fluctuation dissipation relations in complex networks in this paper we study fluctuations over several ensembles of maximum entropy random networks we derive several fluctuation dissipation relations characterizing the susceptibilities of different networks to changes in external fields in the case of networks with a given degree sequence we argue that the scale free topologies of real world networks may arise as a result of the self organization of real systems into sparse structures with low susceptibility to random external disruptions we also show that the ensembles of networks with a given degree sequence and networks characterized by two point correlations are equivalent to random networks with hidden variables

topological properties of citation and metabolic networks topological properties of scale free networks are investigated by determining their spectral dimensions d s which reflect a diffusion process in the corresponding graphs data bases for citation networks and metabolic networks together with simulation results from the growing network model a l barabasi and r albert science 286 509 1999 are probed for completeness and comparisons lattice random and small world models are also investigated we find that d s is around 3 for citation and metabolic networks which is significantly different from the growing network model for which d s is approximately 7 5 this signals a substantial difference in network topology despite the observed similarities in vertex order distributions in addition the diffusion analysis indicates that the citation networks are treelike in structure whereas the metabolic networks contain many loops

random graph models for directed acyclic networks we study random graph models for directed acyclic graphs a class of networks that includes citation networks food webs and feed forward neural networks among others we propose two specific models roughly analogous to the fixed edge number and fixed edge probability variants of traditional undirected random graphs we calculate a number of properties of these models including particularly the probability of connection between a given pair of vertices and compare the results with real world acyclic network data finding that theory and measurements agree surprisingly well far better than the often poor agreement of other random graph models with their corresponding real world networks

radial structure of the internet the structure of the internet at the autonomous system as level has been studied by the physics mathematics and computer science communities we extend this work to include features of the core and the periphery taking a radial perspective on as network structure new methods for plotting as data are described and they are used to analyse datasets that have been extended to contain edges missing from earlier collections the average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure common vertex specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices two datasets are analysed

randomizing world trade i a binary network analysis the international trade network itn has received renewed multidisciplinary interest due to recent advances in network theory however it is still unclear whether a network approach conveys additional nontrivial information with respect to traditional international economics analyses that describe world trade only in terms of local first order properties in this and in a companion paper we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher order patterns of the itn in all its possible representations binary or weighted directed or undirected aggregated or disaggregated by commodity and across several years here we show that remarkably the properties of all binary projections of the network can be completely traced back to the degree sequence which is therefore maximally informative our results imply that explaining the observed degree sequence of the itn which has not received particular attention in economic theory should instead become one the main focuses of models of trade

scale free network clustering in hyperbolic and other random graphs random graphs with power law degrees can model scale free networks as sparse topologies with strong degree heterogeneity mathematical analysis of such random graphs proved successful in explaining scale free network properties such as resilience navigability and small distances we introduce a variational principle to explain how vertices tend to cluster in triangles as a function of their degrees we apply the variational principle to the hyperbolic model that quickly gains popularity as a model for scale free networks with latent geometries and clustering we show that clustering in the hyperbolic model is non vanishing and self averaging so that a single random graph sample is a good representation in the large network limit we also demonstrate the variational principle for some classical random graphs including the preferential attachment model and the configuration model

improvement of the robustness on geographical networks by adding shortcuts abstract in a topological structure affected by geographical constraints on liking the connectivity is weakened by constructing local stubs with small cycles a something of randomness to bridge them is crucial for the robust network design in this paper we numerically investigate the effects of adding shortcuts on the robustness in geographical scale free network models under a similar degree distribution to the original one we show that a small fraction of shortcuts is highly contribute to improve the tolerance of connectivity especially for the intentional attacks on hubs the improvement is equivalent to the effect by fully rewirings without geographical constraints on linking even in the realistic internet topologies these effects are virtually examined

identifying communities within energy landscapes potential energy landscapes can be represented as a network of minima linked by transition states the community structure of such networks has been obtained for a series of small lennard jones lj clusters this community structure is compared to the concept of funnels in the potential energy landscape two existing algorithms have been used to find community structure one involving removing edges with high betweenness the other involving optimization of the modularity the definition of the modularity has been refined making it more appropriate for networks such as these where multiple edges and self connections are not included the optimization algorithm has also been improved using monte carlo methods with simulated annealing and basin hopping both often used successfully in other optimization problems in addition to the small clusters two examples with known heterogeneous landscapes the 13 atom cluster lj13 with one labeled atom and the 38 atom cluster lj38 were studied with this approach the network methods found communities that are comparable to those expected from landscape analyses this is particularly interesting since the network model does not take any barrier heights or energies of minima into account for comparison the network associated with a two dimensional hexagonal lattice is also studied and is found to have high modularity thus raising some questions about the interpretation of the community structure associated with such partitions

detection of topological patterns in complex networks correlation profile of the internet abstract a general scheme for detecting and analyzing topological patterns in large complex networks is presented in this scheme the network in question is compared with its properly randomized version that preserves some of its low level topological properties statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and or evolutionary history we illustrate this basic scheme using the example of the correlation profile of the internet quantifying correlations between degrees of its neighboring nodes this profile distinguishes the internet from previously studied molecular networks with a similar scale free degree distribution we finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the internet to the appropriate null model

pavelka style fuzzy logic in retrospect and prospect we trace the origin and development of pavelka style fuzzy logic discuss its significance and clarify some related misconceptions

organization of complex networks without multiple connections we find a new structural feature of equilibrium complex random networks without multiple and self connections we show that if the number of connections is sufficiently high these networks contain a core of highly interconnected vertices the number of vertices in this core varies in the range between const x n1 2 and const x n2 3 where is the number of vertices in a network at the birth point of the core we obtain the size dependent cutoff of the distribution of the number of connections and find that its position differs from earlier estimates

constrained markovian dynamics of random graphs we introduce a statistical mechanics formalism for the study of constrained graph evolution as a markovian stochastic process in analogy with that available for spin systems deriving its basic properties and highlighting the role of the mobility the number of allowed moves for any given graph as an application of the general theory we analyze the properties of degree preserving markov chains based on elementary edge switchings we give an exact yet simple formula for the mobility in terms of the graph s adjacency matrix and its spectrum this formula allows us to define acceptance probabilities for edge switchings such that the markov chains become controlled glauber type detailed balance processes designed to evolve to any required invariant measure representing the asymptotic frequencies with which the allowed graphs are visited during the process as a corollary we also derive a condition in terms of simple degree statistics sufficient to guarantee that in the limit where the number of nodes diverges even for state independent acceptance probabilities of proposed moves the invariant measure of the process will be uniform we test our theory on synthetic graphs and on realistic larger graphs as studied in cellular biology showing explicitly that for instances where the simple edge swap dynamics fails to converge to the uniform measure a suitably modified markov chain instead generates the correct phase space sampling

direct computation of the noise radiated by a subsonic cavity flow and application of integral methods abstract the goal of this paper is to investigate the acoustic field generated by the flow over a cavity using two different and complementary numerical methods first a direct numerical simulation of the 2 d compressible navier stokes equations is performed to obtain directly the radiated noise the results of the acoustic and aerodynamic fields are compared to the experimental data in the literature second this reference solution is compared to solutions provided by hybrid methods using the flowfield computed inside the cavity combined with an integral formulation to evaluate the far field noise numerical issues of three integral methods are studied the ffowcs williams and hawkings analogy that extends lighthill s theory to account for solid boundaries and two wave extrapolation methods from a control surface the kirchhoff and porous ffowcs williams and hawkings methods all methods show a good agreement with the direct numerical simulation but the first one is more expensive owing to an additional volume integral however the analogy can help in the analysis of wave patterns by separating the direct waves from the reflected ones the wave extrapolation methods from a surface are more efficient and provide a complementary tool to extend computational aeroacoustics near field to the very far field

fuzzy logic of lukasiewicz logic a clarification pavelka 10 had shown in 1979 that the only natural way of formalizing fuzzy logic for truth value in the unit interval 0 1 is by using lukasiewicz s implication operator a b min 1 1 a b or some isomorphic form of it a considerable number of other papers around the same time had attempted to formulate alternative definitions for a b by giving intuitive justifications for them there continues to be some confusion however even today about the right notion of fuzzy logic much of this has its origin in the use of improper and or and the not operations and a misunderstanding of some of the key differences between proofs or inferencing in fuzzy logic and those in lukasiewicz s logic we point out the need for defining the strong conjunction operator in connection with fuzzy modus ponens rule and why we do not need the fuzzy syllogism rule we also point out the shortcomings of many of the alternative definitions of a b which indicate further support for pavelka s result we hope that these discussions help to clarify the misconceptions about fuzzy logic

insights into biological information processing structural and dynamical analysis of a human protein signalling network we present an investigation on the structural and dynamical properties of a human protein signalling network hpsn this biological network is composed of nodes that correspond to proteins and directed edges that represent signal flows in order to gain insight into the organization of cell information processing this network is analysed taking into account explicitly the edge directions we explore the topological properties of the hpsn at the global and the local scale further applying the generating function formalism to provide a suitable comparative model the relationship between the node degrees and the distribution of signals through the network is characterized using degree correlation profiles finally we analyse the dynamical properties of small sub graphs showing high correlation between their occurrence and dynamic stability

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

complex networks in confined comminution the physical process of confined comminution is investigated within the framework of complex networks we first characterize the topology of the unweighted contact networks as generated by the confined comminution process we find this process gives rise to an ultimate contact network which exhibits a scale free degree distribution and small world properties in particular if viewed in the context of networks through which information travels along shortest paths we find that the global average of the node vulnerability decreases as the comminution process continues with individual node vulnerability correlating with grain size a possible application to the design of synthetic networks e g sensor networks is highlighted next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks where each link is weighted by the inverse magnitude of the normal force acting at the associated contact we find that the strong forces i e force chains are transmitted along pathways in the network which are mainly following shortest path routing protocols as typically found for example in communication systems motivated by our earlier studies of the building blocks for self organization in dense granular systems we also explore the properties of the minimal contact cycles the distribution of the contact strain energy intensity of 4 cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale free distribution with infinite variance thereby suggesting that 4 cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking

percolation on correlated networks we reconsider the problem of percolation on an equilibrium random network with degree degree correlations between nearest neighboring vertices focusing on critical singularities at a percolation threshold we obtain criteria for degree degree correlations to be irrelevant for critical singularities we present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents

tailored graph ensembles as proxies or null models for real networks i tools for quantifying structure we study the tailoring of structured random graph ensembles to real networks with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically beyond the level of degree statistics our family of ensembles can produce graphs with any prescribed degree distribution and any degree degree correlation function its control parameters can be calculated fully analytically and as a result we can calculate asymptotically formulae for entropies and complexities and for information theoretic distances between networks expressed directly and explicitly in terms of their measured degree distribution and degree correlations

exploring the assortativity clustering space of a network s degree sequence nowadays there is a multitude of measures designed to capture different aspects of network structure to be able to say if a measured value is expected or not one needs to compare it with a refere

mean field level analysis of epidemics in directed networks the susceptible infected removed spreading model in a directed graph is studied the mean field level rate equations are built with the degree degree connectivity correlation element and the in out degree distribution and the outbreak threshold is obtained analytically it is determined by the combination of connectivity probability and the degree distribution furthermore the methods of calculating the degree degree correlations in directed networks are presented the numerical results of the discrete epidemic processes in networks verify our analyses

generating random networks that consist of a single connected component with a given degree distribution we present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution this approach extends the construction toolbox of random networks beyond the configuration model framework in which one controls the degree distribution but not the number of components and their sizes unlike configuration model networks which are completely uncorrelated the resulting single component networks exhibit degree degree correlations moreover they are found to be disassortative namely high degree nodes tend to connect to low degree nodes and vice versa we demonstrate the method for single component networks with ternary exponential and power law degree distributions

origin of degree correlations in the internet and other networks it has been argued that the observed anticorrelation between the degrees of adjacent vertices in the network representation of the internet has its origin in the restriction that no two vertices have more than one edge connecting them here we propose a formalism for modeling ensembles of graphs with single edges only and derive values for the exponents and correlation coefficients characterizing them our results confirm that the conjectured mechanism does indeed give rise to correlations of the kind seen in the internet although only a part of the measured correlation can be accounted for in this way

diffusion annihilation processes in complex networks we present a detailed analytical study of the a a 0i diffusion annihilation process in complex networks by means of microscopic arguments we derive a set of rate equations for the density of a particles in vertices of a given degree valid for any generic degree distribution and which we solve for uncorrelated networks for homogeneous networks swith bounded fluctuations d we recover the standard mean field solution i e a particle density decreasing as the inverse of time for heterogeneous sscale free networksd in the infinite network size limit we obtain instead a density decreasing as a power law with an exponent depending on the degree distribution we also analyze the role of finite size effects showing that any finite scale free network leads to the mean field behavior with a prefactor depending on the network size we check our analytical predictions with extensive numerical simulations on homogeneous networks with poisson degree distribution and scalefree networks with different degree exponents

percolation in directed scale free networks many complex networks in nature have directed links a property that affects the network s navigability and large scale topology here we study the percolation properties of such directed scale free networks with correlated in and out degree distributions we derive a phase diagram that indicates the existence of three regimes determined by the values of the degree exponents in the first regime we regain the known directed percolation mean field exponents in contrast the second and third regimes are characterized by anomalous exponents which we calculate analytically in the third regime the network is resilient to random dilution i e the percolation threshold is pc 1

multiresolution transmission of the correlation modes between bivariate time series based on complex network theory abstract this study introduces an approach to study the multiscale transmission characteristics of the correlation modes between bivariate time series the correlation between the bivariate time series fluctuates over time the transmission among the correlation modes exhibits a multiscale phenomenon which provides richer information to investigate the multiscale transmission of the correlation modes this paper describes a hybrid model integrating wavelet analysis and complex network theory to decompose and reconstruct the original bivariate time series into sequences in a joint time frequency domain and defined the correlation modes at each time frequency domain we chose the crude oil spot and futures prices as the sample data the empirical results indicate that the main duration of volatility 32 64 days for the strongly positive correlation between the crude oil spot price and the futures price provides more useful information for investors moreover the weighted degree weighted indegree and weighted outdegree of the correlation modes follow power law distributions the correlation fluctuation strengthens the extent of persistence over the long term whereas persistence weakens over the short and medium term the primary correlation modes dominating the transmission process and the major intermediary modes in the transmission process are clustered both in the short and long term

observability transitions in correlated networks yang wang and motter phys rev lett 109 258701 2012 analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable the size of the connected components comprising the observable nodes is a major concern of the model we analyze this model in random heterogeneous networks with degree correlation with numerical simulations and analytical arguments based on generating functions we find that negative degree correlation makes networks more observable this result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors finally we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component optimized networks have negative degree correlation induced by the resulting hub repulsive structure the largest hubs are rarely connected to each other in contrast to the rich club phenomenon of networks

reachability and recoverability of sink nodes in growing acyclic directed networks abstract we study the growth of networks from a set of isolated ground nodes by the addition of one new node per time step and also of a fixed number of directed edges leading from the new node to randomly selected nodes already in the network a fixed width time window is used so that in general only nodes that entered the network within the latest window may receive new incoming edges the resulting directed network is acyclic at all times and allows some of the ground nodes then called sinks to be reached from some of the non ground nodes we regard such networks as representative of abstract systems of partially ordered constituents for example in some of the domains related to technological evolution two properties of interest are the number of sinks that can be reached from a randomly chosen non ground node its reach and for a fixed sink the number of nonoverlapping directed paths through which the sink can be reached at a given time from some of the latest nodes to have entered the network we demonstrate by means of simulations and also of analytic characterizations that reaches are distributed according to a power law and that the desired directed paths are expected to occur in very small numbers perhaps indicating that recovering sinks late in the process of network growth is strongly sensitive to accidental path disruptions

effect of node deleting on network structure abstract the ever increasing knowledge of the structure of various real world networks has uncovered their complex multi mechanism governed evolution processes therefore a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner in this paper we introduce a new type of network growth rule which comprises addition and deletion of nodes and propose an evolving network model to investigate the effect of node deleting on network structure it is found that with the introduction of node deleting network structure is significantly transformed in particular degree distribution of the network undergoes a transition from scale free to exponential forms as the intensity of node deleting increases at the same time nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model we also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small in addition it is found that node deleting will weaken but not eliminate the small world effect of a growing network and generally it will decrease the clustering coefficient in a network

uncovering disassortativity in large scale free networks mixing patterns in large self organizing networks such as the internet the world wide web and social and biological networks are often characterized by degree degree dependencies between neighboring nodes in this paper we propose a new way of measuring degree degree dependencies one of the problems with the commonly used assortativity coefficient is that in disassortative networks its magnitude decreases with the network size we mathematically explain this phenomenon and validate the results on synthetic graphs and real world network data as an alternative we suggest to use rank correlation measures such as spearman s rho our experiments convincingly show that spearman s rho produces consistent values in graphs of different sizes but similar structure and it is able to reveal strong positive or negative dependencies in large graphs in particular we discover much stronger negative degree degree dependencies in web graphs than was previously thought rank correlations allow us to compare the assortativity of networks of different sizes which is impossible with the assortativity coefficient due to its genuine dependence on the network size we conclude that rank correlations provide a suitable and informative method for uncovering network mixing patterns

identification of intrinsic long range degree correlations in complex networks many real world networks exhibit degree degree correlations between nodes separated by more than one step such long range degree correlations lrdcs can be fully described by one joint and four conditional probability distributions with respect to degrees of two randomly chosen nodes and shortest path distance between them while lrdcs are induced by nearest neighbor degree correlations nndcs between adjacent nodes some networks possess intrinsic lrdcs which cannot be generated by nndcs here we develop a method to extract intrinsic lrdc in a correlated network by comparing the probability distributions for the given network with those for nearest neighbor correlated random networks we also demonstrate the utility of our method by applying it to several real world networks

asymptotic properties of degree correlated scale free networks the possible correlation profiles of networks with a given scale free degree distribution are restricted and bounded by maximally correlated configurations dissortative networks consist of nested bilayers in which low degree vertices are connected to high degree vertices the number of these bilayers attains a constant value for large network size n assortative networks exhibit monolayers of low degree vertices the number of which grows monotonously with n analytical relations for the pearson correlation coefficient r of these extremal configurations are derived and shown to provide lower and upper bounds on the possible r values both bounds are found to vanish for large networks

triangular norm based predicate fuzzy logics the paper surveys the present state of knowledge on t norm based predicate fuzzy logics with their double semantics standard the set of truth values being the real interval 0 1 and general with abstract algebras of truth functions

evolutionary construction of geographical networks with nearly optimal robustness and efficient routing properties abstract robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems in this paper based on a percolation theory and a geometric graph property we investigate such a design from the following viewpoints 1 network evolution according to a spatially heterogeneous population 2 trimodal low degrees for the tolerant connectivity against both failures and attacks and 3 decentralized routing within short paths furthermore we point out the weakened tolerance by geographical constraints on local cycles and propose a practical strategy by adding a small fraction of shortcut links between randomly chosen nodes in order to improve the robustness to a similar level to that of the optimal bimodal networks with a larger degree o n for the network size n these properties will be useful for constructing future ad hoc networks in wide area communications

diversity of graphs with highly variable connectivity a popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large scale connectivity while it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent the relationship between competing descriptions is not entirely understood this paper lends perspective on this problem by showing how the degree sequence and other constraints e g connectedness no self loops or parallel edges on a particular graph play a primary role in dictating many features including its correlation structure building on recent work we show how a simple structural metric characterizes key differences between graphs having the same degree sequence more broadly we show how the often implicit choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

emergence of symmetry in complex networks many real networks have been found to have a rich degree of symmetry which is a universal structural property of complex networks yet has been rarely studied so far one of the fascinating problems related to symmetry is exploration of the origin of symmetry in real networks for this purpose we summarized the statistics of local symmetric motifs that contribute to local symmetry of networks analysis of these statistics shows that the symmetry of complex networks is a consequence of similar linkage pattern which means that vertices with similar degrees tend to share common neighbors an improved version of the baraba i albert model integrating similar linkage pattern successfully reproduces the symmetry of real networks indicating that similar linkage pattern is the underlying ingredient that is responsible for the emergence of symmetry in complex networks

link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequences the simplest null models for networks used to distinguish significant features of a particular network from a priori expected features are random ensembles with the degree sequence fixed by the specific network of interest these fixed degree sequence fds ensembles are however famously resistant to analytic attack in this paper we introduce ensembles with partially fixed degree sequences pfds and compare analytic results obtained for them with monte carlo results for the fds ensemble these results include link likelihoods subgraph likelihoods and degree correlations we find that local structural features in the fds ensemble can be reasonably well estimated by simultaneously fixing only the degrees of a few nodes in addition to the total number of nodes and links as test cases we use two protein interaction networks escherichia coli saccharomyces cerevisiae the internet on the autonomous system as level and the world wide web fixing just the degrees of two nodes gives the mean neighbor degree as a function of node degree k k in agreement with results explicitly obtained from rewiring for power law degree distributions we derive the disassortativity analytically in the pfds ensemble the partition function can be expanded diagrammatically we obtain an explicit expression for the link likelihood to lowest order which reduces in the limit of large sparse undirected networks with l links and with k max l to the simple formula p k k kk 2l kk in a similar limit the probability for three nodes to be linked into a triangle reduces to the factorized expression p delta k 1 k 2 k 3 p k 1 k 2 p k 1 k 3 p k 2 k 3

fuzzy logic and arithmetical hierarchy fuzzy logic is understood as a logic with a comparative and truth functional notion of truth arithmetical complexity of sets of tautologies identically true sentences and satisfiable sentences sentences true in at least one interpretation as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated

the data driven null models for information dissemination tree in social networks abstract for the purpose of detecting relatedness and co occurrence between users as well as the distribution features of nodes in spreading path of a social network this paper explores topological characteristics of information dissemination trees idt that can be employed indirectly to probe the information dissemination laws within social networks hence three different null models of idt are presented in this article including the statistical constrained 0 order idt null model the random rewire broken edge 0 order idt null model and the random rewire broken edge 2 order idt null model these null models firstly generate the corresponding randomized copy of an actual idt then the extended significance profile which is developed by adding the cascade ratio of information dissemination path is exploited not only to evaluate degree correlation of two nodes associated with an edge but also to assess the cascade ratio of different length of information dissemination paths the experimental correspondences of the empirical analysis for several sinaweibo idts and twitter idts indicate that the idt null models presented in this paper perform well in terms of degree correlation of nodes and dissemination path cascade ratio which can be better to reveal the features of information dissemination and to fit the situation of real social networks

an algebraic approach to linguistic hedges in zadeh s fuzzy logic the paper addresses the mathematical modelling of domains of linguistic variables i e term sets of linguistic variables in order to obtain a suitable algebraic structure for the set of truth values of zadeh s fuzzy logic we shall give a unified algebraic approach to the natural structure of domains of linguistic variables which was proposed by ho and wechler fuzzy sets and systems 35 1990 281 and then by ho and nam proc ncst vietnam 9 1 1997 15 logic algebra and computer science vol 46 banach center publications pwn warsaw 1999 p 63 in this approach every linguistic domain can be considered as an algebraic structure called hedge algebra because properties of its unary operations reflect semantic characteristics of linguistic hedges many fundamental properties of refined hedge algebras rh algebras are examined especially it is shown that every rh algebra of a linguistic variable with a chain of the primary terms is a distributive lattice rh algebras with exactly two distinct primary terms one being an antonym of the other will also be investigated and they will be called symmetrical rh algebras it is shown that a class of finite symmetrical rh algebras has a rich enough algebraic structure

on a general class of models for interaction this paper develops a class of probability models for configurations of interacting points in a domain the distributions depend on a function which may be viewed as giving the potential energy of the configurations examples include models for interaction in a spatial region and on lattices and graphs new models in the general class arise naturally an example being a spatial model for points of different categories some general methods including series expansions and a simulation method known from statistical mechanics can be useful for many of these models several applications of this kind are considered and some connections between the models and with the statistical mechanics are explored

high order compact schemes for incompressible flows a simple and efficient method with quasi spectral accuracy in this paper a finite difference code for direct and large eddy simulation dns les of incompressible flows is presented this code is an intermediate tool between fully spectral navier stokes solvers limited to academic geometry through fourier or chebyshev representation and more versatile codes based on standard numerical schemes typically only second order accurate the interest of high order schemes is discussed in terms of implementation easiness computational efficiency and accuracy improvement considered through simplified benchmark problems and practical calculations the equivalence rules between operations in physical and spectral spaces are efficiently used to solve the poisson equation introduced by the projection method it is shown that for the pressure treatment an accurate fourier representation can be used for more flexible boundary conditions than periodicity or free slip using the concept of the modified wave number the incompressibility can be enforced up to the machine accuracy the benefit offered by this alternative method is found to be very satisfactory even when a formal second order error is introduced locally by boundary conditions that are neither periodic nor symmetric the usefulness of high order schemes combined with an immersed boundary method ibm is also demonstrated despite the second order accuracy introduced by this wall modelling strategy in particular the interest of a partially staggered mesh is exhibited in this specific context three dimensional calculations of transitional and turbulent channel flows emphasize the ability of present high order schemes to reduce the computational cost for a given accuracy the main conclusion of this paper is that finite difference schemes with quasi spectral accuracy can be very efficient for dns les of incompressible flows while allowing flexibility for the boundary conditions and easiness in the code development therefore this compromise fits particularly well for very high resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments

k core architecture and k core percolation on complex networks abstract we analytically describe the architecture of uncorrelated complex networks with arbitrary degree distributions as a set of successively enclosed substructures k cores we find the structure of k cores their sizes and their birth points the bootstrap percolation thresholds we show that in networks with a finite mean number z 2 of the second nearest neighbours the emergence of a k core is a unique hybrid phase transition with a jump emergence of the k core as at a first order phase transition but also with a critical singularity as at a continuous phase transition in contrast if z 2 diverges the networks contain an infinite sequence of k cores which are ultra robust against random damage we explain the meaning of the order parameter for k core percolation and reveal the origin of the specific critical phenomena we demonstrate that a so called corona of the k core plays a crucial role it turns out that the k core percolation threshold is at the same time the percolation threshold of finite corona clusters the mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point we demonstrate that a random removal of even one vertex from the k core may result in the collapse of a vast region of the k core around the removed vertex the mean size of this region diverges at the critical point we find an exact mapping of k core percolation to a model of cooperative relaxation this model undergoes critical relaxation with a divergent rate at some critical moment

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

detecting link failures in complex network processes using remote monitoring abstract we study whether local structural changes in a complex network can be distinguished from passive remote time course measurements of the network s dynamics specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered by phrasing the detection task as a maximum a posteriori probability hypothesis testing problem we are able to obtain conditions under which the detection is 1 improved over the a priori and 2 asymptotically perfect in terms of the network spectrum and graph we find that in the case where the detector has knowledge of the network s state perfect detection is possible under general connectivity conditions regardless of the measurement location when the detector does not have state knowledge a remote signature permits improved but not perfect detection under the same connectivity conditions at its essence detectability is achieved because of the close connection between a network s topology its eigenvalues and local response characteristics

k core bootstrap percolation on complex networks critical phenomena and nonlocal effects we develop the theory of the k core bootstrap percolation on uncorrelated random networks with arbitrary degree distributions we show that the k core percolation is an unusual hybrid phase transition with a jump emergence of the k core as at a first order phase transition but also with a critical singularity as at a continuous transition we describe the properties of the k core explain the meaning of the order parameter for the k core percolation and reveal the origin of the specific critical phenomena we demonstrate that a so called corona of the k core plays a crucial role corona is a subset of vertices in the k core which have exactly k neighbors in the k core it turns out that the k core percolation threshold is at the same time the percolation threshold of finite corona clusters the mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point we show that a random removal of even one vertex from the k core may result in the collapse of a vast region of the k core around the removed vertex the mean size of this region diverges at the critical point we find an exact mapping of the k core percolation to a model of cooperative relaxation this model undergoes critical relaxation with a divergent rate at some critical moment

spatial network surrogates for disentangling complex system structure from spatial embedding of nodes networks with nodes embedded in a metric space have gained increasing interest in recent years the effects of spatial embedding on the networks structural characteristics however are rarely taken into account when studying their macroscopic properties here we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes embedding in a metric space comparing the original network s and the resulting surrogates global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links we apply our framework to various real world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes spatial embedding depending on the actual performance of the proposed null models the networks are categorized into different classes since many real world complex networks are in fact spatial networks the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields ranging from social systems over infrastructure and neurophysiology to climatology

loops and multiple edges in modularity maximization of networks the modularity maximization model proposed by newman and girvan for the identification of communities in networks works for general graphs possibly with loops and multiple edges however the applications usually correspond to simple graphs these graphs are compared to a null model where the degree distribution is maintained but edges are placed at random therefore in this null model there will be loops and possibly multiple edges sharp bounds on the expected number of loops and their impact on the modularity are derived then building upon the work of massen and doye but using algebra rather than simulation we propose modified null models associated with graphs without loops but with multiple edges graphs with loops but without multiple edges and graphs without loops nor multiple edges we validate our models by using the exact algorithm for clique partitioning of grotschel and wakabayashi

giant strongly connected component of directed networks we describe how to calculate the sizes of all giant connected components of a directed graph including the strongly connected one in particular the world wide web is a directed network the results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out degree distribution p k i k o we show that if p k i k o does not factorize the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in and out components the calculations of the relative sizes of all the giant components are demonstrated using the simplest examples we explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one

scale free networks as preasymptotic regimes of superlinear preferential attachment we study the following paradox associated with networks growing according to superlinear preferential attachment superlinear preference cannot produce scale free networks in the thermodynamic limit but there are superlinearly growing network models that perfectly match the structure of some real scale free networks such as the internet we obtain an analytic solution supported by extensive simulations for the degree distribution in superlinearly growing networks with arbitrary average degree and confirm that in the true thermodynamic limit these networks are indeed degenerate i e almost all nodes have low degrees we then show that superlinear growth has vast preasymptotic regimes whose depths depend both on the average degree in the network and on how superlinear the preference kernel is we demonstrate that a superlinearly growing network model can reproduce in its preasymptotic regime the structure of a real network if the model captures some sufficiently strong structural constraints rich club connectivity for example these findings suggest that real scale free networks of finite size may exist in pre asymptotic regimes of network evolution processes that lead to degenerate network formations in the thermodynamic limit

an efficient two dimensional implementation of the ffowcs williams and hawkings equation abstract this paper describes a two dimensional formulation of the ffowcs williams and hawkings equation in the frequency domain by assuming subsonic rectilinear motion of all acoustic sources an efficient and easily implemented form of the equation is developed this method is capable of predicting the farfield noise from non linear nearfield flow quantities the ability to use non linear input data is a clear advantage over kirchhoff methods that are only valid in regions where the linear wave equation accurately describes the flow several example problems are used to demonstrate that the new method performs well for problems with a mean flow tonal and broadband noise signatures and non linear near fields in most practical acoustic problems three dimensionality is important and should not be neglected for these real world applications two dimensional solutions can be used to guide and augment full three dimensional calculations but not replace them

revising the simple measures of assortativity in complex networks we find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes to counteract and measure the effect of superrich nodes we propose a paradigm to quantify the mixing pattern of a real network in which different mixing patterns may appear among low degree nodes and among high degree nodes this paradigm and the simple revised measure uncover the true complex degree mixing patterns of complex networks with superrich nodes the alternate method indicates that some networks show a false disassortative mixing induced by superrich nodes and have no tendency to be genuinely disassortative our results also show that the previously observed fragility of scale free networks is actually greatly exacerbated by the presence of even a very small number of superrich nodes

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

entropic origin of disassortativity in complex networks why are most empirical networks with the prominent exception of social ones generically degree degree anticorrelated to answer this long standing question we define the ensemble of correlated networks and obtain the associated shannon entropy maximum entropy can correspond to either assortative correlated or disassortative anticorrelated configurations but in the case of highly heterogeneous scale free networks a certain disassortativity is predicted offering a parsimonious explanation for the question above our approach provides a neutral model from which in the absence of further knowledge regarding network evolution one can obtain the expected value of correlations when empirical observations deviate from the neutral predictions as happens for social networks one can then infer that there are specific correlating mechanisms at work

fluctuation driven dynamics of the internet topology we study the dynamics of the internet topology based on empirical data on the level of the autonomous systems it is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the internet dynamics the network s overall growth can be described approximately by a single characteristic degree growth rate g eff approximately 0 016 and the fluctuation strength sigma eff approximately 0 14 together with the vertex growth rate alpha approximately 0 029 a stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real internet topology such as the correlations between the degrees of different vertices

a boundary element extension of curle s analogy for non compact geometries at low mach numbers abstract the aeroacoustic analogy derived by curle for the prediction of the sound resulting from turbulence body interactions has proved quite powerful for low helmholtz numbers i e when the interaction region is acoustically compact in such case incompressible flow modeling can be used to obtain the source field used as the input of the analogy it was however shown in a previous paper that curle s analogy can yield erroneous results for non compact cases when an incompressible flow model is adopted yet at low mach numbers incompressible flow modeling can be substantially more efficient than compressible simulations due to the stiffness issues faced by the latter the present work focuses on the derivation of a method combining curle s analogy with a boundary element method bem in order to compensate for the weaknesses of the traditional approach at high helmholtz numbers the validation of this method is performed by application to a generic test case the spinning of two vortex filaments in an infinite two dimensional duct this flow model is amenable to a nearly exact derivation by an incompressible vortex model moreover the acoustic field can also be obtained very accurately using the tailored green s function based on the duct modes providing a reference solution to validate our numerical approach the sound field predicted using the bem curle approach shows excellent agreement with the reference solution based on the tailored green s function thereby validating the general principle of bem curle method and its numerical implementation

parameterizing the semantics of fuzzy attribute implications by systems of isotone galois connections we study the semantics of fuzzy if then rules called fuzzy attribute implications parameterized by systems of isotone galois connections the rules express dependences between fuzzy attributes in object attribute incidence data the proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches we formalize the general parameterizations propose bivalent and graded notions of semantic entailment of fuzzy attribute implications show their characterization in terms of least models and complete axiomatization and provide characterization of bases of fuzzy attribute implications derived from data

scale free networks as entropy competition complex networks describe several and different real world systems consisting of a number of interacting elements a very important characteristic of such networks is the degree distribution that strongly controls their behavior based on statistical mechanics three classes of uncorrelated complex networks are identified here depending on the role played by the connectivities amongst elements in particular by identifying the connectivities of a node with the number of its nearest neighbors we show that the power law is the most probable degree distribution that both nodes and neighbors in a reciprocal competition assume when the respective entropy functions reach their maxima under mutual constraint as a result we obtain scaling exponent values as a function of the structural characteristics of the whole network moreover our approach sheds light on the exponential and poissonian degree distributions derived respectively when connectivities are thought of as degenerated connections or as half edges thus all three classes of degree distributions are derived starting from a common principle and leading to a general and unified framework for investigating the network structure

interfaces and the edge percolation map of random directed networks the traditional node percolation map of directed networks is reanalyzed in terms of edges in the percolated phase edges can mainly organize into five distinct giant connected components interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components formal equations for the relative sizes in the number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two point correlations the uncorrelated null model is fully solved analytically and compared against simulations finding an excellent agreement interfaces and their particular conformations giving place from hairy ball percolation landscapes to bottleneck straits could bring new light to the discussion of how a structure is interwoven with functionality in flow networks

degree landscapes in scale free networks we generalize the degree organizational view of real world networks with broad degree distributions in a landscape analog with mountains high degree nodes and valleys low degree nodes for exam

reconstructing the world trade multiplex the role of intensive and extensive biases in economic and financial networks the strength of each node has always an important economic meaning such as the size of supply and demand import and export or financial exposure constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown however several studies have proved that real economic networks and multiplexes topologically differ from configurations inferred only from node strengths here we provide a detailed analysis of the world trade multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node we study several temporal snapshots and almost 100 layers commodity classes of the multiplex and find that the observed properties are systematically well reproduced by our model our formalism allows us to introduce the static concept of extensive and intensive bias defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights with respect to a reference case where only strengths are enforced our findings complement the existing economic literature on dynamic intensive and extensive trade margins more generally they show that real world multiplexes can be strongly shaped by layer specific local constraints

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

robustness of acoustic analogies for predicting mixing layer noise acoustic analogies for the prediction of flow noise are exact rearrangements of the flow equations n q 0 into a nominal sound source s q and sound propagation operator c such that l q s q in practice the sound source is typically modeled and the propagation operator inverted to make predictions because the rearrangement is exact any sufficiently accurate model of the source will yield the correct sound and so other factors must determine the merits of any particular formulation using data from a two dimensional mixing layer direct numerical simulation we evaluate the robustness of several formulations to different errors intentionally introduced into the source the motivation is that because s cannot be perfectly modeled analogies that are less sensitive to errors in s are preferable our assessment is made within the framework of goldstein s generalized acoustic analogy a uniform base flow yields a lighthill like analogy which we evaluate against a formulation in which the base flow is the actual mean flow of the direct numerical simulation and also against a globally parallel base flow that gives a lilley like analogy the more complex mean flow formulations are found to be significantly more robust to errors in the energetic turbulent fluctuations but the advantage is less clear when errors are introduced at smaller scales

analysis of complex contagions in random multiplex networks we study the diffusion of influence in random multiplex networks where links can be of r different types and for a given content e g rumor product or political view each link type is associated with a content dependent parameter ci in 0 that measures the relative bias type i links have in spreading this content in this setting we propose a linear threshold model of contagion where nodes switch state if their perceived proportion of active neighbors exceeds a threshold namely a node connected to mi active neighbors and ki mi inactive neighbors via type i links will turn active if cimi ciki exceeds its threshold under this model we obtain the condition probability and expected size of global spreading events our results extend the existing work on complex contagions in several directions by i providing solutions for coupled random networks whose vertices are neither identical nor disjoint ii highlighting the effect of content on the dynamics of complex contagions and iii showing that content dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature

subgraphs in random networks understanding the subgraph distribution in random networks is important for modeling complex systems in classic erdos networks which exhibit a poissonian degree distribution the number of appearances of a subgraph g with n nodes and g edges scales with network size as approximately n n g however many natural networks have a non poissonian degree distribution here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks characterized by an arbitrary degree sequence we find scaling rules for the commonly occurring case of directed scale free networks in which the outgoing degree distribution scales as p k approximately k gamma considering the power exponent of the degree distribution gamma as a control parameter we show that random networks exhibit transitions between three regimes in each regime the subgraph number of appearances follows a different scaling law approximately nalpha where alpha n g s 1 for gamma gamma c where s is the maximal outdegree in the subgraph and gamma c s 1 we find that certain subgraphs appear much more frequently than in erdos networks these results are in very good agreement with numerical simulations this has implications for detecting network motifs subgraphs that occur in natural networks significantly more than in their randomized counterparts

on compressibility assumptions in aeroacoustic integrals a numerical study with subsonic mixing layers two assumptions commonly made in predictions based on lighthill s formalism are investigated a constant density in the quadrupole expression and the evaluation of the source quantity from incompressible simulations numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two dimensional mixing layer at re 400 published results of the direct noise computation dnc of the flow are used as reference and input for hybrid approaches before the assumptions on density are progressively introduced divergence free velocity fields are obtained from an incompressible simulation of the same flow case exhibiting the same hydrodynamic field as the dnc for the tested values of the mach number hybrid predictions reproduce correctly the reference acoustic field validating both assumptions in the source region however in the observer region the inclusion of flow effects in the lighthill source term is not preserved which is illustrated through a comparison with the kirchhoff wave extrapolation formalism and with the use of a convected green function in the integration process