temporal complexity of the order parameter at the phase transition we study a decision making model in a condition where it is equivalent to the two dimensional ising model and we show that at the onset of phase transition it generates temporal complexity namely nonstationary and nonergodic fluctuations we argue that this is a general property of criticality thereby opening the door to the application of the recently discovered phenomenon of complexity matching for an efficient transfer of information to occur a perturbing complex network must share the same temporal complexity as the perturbed complex network

optimal network configuration for maximal coherence resonance in excitable systems we analyze the coherence resonance phenomenon in an ensemble of noise driven excitable neurons giving special attention to the role of the interaction topology the neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale free like with dominating long range connections and a network with mostly adjacent neurons connected we found that besides an optimal noise intensity also an optimal network configuration exists at which the largest average coherence of noise induced spikes is achieved furthermore we show that long as well as short range interactions between neurons should exist in order to achieve the optimal response of the neuronal network

optimal channel efficiency in a sensory network spontaneous neural activity has been increasingly recognized as a subject of key relevance in neuroscience it exhibits nontrivial spatiotemporal structure reflecting the organization of the underlying neural network and has proved to be closely intertwined with stimulus induced activity patterns as an additional contribution in this regard we report computational studies that strongly suggest that a stimulus free feature rules the behavior of an important psychophysical measure of the sensibility of a sensory system to a stimulus the so called dynamic range indeed in this paper we show that the entropy of the distribution of avalanche lifetimes information efficiency since it can be interpreted as the efficiency of the network seen as a communication channel always accompanies the dynamic range in the benchmark model for sensory systems specifically by simulating the kinouchi copelli kc model on two broad families of model networks we generically observed that both quantities always increase or decrease together as functions of the average branching ratio the control parameter of the kc model and that the information efficiency typically exhibits critical optimization jointly with the dynamic range i e both quantities are optimized at the same value of that control parameter that turns out to be the critical point of a nonequilibrium phase transition in contrast with the practice of taking power laws to identify critical points in most studies describing measured neuronal avalanches we rely on data collapses as more robust signatures of criticality to claim that critical optimization may happen even when the distribution of avalanche lifetimes is not a power law as suggested by a recent experiment finally we note that the entropy of the size distribution of avalanches information capacity does not always follow the dynamic range and the information efficiency when they are critically optimized despite being more widely used than the latter to describe the computational capabilities of a neural network this strongly suggests that dynamical rules allowing a proper temporal matching of the states of the interacting neurons is the key for achieving good performance in information processing rather than increasing the number of available units

geographical threshold graphs with small world and scale free properties many real networks are equipped with short diameters high clustering and power law degree distributions with preferential attachment and network growth the model by barabasi and albert simultaneously reproduces these properties and geographical versions of growing networks have also been analyzed however nongrowing networks with intrinsic vertex weights often explain these features more plausibly since not all networks are really growing we propose a geographical nongrowing network model with vertex weights edges are assumed to form when a pair of vertices are spatially close and or have large summed weights our model generalizes a variety of models as well as the original nongeographical counterpart such as the unit disk graph the boolean model and the gravity model which appear in the contexts of percolation wire communication mechanical and solid physics sociology economy and marketing in appropriate configurations our model produces small world networks with power law degree distributions we also discuss the relation between geography power laws in networks and power laws in general quantities serving as vertex weights

network clustering coefficient without degree correlation biases the clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph in real networks it decreases with the vertex degree which has been taken as a signature of the network hierarchical structure here we show that this signature of hierarchical structure is a consequence of degree correlation biases in the clustering coefficient definition we introduce a definition in which the degree correlation biases are filtered out and provide evidence that in real networks the clustering coefficient is constant or decays logarithmically with vertex degree

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

deterministic excitable media under poisson drive power law responses spiral waves and dynamic range when each site of a spatially extended excitable medium is independently driven by a poisson stimulus with rate h the interplay between creation and annihilation of excitable waves leads to an average activity f it has recently been suggested that in the low stimulus regime h approximately 0 the response function f h of hypercubic deterministic systems behaves as a power law f approximately h m moreover the response exponent m has been predicted to depend only on the dimensionality d of the lattice m 1 1 d t ohta and t yoshimura physica d 205 189 2005 in order to test this prediction we study the response function of excitable lattices modeled by either coupled morris lecar equations or greenberg hastings cellular automata we show that the prediction is verified in our model systems for d 1 2 and 3 provided that a minimum set of conditions is satisfied under these conditions the dynamic range which measures the range of stimulus intensities that can be coded by the network activity increases with the dimensionality d of the network the power law scenario breaks down however if the system can exhibit self sustained activity spiral waves in this case we recover a scenario that is common to probabilistic excitable media as a function of the conductance coupling g among the excitable elements the dynamic range is maximized precisely at the critical value g c above which self sustained activity becomes stable we discuss the implications of these results in the context of neural coding

kernel canonical correlation granger causality for multiple time series canonical correlation analysis as a multivariate statistical technique has been applied to multivariate granger causality analysis to infer information flow in complex systems it shows unique appeal and great superiority over the traditional vector autoregressive method due to the simplified procedure that detects causal interaction between multiple time series and the avoidance of potential model estimation problems however it is limited to the linear case here we extend the framework of canonical correlation to include the estimation of multivariate nonlinear granger causality for drawing inference about directed interaction its feasibility and effectiveness are verified on simulated data

equivalence and normal forms of bilinear forms abstract we present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms beginning from basic results developed by riehm our solution to this problem hinges on the classification of indecomposable forms and in how uniquely they fit together to produce all other forms we emphasize the use of split forms i e those bilinear forms such that the minimal polynomial of the asymmetry of their non degenerate part splits over ground field rather than restricting the field to be algebraically closed in order to obtain the most explicit results without resorting to the classification of hermitian symmetric and quadratic forms we merely require that the underlying field be quadratically closed

synchronization transitions on scale free neuronal networks due to finite information transmission delays we investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale free neuronal networks with different average degrees and scaling exponents as the underlying model of neuronal dynamics we use the efficient rulkov map with additive noise we show that increasing the coupling strength enhances synchronization monotonously whereas delay plays a more subtle role in particular we found that depending on the inherent oscillation frequency of individual neurons regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases these delay induced synchronization transitions manifest as well expressed minima in the measure for spatial synchrony appearing at every multiple of the oscillation frequency larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization these results are robust against variations in system size intensity of additive noise and the scaling exponent of the underlying scale free topology we argue that fine tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and indeed they should be seen as important as the coupling strength or the overall density of interneuronal connections we finally discuss some biological implications of the presented results

generalized scaling relations for unidirectionally coupled nonequilibrium systems abstract unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point we find that for initial conditions with isolated particles each hierarchy level exhibits an inhomogeneous active region coupled and uncoupled respectively the particle number of each level increases algebraically in time as n t t with different exponents in each domain this inhomogeneity is a quite general feature of unidirectionally coupled systems and leads to two hyperscaling relations between dynamic and static critical exponents using the contact process and the branching annihilating random walk with two offsprings which belong to the directed percolation and parity conserving classes respectively we numerically confirm the scaling relations

ising like dynamics in large scale functional brain networks brain rest is defined more or less unsuccessfully as the state in which there is no explicit brain input or output this work focuses on the question of whether such state can be comparable to any known dynamical state for that purpose correlation networks from human brain functional magnetic resonance imaging are contrasted with correlation networks extracted from numerical simulations of the ising model in two dimensions at different temperatures for the critical temperature tc striking similarities appear in the most relevant statistical properties making the two networks indistinguishable from each other these results are interpreted here as lending support to the conjecture that the dynamics of the functioning brain is near a critical point

critical exponents for branching annihilating random walks with an even number of offspring recently takayasu and tretyakov phys rev lett 68 3060 1992 studied branching annihilating random walks baws with n 1 char21 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation in this article i study the baw with n 4 using time dependent simulations and finite size scaling obtaining precise estimates for various critical exponents the results are consistent with the conjecture ensuremath beta ensuremath nu mathrm ensuremath perp 1 2 ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp 7 4 ensuremath gamma 0 ensuremath delta 2 7 ensuremath eta 0 and mathrm ensuremath delta mathit h 9 2 these critical exponents characterize respectively the dependence of the order parameter ensuremath beta ensuremath nu mathrm ensuremath perp and relaxation time ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp on system size the growth of fluctuations ensuremath gamma close to the critical point the long time behavior of the probability of survival ensuremath delta and average number of particles ensuremath eta when starting at time zero with just two particles and finally the decay of the order parameter mathrm ensuremath delta mathit h at the critical point in the presence of an external source

structure of isometry group of bilinear spaces abstract we describe the structure of the isometry group g of a finite dimensional bilinear space over an algebraically closed field of characteristic not two if the space has no indecomposable degenerate orthogonal summands of odd dimension it admits a canonical orthogonal decomposition into primary components and g is isomorphic to the direct product of the isometry groups of the primary components each of the latter groups is shown to be isomorphic to the centralizer in some classical group of a nilpotent element in the lie algebra of that group in the general case the description of g is more complicated we show that g is a semidirect product of a normal unipotent subgroup k with another subgroup which in its turn is a direct product of a group of the type described in the previous paragraph and another group h which we can describe explicitly the group h has a levi decomposition whose levi factor is a direct product of several general linear groups of various degrees we obtain simple formulae for the dimensions of h and k

proportional thresholding in resting state fmri functional connectivity networks and consequences for patient control connectome studies issues and recommendations graph theoretical analysis has become an important tool in the examination of brain dysconnectivity in neurological and psychiatric brain disorders a common analysis step in the construction of the functional graph or network involves thresholding of the connectivity matrix selecting the set of edges that together form the graph on which network organization is evaluated to avoid systematic differences in absolute number of edges studies have argued against the use of an absolute threshold in case control studies and have proposed the use of proportional thresholding instead in which a pre defined number of strongest connections are selected as network edges ensuring equal network density across datasets here we systematically studied the effect of proportional thresholding on the construction of functional matrices and subsequent graph analysis in patient control functional connectome studies in a few simple experiments we show that differences in overall strength of functional connectivity fc as often observed between patients and controls can have predictable consequences for between group differences in network organization in individual networks with lower overall fc the proportional thresholding algorithm has to select more edges based on lower correlations which have on average a higher probability of being spurious and thus introduces a higher degree of randomness in the resulting network we show across both empirical and artificial patient control datasets that lower levels of overall fc in either the patient or control group will most often lead to differences in network efficiency and clustering suggesting that differences in fc across subjects will be artificially inflated or translated into differences in network organization based on the presented case control findings we inform about the caveats of proportional thresholding in patient control studies in which groups show a between group difference in overall fc we make recommendations on how to examine report and to take into account overall fc effects in future patient control functional connectome studies

identifying the brain s most globally connected regions recent advances in brain connectivity methods have made it possible to identify hubs the brain s most globally connected regions such regions are essential for coordinating brain functions due to their connectivity with numerous regions with a variety of specializations current structural and functional connectivity methods generally agree that default mode network dmn regions have among the highest global brain connectivity gbc we developed two novel statistical approaches using resting state functional connectivity mri weighted and unweighted gbc wgbc and ugbc to test the hypothesis that the highest global connectivity also occurs in the cognitive control network ccn a network anti correlated with the dmn across a variety of tasks high global connectivity was found in both ccn and dmn the newly developed wgbc approach improves upon existing methods by quantifying inter subject consistency quantifying the highest gbc values by percentage and avoiding arbitrarily connection strength thresholding the ugbc approach is based on graph theory and includes many of these improvements but still requires an arbitrary connection threshold we found high gbc in several subcortical regions e g hippocampus basal ganglia only with wgbc despite the regions extensive anatomical connectivity these results demonstrate the complementary utility of wgbc and ugbc analyses for the characterization of the most highly connected and thus most functionally important regions of the brain additionally the high connectivity of both the ccn and the dmn demonstrates that brain regions outside primary sensory motor networks are highly involved in coordinating information throughout the brain

nonequilibrium critical behavior in unidirectionally coupled stochastic processes phase transitions from an active into an absorbing inactive state are generically described by the critical exponents of directed percolation dp with upper critical dimension d sub c 4 in the framework of single species reaction diffusion systems this universality class is realized by the combined processes a r arrow a a a a r arrow a and a r arrow 0 we study a hierarchy of such dp processes for particle species a b hor ellipsis ital unidirectionally coupled via the reactions a r arrow b hor ellipsis with rates mu sub ab hor ellipsis when the dp critical points at all levels coincide ital multicritical behavior emerges with density exponents beta sub i which are markedly reduced at each hierarchy level i ge 2 this scenario can be understood on the basis of the mean field rate equations which yield beta sub i 1 2 sup i minus 1 at the multicritical point using field theoretic renormalization group techniques in d 4 minus epsilon dimensions we identify a new crossover exponent phi and compute phi 1 o epsilon sup 2 in the multicritical regime for small mu sub ab of the second hierarchy level in the active phase we calculate the fluctuation correction to the density exponent on the second hierarchy level beta sub 2 1 2 minus epsilon 8 o epsilon sup 2 outside the multicritial region we discuss the crossover to ordinary dp behavior with the density exponent beta sub 1 1 minus epsilon 6 o epsilon sup 2 monte carlo simulations are then employed to confirm the crossovermore scenario and to determine the values for the new scaling exponents in dimensions d le 3 including the critical initial slip exponent our theory is connected to specific classes of growth processes and to certain cellular automata and the above ideas are also applied to unidirectionally coupled pair annihilation processes we also discuss some technical as well as conceptual problems of the loop expansion and suggest some possible interpretations of these difficulties copyright ital 1999 ital the american physical society less

small world and scale free organization of voxel based resting state functional connectivity in the human brain the brain is a complex dynamic system of functionally connected regions graph theory has been successfully used to describe the organization of such dynamic systems recent resting state fmri studies have suggested that inter regional functional connectivity shows a small world topology indicating an organization of the brain in highly clustered sub networks combined with a high level of global connectivity in addition a few studies have investigated a possible scale free topology of the human brain but the results of these studies have been inconclusive these studies have mainly focused on inter regional connectivity representing the brain as a network of brain regions requiring an arbitrary definition of such regions however using a voxel wise approach allows for the model free examination of both inter regional as well as intra regional connectivity and might reveal new information on network organization especially a voxel based study could give information about a possible scale free organization of functional connectivity in the human brain resting state 3 tesla fmri recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub cortical voxels with connections reflecting inter voxel functional connectivity graph characteristics from these connectivity networks were computed the clustering coefficient of these networks turned out to be much higher than the clustering coefficient of comparable random graphs together with a short average path length indicating a small world organization furthermore the connectivity distribution of the number of inter voxel connections followed a power law scaling with an exponent close to 2 suggesting a scale free network topology our findings suggest a combined small world and scale free organization of the functionally connected human brain the results are interpreted as evidence for a highly efficient organization of the functionally connected brain in which voxels are mostly connected with their direct neighbors forming clustered sub networks which are held together by a small number of highly connected hub voxels that ensure a high level of overall connectivity

extracting the multiscale backbone of complex weighted networks a large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength in recent years the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern with degree and weight distributions that vary over many orders of magnitude these features along with the large number of elements and links make the extraction of the truly relevant connections forming the network s backbone a very challenging problem more specifically coarse graining approaches and filtering techniques come into conflict with the multiscale nature of large scale systems here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges an important aspect of the method is that it does not belittle small scale interactions and operates at all scales defined by the weight distribution we apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques

complex network based time series analysis abstract recent works show that complex network theory may be a powerful tool in time series analysis we propose in this paper a reliable procedure for constructing complex networks from the correlation matrix of a time series an original stock time series the corresponding return series and its amplitude series are considered the degree distribution of the original series can be well fitted with a power law while that of the return series can be well fitted with a gaussian function the degree distribution of the amplitude series contains two asymmetric gaussian branches reconstruction of networks from time series is a common problem in diverse research the proposed strategy may be a reasonable solution to this problem

critical social networks abstract critical social ensembles are generated using a decision making model dmm consisting of a master equation with two state elements at the nodes of a two dimensional lattice the dynamics of the dmm undergo phase transitions to either a consensus state or another state composed of apparently statistically independent individuals as shown in an ensemble of calculations the critical social ensemble is entailed by the network elements nonlinearly interacting through imperfect social imitation on the backbone of a correlation network an information entropy measure of the difference between coherent and incoherent configurations in the critical social ensemble is constructed the entropy indicates a greater probability for the formation of either opposing groups or universal consensus above that of random disagreement

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

test retest reliability of resting state connectivity network characteristics using fmri and graph theoretical measures characterizing the brain connectome using neuroimaging data and measures derived from graph theory emerged as a new approach that has been applied to brain maturation cognitive function and neuropsychiatric disorders for a broad application of this method especially for clinical populations and longitudinal studies the reliability of this approach and its robustness to confounding factors need to be explored here we investigated test retest reliability of graph metrics of functional networks derived from functional magnetic resonance imaging fmri recorded in 33 healthy subjects during rest we constructed undirected networks based on the anatomic automatic labeling aal atlas template and calculated several commonly used measures from the field of graph theory focusing on the influence of different strategies for confound correction for each subject method and session we computed the following graph metrics clustering coefficient characteristic path length local and global efficiency assortativity modularity hierarchy and the small worldness scalar reliability of each graph metric was assessed using the intraclass correlation coefficient icc overall iccs ranged from low to high 0 to 0 763 depending on the method and metric methodologically the use of a broader frequency band 0 008 0 15 hz yielded highest reliability indices mean icc 0 484 followed by the use of global regression mean icc 0 399 in general the second order metrics small worldness hierarchy assortativity studied here tended to be more robust than first order metrics in conclusion our study provides methodological recommendations which allow the computation of sufficiently robust markers of network organization using graph metrics derived from fmri data at rest

stochastic resonance on weakly paced scale free networks we study the impact of additive gaussian noise and weak periodic forcing on the dynamics of a scale free network of bistable overdamped oscillators the periodic forcing is introduced to a single oscillator and therefore acts as a pacemaker trying to impose its rhythm on the whole ensemble we show that an intermediate intensity of temporally and spatially uncorrelated noise is able to optimally assist the pacemaker in achieving this goal thus providing evidence for stochastic resonance on weakly paced scale free networks because of the inherent degree inhomogeneity of individual oscillators forming the scale free network the placement of the pacemaker within the network is thereby crucial as two extremes we consider separately the introduction of the pacemaker to the oscillator with the highest degree and to one of the oscillators having the lowest degree in both cases the coupling strength plays a crucial role since it determines to what extent the whole network will follow the pacemaker on the expense of a weaker correlation between the pacemaker and the units that are directly linked with the paced oscillator higher coupling strengths facilitate the global outreach of the pacemaker but require higher noise intensities for the optimal response in contrast lower coupling strengths and comparatively low noise intensities localize the optimal response to immediate neighbors of the paced oscillator if the pacemaker is introduced to the main hub the transition between the locally and globally optimal responses is characterized by a double resonance that postulates the existence of an optimal coupling strength for the transmission of weak rhythmic activity across scale free networks we corroborate the importance of the inhomogeneous structure of scale free networks by additionally considering regular networks of oscillators with different degrees of coupling

on the use of correlation as a measure of network connectivity numerous studies have demonstrated that brain networks derived from neuroimaging data have nontrivial topological features such as small world organization modular structure and highly connected hubs in these studies the extent of connectivity between pairs of brain regions has often been measured using some form of statistical correlation this article demonstrates that correlation as a measure of connectivity in and of itself gives rise to networks with non random topological features in particular networks in which connectivity is measured using correlation are inherently more clustered than random networks and as such are more likely to be small world networks partial correlation as a measure of connectivity also gives rise to networks with non random topological features partial correlation networks are inherently less clustered than random networks network measures in correlation networks should be benchmarked against null networks that respect the topological structure induced by correlation measurements prevalently used random rewiring algorithms do not yield appropriate null networks for some network measures null networks are proposed to explicitly normalize for the inherent topological structure found in correlation networks resulting in more conservative estimates of small world organization a number of steps may be needed to normalize each network measure individually and control for distinct features e g degree distribution the main conclusion of this article is that correlation can and should be used to measure connectivity however appropriate null networks should be used to benchmark network measures in correlation networks

reentrant phase diagram of branching annihilating random walks with one and two offspring we investigate the phase diagram of branching annihilating random walks with one and two offspring in one dimension a walker can hop to a nearest neighbor site or branch with one or two offspring with relative ratio two walkers annihilate immediately when they meet in general this model exhibits a continuous phase transition from an active state into the absorbing state vacuum at a finite hopping probability we map out the phase diagram by monte carlo simulations that shows a reentrant phase transition from vacuum to an active state and finally into vacuum again as the relative rate of the two offspring branching process increases this reentrant property apparently contradicts the conventional wisdom that increasing the number of offspring will tend to make the system more active we show that the reentrant property is due to the static reflection symmetry of two offspring branching processes and the conventional wisdom is recovered when the dynamic reflection symmetry is introduced instead of the static one c 1995 the american physical society

time to consensus abstract the dynamics of a two state decision making model dmm with a tunable control parameter k is described on all to all ata networks the system undergoes a phase transition at a critical value of k c 1 scale free networks were also found to undergo phase transitions but the value of k c increases as the scale free exponent increases time to consensus is defined as a first passage time to a specified threshold of the global mean field which represents a level of majority for the network at criticality the time to consensus for sparse networks with broad degree distributions e g scale free networks approaches that of the ata networks although somewhat more cooperation higher k c is required

physical realizability of small world networks supplementing a lattice with long range connections effectively models small world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain if the links have a wiring cost associated with their length l the corresponding distribution q l plays a crucial role uniform length distributions have received the most attention despite indications that q l similar to l alpha exists e g for integrated circuits the internet and cortical networks while length distributions of this type were previously examined in the context of navigability we here discuss for such systems the emergence and physical realizability of small world topology our simple argument allows us to understand under which condition and at what expense a small world results

lie algebras and bilinear forms in characteristic 2 abstract all bilinear forms defined on a finite dimensional vector space over an algebraically closed field of characteristic 2 whose associated lie algebra is reductive are determined

a new type of kinetic critical phenomenon the authors study a new critical phenomenon in an non thermal one dimensional lattice model it is characterised by the transition from stability to instability of kinks between ordered states below the critical point the kinks are stable and move by annihilating random walks above the critical point they are unstable against creation of kink antikink pairs the spontaneous production of pairs is assumed to be absent at the critical point p pcr the density of kinks decreases like n approximately talpha with alpha 0 27 or 0 08 above the critical point the density of kinks in the stationary state is approximately p pcr beta with beta 0 06 or 0 2 possible extensions to two or more dimensions and possible applications are discussed

impact of noise and damage on collective dynamics of scale free neuronal networks we study the role of scale free structure and noise in collective dynamics of neuronal networks for this purpose we simulate and study analytically a cortical circuit model with stochastic neurons we compare collective neuronal activity of networks with different topologies classical random graphs and scale free networks we show that in scale free networks with divergent second moment of degree distribution an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment a very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations we demonstrate tolerance of collective dynamics of the scale free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons a random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing of the alpha rhythm in alzheimer s disease however the networks are vulnerable to targeted attacks a removal of a few excitatory or inhibitory hubs can impair sustained network oscillations

structural and functional networks in complex systems with delay functional networks of complex systems are obtained from the analysis of the temporal activity of their components and are often used to infer their unknown underlying connectivity we obtain the equations relating topology and function in a system of diffusively delay coupled elements in complex networks we solve exactly the resulting equations in motifs directed structures of three nodes and in directed networks the mean field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in degree of the nodes and that the locking frequency decreases with increasing average degree we find that the exponent of a power law degree distribution of the structural topology ensuremath gamma is related to the exponent of the associated functional network as ensuremath alpha 2 ensuremath ensuremath gamma ensuremath 1 for ensuremath gamma l2

network based statistic identifying differences in brain networks large scale functional or structural brain connectivity can be modeled as a network or graph this paper presents a statistical approach to identify connections in such a graph that may be associated with a diagnostic status in case control studies changing psychological contexts in task based studies or correlations with various cognitive and behavioral measures the new approach called the network based statistic nbs is a method to control the family wise error rate in the weak sense when mass univariate testing is performed at every connection comprising the graph to potentially offer a substantial gain in power the nbs exploits the extent to which the connections comprising the contrast or effect of interest are interconnected the nbs is based on the principles underpinning traditional cluster based thresholding of statistical parametric maps the purpose of this paper is to i introduce the nbs for the first time ii evaluate its power with the use of receiver operating characteristic roc curves and iii demonstrate its utility with application to a real case control study involving a group of people with schizophrenia for which resting state functional mri data were acquired the nbs identified a expansive dysconnected subnetwork in the group with schizophrenia primarily comprising fronto temporal and occipito temporal dysconnections whereas a mass univariate analysis controlled with the false discovery rate failed to identify a subnetwork

a mechanism to synchronize fluctuations in scale free networks using growth models abstract in this paper we study the steady state of the fluctuations of the surface for a model of surface growth with relaxation to any of its lower nearest neighbors sram f family j phys a 19 1986 l441 in scale free networks it is known that for euclidean lattices this model belongs to the same universality class as the model of surface relaxation to the minimum srm for the srm model it was found that for scale free networks with broadness the steady state of the fluctuations scales with the system size n as a constant for 3 and has a logarithmic divergence for 3 a l pastore y piontti p a macri l a braunstein phys rev e 76 2007 046117 it was also shown c e la rocca l a braunstein p a macri phys rev e 77 2008 046120 that this logarithmic divergence is due to non linear terms that arises from the topology of the network in this paper we show that the fluctuations for the sram model scale as in the srm model we also derive analytically the evolution equation for this model for any kind of complex graphs and find that as in the srm model non linear terms appear due to the heterogeneity and the lack of symmetry of the network in spite of that the two models have the same scaling but the srm model is more efficient to synchronize systems

functional scale free networks in the two dimensional abelian sandpile model recently the similarity of the functional network of the brain and the ising model was investigated by chialvo nat phys 6 744 2010 this similarity supports the idea that the brain is a self organized critical system in this study we derive a functional network of the two dimensional bak tang wiesenfeld sandpile model as a self organized critical model and compare its characteristics with those of the functional network of the brain obtained from functional magnetic resonance imaging

dynamics of driven recurrent networks of on and off cells a globally coupled network of on and off cells is studied using neural field theory on cells increase their activity when the amplitude of an external stimulus increases while off cells do the opposite given the same stimulus theory predicts that without input multiple transitions to oscillations can occur depending on feedback delay and the difference between on and off resting states static spatial stimuli can induce or suppress global oscillations via a andronov hopf bifurcation this is the case for either polarity of such stimuli in contrast only excitatory inputs can induce or suppress oscillations in an equivalent network built of on cells only even though oscillations are more prevalent in such systems nonmonotonic responses to local stimuli occur where responses lateral to the stimulus switch from excitatory to inhibitory as the input amplitude increases with local time periodic forcing the unforced cells oscillate at twice the driving frequency via full wave rectification mediated by the feedback our results agree with simulations of the neural field model and further qualitative agreement is found with the behavior of a network of spiking stochastic integrate and fire model neurons

generation of scale free networks using a simple preferential rewiring dynamics abstract we propose a simple dynamical process for non growing networks where steady states in the long time limit exhibit power law degree distributions with the exponent 2 at each time step two nodes i and j are randomly selected and one incoming link to i is redirected to j with the rewiring probability r determined only by degrees of two nodes k i and k j while higher degree nodes are preferred to get another link this is an application of the general model introduced earlier s ree phys rev e 73 2006 026115 to take the structure of networks into account we also consider three possible distinctions for the model i how we choose a rewiring link out of all incoming links to i three cases ii whether links are directed or not two cases iii types of networks considering the existence of self loops and multiple links two cases as a result we specify the total of 12 different cases of the model we then observe numerically that networks will evolve to steady states with power law degree distributions when parameters of the model satisfy certain conditions this work is from an effort to find a simple model of the network dynamics generating scale free networks and has a potential to become an underlying mechanism for wide range of scale free non growing networks

low dimensional embedding of fmri datasets abstract we propose a novel method to embed a functional magnetic resonance imaging fmri dataset in a low dimensional space the embedding optimally preserves the local functional coupling between fmri time series and provides a low dimensional coordinate system for detecting activated voxels to compute the embedding we build a graph of functionally connected voxels we use the commute time instead of the geodesic distance to measure functional distances on the graph because the commute time can be computed directly from the eigenvectors of a symmetric version the graph probability transition matrix we use these eigenvectors to embed the dataset in low dimensions after clustering the datasets in low dimensions coherent structures emerge that can be easily interpreted we performed an extensive evaluation of our method comparing it to linear and nonlinear techniques using synthetic datasets and in vivo datasets we analyzed datasets from the ebc competition obtained with subjects interacting in an urban virtual reality environment our exploratory approach is able to detect independently visual areas v1 v2 v5 mt auditory areas and language areas our method can be used to analyze fmri collected during natural stimuli

impact of bounded noise and shortcuts on the spatiotemporal dynamics of neuronal networks abstract the influences of bounded noise together with shortcuts on the spatiotemporal collective behaviors of temporal coherence and spatial synchronization are discussed in neuronal networks firstly we focus on the case of regular neuronal networks with the increase of noise amplitude we find that the spatial synchronizability among coupled neurons is always impaired and coherence resonance however occurs at an appropriately tuned level of noise amplitude then we introduce shortcuts to the regular neuronal networks to formulate small world neuronal networks the results indicate that the spatial synchronization and temporal coherence in the networks can be enhanced with the addition of shortcuts moreover we verify that there exists an optimal amount of added shortcuts such that the small world networks reach much more ordered spatiotemporal patterns i e coupled neurons are nearly synchronized in space and most coherent in time in addition the shortcuts induced much more ordered states are confirmed to be robust against changes of the intensity of the unit wiener process

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

ring structures and mean first passage time in networks in this paper we address the problem of the calculation of the mean first passage time on generic graphs we focus in particular on the mean first passage time on a node s for a random walker starting from a generic unknown node x we introduce an approximate scheme of calculation which maps the original process in a markov process in the space of the so called rings described by a transition matrix of size o ln n ln k ln n ln k where n is the size of the graph and k the average degree in the graph in this way one has a drastic reduction of degrees of freedom with respect to the size n of the transition matrix of the original process corresponding to an extremely low computational cost we first apply the method to the erdos renyi random graphs for which the method allows for almost perfect agreement with numerical simulations then we extend the approach to the barabasi albert graph as an example of scale free graph for which one obtains excellent results finally we test the method with two real world graphs internet and a network of the brain for which we obtain accurate results

non parametric bayesian graph models reveal community structure in resting state fmri modeling of resting state functional magnetic resonance imaging rs fmri data using network models is of increasing interest it is often desirable to group nodes into clusters to interpret the communication patterns between nodes in this study we consider three dierent nonparametric bayesian

measuring interregional functional connectivity using coherence and partial coherence analyses of fmri data understanding functional connectivity within the brain is crucial to understanding neural function even the simplest cognitive operations are supported by highly distributed neural circuits we developed a novel method to measure task related functional interactions between neural regions by applying coherence and partial coherence analyses to functional magnetic resonance imaging fmri data coherence and partial coherence are spectral measures that estimate the linear time invariant lti relationship between time series they can be used to generate maps of task specific connectivity associated with seed regions of interest rois these maps may then be compared across tasks revealing nodes with task related changes of connectivity to the seed roi to validate the method we applied it to an event related fmri data set acquired while subjects performed two sequence tapping tasks one of which required more bimanual coordination areas showing increased functional connectivity with both tasks were the same as those showing increased activity furthermore though there were no significant differences in mean activity between the two tasks significant increases in interhemispheric coherence were found between the primary motor m1 and premotor pm regions for the task requiring more bimanual coordination this increase in interhemispheric connectivity is supported by other brain imaging techniques as well as patient studies

persistent brain network homology from the perspective of dendrogram the brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level the problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold thus we propose a novel multiscale framework that models all brain networks generated over every possible threshold our approach is based on persistent homology and its various representations such as the rips filtration barcodes and dendrograms this new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner the barcode is used to quantify and visualize the evolutionary changes of topological features such as the betti numbers over different scales by incorporating additional geometric information to the barcode we obtain a single linkage dendrogram that shows the overall evolution of the network the difference between the two networks is then measured by the gromov hausdorff distance over the dendrograms as an illustration we modeled and differentiated the fdg pet based functional brain networks of 24 attention deficit hyperactivity disorder children 26 autism spectrum disorder children and 11 pediatric control subjects

a new measure of network efficiency a b s t r a c t we address the issue of the dynamical origin of scale free link distributions we study a two dimensional lattice of cooperatively interacting units although the units interact only with the four nearest neighbors a sufficiently large cooperation strength generates dynamically a scale free network with the power law index approaching 1 we explain this result by using a new definition of network efficiency determined by the euclidean distance between correlated units according to this definition the link distribution favoring long range connections makes efficiency increase we embed an ad hoc scale free network with power index 1 into a euclidean two dimensional space and show that the network efficiency becomes maximal as approaches 1 we therefore conclude that 1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency

canonical matrices of bilinear and sesquilinear forms abstract canonical matrices are given for i bilinear forms over an algebraically closed or real closed field ii sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution and iii sesquilinear forms over a field f of characteristic different from 2 with involution possibly the identity up to classification of hermitian forms over finite extensions of f the canonical matrices are based on any given set of canonical matrices for similarity over f a method for reducing the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings is used to construct the canonical matrices this method has its origins in representation theory and was devised in v v sergeichuk classification problems for systems of forms and linear mappings math ussr izv 31 1988 481 501

stochastic lattice models with several absorbing states we study two models with n equivalent absorbing states that generalize the domany kinzel cellular automaton and the contact process numerical investigations show that for n 2 both models belong to the same universality class as branching annihilating walks with an even number of offspring unlike previously known models these models have no explicit parity conservation law

synchronization in lattice embedded scale free networks abstract in this work we study the effects of embedding a system of non linear phase oscillators in a two dimensional scale free lattice in order to analyze the effects of the embedding we consider two different topologies on the one hand we consider a scale free complex network where no constraint on the length of the links is taken into account on the other hand we use a method recently introduced for embedding scale free networks in regular euclidean lattices in this case the embedding is driven by a natural constraint of minimization of the total length of the links in the system we analyze and compare the synchronization properties of a system of non linear kuramoto phase oscillators when interactions between the oscillators take place in these networks first we analyze the behavior of the kuramoto order parameter and show that the onset of synchronization is lower for non constrained lattices then we consider the behavior of the mean frequency of the oscillators as a function of the natural frequency for the two different networks and also for different values of the scale free exponent we show that in contrast to non embedded lattices that present a mean field like behavior characterized by the presence of a single cluster of synchronized oscillators in embedded lattices the presence of a diversity of synchronized clusters at different mean frequencies can be observed finally by considering the behavior of the mean frequency as a function of the degree we study the role of hubs in the synchronization properties of the system

negative edges and soft thresholding in complex network analysis of resting state functional connectivity data complex network analyses of functional connectivity have consistently revealed non random modular small world scale free like behavior of hard thresholded networks constructed from the right tail of the similarity histogram in the present study we determined network properties resulting from edges constrained to specific ranges across the full correlation histogram in particular the left negative most tail and their dependence on the confound signal removal strategy employed in the absence of global signal correction left tail networks comprised predominantly long range connections associated with weak correlations and were characterized by substantially reduced modularity and clustering negative assortativity and 1 deconvolution of specific confound signals white matter csf and motion resulted in the most robust within subject reproducibility of global network parameters iccs 0 5 global signal removal altered the network topology in the left tail with the clustering coefficient and assortativity converging to zero networks constructed from the absolute value of the correlation coefficient were thus compromised following global signal removal since the different right tail and left tail topologies were mixed these findings informed the construction of soft thresholded networks replacing the hard thresholding or binarization operation with a continuous mapping of all correlation values to edge weights suppressing rather than removing weaker connections and avoiding issues related to network fragmentation a power law adjacency function with 12 yielded modular networks whose parameters agreed well with corresponding hard thresholded values that were reproducible in repeated sessions across many months and evidenced small world like and scale free like properties

scale free networks with exponent one a majority of studied models for scale free networks have degree distributions with exponents greater than two real networks however can demonstrate essentially more heavy tailed degree distributions we explore two models of scale free equilibrium networks that have the degree distribution exponent ensuremath gamma 1 p q ensuremath sim q ensuremath ensuremath gamma such degree distributions can be identified in empirical data only if the mean degree of a network is sufficiently high our models exploit a rewiring mechanism they are local in the sense that no knowledge of the network structure apart from the immediate neighborhood of the vertices is required these models generate uncorrelated networks in the infinite size limit where they are solved explicitly we investigate finite size effects by the use of simulations we find that both models exhibit disassortative degree degree correlations for finite network sizes in addition we observe a markedly degree dependent clustering in the finite networks we indicate a real world network with a similar degree distribution

network algorithmics and the emergence of information integration in cortical models an information theoretic framework known as integrated information theory iit has been introduced recently for the study of the emergence of consciousness in the brain d balduzzi and g tononi plos comput biol 4 e1000091 2008 iit purports that this phenomenon is to be equated with the generation of information by the brain surpassing the information that the brain s constituents already generate independently of one another iit is not fully plausible in its modeling assumptions nor is it testable due to severe combinatorial growth embedded in its key definitions here we introduce an alternative to iit which while inspired in similar information theoretic principles seeks to address some of iit s shortcomings to some extent our alternative framework uses the same network algorithmic cortical model we introduced earlier a nathan and v c barbosa phys rev e 81 021916 2010 and to allow for somewhat improved testability relative to iit adopts the well known notions of information gain and total correlation applied to a set of variables representing the reachability of neurons by messages in the model s dynamics we argue that these two quantities relate to each other in such a way that can be used to quantify the system s efficiency in generating information beyond that which does not depend on integration we give computational results on our cortical model and on variants thereof that are either structurally random in the sense of an erd s renyi random directed graph or structurally deterministic we have found that our cortical model stands out with respect to the others in the sense that many of its instances are capable of integrating information more efficiently than most of those others instances

estimating the clustering coefficient in scale free networks on lattices with local spatial correlation structure abstract when we study the architecture of networks of spatially extended systems the nodes in the network are subject to local correlation structures in this case we show that for scale free networks the traditional way to estimate the clustering coefficient may not be meaningful here we explain why and propose an approach that corrects this problem

non parametric model selection for subject specific topological organization of resting state functional connectivity abstract in recent years graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain most of these networks have shown small world topological characteristics high efficiency in long distance communication between nodes combined with highly interconnected local clusters of nodes moreover functional studies performed at high resolutions have presented convincing evidence that resting state functional connectivity networks exhibits exponentially truncated scale free behavior such evidence however was mostly presented qualitatively in terms of linear regressions of the degree distributions on log log plots even when quantitative measures were given these were usually limited to the r 2 correlation coefficient however the r 2 statistic is not an optimal estimator of explained variance when dealing with truncated power law models recent developments in statistics have introduced new non parametric approaches based on the kolmogorov smirnov test for the problem of model selection in this work we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest the analysis performed at voxel level and in a subject specific fashion confirmed the superiority of a truncated power law model showing high consistency across subjects moreover the most highly connected voxels were found to be consistently part of the default mode network our results provide statistically sound support to the evidence previously presented in literature for a truncated power law model of resting state functional connectivity

structural and functional clusters of complex brain networks recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains it is of importance to understand the implications of such complex network structures in the functional organization of the brain activities here we study this problem from the viewpoint of dynamical complex networks we investigate synchronization dynamics on the corticocortical network of the cat by modeling each node cortical area of the network with a sub network of interacting excitable neurons we find that the network displays clustered synchronization behavior and the dynamical clusters coincide with the topological community structures observed in the anatomical network our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex