shape design in aorto coronaric bypass anastomoses using perturbation theory in this paper we present a new approach in the study of aorto coronaric bypass anastomoses configurations based on small perturbation theory the theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass the toe into the coronary the aim is to provide design indications in the perspective of future development for prosthetic bypasses

configuration model for correlation matrices preserving the node strength correlation matrices are a major type of multivariate data to examine properties of a given correlation matrix a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices such as those derived from random matrix theory that partially preserve properties of the original matrix we propose a model to generate such reference correlation and covariance matrices for the given matrix correlation matrices are often analyzed as networks which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node given this background the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes akin to configuration models for conventional networks our algorithm is derived from the maximum entropy principle we will apply the proposed algorithm to measurement of clustering coefficients and community detection both of which require a null model to assess the statistical significance of the obtained results

shape optimization using the cut finite element method we present a cut finite element method for shape optimization in the case of linear elasticity the elastic domain is defined by a level set function and the evolution of the domain is obtained by

proportional thresholding in resting state fmri functional connectivity networks and consequences for patient control connectome studies issues and recommendations graph theoretical analysis has become an important tool in the examination of brain dysconnectivity in neurological and psychiatric brain disorders a common analysis step in the construction of the functional graph or network involves thresholding of the connectivity matrix selecting the set of edges that together form the graph on which network organization is evaluated to avoid systematic differences in absolute number of edges studies have argued against the use of an absolute threshold in case control studies and have proposed the use of proportional thresholding instead in which a pre defined number of strongest connections are selected as network edges ensuring equal network density across datasets here we systematically studied the effect of proportional thresholding on the construction of functional matrices and subsequent graph analysis in patient control functional connectome studies in a few simple experiments we show that differences in overall strength of functional connectivity fc as often observed between patients and controls can have predictable consequences for between group differences in network organization in individual networks with lower overall fc the proportional thresholding algorithm has to select more edges based on lower correlations which have on average a higher probability of being spurious and thus introduces a higher degree of randomness in the resulting network we show across both empirical and artificial patient control datasets that lower levels of overall fc in either the patient or control group will most often lead to differences in network efficiency and clustering suggesting that differences in fc across subjects will be artificially inflated or translated into differences in network organization based on the presented case control findings we inform about the caveats of proportional thresholding in patient control studies in which groups show a between group difference in overall fc we make recommendations on how to examine report and to take into account overall fc effects in future patient control functional connectome studies

age related changes in modular organization of human brain functional networks graph theory allows us to quantify any complex system e g in social sciences biology or technology that can be abstractly described as a set of nodes and links here we derived human brain functional networks from fmri measurements of endogenous low frequency correlated oscillations in 90 cortical and subcortical regions for two groups of healthy young and older participants we investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks newman s modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra and inter modular connectivity both young and older brain networks demonstrated significantly non random modularity the young brain network was decomposed into 3 major modules central and posterior modules which comprised mainly nodes with few inter modular connections and a dorsal fronto cingulo parietal module which comprised mainly nodes with extensive inter modular connections the mean network in the older group also included posterior superior central and dorsal fronto striato thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced whereas the number of connector nodes in posterior and central modules was increased

the algebra of harmonic functions for a matrix valued transfer operator abstract we analyze matrix valued transfer operators we prove that the fixed points of transfer operators form a finite dimensional c algebra for matrix weights satisfying a low pass condition we identify the minimal projections in this algebra as correlations of scaling functions i e limits of cascade algorithms

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

extracting the multiscale backbone of complex weighted networks a large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength in recent years the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern with degree and weight distributions that vary over many orders of magnitude these features along with the large number of elements and links make the extraction of the truly relevant connections forming the network s backbone a very challenging problem more specifically coarse graining approaches and filtering techniques come into conflict with the multiscale nature of large scale systems here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges an important aspect of the method is that it does not belittle small scale interactions and operates at all scales defined by the weight distribution we apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques

computation of high order derivatives in optimal shape design in shape optimization problems each computation of the cost function by the finite element method leads to an expensive analysis the use of the second order derivative can help to reduce the number of analyses fujii 4 10 was the first to study this problem j simon 19 gave the second order derivative for the navier stokes problem and the authors describe in 8 11 a method which gives an intrinsic expression of the first and second order derivatives on the boundary of the involved domain in this paper we study higher order derivatives but one can ask the following questions are they expensive to calculate are they complicated to use are they imprecise are they useless medskip noindent at first sight the answer seems to be positive but classical results of v strassen 20 and j morgenstern 13 tell us that the higher order derivatives are not expensive to calculate and can be computed automatically the purpose of this paper is to give an answer to the third question by proving that the higher order derivatives of a function can be computed with the same precision as the function itself we prove also that the derivatives so computed are equal to the derivatives of the discrete problem see diagram 1 we call the discrete problem the finite dimensional problem processed by the computer this result allows the use of automatic differentiation 5 6 which works only on discrete problems furthermore the computations of taylor s expansions which are proposed at the end of this paper could be a partial answer to the last question

structured inverse modeling in parabolic diffusion problems often the unknown diffusivity in diffusive processes is structured by piecewise constant patches this paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus a novel shape gradient is derived in parabolic processes furthermore quasi newton techniques are used in order to accelerate shape gradient based iterations in shape space numerical investigations support the theoretical results

on accuracy of approximate boundary and distributed h1 shape gradient flows for eigenvalue optimization abstract the boundary and distributed shape gradients of elliptic eigenvalues in shape optimization are approximated by the finite element method we show a priori error estimates for the two approximate shape gradients in h 1 shape gradient flows the convergence analysis shows that the volume integral formula converges faster and offers higher accuracy when the finite element method is used for discretization numerical results verify the theory for the dirichlet case shape optimization examples solved by algorithms illustrate the more effectiveness of distributed shape gradients for the dirichlet case for optimizing a neumann eigenvalue the boundary and volume h 1 flows have the same efficiency moreover we observe that the distributed h 1 shape gradient flow is more efficient than the boundary l 2 shape gradient flow in literature

a cut finite element method for the bernoulli free boundary value problem we develop a cut finite element method for the bernoulli free boundary problem the free boundary represented by an approximate signed distance function on a fixed background mesh is allowed to i

efficient pde constrained shape optimization based on steklov poincare type metrics recent progress in pde constrained optimization on shape manifolds is based on the hadamard form of shape derivatives i e in the form of integrals at the boundary of the shape under investigation as well as on intrinsic shape metrics from a numerical point of view domain integral forms of shape derivatives seem promising which instead require an outer metric on the domain surrounding the shape boundary this paper tries to harmonize both points of view by employing a steklov poincare type intrinsic metric which is derived from an outer metric based on this metric efficient shape optimization algorithms are proposed which also reduce the analytical labor involved in the derivation of shape derivatives

a high order mixed polygonal finite element for incompressible stokes flow analysis abstract this paper presents a new high order mixed scheme of polygonal finite element method pfem for incompressible flow computation the system of polygonal basis functions with bubble enriched functions is applied to represent the fluid velocity field while the pressure field is approximated by the set of polygonal basis functions the new element is named as minipe from a practical point of view the present element naturally satisfies the well known inf sup condition the numerical tests of the incompressible fluid flow problems governed by stokes equation systems are presented to verify the performance quality of proposed method with respect to the stability and convergence rate

parallel one shot lagrange newton krylov schwarz algorithms for shape optimization of steady incompressible flows we propose and study a new parallel one shot lagrange newton krylov schwarz lnksz algorithm for shape optimization problems constrained by steady incompressible navier stokes equations discretized by finite element methods on unstructured moving meshes most existing algorithms for shape optimization problems iteratively solve the three components of the optimality system the state equations for the constraints the adjoint equations for the lagrange multipliers and the design equations for the shape parameters such approaches are relatively easy to implement but generally are not easy to converge as they are basically nonlinear gauss seidel algorithms with three large blocks in this paper we introduce a fully coupled or the so called one shot approach which solves the three components simultaneously first we introduce a moving mesh finite element method for the shape optimization problems in which the mesh equations are implicitly coupled with the optimization problems second we introd

probabilistic thresholding of functional connectomes application to schizophrenia abstract functional connectomes are commonly analysed as sparse graphs constructed by thresholding cross correlations between regional neurophysiological signals thresholding generally retains the strongest edges correlations either by retaining edges surpassing a given absolute weight or by constraining the edge density the latter more widely used method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities here we apply new wavelet based methods which enable construction of probabilistically thresholded graphs controlled for type i error to a dataset of resting state fmri scans of 56 patients with schizophrenia and 71 healthy controls by thresholding connectomes to fixed edge specific p value we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls exhibiting a lower edge density and a higher number of dis connected components furthermore many participants connectomes could not be built up to the fixed edge densities commonly studied in the literature 5 30 while controlling for type i error additionally we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to non significant edges added when thresholding connectomes to fixed density based on correlation finally by explicitly comparing connectomes thresholded by increasing p value and decreasing correlation we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants our results have implications for future analysis of functional connectivity using graph theory especially within datasets exhibiting heterogenous distributions of edge weights correlations between groups or across participants

shape reconstruction of an inverse stokes problem this paper deals with the shape reconstruction of a viscous incompressible fluid driven by the stokes flow for the approximate solution of the ill posed and nonlinear problem we propose a regularized newton method a theoretical foundation for the newton method is given by establishing the differentiability of the initial boundary value problem with respect to the interior boundary curve in the sense of a domain derivative the numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible

parametric free form shape design with pde models and reduced basis method we present a coupling of the reduced basis methods and free form deformations for shape optimization and design of systems modelled by elliptic pdes the free form deformations give a parameterization of the shape that is independent of the mesh the initial geometry and the underlying pde model the resulting parametric pdes are solved by reduced basis methods an important role in our implementation is played by the recently proposed empirical interpolation method which allows approximating the non affinely parameterized deformations with affinely parameterized ones these ingredients together give rise to an efficient online computational procedure for a repeated evaluation design environment like the one for shape optimization the proposed approach is demonstrated on an airfoil inverse design problem

convergence analysis of mixed finite element approximations to shape gradients in the stokes equation abstract eulerian derivatives of shape functionals in shape optimization can be written in two formulations of boundary and volume integrals the former is widely used in shape gradient descent algorithms the latter holds more generally although rarely being used numerically in literature for shape functionals governed by the stokes equation we consider the mixed finite element approximations to the two types of shape gradients from corresponding eulerian derivatives the standard mini and taylor hood elements are employed to discretize the state equation its adjoint and the resulting shape gradients we present thorough convergence analysis with a priori error estimates for the two approximate shape gradients the theoretical analysis shows that the volume integral formula has superconvergence property numerical results are presented to verify the theory and show that the volume formulation is more accurate

a level set method for shape optimization in semilinear elliptic problems abstract we develop a finite element based level set method for numerically solve shape optimization problems constrained by semilinear elliptic problems by combining the shape sensitivity analysis and level set method a gradient descent algorithm is proposed to solve the model problem different from solving the nonlinear hamilton jacobi equations with finite differences in traditional level set methods we solve the linear convection equation and reinitialization equation using the characteristic galerkin finite element method the methodology can handle topology as well as shape changes in both regular and irregular design regions numerical results are presented to demonstrate the effectiveness of our algorithm as well as to verify symmetry preserving and breaking properties of optimal subdomains

the in stability of functional brain network measures across thresholds the large scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory however many network measures were designed to be calculated on binary graphs whereas functional brain organization is typically inferred from a continuous measure of correlations in temporal signal between brain regions thresholding is a necessary step to use binary graphs derived from functional connectivity data however there is no current consensus on what threshold to use and network measures and group contrasts may be unstable across thresholds nevertheless whole brain network analyses are being applied widely with findings typically reported at an arbitrary threshold or range of thresholds this study sought to evaluate the stability of network measures across thresholds in a large resting state functional connectivity dataset network measures were evaluated across absolute correlation based and proportional sparsity based thresholds and compared between sex and age groups overall network measures were found to be unstable across absolute thresholds for example the direction of group differences in a given network measure may change depending on the threshold network measures were found to be more stable across proportional thresholds these results demonstrate that caution should be used when applying thresholds to functional connectivity data and when interpreting results from binary graph models

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

binary level set methods for topology and shape optimization of a two density inhomogeneous drum abstract we optimize eigenvalues in optimal shape design using binary level set methods the interfaces of subregions are represented implicitly by the discontinuities of binary level set functions taking two values 1 or 1 at convergence a binary constraint is added to the original model problems we propose two variational algorithms to solve the constrained optimization problems one is a hybrid type by coupling the lagrange multiplier approach for the geometry constraint with the augmented lagrangian method for the binary constraint the other is devised using the lagrange multiplier method for both constraints the two iterative algorithms are both largely independent of the initial guess and can satisfy the geometry constraint very accurately during the iterations intensive numerical results are presented and compared with those obtained by level set methods which demonstrate the effectiveness and robustness of our algorithms

frames generated by actions of countable discrete groups we consider dual frames generated by actions of countable discrete groups on a hilbert space module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group this has applications to shift invariant spaces and wavelet theory one of the main findings in this paper is that whenever a shift invariant subspace in l 2 n has compactly supported dual frame generators then it also has compactly supported bi orthogonal generators the crucial part in the proof is a theorem by swan that states that every finitely generated projective module over the laurent polynomials in n variables is free

variational piecewise constant level set methods for shape optimization of a two density drum we apply the piecewise constant level set method to a class of eigenvalue related two phase shape optimization problems based on the augmented lagrangian method and the lagrange multiplier approach we propose three effective variational methods for the constrained optimization problem the corresponding gradient type algorithms are detailed the first uzawa type algorithm having applied to shape optimization in the literature is proven to be effective for our model but it lacks stability and accuracy in satisfying the geometry constraint during the iteration the two other novel algorithms we propose can overcome this limitation and satisfy the geometry constraint very accurately at each iteration moreover they are both highly initial independent and more robust than the first algorithm without penalty parameters the last projection lagrangian algorithm has less severe restriction on the time step than the first two algorithms numerical results for various instances are presented and compared with those obtained by level set methods the comparisons show effectiveness efficiency and robustness of our methods we expect our promising algorithms to be applied to other shape optimization and multiphase problems

pointwise error estimates for finite element solutions of the stokes problem in this paper pointwise error estimates for general finite element approximations of the stokes problem are established on quasi uniform grids in r n the results obtained in this paper improve and extend the existing error estimates in the maximum norm for the stokes problem the new pointwise error estimates exhibit a more local dependence of the errors on the true solution and as a by product provide logarithm free bounds for all errors except the error of the velocity approximation of the lowest order