One-dimensional disordered Ising models by replica and cavity methods

Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor graph (p-spin) ensembles. We present exact analytical expressions, which can be efficiently approximated numerically, for many types of correlation functions and for the average free energies of open and closed finite chains. All the results achieved, with the exception of those involving closed chains, are then rigorously derived without replicas, using a probabilistic approach with the same flavour of cavity method

One-loop diagrams in the Random Euclidean Matching Problem

The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e. the optimal matching problem between points randomly distributed on a $d$-dimensional Euclidean space, where the cost to minimize depends on the points' pairwise distances. Using Mayer's cluster expansion we write a formal expression for the replicated action that is suitable for a saddle point computation. We give the diagrammatic rules for each term of the expansion, and we analyze in detail the one-loop diagrams. A characteristic feature of the theory, when diagrams are perturbatively computed around the mean field part of the action, is the vanishing of the mass at zero momentum. In the non-Euclidean case of uncorrelated costs instead, we predict and numerically verify an anomalous scaling for the sub-sub-leading correction to the asymptotic average cost.Comment: 17 pages, 7 figure

Generalized Approximate Survey Propagation for High-Dimensional Estimation

In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized Approximate Message Passing (GAMP) is known to achieve optimal performance for GLE. However, its performance can significantly degrade whenever there is a mismatch between the assumed and the true generative model, a situation frequently encountered in practice. In this paper, we propose a new algorithm, named Generalized Approximate Survey Propagation (GASP), for solving GLE in the presence of prior or model mis-specifications. As a prototypical example, we consider the phase retrieval problem, where we show that GASP outperforms the corresponding GAMP, reducing the reconstruction threshold and, for certain choices of its parameters, approaching Bayesian optimal performance. Furthermore, we present a set of State Evolution equations that exactly characterize the dynamics of GASP in the high-dimensional limit

Design, ingenuity and imagination

Invention in design means putting into practice a technical/scientific idea that is the result of ingenuity. But it is also the pure capacity for imagination, capable of «altering the sensibility of the human race» (Kubler, 1962), acting as much upon the product’s functions as upon the meaning. And indeed, invention in design is a process that is not in the least ingenuous or visionary, but the outcome of a highly sophisticated process, capable of selecting forms and technologies to obtain the maximum expressive result with the minimum exhibition of formal effort, and of stereotyping itself in formally essential objects. This is why innovation, for design, cannot be resolved only as a “muscular” display of innovative technologies, of use more for simplifying realization processes than for creating new functions or new languages. The designer’s activity is in fact mainly that of serving as a mediator between art, technology, and society, interpreting not only functions, but also the meaning of discoveries in inventions of “sign mediations” and of new “social garments” (Zingale, 2012). Starting from these assumptions, the paper proposes a classification by categories, in which innovation in design is read as the result of a technological transfer process; as a spontaneous or even random activity; as the ability to apply “simplexity” by making the complex simple; or as a reaction to limitations and scant resources, by offering a vantage point that, without denying the potentials offered by recent innovations, aims to reaffirm the more humanistic and less technocratic dimension of our inventive capacity. This inventive capacity is not played out in the aesthetic dimension alone, but can join this imagination to define new uses, functions, and languages. Starting from here, the designer can and must set off again – while keeping his or her role well in mind – to configure a new humanism

The near (bio)future in design

The paper joins the debate on the emerging prospective in design in the near future that will be “bio”. The world has gone through 3.8 billion years of research and development, with failures and successes, in search of the most effective and affordable solutions to facilitate our daily life. This is especially true today, since we realized that energy resources and raw materials are starting to run-out and that they will not be enough for the population in the near future, The planet could literally implode, ceasing to be an "earthly paradise". Human people have therefore always observed Nature, using it as a source of knowledge and inspiration, but with different approaches. Starting from these premises, the present article explores how innovation can be inspired by Nature. Nature, that in this context is deemed to be the model, the measure and the “mentor” from which designers can learn through a fully informed, responsible study of its biological and biomechanical processes, with the ultimate objective of improving human activities and technology to allow full resonance with Nature itself. Today, technology allows us to reproduce natural systems and biofabricate living systems. Everything appears possible today, but we should probably ask ourselves if this is really necessary, as we did when the possibility of replicating and genetically modifying the living being opened up? How can we avoid running into "technological blasphemy"? What role can design play in this

Scaling hypothesis for the Euclidean bipartite matching problem

We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic prediction of the large $N$ limit of the average cost in dimension $d=1,2$ and of the subleading correction in higher dimension. A non-trivial scaling exponent, $\gamma_d=\frac{d-2}{d}$, which differs from the monopartite's one, is found for the subleading correction. We argue that the same scaling holds true for a generic cost exponent in dimension $d>2$.Comment: 11 page

From Science to Design: the Design4Materials virtuous cycle

Despite the large number of innovative materials developed in laboratories worldwide, their application in new mass-produced products is complicated. Design can reduce the risk that the research developed in scientific laboratories could fail to be properly exploited and triggering a beneficial cycle linking Science to Design. This paper present the Design4Materials, an italian network founded by the laboratories of leading schools of design: MaterialdesignLab|Sapienza Rome, Madec|Politecnico di Milano, HybridesignLab|SUN Naples, Soft Surfaces and Polisensoriality|Poliba Bari. After presenting the different skills of the network members, the authors describe the capabilities and the goals of the network and the main results developed like the project that define characteristics and identities for an open material, starting from a research of the IIT of Genoa. The Design4Materials aim is to play a leading role on design-driven innovation process, responding to society’s changing needs and developing a ‘circular’ methodology of innovation from a design standpoint