From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior

The study of neuronal interactions is currently at the center of several neuroscience big collaborative projects (including the Human Connectome, the Blue Brain, the Brainome, etc.) which attempt to obtain a detailed map of the entire brain matrix. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of such synaptic interaction matrix. This work explores the application of free random variables (FRV) to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra of neural networks, we extend them to heavy-tailed distributions of interactions. More importantly, we derive analytically the behavior of eigenvector overlaps, which determine stability of the spectra. We observe that upon imposing the neuronal excitation/inhibition balance, although the eigenvalues remain unchanged, their stability dramatically decreases due to strong non-orthogonality of associated eigenvectors. It leads us to the conclusion that the understanding of the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of FRV analysis in a wide variety of branches disciplines, we hope that the results presented here foster additional application of these ideas in the area of brain sciences.Comment: 24 pages + 4 pages of refs, 8 figure

Spectrum Trading: An Abstracted Bibliography

This document contains a bibliographic list of major papers on spectrum trading and their abstracts. The aim of the list is to offer researchers entering this field a fast panorama of the current literature. The list is continually updated on the webpage \url{http://www.disp.uniroma2.it/users/naldi/Ricspt.html}. Omissions and papers suggested for inclusion may be pointed out to the authors through e-mail (\textit{[email protected]})

Adsorption of Polyisobutylene-Based Dispersants onto Carbon Black

The formation of carbonaceous by-products (e.g. soot) during the operation of an internal combustion engine is unavoidable and the aggregation of this soot leads to deleterious effects including abrasive wear of the engine, increased oil viscosities, and sludge deposition. Dispersants, which are composed of a hydrophobic tail and a polar headgroup, are used as oil additives to aid in the suspension and stabilization of the soot particles. Polyisobutylene succinimide (PIBSI) is the most well-studied class of dispersants and is characterized by a linear architecture and polyamine headgroup that interacts with soot by acid-base and dipole-dipole interactions. As such, there remains a lack in understanding on the effect of dispersant architecture and alternative dispersant-soot interactions and the governing characteristics of these interactions. In the first project, we synthesized a library of polyisobutylene (PIB)-based dispersants with varying architecture. Linear dispersants were prepared via living cationic polymerization and grafted dispersants by the acid-catalyzed cleavage/alkylation of butyl rubber. Comb dispersants were prepared from the alternating copolymerization of vinyl-ether PIB (VE-PIB) macromers with maleic anhydride where the rate of copolymerization was found to be heavily influenced by molecular weight of the VE-PIB macromer. The affinity and degree to which comb and grafted dispersants adsorbed to carbon black was found to be similar whereas a linear dispersant exhibited reduced affinity yet increased adsorption capacity. In the second project, we investigated the effect of PIB-based dispersants containing exclusively non-nucleophilic nitrogen in addition to how π-π interactions can be leveraged for the adsorption of dispersants. Linear PIB was functionalized with 1-(2-aminoethylpiperazine) and was subsequently functionalized with cyclic anhydrides of varying degrees of aromaticity. Metal corrosion and fluoroelastomer compatibility indicated that dispersants with non-nucleophilic nitrogen were less aggressive while providing a greater degree of total base number in comparison to PIBSI dispersants. A critical size of at least two terminal aromatic rings was found to be able to leverage advantageous π-π interactions between dispersants and carbon black for increased adsorption. In the third project, we investigated cation-π interactions between carbon black and ionic-liquid terminated PIB (PIB-IL) dispersants. Interaction of the nitrogenous cation with the quadrupole moment of the aromatic surface provided for strong non-covalent interactions which can be used as an alternative mechanism for adsorption. A library of PIB-IL dispersants was prepared through the quaternization of aromatic amines and metathesis of counterions. The characteristics of PIB-IL micellization (Nagg, CMC, Mmicelle, Rh) were heavily influenced by anion hydrophobicity whereas PIB-IL adsorption to carbon black was dictated by the molar volume of the cation. The fourth project, which was of an alternative focus, investigated Diels-Alder crosslinked PIB networks which were prepared from multifunctional PIB-Furan and PIB-Maleimide macromers utilizing the acid catalyzed cleavage/alkylation of butyl rubber. Thermal stability, including decomposition temperature and retro Diels-Alder temperatures (TRDA) were independent of macromer choice however the viscoelastic properties were heavily influenced. Recyclability was demonstrated by remolding and recasting of destroyed networks at elevated temperatures and a slight hysteresis in mechanical properties was observed as compared to original networks

Linear processes in high-dimension: phase space and critical properties

In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable and an unstable phase. We find that along the transition region separating the two regimes, the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become power-laws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of self-interaction are naturally characterized by this type of slow relaxation of the correlations.Comment: 40 pages, 5 figure

Modeling, analysis, and optimization for wireless networks in the presence of heavy tails

The heavy-tailed traffic from wireless users, caused by the emerging Internet and multimedia applications, induces extremely dynamic and variable network environment, which can fundamentally change the way in which wireless networks are conceived, designed, and operated. This thesis is concerned with modeling, analysis, and optimization of wireless networks in the presence of heavy tails. First, a novel traffic model is proposed, which captures the inherent relationship between the traffic dynamics and the joint effects of the mobility variability of network users and the spatial correlation in their observed physical phenomenon. Next, the asymptotic delay distribution of wireless users is analyzed under different traffic patterns and spectrum conditions, which reveals the critical conditions under which wireless users can experience heavy-tailed delay with significantly degraded QoS performance. Based on the delay analysis, the fundamental impact of heavy-tailed environment on network stability is studied. Specifically, a new network stability criterion, namely moment stability, is introduced to better characterize the QoS performance in the heavy-tailed environment. Accordingly, a throughput-optimal scheduling algorithm is proposed to maximize network throughput while guaranteeing moment stability. Furthermore, the impact of heavy-tailed spectrum on network connectivity is investigated. Towards this, the necessary conditions on the existence of delay-bounded connectivity are derived. To enhance network connectivity, the mobility-assisted data forwarding scheme is exploited, whose important design parameters, such as critical mobility radius, are derived. Moreover, the latency in wireless mobile networks is analyzed, which exhibits asymptotic linearity in the initial distance between mobile users.Ph.D

Can we avoid high coupling?

It is considered good software design practice to organize source code into modules and to favour within-module connections (cohesion) over between-module connections (coupling), leading to the oft-repeated maxim "low coupling/high cohesion". Prior research into network theory and its application to software systems has found evidence that many important properties in real software systems exhibit approximately scale-free structure, including coupling; researchers have claimed that such scale-free structures are ubiquitous. This implies that high coupling must be unavoidable, statistically speaking, apparently contradicting standard ideas about software structure. We present a model that leads to the simple predictions that approximately scale-free structures ought to arise both for between-module connectivity and overall connectivity, and not as the result of poor design or optimization shortcuts. These predictions are borne out by our large-scale empirical study. Hence we conclude that high coupling is not avoidable--and that this is in fact quite reasonable

Stochastic timeseries analysis in electric power systems and paleo-climate data

In this thesis a data science study of elementary stochastic processes is laid, aided with the development of two numerical software programmes, applied to power-grid frequency studies and Dansgaard--Oeschger events in paleo-climate data. Power-grid frequency is a key measure in power grid studies. It comprises the balance of power in a power grid at any instance. In this thesis an elementary Markovian Langevin-like stochastic process is employed, extending from existent literature, to show the basic elements of power-grid frequency dynamics can be modelled in such manner. Through a data science study of power-grid frequency data, it is shown that fluctuations scale in an inverse square-root relation with their size, alike any other stochastic process, confirming previous theoretical results. A simple Ornstein--Uhlenbeck is offered as a surrogate model for power-grid frequency dynamics, with a versatile input of driving deterministic functions, showing not surprisingly that driven stochastic processes with Gaussian noise do not necessarily show a Gaussian distribution. A study of the correlations between recordings of power-grid frequency in the same power-grid system reveals they are correlated, but a theoretical understanding is yet to be developed. A super-diffusive relaxation of amplitude synchronisation is shown to exist in space in coupled power-grid systems, whereas a linear relation is evidenced for the emergence of phase synchronisation. Two Python software packages are designed, offering the possibility to extract conditional moments for Markovian stochastic processes of any dimension, with a particular application for Markovian jump-diffusion processes for one-dimensional timeseries. Lastly, a study of Dansgaard--Oeschger events in recordings of paleoclimate data under the purview of bivariate Markovian jump-diffusion processes is proposed, augmented by a semi-theoretical study of bivariate stochastic processes, offering an explanation for the discontinuous transitions in these events and showing the existence of deterministic couplings between the recordings of the dust concentration and a proxy for the atmospheric temperature