kernelization and parameterized algorithms for covering a tree by a set of stars or paths two restricted versions of the subforest isomorphism problem the covering a tree by a set of stars ctss and the covering a tree by a set of paths ctsp problems are studied both problems are np complete the problems are closely related to a number of well studied problems including the problems subgraph isomorphism tree editing and graph packing it is shown that the problems ctss and ctsp are fixed parameter tractable thorough development of parameterized algorithms and kernelization algorithms for these problems are presented

perturbative solutions of the extended constraint equations in general relativity the extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface mathcal z in an asymptotically simple space time satisfying the vacuum conformal einstein equations developed by h friedrich the extended constraint equations consist of a quasi linear system of partial differential equations for the induced metric the second fundamental form and two other tensorial quantities defined on mathcal z and are equivalent to the usual constraint equations that mathcal z satisfies as a space like hypersurface in a space time satisfying einstein s vacuum equation this article develops a method for finding perturbative asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on euclidean space this method is fundamentally different from the classical method of lichnerowicz and york that is used to solve the usual constraint equations

a penrose like inequality for the mass of riemannian asymptotically flat manifolds we prove an optimal penrose like inequality for the mass of any asymptotically flat riemannian 3 manifold having an inner minimal 2 sphere and nonnegative scalar curvature our result shows that the mass is bounded from below by an expression involving the area of the minimal sphere as in the original penrose conjecture and some nomalized sobolev ratio as expected the equality case is achieved if and only if the metric is that of a standard spacelike slice in the schwarzschild space

reduction rules for the maximum parsimony distance on phylogenetic trees in phylogenetics distances are often used to measure the incongruence between a pair of phylogenetic trees that are reconstructed by different methods or using different regions of genome motivated by the maximum parsimony principle in tree inference we recently introduced the maximum parsimony mp distance which enjoys various attractive properties due to its connection with several other well known tree distances such as tbr and spr here we show that computing the mp distance between two trees a np hard problem in general is fixed parameter tractable in terms of the tbr distance between the tree pair our approach is based on two reduction rules the chain reduction and the subtree reduction that are widely used in computing tbr and spr distances more precisely we show that reducing chains to length 4 but not shorter preserves the mp distance in addition we describe a generalization of the subtree reduction which allows the pendant subtrees to be rooted in different places and show that this still preserves the mp distance on a slightly different note we also show that monadic second order logic msol posited over an auxiliary graph structure known as the display graph obtained by merging the two trees at their leaves can be used to obtain an alternative proof that computation of mp distance is fixed parameter tractable in terms of tbr distance we conclude with an extended discussion in which we focus on similarities and differences between mp distance and tbr distance and present a number of open problems one particularly intriguing question emerging from the msol formulation is whether two trees with bounded mp distance induce display graphs of bounded treewidth

universal positive mass theorems in this paper we develop a general study of contributions at infinity of bochner weitzenbock type formulas on asymptotically flat manifolds inspired by witten s proof of the positive mass theorem as an application we show that similar proofs can be obtained in a much more general setting as any choice of an irreducible natural bundle and a very large choice of first order operators may lead to a positive mass theorem along the same lines if the necessary curvature conditions are satisfied

infinitesimal moduli for the strominger system and killing spinors in generalized geometry we construct the space of infinitesimal variations for the strominger system and an obstruction space to integrability using elliptic operator theory we initiate the study of the geometry of the moduli space describing the infinitesimal structure of a natural foliation on this space the associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable killing spinor equations on a courant algebroid as an application we propose a unifying framework for metrics with holonomy mathrm su 3 and solutions of the strominger system

pacemakers in large arrays of oscillators with nonlocal coupling we model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling we assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation we concentrate on the case of heterogeneities with positive average and show that steady solutions to the nonlocal problem exist in particular we show that these heterogeneities act as a wave source this effect is not possible in 3 dimensional systems such as the complex ginzburg landau equation where the wavenumber of weak sources decays at infinity to obtain our results we use a series of isomorphisms to relate the nonlocal problem to the viscous eikonal equation we then use fredholm properties of the laplace operator in kondratiev spaces to obtain solutions to the eikonal equation and by extension to the nonlocal problem

cyclic accessibility of reachable states characterizes von neumann regular rings abstract the class of commutative von neumann regular rings is characterized by a generalization of the feedback cyclization property to non necessarily reachable systems for any system a b there exist a matrix k and a vector u such that a b and the single input system a bk bu have the same submodule of reachable states an explicit algorithm is presented to obtain k u for a given system a b

algorithms for parameterized maximum agreement forest problem on multiple trees the maximum agreement forest problem maf asks for a largest common subforest of a collection of phylogenetic trees the maf problem on two binary phylogenetic trees has been studied extensively in the literature in this paper we present a group of fixed parameter tractable algorithms for the maf problem on multiple i e two or more binary phylogenetic trees our techniques work fine for the problem for both rooted trees and unrooted trees the computational complexity of our algorithms is comparable with that of the known algorithms for two trees and is independent of the number of phylogenetic trees for which a maximum agreement forest is constructed

on the asymptotic behavior of solutions of the 2d euler equation abstract we prove that the 2d euler equation is globally well posed in a space of vector fields having spatial asymptotic expansion at infinity of any a priori given order the asymptotic coefficients of the solutions are holomorphic functions of t do not involve spacial logarithmic terms and develop even when the initial data has fast decay at infinity we discuss the evolution in time of the asymptotic terms and their approximation properties

ricci ollivier curvature of the rooted phylogenetic subtree prune regraft graph abstract statistical phylogenetic inference methods use tree rearrangement operations such as subtree prune regraft spr to perform markov chain monte carlo mcmc across tree topologies the structure of the graph induced by tree rearrangement operations is an important determinant of the mixing properties of mcmc motivating the study of the underlying spr graph in greater detail in this paper we investigate the spr graph of rooted trees rspr graph in a new way by calculating the ricci ollivier curvature with respect to uniform and metropolis hastings random walks this value quantifies the degree to which a pair of random walkers from specified points move towards each other negative curvature means that they move away from one another on average while positive curvature means that they move towards each other in order to calculate this curvature we develop fast new algorithms for rspr graph computation we then develop formulas characterizing how the number of rspr neighbors of a tree changes after an rspr operation is applied to that tree these give bounds on the curvature as well as a flatness in the limit theorem indicating that paths of small topology changes are easy to traverse however we find that large topology changes i e moving a large subtree give pairs of trees with negative curvature we show using simulation that mean access time distributions depend on distance degree and curvature demonstrating the relevance of these results to stochastic tree search

gluing and wormholes for the einstein constraint equations we establish a general gluing theorem for constant mean curvature solutions of the vacuum einstein constraint equations this allows one to take connected sums of solutions or to glue a handle wormhole onto any given solution away from this handle region the initial data sets we produce can be made as close as desired to the original initial data sets these constructions can be made either when the initial manifold is compact or asymptotically euclidean or asymptotically hyperbolic with suitable corresponding conditions on the extrinsic curvature in the compact setting a mild nondegeneracy condition is required in the final section of the paper we list a number ways this construction may be used to produce new types of vacuum spacetimes

parameterized and approximation algorithms for maximum agreement forest in multifurcating trees we study parameterized algorithms and approximation algorithms for the maximum agreement forest problem which for two given leaf labeled trees is to find a maximum forest that is a subgraph of both trees the problem was motivated by research in phylogenetics for parameterized algorithms while the problem is known to be fixed parameter tractable for binary trees it was an open problem whether the problem is still fixed parameter tractable for general trees we resolve this open problem by developing an o 3 k n time parameterized algorithm for general trees our techniques on tree structures also lead to a polynomial time approximation algorithm of ratio 3 for the problem giving the first constant ratio approximation algorithm for general trees

notes on exterior lp boundary value problems for nonhomogeneous elliptic operators abstract in terms of non smooth domains and non homogeneous elliptic operators this paper is devoted to study non tangential maximal function estimates for exterior l p regular problems we do not repeat the layer potential arguments which is a possible way instead appealing to a radial maximal function we can employ the results on homogeneous operators to make the proof much easier nevertheless this method relies on an exterior w 1 p estimate which is established in the course of the proof

pole assignment a new proof and algorithm in this paper a new proof of the pole assignment theorem is given this proof is a very straightforward one it is not based on canonical forms and also the reduction to the single input case heymann s lemma is not used furthermore an algorithm is given which allows to take into account numerical aspects with respect to the feedback construction for the multi input case furthermore the non uniqueness of the feedback matrix in the multi input case may be exploited in order to reduce the gains

an optimization approach to design of generalized bsb neural associative memories this article is concerned with the synthesis of the optimally performing gbsb generalized brain state in a box neural associative memory given a set of desired binary patterns to be stored as asymptotically stable equilibrium points based on some known qualitative properties and newly observed fundamental properties of the gbsb model the synthesis problem is formulated as a constrained optimization problem next we convert this problem into a quasi convex optimization problem called gevp generalized eigenvalue problem this conversion is particularly useful in practice because gevps can be efficiently solved by recently developed interior point methods design examples are given to illustrate the proposed approach and to compare with existing synthesis methods

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

a variational approach in weighted sobolev spaces to the operator x1 in exterior domains of ir3 consider the dirichlet problem v u k 1 u f withv k 0 in 3 or in an exterior domain of 3 where the skew symmetric differential operator 1 x1 is a singular perturbation of the laplacian because of the inhomogeneity of the fundamental solution we study existence uniqueness and regularity in sobolev spaces with anisotropic weights in these spaces the operator 1 yields an additional positive definite term giving better results than in sobolev spaces with radial weights the elliptic equation v u k 1 u f can be taken as a model problem for the oseen equations a linearized form of the navier stokes equations

fredholm and regularity theory of douglis nirenberg elliptic systems on mathbb r n we give a fairly complete exposition of the fredholm properties of the douglis nirenberg elliptic systems on mathbb r n in the classical unweighted lp sobolev spaces and under minimal assumptions about the coefficients these assumptions rule out the use of classical pseudodifferential operator theory although it is indirectly of assistance in places after generalizing a necessary and sufficient condition for fredholmness already known in special cases various invariance properties are established index null space etc with respect to p and the douglis nirenberg numbers among other things this requires getting around the problem that the lp spaces are not ordered by inclusion in turn with some work invariance leads to a regularity theory more general than what can be obtained by the method of differential quotients

computation of the index of linear elliptic operators in unbounded cylinders abstract linear fredholm elliptic operators in unbounded cylinders are considered a formula for the index of the operator i e the difference between the dimensions of the kernel and cokernel is obtained the key point is the splitting of the operator obtained by using spectral projectors of the laplace operator in the bounded transverse domain this together with a continuation method allows the reduction to one dimensional systems for which the index may be computed explicitly

the local structure of zero mode producing magnetic potentials we consider the class of continuous magnetic potentials on 3 which decay as o x 1 within this class it is shown that the set of potentials whose associated weyl dirac operator produces zero modes with multiplicity m forms a smooth submanifold of co dimension m2 when m 0 1 2 and is contained in a smooth submanifold of co dimension 2m 1 when m 3

strong feedback cyclization for systems over rings abstract for nonnecessarily reachable systems over a commutative ring r we define a strong form of feedback cyclization fc with this natural generalization of the fc property we obtain a feedback reduced form for systems over strong fc rings i e rings for which every system verifies the fc property in the particular case of reachable single input systems this gives the usual control canonical form of bumby et al remarks on the pole shifting problem over rings j pure appl algebra 20 1981 113 127 also it is proved that a commutative ring with 1 in its stable range has the strong fc property if and only if it has the ucu property which is the natural parallel form of the result given by brewer et al pole assignability in polynomial rings power series rings and prufer domains j algebra 106 1987 265 286 for the reachable case many classes of rings which were known to be fc rings are in fact strong fc rings but there are fc rings which are not strong fc rings

existence of ground states with exponential decay for semi linear elliptic equations in ofrn abstract in this paper we prove the existence of a positive solution tending exponentially to zero at infinity for a class of semi linear elliptic equations with nonconstant coefficients in ofr n

yamabe flow and adm mass on asymptotically flat manifolds in this paper we investigate the behavior of adm mass and einstein hilbert functional under the yamabe flow through studying the yamabe flow by weighted spaces for parabolic operators we show that the asymptotically flat property is preserved under the yamabe flow we also obtain that adm mass is invariant under the yamabe flow and yamabe flow is the gradient flow of einstein hilbert functional on n dimensional n 3 asymptotically flat manifolds with order n 22 for n 3 4 or n 3 for n 4 moreover we show that adm mass and einstein hilbert functional are non increasing under the yamabe flow on n dimensional asymptotically flat manifolds if we only assume the order n 22 for n 4

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

a geometric approach to dynamic feedback cyclization over commutative rings a different geometric point of view is introduced in the study of dynamic feedback cyclization over rings this considerably simplifies the theory in the free case in the sense that the main results can now be obtained by simple proofs the non free case remains to be examined

maximum agreement subtree in a set of evolutionary trees metrics and efficient algorithms the maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species an agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent under a suitable definition in all given evolutionary trees recently dynamic programming ideas were used to provide polynomial time algorithms for finding a maximum homeomorphic agreement subtree of two trees generalizing these methods to sets of more than two trees yields algorithms that are exponential in the number of trees unfortunately it turns out that in reality one is usually presented with more than two trees sometimes as many as thousands of trees in this paper we prove that the maximum homeomorphic agreement subtree problem is cal np complete for three trees with unbounded degrees we then show an approximation algorithm of time o kn5 for choosing the species that are not in a maximum agreement subtree of a set of k trees our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution while the set of evolutionary trees may be large in practice the trees usually have very small degrees typically no larger than three we develop a new method for finding a maximum agreement subtree of k trees of which one has degree bounded by d this new method enables us to find a maximum agreement subtree in time o knd 1 n2d

stability in yang mills theories at a solution of the yang mills equations ons4 or the yang mills higgs equation on 3 the hessian of the action functional defines a natural second order elliptic operator the number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge the proof of this assertion requires a relative index theorem for dirac type operators on n n 3

the maximum agreement forest problem approximation algorithms and computational experiments there are various techniques for reconstructing phylogenetic trees from data and in this context the problem of determining how distant two such trees are from each other arises naturally various metrics for measuring the distance between two phylogenies have been defined another way of comparing two trees t and u is to compute the so called maximum agreement forest of these trees informally the number of components of an agreement forest tells how many edges from each of t and u need to be cut so that the resulting forests agree after performing all forced edge contractions this problem is np hard even when the input trees have maximum degree 2 hein et al j hein t jiang l wang k zhang on the complexity of comparing evolutionary trees discrete applied mathematics 71 1996 153 169 presented an approximation algorithm for it claimed to have performance ratio 3 we show that the performance ratio of the algorithm proposed by hein et al is 4 and we also present two new 3 approximation algorithms for this problem we show how to modify one of the algorithms into a d 1 approximation algorithm for trees with bounded degree d d 2 finally we report on some computational experiments comparing the performance of the algorithms presented in this paper

fast and slow solutions in general relativity the initialization procedure we apply recent results in the theory of pde specifically in problems with two different time scales to einstein s equations near their newtonian limit the results imply a justification to post newtonian approximations when initialization procedures to different orders are made on the initial data we determine up to what order initialization is needed in order to detect the contribution to the quadrupole moment due to the slow motion of a massive body as distinct from initial data contributions to fast solutions and prove that such initialization is compatible with the constraint equations using the results mentioned the first post newtonian equations and their solutions in terms of green s functions are presented in order to indicate how to proceed in calculations with this approach

on the design of bsb neural associative memories using semidefinite programming this article is concerned with the reliable search for optimally performing bsb brain state in a box neural associative memories given a set of prototype patterns to be stored as stable equilibrium points by converting and or modifying the nonlinear constraints of a known formulation for the synthesis of bsb based associative memories into linear matrix inequalities we recast the synthesis into semidefinite programming problems and solve them by recently developed interior point methods the validity of this approach is illustrated by a design example

feedback cyclization for rings with finite stable range abstract for systems over commutative rings we introduce a property called fc s s 0 which means feedback cyclization with s inputs given a controllable system a b there exist a feedback matrix k and a matrix u with s columns such that a bk bu is controllable clearly fc 1 is the usual fc property the main result of this paper is the following for a ring r with the gcu property whenever a b is controllable there exists a vector u with bu unimodular r satisfies a strong form of the fc s property if and only if r is s stable i e r has s in its stable range this generalizes the known facts that 1 stable gcu rings have the fc property and principal ideal domains which are 2 stable gcu rings satisfy an analogous cyclization property with 2 inputs examples are given of fc s rings for s 1 which are not fc rings

the behavior of the heat operator on weighted sobolev spaces denoting by h the heat operator in rn 1 we investigate its properties as a bounded operator from one weighted sobolev space to another our main result gives conditions on the weights under which h is an injection a surjection or an isomorphism we also describe the range and kernel of h in all the cases our results are analogous to those obtained by r c mcowen for the laplace operator in rn

on elliptic systems in rn on etudie des systemes elliptiques k k d operateurs differentiels dans r n qui peuvent s ecrire sous la forme a a q ou a est un systeme elliptique d operateurs a coefficients constants et q est une perturbation a coefficient variable avec certaines proprietes de decroissance a x

geometry and analysis of spin equations we introduce w spin structures on a riemann surface and give a precise definition to the corresponding w spin equations for any quasi homogeneous polynomial w then we construct examples of nonzero solutions of spin equations in the presence of ramond marked points the main result of the paper is a compactness theorem for the moduli space of the solutions of w spin equations when w w x1 xt is a non degenerate quasi homogeneous polynomial with fractional degrees or weights qi 1 2 for all i in particular the compactness theorem holds for the superpotentials e6 e7 e8 or an 1 dn 1 for n 3

gauge choice in witten s energy expression witten s equation not d psi 0 can be interpreted as a gauge fixing condition for classical supergravity we rigorously prove the existence of asymptotically constant solutions of the more general gauge condition not d psi a psi for almost all endomorphismsa of the spin bundle each gives an expression for the gravitational energy similar to witten s these include the choice a sqrt r which yields the particularly elegant energy expression first noticed by deser

fixed parameter algorithms for maximum agreement forests we present new and improved fixed parameter algorithms for computing maximum agreement forests of pairs of rooted binary phylogenetic trees the size of such a forest for two trees corresponds to their subtree prune and regraft distance and if the agreement forest is acyclic to their hybridization number these distance measures are essential tools for understanding reticulate evolution our algorithm for computing maximum acyclic agreement forests is the first depth bounded search algorithm for this problem our algorithms substantially outperform the best previous algorithms for these problems

pole assignment for systems over rings a very simple proof of the pole assignment theorem for systems over a principal ideal domain and other rings is given furthermore an algorithm is presented extensions are also indicated

ricci flow on surfaces with cusps we consider the normalized ricci flow tg r g with initial condition a complete metric g0 on an open surface m where m is conformal to a punctured compact riemann surface and g0 has ends which are asymptotic to hyperbolic cusps we prove that when m 0 and 0 the flow g t converges exponentially to the unique complete metric of constant gauss curvature 2 in the conformal class

toda flows inverse spectral transform and realization theory abstract in this paper we establish some new relationships between the solution techniques for completely integrable nonlinear differential equations of the toda type and topics in realization theory

heat polynomial analogues for equations with higher order time derivatives abstract we generalize the heat polynomials for the heat equation to more general partial differential equations of higher order with respect to both the time variable and the space variables whereas the heat equation requires only one family of polynomials for an equation of the lth order with respect to time we introduce l families of polynomials these families correspond to the l initial conditions specified by the cauchy problem