formed in TDGs. This is consistent with the episodic star formation histories found for nearby TDGs.Comment: 9 pages, 5 figures, Accepted for publication in Astrophysics & Space Scienc

Three-body non-additive forces between spin-polarized alkali atoms

Three-body non-additive forces in systems of three spin-polarized alkali atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio calculations. The non-additive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by 0.9 A. The non-additive forces originate principally from chemical bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files

An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and Gravitation

Nonequilibrium wetting

When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the Kardar-Parisi-Zhang equation, which defines a very robust universality class for nonequilibrium moving interfaces, with a soft-wall potential is considered. While in the second, microscopic models, in the corresponding universality class, with evaporation and deposition of particles in the presence of hard-wall are studied. Equilibrium wetting is related to a particular case of the problem, it corresponds to the Edwards-Wilkinson equation with a potential in the continuum approach or to the fulfillment of detailed balance in the microscopic models. In this review we present the analytical and numerical methods used to investigate the problem and the very rich behavior that is observed with them.Comment: Review, 36 pages, 16 figure

Urgent need to clarify the definition of chronic critical limb ischemia - a position paper from the European Society for Vascular Medicine

Chronic critical lower limb ischemia (CLI) has been defined as ischemia that endangers the leg. An attempt was made to give a precise definition of CLI, based on clinical and hemodynamic data (Second European Consensus). CLI may be easily defined from a clinical point of view as rest pain of the distal foot or gangrene or ulceration. It is probably useful to add leg ulcers of other origin which do not heal because of severe ischemia, and to consider the impact of frailty on adverse outcome. From a hemodynamic viewpoint there is no consensus and most of the existing classifications are not based upon evidence. We should thus propose a definition and then validate it in a prospective cohort in order to define the patients at major risk of amputation, and also to define the categories of patients whose prognosis is improved by revascularisation. From today\u27s available data, it seems clear that the patients with a systolic toe pressure (STP) below 30 mmHg must be revascularised whenever possible. However other patients with clinically suspected CLI and STP above 30 mmHg must be evaluated and treated in specialised vascular units and revascularisation has to be discussed on a case by case basis, taking into account other data such as the WiFi classification for ulcers.In conclusion, many useful but at times contradictory definitions of CLI have been suggested. Only a few have taken into account evidence, and none have been validated prospectively. This paper aims to address this and to give notice that a CLI registry within Europe will be set up to prospectively validate, or not, the previous and suggested definitions of CLI