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

The Gap Between Linear Elasticity and the Variational Limit of Finite Elasticity in Pure Traction Problems

A limit elastic energy for the pure traction problem is derived from re-scaled nonlinear energies of a hyperelastic material body subject to an equilibrated force field. We prove that the strains of minimizing sequences associated to re-scaled nonlinear energies weakly converge, up to subsequences, to the strains of minimizers of a limit energy, provided an additional compatibility condition is fulfilled by the force field. The limit energy is different from the classical energy of linear elasticity; nevertheless, the compatibility condition entails the coincidence of related minima and minimizers. A strong violation of this condition provides a limit energy which is unbounded from below, while a mild violation may produce unboundedness of strains and a limit energy which has infinitely many extra minimizers which are not minimizers of standard linear elastic energy. A consequence of this analysis is that a rigorous validation of linear elasticity fails for compressive force fields that infringe up on such a compatibility condition

Blow-up of the quantum potential for a free particle in one dimension

We derive a non-linear differential equation that must be satisfied by the quantum potential, in the context of the Madelung equations, in one dimension for a particular class of wave functions. In this case, we exhibit explicit conditions leading to the blow-up of the quantum potential of a free particle at the boundary of the compact support of the probability density

On some topological games involving networks

In these notes we introduce and investigate two new games called R-nw-selective game and the M-nw-selective game. These games naturally arise from the corresponding selection principles involving networks introduced in \cite{BG}

On crowdsourcing relevance magnitudes for information retrieval evaluation

4siMagnitude estimation is a psychophysical scaling technique for the measurement of sensation, where observers assign numbers to stimuli in response to their perceived intensity. We investigate the use of magnitude estimation for judging the relevance of documents for information retrieval evaluation, carrying out a large-scale user study across 18 TREC topics and collecting over 50,000 magnitude estimation judgments using crowdsourcing. Our analysis shows that magnitude estimation judgments can be reliably collected using crowdsourcing, are competitive in terms of assessor cost, and are, on average, rank-aligned with ordinal judgments made by expert relevance assessors. We explore the application of magnitude estimation for IR evaluation, calibrating two gain-based effectiveness metrics, nDCG and ERR, directly from user-reported perceptions of relevance. A comparison of TREC system effectiveness rankings based on binary, ordinal, and magnitude estimation relevance shows substantial variation; in particular, the top systems ranked using magnitude estimation and ordinal judgments differ substantially. Analysis of the magnitude estimation scores shows that this effect is due in part to varying perceptions of relevance: different users have different perceptions of the impact of relative differences in document relevance. These results have direct implications for IR evaluation, suggesting that current assumptions about a single view of relevance being sufficient to represent a population of users are unlikely to hold.partially_openopenMaddalena, Eddy; Mizzaro, Stefano; Scholer, Falk; Turpin, AndrewMaddalena, Eddy; Mizzaro, Stefano; Scholer, Falk; Turpin, Andre

Durable graphite oxide nanocoating for high performing flame retarded foams

Recent developments in the design of water-based coatings encompassing platelet-like nanoparticles have clearly demonstrated the flame retardant potential of this approach for open cell flexible foams. However, the relatively high number of deposition steps required and the limited reports on the durability of the deposited coatings to multiple compression cycles currently represent the main constraints to this approach. This paper addresses these limitations by exploiting a few steps deposition procedure to produce coatings with durable flame retardant properties. Graphite oxide, sodium alginate and sodium hexametaphosphate were combined in a continuous protective coating that extends to the complex three-dimensional structure of the foam. The flame retardant properties of the coatings were evaluated before and after 1000 compression cycles. Even after such multiple deformations, the coated foams showed no melt dripping and self-extinguishment during flammability tests, as well as a highly reduced heat release rates (-70%) and total smoke release (-70%) during cone calorimetry tests. Furthermore, the ability to withstand the penetration of an impinging flame focused on one side of the coated foam for more than 5 min was also maintained. These results clearly demonstrate the durability of the coated foams, opening to real life application fields such as transports seats where high levels of flame retardancy must be maintained for long time under frequent mechanical stress

Nonlinear waves in adhesive strings

We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state, beyond such a value the stress discontinuously drops to zero. Therefore the semilinear equation is characterized by a source term presenting jump discontinuity. Well-posedness of the initial boundary value problem of Neumann type, as well as qualitative properties of the solutions are studied and the evolution of different initial conditions are numerically investigated