Does the brain behave like a (complex) network? I. Dynamics.

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Brain synchronizability, a false friend.

Synchronization plays a fundamental role in healthy cognitive and motor function. However, how synchronization depends on the interplay between local dynamics, coupling and topology and how prone to synchronization a network is, given its topological organization, are still poorly understood issues. To investigate the synchronizability of both anatomical and functional brain networks various studies resorted to the Master Stability Function (MSF) formalism, an elegant tool which allows analysing the stability of synchronous states in a dynamical system consisting of many coupled oscillators. Here, we argue that brain dynamics does not fulfil the formal criteria under which synchronizability is usually quantified and, perhaps more importantly, this measure refers to a global dynamical condition that never holds in the brain (not even in the most pathological conditions), and therefore no neurophysiological conclusions should be drawn based on it. We discuss the meaning of synchronizability and its applicability to neuroscience and propose alternative ways to quantify brain networks synchronization.

Role of inter-hemispheric connections in functional brain networks.

Today the human brain can be modeled as a graph where nodes represent different regions and links stand for statistical interactions between their activities as recorded by different neuroimaging techniques. Empirical studies have lead to the hypothesis that brain functions rely on the coordination of a scattered mosaic of functionally specialized brain regions (modules or sub-networks), forming a web-like structure of coordinated assemblies (a network of networks. NoN). The study of brain dynamics would therefore benefit from an inspection of how functional sub-networks interact between them. In this paper, we model the brain as an interconnected system composed of two specific sub-networks, the left (L) and right (R) hemispheres, which compete with each other for centrality, a topological measure of importance in a networked system. Specifically, we considered functional scalp EEG networks (SEN) derived from high-density electroencephalographic (EEG) recordings and investigated how node centrality is shaped by interhemispheric connections. Our results show that the distribution of centrality strongly depends on the number of functional connections between hemispheres and the way these connections are distributed. Additionally, we investigated the consequences of node failure on hemispherical centrality, and showed how the abundance of inter-hemispheric links favors the functional balance of centrality distribution between the hemispheres.

Synchronization of interconnected networks: the role of connector nodes.

In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically, and experimentally how the degree of the nodes through which two networks are connected influences the ability of the whole system to synchronize. We show that connecting the high-degree (low-degree) nodes of each network turns out to be the most (least) effective strategy to achieve synchronization. We find the functional relation between synchronizability and size for a given network of networks, and report the existence of the optimal connector link weights for the different interconnection strategies. Finally, we perform an electronic experiment with two coupled star networks and conclude that the analytical results are indeed valid in the presence of noise and parameter mismatches.

Drug polyconsumption is associated with increased synchronization of brain electrical-activity at rest and in a counting task.

Drug abusers typically consume not just one but several types of drugs, starting from alcohol and marijuana consumption, and then dramatically lapsing into addiction to harder drugs, such as cocaine, heroin, or amphetamine. The brain of drug abusers presents various structural and neurophysiological abnormalities, some of which may predate drug consumption onset. However, how these changes translate into modifications in functional brain connectivity is still poorly understood. To characterize functional connectivity patterns, we recorded Electroencephalogram (EEG) activity from 21 detoxified drug abusers and 20 age-matched control subjects performing a simple counting task and at rest activity. To evaluate the cortical brain connectivity network we applied the Synchronization Likelihood algorithm. The results showed that drug abusers had higher synchronization levels at low frequencies, mainly in the θ band (4-8 Hz) between frontal and posterior cortical regions. During the counting task, patients showed increased synchronization in the ß (14-35 Hz), and γ (35-45 Hz) frequency bands, in fronto-posterior and interhemispheric temporal regions. Taken together 'slow-down' at rest and task-related 'over-exertion' could indicate that the brain of drug abusers is suffering from a premature form of ageing. Future studies will clarify whether this condition can be reversed following prolonged periods of abstinence.

Explosive transitions to synchronization in networks of phase oscillators.

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. The occurrence of a first-order phase transition to synchronization of an ensemble of networked phase oscillators was reported, so far, for very particular network architectures. Here, we show how a sharp, discontinuous transition can occur, instead, as a generic feature of networks of phase oscillators. Precisely, we set conditions for the transition from unsynchronized to synchronized states to be first-order, and demonstrate how these conditions can be attained in a very wide spectrum of situations. We then show how the occurrence of such transitions is always accompanied by the spontaneous setting of frequency-degree correlation features. Third, we show that the conditions for abrupt transitions can be even softened in several cases. Finally, we discuss, as a possible application, the use of this phenomenon to express magnetic-like states of synchronization.

Topological measure locating the effective crossover between segregation and integration in a modular network.

We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is expressed in terms of the algebraic connectivity of an associated hypergraph. The rigorous treatment of the simplified case of cliques of equal size that are gradually rewired until they become completely merged, allows us to show that this topological crossover can be made to coincide with a dynamical crossover from cluster to global synchronization of a system of coupled phase oscillators. The dynamical crossover is signaled by a peak in the product of the measures of intracluster and global synchronization, which we propose as a dynamical measure of complexity. This quantity is much easier to compute than the entropy (of the average frequencies of the oscillators), and displays a behavior which closely mimics that of the dynamical complexity index based on the latter. The proposed topological measure simultaneously provides information on the dynamical behavior, sheds light on the interplay between modularity and total integration, and shows how this affects the capability of the network to perform both local and distributed dynamical tasks.

Computation as an emergent feature of adaptive synchronization.

We report on the spontaneous emergence of computation from adaptive synchronization of networked dynamical systems. The fundamentals are nonlinear elements, interacting in a directed graph via a coupling that adapts itself to the synchronization level between two input signals. These units can emulate different Boolean logics, and perform any computational task in a Turing sense, each specific operation being associated with a given network's motif. The resilience of the computation against noise is proven, and the general applicability is demonstrated with regard to periodic and chaotic oscillators, and excitable systems mimicking neural dynamics.

[Psoriasis as an independent risk factor for development of coronary artery disease]. / Psoriasis als unabhängiger Risikofaktor für die Entwicklung einer koronaren Herzkrankheit.

Psoriasis is a chronic inflammatory dermatosis with a relapsing course. The best known comorbidity is psoriatic arthritis. In daily clinical practise it is well known, that patients with psoriasis show more often classic cardiovascular risk factors such as obesity, Diabetes mellitus, hyperlipoproteinemia, hypertension, nicotine abuse often presenting as Metabolic Syndrome and suffer more often from coronary heart disease than patients without psoriasis. This could be demonstrated in numerous clinical and epidemiologic studies. In the last few years there is increasing evidence for psoriasis being an independent cardiovascular risk factor despite of concomitant classic risk factors. This review summarizes the current state of research and discusses possible common immunopathogenetic mechanisms.

Feedback modulates the temporal scale-free dynamics of brain electrical activity in a hypothesis testing task.

We used the electroencephalogram (EEG) to investigate whether positive and negative performance feedbacks exert different long-lasting modulations of electrical activity in a reasoning task. Nine college students serially tested hypotheses concerning a hidden rule by judging its presence or absence in triplets of digits, and revised them on the basis of an exogenous performance feedback. The scaling properties of the transition period between feedback and triplet presentation were investigated with detrended fluctuation analysis (DFA). DFA showed temporal scale-free dynamics of EEG activity in both feedback conditions for time scales larger than 150 ms. Furthermore, DFA revealed that negative feedback elicits significantly higher scaling exponents than positive feedback. This effect covers a wide network comprising parieto-occipital and left frontal regions. We thus showed that specific task demands can modify the temporal scale-free dynamics of the ongoing brain activity. Putative neural correlates of these long-lasting feedback-specific modulations are proposed.