Approximation processes for resolvent operators

We introduce general sequences of linear operators obtained from classical approximation processes which are useful in the approximation of the resolvent operators of the generators of suitable C ₀-semigroups. The main aim is the representation of the resolvent operators in terms of classical approximation operators. Work performed under the auspices of PRIN 2006–07 “Kolmogorov equations” (coordinator G. Da Prato)     

Immersive and desktop virtual reality in virtual fashion stores: a comparison between shopping experiences

Virtual Reality - With the high growth and prosperity of e-commerce, the retail industry needs to explore new technologies that improve digital shopping experiences. In the current technological...     

Exploiting probability density function of deep convolutional autoencoders’ latent space for reliable COVID-19 detection on CT scans

The Journal of Supercomputing - We present a probabilistic method for classifying chest computed tomography (CT) scans into COVID-19 and non-COVID-19. To this end, we design and train, in an...     

Optimal-tuning PID control of adaptive materials for structural efficiency

The objective of this paper was solving the optimization problem of lightweight stiffened structures modelled as a two-dimensional domain in an efficient computational way. The underlying premise was that mass should be distributed in an efficient way, so as to use a minimum amount of material to accomplish the mechanical function. This premise was expressed as a global, multi-objective optimization problem in which stiffness and mass were conflicting objectives. Alternative local evolution rules were implemented to update mass density or Young’s modulus at each step of the iterative procedure. The solution of the structural optimization problem was accomplished by a novel automatic procedure consisting of two consecutive stages of control and optimization. In the first stage of Proportional Integral Derivative (PID) control gains were manually selected whereas in the second stage the finding of optimal values of control gains, target, and cost indices was allowed. In this study a bone-like material was adopted and a thin slab was analysed as a sample problem.     

A declarative two-level framework to specify and verify workflow and authorization policies in service-oriented architectures

The specification of distributed service-oriented applications spans several levels of abstraction, e.g., the protocol for exchanging messages, the set of interface functionalities, the types of the manipulated data, the workflow, the access policy, etc. Many (even executable) specification languages are available to describe each level in separation. However, these levels may interact in subtle ways (for example, the control flow may depend on the values of some data variables) so that a precise abstraction of the application amounts to more than the sum of its per level components. This problem is even more acute in the design phase when automated analysis techniques may greatly help the difficult task of building “correct” applications faced by designers. To alleviate this kind of problems, this paper introduces a framework for the formal specification and automated analysis of distributed service-oriented applications in two levels: one for the workflow and one for the authorization policies. The former allows one to precisely describe the control and data parts of an application with their mutual dependencies. The latter focuses on the specification of the criteria for granting or denying third-party applications the possibility to access shared resources or to execute certain interface functionalities. These levels can be seen as abstractions of one or of several levels of specification mentioned above. The novelty of our proposal is the possibility to unambiguously specify the—often subtle—interplay between the workflow and policy levels uniformly in the same framework. Additionally, our framework allows us to define and investigate verification problems for service-oriented applications (such as executability and invariant checking) and give sufficient conditions for their decidability. These results are non-trivial because their scope of applicability goes well beyond the case of finite state spaces allowing for applications manipulating variables ranging over infinite domains. As proof of concept, we show the suitability and flexibility of our approach on two quite different examples inspired by industrial case studies.     

Modified HSS iteration methods for a class of complex symmetric linear systems

In this paper, we introduce and analyze a modification of the Hermitian and skew-Hermitian splitting iteration method for solving a broad class of complex symmetric linear systems. We show that the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method is unconditionally convergent. Each iteration of this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. These two systems can be solved inexactly. We consider acceleration of the MHSS iteration by Krylov subspace methods. Numerical experiments on a few model problems are used to illustrate the performance of the new method.     

Performance of One-Round Walks in Linear Congestion Games

We investigate the approximation ratio of the solutions achieved after a one-round walk in linear congestion games. We consider the social functions Sum, defined as the sum of the players’ costs, and Max, defined as the maximum cost per player, as a measure of the quality of a given solution. For the social function Sum and one-round walks starting from the empty strategy profile, we close the gap between the upper bound of \(2+\sqrt{5}\approx 4.24\) given in Christodoulou et al. (Proceedings of the 23rd International Symposium on Theoretical Aspects of Computer Science (STACS), LNCS, vol. 3884, pp. 349–360, Springer, Berlin, 2006) and the lower bound of 4 derived in Caragiannis et al. (Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP), LNCS, vol. 4051, pp. 311–322, Springer, Berlin, 2006) by providing a matching lower bound whose construction and analysis require non-trivial arguments. For the social function Max, for which, to the best of our knowledge, no results were known prior to this work, we show an approximation ratio of \(\Theta(\sqrt[4]{n^{3}})\) (resp. \(\Theta(n\sqrt{n})\)), where n is the number of players, for one-round walks starting from the empty (resp. an arbitrary) strategy profile.     

On the Convergence of Multicast Games in Directed Networks

We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication network is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In particular, assuming that the initial set of connecting paths can be arbitrary, we show an $O(r\sqrt{r})We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication network is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In particular, assuming that the initial set of connecting paths can be arbitrary, we show an O(r?r)O(r\sqrt{r}) upper bound on the price of anarchy after 2 rounds, during each of which all the receivers move exactly once, and a matching lower bound, that we also extend to W(r^k?{r})\Omega(r\sqrt[k]{r}) for any number k≥2 rounds, where r is the number of receivers. Similarly, exactly matching upper and lower bounds equal to r are determined for any number of rounds when starting from the empty state in which no path has been selected. Analogous results are obtained also with respect to other three natural cost sharing methods considered in the literature, that is the egalitarian, path-proportional and egalitarian-path proportional ones. Most results are also extended to the undirected case in which the communication links are bidirectional.