Random Networks Tossing Biased Coins

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with, asymptotically, scale-free outdegree and compact indegree. Entries in each row of the adjacency matrix are set to be zero or one according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n ~ 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs

Exchangeable Random Networks

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the degree distribution of the ensemble graphs, together with some features that are important for applications, such as subgraph distributions and kernel of the adjacency matrix. These results are used to compare to other models of simple and complex networks. A particular case of directed networks with power-law out--degree is studied in more detail, as an example of the flexibility of the model in applications.Comment: to appear on "Internet Mathematics

Family well-being during the COVID-19 lockdown in Italy: Gender differences and solidarity networks of care

During the COVID-19 pandemic, families experienced new challenges related to reorganizing living spaces and the need to renegotiate domestic and care roles. This paper aims to understand how Italian families have reacted to this situation with respect to psychological well-being, the management of domestic and care activities and solidarity networks of care. The participants were 560 Italian subjects who reported having a parental role. The protocol included a measure of well-being (the General Health Questionnaire-12) and some questions related to the time dedicated to domestic activities or to caring for people, the perception of conflict within the family and solidarity networks of care. The data underline how mothers continued to devote more time to home and care activities than fathers, despite the presence of both partners at home during the lockdown. The results also indicate that mothers participated to a greater extent than fathers in solidarity activities, confirming that this dimension is linked to gender. Furthermore, fathers and mothers perceived a lower condition of well-being in relation to the pre-pandemic period

Micro-beam and pulsed laser beam techniques for the micro-fabrication of diamond surface and bulk structures

Micro-fabrication in diamond is involved in a wide set of emerging technologies, exploiting the exceptional characteristics of diamond for application in bio-physics, photonics, radiation detection. Micro ion-beam irradiation and pulsed laser irradiation are complementary techniques, which permit the implementation of complex geometries, by modification and functionalization of surface and/or bulk material, modifying the optical, electrical and mechanical characteristics of the material. In this article we summarize the work done in Florence (Italy) concerning ion beam and pulsed laser beam micro-fabrication in diamond.Comment: 14 pages, 5 figure

Global climate change and tree nutrition: effects of elevated CO2 and temperature

Although tree nutrition has not been the primary focus of large climate change experiments on trees, we are beginning to understand its links to elevated atmospheric CO2 and temperature changes. This review focuses on the major nutrients, namely N and P, and deals with the effects of climate change on the processes that alter their cycling and availability. Current knowledge regarding biotic and abiotic agents of weathering, mobilization and immobilization of these elements will be discussed. To date, controlled environment studies have identified possible effects of climate change on tree nutrition. Only some of these findings, however, were verified in ecosystem scale experiments. Moreover, to be able to predict future effects of climate change on tree nutrition at this scale, we need to progress from studying effects of single factors to analysing interactions between factors such as elevated CO2, temperature or water availability

Evidence of light guiding in ion-implanted diamond

We demonstrate the feasibility of fabricating light-waveguiding microstructures in bulk single-crystal diamond by means of direct ion implantation with a scanning microbeam, resulting in the modulation of the refractive index of the ion-beam damaged crystal. Direct evidence of waveguiding through such buried microchannels is obtained with a phase-shift micro-interferometric method allowing the study of the multimodal structure of the propagating electromagnetic field. The possibility of defining optical and photonic structures by direct ion writing opens a range of new possibilities in the design of quantumoptical devices in bulk single-crystal diamond

Feedback topology and XOR-dynamics in Boolean networks with varying input structure

We analyse a model of fixed in-degree Random Boolean Networks in which the fraction of input-receiving nodes is controlled by a parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control, and as rich as the one of general Boolean networks. Biologically, it is justified on abstract grounds by the fact that all existing interactions play a dynamical role. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying gamma, this graph ensemble shows a phase transition that separates a tree-like graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact we provide analytical estimates of the maximum period starting from topological considerations

Fluctuations of a driven membrane in an electrolyte

We develop a model for a driven cell- or artificial membrane in an electrolyte. The system is kept far from equilibrium by the application of a DC electric field or by concentration gradients, which causes ions to flow through specific ion-conducting units (representing pumps, channels or natural pores). We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain the membrane equation of motion within Stokes hydrodynamics. At steady state, the applied field causes an accumulation of charges close to the membrane, which, similarly to the equilibrium case, can be described with renormalized membrane tension and bending modulus. However, as opposed to the equilibrium situation, we find new terms in the membrane equation of motion, which arise specifically in the out-of-equilibrium case. We show that these terms lead in certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let