maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction abstract for second order linear equations and inequalities which are degenerate elliptic but which possess a uniformly elliptic direction we formulate and prove weak maximum principles which are compatible with a solvability theory in suitably weighted versions of l 2 based sobolev spaces the operators are not necessarily in divergence form have terms of lower order and have low regularity assumptions on the coefficients the needed weighted sobolev spaces are in general anisotropic spaces defined by a non negative continuous matrix weight as preparation we prove a poincare inequality with respect to such matrix weights and analyze the elementary properties of the weighted spaces comparisons to known results and examples of operators which are elliptic away from a hyperplane of arbitrary codimension are given finally in the important special case of operators whose principal part is of grushin type we apply these results to obtain some spectral theory results such as the existence of a principal eigenvalue

quantifying and interpreting collective behavior in financial markets firms having similar business activities are correlated we analyze two different cross correlation matrices c constructed from i 30 min price fluctuations of 1000 us stocks for the two year period 1994 95 and ii one day price fluctuations of 422 us stocks for the 35 year period 1962 96 we find that the eigenvectors of c corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets these subsets are similar to business sectors and are stable for extended periods of time we find that price fluctuations of these subsets are characterized by power law decaying time correlations reminiscent of strongly interacting systems the internal structure of a complex system manifests itself in correlations among its constituents in complex physical systems interactions between constituents cause collective modes having special statistical properties which reflect the underlying dynamics can we quantify collective movement of stock prices in analogous terms to address this question we analyze the equal time correlation matrix c constructed from the price fluctuations of a large number of stocks first we find that the collective modes for the stock market problem partition the set of all stocks studied into distinct subsets typically these subsets are formed by combinations of related industries and in some cases they go beyond grouping by industry due to company diversification the traditional partitioning of firms into subsets by products and services is difficult and sometimes arbitrary and thus our results could be viewed as a statistical alternative to traditional industry classification 1 furthermore we find that the price fluctuations of the collective modes display long range power law time correla

a t 1 theorem for singular radon transforms we prove an analogue for singular radon transforms to the t 1 theorem of david and journe

the coupling analysis between stock market indices based on permutation measures abstract many information theoretic methods have been proposed for analyzing the coupling dependence between time series and it is significant to quantify the correlation relationship between financial sequences since the financial market is a complex evolved dynamic system recently we developed a new permutation based entropy called cross permutation entropy cpe to detect the coupling structures between two synchronous time series in this paper we extend the cpe method to weighted cross permutation entropy wcpe to address some of cpe s limitations mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor it shows more stable and reliable results than cpe does when applied it to spiky data and ar 1 processes besides we adapt the cpe method to infer the complexity of short length time series by freely changing the time delay and test it with gaussian random series and random walks the modified method shows the advantages in reducing deviations of entropy estimation compared with the conventional one finally the weighted cross permutation entropy of eight important stock indices from the world financial markets is investigated and some useful and interesting empirical results are obtained

algorithms of maximum likelihood data clustering with applications abstract we address the problem of data clustering by introducing an unsupervised parameter free approach based on maximum likelihood principle starting from the observation that data sets belonging to the same cluster share a common information we construct an expression for the likelihood of any possible cluster structure the likelihood in turn depends only on the pearson s coefficient of the data we discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations compared to standard clustering methods our approach has the advantages that i it is parameter free ii the number of clusters need not be fixed in advance and iii the interpretation of the results is transparent in order to test our approach and compare it with standard clustering algorithms we analyze two very different data sets time series of financial market returns and gene expression data we find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability

a comparison of implicit solvers for the immersed boundary equations explicit time discretizations of the immersed boundary method are known to require small timesteps to maintain stability a number of implicit methods have been introduced to alleviate this restriction to allow for a more ecient method but many of these methods still have a stability restriction on the timestep furthermore almost no comparisons have appeared in the literature of the relative computational costs of the implicit methods and the explicit method a recent paper e p newren a l fogelson r d guy and r m kirby unconditionally stable discretizations of the immersed boundary equations journal of computational physics vol 222 702 719 2007 addressed the confusion over stability of immersed boundary discretizations this paper identified the cause of instability in previous immersed boundary discretizations as lack of conservation of energy and introduced a new semi implicit discretization proven to be unconditionally stable i e it has bounded discrete energy the current paper addresses the issue of the eciency of the implicit solvers existing and new methods to solve implicit immersed boundary equations are described systematic comparisons of computational cost are presented for a number of these solution methods for our stable semi implicit immersed boundary discretization and an explicit discretization for two distinct test problems these comparisons show that two of the implicit methods are at least competitive with the explicit method on one test problem and outperform it on the other test problem in which the elastic stiness of the boundary does not dictate the timescale of the fluid motion

a characterization of hajlasz sobolev and triebel lizorkin spaces via grand littlewood paley functions abstract in this paper we establish the equivalence between the hajlasz sobolev spaces or classical triebel lizorkin spaces and a class of grand triebel lizorkin spaces on euclidean spaces and also on metric spaces that are both doubling and reverse doubling in particular when p n n 1 we give a new characterization of the hajlasz sobolev spaces m 1 p r n via a grand littlewood paley function

strong hypercontractivity and strong logarithmic sobolev inequalities for log subharmonic functions on stratified lie groups abstract on a stratified lie group g equipped with hypoelliptic heat kernel measure we study the behavior of the dilation semigroup on l p spaces of log subharmonic functions we consider a notion of strong hypercontractivity and a strong logarithmic sobolev inequality and show that these properties are equivalent for any group g moreover if g satisfies a classical logarithmic sobolev inequality then both properties hold this extends similar results obtained by graczyk kemp and loeb in the euclidean setting

eulerian lagrangian treatment of nondilute two phase gels we develop a three dimensional eulerian lagrangian two phase mixture model for a gel in which fluid is represented in eulerian coordinates and network in lagrangian coordinates the equations of motion and boundary conditions in their respective frames are derived using a principle of virtual power the volume fractions of each material at each point of eulerian space are calculated using the position and volume density of network particles network and fluid have separate velocity fields and the model includes viscous elastic and applied forces as well as those due to chemical potentials pressure and intermaterial drag we also develop a second order accurate numerical method for solving the model equations in one dimension illustrations of model behavior under a variety of conditions are shown

new properties of convex functions in the heisenberg group we prove some new properties of the weakly h convex functions recently introduced by danielli garofalo and nhieu as an interesting application of our results we prove a theorem of busemann feller alexandrov type in the heisenberg groups h n 1 2

corrections to sub riemannian geometry an error in the proof of corollary 6 2 of 1 has been pointed out by gerard ben arous the computation of m x in the case o 0 on p 243 is incorrect because m x 0 when 0 0 and jg x 0 for all k there is also a factor of missing in the formula as stated for 0 0 but this is not significant thus when applying the pontryagin theorem theorem 6 1 it is necessary to consider one additional case o 0 and m x9 0 along the curve the conditions of the theorem in this case lead to the equations

implicit second order immersed boundary methods with boundary mass abstract the immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures immersed boundary computations typically evaluate the elastic forces explicitly in the configuration of the immersed elastic structure in many applications this results in a severe restriction on the time step we present a semi implicit and a fully implicit second order accurate immersed boundary method the methods provide a natural way to handle mass on the immersed elastic structures we demonstrate their performance for a prototypical fluid structure interaction problem the methods are shown to possess superior stability properties that significantly alleviate the typically severe time step restriction of explicit computations

scale invariance and criticality in financial markets abstract we discuss the evidences supporting the view of financial markets as system operating close to a critical point from the theoretical side this picture is based on detailed knowledge of the behavior of minority games these are models of heterogeneous agents interacting through a market mechanism which can be solved analytically with tools of statistical mechanics from the empirical side we extend these evidences showing that market sector structure is itself scale invariant scale invariant features also appear in the classification of states in the time domain

an algebra containing the two sided convolution operators abstract we present an intrinsically defined algebra of operators containing the right and left invariant calderon zygmund operators on a stratified group the operators in our algebra are pseudolocal and bounded on l p 1 p this algebra provides an example of an algebra of singular integrals that falls outside of the classical calderon zygmund theory

sub riemannian geometry of the coefficients of univalent functions abstract we consider coefficient bodies m n for univalent functions based on the lowner kufarev parametric representation we get a partially integrable hamiltonian system in which the first integrals are kirillov s operators for a representation of the virasoro algebra then m n are defined as sub riemannian manifolds given a lie poisson bracket they form a grading of subspaces with the first subspace as a bracket generating distribution of complex dimension two with this sub riemannian structure we construct a new hamiltonian system to calculate regular geodesics which turn to be horizontal lagrangian formulation is also given in the particular case m 3

area stationary surfaces in the heisenberg group h1 we consider area stationary surfaces perhaps with a volume constraint in the heisenberg group h1 endowed with its carnot caratheodory distance by analyzing the first variation of area we characterize c2 area stationary surfaces as those with mean curvature zero or constant if a volume preserving condition is assumed and such that the characteristic curves meet orthogonally the singular curves moreover a minkowski type formula relating the area the mean curvature and the volume is obtained for volume preserving area stationary surfaces enclosing a given region as a consequence of the characterization of area stationary surfaces we refine the bernstein type theorem given in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 and nicola garofalo scott pauls the bernstein problem in the heisenberg group arxiv math dg 0209065 to describe all c2 entire area stationary graphs over the xy plane in a calibration argument shows that these graphs are globally area minimizing finally by using the description of the singular set in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 the characterization of area stationary surfaces and the ruling property of constant mean curvature surfaces we prove our main results where we classify area stationary surfaces in with or without a volume constraint and non empty singular set in particular we deduce the following counterpart to alexandrov uniqueness theorem in euclidean space any compact connected c2 surface in area stationary under a volume constraint must be congruent to a rotationally symmetric sphere obtained as the union of all the geodesics of the same curvature joining two points as a consequence we solve the isoperimetric problem in assuming c2 smoothness of the solutions 13 completely reducible hypersurfaces in a pencil pages 672 688 j v pereira s yuzvinsky preview pdf 324 k related articles 14 modules over motivic cohomology pages 689 727 oliver rondigs paul arne ostvaer preview pdf 303 k related articles 15 the fundamental group of period domains over finite fields pages 728 741 sascha orlik preview pdf 154 k related articles articles 1 15

existence of weak solutions to degenerate p laplacian equations and integral formulas abstract we study the problem of solving some general integral formulas and then apply the conclusions to obtain results about the existence of weak solutions of various degenerate p laplacian equations we adapt variational calculus methods and the mountain pass lemma without the palais smale condition and we use an abstract version of lions concentration compactness principle ii

lipschitz continuity aleksandrov theorem and characterizations for h convex functions in the geometries of stratified groups we show that h convex functions locally bounded from above are locally lipschitz continuous and that the class of v convex functions exactly corresponds to the class of upper semicontinuous h convex functions as a consequence v convex functions are locally lipschitz continuous in every stratified group in the class of step 2 groups we characterize locally lipschitz h convex functions as measures whose distributional horizontal hessian is positive semidefinite in euclidean space the same results were obtained by dudley and reshetnyak we prove that a continuous h convex function is a e twice differentiable whenever its second order horizontal derivatives are radon measures

strong maximum principle for mean curvature operators on subriemannian manifolds we study the strong maximum principle for horizontal p mean curvature operator and p sub laplacian operator on subriemannian manifolds including in particular heisenberg groups and heisenberg cylinders under a certain hormander type condition on vector fields we show the strong maximum principle holds in higher dimensions for two cases a the touching point is nonsingular b the touching point is an isolated singular point for one of comparison functions for a background subriemannian manifold with local symmetry of isometric translations we have the strong maximum principle for associated graphs which include among others intrinsic graphs with constant horizontal p mean curvature as applications we show a rigidity result of horizontal p minimal hypersurfaces in any higher dimensional heisenberg cylinder and a pseudo halfspace theorem for any heisenberg group

area stationary surfaces inside the sub riemannian three sphere we consider the sub riemannian metric gh on mathbb s 3 given by the restriction of the riemannian metric of curvature 1 to the plane distribution orthogonal to the hopf vector field we compute the geodesics associated to the carnot caratheodory distance and we show that depending on their curvature they are closed or dense subsets of a clifford torus we study area stationary surfaces with or without a volume constraint in mathbb s 3 g h by following the ideas and techniques by ritore and rosales area stationary surfaces in the heisenberg group mathbb h 1 arxiv math dg 0512547 we introduce a variational notion of mean curvature characterize stationary surfaces and prove classification results for complete volume preserving area stationary surfaces with non empty singular set we also use the behaviour of the carnot caratheodory geodesics and the ruling property of constant mean curvature surfaces to show that the only c2 compact connected embedded surfaces in mathbb s 3 g h with empty singular set and constant mean curvature h such that h sqrt 1 h 2 is an irrational number are clifford tori finally we describe which are the complete rotationally invariant surfaces with constant mean curvature in mathbb s 3 g h

the square_ b heat equation and multipliers via the wave equation recently nagel and stein studied the square b heat equation where square b is the kohn laplacian on the boundary of a weakly pseudoconvex domain of finite type in mathbb c 2 they showed that the schwartz kernel of e t square b satisfies good off diagonal estimates while that of e t square b pi satisfies good on diagonal estimates where denotes the szego projection we offer a simple proof of these results which easily generalizes to other similar situations our methods involve adapting the well known relationship between the heat equation and the finite propagation speed of the wave equation to this situation in addition we apply these methods to study multipliers of the form m square b in particular we show that m square b is an nis operator where m satisfies an appropriate mihlin hormander condition

bootstrap validation of links of a minimum spanning tree abstract we describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables we show that two different bootstrap procedures provide partly distinct information that can be informative about the investigated complex system we investigate two case studies by considering daily returns of two portfolios of stocks traded in the us equity markets in different time periods the first method performs a row bootstrap whereas the second method performs a pair bootstrap to obtain a bootstrap replica of each correlation coefficient we show that the parallel use of the two methods can highlight details about the stability of links selected by the minimum spanning tree associated with the correlation matrix of stock portfolios that can be missed by applying only a single bootstrap methods

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

an efficient semi implicit immersed boundary method for the navier stokes equations the immersed boundary method is one of the most useful computational methods in studying fluid structure interaction on the other hand the immersed boundary method is also known to require small time steps to maintain stability when solved with an explicit method many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability constraint but none of them give satisfactory performance in this paper we propose an efficient semi implicit scheme to remove this stiffness from the immersed boundary method for the navier stokes equations the construction of our semi implicit scheme consists of two steps first we obtain a semi implicit discretization which is proved to be unconditionally stable this unconditionally stable semi implicit scheme is still quite expensive to implement in practice next we apply the small scale decomposition to the unconditionally stable semi implicit scheme to construct our efficient semi implicit scheme unlike other implicit or semi implicit schemes proposed in the literature our semi implicit scheme can be solved explicitly in the spectral space thus the computational cost of our semi implicit schemes is comparable to that of an explicit scheme our extensive numerical experiments show that our semi implicit scheme has much better stability property than an explicit scheme this offers a substantial computational saving in using the immersed boundary method

lq l holder continuity for quasilinear parabolic equations associated to sobolev derivations abstract let x be a locally compact metrizable space endowed with a couple of equivalent finite radon measures m and and let e be a hilbert c monomodule over c0 x we consider a class of abstract nonlinear parabolic equations defined as follows let be a closed derivation from l2 x m to l2 e and tt be the strongly continuous nonlinear semigroup naturally associated in the sense of brezis 1973 to the convex l s c functional e u x u x p d x where is the natural modulus function associated to e the generator of the semigroup considered is a natural generalization of the usual p laplacian operator we suppose that a suitable sobolev like inequality of the form u l2d d 2 x m c u l2 e holds true for some d 2 with p 2 d then tt is a nonlinear markov semigroup in the sense that it is order preserving and nonexpansive on each lq x m for any q 2 and moreover it satisfies ttu ttv l x m cm x t u v lq x m for all q 2 and suitable constants depending only on p q d examples include the semigroup generated by the p laplacian on finite measure manifolds with boundary and homogeneous dirichlet boundary conditions as well as by p laplacian like operators associated both to regular sub riemannian structures and to systems of possibly singular or degenerate vector fields satisfying the appropriate sobolev inequalities

global behavior of the heat kernel associated with certain sub laplacians on semisimple lie groups abstract we prove global sharp estimates for the heat kernel related to certain sub laplacians on a real semisimple lie group from which we deduce an estimate for the corresponding green function

h p boundedness of calderon zygmund operators on product spaces in this paper we prove the product h p boundedness of calderon zygmund operators which were considered by fefferman and stein the methods used in this paper are new even for the classical h p boundedness of calderon zygmund operators namely using some subtle estimates together with the h p l p boundedness of product vector valued calderon zygmund operators

isoholonomic problems and some applications we study the problem of finding the shortest loops with a given holonomy we show that the solutions are the trajectories of particles in yang mills potentials theorem 4 or equivalently the projections of kaluza klein geodesics theorem 2 applications to quantum mechanics berry s phase sect 3 and the optimal control of deformable bodies sect 6 are touched upon

non minimality of corners in subriemannian geometry we give a short solution to one of the main open problems in subriemannian geometry namely we prove that length minimizers do not have corner type singularities with this result we solve problem ii of agrachev s list and provide the first general result toward the 30 year old open problem of regularity of subriemannian geodesics

identification of clusters of companies in stock indices via potts super paramagnetic transitions the clustering of companies within a specic stock market index is studied by means of super paramagnetic transitions of an appropriate q state potts model where the spins correspond to companies and the interactions are functions of the correlation coecients determined from the time dependence of the companies individual stock prices the method is a generalization of the clustering algorithm by domany et al to the case of anti ferromagnetic interactions corresponding to anti correlations for the dow jones industrial average where no anti correlations were observed in the investigated time period the previous results obtained by dierent tools were well reproduced for the standard poor s 500 where anti correlations occur repulsion between stocks modify the cluster structure c 2000 elsevier science b v all rights reserved stock market indices like the dow jones dj or standard poor s 500 s p 500 are used as indicators of the status of the markets they are averaged values of a dierent number of selected companies indicative of the economy of a given market it is of both theoretical and practical importance to analyze how individual contributions to the average behave the customary approach in the nancial literature focuses on the investigation of the properties of the covariance matrix here we take a dierent approach aiming to identify the presence of a hierarchical structure inside the set of stocks simultaneously traded in a market the identication of the hierarchy of clusters is of central importance both from the point of view of understanding the dynamics of

emergence of time horizon invariant correlation structure in financial returns by subtraction of the market mode we investigate the emergence of a structure in the correlation matrix of assets returns as the time horizon over which returns are computed increases from the minutes to the daily scale we analyze data from different stock markets new york paris london milano and with different methods in addition to the usual correlations we also analyze those obtained by subtracting the dynamics of the center of mass i e the market mode we find that when the center of mass is not removed the structure emerges as the time horizon increases from splitting a single large cluster into smaller ones by contrast when the market mode is removed the structure of correlations observed at the daily scale is already well defined at very high frequency 5 min in the new york stock exchange moreover this structure accounts for 80 of the classification of stocks in economic sectors similar results though less sharp are found for the other markets we also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity

fast super paramagnetic clustering abstract we map stock market interactions to spin models to recover their hierarchical structure using a simulated annealing based super paramagnetic clustering spc algorithm this is directly compared to a modified implementation of a maximum likelihood approach we call fast super paramagnetic clustering f spc the methods are first applied to standard toy test case problems and then to a data set of 447 stocks traded on the new york stock exchange nyse over 1249 days the signal to noise ratio of stock market correlation matrices is briefly considered our result recover approximately clusters representative of standard economic sectors and mixed ones whose dynamics shine light on the adaptive nature of financial markets and raise concerns relating to the effectiveness of industry based static financial market classification in the world of real time data analytics a key result is that we show that f spc maximum likelihood solutions converge to ones found within the super paramagnetic phase where the entropy is maximum and those solutions are qualitatively better for high dimensionality data sets

smoothness of subriemannian isometries we show that the group of isometries i e distance preserving homeomorphisms of an equiregular subriemannian manifold is a finite dimensional lie group of smooth transformations the proof is based on a new pde argument in the spirit of harmonic coordinates establishing that in an arbitrary subriemannian manifold there exists an open dense subset where all isometries are smooth

a fast robust and non stiff immersed boundary method we propose a fast and non stiff approach for the solutions of the immersed boundary method for newtonian incompressible flows in two or three dimensions the proposed methodology is built on a robust semi implicit discretization introduced by peskin in the late 70s which is solved efficiently through the novel use of a fast treecode strategy to compute flow structure interactions optimal multipole type expansions are performed numerically by solving a least squares problem with a new fast iterative algorithm the new immersed boundary method is particularly well suited for three dimensional applications and or for problems where the number of immersed boundary points is large we demonstrate the efficacy and superiority of the method over existing approaches with two simple but illustrative examples in 3d

duality on gradient estimates and wasserstein controls abstract we establish a duality between l p wasserstein control and l q gradient estimate in a general framework our result extends a known result for a heat flow on a riemannian manifold especially we can derive a wasserstein control of a heat flow directly from the corresponding gradient estimate of the heat semigroup without using any other notion of lower curvature bound by applying our result to a subelliptic heat flow on a lie group we obtain a coupling of heat distributions which carries a good control of their relative distance

a poroelastic immersed boundary method with applications to cell biology the immersed boundary method is a widely used mixed eulerian lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids in the traditional immersed boundary method the fluid and structure move with the same velocity field in this work a model based on the immersed boundary method is presented for simulating poroelastic media in which the fluid permeates a porous elastic structure of small volume fraction that moves with its own velocity field two distinct methods for calculating elastic stresses are presented and compared the methods are validated on a radially symmetric test problem by comparing with a finite difference solution of the classical equations of poroelasticity finally two applications of the modeling framework to cell biology are provided cellular blebbing and cell crawling it is shown that in both examples poroelastic effects are necessary to explain the relevant mechanics

path planning on compact lie groups using a homotopy method abstract in this paper we address the issue of solving the motion planning problems mpp for short for a class of left invariant control systems whose state spaces are semisimple compact lie groups the sub riemannian metrics induced by the dynamics of admit nontrivial abnormal extremals this fact a priori represents an obstruction for the procedure we use to tackle the mpp which consists of a homotopy or continuation method we are however able to provide complete answers for the mpp

radial maximal function characterizations of hardy spaces on rd spaces and their applications let x be an rd space i e a space of homogeneous type in the sense of coifman and weiss which has the reverse doubling property assume that x has a dimension n f or 0 d enote byh p x h p d x and h p x the corresponding hardy spaces on x defined by the nontangential maximal function the dyadic maximal function and the grand maximal function respectively using a new inhomogeneous calderon reproducing formula it is shown that all these hardy spaces coincide with l p x w henp 1 and with each other when p n n 1 1 an atomic characterization for h p x w ithp n n 1 1 is also established moreover in the range p n n 1 1 it is proved that the spaceh p x the hardy space h p x defined via the littlewood paley function and the atomic hardy space of coifman and weiss coincide furthermore it is proved that a sublinear operator t uniquely extends to a bounded sublinear operator from h p x t o some quasi banach space b if and only if t maps all p q atoms when q p 1 or continuous p atoms into uniformly bounded elements of b

unconditionally stable discretizations of the immersed boundary equations the immersed boundary ib method is known to require small timesteps to maintain stability when solved with an explicit or approximately implicit method many implicit methods have been proposed to try to mitigate this timestep restriction but none are known to be unconditionally stable and the observed instability of even some of the fully implicit methods is not well understood in this paper we prove that particular backward euler and crank nicolson like discretizations of the nonlinear immersed boundary terms of the ib equations in conjunction with unsteady stokes flow can yield unconditionally stable methods we also show that the position at which the spreading and interpolation operators are evaluated is not relevant to stability so as long as both operators are evaluated at the same location in time and space we further demonstrate through computational tests that approximate projection methods which do not provide a discretely divergence free velocity field appear to have a stabilizing influence for these problems and that the implicit methods of this paper when used with the full navier stokes equations are no longer subject to such a strict timestep restriction and can be run up to the cfl constraint of the advection terms

sub riemannian calculus on hypersurfaces in carnot groups we develop a sub riemannian calculus for hypersurfaces in graded nilpotent lie groups we introduce an appropriate geometric framework such as horizontal levi civita connection second fundamental form and horizontal laplace beltrami operator we analyze the relevant minimal surfaces and prove some basic integration by parts formulas using the latter we establish general first and second variation formulas for the horizontal perimeter in the heisenberg group such formulas play a fundamental role in the sub riemannian bernstein problem

2 d parachute simulation by the immersed boundary method parachute aerodynamics involves an interaction between the flexible elastic porous parachute canopy and the high speed airflow relative to the parachute through which the parachute falls computer simulation of parachute dynamics typically simplifies the problem in various ways e g by considering the parachute as a rigid bluff body here we avoid such simplification by using the immersed boundary ib method to study the full fluid structure interaction the ib method is generalized to handle porous immersed boundaries and the generalized method is used to study the influence of porosity on parachute stability

multiparameter hardy space theory on carnot caratheodory spaces and product spaces of homogeneous type this paper is inspired by the work of nagel and stein in which the lp 1 p theory has been developed in the setting of the product carnot caratheodory spaces m m1 mn formed by vector fields satisfying hormander s finite rank condition the main purpose of this paper is to provide a unified approach to develop the multiparameter hardy space theory on product spaces of homogeneous type this theory includes the product hardy space its dual the product bmo space the boundedness of singular integral operators and calderon zygmund decomposition and interpolation of operators as a consequence we obtain the endpoint estimates for those singular integral operators considered by nagel and stein 2004 in fact we will develop most of our theory in the framework of product spaces of homogeneous type which only satisfy the doubling condition and some regularity assumption on the metric all of our results are established by introducing certain banach spaces of test functions and distributions developing discrete calderon identity and discrete littlewood paley stein theory our methods do not rely on the journe type covering lemma which was the main tool to prove the boundedness of singular integrals on the classical product hardy spaces

extended aic model based on high order moments and its application in the financial market abstract in this paper an extended method of traditional akaike information criteria aic is proposed to detect the volatility of time series by combining it with higher order moments such as skewness and kurtosis since measures considering higher order moments are powerful in many aspects the properties of asymmetry and flatness can be observed furthermore in order to reduce the effect of noise and other incoherent features we combine the extended aic algorithm with multiscale wavelet analysis in which the newly extended aic algorithm is applied to wavelet coefficients at several scales and the time series are reconstructed by wavelet transform after that we create aic planes to derive the relationship among aic values using variance skewness and kurtosis respectively when we test this technique on the financial market the aim is to analyze the trend and volatility of the closing price of stock indices and classify them and we also adapt multiscale analysis to measure complexity of time series over a range of scales empirical results show that the singularity of time series in stock market can be detected via extended aic algorithm

boundedness and regularity of solutions of degenerate elliptic partial differential equations abstract we study quasilinear degenerate equations with their associated operators satisfying sobolev and poincare inequalities our problems are similar to those in sawyer and wheeden 2006 20 but we consider more general integral equations on abstract sobolev spaces indeed we provide a unified approach via abstract setting our main tool is moser iteration we obtain boundedness assuming a weighted sobolev embedding of weak solutions and also harnack inequalities for nonnegative solutions assuming further that a weighted poincare inequality holds for their logarithm and existence of a sequence of cutoff functions and hence holder s continuity of solutions our assumption is weaker than the above mentioned paper and other existing papers even in the case where the setting is on r n for example we do not assume any doubling condition and we are able to deal with weighted estimates our results are new even when the leading term in the equations are vector fields that satisfy hormander s conditions

detrended moving average partial cross correlation analysis on financial time series abstract cross correlations between nonlinear time series widely exist in complex systems it is of great importance to accurately measure the correlations between time series in this work we suggest a combination methodology of detrended moving average processing and partial cross correlation analysis to quantify the correlations between different time series which we call as detrended moving average partial cross correlation analysis d m p c c a this novel approach combines the advantages of detrended moving average processing and partial cross correlation analysis not only exploring power law cross correlations between two signals but removing underlying impacts of other signals on those two signals to demonstrate the advantages of this approach we carry out experiments with synthetic data generated by correlated processes and compare the performance of this measurement to traditional cross correlation techniques it is found that this method can reveal the real cross correlations between systems even when the indirect cross correlations established by other common factors exist then we go further study into the application of d m p c c a to financial time series in order to report its performance in stock markets and investigate cross correlations between different stock indices furthermore the rolling windows method is used in conjunction with d m p c c a to capture the changes of cross correlations between stock indices as time goes on we notice that there is a special period when d m p c c a coefficients between stock indices are obviously different from those of other periods

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

on 2 step corank 2 nilpotent sub riemannian metrics in this paper we study the nilpotent 2 step corank 2 sub riemannian metrics that are nilpotent approximations of general sub riemannian metrics we exhibit optimal syntheses for these problems it turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression as a by product of this study we get some smoothness properties of the spherical hausdorff measure in the case of a generic 6 dimensional 2 step corank 2 sub riemannian metric

efficient solutions to robust semi implicit discretizations of the immersed boundary method the immersed boundary method is a versatile tool for the investigation of flow structure interaction in a large number of applications the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well known severe time step restriction for explicit discretizations this excessive stability constraint can be removed with fully implicit or suitable semi implicit schemes but at a seemingly prohibitive computational cost while economical alternatives have been proposed recently for some special cases there is a practical need for a computationally efficient approach that can be applied more broadly in this context we revisit a robust semi implicit discretization introduced by peskin in the late 1970s which has received renewed attention recently this discretization in which the spreading and interpolation operators are lagged leads to a linear system of equations for the interface configuration at the future time when the interfacial force is linear however this linear system is large and dense and thus it is challenging to streamline its solution moreover while the same linear system or one of similar structure could potentially be used in newton type iterations nonlinear and highly stiff immersed structures pose additional challenges to iterative methods in this work we address these problems and propose cost effective computational strategies for solving peskin s lagged operators type of discretization we do this by first constructing a sufficiently accurate approximation to the system s matrix and we obtain a rigorous estimate for this approximation this matrix is expeditiously computed by using a combination of pre calculated values and interpolation the availability of a matrix allows for more efficient matrix vector products and facilitates the design of effective iterative schemes we propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points one of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force we demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method in addition to considering the standard elliptical drop test case we show both the robustness and efficacy of the proposed methodology with a 2d model of a heart valve

two finite element approaches for darcy and darcy brinkman flow through deformable porous media mixed method vs nurbs based isogeometric continuity abstract porous media problems with coupled finite deformations and flow are still quite challenging if large deformations occur a non homogeneous porosity field is almost inevitable as the porosity can vary due to deformation or due to flow and pore pressure from a numerical point of view this significantly changes the mathematical description of the problem in this contribution we will analyze the consequences of the occurrence of porosity gradients on the finite element formulations of saturated two phase porous media for darcy and darcy brinkman flow we will present two approaches which are capable of fulfilling the numerical requirements for convergence the first will be an approach based on nurbs shape functions the second is a mixed formulation including the porosity as primary solution field in addition we will propose a method to include no penetration or no slip constraints into the monolithic system using a dual lagrange multiplier method the potential of the proposed methods for solving porous flow structure interaction undergoing large deformations will be illustrated by numerical examples

intrinsic random walks and sub laplacians in sub riemannian geometry on a sub riemannian manifold we define two type of laplacians the macroscopic laplacian as the divergence of the horizontal gradient once a volume is fixed and the microscopic laplacian as the operator associated with a geodesic random walk we consider a general class of random walks where all sub riemannian geodesics are taken in account this operator depends only on the choice of a complement c to the sub riemannian distribution and is denoted l c we address the problem of equivalence of the two operators this problem is interesting since on equiregular sub riemannian manifolds there is always an intrinsic volume e g popp s one p but not a canonical choice of complement the result depends heavily on the type of structure under investigation on contact structures for every volume there exists a unique complement c such that l c on carnot groups if h is the haar volume then there always exists a complement c such that h l c however this complement is not unique in general for quasi contact structures in general p l c for any choice of c in particular l c is not symmetric w r t popp s measure this is surprising especially in dimension 4 where in a suitable sense p is the unique intrinsic macroscopic laplacian a crucial notion that we introduce here is the n intrinsic volume i e a volume that depends only on the set of parameters of the nilpotent approximation when the nilpotent approximation does not depend on the point a n intrinsic volume is unique up to a scaling by a constant and the corresponding n intrinsic sub laplacian is unique this is what happens for dimension smaller or equal than 4 and in particular in the 4 dimensional quasi contact structure mentioned above

network analysis of the chinese stock market during the turbulence of 2015 2016 using log returns volumes and mutual information abstract we use mutual information and symbolization method of time series to construct minimum spanning tree of the financial network of log returns and trading volumes of the top 110 companies on the chinese stock market listed on the csi 300 index from january 2014 to december 2017 to analyze the chinese stock market s turbulence during 2015 to 2016 we construct three minimum spanning trees of pre turbulence turbulence and post turbulence the findings show that minimum spanning tree of turbulence has the significant differences in topological characteristics and network s measures with pre turbulence and post turbulence networks furthermore the pre turbulence network is robust against nodes attack while turbulence network is fragile against it

local normalization uncovering correlations in non stationary financial time series abstract the measurement of correlations between financial time series is of vital importance for risk management in this paper we address an estimation error that stems from the non stationarity of the time series we put forward a method to rid the time series of local trends and variable volatility while preserving cross correlations we test this method in a monte carlo simulation and apply it to empirical data for the s p 500 stocks

on the hyper elastic formulation of the immersed boundary method abstract the immersed boundary ib method is both a mathematical formulation and a numerical method for fluid structure interaction problems in which immersed incompressible visco elastic bodies or boundaries interact with an incompressible fluid previous formulations of the ib method were not able to treat appropriately immersed materials of finite nonzero thickness modeled by general hyper elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid fluid interface such a jump does not arise when the solid is comprised of fibers that run parallel to the interface but typically does arise in other cases e g when the solid contains elastic fibers that terminate at the solid fluid interface we present a derivation of the ib method that takes into account in an appropriate way the missing term the derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work the stress is divided into its fluid like and solid like components and each of these two terms is treated in its natural framework i e the eulerian framework for the fluid like stress and the lagrangian framework for the solid like stress we describe how the ib method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments

curvature in sub riemannian geometry we study curvature problems on a nearly riemannian manifold which is a sub riemannian manifold m hm g vm whose adapted tensor field given by 2 2 vanishes identically first we prove the existence and uniqueness of what we call horizontal riemannian connection which is a torsion free and metric linear connection on the horizontal distribution hm then we define the horizontal sectional curvature of m and study nearly riemannian space forms which are nearly riemannian manifolds of constant horizontal sectional curvature several horizontal geometric objects are introduced and studied for example horizontal ricci tensor horizontal scalar curvature horizontal laplacian finally as a prelude to applications to kaluza klein theories we define the horizontal einstein gravitational tensor field and show that its horizontal divergence vanishes identically on m some examples are presented to illustrate the theory developed in the paper

minimum entropy density method for the time series analysis abstract the entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems we develop the minimum entropy density method medm to detect the structure scale of a given time series which is defined as the scale in which the uncertainty is minimized hence the pattern is revealed most the medm is applied to the financial time series of standard and poor s 500 index from february 1983 to april 2006 then the temporal behavior of structure scale is obtained and analyzed in relation to the information delivery time and efficient market hypothesis

data clustering and noise undressing of correlation matrices we discuss an approach to data clustering we find that maximum likelihood leads naturally to an hamiltonian of potts variables that depends on the correlation matrix and whose low temperature behavior describes the correlation structure of the data for random uncorrelated data sets no correlation structure emerges on the other hand for data sets with a built in cluster structure the method is able to detect and recover efficiently that structure finally we apply the method to financial time series where the low temperature behavior reveals a nontrivial clustering