topological fractal networks introduced by mixed degree distribution abstract several fundamental properties of real complex networks such as the small world effect the scale free degree distribution and recently discovered topological fractal structure have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors however highly clustered scale free network with power law degree distribution or small world network models with exponential degree distribution are not self similarity we investigate networks growth mechanism of the branching deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors it yields high clustering and spectrums of degree distribution ranging from algebraic to exponential average shortest path length ranging from linear to logarithmic we observe that the present networks fit well with small world graphs and scale free networks in both limit cases exponential and algebraic degree distribution respectively obviously lacking self similar property under a length scale transformation interestingly we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values the results present a reliable connection among small world graphs scale free networks and topological fractal networks and promise a natural way to investigate universal origins of collective behaviors

growing scale free networks with tunable clustering we extend the standard scale free network model to include a triad formation step we analyze the geometric properties of networks generated by this algorithm both analytically and by numerical c

the similarity of weights on edges and discovering of community structure abstract in this paper we propose a weighted modularity q w based on the similarity of weights on edges and a threshold coefficient to evaluate the equivalence of edge weights simulations on benchmark networks and real networks show that optimization on the modularity enable us to obtain groups of nodes within which the edge weights are distributed uniformly but at random between them the communities can reveal the uniform connections stable relationships measured by the similarity of weights on edges between nodes or some similarity between nodes functions furthermore with the dynamical moving of we observe that optimization on the q w allows for the discovering of a special hierarchical organization which reveals different levels of uniform connections between nodes in networks the substructures revealed by the hierarchical organization enable us to obtain more information of networks and give a potential way for partly remedying the intrinsic resolution problem of modularity

stabilized formulation for the advection diffusion absorption equation using finite calculus and linear finite elements abstract a stabilized finite element method fem for the steady state advection diffusion absorption equation is presented the stabilized formulation is based on the modified governing differential equations derived via the finite calculus fic method the basis of the method is detailed for the 1d problem it is shown that the stabilization terms act as a non linear additional diffusion governed by a single stabilization parameter a critical constant value of this parameter ensuring a stabilized solution using two node linear elements is given more accurate numerical results can be obtained by using a simple expression of the non linear stabilization parameter depending on the signs of the numerical solution and of its derivatives a straightforward two steps algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described the extension to the multi dimensional case is briefly described numerical results for 1d and 2d problems are presented showing the efficiency and accuracy of the new stabilized formulation

a topological phase transition between small worlds and fractal scaling in urban railway transportation networks abstract fractal and small worlds scaling laws are applied to study the growth of urban railway transportation networks using total length and total population as observational parameters in spite of the variety of populations and urban structures the variation of the total length of the railway network with the total population of conurbations follows similar patterns for large and middle metropolis diachronous analysis of data for urban transportation networks suggests that there is second order phase transition from small worlds behaviour to fractal scaling during their early stages of development

a simple subgrid scale stabilized method for the advection diffusion reaction equation abstract a subgrid scale method has been developed for the advection diffusion reaction equation with a simple intrinsic time scale parameter the proposed formulation combines very good accuracy and stability in all the physical regimes of the equation that is in the exponential regime for both negative and positive source terms and in the propagation regime numerical examples confirm the robustness and accuracy of the method

parameters of goppa codes revisited we discuss parameters of goppa 1970 codes such as minimum distance covering radius distance distribution and generalized hamming weights by a variation on the exponential sums method and combinatorial arguments we sharpen known bounds on these parameters

variational subgrid scale formulations for the advection diffusion reaction equation abstract the exact variational multiscale vms and the subgrid scale sgs methods have been developed for the advection reaction and the advection diffusion reaction equations from the element green s function approximate intrinsic time scale parameters have been derived for these cases and are shown to be similar to other expressions obtained in the literature out of the maximum principle and convergence error analysis the methods have been compared with typical stabilized finite element methods as expected the vms is nodally exact for the one dimensional case

the weight hierarchy of some reducible cyclic codes the generalized hamming weights ghws of linear codes are fundamental parameters the knowledge of which is of great interest in many applications however to determine the ghws of linear codes is difficult in general in this paper we study the ghws for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases this is achieved by extending the idea of yang et al into higher dimension and by employing some interesting combinatorial arguments it shall be noted that these cyclic codes may have arbitrary number of nonzeros

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

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

on the generalized hamming weights of cyclic codes we prove several results on the generalized hamming weights ghw s of linear codes particularly for cyclic codes based on these and previously known results we give some efficient algorithms for computing ghw hierarchy of cyclic codes we give complete weight hierarchy for each of the binary cyclic codes of odd lengths spl les 31 a table of second and third ghw s of binary cyclic codes of odd lengths spl les 57 is also presented we have also computed the second ghw of all binary cyclic codes of length 63 and the third ghw of one code from each dimension

generalized hamming weights of bch 3 revisited determines the first five generalized hamming weights of 3 error correcting primitive binary bch codes

rise and fall of historic tram networks logistic approximation and discontinuous events abstract a logistic approximation was used to describe in terms of total length l and population h variables the growth and decay of historic transportation systems three successive stages separated for sharp discontinuities were detected for several european tramway and metro systems corresponding to a fast initial growth followed by an intermediate step of slow growth and a final stage of rapid decay a common generalized behaviour was obtained in the l h vs h variations relative to critical values of l and h parameters defined from the maximum in the l h ratio

fractal small world dichotomy in real world networks we draw attention to a clear dichotomy between small world networks exhibiting exponential neighborhood growth and fractal like networks where neighborhoods grow according to a power law this distinction is observed in a number of real world networks and is related to the degree correlations and geographical constraints we conclude by pointing out that the status of human social networks in this dichotomy is far from clear

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

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

on generalized hamming weights of bch codes introduces methods from algebraic geometry to determine generalized hamming weights of bch codes as an application of these methods the authors determine for primitive 2 resp 3 error correcting bch codes the third resp the second generalized hamming weight

a note on generalized hamming weights of bch 2 determines results for the first six generalized hamming weights of double error correcting primitive binary bch codes

trellis decoding complexity of linear block codes in this partially tutorial paper we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity maximum state and edge dimensions total span length and total vertices edges and mergers we obtain bounds on these complexities as extensions of well known dimension length profile dlp bounds codes meeting these bounds minimize all the complexity measures simultaneously conversely a code attaining the bound for total span length vertices or edges must likewise attain it for all the others we define a notion of uniform optimality that embraces different domains of optimization such as different permutations of a code or different codes with the same parameters and we give examples of uniformly optimal codes and permutations we also give some conditions that identify certain cases when no code or permutation can meet the bounds in addition to dlp based bounds we derive new inequalities relating one complexity measure to another which can be used in conjunction with known bounds on one measure to imply bounds on the others as an application we infer new bounds on maximum state and edge complexity and on total vertices and edges from bounds on span lengths

finite element formulation for convective diffusive problems with sharp gradients using finite calculus abstract a finite element method fem for steady state convective diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented the necessary stabilization of the numerical solution is provided by the finite calculus fic approach the fic method is based in the solution by the galerkin fem of a modified set of governing equations which include characteristic length parameters it is shown that the fic balance equation for the multidimensional convection diffusion problem written in the principal curvature axes of the solution introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients the dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

on generalized hamming weights of binary primitive bch codes with minimum distance one less than a power of two the generalized hamming weights introduced by wei 1991 have been shown to be fundamental descriptive parameters of a linear block code they have been found to be useful in certain cryptographic applications and in the studies of minimal trellis diagrams of linear block codes in this correspondence we determine the first few and the last few generalized hamming weights of binary primitive bch codes with minimum distance one less than a power of two of their extensions and of the duals of both

surfaces and the weight distribution of a family of codes we derive the weight distribution of the binary trace codes with words tr ax sup q 1 bx sup 3 cx sub x spl isin f q2 where a b c spl isin f q sup 2 and tr is the trace map from f q sup 2 to f sub 2 the weights of these words determine the exponential sums which were considered earlier by moreno and kumar 1994 and lahtonen 1995 results from the theory of quadratic forms play a role but the decisive argument is of an algebraic geometric nature namely from the theory of surfaces

topology and correlations in structured scale free networks we study a recently introduced class of scale free networks showing a high clustering coefficient and nontrivial connectivity correlations we find that the connectivity probability distribution strongly depends on the fine details of the model we solve exactly the case of low average connectivity providing also exact expressions for the clustering and degree correlation functions the model also exhibits a lack of small world properties in the whole parameter range we discuss the physical properties of these networks in the light of the present detailed analysis

the twisted squaring construction trellis complexity and generalized weights of bch and qr codes the structure of the twisted squaring construction a generalization of the squaring construction is studied with respect to trellis diagrams and complexity we show that binary affine invariant codes which include the extended primitive bch codes and the extended binary quadratic residue codes are equivalent to twisted squaring construction codes in particular a recursive symmetric reversible design of the bch codes is derived using these constructions the parameters of the minimal trellis diagram of the bch codes are determined including the componentwise state space profile and trellis complexity new designs and permutations that yield low trellis complexity for the quadratic residue codes are presented generalized hamming weights are derived from these constructions as an example the 48 24 12 quadratic residue code is analyzed a strictly componentwise optimal permutation is derived and the corresponding state space profile and complete generalized hamming weight hierarchy are obtained

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented