a penalty method for the vorticity velocity formulation we present a new vorticity velocity formulation and implementation for the unsteady three dimensional navier stokes equations based on a penalty method it relies on an equivalence theorem that employs exact boundary conditions and the vorticity definition on the domain boundary this approach is particularly attractive for high order methods for which the often used influence matrix method fails to converge for t 0 the accuracy and the robustness of the new method is demonstrated in the context of several spectral element simulations of unsteady two and three dimensional internal and external flows in particular the flow past a finite span cylinder attached to end plates is studied in some detail in order to evaluate the effects of the aspect ratio on the formation length

non planar curvature and branching of arteries and non planar type flow in this study magnetic resonance imaging techniques have been used to examine the geometry of arterial curvature and branching in casts and in vivo and to measure the distribution of axial velocity in the associated flow it is found contrary to a widely held view that the geometry is commonly non planar moreover relatively small values of the parameters which render the geometry non planar appear significantly to affect the velocity distribution the findings suggest that non planarity is an important factor influencing arterial flows including wall shear the implications are not restricted to vascular biology pathology and surgery but may extend to the design of general piping systems

weak leopoldt s conjecture for hecke characters of imaginary quadratic fields we give a proof of weak leopoldt s conjecture a la perrin riou under some technical condition for the p adic realizations of the motive associated to hecke characters over an imaginary quadratic fleld k of class number 1 where p is a prime 3 and where the cm elliptic curve associated to the hecke character has good reduction at the primes above p in k this proof makes use of the 2 variable iwasawa main conjecture proved by rubin thus we prove the jannsen conjecture for the above p adic realizations for almost all tate twists 1 the formulation of weak leopoldt s conjecture and weak jannsen s conjecture for hecke characters let us flrst introduce the p adic integer realizations associated to hecke characters the aim of this paper is verify for these realizations the weak leopoldt conjecture a la perrin riou and jannsen s conjecture for almost all tate twists let e be a flxed elliptic curve with cm which is deflned over an imaginary quadratic fleld k with cm by ok the ring of integers of k note that this implies cl k 1 associated to this elliptic curve there is a cm character of the imaginary quadratic fleld k with conductor f an ideal of ok that coincides with the conductor of the elliptic curve e let us consider once for all p be an odd prime where e has good reduction at the primes above p in k ordinary or supersingular we impose p 6 3 in order that any primitive p root of unity is in k thus in particular p dk the discriminant of k let us introduce the motives and the p adic realizations on which we study the conjectures consider the category of chow motives mq k over k with morphisms induced by graded correspondences in chow theory tensored with q then the motive of the elliptic curve e has a canonical decomposition h e q h 0 e q h 1 e q h 2 e q the motive h 1 e q has a multiplication by k 5 let us consider the motive wh 1 e q for w a strictly positive integer which has multiplication by tw wk observe that tw has a decomposition q

routing betweenness centrality betweenness centrality measure is often used in social and computer communication networks to estimate the potential monitoring and control capabilities a vertex may have on data flowing in the network in this article we define the routing betweenness centrality rbc measure that generalizes previously well known betweenness measures such as the shortest path betweenness flow betweenness and traffic load centrality by considering network flows created by arbitrary loop free routing strategies we present algorithms for computing rbc of all the individual vertices in the network and algorithms for computing the rbc of a given group of vertices where the rbc of a group of vertices represents their potential to collaboratively monitor and control data flows in the network two types of collaborations are considered i conjunctive the group is a sequences of vertices controlling traffic where all members of the sequence process the traffic in the order defined by the sequence and ii disjunctive the group is a set of vertices controlling traffic where at least one member of the set processes the traffic the algorithms presented in this paper also take into consideration different sampling rates of network monitors accommodate arbitrary communication patterns between the vertices traffic matrices and can be applied to groups consisting of vertices and or edges for the cases of routing strategies that depend on both the source and the target of the message we present algorithms with time complexity of o n2m where n is the number of vertices in the network and m is the number of edges in the routing tree or the routing directed acyclic graph dag for the cases of multi path routing strategies the time complexity can be reduced by an order of n if we assume that the routing decisions depend solely on the target of the messages finally we show that a preprocessing of o n2m time supports computations of rbc of sequences in o kn time and computations of rbc of sets in o n3n time where k in the number of vertices in the sequence or the set

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

from h to p efficiently implementing finite and spectral hp element methods to achieve optimal performance for low and high order discretisations the spectral hp element method can be considered as bridging the gap between the traditionally low order finite element method on one side and spectral methods on the other side consequently a major challenge which arises in implementing the spectral hp element methods is to design algorithms that perform efficiently for both low and high order spectral hp discretisations as well as discretisations in the intermediate regime in this paper we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders furthermore based upon this efficient implementation we analyse which spectral hp discretisation which specific combination of mesh size h and polynomial order p minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy we investigate this question for a set of both smooth and non smooth problems

p 2 continuous finite elements on tetrahedra with local mass matrix inversion abstract when using continuous finite element methods for unsteady simulations one must invert a global mass matrix even for an explicit time advancement scheme in this paper we develop a local mass matrix inversion procedure for p 2 c 0 tetrahedral elements and also show that unlike on triangles b t helenbrook siam j numer anal 47 2009 1304 1318 this procedure does not generalize to higher order for the p 2 basis it is demonstrated that the accuracy of the local inversion is better than any previous mass lumping scheme this allows the development of fast and low memory iterative algorithms as well as accurate explicit computations to be performed the efficiency of using the approach as an iterative relaxation scheme for solving the helmholtz equation is shown by comparing to more standard approaches such as p multigrid with jacobi relaxation lastly the local mass matrix inversion is used to march the unsteady heat equation explicitly with third order spatial accuracy

numerical investigation of the non newtonian blood flow in a bifurcation model with a non planar branch the pulsatile flow of non newtonian fluid in a bifurcation model with a non planar daughter branch is investigated numerically by using the carreau yasuda model to take into account the shear thinning behavior of the analog blood fluid the objective of this study is to deal with the influence of the non newtonian property of fluid and of out of plane curvature in the non planar daughter vessel on wall shear stress wss oscillatory shear index osi and flow phenomena during the pulse cycle the non newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior the non planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of wss along the vessel in particular in systole phase downstream of the bifurcation the velocity profiles are shifted toward the flow divider and low wss and high shear stress temporal oscillations characterized by osi occur on the outer wall region of the daughter vessels close to the bifurcation secondary motions become stronger with the addition of the out of plane curvature induced by the bending of the vessel and the secondary flow patterns swirl along the non planar daughter vessel a significant difference between the non newtonian and the newtonian pulsatile flow is revealed during the pulse cycle however reasonable agreement between the non newtonian and the rescaled newtonian flow is found calculated results for the pulsatile flow support the view that the non planarity of blood vessels and the non newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology

on ultrametric 1 median selection abstract consider the problem of finding a point in a finite ultrametric space with the minimum average distance to all points we give this problem a monte carlo o log 2 1 3 time 1 approximation algorithm with success probability 1 o for all 0

on the potentialities of 3d 1d coupled models in hemodynamics simulations this work comprises a step towards the quantitative and qualitative analysis of coupled local and global hemodynamics phenomena in the arterial system the aim of this work is to present some numerical examples to put in evidence the importance of the use of 3d 1d coupled models in hemodynamics problems when carrying out simulations of rather complex situations accordingly some cases for which classical modeling cannot be applied are identified and solved the results obtained here allow us to assess some interrelations between local pointwise quantities defined at the level of the 3d model and global mean quantities defined at the level of the 1d model

data stability in clustering a closer look we consider the model introduced by bilu and linial 2010 13 who study problems for which the optimal clustering does not change when distances are perturbed they show that even when a problem is np hard it is sometimes possible to obtain efficient algorithms for instances resilient to certain multiplicative perturbations e g on the order of o n for max cut clustering awasthi et al 2012 6 consider center based objectives and balcan and liang 2012 9 analyze the k median and min sum objectives giving efficient algorithms for instances resilient to certain constant multiplicative perturbations here we are motivated by the question of to what extent these assumptions can be relaxed while allowing for efficient algorithms we show there is little room to improve these results by giving np hardness lower bounds for both the k median and min sum objectives on the other hand we show that constant multiplicative resilience parameters can be so strong as to make the clustering problem trivial leaving only a narrow range of resilience parameters for which clustering is interesting we also consider a model of additive perturbations and give a correspondence between additive and multiplicative notions of stability our results provide a close examination of the consequences of assuming stability in data

stability analysis for different formulations of the nonlinear term in p n p n 2 spectral element discretizations of the navier stokes equations we show that for the pn pn 2 spectral element method in which velocity and pressure are approximated by polynomials of order n and n 2 respectively numerical instabilities can occur in the spatially discretized navier stokes equations both a staggered and nonstaggered arrangement of the n 2 pressure points are considered these instabilities can be masked by viscous damping at low reynolds numbers we demonstrate that the instabilities depend on the formulation of the nonlinear term the numerical discretization is stable for the convective form but unstable for the divergence and the skew symmetric form further numerical analysis indicates that this instability is not caused by nonlinear effects since it occurs for linearized systems as well an eigenvalue analysis of the fully discretized system shows that an instability is introduced by the formulation of the nonlinear term we demonstrate that the instability is related to the divergence error of the computed solution at those velocity points at which the continuity equation is not enforced

all pairs almost shortest paths let g v e be an unweighted undirected graph on n vertices a simple argument shows that computing all distances in g with an additive one sided error of at most 1 is as hard as boolean matrix multiplication building on recent work of aingworth et al siam j comput 28 1999 pp 1167 1181 we describe an ot min n 3 2 m 1 2 n 7 3 time algorithm apasp2 for computing all distances in g with an additive one sided error of at most 2 algorithm apasp2 is simple easy to implement and faster than the fastest known matrix multiplication algorithm furthermore for every even k 2 we describe an tilde o min n 2 2 k 2 m 2 k 2 n 2 2 3k 2 time algorithm apaspk for computing all distances in g with an additive one sided error of at most k we also give an tilde o n 2 time algorithm bf apasp infty for producing stretch 3 estimated distances in an unweighted and undirected graph on n vertices no constant stretch factor was previously achieved in tilde o n 2 time we say that a weighted graph f v e k emulates an unweighted graph g v e if for every u v in v we have delta g u v le delta f u v le delta g u v k we show that every unweighted graph on n vertices has a 2 emulator with tilde o n 3 2 edges and a 4 emulator with tilde o n 4 3 edges these results are asymptotically tight finally we show that any weighted undirected graph on n vertices has a 3 spanner with tilde o n 3 2 edges and that such a 3 spanner can be built in tilde o mn 1 2 time we also describe an tilde o n m 2 3 n time algorithm for estimating all distances in a weighted undirected graph on n vertices with a stretch factor of at most 3

on the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation abstract here we present a study on the impact of assumptions on image based hemodynamic simulations of healthy carotid bifurcations in particular we evaluate to which extent assumptions on blood rheology influence bulk flow features driven by the fact that few studies have provided adequate insights into the influence of assumptions to confidently model the 4d hemodynamics within the bifurcation the final goal is to complement integrate and extend with a quantitative characterization of the bulk flow the description currently adopted to classify altered hemodynamics which is based on wall shear stress wss hemodynamic simulations of two image based carotid bifurcation geometries were carried out assuming a reference newtonian viscosity two non newtonian rheology models and newtonian viscosities based on characteristic shear rates wss based and lagrangian based metrics for helical flow quantification and for vorticity dynamics quantification were calculated our findings suggest that the assumption of newtonian rheology 1 could be reasonable for bulk flow metrics differences from non newtonian behavior are lower than 10 2 influences at different levels the wss based indicators depending on the bifurcation model even if in our study it is lower than the major source of uncertainty as recognized by the literature i e uncertainty on geometry reconstruction

a nearly linear time approximation scheme for the euclidean k median problem this paper provides a randomized approximation scheme for the k median problem when the input points lie in the d dimensional euclidean space the worst case running time is o 2 o log 1 epsilon varepsilon d 1 n log d 6 n which is nearly linear for any fixed varepsilon and d moreover our method provides the first polynomial time approximation scheme for and uncapacitated facility location instances in d dimensional euclidean space for any fixed d 2 our work extends techniques introduced originally by arora for the euclidean traveling salesman problem tsp to obtain the improvement we develop a structure theorem to describe hierarchical decomposition of solutions the theorem is based on an adaptive decomposition scheme which guesses at every level of the hierarchy the structure of the optimal solution and accordingly modifies the parameters of the decomposition we believe that our methodology is of independent interest and may find applications to further geometric problems

on the birch and swinnerton dyer conjecture let f be a finite extension of the rational field q if e is an elliptic curve defined over f then the mordell weil group e f of points on e with coordinates in f is a finitely generated abelian group let l e f s be the hasseweil zeta function of e over f which at least in the case where e has complex multiplication is known to be an analytic function on the entire complex plane birch and swinnerton dyer have conjectured that l e f s has a zero at s l of order precisely equal to the rank of e f over z the strongest result known in support of this conjecture is the following theorem of coates and wiles 4

all pairs nearly 2 approximate shortest paths in o n2polylogn time let g v e be an unweighted undirected graph on v n vertices and e m edges let d u v denote the distance between vertices u v v an algorithm is said to compute all pairs t approximate shortest paths distances for some t 1 if for each pair of vertices u v v the path distance reported by the algorithm is not longer greater than t d u v this paper presents two extremely simple randomized algorithms for computing all pairs nearly 2 approximate distances the first algorithm requires an expected o m 2 3nlogn n 2 time and for any u v v reports a distance no greater than 2 d u v 1 our second algorithm requires an expected o n 2log 3 2n time and for any u v v reports a distance bounded by 2 d u v 3

more algorithms for all pairs shortest paths in weighted graphs in the first part of the paper we reexamine the all pairs shortest path apsp problem and present a new algorithm with running time o n 3 log 3 log n log 2n which improves all known algorithms for general real weighted dense graphs in the second part of the paper we use fast matrix multiplication to obtain truly subcubic apsp algorithms for a large class of geometrically weighted graphs where the weight of an edge is a function of the coordinates of its vertices for example for graphs embedded in euclidean space of a constant dimension d we obtain a time bound near o n 3 3 omega 2d 4 where omega 2 376 in two dimensions this is o n 2 922 our framework greatly extends the previously considered case of small integer weighted graphs and incidentally also yields the first truly subcubic result near o n 3 3 omega 4 o n 2 844 time for apsp in real vertex weighted graphs as well as an improved result near o n 3 omega 2 o n 2 688 time for the all pairs lightest shortest path problem for small integer weighted graphs

the influence of out of plane geometry on pulsatile flow within a distal end to side anastomosis we present an experimental and computational investigation of time varying flow in an idealized fully occluded 45 distal end to side anastomosis two geometric configurations are assessed one where the centerlines of host and bypass vessels lie within a plane and one where the bypass vessel is deformed out of the plane of symmetry respectively termed planar and non planar flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral hp algorithm results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time averaged peak wall shear stress magnitude by 10 in the non planar model as compared to the planar configuration in the planar geometry the stagnation point follows a straight line path along the host artery bed with a path length of 0 8 diameters by contrast in the non planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall and follows a parabolic path with a 0 7 diameter longitudinal and 0 5 diameter transverse excursion a definition of the oscillatory shear index osi is introduced that varies between 0 and 0 5 and that accounts for a continuous range of wall shear stress vector angles in both models regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow the mean oscillatory shear magnitude considering sites where osi 0 1 in the non planar geometry was reduced by 22 as compared to the planar configuration these changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out of plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions

space time tradeoffs for approximate nearest neighbor searching nearest neighbor searching is the problem of preprocessing a set of n point points in d dimensional space so that given any query point q it is possible to report the closest point to q rapidly in approximate nearest neighbor searching a parameter e 0 is given and a multiplicative error of 1 e is allowed we assume that the dimension d is a constant and treat n and e as asymptotic quantities numerous solutions have been proposed ranging from low space solutions having space o n and query time o log n 1 ed 1 to high space solutions having space roughly o n log n ed and query time o log n e we show that there is a single approach to this fundamental problem which both improves upon existing results and spans the spectrum of space time tradeoffs given a tradeoff parameter where 2 1 e we show that there exists a data structure of space o n d 1 log 1 e that can answer queries in time o log n 1 e d 1 2 when e 2 this yields a data structure of space o n log 1 e that can answer queries in time o log n 1 e d 1 2 when e 1 e it provides a data structure of space o n ed 1 log 1 e that can answer queries in time o log n e our results are based on a data structure called a t e avd which is a hierarchical quadtree based subdivision of space into cells each cell stores up to t representative points of the set such that for any query point q in the cell at least one of these points is an approximate nearest neighbor of q we provide new algorithms for constructing avds and tools for analyzing their total space requirements we also establish lower bounds on the space complexity of avds and show that up to a factor of o log 1 e our space bounds are asymptotically tight in the two extremes e 2 and e 1 e

a pseudo spectral scheme for the incompressible navier stokes equations using unstructured nodal elements a pseudo spectral scheme for solving the incompressible navier stokes equations using unstructured nodal triangles is proposed efficient algorithms are developed with numerical evidence that indicates optimal rates of convergence can be achieved navier stokes simulations of kovasznay shear layer roll up and row past a cylinder are included to show comparisons between the different nodal sets considered and an alternative modal approach c 2000 academic press

some results on approximate 1 median selection in metric spaces a 1 median in a finite metric space is a point with the minimum average distance to all other points given a positive integer n and oracle access to a distance metric on 1 2 n we study the problem of finding a 1 median in particular we show the nonexistence of 1 deterministic o 1 approximation o n query algorithms 2 deterministic email protected 1 approximation o n 2 query algorithms for graph metrics 3 deterministic email protected 1 approximation o n 2 query algorithms and 4 monte carlo email protected 1 approximation o n query algorithms with an w 1 probability of success we also show a monte carlo email protected approximation o log 2 1 e e 3 query algorithm with a 1 o e probability of success where email protected 0 1

mesh generation in curvilinear domains using high order elements the ability to construct suitable computational meshes is currently a significant limiting factor in the development of compact high order algorithms in very complex geometries compact high order algorithms such as spectral element or p type finite element techniques offer the potential of high accuracy if the solution is smooth and a well behaved mapping exists between the local sub domains and a standard region in this paper we address the problem of coupling high order algorithms with unstructured mesh generation and cad representation techniques we present three complementary strategies to alleviate the problem of generation of elemental regions with singular elemental mappings the first strategy investigates the influence of an anisometric parametric surface representation on the quality of high order unstructured meshes we show that a straightforward splitting of a standard linear mesh for use in a high order method can lead to the generation of distorted possibly invalid meshes even for simple computational domains such as cubes the second strategy uses hybrid meshes applying prismatic elements near curvilinear boundaries in the third and final strategy we investigate the use of curvature driven surface discretization to incorporate higher order information about the surface into the mesh generation using the computational reconstruction of the arterial bypass graft as an example computational domain we demonstrate how the combination of all three strategies leads to a valid high order discretization of the computational domain copyright 2001 john wiley sons ltd

on l functions of elliptic curves and cyclotomic towers in this paper we shall strengthen a recent theorem of ralph greenberg 1 concerning l functions of elliptic curves and anticyclotomic towers let k be an imaginary quadratic field and m an abelian extension of k possibly of infinite degree we say that the extension m k is anticyclotomic if m is galois over q and if the nontrivial element of gal k q acts on gal m k by inversion now fix a finite set p of rational primes and consider the compositum in an algebraic closure of k of all anticyclotomic extensions of k which are unramified outside p we denote this compositum by l and refer to it as the maximal anticyclotomic extension of k unramified outside p the field l may also be described as the union of all ring class fields of k with conductor divisible only by primes in p class field theory shows that gal l k is isomorphic to the product of a finite group and the group

helical flow in carotid bifurcation as surrogate marker of exposure to disturbed shear abstract the main purpose of the study is to verify if helical flow might be a surrogate marker of the exposure to disturbed shear in normal carotid bifurcations based on hemodynamic simulations data of 50 carotid bifurcations we defined appropriate helicity based bulk flow descriptors and multivariate linear regression analysis was performed to assess the potential for a combination of helicity based indicators in describing the exposure to disturbed shear to select the optimal combination of helicity based descriptors in the regression model the akaike information criterion was applied the identified statistical model is composed of two bulk flow descriptors proposed here to quantify helicity intensity and the balance between counter rotating helical flow patterns in the flow field the model revealed the existence of a significant relationship with adjusted squared pearson s correlation coefficient in the range 0 4 0 7 p

assessment of blood volume flow in slightly curved arteries from a single velocity profile abstract non invasive estimation of arterial blood volume flow bvf has become a central issue in assessment of cardiovascular risk poiseuille and womersley approaches are commonly used to assess the bvf from centerline velocity but both methods neglect the influence of curvature based on the assumption that the velocity in curved tubes as function of the circumferential position for a given radial position can be approximated by a cosine the bvf can also be estimated by averaging velocities at opposite radial positions referred to as the cosine model ctm this study investigates the accuracy of bvf estimation in slightly curved arteries for bvf waveforms obtained in the brachial artery of 6 volunteers computational fluid dynamics simulations were used to compute the influence of curvature on velocity profiles the bvf was then estimated from the simulation results with the ctm and methods based on poiseuille womersley and using the center stream velocity and the velocity waveform at the position where the maximum velocity is observed and compared to the prescribed bvf the simulations show that the influence of curvature is strongest when the flow decelerates for poiseuille and womersley the time average bvf was underestimated by maximally 10 4 and 7 8 for a radius of curvature of 50 and 100 mm respectively the estimation error is lower for the ctm and equals 4 2 and 1 2 for a radius of curvature of 50 and 100 mm respectively from this study we can conclude that the velocity waveform at the position of the maximum rather than the center stream velocity waveform combined with the womersley method should be chosen the ctm improves current estimation techniques if in vivo velocity distributions are available

a numerical comparison of seven grids for polynomial interpolation on the interval abstract seven types of chebyshev like grids in one dimension are compared according to four different criteria for accuracy the grid which minimizes the lebesgue constant is the best because it performs fairly well by all four criteria for the same reason minimizing the lebesgue constant seems to be the most useful measure of optimality because grids that are good according to this criterion are good when measured by other criteria too cfm optimality which is the property that all cardinal functions lagrange fundamental polynomials have maxima at the interpolation points seems to be the least discriminating criterion because all seven grids generate cardinal functions that have maxima at or very near the interpolation points the difference between these grids on all four criteria always less than a factor of two and usually much smaller are sufficiently modest so that the final choice between grids should probably not be made because of accuracy but rather based on other criteria such as ease of programming analytical simplicity conformality with other approximations and timestep in applications to partial differential equations to explore such nonaccuracy issues we also compared six of the grids on the basis of maximum allowed timestep when the grid is used to discretize the spatial coordinate and an explicit scheme is used for time marching the lebesgue optimal grid is also nearly optimal in the sense of allowing the longest timestep with a pseudospectral collocation algorithm the lebesgue grid allows a timestep three halves as long as that of the legendre lobatto spectral element method

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

tetrahedralhpfinite elements we present a new discretisation for the incompressible navier stokes equations that extends spectral methods to three dimensional complex domains consisting of tetrahedral subdomains the algorithm is based on standard concepts ofhpfinite elements as well as tensorial spectral elements this new formulation employs a hierarchical modal basis constructed from a new apex co ordinate system which retains a generalised tensor product these properties enable the development of computationally efficienct algorithms for use on standard finite volume unstructured meshes a detailed analysis is presented that documents the stability and exponential convergence of the method and several flow cases are simulated and compared with analytical and experimental results

bending and twisting of an in vivo coronary artery at a bifurcation abstract dynamic changes in the geometric shape and dimensions of a left coronary artery tree were extracted from the computer tomographically reconstructed three dimensional images of an in situ beating heart of an anesthetized dog wireframe models of the left coronary artery tree at 16 different instants of a cardiac cycle were constructed for the study of its flexing motion for quantifying the local bending and twisting of the left coronary artery tree the anatomic landmarks of the bifurcation points are selected as focussed locations at these points the space curves of the tree at different cardiac instants were first derived in parametric forms curvature and torsion expressions are next obtained in terms of the derivatives with respect to the parameter this analysis revealed that during the initial contraction of the heart wall a 2 reduction per millisecond in the radius of curvature occurred near the bifurcation point where the left circumflex coronary artery descends toward the apex of the heart when the left ventricular chamber reached a maximum value the radius of curvature was found to decrease at a rate of 2 3 ms 1 at the end of diastole an increase in the radius of curvature at a rate of 5 7 ms 1 was observed the twisting rates per unit length of artery near the bifurcation point of the selected artery were found to range from 0 62 to 0 63 ms 1

all pairs shortest distances for graphs with small integer length edges abstract there is a way to transform the all pairs shortest distances apsd problem where the edge lengths are integers with small m absolute value into a problem with edge lengths in 1 0 1 this transformation allows us to use the algorithms we developed earlier 1 and yields quite efficient algorithms in this paper we give new improved algorithms for these problems forn v the number of vertices mthe bound on edge length and the exponent of matrix multiplication we get the following results 1 a directed nonnegative apsd n m algorithm which runs ino t n m time where formula 2 a undirected apsd n m algorithm which runs ino m 1 2n log mn time

elliptic curves with complex multiplication and the conjecture of birch and swinnerton dyer 1 quick review of elliptic curves 2 2 elliptic curves over c 4 3 elliptic curves over local fields 6 4 elliptic curves over number fields 12 5 elliptic curves with complex multiplication 15 6 descent 22 7 elliptic units 27 8 euler systems 37 9 bounding ideal class groups 43 10 the theorem of coates and wiles 47 11 iwasawa theory and the main conjecture 50 12 computing the selmer group 61

hybrid element based approximation for the navier stokes equations in pipe like domains abstract motivated by its applicability to model blood flow in the cardiovascular system in this work we propose a numerical approximation of the navier stokes equations maintaining comparable accuracy with traditional finite element methods while performing a substantial reduction in the problem size the method is envisaged for domains in which flow phenomena exhibits a dominant axial direction the strategy consists of combining a finite element approximation for the description of fields velocity components and pressure in the primary axial direction while taking a polynomial spectral approximation for the description of fields across the secondary transversal direction in essence this method can be understood as an extension of the so called hierarchical modeling himod approach special attention is given to domains featuring sudden constrictions expansions and bifurcations for which a modified spectral approximation is considered the capabilities and potentialities of the proposed approach to simulate fluid flow phenomena in pipe like domains are presented through several examples

the nonlinear dynamics of elastic tubes conveying a fluid abstract the kirchhoff equations for elastic tubes are modified to include the effect of fluid flow using the techniques of linear and nonlinear analysis specially developed for the kirchhoff equations the effect of the fluid flow on the basic twist to writhe instability is investigated the results suggest an intriguing modification of the bifurcation threshold due to the flow beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics

clustering through continuous facility location problems we consider the continuous facility location problem conflp given a finite set of clients c r d and a number f r conflp consists in opening a set f r d of facilities each at cost f and connecting each client to an open facility the objective is to minimize the costs of opening facilities and connecting clients we reduce conflp to the standard facility location problem flp by using the so called approximate center sets this reduction preserves the approximation except for an error e and implies 1 488 e and 2 04 e approximations when the connection cost is given by the euclidean distance and the squared euclidean distance respectively moreover we obtain approximate center sets for the case that the connection cost is the th power of the euclidean distance achieving approximations for the corresponding problems for any 1 as a byproduct we also obtain a polynomial time approximation scheme for the k median problem with this cost function for any fixed k

polynomial time approximation schemes for euclidean traveling salesman and other geometric problems we present a polynomial time approximation scheme for euclidean tsp in fixed dimensions for every fixed c 1 and given any n nodes in r 2 a randomized version of the scheme finds a 1 1 c approximation to the optimum traveling salesman tour in o n log n o c time when the nodes are in r d the running time increases to o n log n o d c d 1 for every fixed c d the running time is n poly log n that is nearly linear in n the algorithmm can be derandomized but this increases the running time by a factor o n d the previous best approximation algorithm for the problem due to christofides achieves a 3 2 aproximation in polynomial time we also give similar approximation schemes for some other np hard euclidean problems minimum steiner tree k tsp and k mst the running times of the algorithm for k tsp and k mst involve an additional multiplicative factor k the previous best approximation algorithms for all these problems achieved a constant factor approximation we also give efficient approximation schemes for euclidean min cost matching a problem that can be solved exactly in polynomial time all our algorithms also work with almost no modification when distance is measured using any geometric norm such as e p for p 1 or other minkowski norms they also have simple parallel i e nc implementations

linear time approximation schemes for clustering problems in any dimensions we present a general approach for designing approximation algorithms for a fundamental class of geometric clustering problems in arbitrary dimensions more specifically our approach leads to simple randomized algorithms for the k means k median and discrete k means problems that yield 1 e approximations with probability 1 2 and running times of o 2 k e o 1 dn these are the first algorithms for these problems whose running times are linear in the size of the input nd for n points in d dimensions assuming k and e are fixed our method is general enough to be applicable to clustering problems satisfying certain simple properties and is likely to have further applications