Transport Problems and Disintegration Maps

By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case

Analytical Model of Thermo-electrical Behaviour in Superconducting Resistive Core Cables

High field superconducting Nb$_{3}$Sn accelerators magnets above 14 T, for future High Energy Physics applications, call for improvements in the design of the protection system against resistive transitions. The longitudinal quench propagation velocity (vq) is one of the parameters defining the requirements of the protection. Up to now vq has been always considered as a physical parameter defined by the operating conditions (the bath temperature, cooling conditions, the magnetic field and the over all current density) and the type of superconductor and stabilizer used. It is possible to enhance the quench propagation velocity by segregating a percent of the stabilizer into the core, although keeping the total amount constant and tuning the contact resistance between the superconducting strands and the core. Analytical model and computer simulations are presented to explain the phenomenon. The consequences with respect to minimum quench energy are evidenced and the strategy to optimize the cable designed is discussed

Stability Analysis of the LHC Cables for Transient Heat Depositions

The commissioning and the exploitation of the LHC require a good knowledge of the stability margins of the superconducting magnets with respect to beam induced heat depositions. Previous studies showed that simple numerical models are suitable to carry out stability calculations of multi-strands cables, and highlighted the relevance of the heat transfer model with the surrounding helium. In this paper we present a systematic scan of the stability margin of all types of LHC cables working at 1.9 Kagainst transient heat depositions. We specifically discuss the dependence of the stability margin on the parameters of the model, which provide an estimate of the uncertainty of the values quoted. The stability margin calculations have been performed using a zero-dimensional (0-D) numerical model, and a cooling model taking into account the relevant helium phases which may appear during a stability experiment: it includes Kapitza thermal resistance in superfluid He, boundary layer formation and heat transfer in He I, and considers the transition from nucleating boiling to film boiling during He gas formation

Multi-Institutional Outcomes of Minimally Invasive Harvest of Rectal Mucosa Graft for Anterior Urethral Reconstruction.

PurposeWe report multi-institutional outcomes in patients who underwent urethroplasty with a rectal mucosa graft.Materials and methodsWe used the TURNS (Trauma and Urologic Reconstructive Network of Surgeons) database to identify patients who underwent urethral reconstruction with transanal harvest of a rectal mucosa graft. We reviewed preoperative demographics, stricture etiology, previous management and patient outcomes.ResultsWe identified 13 patients from April 2013 to June 2017. Median age at surgery was 54 years. The stricture etiology was lichen sclerosus in 6 of 13 patients (46%), idiopathic in 2 (15%), hypospadias in 1 (7%), prior gender confirming surgery in 3 (23%) and rectourethral fistula after radiation for prostate cancer in 1 (7%). Prior procedures included failed urethroplasty with a buccal mucosa graft in 9 of 13 patients (69%), direct vision internal urethrotomy in 2 (15%) and none in 2 (15%). Median stricture length was 13 cm. Stricture location in the 9 cisgender patients was panurethral in 5 (56%), bulbopendulous in 2 (22%) and bulbar in 2 (22%). It was located at the junction of the fixed urethra extending into the neophallus in all 3 patients (100%) who underwent prior gender confirming surgery. Mean rectal mucosa graft length for urethroplasty was 10.6 cm (range 3 to 16). Repair types included dorsal or ventral onlay, or 2-stage repair. Stricture recurred at a median followup of 13.5 months in 2 of 13 patients (15%). Postoperative complications included glans dehiscence, urethrocutaneous fistula and compartment syndrome in 1 patient each (7%). No rectal or bowel related complications were reported.ConclusionsUrethral reconstruction with a transanal harvested rectal mucosa graft is a safe technique when a buccal mucosa graft is unavailable or not indicated

A Metric Approach to Elastic Reformations

We study a variational framework to compare shapes, modeled as Radon measures on R^N, in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as integral functionals having some kind of isometries as minimizers. The approach pursued is based on the notion of pointwise Lipschitz constant leading to a space metric framework. In particular, to compare general shapes, we study this reformation problem by using the notion of transport plan and of Wasserstein distances as in optimal mass transportation theory

Tomograms and other transforms. A unified view

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.Comment: 19 pages latex, submitted to J. Phys. A: Math and Ge

Promoting SME cooperative aggregations: main criteria and contractual models

Collaboration is considered an effective solution to improve business strategies. However, small and medium enterprises (SMEs) often lack common principles and common forms of contractual coordination. Several policies implemented by the EU have addressed the set-up of a comprehensive SME policy framework, but European institutions seem to have focused more on organisational devices to conduct business activities rather than on contractual forms of coordination. In April 2009, Italy adopted a law in network contract to promote the development of inter-firm cooperation strategies to foster enterprises' innovation and growth. Even if this law represents a novelty in Europe and may offer new challenges and hints, it still presents some lacks in its formulation. The current research aims at presenting the Italian law for network contract and a comparison with other models of SME aggregations adopted in EU countries. A formal model to support the design of an SME network was proposed, by providing both an ontology-based model to help the definition of the contract in a structured way, and a basic workflow to identify the important phases of the network design, i.e. the feasibility study and the negotiatio