Scale-free networks in complex systems

In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic dynamics, the results demonstrate that most systems under consideration tend to self-organize into structures that share common features. In particular, the networks of interaction are characterized by a power law distribution, $P(k)\sim k^{-\alpha}$, in the number of connections per node, $k$, over several orders of magnitude. Networks that fulfill this propriety of scale-invariance are referred to as ``scale-free''. In the present work we explore the implication of scale-free topologies in the antiferromagnetic (AF) Ising model and in a stochastic model of opinion formation. In the first case we show that the implicit disorder and frustration lead to a spin-glass phase transition not observed for the AF Ising model on standard lattices. We further illustrate that the opinion formation model produces a coherent, turbulent-like dynamics for a certain range of parameters. The influence, of random or targeted exclusion of nodes is studied.Comment: 9 pages, 4 figures. Proceeding to "SPIE International Symposium Microelectronics, MEMS, and Nanotechnology", 11-15 December 2005, Brisbane, Australi

Applications of physical methods in high-frequency futures markets

In the present work we demonstrate the application of different physical methods to high-frequency or tick-by-tick financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price time series taken from a range of futures indices. Additionally, we show that in a limit order book the relaxation times of an imbalanced book state with more demand or supply can be described by stretched exponential laws analogous to those seen in many physical systems.Comment: 14 Pages and 10 figures. Proceeding to the SPIE conference, 4 - 7 December 2007 Australian National Univ. Canberra, ACT, Australi

Self-Similar Log-Periodic Structures in Western Stock Markets from 2000

The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work we analyze the daily closures of three of the most important indices worldwide since 2000: the DAX for Germany and the Nasdaq100 and the S&P500 for the United States. The qualitative behaviour of these different markets is similar during the temporal frame studied. Evidence is found for decelerating log-periodic oscillations of duration about two years and starting in September 2000. Moreover, a nested sub-structure starting in May 2002 is revealed, bringing more evidence to support the hypothesis of self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also revealed. A Lomb analysis over the aforementioned periods indicates a preferential scaling factor $\lambda \sim 2$. Higher order harmonics are also present. The spectral pattern of the data has been found to be similar to that of a Weierstrass-type function, used as a prototype of a log-periodic fractal function.Comment: 17 pages, 14 figures. International Journal of Modern Physics C, in pres

A Multi Agent Model for the Limit Order Book Dynamics

In the present work we introduce a novel multi-agent model with the aim to reproduce the dynamics of a double auction market at microscopic time scale through a faithful simulation of the matching mechanics in the limit order book. The agents follow a noise decision making process where their actions are related to a stochastic variable, "the market sentiment", which we define as a mixture of public and private information. The model, despite making just few basic assumptions over the trading strategies of the agents, is able to reproduce several empirical features of the high-frequency dynamics of the market microstructure not only related to the price movements but also to the deposition of the orders in the book.Comment: 20 pages, 11 figures, in press European Physical Journal B (EPJB

Neuromorphic decoding of spinal motor neuron behaviour during natural hand movements for a new generation of wearable neural interfaces

We propose a neuromorphic framework to process the activity of human spinal motor neurons for movement intention recognition. This framework is integrated into a non-invasive interface that decodes the activity of motor neurons innervating intrinsic and extrinsic hand muscles. One of the main limitations of current neural interfaces is that machine learning models cannot exploit the efficiency of the spike encoding operated by the nervous system. Spiking-based pattern recognition would detect the spatio-temporal sparse activity of a neuronal pool and lead to adaptive and compact implementations, eventually running locally in embedded systems. Emergent Spiking Neural Networks (SNN) have not yet been used for processing the activity of in-vivo human neurons. Here we developed a convolutional SNN to process a total of 467 spinal motor neurons whose activity was identified in 5 participants while executing 10 hand movements. The classification accuracy approached 0.95 ±0.14 for both isometric and non-isometric contractions. These results show for the first time the potential of highly accurate motion intent detection by combining non-invasive neural interfaces and SNN

Self-reported adherence supports patient preference for the single tablet regimen (STR) in the current cART era

Objective: To analyze self-reported adherence to antiretroviral regimens containing ritonavir-boosted protease inhibitors, non-nucleoside reverse transcriptase inhibitors (NNRTI), raltegravir, and maraviroc. Methods: Overall, 372 consecutive subjects attending a reference center for HIV treatment in Florence, Italy, were enrolled in the study, from December 2010 to January 2012 (mean age 48 years). A self-report questionnaire was filled in. Patients were defined as “non-adherent” if reporting one of the following criteria:<90% of pills taken in the last month, ≥1 missed dose in the last week, spontaneous treatment interruptions reported, or refill problems in the last 3 months. Gender, age, CD4, HIV-RNA, years of therapy, and type of antiretroviral regimen were analyzed with respect to adherence. Results: At the time of the questionnaire, 89.8% of patients had <50 copies/mL HIV-RNA and 14.2% were on their first combined antiretroviral therapy. 57% of patients were prescribed a regimen containing ritonavir boosted protease inhibitors (boosted PI), 41.7% NNRTI, 17.2% raltegravir, and 4.8% maraviroc; 49.5% of the subjects were on bis-in-die regimens, while 50.5% were on once-daily regimens, with 23.1% of these on the single tablet regimen (STR): tenofovir/emtricitabine/efavirenz. The non-adherence proportion was lower in NNRTI than in boosted-PI treatments (19.4% vs 30.2%), and even lower in STR patients (17.4%). In multivariable logistic regression, patients with the NNRTI regimen (OR: 0.56, 95% CI: 0.34–0.94) and the STR (OR: 0.45, 95% CI: 0.22–0.92) reported lower non-adherence. Efavirenz regimens were also associated with lower non-adherence (OR: 0.42, 95% CI: 0.21–0.83), while atazanavir/ritonavir regimens were associated with higher non-adherence. No other relation to specific antiretroviral drugs was found. A higher CD4 count, lower HIV-RNA, and older age were also found to be associated with lower non-adherence, while a longer time on combined antiretroviral therapy was related to higher non-adherence. Conclusion: In conclusion, older age, higher CD4 cell counts, lower HIV-RNA viral loads, and the use of STR are all related to lower non-adherence. In particular, the use of STR maintains an advantage in improving adherence with respect to other cARTs, even with the availability of new, well-tolerated antiretroviral drugs and drug classes in recent years

Stochastic Opinion Formation in Scale-Free Networks

The dynamics of opinion formation in large groups of people is a complex non-linear phenomenon whose investigation is just at the beginning. Both collective behaviour and personal view play an important role in this mechanism. In the present work we mimic the dynamics of opinion formation of a group of agents, represented by two state $\pm 1$, as a stochastic response of each of them to the opinion of his/her neighbours in the social network and to feedback from the average opinion of the whole. In the light of recent studies, a scale-free Barab\'asi-Albert network has been selected to simulate the topology of the interactions. A turbulent-like dynamics, characterized by an intermittent behaviour, is observed for a certain range of the model parameters. The problem of uncertainty in decision taking is also addressed both from a topological point of view, using random and targeted removal of agents from the network, and by implementing a three state model, where the third state, zero, is related to the information available to each agent. Finally, the results of the model are tested against the best known network of social interactions: the stock market. A time series of daily closures of the Dow Jones index has been used as an indicator of the possible applicability of our model in the financial context. Good qualitative agreement is found.Comment: 24 pages and 13 figures, Physical Review E, in pres