Domain formation in magnetic polymer composites: an approach via stochastic homogenization

We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter $\varepsilon$ and the magnets as classical $\pm 1$ spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of $\Gamma$-convergence that, up to subsequences, the (continuum) $\Gamma$-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it has a local integral structure. Assuming stationarity of the stochastic lattice, we can make use of ergodic theory to further show that the $\Gamma$-limit exists and that the integrand is given by an asymptotic homogenization formula which becomes deterministic if the lattice is ergodic.Comment: 31 page

Verbi locativi in italiano come varianti di verbi supporto

In questo articolo discuteremo la nozione di "carrier verbs" (secondo la definizione del linguista americano Zellig Harris) o di "light verbs" (come denominata all'inizio del XX secolo da Otto Jespersen). La nostra cornice teorica è rappresentata dal lessico-grammatica di Maurice Gross, una teoria iniziata negli anni settanta a partire dalla sintassi del francese sulle basi matematiche già individuate per la lingua inglese da Zellig Harris. In particolare, discuteremo di come alcuni verbi locativi dell'italiano possano essere usati come verbi supporto (secondo la definizione data da Gross dei "light verbs" harrisiani) e assumano il ruolo sintattico una volta attribuito dai grammatici greci e latini alla copula esse.En aquest article discutirem la noció de "carrier verbs" (segons la definició del lingüista americà Zellig Harris) o de "light verbs" (segons la denominació que Otto Jespersen n'havia donat a principi del segle XX). El nostre marc teòric de referència és el lèxic-gramàtica de Maurice Gross, una teoria començada els anys setanta a partir de la sintaxi del francès en les bases matemàtiques ja individuades per a la llengua anglesa per Zelling Harris. Concretament, tractarem de com alguns verbs locatius de l'italià es poden emprar com a verbs de suport (tal com Gross va definir els "light verbs" harrisians) i de com assumeixen el paper sintàctic que els gramàtics grecs i llatins atribuïen a la còpula esse.In this article we aim at discussing the notion of carrier verbs (according to the definition provided by the American linguist Zellig Harris) or of light verbs (as defined at the beginning of the twentieth century by Otto Jespersen). Our theoretical framework is represented by Maurice Gross' lexicon-grammar, a theory developed during the seventies on the French syntax and directly inspired by Zellig Harris' mathematical grammar of English. Particularly, we are going to discuss of how some Italian locative verbs can be used as support verbs (according to the definition which Maurice Gross has given of the harrisian light verbs) and can play the syntactic role traditionally given to the copula esse by the Greek and Latin grammarians

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

Negative-Pressure Ventilation in Neuromuscular Diseases in the Acute Setting

Mechanical ventilation started with negative-pressure ventilation (NPV) during the 1950s to assist patients with respiratory failure, secondary to poliomyelitis. Over the years, technological evolution has allowed for the development of more comfortable devices, leading to an increased interest in NPV. The patients affected by neuromuscular diseases (NMD) with chronic and acute respiratory failure (ARF) may benefit from NPV. The knowledge of the available respiratory-support techniques, indications, contraindications, and adverse effects is necessary to offer the patient a personalized treatment that considers the pathology's complexity

Influence Diffusion in Social Networks under Time Window Constraints

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network $G=(V,E)$, an integer value $t(v)$ for each node $v\in V$, and a time window size $\lambda$. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node $v$ becomes influenced if the number of its neighbors that have been influenced in the previous $\lambda$ rounds is greater than or equal to $t(v)$. We prove that the problem of finding a minimum cardinality target set that influences the whole network $G$ is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared in: Proceedings of 20th International Colloquium on Structural Information and Communication Complexity (Sirocco 2013), Lectures Notes in Computer Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201