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Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Different MRI acquisitions provide different brain networks at the macroscale; whilst diffusion-weighted MRI (dMRI) provides a structural connectivity (SC) coincident with the bundles of parallel fibers between brain areas, functional MRI (fMRI) accounts for the variations in the blood-oxygenation-level-dependent T2* signal, providing functional connectivity (FC).Understanding the precise relation between FC and SC, that is, between brain dynamics and structure, is still a challenge for neuroscience. To investigate this problem, we acquired data at rest and built the corresponding SC (with matrix elements corresponding to the fiber number between brain areas) to be compared with FC connectivity matrices obtained by 3 different methods: directed dependencies by an exploratory version of structural equation modeling (eSEM), linear correlations (C) and partial correlations (PC). We also considered the possibility of using lagged correlations in time series; so, we compared a lagged version of eSEM and Granger causality (GC). Our results were two-fold: firstly, eSEM performance in correlating with SC was comparable to those obtained from C and PC, but eSEM (not C nor PC) provides information about directionality of the functional interactions. Second, interactions on a time scale much smaller than the sampling time, captured by instantaneous connectivity methods, are much more related to SC than slow directed influences captured by the lagged analysis. Indeed the performance in correlating with SC was much worse for GC and for the lagged version of eSEM. We expect these results to supply further insights to the interplay between SC and functional patterns, an important issue in the study of brain physiology and function., Comment: Accepted and published in Frontiers in Psychology in its current form. 27 pages, 1 table, 5 figures, 2 suppl. figures

A great improvement to the insight on brain function that we can get from fMRI data can come from effective connectivity analysis, in which the flow of information between even remote brain regions is inferred by the parameters of a predictive dynamical model. As opposed to biologically inspired models, some techniques as Granger causality (GC) are purely data-driven and rely on statistical prediction and temporal precedence. While powerful and widely applicable, this approach could suffer from two main limitations when applied to BOLD fMRI data: confounding effect of hemodynamic response function (HRF) and conditioning to a large number of variables in presence of short time series. For task-related fMRI, neural population dynamics can be captured by modeling signal dynamics with explicit exogenous inputs; for resting-state fMRI on the other hand, the absence of explicit inputs makes this task more difficult, unless relying on some specific prior physiological hypothesis. In order to overcome these issues and to allow a more general approach, here we present a simple and novel blind-deconvolution technique for BOLD-fMRI signal. Coming to the second limitation, a fully multivariate conditioning with short and noisy data leads to computational problems due to overfitting. Furthermore, conceptual issues arise in presence of redundancy. We thus apply partial conditioning to a limited subset of variables in the framework of information theory, as recently proposed. Mixing these two improvements we compare the differences between BOLD and deconvolved BOLD level effective networks and draw some conclusions.

We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion are associated to informational circuits present in the system, with an informational character which can be associated to the sign of the contribution. For the sake of computational complexity, we adopt the assumption of Gaussianity and use the corresponding exact formula for the conditional mutual information. We report the application of the proposed methodology on two EEG data sets.

We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under-estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations., Comment: 4 pages, 5 figures. Accepted for publication in Physical Review E

We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions and mechanical systems. We let the global coupling k be a function of the Kuramoto order parameter r through an exponent z such that z=1 corresponds to the standard Winfree model, z<1 strengthens the coupling at low r (low amount of synchronization) and, at z>1, the coupling is weakened for low r. Using both analytical and numerical approaches, we find that z controls the size of the incoherent phase region, and one may make the incoherent behavior less typical by choosing z<1. We also find that the original Winfree model is a rather special case, indeed the partial locked behavior disappears for z>1. At fixed k and varying gamma, the stability boundary of the locked phase corresponds to a transition that is continuous for z<1 and first-order for z>1. This change in the nature of the transition is in accordance with a previous study on a similarly modified Kuramoto model., Comment: 9 pages, 3 figures

AdS/QCD correspondence predicts the structure of quark-antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schr\"odinger equation with relativistic kinematics) and a short range hyperfine splitting potential to determine quark masses and the quark potential parameters from the meson spectrum. The agreement between theory and experimental data is satisfactory provided one considers only mesons comprising at least one heavy quark. We use the same potential (in the one-gluon-exchange approximation) and these data to estimate constituent diquark masses. Using these results as an input we compute tetraquark masses using a diquark-antidiquark model. The masses of the states X(3872) or Y(3940) are predicted rather accurately. We also compute tetraquark masses with open charm and strangeness. Our result is that tetraquark candidates such as D_s(2317), D_s(2457) or X(2632) can hardly be interpreted as diquark-antidiquark states within the present approach., Comment: 15 pages, 4 figures

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally in the case of clustering algorithms that are rooted in Statistical Mechanics and use the analogy with a physical system., Comment: 11 pages, 5 figure enlarged version

We present the multiscale entropy analysis of short term physiological time series of simultaneously acquired samples of heart rate, blood pressure and lung volume, from healthy subjects and from subjects with Chronic Heart Failure. Evaluating the complexity of signals at the multiple time scales inherent in physiologic dynamics, we find that healthy subjects show more complex time series at large time scales; on the other hand, at fast time scales, which are more influenced by respiration, the pathologic dynamics of blood pressure is the most random. These results robustly separate healthy and pathologic groups. We also propose a multiscale approach to evaluate interactions between time series, by performing a multivariate autoregressive modelling of the coarse grained time series: this analysis provides several new quantitative indicators which are statistically correlated with the pathology., Comment: 9 pages 10 figures

In this paper we show that different physiological states and pathological conditions may be characterized in terms of predictability of time series signals from the underlying biological system. In particular we consider systolic arterial pressure time series from healthy subjects and Chronic Heart Failure patients, undergoing paced respiration. We model time series by the regularized least squares approach and quantify predictability by the leave-one-out error. We find that the entrainment mechanism connected to paced breath, that renders the arterial blood pressure signal more regular, thus more predictable, is less effective in patients, and this effect correlates with the seriousness of the heart failure. The leave-one-out error separates controls from patients and, when all orders of nonlinearity are taken into account, alive patients from patients for which cardiac death occurred.

We show that a general purpose clusterization algorithm, Deterministic Annealing, can be adapted to the problem of jet identification in particle production by high energy collisions. In particular we consider the problem of jet searching in events generated at hadronic colliders. Deterministic Annealing is able to reproduce the results obtained by traditional jet algorithms and to exhibit a higher degree of flexibility., Comment: 13 pages, 6 figures

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli., Comment: 4 pages

We study the phase-synchronization properties of systolic and diastolic arterial pressure in healthy subjects. We find that delays in the oscillatory components of the time series depend on the frequency bands that are considered, in particular we find a change of sign in the phase shift going from the Very Low Frequency band to the High Frequency band. This behavior should reflect a collective behavior of a system of nonlinear interacting elementary oscillators. We prove that some models describing such systems, e.g. the Winfree and the Kuramoto models offer a clue to this phenomenon. For these theoretical models there is a linear relationship between phase shifts and the difference of natural frequencies of oscillators and a change of sign in the phase shift naturally emerges., Comment: 8 figures, 9 pages

Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1), and the second parts (HD2) of $90^{\circ}$ head down tilt and during recovery (REC). The wavelet transform was performed using the Haar function of period $T=2^j$ ($% j=1$,2,$... $,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frequency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident difference than the R-R intervals. This study suggests a difference in the response of the vessels and the heart to different body positions. The partial dissociation between VLF and LF results is a physiologically relevant finding of this work., Comment: RevTex,8 figures

We calculate the specific heats of quasi-particles of two-flavor QCD in its crystalline phases for low temperature. We show that for the different crystalline structures considered here there are gapless modes contributing linearly in temperature to the specific heat. We evaluate also the phonon contributions which are cubic in temperature. These features might be relevant for compact stars with an inner shell in a color superconducting crystalline phase., Comment: LaTex, 13 pages. Final version published on Physics Letters including an ERRATA (to be published)

We perform a comparison of two jet clusterization algorithms. The first one is the standard Durham algorithm and the second one is a global optimization scheme, Deterministic Annealing, often used in clusterization problems, and adapted to the problem of jet identification in particle production by high energy collisions; in particular we study hadronic jets in WW production by high energy electron positron scattering. Our results are as follows. First, we find that the two procedures give basically the same output as far as the particle clusterization is concerned. Second, we find that the increase of CPU time with the particle multiplicity is much faster for the Durham jet clustering algorithm in comparison with Deterministic Annealing. Since this result follows from the higher computational complexity of the Durham scheme, it should not depend on the particular process studied here and might be significant for jet physics at LHC as well., Comment: 15 pages, 4 figures

Cost functions for non-hierarchical pairwise clustering are introduced, in the probabilistic autoencoder framework, by the request of maximal average similarity between the input and the output of the autoencoder. The partition provided by these cost functions identifies clusters with dense connected regions in data space; differences and similarities with respect to a well known cost function for pairwise clustering are outlined., Comment: 5 pages, 4 figures

Diluted neural networks with continuous neurons and nonmonotonic transfer function are studied, with both fixed and dynamic synapses. A noisy stimulus with periodic variance results in a mechanism for controlling chaos in neural systems with fixed synapses: a proper amount of external perturbation forces the system to behave periodically with the same period as the stimulus., Comment: 11 pages, 8 figures

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.

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system corresponds to a macroscopic attractor independent of the initial conditions. The mutual information between couples of maps serves to partition the data set in clusters, without prior assumptions about the structure of the underlying distribution of the data. Experiments on simulated and real data sets show the effectiveness of the proposed algorithm., Comment: 8 pages, 6 figures. Revised version accepted for publication on Physical Review Letters

We generalize the Cottingham formula at finite (T\neq 0) temperature by using the imaginary time formalism. The Cottingham formula gives the theoretical framework to compute the electromagnetic mass differences of the hadrons using a dispersion relation approach. It can be also used in other contexts, such as non leptonic weak decays, and its generalization to finite temperature might be useful in evaluating thermal effects in these processes. As an application we compute the \pi^+-\pi^0 mass difference at T\neq 0; at small T we reproduce the behaviour found by other authors: \delta m^2(T)= \delta m^2(0)+\mathcal{O}(\alpha T^2), while for moderate T, near the deconfinement temperature, we observe deviations from this behaviour., Comment: 11 pages, 1 figure

We describe the multiresolution wavelet analysis of blood pressure waves in vasovagal syncope-affected patients compared with those in healthy people, using Haar and Gaussian bases. A comparison between scale-dependent and scale-independent measures discriminating the two classes of subjects is made. What emerges is a sort of equivalence between these two methodological approaches, that is, both methods reach the same statistical significance of separation between the two classes., Comment: 4 pages, 3 figures. Accepted for publication in Physical Review E

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and chaos. We examine in detail the structure of the strange attractor and in particular we study the main features of the stable and unstable manifolds, the hyperbolicity of the attractor and the existence of homoclinic intersections. We also discuss the problem of the robustness of the chaos and we prove that in the present model chaotic behaviour is fragile (chaotic regions are densely intercalated with periodicity windows), according to a recently discussed conjecture. Finally we perform an analysis of the microscopic behaviour and in particular we examine the occurrence of damage spreading by studying the time evolution of two almost identical initial configurations. We show that for any choice of the parameters the two initial states remain microscopically distinct., Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E. Originally submitted to the neuro-sys archive which was never publicly announced (was 9905001)

We describe the multiresolution wavelet analysis of blood pressure waves in vasovagal syncope affected patients compared with healthy people. We argue that there exist discriminating criteria which allow us to isolate particular features, common to the syncope-affected patients sample, indicating an alternative diagnosis methodology for this syndrome. We perform a throughout analysis both in the Haar basis and in a Gaussian one, with an attempt to grasp the underlying dynamics., Comment: 13 pages, LaTeX, with 6 figures, changed content

We analyze the dynamical scaling behavior in a two-dimensional spin model with competing interactions after a quench to a striped phase. We measure the growth exponents studying the scaling of the interfaces and the scaling of the shrinking time of a ball of one phase plunged into the sea of another phase. Our results confirm the predictions found in previous papers. The correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. Our simulations show anisotropic features for the correlations both in the case of single-spin-flip and spin-exchange dynamics., Comment: 15 pages, ReVTeX

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are $n$-states variables which evolve in time according to Stochastic Learning rules; a parallel stochastic dynamics is assumed for neurons. Since the network maintains the same dynamics whether it is engaged in computation or in learning new memories, a very low probability of synaptic transitions is assumed. In the limit $N\to\infty$ with $K$ large and finite, the correlations of neurons and synapses can be neglected and the dynamics can be analitically calculated by flow equations for the macroscopic parameters of the system., Comment: 25 pages, LaTeX file

Results are presented for the kinetics of domain growth of a two-dimensional Ising spin model with competing interactions quenched from a disordered to a striped phase. The domain growth exponent are $\beta=1/2$ and $\beta=1/3$ for single-spin-flip and spin-exchange dynamics, as found in previous simulations. However the correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. In the case of single-spin-flip dynamics an anisotropic version of the Ohta-Jasnow-Kawasaki theory for the pair scaling function can be used to fit our data., Comment: 4 pages, REVTeX file

In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is established. This relationship enables one to present several more or less closed expressions for the oscillator energy. One of such expressions is given in the form of simple recurrence relations derived by means of the method of orthogonal polynomials which is one of the basic tools in the theory of random matrices., Comment: 12 pages in Latex

A matrix model to describe dynamical loops on random planar graphs is analyzed. It has similarities with a model studied by Kazakov, few years ago, and the O(n) model by Kostov and collaborators. The main difference is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the two critical phases are analyzed, where the free energy exhibits the same critical behaviour of Kazakov's model, thus confirming the universality of the description in the continuum limit (surface with small holes, and the tearing phase). A third phase occurs on the boundary separating the above phase regions, and is characterized by a different singular behaviour, presumably due to the orientation of loops., Comment: 20 pages in Plain Tex, 4 figures not enclosed