Unsupervised classification of children’s bodies using currents

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current. A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, through integration of vector fields along them. As a consequence of the choice of a vector-valued reproducing kernel Hilbert space (RKHS) as a test space for integrating manifolds, it is possible to consider that shapes are embedded in this Hilbert Space. A vector-valued RKHS is a Hilbert space of vector fields; therefore, it is possible to compute a mean of shapes, or to calculate a distance between two manifolds. This embedding enables us to consider size-and-shape clustering algorithms. These algorithms are applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children’s wear.     

Invariant measures for stochastic evolution equations in M-type 2 Banach spaces

In this paper, we study invariant measures for stochastic evolution equations in M-type 2 Banach spaces. The existence and uniqueness of invariant measure in this general setting are established under global (or local) Lipschitz conditions and certain dissipativity conditions.     

Dynamic fleet management as a logistics queueing network

This paper introduces a new framework for modeling and solving dynamic fleet management problems, which we call the Logistics Queueing Network (LQN). A variety of problems in logistics involve the combined problem of moving freight from origin to destination while simultaneously managing the capacity required to move this freight. Standard formulations for real-world problems usually lead to intractably large linear programs. The LQN approach can take into account more real-world detail and is considerably faster than classical LP formulations. The solutions generated using the LQN approach are shown to be within a few percentage points of the LP optimal solutions depending on the size of the capacity fleets.     

Performance of an unscheduled shuttle system with two classes of vehicles

A queuing model is proposed to study the performance of an unscheduled shuttle system with two classes of vehicles. An efficient iterative algorithm is developed to obtain system performance measures. This is generalization of the model of Zuckerman and Tapiero (1980) to allow for finite reserve vehicle pool and finite vehicle capacity.     

Subgraphs as circuits and bases of matroids

As is well known, the cycles of any given graph G may be regarded as the circuits of a matroid defined on the edge set of G. The question of whether other families of connected graphs exist such that, given any graph G, the subgraphs of G isomorphic to some member of the family may be regarded as the circuits of a matroid defined on the edge set of G led us, in two other papers, to the proof of some results concerning properties of the cycles when regarded as circuits of such matroids. Here we prove that the wheels share many of these properties with the cycles. Moreover, properties of subgraphs which may be regarded as bases of such matroids are also investigated.     

Almost optimality of an axiomatic bound for π0π0 scattering

We produce a π⁰π⁰ → π⁰π⁰ amplitude F(s,t) which fulfils all the analyticity, crossing and unitarity conditions used in the derivation of rigorous absolute bounds, and such that $\text{F(}\text{4}\text{3}\text{,}\text{4}\text{3}\text{) = 2.62}$. When compared to the axiomatic result of Lopez and Mennessier, $\text{?8.2< F(}\text{4}\text{3}\text{,}\text{4}\text{3}\text{) < 2.75}$, this example shows that no further significant improvement of the upper bound can be expected.     

Observations of ω0/2 harmonic emission from 0.35μm laser-irradiated plasmas

Observations of ω₀/2 harmonic emission from both spherical and plane targets irradiated by 0.35 μm, 800 ps laser pulses have been obtained with simultaneous high spectral and temporal resolutions of 16 Å and 20 ps respectively. The ω₀/2 harmonic emission spectrum is interpreted as providing a direct measurement of the frequency of the ω₀/2 plasma waves and hence can be used to estimate the electron temperature.     

Systematic Solution of the Mean Field Equation for Liquid Crystals

Starting with a pairwise, spatially and orientationally dependent intermolecular potential of the Kobayashi-McMillan form, we carry out a systematic solution of the mean field equation for liquid crystals. The mean field equation, presented as first of a hierarchy of BBGKY equations, is first reduced to a set of coupled integrodifferential equations by means of expanding the distribution function f (r, δ) and In f (r, δ) in Legendre polynomials and the reciprocal lattice space. In the first level of approximation, the expansion retains only the lowest-order coefficients, permitting a complete decoupling of the equations. In the second level of approximation, the leading coefficient which couples spatial order to orientational order is included. In the third level of approximation two more higher order coefficients are included. At each level, the free energy functional is evaluated to determine the equilibrium phase at given temperatures and chainlengths of a homologous series. It is shown that the expansion converges very rapidly, the second level of approximation being entirely sufficient. This lends support to our earlier variational calculation which contained only three variational parameters.