violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

the duality relation between glauber dynamics and the diffusion annihilation model as a similarity transformation in this paper we address the relationship between zero temperature glauber dynamics and the diffusion annihilation problem in the free fermion case we show that the well known duality transformation between the two problems can be formulated as a similarity transformation if one uses appropriate toroidal boundary conditions this allows us to establish and clarify the precise nature of the relationship between the two models in this way we obtain a one to one correspondence between observables and initial states in the two problems a random initial state in glauber dynamics is related to a short range correlated state in the annihilation problem in particular the long time behaviour of the density in this state is seen to depend on the initial conditions hence we show that the presence of correlations in the initial state determine the dependence of the long time behaviour of the density on the initial conditions even if such correlations are short ranged we also apply a field theoretical method to the calculation of multi time correlation functions in this initial state

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

spin bond and global fluctuation dissipation relations in the non equilibrium spherical ferromagnet we study the out of equilibrium dynamics of the spherical ferromagnet after a quench to its critical temperature we calculate correlation and response functions for spin observables which probe length scales much larger than the lattice spacing but smaller than the system size and find that the asymptotic fluctuation dissipation ratio fdr x is the same as for local observables this is consistent with our earlier results for the ising model in dimension d 1 and d 2 we also check that bond observables both local and long range give the same asymptotic fdr in the second part of the paper the analysis is extended to global observables which probe correlations among all n spins here non gaussian fluctuations arising from the spherical constraint need to be accounted for and we develop a systematic expansion in to do this applying this to the global bond observable i e the energy we find that non gaussian corrections change its fdr to a nontrivial value which we calculate exactly for all dimensions d 2 finally we consider quenches from magnetized initial states here even the fdr for the global spin observable i e the magnetization is nontrivial it differs from the one for unmagnetized states even in d 4 signalling the appearance of a distinct dynamical universality class of magnetized critical coarsening for lower d the fdr is irrational even to first order in 4 d and d 2 the latter in contrast to recent results for the transverse fdr in the n vector model

epidemic spreading in correlated complex networks we study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node s connectivities for the case of markovian complex networks showing only correlations between pairs of nodes we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links which from a node with connectivity k go to nodes with connectivity k ensuremath numerical simulations on a correlated growing network model provide support for our conclusions

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

homotopy invariance of η invariants abstract intersection homology and results related to the higher signature problem are applied to show that certain combinations of invariants of the signature operator are homotopy invariant in various circumstances

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

ageing in one dimensional coagulation diffusion processes and the fredrickson andersen model we analyse the ageing dynamics of the one dimensional fredrickson andersen fa model in the nonequilibrium regime following a low temperature quench relaxation then effectively proceeds via diffusion limited pair coagulation dlpc of mobility excitations by employing a familiar stochastic similarity transformation we map exact results from the free fermion case of diffusion limited pair annihilation to dlpc crucially we are able to adapt the mapping technique to averages involving multiple time quantities this relies on knowledge of the explicit form of the evolution operators involved exact results are obtained for two time correlation and response functions in the free fermion dlpc process the corresponding long time scaling forms apply to a wider class of dlpc processes including the fa model we are thus able to exactly characterize the violations of the fluctuation dissipation theorem fdt in the ageing regime of the fa model we find nontrivial scaling forms for the fluctuation dissipation ratio fdr x x tw t but with a negative asymptotic value x 3 6 16 3 307 while this prevents a thermodynamic interpretation in terms of an effective temperature it is a direct consequence of probing fdt with observables that couple to activated dynamics the existence of negative fdrs should therefore be a widespread feature in non mean field systems

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

generation of arbitrarily two point correlated random networks random networks are intensively used as null models to investigate properties of complex networks we describe an efficient and accurate algorithm to generate arbitrarily two point degree degree correlated undirected random networks without self edges or multiple edges among vertices with the goal to systematically investigate the influence of two point correlations we furthermore develop a formalism to construct a joint degree distribution p j k which allows one to fix an arbitrary degree distribution p k and an arbitrary average nearest neighbor function k nn k simultaneously using the presented algorithm this formalism is demonstrated with scale free networks p k proportional variantk gamma and empirical complex networks p k taken from network as examples finally we generalize our algorithm to annealed networks which allows networks to be represented in a mean field like manner

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

cavity analysis on the robustness of random networks against targeted attacks influences of degree degree correlations we developed a scheme for evaluating the size of the largest connected subnetwork giant component in random networks and the percolation threshold when sites nodes and or bonds edges are removed from the networks based on the cavity method of statistical mechanics of disordered systems we apply our scheme particularly to random networks of bimodal degree distribution two peak networks which have been proposed in earlier studies as robust networks against random failures of site and or targeted random degree dependent attacks on sites our analysis indicates that the correlations among degrees affect a network s robustness against targeted attacks on sites or bonds nontrivially depending on details of network configurations

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

epidemic incidence in correlated complex networks a few years ago watts and strogatz 1 introduced a model able to produce networks with properties of both regu lar lattices and random graphs with small diameter their model soon led to a burst of activity in the field 2 3 further spurred by barabasi and co workers who found that many seemingly diverse systems share several topological proper ties such as a power law behavior in their connectivity dis tributions when represented as networks 4 these complex networks are formed by a set of many elements or nodes that are linked together through edges or links if they in teract directly empirical evidence supports that in notable networks such as metabolic or communication webs the probability p k that any node has k links to other nodes is distributed accordingly to a power law p k k 2g 5 7

resilience to damage of graphs with degree correlations the existence or nonexistence of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking in this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena we obtain some general expressions that allow the computation of the transition thresholds or their bounds using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks

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

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

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

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

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

finite size scaling studies of one dimensional reaction diffusion systems part i analytical results we consider two single species reaction diffusion models on one dimensional lattices of lengthl the coagulation decoagulation model and the annihilation model for the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions this system of differential equations grows quadratically withl in the latter case the equations are solved analytically and exact expressions for the concentration are derived we investigate the finite size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions we show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions a similarity transformation between the two models is derived and used to connect the corresponding scaling functions

the higson roe exact sequence and l2 eta invariants abstract the goal of this paper is to solve the problem of existence of an l 2 relative eta morphism on the higson roe structure group using the cheeger gromov l 2 eta invariant we construct a group morphism from the higson roe maximal structure group constructed in 35 to the reals when we apply this morphism to the structure class associated with the spin dirac operator for a metric of positive scalar curvature we get the spin l 2 rho invariant when we apply this morphism to the structure class associated with an oriented homotopy equivalence we get the difference of the l 2 rho invariants of the corresponding signature operators we thus get new proofs for the classical l 2 rigidity theorems of keswani obtained in 41

self similar scale free networks and disassortativity self similar networks with scale free degree distribution have recently attracted much attention since these apparently incompatible properties were reconciled in c song s havlin and h a makse nature 433 392 2005 by an appropriate box counting method that enters the measurement of the fractal dimension we study two genetic regulatory networks saccharomyces cerevisiae n m luscombe m m babu h yu m snyder s teichmann and m gerstein nature 431 308 2004 and escherichia coli http www ccg unam mx computationalgenomics regulondb datasets regulonnetdatasets html and http www gbf de systemsbiology and show their self similar and scale free features in extension to the datasets studied by c song s havlin and h a makse nature 433 392 2005 moreover by a number of numerical results we support the conjecture that self similar scale free networks are not assortative from our simulations so far these networks seem to be disassortative instead we also find that the qualitative feature of disassortativity is scale invariant under renormalization but it appears as an intrinsic feature of the renormalization prescription as even assortative networks become disassortative after a sufficient number of renormalization steps

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

general solutions for multispin two time correlation and response functions in the glauber ising chain the kinetic glauber ising spin chain is one of the very few exactly solvable models of non equilibrium statistical mechanics nevertheless existing solutions do not yield tractable expressions for two time correlation and response functions of observables involving products of more than one or two spins we use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions from this general solution follow closed expressions for arbitrary multispin two time correlation and response functions for the case where the system is quenched from equilibrium at ti 0 to some arbitrary t 0 by way of application we give the results for two and four spin two time correlation and response functions from the standard mapping these also imply new exact results for two time particle correlation and response functions in one dimensional diffusion limited annihilation

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

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

robustness of onionlike correlated networks against targeted attacks recently it was found by schneider et al proc natl acad sci usa 108 3838 2011 using simulations that scale free networks with onion structure are very robust against targeted high degree attacks the onion structure is a network where nodes with almost the same degree are connected motivated by this work we propose and analyze based on analytical considerations an onionlike candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks the nearly optimal structure can be viewed as a set of hierarchically interconnected random regular graphs the degrees and populations of whose nodes are specified by the degree distribution this network structure exhibits an extremely assortative degree degree correlation and has a close relationship to the onion structure after deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal we apply the theory to the cases of random scale free networks that are highly vulnerable against targeted high degree node removal our results show that this vulnerability can be significantly reduced by implementing this onionlike type of degree degree correlation without much undermining the almost complete robustness against random node removal we also investigate in detail the robustness enhancement due to assortative degree degree correlation by introducing a joint degree degree probability matrix that interpolates between an uncorrelated network structure and the onionlike structure proposed here by tuning a single control parameter the optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined our analytical calculations are supported by numerical simulations

percolation transition in networks with degree degree correlation we introduce an exponential random graph model for networks with a fixed degree distribution and a tunable degree degree correlation we then investigate the nature of the percolation transition in a correlated network with a poisson degree distribution it is found that negative correlation is irrelevant in that the percolation transition in the disassortative network belongs to the same universality class as in the uncorrelated network positive correlation turns out to be relevant the percolation transition in the assortative network is characterized by the nondiverging mean size of finite clusters and power law scalings of the density of the largest cluster and the cluster size distribution in the nonpercolating phase as well as at the critical point our results suggest that the unusual type of percolation transition in the growing network models reported recently may be inherited from the assortative degree degree correlation

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

smooth dense subalgebras of reduced group c algebras schwartz cohomology of groups and cyclic cohomology abstract we introduce the notion of schwartz co homology of a discrete group with a length function which is the natural generalization of the bounded cohomology of a discrete group we prove that if the length function is chosen to be a word length on a group of polynomial growth then its schwartz cohomology is canonically isomorphic to the usual group cohomology with complex coefficients using this result we will show that the group cohomology of a discrete group of polynomial growth is of polynomial growth in the sense of connes and moscovici and that there are no nontrivial idempotents in the group c algebra of a torsion free group of polynomial growth by the method of cyclic cohomology of connes

scale free networks with a large to hypersmall world transition abstract recently there has been a tremendous interest in models of networks with a power law distribution of degree so called scale free networks it has been observed that such networks normally have extremely short path lengths scaling logarithmically or slower with system size as an exotic and counterintuitive example we propose a simple stochastic model capable of generating scale free networks with linearly scaling distances furthermore by tuning a parameter the model undergoes a phase transition to a regime with extremely short average distances apparently slower than log log n which we call a hypersmall world regime we characterize the degree degree correlation and clustering properties of this class of networks

observability transition in real networks we consider the observability model in networks with arbitrary topologies we introduce a system of coupled nonlinear equations valid under the locally treelike ansatz to describe the size of the largest observable cluster as a function of the fraction of directly observable nodes present in the network we perform a systematic analysis on 95 real world graphs and compare our theoretical predictions with numerical simulations of the observability model our method provides almost perfect predictions in the majority of the cases even for networks with very large values of the clustering coefficient potential applications of our theory include the development of efficient and scalable algorithms for real time surveillance of social networks and monitoring of technological networks

dirac index classes and the noncommutative spectral flow abstract we present a detailed proof of the existence theorem for noncommutative spectral sections see the noncommutative spectral flow unpublished preprint 1997 we apply this result to various index theoretic situations extending to the noncommutative context results of booss wojciechowski melrose piazza and dai zhang in particular we prove a variational formula in k c r for the index classes associated to 1 parameter family of dirac operators on a covering with boundary this formula involves a noncommutative spectral flow for the boundary family next we establish an additivity result in k c r for the index class defined by a dirac type operator associated to a closed manifold m and a map r m b when we assume that m is the union along a hypersurface f of two manifolds with boundary m m f m finally we prove a defect formula for the signature index classes of two cut and paste equivalent pairs m1 r1 m1 b and m2 r2 m2 b where m 1 m f 1 m m 2 m f 2 m and j diff f the formula involves the noncommutative spectral flow of a suitable 1 parameter family of twisted signature operators on f we give applications to the problem of cut and paste invariance of novikov s higher signatures on closed oriented manifolds

adiabatic groupoid and secondary invariants in k theory abstract in this paper we define new k theoretic secondary invariants attached to a lie groupoid g the receptacle for these invariants is the k theory of c r g a d where g a d is the adiabatic deformation g restricted to the interval 0 1 our construction directly generalises the cases treated in 29 30 in the setting of the coarse geometry to more involved geometrical situations such as foliations moreover we tackle the problem of producing a wrong way functoriality between adiabatic deformation groupoid k groups associated to transverse maps this extends the construction of the lower shriek map in 6 furthermore we prove a lie groupoid version of the delocalized aps index theorem of piazza and schick finally we give a product formula for secondary invariants

realizing the analytic surgery group of higson and roe geometrically part iii higher invariants we construct an isomorphism between the geometric model and higson roe s analytic surgery group reconciling the constructions in the previous papers in the series on realizing the analytic surgery group of higson and roe geometrically with their analytic counterparts following work of lott and wahl we construct a chern character on the geometric model for the surgery group it is a delocalized chern character from which lott s higher delocalized rho invariants can be retrieved following work of piazza and schick we construct a geometric map from stolz positive scalar curvature sequence to the geometric model of higson roe s analytic surgery exact sequence

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

k homology and index theory on contact manifolds this paper applies k homology to solve the index problem for a class of hypoelliptic but not elliptic operators on contact manifolds k homology is the dual theory to k theory we explicitly calculate the k cycle i e the element in geometric k homology determined by any hypoelliptic fredholm operator in the heisenberg calculus

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

distribution of domain sizes in the zero temperature glauber dynamics of the one dimensional potts model for the zero temperature glauber dynamics of the q state potts model we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one species coagulation model a1a a in the long time limit this distribution is universal and from its complicated exact expression we extract its behavior in various regimes our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently considering the dynamics of domain walls as a reaction diffusion model a1a a with probability q22 q21 and a1a f with probability 1 q21 we calculate the pair correlation function in the long time regime s1063 651x 96 12809 9

zero pearson coefficient for strongly correlated growing trees we obtained pearson s coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by m edges we found that the pearson coefficient is exactly zero in the infinite network limit for the recursive trees m 1 if the number of connections of new vertices exceeds one mg1 then the pearson coefficient in the infinite networks equals zero only when the degree distribution exponent ensuremath gamma does not exceed 4 we calculated the pearson coefficient for finite networks and observed a slow power law like approach to an infinite network limit our findings indicate that pearson s coefficient strongly depends on size and details of networks which makes this characteristic virtually useless for quantitative comparison of different networks

fluctuation dissipation ratio in the one dimensional kinetic ising model the exact relation between the response function r t t and the two time correlation function c t t is derived analytically in the one dimensional kinetic ising model subjected to a temperature quench the fluctuation dissipation ratio x t t is found to depend on time through c t t in the time region where scaling c t t f t t holds the crossover from the nontrivial form x c t t to x t t identical with1 takes place as the waiting time t w is increased from below to above the equilibration time t eq

positive scalar curvature higher rho invariants and localization algebras abstract in this paper we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics the higher rho invariant is a secondary invariant and is closely related to positive scalar curvature problems the main result of the paper connects the higher index of the dirac operator on a spin manifold with boundary to the higher rho invariant of the dirac operator on the boundary where the boundary is endowed with a positive scalar curvature metric our result extends a theorem of piazza and schick 27 theorem 1 17

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

generating function of spin correlation functions for kinetic glauber ising model with time dependent transition rates the exact analytical solution in quadratures have been found for the generating function of spin correlation functions for the reiss variant of the kinetic ising model that is the extension of the glauber ising model to account for the dependence of heat bath temperature on time