a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

hamiltonian dynamics of preferential attachment prediction and control of network dynamics are grand challenge problems in network science the lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades here we study the dynamics of networks evolving according to preferential attachment pa known to approximate well the large scale growth dynamics of a variety of real networks we show that this dynamics is hamiltonian thus casting the study of complex networks dynamics to the powerful canonical formalism in which the time evolution of a dynamical system is described by hamilton s equations we derive the explicit form of the hamiltonian that governs network growth in pa this hamiltonian turns out to be nearly identical to graph energy in the configuration model which shows that the ensemble of random graphs generated by pa is nearly identical to the ensemble of random graphs with scale free degree distributions in other words pa generates nothing but random graphs with power law degree distribution the extension of the developed canonical formalism for network analysis to richer geometric network models with non degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales

connectivity degrees in the threshold preferential attachment model abstract in this paper we present a study of the connectivity degrees of the threshold preferential attachment model a generalization of the barabasi albert model to heterogeneous complex networks the threshold model incorporates the states of the nodes in its preferential linking rule and assumes that the affinity between network nodes follows an inverse relationship with the distance between their states we numerically analyze the connectivity degrees of the model studying the influence of the main parameters on the distribution of connectivity degrees and its statistics the average degree and highest degree of the network we show that such statistics exhibit markedly different behaviors in the dependence on the model parameters particularly as regards the interaction threshold nevertheless we show that the two statistics converge in the limit of null threshold and often exhibit scaling that can be described by power laws of the model parameters

clustering of random scale free networks we derive the finite size dependence of the clustering coefficient of scale free random graphs generated by the configuration model with degree distribution exponent 2l ensuremath gamma l3 degree heterogeneity increases the presence of triangles in the network up to levels that compare to those found in many real networks even for extremely large nets we also find that for values of ensuremath gamma ensuremath approx 2 clustering is virtually size independent and at the same time becomes a de facto non self averaging topological property this implies that a single instance network is not representative of the ensemble even for very large network sizes

statistical mechanics of multiedge networks statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones there are however subtle yet important considerations to be made regarding the nature of the weights used in this generalization weights can be either continuous or discrete magnitudes and in the latter case they can additionally have undistinguishable or distinguishable nature this fact has not been addressed in the literature insofar and has deep implications on the network statistics in this work we face this problem introducing multiedge networks as graphs where multiple distinguishable connections between nodes are considered we develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection the latter case is particularly interesting as we show that binary projections can be understood from multiedge processes the implications of these results are important as many real agent based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

efficient planar affine canonicalization abstract this paper presents a fast and accurate affine canonicalization method for planar shapes this method improves on previous ones based on iterative optimization that produce multiple canonical versions canonicalization provides a common reference frame for shape comparison without the loss of discrimination ability often caused by invariant features it also gives for free the alignment transformation between any pair of shapes the proposed method is based on the properties of the joint angular distribution of marginal skewness and kurtosis the so called sk signature which can be efficiently computed in closed form from the raw image moments the experiments demonstrate that the method is robust to the non affine distortions caused by natural perspective image conditions thus it can be used as an automatic preprocessing step to add affine invariance in statistical pattern recognition applications

robust similarity registration technique for volumetric shapes represented by characteristic functions this paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by characteristic functions cfs here the calculation of rotation parameters is considered as a spherical cross correlation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis pca thus fast fourier transform fft is employed to vastly improve efficiency and robustness geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters it is numerically demonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses further validation of our method is performed by registering a lung database highlightswe propose a similarity registration method that registers volumetric shapes the method naturally handles shapes with topological differences the method is validated by registering a lung database the method can be applied to shape based image segmentation

highly clustered scale free networks we propose a model for growing networks based on a finite memory of the nodes the model shows stylized features of real world networks power law distribution of degree linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate notably the degree distribution is conserved even though only the most recently grown part of the network is considered as the network grows the clustering reaches an asymptotic value larger than that for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors coauthorship in science and word synonyms these highly clustered scale free networks indicate that memory effects are crucial for a correct description of the dynamics of growing networks

compactly supported radial basis functions based collocation method for level set evolution in image segmentation the partial differential equation driving level set evolution in segmentation is usually solved using finite differences schemes in this paper we propose an alternative scheme based on radial basis functions rbfs collocation this approach provides a continuous representation of both the implicit function and its zero level set we show that compactly supported rbfs csrbfs are particularly well suited to collocation in the framework of segmentation in addition csrbfs allow us to reduce the computation cost using a kd tree based strategy for neighborhood representation moreover we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1 norm of the csrbf parameters as a consequence the final solution is topologically more flexible and may develop new contours i e new zero level components which are difficult to obtain using reinitialization the behavior of this approach is evaluated from numerical simulations and from medical data of various kinds such as 3 d ct bone images and echocardiographic ultrasound images

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

spin models on random graphs with controlled topologies beyond degree constraints we study ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution p k can be chosen arbitrarily but which allows for further fine tuning of the topology via preferential attachment of edges on the basis of an arbitrary function q k k of the degrees of the vertices involved we solve these models using finite connectivity equilibrium replica theory within the replica symmetric ansatz in our ensemble of graphs phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution but also on the choice made for q k k the increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real world interacting particle systems by spin systems on suitably defined random graphs

rate equation approach for correlations in growing network models we propose a rate equation approach to compute two vertex correlations in scale free growing network models based on the preferential attachment mechanism the formalism based on previous work of szabo et al fphys rev e 67 056102 s2002dg for the clustering spectrum measuring three vertex correlations is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k with an appropriate boundary condition we study the properties of both two and three vertex correlations for linear preferential attachment models and also for a model yielding a large clustering coefficient the expressions obtained are checked by means of extensive numerical simulations the rate equation proposed can be generalized to more sophisticated growing network models and also extended to deal with related correlation measures as an example we consider the case of a recently proposed model of weighted networks for which we are able to compute a weighted two vertex correlation function taking into account the strength of the interactions between connected vertices

scale free property of directed networks with two intrinsic node weights abstract this paper proposes a network model to understand the scale free property of directed networks the proposed model assigns two intrinsic variables incoming and outgoing weights to every node a directed link is established from node i to node j if the sum of the outgoing weight of node i and the incoming weight of node j exceeds a predetermined threshold the proposed model allows us to know the exact analytical expressions for degree distributions and clustering we analytically find that the in degree and out degree distributions have power law tails and their scaling exponents are controllable within the range 1 the average clustering coefficient of nodes with out degree or in degree n also has a power law tail as a function of n we also find that the scaling exponent of the clustering coefficient depends on the correlation between incoming and outgoing weights

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

correlated random networks we develop a statistical theory of networks a network is a set of vertices and links given by its adjacency matrix c and the relevant statistical ensembles are defined in terms of a partition function z summation operator exp betah c the simplest cases are uncorrelated random networks such as the well known erdos renyi graphs here we study more general interactions h c which lead to correlations for example between the connectivities of adjacent vertices in particular such correlations occur in optimized networks described by partition functions in the limit beta infinity they are argued to be a crucial signature of evolutionary design in biological networks

what big data tells sampling the social network by communication channels big data has become the primary source of understanding the structure and dynamics of the society at large scale the network of social interactions can be considered as a multiplex where each layer corresponds to one communication channel and the aggregate of all of them constitutes the entire social network however usually one has information only about one of the channels or even a part of it which should be considered as a subset or sample of the whole here we introduce a model based on a natural bilateral communication channel selection mechanism which for one channel leads to consistent changes in the network properties for example while it is expected that the degree distribution of the whole social network has a maximum at a value larger than one we get a monotonically decreasing distribution as observed in empirical studies of single channel data we also find that assortativity may occur or get strengthened due to the sampling method we analyze the far reaching consequences of our findings

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

shape tracking with occlusions via coarse to fine region based sobolev descent we present a method to track the shape of an object from video the method uses a joint shape and appearance model of the object which is propagated to match shape and radiance in subsequent frames determining object shape self occlusions and dis occlusions of the object from camera and object motion pose difficulties to joint shape and appearance models in tracking they are unable to adapt to new shape and appearance information leading to inaccurate shape detection in this work we model self occlusions and dis occlusions in a joint shape and appearance tracking framework self occlusions and the warp to propagate the model are coupled thus we formulate a joint optimization problem we derive a coarse to fine optimization method advantageous in tracking that initially perturbs the model by coarse perturbations before transitioning to finer scale perturbations seamlessly this coarse to fine behavior is automatically induced by gradient descent on a novel infinite dimensional riemannian manifold that we introduce the manifold consists of planar parameterized regions and the metric that we introduce is a novel sobolev metric experiments on video exhibiting occlusions dis occlusions complex radiance and background show that occlusion dis occlusion modeling leads to superior shape accuracy

prior knowledge level set representations visual grouping in this paper we propose a level set method for shape driven object extraction we introduce a voxel wise probabilistic level set formulation to account for prior knowledge to this end objects are represented in an implicit form constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation the optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image upon convergence a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered promising experimental results demonstrate the potential of such an approach

scale free networks in evolution abstract in this paper we address the emergence of scale free behavior in a simple evolutionary model we model a growing population that starts from a small number of genotypes and then starts to grow due to an unlimited amount of available resources these genotypes are subjected to the action of natural selection and mutation and increase in number according to their malthusian rates we show that the distribution of links for the genotypes is well described by a scale free distribution this is an evidence that combinatorial optimization processes can yield scale free patterns

the number of small amplitude limit cycles in arbitrary polynomial systems abstract in this paper we study the number of small amplitude limit cycles in arbitrary polynomial systems it is found that almost all the results for the number of small amplitude limit cycles are obtained by calculating lyapunov constants and determining the order of the corresponding hopf bifurcation it is well known that the difficulty in calculating the lyapunov constants increases with the increasing of the degree of polynomial systems so it is necessary and valuable for us to achieve some general results about the number of small amplitude limit cycles in arbitrary polynomial systems with degree m which is denoted by m m in this paper by applying the method developed by c christopher and n lloyd in 1995 and m han and j li in 2012 we first obtain the lower bounds for m 6 m 14 and then prove that m m m 2 if m 23 finally we obtain that m m grows as least as rapidly as 18 25 1 2 ln 2 m 2 2 ln m 2 for all large m it is proved by m han j li lower bounds for the hilbert number of polynomial systems j differential equations 252 2012 3278 3304 that the number of all limit cycles in arbitrary polynomial systems with degree m grows as least as rapidly as 1 2 ln 2 m 2 2 ln m 2

general formalism for inhomogeneous random graphs we present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models where vertices come in different types and the probability of realizing an edge depends on the types of its terminal vertices this approach provides a general framework for the analysis of a large class of models the generic phase structure is derived using generating function techniques and relations to other classes of models are pointed out

generating multi scaling networks with two types of vertices abstract a variety of scale free networks have been created since the pioneer work by barabasi and albert science 286 1999 509 most of these models are homogeneous since they are composed of the same kind of nodes in the realistic world however elements nodes or vertices in the network may play different roles or have different functions in this work we develop an alternative way of vertex classification other than the ordinary modularity method by introducing two types of vertices the interaction between two neighbor vertices is dependent on their types it is found that the vertex degree exhibits a multi scaling law distribution with the scaling exponent of each types of vertex adjustable this network model may exhibit some interesting properties concerning the dynamical processes on it

direct estimation of nonrigid registrations with image based self occlusion reasoning the registration problem for images of a deforming surface has been well studied external occlusions are usually well handled in 2d image based registration self occlusions are more challenging consequently the surface is usually assumed to be only slightly self occluding this paper is about image based nonrigid registration with self occlusion reasoning a specific framework explicitly modeling self occlusions is proposed it is combined with an intensity based ldquodirectrdquo data term for registration self occlusions are detected as shrinkage areas in the 2d warp experimental results on several challenging data sets show that our approach successfully registers images with self occlusions while effectively detecting the self occluded regions

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

error threshold transition in the random energy model we perform a statistical analysis of the error threshold transition in quasispecies evolution on a random energy fitness landscape we obtain a precise description of the genealogical properties of the population through extensive numerical simulations we find a clear phase transition and can distinguish two regimes of evolution the first for low mutation rates is characterized by strong selection and the second for high mutation rates is characterized by quasineutral evolution

vertex intrinsic fitness how to produce arbitrary scale free networks we study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness the vertex fitnesses are drawn from a given probability distribution density the edges between pairs of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved we study here different choices for the probability distribution densities and the linking functions we find that irrespective of the particular choices the generation of scale free networks is straightforward we then derive the general conditions under which scale free behavior appears this model could then represent a possible explanation for the ubiquity and robustness of such structures

a spatial weighted network model based on optimal expected traffic abstract we propose a spatial weighted network model based on the optimal expected traffic the expected traffic represents the prediction of the flow created by two vertices and is calculated by the improved gravity equation the model maximizes the total expected traffic of the network by changing two parameters which control the fitness and the geographical constraints the model can vary its topology and give rise to a variety of statistical properties observed in the real world network notably our study shows that a linear and a nonlinear strength degree correlation can emerge when considering and neglecting the transport effect respectively

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

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

point set registration coherent point drift point set registration is a key component in many computer vision tasks the goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other multiple factors including an unknown nonrigid spatial transformation large dimensionality of point set noise and outliers make the point set registration a challenging problem we introduce a probabilistic method called the coherent point drift cpd algorithm for both rigid and nonrigid point set registration we consider the alignment of two point sets as a probability density estimation problem we fit the gaussian mixture model gmm centroids representing the first point set to the data the second point set by maximizing the likelihood we force the gmm centroids to move coherently as a group to preserve the topological structure of the point sets in the rigid case we impose the coherence constraint by reparameterization of gmm centroid locations with rigid parameters and derive a closed form solution of the maximization step of the em algorithm in arbitrary dimensions in the nonrigid case we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation we also introduce a fast algorithm that reduces the method computation complexity to linear we test the cpd algorithm for both rigid and nonrigid transformations in the presence of noise outliers and missing points where cpd shows accurate results and outperforms current state of the art methods

tuning clustering in random networks with arbitrary degree distributions we present a generator of random networks where both the degree dependent clustering coefficient and the degree distribution are tunable following the same philosophy as in the configuration model the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori the algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs the procedure unveils an universal relation among clustering and degree degree correlations for all networks where the level of assortativity establishes an upper limit to the level of clustering maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior correlation measures in real networks are seen to observe this structural bound

surveying network community structure in the hidden metric space abstract most real world networks from various fields share a universal topological property as community structure in this paper we propose a node similarity based mechanism to explore the formation of modular networks by applying the concept of hidden metric spaces of complex networks it is demonstrated that network community structure could be formed according to node similarity in the underlying hidden metric space to clarify this we generate a set of observed networks using a typical kind of hidden metric space model by detecting and analyzing corresponding communities both in the observed network and the hidden space we show that the values of the fitness are rather close and the assignments of nodes for these two kinds of community structures detected based on the fitness parameter are extremely matching ones furthermore our research also shows that networks with strong clustering tend to display prominent community structures with large values of network modularity and fitness

approximately global optimization for robust alignment of generalized shapes in this paper we introduce a novel method to solve shape alignment problems we use gray scale images to represent source shapes and propose a novel two component gaussian mixture gm distance map representation for target shapes this asymmetric representation is a flexible image based representation which is able to represent different kinds of shape data including continuous contours unstructured sparse point sets edge maps and even gray scale gradient maps using this representation a new energy function based on a novel two component gaussian mixture distance model is proposed the new energy function was empirically evaluated to be a more robust shape dissimilarity metric that can be computed efficiently such high efficiency is essential for global optimization methods we adopt and modify one of them the particle swarm optimization pso to effectively estimate the global optimum of the new energy function differently from the original pso several new strategies were employed to make the optimization more robust and prevent it from converging prematurely the overall performance of the proposed framework as well as the properties of each algorithmic component were evaluated and compared with those of some state of the art methods extensive experiments and comparison performed on generalized 2d and 3d shape data demonstrate the robustness and effectiveness of the method

registration with uncertainties and statistical modeling of shapes with variable metric kernels registration and modeling of shapes are two important problems in computer vision and pattern recognition despite enormous progress made over the past decade these problems are still open in this paper we advance the state of the art in both directions first we consider an efficient registration method that aims to recover a one to one correspondence between shapes and introduce measures of uncertainties driven from the data which explain the local support of the recovered transformations to this end a free form deformation is used to describe the deformation model the transformation is combined with an objective function defined in the space of implicit functions used to represent shapes once the registration parameters have been recovered we introduce a novel technique for model building and statistical interpretation of the training examples based on a variable bandwidth kernel approach the support on the kernels varies spatially and is determined according to the uncertainties of the registration process such a technique introduces the ability to account for potential registration errors in the model hand written character recognition and knowledge based object extraction in medical images are examples of applications that demonstrate the potentials of the proposed framework

on rational cuspidal curves let c subset bold p 2 be a rational curve of degree d which has only one analytic branch at each point denote by m the maximal multiplicity of singularities of c it is proven in ms that d alpha m and this estimate is sharp the main tool used here is the logarithmic version of the bogomolov miyaoka yau inequality for curves as above we give an interpretation of this inequality in terms of the number of parameters describing curves of a given degree and the number of conditions imposed by singularity types

correlation structure of the landscape of the graph bipartitioning problem the relaxation of random walks and the autocorrelation function on the landscape of the graph bipartitioning problem are calculated

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

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

langevin approach for the dynamics of the contact process on annealed scale free networks we study the dynamics of the contact process one of the simplest nonequilibrium stochastic processes taking place on a scale free network we consider the network topology as annealed i e all links are rewired at each microscopic time step so that no dynamical correlation can build up this is a practical implementation of the absence of correlations assumed by mean field approaches we present a detailed analysis of the contact process in terms of a langevin equation including explicitly the effects of stochastic fluctuations in the number of particles in finite networks this allows us to determine analytically the survival time for spreading experiments and the density of active sites in surviving runs the fluctuations in the topological structure induce anomalous scaling effects with respect to the system size when the degree distribution has a hard upper bound when the upper bound is soft the presence of outliers with huge connectivity perturbs the picture even more inducing an apparent shift of the critical point in light of these findings recent theoretical and numerical results in the literature are critically reviewed

hyperbolic geometry of complex networks we develop a geometric framework to study the structure and function of complex networks we assume that hyperbolic geometry underlies these networks and we show that with this assumption heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry conversely we show that if a network has some metric structure and if the network degree distribution is heterogeneous then the network has an effective hyperbolic geometry underneath we then establish a mapping between our geometric framework and statistical mechanics of complex networks this mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes while the auxiliary fields coupled to edges are linear functions of these energies or distances the geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures finally we show that targeted transport processes without global topology knowledge made possible by our geometric framework are maximally efficient according to all efficiency measures in networks with strongest heterogeneity and clustering and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

shape registration in implicit spaces using information theory and free form deformations we present a novel variational and statistical approach for shape registration shapes of interest are implicitly embedded in a higher dimensional space of distance transforms in this implicit embedding space registration is formulated in a hierarchical manner the mutual information criterion supports various transformation models and is optimized to perform global registration then a b spline based incremental free form deformations iffd model is used to minimize a sum of squared differences ssd measure and further recover a dense local nonrigid registration field the key advantage of such framework is twofold 1 it naturally deals with shapes of arbitrary dimension 2d 3d or higher and arbitrary topology multiple parts closed open and 2 it preserves shape topology during local deformation and produces local registration fields that are smooth continuous and establish one to one correspondences its invariance to initial conditions is evaluated through empirical validation and various hard 2d 3d geometric shape registration examples are used to show its robustness to noise severe occlusion and missing parts we demonstrate the power of the proposed framework using two applications one for statistical modeling of anatomical structures another for 3d face scan registration and expression tracking we also compare the performance of our algorithm with that of several other well known shape registration algorithms

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

a mixture of transformed hidden markov models for elastic motion estimation elastic motion is a nonrigid motion constrained only by some degree of smoothness and continuity consequently elastic motion estimation by explicit feature matching actually contains two correlated subproblems shape registration and motion tracking which account for spatial smoothness and temporal continuity respectively if we ignore their interrelationship solving each of them alone will be rather challenging especially when the cluttered features are involved to integrate them into a probabilistic model one straightforward approach is to draw the dependence between their hidden states with regard to their separated states there are however two different explanations of motion which are still made under the individual constraint of smoothness or continuity each one can be error prone and their coupling causes error propagation therefore it is highly desirable to design a probabilistic model in which a unified state is shared by the two subproblems this paper is intended to propose such a model i e a mixture of transformed hidden markov models mthmm where a unique explanation of motion is made simultaneously under the spatiotemporal constraints as a result the mthmm could find a coherent global interpretation of elastic motion from local cluttered edge features and experiments show its robustness under ambiguities data missing and outliers

adaptive walk on complex networks we investigate the properties of adaptive walks on an uncorrelated fitness landscape which is established in sequence spaces of complex structure in particular we perform numerical simulations of adaptive walks on random graphs and scale free networks for the former we also derive some analytical approximations for the density of local optima of the fitness landscape and the mean length walk we compare our results with those obtained for regular lattices we obtain that the density of local optima decreases as 1 z where z is the mean connectivity for all networks we have investigated in random graphs the mean length walk overline l reaches the asymptotic value e ensuremath 1 for large z which corresponds to the result for regular networks although we could not find an exact estimate we derive an underestimated value for overline l unlike random graphs scale free networks show an upper asymptotic value of overline l

curve surface representation and evolution using vector level sets with application to the shape based segmentation problem in this paper we revisit the implicit front representation and evolution using the vector level set function vlsf proposed in h e abd el munim et al oct 2005 unlike conventional scalar level sets this function is designed to have a vector form the distance from any point to the nearest point on the front has components projections in the coordinate directions included in the vector function this kind of representation is used to evolve closed planar curves and 3d surfaces as well maintaining the vlsf property as the distance projections through evolution will be considered together with a detailed derivation of the vector partial differential equation pde for such evolution a shape based segmentation framework will be demonstrated as an application of the given implicit representation the proposed level set function system will be used to represent shapes to give a dissimilarity measure in a variational object registration process this kind of formulation permits us to better control the process of shape registration which is an important part in the shape based segmentation framework the method depends on a set of training shapes used to build a parametric shape model the color is taken into consideration besides the shape prior information the shape model is fitted to the image volume by registration through an energy minimization problem the approach overcomes the conventional methods problems like point correspondences and weighing coefficients tuning of the evolution pdes it is also suitable for multidimensional data and computationally efficient results in 2d and 3d of real and synthetic data will demonstrate the efficiency of the framework

compatibility as underlying mechanism behind the evolution of networks abstract in this work we propose a dynamic network model based on an evolutive rule called compatibility the presence of common topological properties observed in two real complex networks are well reproduced by the proposed model these results suggest that the compatibility between nodes is sufficient to generate the complexity observed in real systems even considering that the new added nodes do not have the ability to know global information of the system

entropy measures for networks toward an information theory of complex topologies the quantification of the complexity of networks is today a fundamental problem in the physics of complex systems a possible roadmap to solve the problem is via extending key concepts of information theory to networks in this rapid communication we propose how to define the shannon entropy of a network ensemble and how it relates to the gibbs and von neumann entropies of network ensembles the quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum entropy arguments and will contribute to inference problems emerging in the field of complex networks

spatial evolution character of multi objective evolutionary algorithm based on self organized criticality theory abstract this paper analyzes the spatial evolution character of multi objective evolutionary algorithms using self organized criticality theory the spatial evolution character is modeled by the statistical property of crowding distance which displays a scale free feature and a power law distribution we propose that the evolutional rule of multi objective optimization algorithms is a self organized state transition from an initial scale free state to a final scale free state the target is to get close to a critical state representing the true pareto optimal front besides the anti matthew effect is the internal incentive factor of most strategies the final scale free state reflects the quality of the final pareto optimal front the speed of the state transition reflects the efficiency of the algorithm we simulate the spatial evolution characters of three typical multi objective evolutionary algorithms representing three fields i e genetic algorithm differential evolution and the artificial immune system algorithm the results prove that the model and the explanation are effective for analyzing the evolutional rule of multi objective evolutionary algorithms

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

a novel approach for lung nodules segmentation in chest ct using level sets a new variational level set approach is proposed for lung nodule segmentation in lung ct scans a general lung nodule shape model is proposed using implicit spaces as a signed distance function the shape model is fused with the image intensity statistical information in a variational segmentation framework the nodule shape model is mapped to the image domain by a global transformation that includes inhomogeneous scales rotation and translation parameters a matching criteria between the shape model and the image implicit representations is employed to handle the alignment process transformation parameters evolve through gradient descent optimization to handle the shape alignment process and hence mark the boundaries of the nodule head the embedding process takes into consideration the image intensity as well as prior shape information a nonparametric density estimation approach is employed to handle the statistical intensity representation of the nodule and background regions the proposed technique does not depend on nodule type or location exhaustive experimental and validation results are demonstrated on 742 nodules obtained from four different ct lung databases illustrating the robustness of the approach

curvature based algorithms for nonrigid motion and correspondence estimation we present a novel technique for utilizing the gaussian curvature information in 3d nonrigid motion estimation in the absence of known correspondence differential geometric constraints derived in the paper allow one to estimate parameters of the local affine motion model given the values of gaussian curvature before and after motion these constraints can be further combined with the previously known constraints based on the unit normals before and after motion our experiments demonstrate that the resulting hybrid algorithm is more accurate than each of its constituents and more accurate than the classical icp algorithm we also present a technique for curvilinear orthogonalization of quadratic monge patches that is essential in our derivation and useful in other applications

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

riemannian geometric entropy for measuring network complexity a central issue in the science of complex systems is the quantitative characterization of complexity in the present work we address this issue by resorting to information geometry actually we propose a constructive way to associate with a in principle any network a differentiable object a riemannian manifold whose volume is used to define the entropy the effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale free networks as well as of characterizing small exponential random graphs configuration models and real networks

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

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

metamorphs deformable shape and appearance models this paper presents a new deformable modeling strategy that is aimed at integrating shape and appearance in a unified space if we think of traditional deformable models as active contours or evolving curve fronts the new deformable shape and appearance models that we propose are deforming disks or volumes each model not only has boundary shape but also interior appearance the model shape is implicitly embedded in a higher dimensional space of distance transforms and is thus represented by a distance map image this way both the shape and the appearance of the model are defined in the pixel space a common deformation scheme that is the free form deformations ffds parameterizes warping deformations of the volumetric space in which the model is embedded hence simultaneously deforming both model boundary and interior when applied to segmentation a metamorphs model can be initialized by covering a seed region far from the object boundary and then the model efficiently evolves and converges to an optimal solution the model dynamics are derived in a unified variational framework that consists of edge based and region based energy terms both of which are differentiable with respect to the common set of ffd parameters as the model deforms its interior appearance statistics are adaptively learned and then toward the next step deformation the model examines not only edge information but also its exterior region statistics to ensure that it only expands to new territory with consistent appearance statistics the metamorphs formulation also allows natural merging and competition of multiple models we demonstrate the robustness of metamorphs by using both natural and medical images that have high noise levels intensity inhomogeneity and complex texture

bifurcations of limit cycles in equivariant quintic planar vector fields abstract in this paper we obtain 23 limit cycles for a z 3 equivariant near hamiltonian system of degree 5 which is the perturbation of a z 6 equivariant quintic hamiltonian system the configuration of these limit cycles is new and different from the configuration obtained by h s y chan k w chung and j li where the unperturbed system is a z 3 equivariant quintic hamiltonian system our unperturbed system is different from the unperturbed systems studied by y wu and m han the limit cycles are obtained by poincare pontryagin theorem and poincare bendixson theorem

gibbs entropy of network ensembles by cavity methods the gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints this quantity characterizes the level of order and randomness encoded in features of a given real network here we show how to relate this entropy to large deviations of conjugated canonical ensembles we derive exact expression for this correspondence using the cavity methods for the configuration model for the ensembles with constraint degree sequence and community structure and for the ensemble with constraint degree sequence and number of links at a given distance

duality between equilibrium and growing networks in statistical physics any given system can be either at an equilibrium or away from it networks are not an exception most network models can be classified as either equilibrium or growing here we show that under certain conditions there exists an equilibrium formulation for any growing network model and vice versa the equivalence between the equilibrium and nonequilibrium formulations is exact not only asymptotically but even for any finite system size the required conditions are satisfied in random geometric graphs in general and causal sets in particular and to a large extent in some real networks

number of cliques in random scale free network ensembles abstract in this paper we calculate the average number of cliques in random scale free networks in the limit of large network size n 1 we consider first the hidden variable ensemble and subsequently the molloy reed ensemble in both cases we find that cliques i e fully connected subgraphs appear also when the average degree is finite this is in contrast to what happens in erdos and renyi graphs in which diverging average degree is required to observe cliques of size c 3 moreover we show that in random scale free networks the clique number i e the size of the largest clique present in the network diverges with the system size

multifractal network generator we introduce a new approach to constructing networks with realistic features our method in spite of its conceptual simplicity it has only two parameters is capable of generating a wide variety of network types with prescribed statistical properties e g with degree or clustering coefficient distributions of various very different forms in turn these graphs can be used to test hypotheses or as models of actual data the method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies the main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously a very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured we present analytic expressions derived from the parameters of the to be iterated initial generating measure for such major characteristics of graphs as their degree clustering coefficient and assortativity coefficient distributions the optimal parameters of the generating measure are determined from a simple simulated annealing process thus the present work provides a tool for researchers from a variety of fields such as biology computer science biology or complex systems enabling them to create a versatile model of their network data

rigid affine and locally affine registration of free form surfaces in this paper we propose a new framework to perform nonrigid surface registration it is based on various extensions of an iterative algorithm recently presented by several researchers besl and mckay 1992 champleboux et al 1992 chen and medioni 1992 menq and lai 1992 zhang 1994 to rigidly register surfaces represented by a set of 3d points when a prior estimate of the displacement is available our framework consists of three stages first we search for the best rigid displacement to superpose the two surfaces we show how to efficiently use curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm second we search for the best affine transformation we introduce differential information in points coordinates this allows us to match locally similar points then we show how principal frames and curvatures are transformed by an affine transformation finally we introduce this differential information in a global criterion minimized by extended kalman filtering in order to ensure the convergence of the algorithm third we locally deform the surface instead of computing a global affine transformation we attach to each point a local affine transformation varying smoothly along the surface we call this deformation a locally affine deformation all these stages are illustrated with experiments on various real biomedical surfaces teeth faces skulls brains and hearts which demonstrate the validity of the approach

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality

small amplitude limit cycles for the polynomial lienard system abstract we estimate for the maximal number of limit cycles bifurcating from a focus for the lienard equation x f x x g x 0 where f and g are polynomials of degree m and n respectively these estimates are quadratic in m and n and improve the existing bounds in the proof we use methods of complex algebraic geometry to bound the number of double points of a rational affine curve

average path length in random networks analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found we apply the approach to classical random graphs of erdos and renyi er evolving networks introduced by barabasi and albert as well as random networks with asymptotic scale free connectivity distributions characterized by an arbitrary scaling exponent alpha 2 our result for 2 infinity there is a saturation effect for the average path length

correlation networks from random walk time series stimulated by the growing interest in the applications of complex networks framework for time series analysis we devise a network model in which each of n nodes is associated with a random walk of length l connectivity between any two nodes is established when the pearson correlation coefficient pcc between the corresponding time series is greater than or equal to a threshold h resulting in similarity networks with interesting properties in particular these networks can have high average clustering coefficients and the small world property and their degree distribution can vary from scale free to quasiconstant depending on h a giant component of size n exists until a critical threshold h c is crossed at which point relatively rare walks begin to detach from it and remain isolated this model can be used as a first step for building a null hypothesis for networks constructed from time series

new mathematical and algorithmic schemes for pattern classification with application to the identification of writers of important ancient documents abstract in this paper a novel approach is introduced for classifying curves into proper families according to their similarity first a mathematical quantity we call plane curvature is introduced and a number of propositions are stated and proved proper similarity measures of two curves are introduced and a subsequent statistical analysis is applied first the efficiency of the curve fitting process has been tested on 2 shapes datasets of reference next the methodology has been applied to the very important problem of classifying 23 byzantine codices and 46 ancient inscriptions to their writers thus achieving correct dating of their content the inscriptions have been attributed to ten individual hands and the byzantine codices to four writers

betweenness centrality of an edge in tree like components with finite size using the generating function formalism we propose an exact formula for estimating betweenness centrality of an edge in finite tree like components of random networks with arbitrary degree distributions as a function of the degrees of two vertices interconnected by the edge and the size of the component to which the edge belongs the formula can give an estimation of the mean value of the edge betweenness we confirm the formula by simulations for poisson and power law distributions respectively we also study the asymptotic behavior of the formula and find that there is an asymptotic power law relation with an exponent 1 5 between the edge betweenness and the size of the component to which the edge belongs

topology of technology graphs small world patterns in electronic circuits recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological social and technological networks the presence of small world patterns here we analyze this problem by using several graphs obtained from one of the most common technological systems electronic circuits it is shown that both analogic and digital circuits exhibit small world behavior we conjecture that the small world pattern arises from the compact design in which many elements share a small close physical neighborhood plus the fact that the system must define a single connected component which requires shortcuts connecting different integrated clusters the degree distributions displayed are consistent with a conjecture concerning the sharp cutoffs associated to the presence of costly connections amaral et al proc natl acad sci usa 97 11 149 2000 thus providing a limit case for the classes of universality of small world patterns from real artificial networks the consequences for circuit design are outlined

robust l_ 2 e estimation of transformation for non rigid registration we introduce a new transformation estimation algorithm using the l 2 e estimator and apply it to non rigid registration for building robust sparse and dense correspondences in the sparse point case our method iteratively recovers the point correspondence and estimates the transformation between two point sets feature descriptors such as shape context are used to establish rough correspondence we then estimate the transformation using our robust algorithm this enables us to deal with the noise and outliers which arise in the correspondence step the transformation is specified in a functional space more specifically a reproducing kernel hilbert space in the dense point case for nonrigid image registration our approach consists of matching both sparsely and densely sampled sift features and it has particular advantages in handling significant scale changes and rotations the experimental results show that our approach greatly outperforms state of the art methods particularly when the data contains severe outliers

shape representation and registration in vector implicit spaces adopting a closed form solution in the optimization process in this paper a novel method to solve the shape registration problem covering both global and local deformations is proposed the vector distance function vdf is used to represent source and target shapes the problem is formulated as an energy optimization process by matching the vdfs of the source and target shapes the minimization process results in estimating the transformation parameters for the global and local deformation cases gradient descent optimization handles the computation of scaling rotation and translation matrices used to minimize the global differences between source and target shapes nonrigid deformations require a large number of parameters which make the use of the gradient descent minimization a very time consuming process we propose to compute the local deformation parameters using a closed form solution as a linear system of equations derived from approximating an objective function extensive experimental validations and comparisons performed on generalized 2d shape data demonstrate the robustness and effectiveness of the method

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

entropy of network ensembles in this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach this framework is able to describe undirected and directed network ensembles as well as weighted network ensembles these networks might have nontrivial community structure or in the case of networks embedded in a given space they might have a link probability with a nontrivial dependence on the distance between the nodes these ensembles are characterized by their entropy which evaluates the cardinality of networks in the ensemble in particular in this paper we define and evaluate the structural entropy i e the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence we stress the apparent paradox that scale free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural social and technological complex systems we propose a solution to the paradox by proving that scale free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy finally the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden variable network ensembles with significant implications for the formulation of network constructing algorithms

automatic renal cortex segmentation using implicit shape registration and novel multiple surfaces graph search in this paper we present an automatic renal cortex segmentation approach using the implicit shape registration and novel multiple surfaces graph search the proposed approach is based on a hierarchy system first the whole kidney is roughly initialized using an implicit shape registration method with the shapes embedded in the space of euclidean distance functions second the outer and inner surfaces of renal cortex are extracted utilizing multiple surfaces graph searching which is extended to allow for varying sampling distances and physical constraints to better separate the renal cortex and renal column third a renal cortex refining procedure is applied to detect and reduce incorrect segmentation pixels around the renal pelvis further improving the segmentation accuracy the method was evaluated on 17 clinical computed tomography scans using the leave one out strategy with five metrics dice similarity coefficient dsc volumetric overlap error oe signed relative volume difference svd average symmetric surface distance davg and average symmetric rms surface distance drms the experimental results of dsc oe svd davg and drms were 90 50 1 19 4 38 3 93 2 37 1 72 0 14 mm 0 09 mm and 0 80 mm 0 64 mm respectively the results showed the feasibility efficiency and robustness of the proposed method

group selection models in prebiotic evolution the evolution of enzyme production is studied analytically using ideas of the group selection theory for the evolution of altruistic behavior in particular we argue that the mathematical formulation of wilson s structured deme model the evolution of populations and communities benjamin cumings menlo park 1980 is a mean field approach in which the actual environment that a particular individual experiences is replaced by an average environment that formalism is further developed so as to avoid the mean field approximation and then applied to the problem of enzyme production in the prebiotic context where the enzyme producer molecules play the altruists role while the molecules that benefit from the catalyst without paying its production cost play the nonaltruists role the effects of synergism i e division of labor as well as of mutations are also considered and the results of the equilibrium analysis are summarized in phase diagrams showing the regions of the space of parameters where the altruistic nonaltruistic and the coexistence regimes are stable in general those regions are delimitated by discontinuous transition lines which end at critical points

an evolutionary version of the random energy model we consider eigen s quasispecies model 1971 of molecular evolution in the case in which the reproduction rates of different molecular species are quenched independent random variables we show by analogy with the random energy model the existence of two phases a neutral phase where no adaptation effects are exhibited and a pathological adapted phase where the population is made of identical optimally adapted molecules and does not evolve