Causal interactions and delays in a neuronal ensemble

We analyze a neural system which mimics a sensorial cortex, with different input characteristics, in presence of transmission delays. We propose a new measure to characterize collective behavior, based on the nonlinear extension of the concept of Granger causality, and an interpretation is given of the variation of the percentage of the causally relevant interactions with transmission delays.Comment: 7 pages, 3 figures. To appear in the AIP seminar notes of 9th Granada seminar on Computational Physics: Computational and Mathematical Modeling of Cooperative Behavior in Neural System

Effects of Local Specialization of Investment Subsides in Italy

In Italy we currently have a lot of national and regional instruments for financial aids to enterprises. Most of them are not specialized, as syntethetized in the following points: 1. they are refferred to the whole Italian territory; 2. they have generic objects (increase of GNP, reduction of growth differences among regions, employment); 3. they are applied to all the sectors of production; 4. they have common methods of application (automatic, discretional,negotiated). This means that we establish general purposes without further specialization even if we fall into particular purposes.In addition to this types of subsides, there are anymore that are specialized both at territorial and at sectorial level. Among these, the most important are distributed by the Territorial Pacts that are one of the instruments of concerted planning. In this paper we firstly define the specialization of some forms of subsidies; then we analize the performance of two samples of enterprises, that are located in the Apulia Region (NUTS III), the first of which has been benefiting from the state support provided by law n.488/92 (Financial support of the productive activities in depressed zones), and the second one that has been benefiting from the support provided by Territorial Pacts. The enterprises performance have been assessed through quantitative index measured by three main relations: 1. Sales / Assets, that is an indicator measuring the firms efficiency. So it indicates if the total value of sales they?ve carried out, can account for the effectuated investments. 2. Profit / Sales, that estimate the enterprise ability to obtain profits, aging in the market, and let us having indications about prospects of success. 3. Profit / Assets, that assess, in a better way, the capacity in terms of global income of the enterprise. Comparing the average of the three indicators considered, related to supported enterprises, with the same indexes of Mediobanca sample about not-supported enterprises, we obtain interesting results. They have proved that: A. the enterprises having supports are, generally, less efficient than those having no support; B. the firms subsided by Territorial Pacts are more efficient than the other ones subsided by law n.488/92. From the investigation it emerges that the subsides territorially oriented are more efficient than the general support, referred to the same area. So, if we privilege efficiency results, putting the effectiveness ones in a secondary position, we probably should prefer an automatic but specialized aid system, at least from the territorial, dimensional and productive point of view according to preference scales. But, if we want to obtain effectiveness standards too, it is necessary to specialize the interventions and determine specific goals and result indicators.

Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone

On the interpretability and computational reliability of frequency-domain Granger causality

This is a comment to the paper 'A study of problems encountered in Granger causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name 'causality', as nicely described in previous literature). On the other hand we think that the paper uses a formulation of Granger causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even written in good faith, became a wildcard against all possible applications of Granger Causality, regardless of the hard work of colleagues aiming to seriously address the methodological and interpretation pitfalls. In order to provide a balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved

Synergy and redundancy in the Granger causal analysis of dynamical networks

We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst we show that fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned Granger causality is an effective approach if the set of conditioning variables is properly chosen. We consider here two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for partially conditioned Granger causality and show that depending on the data structure either one or the other might be valid. On the other hand, we observe that fully conditioned approaches do not work well in presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the fully conditioned Granger causality (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in presence of redundancy. We finally apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy

Statistical mechanics approach to the phase unwrapping problem

The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem is formulated as that of finding the ground state of a locally constrained, finite size, spin-L Ising model under a non-uniform magnetic field. The optimization problem is solved by the Mean-Field Annealing technique. Synthetic experiments show the effectiveness of the proposed algorithm

Universality of the Tearing Phase in Matrix Models

The spontaneous symmetry breaking associated to the tearing of a random surface, where large dynamical holes fill the surface, was recently analized obtaining a non-universal critical exponent on a border phase. Here the issue of universality is explained by an independent analysis. The one hole sector of the model is useful to manifest the origin of the (limited) non-universal behaviour, that is the existence of two inequivalent critical points.Comment: 9 pages, 1 figure non include