A Benamou-Brenier approach to branched transport

The problem of branched transportation aims to describe the movement of masses when, due to concavity effects, they have the interest to travel together as much as possible, because the cost for a path of length $\ell$ covered by a mass $m$ is proportional to $m^\alpha\ell$ with $0<\alpha<1$. The optimization of this criterion let branched structures appear and is suitable to applications like road systems, blood vessels, river networks\dots Several models have been employed in the literature to present this transport problem, and the present paper looks at a dynamical one, similar to the celebrated Benamou-Brenier formulation of Kantorovitch optimal transport. The movement is represented by a path $\rho_t$ of probabilities, connecting an initial state $\mu_0$ to a final state $\mu_1$, satisfying the continuity equation \partial_t\rho+\dive_xq=0 together with a velocity field $v$ (with $q=\rho v$ being the momentum). The transportation cost to be minimized is non-convex and finite on atomic measures: $\int_0^1\big(\int_\Omega\rho^{\alpha-1}|q|\,d\#(x)\big)\,dt$

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

The Monge problem with vanishing gradient penalization: Vortices and asymptotic profile

We investigate the approximation of the Monge problem (minimizing ?????|T(x)???x|d??(x) among the vector-valued maps T with prescribed image measure T_\\#\mu) by adding a vanishing Dirichlet energy, namely ???????|DT|2, where ?????0. We study the ??-convergence as ?????0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we analyze in details, when no optimal plan is induced by an H1 map, we study the selected limit map, which is a new "special" Monge transport, different from the monotone one, and we find the precise asymptotics of the optimal cost depending on ??, where the leading term is of order ??|log??

A valid academic path to promote respiratory physiotherapy

A one- year post- graduate Master in Physiotherapy and Pulmonary Rehabilitation has been offered within the University of Milan Medical School in collaboration with Associaz ione Italiana Riabilitatori dell\u2019Insufficienz a Respiratoria (ARIR). The aim is to cover a gap in Italian Physiotherapy academic curricula offering a course with theoretical and practical teaching that make students capable of using different techniques and procedures in respiratory physiotherapy. After the recognition by the International Education Recognition System (IERS), ARIR wanted to investigate if and how this course has affected students'attitude and their profession. METHODS A structured questionnaire made up of 15 multiple- choices items (8 on perceived quality of education and 7 on professional change) was sent by email to all physiotherapists who graduated in the previous four editions of the Master. One month was given for completion. Age, gender, year of degree and year of Master where considered as background variables. RESULTS We had a 78% response rate with 57 out of 73 physiotherapists sending the questionnaire back. Mean age was 37 years (23- 60) and women were the majority (78%). Forty- two students (74%) worked in the respiratory field at the time of application but only 15 (36%) dealt with respiratory patients only. Expectations were completely met at the end of Master for 71% of physiotherapists. 96% reported greater professional and clinical skills after the master with a 67% saying working team relationship has improved. 28% improved their job position thanks to the master degree and physiotherapy working in the respiratory field increased by 22%. CONCLUSIONS This course seems to meet students expectations and offer a solid knowledge to better work within the field of respiratory physiotherapy. It is also a way to promote the profession of respiratory physiotherapy in Italy

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

Monge's transport problem in the Heisenberg group

We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group

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

Open-String Actions and Noncommutativity Beyond the Large-B Limit

In the limit of large, constant B-field (the ``Seiberg-Witten limit''), the derivative expansion for open-superstring effective actions is naturally expressed in terms of the symmetric products *n. Here, we investigate corrections around the large-B limit, for Chern-Simons couplings on the brane and to quadratic order in gauge fields. We perform a boundary-state computation in the commutative theory, and compare it with the corresponding computation on the noncommutative side. These results are then used to examine the possible role of Wilson lines beyond the Seiberg-Witten limit. To quadratic order in fields, the entire tree-level amplitude is described by a metric-dependent deformation of the *2 product, which can be interpreted in terms of a deformed (non-associative) version of the Moyal * product.Comment: 30 pages, harvma