Optimal transportation with traffic congestion and Wardrop equilibria

In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the notion of traffic intensity, we propose a variant taking into account congestion. This leads to an optimization problem posed on a set of probability measures on a suitable paths space. We establish existence of minimizers and give a characterization. As an application, we obtain existence and variational characterization of equilibria of Wardrop type in a continuous space setting

Quantitative Comparison of Locomotor Performance in Different Race Walkers

Biomechanics of track and field activities has been investigated by many authors. A literature overview on race walking points out various analyses on: supporting energy (Zarrough et al. 1974), mechanical energy variations (Marchetti et at. 1983), potential versus kinetic energy variations (Ralston and Lukin, 1969), muscular work efficiency (Marchetti et at. 1983), Payne (1979) reported the ground reaction components measured during race walking while some aspects of the related biomechanics were discussed by Boccardi et al. (1978) by displaying a vectorial representation of the ground reaction evolution. As the trainers know well, the primary needs of the race walkers involve something more than a general description of the basic executive mechanism. The athletes have to solve a very complex problem: walk under restrictive Jules for a time varying from 18 to more than 200 minutes at a speed that is usually more than two times higher the threshold at which a man begins running naturally (Cavagna et at., 1977). Such goal is obtained through a proper modification of the normal motor-patterns aimed to the best use of the endurance qualities. By the way, the critical importance of optimal motor efficiency to reduce any possible noisy factor is evident. The aim of this study is to quantify locomotor performances of two homogeneous groups of differently ranked walkers. The vectorial representation of the ground reaction force is used to identify and compare typical biomechanical features associating with the athletic level. A further data processing, including normalization and statistical estimation of the differences between the results from the two groups. leads to a practical and powerful tool for the investigation of motorcoordination and asymmetry in race walking

Spatial distribution of ions in a linear octopole radio-frequency ion trap in the space-charge limit

We have explored the spatial distribution of an ion cloud trapped in a linear octopole radio-frequency (rf) ion trap. The two-dimensional distribution of the column density of stored silver dimer cations was measured via photofragment-ion yields as a function of the position of the incident laser beam over the transverse cross section of the trap. The profile of the ion distribution was found to be dependent on the number of loaded ions. Under high ion-loading conditions with a significant space-charge effect, ions form a ring profile with a maximum at the outer region of the trap, whereas they are localized near the center axis region at low loading of the ions. These results are explained quantitatively by a model calculation based on equilibrium between the space-charge-induced potential and the effective potential of the multipole rf field. The maximum adiabaticity parameter \eta_max is estimated to be about 0.13 for the high ion-density condition in the present octopole ion trap, which is lower than typical values reported for low ion densities; this is probably due to additional instability caused by the space charge.Comment: 8 pages, 5 figure

Embedding Branes in Flat Two-time Spaces

We show how non-near horizon, non-dilatonic $p$-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.Comment: LaTex, 8 pages. Contribution to the TMR Conference on Quantum aspects of gauge theories, supersymmetry and unification. Paris, 1-7 September 199

Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories

Using N=2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved, references adde

Finite-size effects in the superconformal beta-deformed N=4 SYM

We study finite size effects for composite operators in the SU(2) sector of the superconformal beta-deformed N=4 SYM theory. In particular we concentrate on the spectrum of one single magnon. Since in this theory one-impurity states are non BPS we compute their anomalous dimensions including wrapping contributions up to four loops and discuss higher order effects.Comment: LaTeX, mpost, feynmf, 20 pages, 4 figures, 5 tables; v2: references added, equations (4.13) and (4.17) correcte

Three-dimensional easy morphological (3-DEMO) classification of scoliosis, part I

BACKGROUND: While scoliosis has, for a long time, been defined as a three-dimensional (3D) deformity, morphological classifications are confined to the two dimensions of radiographic assessments. The actually existing 3-D classification proposals have been developed in research laboratories and appear difficult to be understood by clinicians. AIM OF THE STUDY: The aim of this study was to use the results of a 3D evaluation to obtain a simple and clinically oriented morphological classification (3-DEMO) that might make it possible to distinguish among different populations of scoliotic patients. METHOD: We used a large database of evaluations obtained through an optoelectronic system (AUSCAN) that gives a 3D reconstruction of the spine. The horizontal view was used, with a spinal reference system (Top View). An expert clinician evaluated the morphological reconstruction of 149 pathological spines in order to find parameters that could be used for classificatory ends. These were verified in a mathematical way and through computer simulations: some parameters had to be excluded. Pathological data were compared with those of 20 normal volunteers. RESULTS: We found three classificatory parameters, which are fully described and discussed in this paper: Direction, the angle between spinal pathological and normal AP axis; Shift, the co-ordinates of the barycentre of the Top View ; Phase, the parameter describing the spatial evolution of the curve. Using these parameters it was possible to distinguish normal and pathological spines, to classify our population and to differentiate scoliotic patients with identical AP classification but different 3D behaviors. CONCLUSION: The 3-DEMO classification offers a new and simple way of viewing the spine through an auxiliary plane using a spinal reference system. Further studies are currently under way to compare this new system with the existing 3-D classifications, to obtain it using everyday clinical and x-rays data, and to develop a triage for clinical use

A protocol for qualitative and quantitative measurement of endosomal processing using hot spot analysis

A detailed quantification of antigen processing by endosomal compartments provides important information on the pattern of protein fragmentation. Here, we describe a protocol that combines gradient purified endosomes, incubated with antigens, followed by hot spot analysis of MS/MS-sequenced peptides. The analysis identifies differences in endosomal antigen processing by dendritic cells under diverse experimental conditions. For complete details on the use and execution of this protocol, please refer to Clement et al. (2021)

Induction and suppression of an autoimmune disease by oligomerized T cell epitopes: enhanced in vivo potency of encephalitogenic peptides

T cell epitope peptides derived from proteolipid protein (PLP139-151) or myelin basic protein (MBP86-100) induce experimental autoimmune encephalomyelitis (EAE) in "susceptible" strains of mice (e.g., SJL/J). In this study, we show that the encephalitogenic effect of these epitopes when injected subcutaneously in complete Freund's adjuvant was significantly enhanced if administered to the animal in a multimerized form as a T cell epitope oligomer (i.e., as multiple repeats of the peptide epitope, such as 16-mers). Oligomer-treated SJL/J mice developed EAE faster and showed a more severe progression of the disease than animals treated with peptide alone. In addition, haplotype-matched B10.S mice, "resistant" to EAE induction by peptide, on injection of 16-mers developed a severe form of EAE. Even more striking, however, was the dramatic suppression of incidence and severity of the disease, seen after single intravenous injections of only 50 microg of the PLP139-151 16-mer, administered to SJL/J mice 7 d after the induction of the disease. Although relapse occurred at about day 45, an additional injection several days before that maintained the suppression. Importantly, the specific suppressive effect of oligomer treatment was also evident if EAE was induced with spinal cord homogenate instead of the single peptide antigen. By contrast, the PLP139-151 peptide accelerated rather than retarded the progression of disease