community detection algorithms a comparative analysis uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents many algorithms have been proposed so far but none of them has been subjected to strict tests to evaluate their performance most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure which is very uncommon in real systems here we test several methods against a recently introduced class of benchmark graphs with heterogeneous distributions of degree and community size the methods are also tested against the benchmark by girvan and newman proc natl acad sci u s a 99 7821 2002 and on random graphs as a result of our analysis three recent algorithms introduced by rosvall and bergstrom proc natl acad sci u s a 104 7327 2007 proc natl acad sci u s a 105 1118 2008 blondel et al j stat mech theory exp 2008 p10008 and ronhovde and nussinov phys rev e 80 016109 2009 have an excellent performance with the additional advantage of low computational complexity which enables one to analyze large systems

benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups this feature is known as community structure and encodes precious information about the organization and the function of the nodes many algorithms have been proposed but it is not yet clear how they should be tested recently we have proposed a general class of undirected and unweighted benchmark graphs with heterogeneous distributions of node degree and community size an increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links which require suitable benchmark graphs for testing in this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built in community structure we also consider the possibility that nodes belong to more communities a feature occurring in real systems such as social networks as a practical application we show how modularity optimization performs on our benchmark

fuzzy communities and the concept of bridgeness in complex networks we consider the problem of fuzzy community detection in networks which complements and expands the concept of overlapping community structure our approach allows each vertex of the graph to belong to multiple communities at the same time determined by exact numerical membership degrees even in the presence of uncertainty in the data being analyzed we create an algorithm for determining the optimal membership degrees with respect to a given goal function based on the membership degrees we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities bridge vertices that have significant membership in more than one single community and regular vertices that fundamentally restrict their interactions within their own community while also being able to quantify the centrality of a vertex with respect to its dominant community the method can also be used for prediction in case of uncertainty in the data set analyzed the number of communities can be given in advance or determined by the algorithm itself using a fuzzified variant of the modularity function the technique is able to discover the fuzzy community structure of different real world networks including but not limited to social networks scientific collaboration networks and cortical networks with high confidence

pure tone threshold estimation from extrapolated distortion product otoacoustic emission i o functions in normal and cochlear hearing loss ears a new method for direct pure tone threshold estimation from input output functions of distortion product otoacoustic emissions dpoaes in humans is presented previous methods use statistical models relating dpoae level to hearing threshold including additional parameters e g age or slope of dpoae i o function here we derive a dpoae threshold from extrapolated dpoae i o functions directly cubic 2 f1 f2 distortion products and pure tone threshold at f2 were measured at 51 frequencies between f2 500 hz and 8 khz at up to ten primary tone levels between l2 65 and 20 db spl in 30 normally hearing and 119 sensorineural hearing loss ears using an optimized primary tone level setting l1 0 4l2 39 db that accounts for the nonlinear interaction of the two primaries at the dpoae generation site at f2 the pressure of the 2 f1 f2 distortion product pdp is a linear function of the primary tone level l2 linear regression yields correlation coefficients higher than 0 8 in the majority of the dpoae i o functions

fine structure of the 2f1 f2 acoustic distortion product changes with primary level the fine frequency structure of the 2f1 f2 acoustic distortion product adp fine structure was examined in ten human subjects with normal hearing primary frequencies f1 and f2 were incremented in steps of 1 32 octave with an f2 f1 ratio of 1 2 the primary levels were kept equal to each other and varied from 45 to 65 db spl in 2 5 db steps the results show that the adp fine structure is characterized by a series of peaks and valleys across frequency with a peak to peak frequency spacing of about 3 32 octave and a peak to valley amplitude ratio of up to 20 db at frequencies below 4000 hz as primary level increases the sharpness of the adp fine structure is not significantly reduced and the pattern gradually shifts to lower frequencies at frequencies above 4000 hz a flattening of the pattern is sometimes observed at high levels a consequence of the underlying process responsible for the fine structure is that adp input output i o functions can be highly variable in shape dramatic shape change

reducing reflected contributions to ear canal distortion product otoacoustic emissions in humans distortion product otoacoustic emission dpoae fine structure has been attributed to the interaction of two cochlear source mechanisms distortion and reflection sources a suppressor presented near the 2f1 f2 frequency reduces the reflection source contribution and therefore dpoae fine structure optimal relationships between stimulus and suppressor conditions however have not been described in this study the relationship between suppressor level l3 and stimulus level l2 was evaluated to determine the l3 that was most effective at reducing fine structure subjects were initially screened to find individuals who produced dpoae fine structure a difference in the prevalence of fine structure in two frequency intervals was observed at 2 khz 11 of 12 subjects exhibited fine structure as compared to 5 of 22 subjects at 4 khz only subjects demonstrating fine structure participated in subsequent measurements dpoae responses were evaluated in 1 3 octave intervals centered at 2 or 4 khz with 4 subjects contributing data at each interval multiple l3 s were evaluated for each l2 which ranged from 20 to 80 db spl the results indicated that one or more l3 s at each l2 were roughly equally effective at reducing dpoae fine structure however no single l3 was effective at all l2 s in every subject

social networks evolving graphs with memory dependent edges abstract the plethora of digital communication technologies and their mass take up has resulted in a wealth of interest in social network data collection and analysis in recent years within many such networks the interactions are transient thus those networks evolve over time in this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges which may appear and disappear according to their recent history we consider time discrete and time continuous variants of the model we consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence in particular we show that such networks may continue evolving forever or else may quench and become static containing immortal and or extinct edges this depends on the existence or otherwise of certain infinite products and series involving age dependent model parameters we show how to differentiate between the alternatives based on a finite set of observations to test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data and we apply these concepts to three real networks summary data on mobile phone use from a developing region online social business network data from china and disaggregated mobile phone communications data from a reality mining experiment in the us in each case we show that there is evidence for memory dependent dynamics such as that embodied within the class of models proposed here

measuring distortion product otoacoustic emissions using continuously sweeping primaries distortion product otoacoustic emission dpoae level from normal hearing individuals can vary by as much as 30db with small frequency changes a phenomenon known as dpoae fine structure this fine structure is hypothesized to stem from the interaction of components from two different regions of the cochlea the nonlinear generator region and the reflection component from the dp region an efficient procedure to separate these two components would improve the clinical and research utility of dpoae by permitting separate evaluation of different cochlea regions in this paper two procedures for evaluating dpoae fine structure are compared dpoae generated by fixed frequency primaries versus continuously sweeping primaries the sweep dpoae data are analyzed with a least squares fit filter sweep rates of greater than 8s per octave permit rapid evaluation of the cochlear fine structure a higher sweep rate of 2s per octave provided dpoae without fine structure under these conditions the longer latency reflection component falls outside the range of the filter consequently dpoae obtained with sweeping tones can be used either to get more rapid estimates of dpoae fine structure or to obtain estimates of dpoae from the generator region uncontaminated by energy from the reflection region

multiresolution community detection for megascale networks by information based replica correlations we use a potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph our multiresolution algorithm calculates correlations among multiple copies replicas of the same graph over a range of resolutions significant multiresolution structures are identified by strongly correlated replicas the average normalized mutual information the variation in information and other measures in principle give a quantitative estimate of the best resolutions and indicate the relative strength of the structures in the graph because the method is based on information comparisons it can in principle be used with any community detection model that can examine multiple resolutions our approach may be extended to other optimization problems as a local measure our potts model avoids the resolution limit that affects other popular models with this model our community detection algorithm has an accuracy that ranks among the best of currently available methods using it we can examine graphs over 40 ifmmode times else texttimes fi 10 6 nodes and more than 1 ifmmode times else texttimes fi 10 9 edges we further report that the multiresolution variant of our algorithm can solve systems of at least 200 text 000 nodes and 10 ifmmode times else texttimes fi 10 6 edges on a single processor with exceptionally high accuracy for typical cases we find a superlinear scaling o l 1 3 for community detection and o l 1 3 text text log text n for the multiresolution algorithm where l is the number of edges and n is the number of nodes in the system

line graphs link partitions and overlapping communities in this paper we use a partition of the links of a network in order to uncover its community structure this approach allows for communities to overlap at nodes so that nodes may be in more than one community we do this by making a node partition of the line graph of the original network in this way we show that any algorithm that produces a partition of nodes can be used to produce a partition of links we discuss the role of the degree heterogeneity and propose a weighted version of the line graph in order to account for this

relation of distortion product otoacoustic emission input output functions to loudness the aim of this study is to further explore the relationship between distortion product otoacoustic emission dpoae measurements and categorical loudness scaling cls measurements using multiple linear regression mlr analysis recently thorson et al j acoust soc am 131 1282 1295 2012 obtained predictions of cls loudness ratings from dpoae input output i o functions using mlr analysis the present study extends that work by 1 considering two different and potentially improved mlr models one for predicting loudness rating at specified input level and the other for predicting the input level for each loudness category and 2 validating the new models predictions using an independent set of data strong correlations were obtained between predicted and measured data during the validation process with overall root mean square errors in the range 10 43 16 78 db for the prediction of cls input level supporting the view that dpoae i o measurements can predict cls loudness ratings and input levels and thus may be useful for fitting hearing aids

uncovering the detailed structure of the algebra formed by the invariant charges of closed bosonic strings moving in 1 2 dimensional minkowski space for the nambu goto theory of closed bosonic strings moving in three space time dimensions generating relations of degree 6 for the poisson algebra of the infinitesimal generators of observable symmetry transformations have been computed these computations result in a deeper insight into the structure of the symmetry algebra in addition a parametrization of the quantum corrections for the generating relations of degree 3 is given

group theoretical quantization of 2 1 gravity in the metric torus sector a symmetry based quantization method of reparametrization invariant systems is described it will work for all systems that possess complete sets of perennials whose lie algebras close and those that generate sufficiently large symmetry groups the construction leads to a quantum theory including a hilbert space a complete system of operator observables and a unitary time evolution the method is applied to the 2 1 gravity the paper is restricted to the metric torus sector zero cosmological constant and it makes strong use of the so called homogeneous gauge the chosen algebra of perennials is that of martin two frequent problems are tackled first the lie algebra of perennials does not generate a group of symmetries the notion of group completion of a reparametrization invariant system is introduced so that the group does act the group completion of the physical phase space of our model is shown to add only some limit points to it so that the ranges of observables are not unduly changed second a relatively large number of relations between observables exists they are transferred to the quantum theory by the well known methods of kostant and kirillov in this way a uniqueness of the physical representation of some extension of martin s algebra is shown the hamiltonian is defined by a systematic procedure due to dirac for the torus sector the result coincides with that by moncrief the construction may be extended to higher genera and nonzero of the 2 1 gravity because some complete sets of perennials are well known and there are no obstructions to the closure of the algebra

correspondence between behavioral and individually optimized otoacoustic emission estimates of human cochlear input output curves previous studies have shown a high within subject correspondence between distortion product otoacoustic emission dpoae input output i o curves and behaviorally inferred basilar membrane bm i o curves for frequencies above 2 khz for lower frequencies dpoae i o curves contained notches and plateaus that did not have a counterpart in corresponding behavioral curves it was hypothesized that this might improve by using individualized optimal dpoae primary levels here data from previous studies are re analyzed to test this hypothesis by comparing behaviorally inferred bm i o curves and dpoae i o curves measured with well established group average primary levels and two individualized primary level rules one optimized to maximize dpoae levels and one intended for primaries to evoke comparable bm responses at the f2 cochlear region test frequencies were 0 5 1 and 4 khz behavioral i o curves were obtained from temporal forward masking curves results showed high within subject correspondence between behavioral and dpoae i o curves at 4 khz only regardless of the primary level rule plateaus and notches were equally common in low frequency dpoae i o curves for individualized and group average dpoae primary levels at 0 5 and 1 khz results are discussed in terms of the adequacy of dpoae i o curves for inferring individual cochlear nonlinearity characteristics

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

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

reliability of distortion product otoacoustic emissions and their relation to loudness the reliability of distortion product otoacoustic emission dpoae measurements and their relation to loudness measurements was examined in 16 normal hearing subjects and 58 subjects with hearing loss the level of the distortion product l d was compared across two sessions and resulted in correlations that exceeded 0 90 the reliability of dpoaes was less when parameters from nonlinear fits to the input output i o functions were compared across visits next the relationship between dpoae i o parameters and the slope of the low level portion of the categorical loudness scaling cls function soft slope was assessed correlations of 0 65 0 74 and 0 81 at 1 2 and 4 khz were observed between cls soft slope and combined dpoae parameters behavioral threshold had correlations of 0 82 0 83 and 0 88 at 1 2 and 4 khz with cls soft slope combining dpoaes and behavioral threshold provided little additional information lastly a multivariate approach utilizing the entire dpoae i o function was used to predict the cls rating for each input level db spl standard error of the estimate when using this method ranged from 2 4 to 3 0 categorical units cu suggesting that dpoae i o functions can predict cls measures within the cu step size used in this study 5

subgraphs and network motifs in geometric networks many real world networks describe systems in which interactions decay with the distance between nodes examples include systems constrained in real space such as transportation and communication networks as well as systems constrained in abstract spaces such as multivariate biological or economic data sets and models of social networks these networks often display network motifs subgraphs that recur in the network much more often than in randomized networks to understand the origin of the network motifs in these networks it is important to study the subgraphs and network motifs that arise solely from geometric constraints to address this we analyze geometric network models in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes we present analytical solutions for the numbers of all three and four node subgraphs in both directed and nondirected geometric networks we also analyze geometric networks with arbitrary degree sequences and models with a bias for directed edges in one direction scaling rules for scaling of subgraph numbers with system size lattice dimension and interaction range are given several invariant measures are found such as the ratio of feedback and feed forward loops which do not depend on system size dimension or connectivity function we find that network motifs in many real world networks including social networks and neuronal networks are not captured solely by these geometric models this is in line with recent evidence that biological network motifs were selected as basic circuit elements with defined information processing functions

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

distortion product otoacoustic emissions cochlear source contributions and clinical test performance it has been proposed that the clinical accuracy of distortion product otoacoustic emissions dpoaes is affected by the interaction of distortion and reflection sources contributing to the response this study evaluated changes in dichotomous decision test performance and threshold prediction accuracy when dpoae source contribution was controlled data were obtained from 205 normal and impaired ears with l2 ranging from 0 to 80db spl and f2 2 and 4khz data were collected for control conditions no suppressor f3 and with f3 presented at three levels that previously had been shown to reduce the reflection source contribution the results indicated that controlling source contribution with a suppressor did not improve diagnostic accuracy as reflected by relative operating characteristic curve area and frequently resulted in poorer test performance compared to control conditions likewise correlations between dpoae and behavioral thresholds were not strengthened when using the suppressors to control sou

distance measures for dynamic citation networks abstract acyclic digraphs arise in many natural and artificial processes among the broader set dynamic citation networks represent an important type of acyclic digraph for example the study of such networks includes the spread of ideas through academic citations the spread of innovation through patent citations and the development of precedent in common law systems the specific dynamics that produce such acyclic digraphs not only differentiate them from other classes of graphs but also provide guidance for the development of meaningful distance measures in this article we develop and apply our sink distance measure together with the single linkage hierarchical clustering algorithm to both a two dimensional directed preferential attachment model as well as empirical data drawn from the first quarter century of decisions of the united states supreme court despite applying the simplest combination of distance measure and clustering algorithm analysis reveals that more accurate and more interpretable clusterings are produced by this scheme

finding local community structure in networks although the inference of global community structure in networks has recently become a topic of great interest in the physics community all such algorithms require that the graph be completely known here we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time this algorithm runs in time o k2d for general graphs when d is the mean degree and k is the number of vertices to be explored for graphs where exploring a new vertex is time consuming the running time is linear o k we show that on computer generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge as an application we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer

cochlear generation of intermodulation distortion revealed by dpoae frequency functions in normal and impaired ears distortion product otoacoustic emission dpoae frequency functions were measured in normal hearing and hearing impaired ears a fixed f2 swept f1 paradigm was used with f2 fixed at half octave intervals from 1 to 8 khz l1 was always 10 db greater than l2 and l2 was varied from 65 to 10 db spl in 5 db steps the responses were quantified by the frequency and amplitude of the peak response peak responses were closer to f2 in higher frequency regions and for lower intensity stimulation results from hearing impaired subjects suggest that audiometric thresholds at the distortion product frequency fdp in addition to hearing status at f2 can affect dpoae results results are discussed in terms of several manifestations of a second resonance model as well as a dual source model for the generation of dpoaes as measured in the ear canal of humans it appears that a dual source model accounts for the data better than second filter models

when are networks truly modular abstract the study of cluster or community structure of complex networks contributes to the understanding of networks at a functional level in many networks latent classes of nodes are suspected which manifest themselves as communities i e groups of nodes with a high link density among the nodes of the same class and low link density between nodes of different classes community detection algorithms are used to infer these classes e g by finding a partition of the network which maximizes a quality function such as the network modularity q m newman m girvan finding and evaluating community structure in networks phys rev e 69 2004 026113 however it is known from numerical experiments that even purely random networks display intrinsic modularity and may be partitioned yielding high values of q extending on our earlier results j reichardt s bornholdt statistical mechanics of community detection phys rev e 74 2006 016110 the mapping of the community detection problem onto finding the ground state of a spin glass is exploited in order to derive analytical expressions for the expected modularity in random graphs and assess the theoretical limits to community detection the results are independent of any specific community detection algorithm and allow for differentiation between modularity arising purely due to the search process in the large configuration space of possible partitionings on the one hand or due to the actual presence of different classes of nodes on the other hand

sources of variability in distortion product otoacoustic emissions the goal of this study was to determine the extent to which the variability seen in distortion product otoacoustic emissions dpoaes among ears with normal hearing could be accounted for several factors were selected for investigation including behavioral threshold differences in middle ear transmission characteristics either in the forward or the reverse direction and differences in contributions from the distortion and reflection sources these variables were assessed after optimizing stimulus parameters for individual ears at each frequency a multiple linear regression was performed to identify whether the selected variables either individually or in combination explained significant portions of variability in dpoae responses behavioral threshold at the f2 frequency and behavioral threshold squared at that same frequency explained the largest amount of variability in dpoae level compared to the other variables the combined model explained a small but significant amount of variance in dpoae level at five frequencies a large amount of residual variability remained even at frequencies where the model accounted for significant amounts of variance

the use of distortion product otoacoustic emission suppression as an estimate of response growth distortion product otoacoustic emission dpoae levels in response to primary pairs f2 2 or 4 khz l2 ranging from 20 to 60 db spl l1 0 4l2 39 db were measured with and without suppressor tones f3 which varied from 1 octave below to 12 octave above f2 in normal hearing subjects suppressor level l3 varied from 5 to 85 db spl dpoae levels were converted into decrements by subtracting the level in the presence of the suppressor from the level in the absence of a suppressor dpoae decrement vs l3 functions showed steeper slopes when f3 f2 this pattern is similar to other measurements of response growth such as direct measures of basilar membrane motion single unit rate level functions suppression of basilar membrane motion and discharge rate suppression from lower animals as l2 increased the l3 necessary to maintain 3 db of suppression increased at a rate of about 1 db db when f3 was approximately equal to f2 but increased more slowly when f3 f2 functions r

detection of community structures in networks via global optimization abstract we present an analysis of communality structure in networks based on the application of simulated annealing techniques in this case we use as cost function the already introduced modularity q 1 which is based on the relative number of links within a commune against the number of links that would correspond in case the links were distributed randomly we compare the results of our approach against other methodologies based on betweenness analysis and show that in all cases a better community structure can be attained

the invariant charges of the nambu goto theory in wkb approximation renormalization we discuss the one loop renormalization of the reparametrization invariant non local conserved charges of the nambu goto string theory in addition we show the stability of a special well known state under the corresponding infinitesimal symmetry transformations at least in the wkb approximation

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

algebraic properties of the invariant charges of the nambu goto theory we analyse the infinite dimensional algebra of observable non local integrals of motion of the nambu goto string theory

modularity from fluctuations in random graphs and complex networks the mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection we show that finding the modularity of a network is analogous to finding the ground state energy of a spin system moreover we demonstrate that due to fluctuations stochastic network models give rise to modular networks specifically we show both numerically and analytically that random graphs and scale free networks have modularity we argue that this fact must be taken into consideration to define statistically significant modularity in complex networks

distortion product otoacoustic emission measured with continuously varying stimulus level distortion product otoacoustic emissions dpoae are measured by stimulating the ear with two simultaneous tones a novel method for measuring dpoaes has been developed in which the tone levels vary continuously instead of in discrete steps varying the tone levels continuously may offer advantages for characterizing dpoae level as a function of stimulus level for equivalent primary levels dpoae levels measured with the continuous level method were the same as levels obtained with the discrete level method thus validating the new method continuous level measurements were used to determine the optimal l1 for each l2 in individual subjects n 20 at f2 1 2 4 and 8 khz by using a lissajous path that covered a wide range of stimulus levels the optimal l1 defined as the l1 that resulted in the largest dpoae for each l2 varied across subjects and across frequency the optimal difference between l1 and l2 decreased with increasing l2 at all frequencies and increased with frequency when l2 was low whe

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

evaluating transport in irregular pore networks a general approach for investigating transport phenomena in porous media is presented this approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort the overall method combines a generalized effective medium approximation ema with a macroscopic continuum model in order to derive a transport equation with explicit analytical expressions for the transport coefficients the proposed form of the ema is an anisotropic and heterogeneous extension of kirkpatrick s ema which allows the overall model to account for microscopic alterations in connectivity with the locations of the pores and the orientation and length of the throat as well as macroscopic variations in transport properties a comparison to numerical results for randomly generated networks with different properties is given indicating the potential for this methodology to handle cases that would pose significant difficulties to many other analytical models

inversion method for content based networks in this paper we generalize a recently introduced expectation maximization em method for graphs and apply it to content based networks the em method provides a classification of the nodes of a graph and allows one to infer relations between the different classes content based networks are ideal models for graphs displaying any kind of community and or multipartite structure we show both numerically and analytically that the generalized em method is able to recover the process that led to the generation of such networks we also investigate the conditions under which our generalized em method can recover the underlying contentbased structure in the presence of randomness in the connections two entropies sq and sc are defined to measure the quality of the node classification and to what extent the connectivity of a given network is content based sq and sc are also useful in determining the number of classes for which the classification is optimal

the invariant charges of the nambu goto theory their geometric origin and their completeness we give an alternative construction of the reparametrization invariant non local conserved charges of the nambu goto theory which elucidates their geometric nature and their completeness property

the poisson algebra of the invariant charges of the nambu goto theory casimir elements the reparametrization invariant non local conserved charges of the nambu goto theory form an algebra under poisson bracket operation the center of the formal closure of this algebra is determined the relation of the central elements to the constraints of the nambu goto theory is clarified

identification of overlapping community structure in complex networks using fuzzy c means clustering abstract identification of overlapping communities clusters in a complex network is a general problem in data mining of network data sets in this paper we devise a novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing ng s q function an approximation mapping of network nodes into euclidean space and fuzzy c means clustering experimental results indicate that the new algorithm is efficient at detecting both good clusterings and the appropriate number of clusters

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

level dependence of the nonlinear distortion component of distortion product otoacoustic emissions in humans distortion product otoacoustic emissions dpoaes emerge when presenting two primary tones with different frequencies f1 and f2 to the cochlea and are commonly used in diagnosis and research to evaluate the functional state of the cochlea optimal primary tone stimulus levels accounting for the different level dependencies of the traveling wave amplitudes of the two primary tones near the f2 tonotopic place on the basilar membrane are often used to maximize dpoae amplitudes however parameters defining the optimal levels can be affected by wave interference between the nonlinear distortion and coherent reflection components of the dpoae here the components were separated in the time domain using a pulsed stimulus paradigm and optimal levels determined based on the amplitude dependence of the nonlinear distortion components on primary tone stimulus levels level parameters yielding maximum dpoae amplitudes were derived for six normal hearing adults and compared to data recorded with continuous two tone stimulation the level parameters resulting from analysis of the nonlinear distortion components show dependence on stimulus frequency and small standard deviations dpoae input output functions derived for optimal levels exhibit larger slopes wider dynamic range and less variability across subjects than those derived for conventional stimulus and analysis conditions potentially increasing their reliability and sensitivity for assessing cochlea function

input output functions of the nonlinear distortion component of distortion product otoacoustic emissions in normal and hearing impaired human ears distortion product otoacoustic emissions dpoaes arise in the cochlea in response to two tones with frequencies f1 and f2 and mainly consist of two components a nonlinear distortion and a coherent reflection component wave interference between these components limits the accuracy of dpoaes when evaluating the function of the cochlea with conventional continuous stimulus tones here dpoae components are separated in the time domain from dpoae signals elicited with short stimulus pulses the extracted nonlinear distortion components are used to derive estimated distortion product thresholds edpts from semi logarithmic input output i o functions for 20 normal hearing and 21 hearing impaired subjects i o functions were measured with frequency specific stimulus levels at eight frequencies f2 1 8 khz f2 f1 1 2 for comparison dpoaes were also elicited with continuous primary tones both acquisition paradigms yielded edpts which significantly correlated with behavioral thresholds p 0 001

further efforts to predict pure tone thresholds from distortion product otoacoustic emission input output functions recently boege and janssen j acoust soc am 111 1810 1818 2002 fit linear equations to distortion product otoacoustic emission dpoae input output i o functions after the dpoae level in db spl was converted into pressure in pa significant correlations were observed between these dpoae thresholds and audiometric thresholds the present study extends their work by 1 evaluating the effect of frequency 2 determining the behavioral thresholds in those conditions that did not meet inclusion criteria and 3 including a wider range of stimulus levels dpoae i o functions were measured in as many as 278 ears of subjects with normal and impaired hearing nine f2 frequencies 500 to 8000 hz in 12 octave steps were used l2 ranged from 10 to 85 db spl 5 db steps and l1 was set according to the equation l1 0 4l2 39 db kummer et al j acoust soc am 103 3431 3444 1998 for l2 levels up to 65 db spl beyond which l1 l2 for the same conditions as those used by boege and janssen we o

the algebra formed by the invariant charges of the nambu goto theory identification of a maximal abelian subalgebra continuing the analysis of the algebraic structure of the invariant charges of the nambu goto theory we identify a complete set of commuting observables for the bosonic strings

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

detect local communities in networks with an outside rate coefficient abstract in this paper we present a local method for detecting communities in networks we define an outside rate coefficient o u t in our method o u t has a very simple form and is easy to calculate the local community enclosing a starting node can be detected by agglomerating the node with the smallest o u t at each time step when there are two or more nodes having the same smallest outside rate coefficient o u t we agglomerate the node with the largest k i n this operation is remarkably beneficial to the accuracy of our method and simulations on benchmark networks and real networks demonstrate that our local method is efficient to detect communities in networks

partitioning and modularity of graphs with arbitrary degree distribution we solve the graph bipartitioning problem in dense graphs with arbitrary degree distribution using the replica method we find the cut size to scale universally with k in contrast earlier results studying the problem in graphs with a poissonian degree distribution had found a scaling with kfu and anderson j phys a 19 1605 1986 our results also generalize to the problem of q partitioning they can be used to find the expected modularity q newman and girvan phys rev e 69 026113 2004 of random graphs and allow for the assessment of the statistical significance of the output of community detection algorithms given a graph or network gn m of n nodes and m edges the problem of graph partitioning is finding a partition of the nodes into q equal sized parts such that the number of edges connecting different parts the cut size is minimal the solution of this problem has many important practical applications in multiprocessor scheduling for parallel computing very large scale integrated chip design vlsi and data mining 1 due to the problem being np complete 2 i e no algorithm is known which is guaranteed to find an optimal solution in a number of steps that grows only polynomially with the size of the graph only heuristics exist to approximate a solution furthermore one cannot determine in polynomial time whether a solution found is indeed optimal the only way to assess the quality of a heuristic algorithm or a particular result is to compare with rigorous bounds on the cut size

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