asymptotic stability of impulsive stochastic partial differential equations with infinite delays in this paper we study the existence and asymptotic stability in pth moment of mild solutions to nonlinear impulsive stochastic partial differential equations with infinite delay by employing a fixed point approach sufficient conditions are derived for achieving the required result these conditions do not require the monotone decreasing behaviour of the delays

fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

h asymptotic stability by fixed point in neutral nonlinear differential equations with delay abstract we use fixed point theory to obtain h asymptotic stability results about the zero solution of nonlinear differential equations with functional delay neither boundedness of the deviations nor a fixed sign on the coefficients functions are asked an explicit estimation of the solutions is obtained and a necessary and sufficient condition is determined classical results are improved and generalized

the equality of the siler cones k3 and k4 the general case abstract in this paper it is shown that siler cones k 3 and k 4 of positive semidefinite preserving linear transformations are equal in the process of showing this a common characterization theorem is given

on the shape of a set of points in the plane a generalization of the convex hull of a finite set of points in the plane is introduced and analyzed this generalization leads to a family of straight line graphs alpha shapes which seem to capture the intuitive notions of fine shape and crude shape of point sets it is shown that a shapes are subgraphs of the closest point or furthest point delaunay triangulation relying on this result an optimal o n log n algorithm that constructs alpha shapes is developed

from gene trees to species trees this paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model this is a fundamental problem in computational molecular biology our main results are as follows a linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree this answers a problem raised recently by eulenstein mirkin and vingron j comput bio 5 1998 pp 135 148 the complexity of finding an optimal species tree from gene trees is studied the problem is proved to be np hard for the duplication cost and for the mutation cost further the concept of reconciled trees was introduced by goodman et al and formalized by page for visualizing the relationship between gene and species trees we show that constructing an optimal reconciled tree for gene trees is also np hard finally we consider a general reconstruction problem and show it to be np hard even for the well known nearest neighbor interchange distance a new and efficiently computable metric is defined based on the duplication cost we show that the problem of finding an optimal species tree from gene trees is np hard under this new metric but it can be approximated within factor 2 in polynomial time using this approximation result we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other our heuristic method is significantly better than the existing program in page s genetree 1 0 that starts the search from a random tree

bounded hairpin completion hairpin completion is a formal operation inspired from biochemistry here we consider a restricted variant of hairpin completion called bounded hairpin completion applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x hairpin completion produces a new word z which is a prolongation of x to the right or to the left by annealing although this operation is a purely mathematical one and the biological reality is just a source of inspiration it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion the restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion they cannot be longer than a given constant closure properties of some classes of formal languages under the non iterated and iterated bounded hairpin completion are investigated we consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them finally also the inverse operation namely bounded hairpin reduction as well as the set of all primitive bounded hairpin roots of a regular language are considered

reflexivity defect of kernels of the elementary operators of length 2 abstract let x be a finite dimensional complex vector space we give an explicit formula for the reflexivity defect of the kernel of an arbitrary elementary operator of length 2 i e an elementary operator of the form t a 1 tb 1 a 2 tb 2 t l x where a 1 a 2 and b 1 b 2 are linearly independent

fixed points stability and exact linearization abstract we study the scalar equation x f t x x x b t g x t l 0 by means of contraction mappings conditions are obtained to ensure that each solution x t x t 0 0 as t the conditions allow f to grow as large as t but not as large as t 2 this is parallel to the classical result of smith quart j math oxford ser 12 2 1961 123 for the linear equation without a delay

dynamic 3 sided planar range queries with expected doubly logarithmic time the priority search tree is the classic solution for the problem of dynamic 2 dimensional searching for the orthogonal query range of the form a b x c 3 sided rectangle it supports all operations in logarithmic worst case complexity in both main and external memory in this work we show that the update and query complexities can be improved to expected doubly logarithmic when the input coordinates are being continuously drawn from specific probability distributions we present three pairs of linear space solutions for the problem i e a ram and a corresponding i o model variant 1 first we improve the update complexity to doubly logarithmic expected with high probability under the most general assumption that both the x and y coordinates of the input points are continuously being drawn from a distribution whose density function is unknown but fixed 2 next we improve both the query complexity to doubly logarithmic expected with high probability and the update complexity to doubly logarithmic amortized expected by assuming that only the x coordinates are being drawn from a class of smooth distributions and that the deleted points are selected uniformly at random among the currently stored points in fact the y coordinates are allowed to be arbitrarily distributed 3 finally we improve both the query and the update complexity to doubly logarithmic expected with high probability by moreover assuming the y coordinates to be continuously drawn from a more restricted class of realistic distributions all data structures are deterministic and their complexity s expectation is with respect to the assumed distributions they comprise combinations of known data structures and of two new data structures introduced here namely the weight balanced exponential tree and the external modified priority search tree

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

recursive voids for identifying a nonconvex boundary of a set of points in the plane we introduce a method that identifies the boundary of a nonconvex shape of a set of points in the plane the boundary of the shape is explored through finding empty regions recursively within a shell that encapsulates all of the points our algorithm is output sensitive and runs in linear o n time determined by the output parameter which is proportional to the length of the nonconvex boundary measured by a threshold unit distance the recursive nature of our algorithm allows a tree structure that characterizes the empty regions and by complementarity the nonconvex shape itself we use a distance measure based on lowest common ancestor of a pair of nodes in this tree and define the complexity of a shape as the average of the distances between all pairs we present computational results on data size threshold shape complexity and noise on a set of different nonconvex shapes

improved data structures for fully dynamic biconnectivity we present fully dynamic algorithms for maintaining the biconnected components in general and plane graphs a fully dynamic algorithm maintains a graph during a sequence of insertions and deletions of edges or isolated vertices let m be the number of edges and n be the number of vertices in a graph the time per operation of the best deterministic algorithms is o sqrt n in general graphs and o log n in plane graphs for fully dynamic connectivity and o min m2 3 n in general graphs and o sqrt n in plane graphs for fully dynamic biconnectivity we improve the later running times to o sqrt m log n in general graphs and o log 2 n in plane graphs our algorithm for general graphs can also find the biconnected components of all vertices in time o n

efficient generation of simple polygons for characterizing the shape of a set of points in the plane this paper presents a simple flexible and efficient algorithm for constructing a possibly non convex simple polygon that characterizes the shape of a set of input points in the plane termed a characteristic shape the algorithm is based on the delaunay triangulation of the points the shape produced by the algorithm is controlled by a single normalized parameter which can be used to generate a finite totally ordered family of related characteristic shapes varying between the convex hull at one extreme and a uniquely defined shape with minimum area an optimal o nlogn algorithm for computing the shapes is presented characteristic shapes possess a number of desirable properties and the paper includes an empirical investigation of the shapes produced by the algorithm this investigation provides experimental evidence that with appropriate parameterization the algorithm is able to accurately characterize the shape of a wide range of different point distributions and densities the experiments detail the effects of changing parameter values and provide an indication of some good parameter values to use in certain circumstances

novel transformation techniques using q heaps with applications to computational geometry using the notions of q heaps and fusion trees developed by fredman and willard we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces in particular we develop a fast fractional cascading technique which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by o log epsilon n for some constant epsilon 0 where n is the total size of all the lists stored in the tree we apply the fast fractional cascading technique in combination with the other techniques to derive the first linear space sublogarithmic time algorithms for two fundamental geometric retrieval problems orthogonal segment intersection and rectangular point enclosure

a hermitian canonical form for complex matrices under consimilarity abstract we produce an explicit hermitian canonical form for complex square matrices under consimilarity we apply a simple algorithmic procedure to a concanonical form for complex matrices to construct a form that is not only canonical but also hermitian we also show that a similar algorithmic procedure can be used to produce an explicit real canonical form for complex matrices under consimilarity

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

selection of alpha for alpha hull in r2 abstract for finding the shape of a planar set edelsbrunner kirkpatrick and seidel introduced the concept of hulls as a natural generalization of convex hulls while the hull is elegant and efficient to compute it still suffers from a major drawback i e the single parameter namely must nevertheless be tuned this paper deals with finding a way to overcome this drawback i e we proposed here a selection criterion of for hulls corresponding to a point set in r 2 the selection criterion of is based on the concept of minimum spanning trees and certain existing results the effectiveness of the proposed selection criterion is demonstrated on some artificially generated data sets the convergence with sample size of the hull based on the proposed selection criterion for to the original pattern class has also been verified using symmetric difference the hausdorff metric and a similarity metric

delaunay triangulations in o sort n time and more we present several results about delaunay triangulations dts and convex hulls in transdichotomous and hereditary settings i the dt of a planar point set can be computed in expected time o sort n on a word ram where sort n is the time to sort n numbers we assume that the word ram supports the shuffle operation in constant time ii if we know the ordering of a planar point set in x and in y direction its dt can be found by a randomized algebraic computation tree of expected linear depth iii given a universe u of points in the plane we construct a data structure d for delaunay queries for any p s u d can find the dt of p in expected time o vpv log log vuv iv given a universe u of points in 3 space in general convex position there is a data structure d for convex hull queries for any p s u d can find the convex hull of p in expected time o vpv log log vuv 2 v given a convex polytope in 3 space with n vertices which are colored with g 2 colors we can split it into the convex hulls of the individual color classes in expected time o n log log n 2 the results i iii generalize to higher dimensions where the expected running time now also depends on the complexity of the resulting dt we need a wide range of techniques most prominently we describe a reduction from dts to nearest neighbor graphs that relies on a new variant of randomized incremental constructions using dependent sampling

fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays the fixed point theory is first used to consider the stability for stochastic partial differential equations with delays some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given these conditions do not require the monotone decreasing behavior of the delays which is necessary in t caraballo k liu exponential stability of mild solutions of stochastic partial differential equations with delays stoch anal appl 17 1999 743 763 ruhollan jahanipur stability of stochastic delay evolution equations with monotone nonlinearity stoch anal appl 21 2003 161 181 even in this special case our results also improve the results in t caraballo k liu exponential stability of mild solutions of stochastic partial differential equations with delays stoch anal appl 17 1999 743 763

fixed points and stability in differential equations with variable delays abstract in this paper we consider a linear scalar differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic stability theorem with a necessary and sufficient condition is proved

trace inequalities in nonextensive statistical mechanics abstract in this short paper we establish a variational expression of the tsallis relative entropy in addition we derive a generalized thermodynamic inequality and a generalized peierls bogoliubov inequality finally we give a generalized golden thompson inequality

stability analysis of neutral stochastic delay differential equations by a generalisation of banach s contraction principle abstractin this paper we consider a class of neutral stochastic differential systems with variable delays and give sufficient conditions to ensure that the zero solution is asymptotically stable in the mean square by means of a generalisation of banach s contraction principle these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions the results are shown to improve the previous globally stable results derived in the literature

fixed points and exponential stability for stochastic volterra levin equations in this paper we study a stochastic volterra levin equation by using fixed point theory we give some conditions for ensuring that this equation is exponentially stable in mean square and is also almost surely exponentially stable our result generalizes and improves on the results in 14 1 30

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

efficient seed computation revisited the notion of the cover is a generalization of a period of a string and there are linear time algorithms for finding the shortest cover the seed is a more complicated generalization of periodicity it is a cover of a superstring of a given string and the shortest seed problem is of much higher algorithmic difficulty the problem is not well understood no linear time algorithm is known in the paper we give linear time algorithms for some of its versions computing shortest left seed array longest left seed array and checking for seeds of a given length the algorithm for the last problem is used to compute the seed array of a string i e the shortest seeds for all the prefixes of the string in o n 2 time we describe also a simpler alternative algorithm computing efficiently the shortest seeds as a by product we obtain an o nlog n m time algorithm checking if the shortest seed has length at least m and finding the corresponding seed we also correct some important details missing in the previously known shortest seed algorithm iliopoulos et al 1996 14

characterizations of products of symmetric matrices abstract characterizations are obtained for matrices c of the form c a where a are n n matrices over the real field such that a is symmetric and c is nonnegative definite among others a proof of recent generalization of cochran s theorem is given

products of positive semidefinite matrices abstract we characterize the complex square matrices which are expressible as the product of finitely many positive semidefinite matrices a matrix t can be expressed as such if and only if det t 0 moreover the number of factors can always be limited to five we also determine those matrices which can be expressed as the product of two or four positive semidefinite matrices these results are analogous to the ones obtained before by c s ballantine for products of positive definite matrices

a canonical form for matrices under consimilarity abstract square complex matrices a b are said to be consimilar if a sb s 1 for some nonsingular matrix s consimilarity is an equivalence relation that is a natural matrix generalization of rotation of scalars in the complex plane we survey the known forms to which a given complex matrix may be reduced by unitary consimilarity and describe a canonical form to which it may be reduced by a general consimilarity we derive a useful criterion for two matrices to be consimilar and show that every matrix is consimilar to its own conjugate transpose and adjoint to a real matrix and to a hermitian matrix

stability results for neutral stochastic functional differential equations via fixed point methods in this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle name

efficient algorithms for shortest partial seeds in words abstract a factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w a factor u is a seed of w if it is a cover of a superstring of w covers and seeds extend the classical notions of periodicity we introduce a new notion of partial seed that is a factor covering as a seed at least positions in a given word we use the cover suffix tree recently introduced in the context of partial covers kociumaka et al 2015 13 an o n log n time algorithm constructing such a tree is known however it appears that partial seeds are more complicated than partial covers our algorithms require algebraic manipulations of special functions related to edges of the modified cover suffix tree and the border array we present a procedure for computing shortest partial seeds that works in o n time if the cover suffix tree is already given this is a full version which includes all the proofs of a paper that appeared at cpm 2014 1

tight bounds on the solutions of multidimensional divide and conquer maximin recurrences abstract in this paper upper bounds are presented for the solution of the following multidimensional divide and conquer maximin recurrence g n max n 1 n 2 n p n n 1 n 2 n p 1 i 1 p g n i smin 1 i p k f n i where p 2 1 k f is an arbitrary nondecreasing function and smin 1 i p k f n i denotes the sum of the smallest k numbers among f n 1 f n 2 and f n p all the presented upper bounds are at most log 2 k p times the exact solution of g n the derivation of the upper bounds is based on properties of partition trees for k 1 and k p 1 we obtain respectively two of the recurrences previously studied by alonso et al siam j discrete math 8 1995 428 447 in both of these two cases our results improve theirs

the jordan cononical form of a product of a hermitian and a positive semidefinite matrix abstract a given square complex matrix c is the product of a positive semidefinite matrix a and a hermitian matrix b if and only if c 2 is diagonalizable and has nonnegative eigenvalues this condition is equivalent to requiring that c have real eigenvalues and a jordan canonical form that is diagonal except for r copies of a 2 by 2 nilpotent jordan block we show that r is bounded from above by the rank of a the nullity of a and both the positive and negative inertia of b it follows that a product of two positive semidefinite matrices is diagonalizable and has nonnegative eigenvalues a result that leads to a characterization of the possible concanonical forms of a positive semidefinite matrix

minimal spanning tree based clustering technique relationship with bayes classifier a minimal spanning tree mst based clustering technique along with its theoretical formulation is presented in this paper the proposed technique is compared with bayes classifier and it is shown theoretically that the clustering technique although an unsupervised one approaches the performance of bayes classifier under a condition as the number of sample points from each class increases experimental results with many synthetic data sets in 2 d and 3 d validate the theoretical prediction

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors

verification and sensitivity analysis of minimum spanning trees in linear time komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree the total computational work required by his method is much larger than linear however this paper describes a linear time algorithm for verifying a minimum spanning tree this algorithm combines the result of komlos with a preprocessing and table look up method for small subproblems and with a previously known almost linear time algorithm additionally an optimal deterministic algorithm and a linear time randomized algorithm for sensitivity analysis of minimum spanning trees are presented

algorithms for finding the weight constrained k longest paths in a tree and the length constrained k maximum sum segments of a sequence in this work we obtain the following new results given a tree t v e with a length function e r and a weight function w e r a positive integer k and an interval l u the weight constrainedklongest paths problem is to find the k longest paths among all paths in t with weights in the interval l u we show that the weight constrainedklongest paths problem has a lower bound w vlogv k in the algebraic computation tree model and give an o vlogv k time algorithm for it given a sequence a a 1 a 2 a n of numbers and an interval l u we define the sum and length of a segment a i j to be a i a i 1 a j and j i 1 respectively the length constrainedkmaximum sum segments problem is to find the k maximum sum segments among all segments of a with lengths in the interval l u we show that the length constrainedkmaximum sum segments problem can be solved in o n k time