Model-based clustering of probability density functions

Complex data such as those where each statistical unit under study is described not by a single observation (or vector variable), but by a unit-specific sample of several or even many observations, are becoming more and more popular. Reducing these sample data by summary statistics, like the average or the median, implies that most inherent information (about variability, skewness or multi-modality) gets lost. Full information is preserved only if each unit is described by a whole distribution. This new kind of data, a.k.a. “distribution-valued data”, require the development of adequate statistical methods. This paper presents a method to group a set of probability density functions (pdfs) into homogeneous clusters, provided that the pdfs have to be estimated nonparametrically from the unit-specific data. Since elements belonging to the same cluster are naturally thought of as samples from the same probability model, the idea is to tackle the clustering problem by defining and estimating a proper mixture model on the space of pdfs. The issue of model building is challenging here because of the infinite-dimensionality and the non-Euclidean geometry of the domain space. By adopting a wavelet-based representation for the elements in the space, the task is accomplished by using mixture models for hyper-spherical data. The proposed solution is illustrated through a simulation experiment and on two real data sets.     

Computation of the Maslov index and the spectral flow via partial signatures

Given a smooth Lagrangian path, both in the finite and in the infinite dimensional (Fredholm) case, we introduce the notion of partial signatures at each isolated intersection of the path with the Maslov cycle. For real-analytic paths, we give a formula for the computation of the Maslov index using the partial signatures; a similar formula holds for the spectral flow of real-analytic paths of Fredholm self-adjoint operators on real separable Hilbert spaces. As applications of the theory, we obtain a semi-Riemannian version of the Morse index theorem for geodesics with possibly conjugate endpoints, and we prove a bifurcation result at conjugate points along semi-Riemannian geodesics. To cite this article: R. Giambò et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Wave features of a hyperbolic model for the within-season dynamics of insect pathogens

Hyperbolic models are suitable for describing invasive phenomena with a well-defined boundary. In fact, for a class of hyperbolic reaction–diffusion models derived in the context of extended thermodynamics (ET), the non-existence of smooth travelling waves has been proved under suitable assumptions on the wave speed. In this paper a hyperbolic model for the within-season dynamics of insect pathogens is derived and smooth and discontinuous travelling wave solutions are investigated. Validation of the model in point is also accomplished by searching for numerical solutions of the system of PDEs.     

Bayesian methods in global optimization

This paper reviews methods which have been proposed for solving global optimization problems in the framework of the Bayesian paradigm.     

A <Emphasis Type="Italic">V</Emphasis>-cycle Multigrid for multilevel matrix algebras: proof of optimality

We analyze the convergence rate of a multigrid method for multilevel linear systems whose coefficient matrices are generated by a real and nonnegative multivariate polynomial f and belong to multilevel matrix algebras like circulant, tau, Hartley, or are of Toeplitz type. In the case of matrix algebra linear systems, we prove that the convergence rate is independent of the system dimension even in presence of asymptotical ill-conditioning (this happens iff f takes the zero value). More precisely, if the d-level coefficient matrix has partial dimension n _r at level r, with , then the size of the system is , , and O(N(n)) operations are required by the considered V-cycle Multigrid in order to compute the solution within a fixed accuracy. Since the total arithmetic cost is asymptotically equivalent to the one of a matrix-vector product, the proposed method is optimal. Some numerical experiments concerning linear systems arising in 2D and 3D applications are considered and discussed.     

The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions

We consider nonholonomic systems with linear, time-independent constraints subject to positional conservative active forces. We identify a distribution on the configuration manifold, that we call the reaction-annihilator distribution ℜ°, the fibers of which are the annihilators of the set of all values taken by the reaction forces on the fibers of the constraint distribution. We show that this distribution, which can be effectively computed in specific cases, plays a central role in the study of first integrals linear in the velocities of this class of nonholonomic systems. In particular we prove that, if the Lagrangian is invariant under (the lift of) a group action in the configuration manifold, then an infinitesimal generator of this action has a conserved momentum if and only if it is a section of the distribution ℜ°. Since the fibers of ℜ° contain those of the constraint distribution, this version of the nonholonomic Noether theorem accounts for more conserved momenta than what was known so far. Some examples are given.      

Spin-flip limited exciton dephasing in CdSe/ZnS colloidal quantum dots

The dephasing time of the lowest bright exciton in CdSe/ZnS wurtzite quantum dots is measured from 5 to 170 K and compared with density dynamics within the exciton fine structure using a sensitive three-beam four-wave-mixing technique unaffected by spectral diffusion. Pure dephasing via acoustic phonons dominates the initial dynamics, followed by an exponential zero-phonon line dephasing of 109 ps at 5 K, much faster than the ~10 ns exciton radiative lifetime. The zero-phonon line dephasing is explained by phonon-assisted spin flip from the lowest bright state to dark-exciton states. This is confirmed by the temperature dependence of the exciton lifetime and by direct measurements of the bright-dark-exciton relaxation. Our results give an unambiguous evidence of the physical origin of the exciton dephasing in these nanocrystals.     

Fourier Self-Deconvolution Analysis of β-Sheet Contents in the Amide I Region of Hemoglobin Aqueous Solutions under Exposure to 900 MHz Microwaves and Bioprotective Effectiveness of Sugar and Salt Solutions

Spectroscopic Fourier self-deconvolution analysis was used to investigate β-sheet features in the secondary structure of hemoglobin under mobile phone microwaves at 900 MHz. To this end, four samples of hemoglobin in bidistilled water, sucrose, trehalose, and sodium chloride aqueous solutions were exposed for up to 4 hr to 900 MHz microwaves at an average H-field intensity of 42 mA/m. Quantitative spectral analyses highlighted significant increases in β-sheet contents in the Amide I region of hemoglobin samples in bidistilled water solution, but no appreciable change was observed in hemoglobin samples in sucrose, trehalose, and sodium chloride solutions. These results led us to conclude that mobile phone microwaves can denaturate hemoglobin in bidistilled water solution whereas sucrose, trehalose, and sodium chloride solutions produce a protective effect against microwaves, preserving the protein from unfolding.     

Lepton spectrum in semileptonic b-decay

We present some results from the computation of the charged lepton energy distribution in the decay b → c + $\text{l}$^? + $\text{ν}$ taking into account first order QCD corrections.