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

Conformal boundary and geodesics for AdS5×S5AdS_5\times S^5 and the plane wave: Their approach in the Penrose limit

Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times S^5$ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of $AdS_5\times S^5$ to that of the plane wave is studied in detail. At each point these null geodesics of $AdS_5\times S^5$ form a cone which degenerates in the limit.Comment: some statements refined, chapter 5 rewritten to make it more precise, some typos correcte

The heart of a convex body

We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\heartsuit(\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\heartsuit(\mathcal{K})$ and the mirror symmetries of $\mathcal{K};$ we show that $\heartsuit(\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\heartsuit(\mathcal{K});$ we also prove an upper estimate for the area of $\heartsuit(\mathcal{K}),$ when $\mathcal{K}$ is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6

Depicting conformational ensembles of \u3b1-synuclein by single molecule force spectroscopy and native mass spectroscopy

Description of heterogeneous molecular ensembles, such as intrinsically disordered proteins, represents a challenge in structural biology and an urgent question posed by biochemistry to interpret many physiologically important, regulatory mechanisms. Single-molecule techniques can provide a unique contribution to this field. This work applies single molecule force spectroscopy to probe conformational properties of \u3b1-synuclein in solution and its conformational changes induced by ligand binding. The goal is to compare data from such an approach with those obtained by native mass spectrometry. These two orthogonal, biophysical methods are found to deliver a complex picture, in which monomeric \u3b1-synuclein in solution spontaneously populates compact and partially compacted states, which are differently stabilized by binding to aggregation inhibitors, such as dopamine and epigallocatechin-3-gallate. Analyses by circular dichroism and Fourier-transform infrared spectroscopy show that these transitions do not involve formation of secondary structure. This comparative analysis provides support to structural interpretation of charge-state distributions obtained by native mass spectrometry and helps, in turn, defining the conformational components detected by single molecule force spectroscopy

BMN operators with vector impurities, Z_2 symmetry and pp-waves

We calculate the coefficients of three-point functions of BMN operators with two vector impurities. We find that these coefficients can be obtained from those of the three-point functions of scalar BMN operators by interchanging the coefficient for the symmetric-traceless representation with the coefficient for the singlet. We conclude that the Z_2 symmetry of the pp-wave string theory is not manifest at the level of field theory three-point correlators.Comment: 25 pages, 7 figures. v1: A reference and a footnote added; v2: New contributions found, Z_2 symmetry lost in 3-point function

Predictions for PP-wave string amplitudes from perturbative SYM

The role of general two-impurity multi-trace operators in the BMN correspondence is explored. Surprisingly, the anomalous dimensions of all two-impurity multi-trace BMN operators to order g_2^2\lambda' are completely determined in terms of single-trace anomalous dimensions. This is due to suppression of connected field theory diagrams in the BMN limit and this fact has important implications for some string theory processes on the PP-wave background. We also make gauge theory predictions for the matrix elements of the light-cone string field theory Hamiltonian in the two string-two string and one string-three string sectors.Comment: 46 pages, 12 figures. V3:typos correcte