pareto and boltzmann gibbs behaviors in a deterministic multi agent system a b s t r a c t a deterministic system of interacting agents is considered as a model for economic dynamics the dynamics of the system is described by a coupled map lattice with nearest neighbor interactions the evolution of each agent results from the competition between two factors the agent s own tendency to grow and the environmental influence that moderates this growth depending on the values of the parameters that control these factors the system can display pareto or boltzmann gibbs statistical behaviors in its asymptotic dynamical regime the regions where these behaviors appear are calculated on the space of parameters of the system other statistical properties such as the mean wealth the standard deviation and the gini coefficient characterizing the degree of equity in the wealth distribution are also calculated

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

a small world of weak ties provides optimal global integration of self similar modules in functional brain networks the human brain is organized in functional modules such an organization presents a basic conundrum modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer it is commonly accepted that small world architecture of short paths and large local clustering may solve this problem however there is intrinsic tension between shortcuts generating small worlds and the persistence of modularity a global property unrelated to local clustering here we present a possible solution to this puzzle we first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks these modules are large world self similar structures and therefore are far from being small world however incorporating weaker ties to the network converts it into a small world preserving an underlying backbone of well defined modules remarkably weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost this trade off architecture is reminiscent of the strength of weak ties crucial concept of social networks such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain

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

kolmogorov landau inequalities for monotone functions where llfll ess su if t kolmogorov 2 suceeded in finding the best possible constants in 1 where the norm is as in 2 except for isolated results no new progress was made until schoenberg and cavaretta 3 found the best possible constants for llfll su if f we propose to prove inequalities about various clases of monotone functions which yield as special cases pointwise inequalities of the form 1 for example

periodic solutions of some autonomous lienard equations with relativistic acceleration abstract after giving a new proof of the existence of a stable limit cycle for the relativistic van der pol equation d d t x 1 x 2 k x 2 1 x x 0 we find sufficient conditions upon f and g in order that the relativistic lienard equation d d t x 1 x 2 f x x g x 0 has a stable limit cycle the approach and the existence conditions are distinct from those recently obtained by perez gonzalez et al 2016

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

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

explicit expressions for a family of the bell polynomials and applications in the paper the authors first inductively establish explicit formulas for derivatives of the arc sine function then derive from these explicit formulas explicit expressions for a family of the bell polynomials of the second kind related to the square function and finally apply these explicit expressions to find explicit formulas for derivatives of some elementary functions

completely monotonic and related functions abstract we study completely monotonic and related functions whose firstnderivatives are definite on an interval let l ndenote the class of functions defined by f in cal l n leftrightarrow 1 k f k t ge0 qquad forall t 0 forall k 0 le k le n forn we writef l such functions are called completely monotonic on 0 we prove in particular that the implication f in cal l n rightarrow bigl forall alpha 1 colon f alpha in cal l n bigr is true for 0 n 5 but false forn 6 in contrast l lorch and d j newman j london math soc 2 28 1983 31 45 theorem 8 claimed this implication to be false forn 5 further we prove that the implication f in cal l rightarrow bigl forall alpha 1 colon f alpha in cal l n bigr is true for 0 n 6 but false forn 20

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

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

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

random long range connections induce activity of complex hindmarsh rose neural networks abstract in this paper we investigate how activity of complex neural networks depends on random long range connections network elements are described by hindmarsh rose hr neurons assumed to be inactive it is found that for a given coupling strength when the number of random connections or randomness is greater than a threshold the spiking neurons which are absent in the nearest neighbor neural network occur the spiking activity becomes stronger in intensity and higher in frequency as the randomness is further increased these phenomena imply that random long range connections can induce and enhance the activity of neural networks furthermore the possible mechanism behind the action of random long range connections is also addressed our results may provide a useful hint for understanding the properties of collective dynamics in coupled real neurons

an extension of dragilev s theorem for the existence of periodic solutions of the lienard equation abstract the problem of the existence of periodic solution for the lienard equation is investigated and a result which improves the classical dragilev s theorem is presented together with a corollary in which there are no assumptions on the function g x and hence on g x besides the standard sign condition in the final part of the paper constructive examples with several limit cycles are provided

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

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

transient spatiotemporal chaos is extensive in three reaction diffusion networks extensive asymptotic spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly a systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction diffusion networks for various boundary conditions the lyapunov dimension the sum of positive lyapunov exponents and the logarithm of the transient lifetime grow linearly with the system size the unstable manifold of the chaotic saddle has nearly the same dimension as the saddle itself and the stable manifold is nearly space filling

dynamic scaling behavior of human brain electroencephalogram abstract after filtering out the and peaks in the power spectrum of the human brain electroencephalogram signals y t the probability distribution of the variation y t y t t y t exhibits a dynamic scaling behavior the auto correlation functions persistence probabilities and detrended fluctuation functions of the time series y t all show a nontrivial power law behavior these results indicate that the dynamics of the human brain electroencephalogram is long range correlated in time

length scale of interaction in spatiotemporal chaos extensive systems have no long scale correlations and behave as a sum of their parts various techniques are introduced to determine a characteristic length scale of interaction beyond which spatiotemporal chaos is extensive in reaction diffusion networks information about network size boundary condition or abnormalities in network topology gets scrambled in spatiotemporal chaos and the attenuation of information provides such characteristic length scales space time information flow associated with the recovery of spatiotemporal chaos from finite perturbations a concept somewhat opposite to the paradigm of lyapunov exponents defines another characteristic length scale high precision computational studies of asymptotic spatiotemporal chaos in the complex ginzburg landau system and transient spatiotemporal chaos in the gray scott network show that these different length scales are comparable and thus suitable to define a length scale of interaction preliminary studies demonstrate the relevance of these length scales for stable chaos

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

network synchronization diffusion and the paradox of heterogeneity many complex networks display strong heterogeneity in the degree connectivity distribution heterogeneity in the degree distribution often reduces the average distance between nodes but paradoxically may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength here we offer a solution to this apparent paradox our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states we show that for a given degree distribution the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum this enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size numerical verification of the main results is provided for representative classes of small world and scale free networks

pairwise network information and nonlinear correlations reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines the fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and thus can be modeled as an interaction network with simple links corresponding to pairwise interactions in principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy in many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated or the optimization is too computationally expensive here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions this has the advantage of being less computationally expensive and easier to estimate we achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations this renders our approach typically superior to other methods based on linear approximations the advantages of the proposed method are documented using oscillator networks and a resting state human brain network as generic relevant examples

integral representations of bivariate complex geometric mean and their applications abstract in the paper the authors survey integral representations including the levy khintchine representations and applications of some bivariate means including the logarithmic mean the identric mean stolarsky s mean the harmonic mean the weighted geometric means and their reciprocals and the toader qi mean and the multivariate weighted geometric means and their reciprocals derive integral representations of bivariate complex geometric mean and its reciprocal and apply these newly derived integral representations to establish integral representations of heronian mean of power 2 and its reciprocal

when noise decreases deterministic diffusion dynamical noise acting homogeneously in each time step can enhance the stability of an unstable fixed point however if dynamical noise is added locally in state space additional clear enhancement can be achieved if this restriction is chosen properly a systematic analysis of the influence of local and global dynamical noise on the residence time of an unstable state is presented and optimal parameters for the stabilizing mechanisms are discussed as a consequence it is demonstrated that local dynamical noise can yield increased localization in deterministic diffusion models

origin of chaotic transients in excitatory pulse coupled networks we develop an approach to understanding long chaotic transients in networks of excitatory pulse coupled oscillators our idea is to identify a class of attractors sequentially active firing saf attractors in terms of the temporal event structure of firing and receipt of pulses then all attractors can be classified into two groups saf attractors and non saf attractors we establish that long transients typically arise in the transitional region of the parameter space where the saf attractors are collectively destabilized bifurcation behavior of the saf attractors is analyzed to provide a detailed understanding of the long irregular transients although demonstrated using pulse coupled oscillator networks our general methodology may be useful in understanding the origin of transient chaos in other types of networked systems an extremely challenging problem in nonlinear dynamics and complex systems

asymptotic behavior of periodic solutions in one parameter families of lienard equations abstract in this paper we consider one parameter 0 families of lienard differential equations we are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of 0 to prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory more specifically the first one is appropriate for studying the periodic solutions for large values of and the second one for small values of in particular our hypotheses allow us to establish a link between these two theories

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

nonlocal coupling can prevent the collapse of spatiotemporal chaos spatiotemporal chaos on a regular ring network of excitable gray scott dynamical elements is transient we find that the addition of very few nonlocal network connections drastically changes the average lifetime of spatiotemporal chaos in the presence of a single shortcut local interface formation delays the collapse of spatiotemporal chaos this competes with a reduced average characteristic path length that advances the collapse process two added shortcuts can prevent the collapse of spatiotemporal chaos by causing an asymptotic local collapse

frustration drift and antiphase coupling in a neural array synchronization among neurons is critical for many processes in the nervous system ranging from the processing of sensory information to the onset of pathological conditions such as epilepsy here we study synchronization in an array of neurons each modeled by a set of nonlinear ordinary differential equations we find that an array of 20x20 coupled neurons undergoes a series of alternating low and high synchronization states as measured by phase locking and frequency entrainment as the coupling constant is tuned the role of long range connections in inducing small world networks has recently been of great interest in many physical and biological problems since long range connections do exist in the brain we investigated the role of such connections in our neural array introducing a biologically realistic percentage of long range connections has no significant effect on synchronization we find that it is rather the type of coupling and the total number of connections that determine the synchronization state of the array we also show that some coupling conditions can lead to frustration in the system resulting from an inability to simultaneously satisfy conflicting phase requirements this frustration leads to a drift in the overall behavior of the network which may offer an explanation for transitions between different types of neural oscillations observed experimentally

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

turbulence in small world networks the transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small world networks the local dynamics is given by the chate manneville minimal map previously used in studies of spatiotemporal intermittency in ordered lattice the critical boundary separating laminar and turbulent regimes is calculated on the parameter space of the system given by the coupling strength and the rewiring probability of the network windows of relaminarization are present in some regions of the parameter space new features arise in small world networks for instance the character of the transition to turbulence changes from second order to a first order phase transition at some critical value of the rewiring probability a linear relation characterizing the change in the order of the phase transition is found the global quantity used as order parameter for the transition also exhibits nontrivial collective behavior for some values of the parameters these models may describe several processes occurring in nonuniform media where the degree of disorder can be continuously varied through a parameter

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

on the nonexistence of periodic solutions for lie nard equations we consider the lienard equation x f x x g x 0 and the generalized lienard equation x f x x x g x 0 results of nonexistence of periodic solutions for lienard equations have seldom appeared to deal with this problem the dulac function method is usually employed we give new results based on some distinct ideas we shall prove that a trajectory of system exists such that one side of it tends to the origin and the other side approaches to infinity hence implying the nonexistence of periodic solutions

topology of whole brain functional mri networks improving the truncated scale free model abstract networks of connections within the human brain have been the subject of intense recent research yet their topology is still only partially understood we analyze weighted networks calculated from functional magnetic resonance imaging fmri data acquired during task performance expanding previous work in the area our analysis retains all of the connections between all of the voxels in the full brain fmri data computing correlations between approximately 200 000 voxels per subject for 10 subjects we evaluate the extent to which this rich dataset can be described by existing models of scale free or exponentially truncated scale free topology comparing results across a large number of more complex topological models as well our results suggest that the novel log quadratic model presented in this paper offers a significantly better fit to networks of functional connections at the voxel level in the human brain

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

some properties of central delannoy numbers abstract in the paper by investigating the generating function of central delannoy numbers the authors establish several explicit expressions including determinantal expressions for central delannoy numbers present three identities involving the cauchy products of central delannoy numbers discover an integral representation for central delannoy numbers find absolute monotonicity convexity and logarithmic convexity for the sequence of central delannoy numbers and construct several product and determinantal inequalities for central delannoy numbers

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

some best approximation formulas and inequalities for the wallis ratio in the paper the authors establish some best approximation formulas and inequalities for the wallis ratio these formulas and inequalities improve an approximation formula and a double inequality for the wallis ratio presented in 2013 by three mathematicians

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

spectral properties and pattern selection in fractal growth networks a model for the generation of fractal growth networks in euclidean spaces of arbitrary dimension is presented these networks are considered as the spatial support of reaction diffusion and pattern formation processes the local dynamics at the nodes of a fractal growth network is given by a nonlinear map giving raise to a coupled map system the coupling is described by a matrix whose eigenvectors constitute a basis on which spatial patterns on fractal growth networks can be expressed by linear combination the spectrum of eigenvalues the coupling matrix exhibits a nonuniform distribution that is reflected in the presence of gaps or niches in the boundaries of stability of the synchronized states on the space of parameters of the system these gaps allow for the selection of specific spatial patterns by appropriately varying the parameters of the system

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

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

a complete monotonicity property of the gamma function abstract a logarithmically completely monotonic function is completely monotonic the function 1 ln x 1 x ln x 1 is strictly completely monotonic on 0 the function x 1 x x is strictly logarithmically completely monotonic on 0

qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method abstract the phase portrait of the second order differential equation x l 0 n f l x x l 0 is studied some results concerning existence non existence and uniqueness of limit cycles are presented in particular a generalization of the classical massera uniqueness result is proved

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

enhancing neural network performance via assortativity the performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology we take this analysis a step further by examining the effect of degree degree correlations assortativity on neural network behavior we make use of a method recently put forward for studying correlated networks and dynamics thereon both analytically and computationally which is independent of how the topology may have evolved we show how the robustness to noise is greatly enhanced in assortative positively correlated neural networks especially if it is the hub neurons that store the information

spatio temporal chaos for the gray scott model abstract a new geometrical criterion for the transition to spatio temporal chaos stc arising in the gray scott model is presented this is based on the inter relationship of global bifurcating branches of ordered patterns with respect to supply and removal rates contained in the model this viewpoint not only gives us a new criterion for the onset of stc but also clarifies how the orbit itinerates among several ordered patterns in infinite dimensional space moreover the geometrical characterization gives us a universal viewpoint about the onset and termination of stc there are at least two different mechanisms that cause re injection dynamics and drive the stc one is a generalized heteroclinic cycle consisting of self replication and self destruction processes and the other involves annihilation of colliding waves instead of self destruction

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

direction coherence in scale free lattices of chaotic maps abstract we considered a coupled chaotic logistic map lattice exhibiting the scale free property the outreach connectivity of each node obeys a power law distribution we analyzed a weak form of coherent spatio temporal behavior direction coherence which presents features common to completely synchronized states like a transitional behavior with intermittent bursting we studied such phenomena and their dependence on the parameters of the coupled scale free lattice prospective applications in neuronal networks are emphasized

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

mapping from structure to dynamics a unified view of dynamical processes on networks although it is unambiguously agreed that structure plays a fundamental role in shaping the collective dynamics of complex systems how structure determines dynamics exactly still remains unclear we investigate a general computational transformation by which we can map the network topology directly to the dynamical patterns emergent on it independent of the nature of the dynamical processes remarkably we find that many seemingly different dynamical processes on networks such as coupled oscillators ensemble neuron firing epidemic spreading and diffusion can all be understood and unified through this same procedure utilizing the inherent multiscale nature of this structure dynamics transformation we further define a multiscale complexity measure which can quantify the functional diversity a general network can support at different organization levels using only its structure we find that a wide variety of topological features observed in real networks such as modularity hierarchy degree heterogeneity and mixing all result in higher complexity this result suggests that the demand for functional diversity is driving the structural evolution of physical networks

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

degree distribution rank size distribution and leadership persistence in mediation driven attachment networks abstract we investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with m randomly chosen neighbors of the mediator at each time step we show that the degree distribution in such a mediation driven attachment mda network exhibits power law p k k m with a spectrum of exponents depending on m to appreciate the contrast between mda and barabasi albert ba networks we then discuss their rank size distribution to quantify how long a leader the node with the maximum degree persists in its leadership as the network evolves we investigate the leadership persistence probability f i e the probability that a leader retains its leadership up to time we find that it exhibits a power law f m with persistence exponent m 1 51 m in mda networks and m 1 53 exponentially with m in ba networks

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

existence and uniqueness of limit cycles for generalized φ laplacian lienard equations abstract the lienard equation x f x x g x 0 appears as a model in many problems of science and engineering since the first half of the 20th century many papers have appeared providing existence and uniqueness conditions for limit cycles of lienard equations in this paper we extend some of these results for the case of the generalized laplacian lienard equation x f x x g x 0 this generalization appears when derivations of the equation different from the classical one are considered in particular the relativistic van der pol equation x 1 x c 2 x 2 1 x x 0 has a unique periodic orbit when 0

special values of the bell polynomials of the second kind for some sequences and functions abstract in the paper after concisely surveying some closed formulas and applications of special values of the bell polynomials of the second kind for some special sequences and elementary functions the authors newly establish some closed formulas for some special values of the bell polynomials of the second kind

functional structure of cortical neuronal networks grown in vitro we apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro we infer connectivity between two neurons via the measurement of the mutual information between their spike trains in addition we measure higher point multi information between any two spike trains conditional on the activity of a third cell as a means to identify and distinguish classes of functional connectivity among three neurons the use of a conditional three cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light on the functional connectivity arrangements of any three cells we analyze the resultant connectivity graphs in light of other complex networks and demonstrate that despite their ex vivo development the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient network diameter and assortative mixing specifically we show that these networks are weakly disassortative small world graphs which differ significantly in their structure from randomized graphs with the same degree we expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks derived from time series data