an o n log log n time algorithm for triangulating a simple polygon given a simple n vertex polygon the triangulation problem is to partition the interior of the polygon into n 2 triangles by adding n 3 nonintersecting diagonals we propose an o n log log n time algorithm for this problem improving on the previously best bound of o n log n and showing that triangulation is not as hard as sorting improved algorithms for several other computational geometry problems including testing whether a polygon is simple follow from our result

asymptotics in asep with step initial condition in previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition particles beginning at the positive integers there it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a fredholm determinant here we use this formula to obtain three asymptotic results for the positions of these particles in one an apparently new distribution function arises and in another the distribution function f2 arises the latter extends a result of johansson on tasep to asep and hence proves kpz universality for asep with step initial condition

on the efficiency of pairing heaps and related data structures the pairing heap is well regarded as an efficient data structure for implementing priority queue operations it is included in the gnu c library strikingly simple in design the pairing heap data structure nonetheless seems difficult to analyze belonging to the genre of self adjusting data structures with its design originating as a self adjusting analogue of the fibonacci heap it has been previously conjectured that the pairing heap provides constrant amortized time decrease key operations and experimental studies have supported this conjecture this paper demonstrates contrary to conjecture that the pairing heap requires more than constant amortized time to perform decrease key operations moreover new experimental findings are presented that reveal detectable growth in the amortized cost of the decrease key operation second a unifying framework is developed that includes both pairing heaps and fibonacci heaps the parameter of interest in this framework is the storage capacity available in the nodes of the data structure for auxiliary balance information fields in this respect fibonacci heaps require log log n bits per node when n items are present this is shown to be asymptotically optimal for data structures that achieve the same asymptotic performance bounds as fibonacci heaps and fall within this framework

various equations for gap probabilities of coupled gaussian matrices versions of tracy widom tw and adler shiota van moerbeke asvm approaches are applied to derive various partial differential equations pde satisfied by joint eigenvalue spacing probabilities of two coupled gaussian hermitian matrices coupled gue all the lowest third order pde satisfied by the probabilities for the largest eigenvalues of two coupled gue are found and the results of both approaches are compared the tw approach allows us to derive all pde at once while in the asvm one starting with different bilinear identities leads to different subsets of the full set of equations an interesting result is that the joint probability for the largest eigenvalues of coupled gaussian matrices satisfies a number of different pde and the previously known adler van moerbeke equation avm 1999 ann math 149 921 76 is only one of them some of the new equations appear like coupled painlev iv and have the usual painlev iv equation as the one matrix limit i e when the spectral endpoint of one of the matrices goes to infinity this is in contrast to the avm equation which becomes trivial in this limit moreover the new pde which stem from the matrix kernel approach of tracy and widom 2004 commun math phys 252 7 41 do not contain derivatives w r t the strength of coupling unlike the avm equation in other words they contain fewer independent variables and in this sense are simpler

randomized algorithms for metrical task systems abstract borodin et al 1992 introduce a general model for online systems in 3 called task systems and show a deterministic algorithm which achieves a competitive ratio of 2n 1 for any metrical task system with n states we present a randomized algorithm which achieves a competitive ratio of e e 1 n 1 e 1 1 5820n 0 5820 for this same problem for the uniform metric space borodin et al present an algorithm which achieves a competitive ratio of 2hn and they show a lower bound of hn for any randomized algorithm we improve their upper bound for the uniform metric space by showing a randomized algorithm which is hn o log n competitive

on the mazur ulam property for the space of hilbert space valued continuous functions abstract let k be a compact hausdorff space and let h be a real or complex hilbert space with dim h r 2 we prove that the space c k h of all h valued continuous functions on k equipped with the supremum norm satisfies the mazur ulam property that is if y is any real banach space every surjective isometry from the unit sphere of c k h onto the unit sphere of y admits a unique extension to a surjective real linear isometry from c k h onto y our strategy relies on the structure of c k module of c k h and several results in jb triple theory for this purpose we determine the facial structure of the closed unit ball of a real jb triple and its dual space

the correspondence between tracy widom and adler shiota van moerbeke approaches in random matrix theory the gaussian case two approaches to the derivation of integrable differential equations for random matrix probabilities are compared both methods are rewritten in such a form that simple and explicit relations between all tw dependent variables and functions of asvm are found for the example of finite size gaussian matrices orthogonal function systems and toda lattice are seen as the core structure of both approaches and their relationship

on the facial structure of the unit ball in the dual space of a jb triple it is shown that every proper weak closed face of the closed unit ball e 1 in the dual space of a jb triple e coincides with set of all elements in the unit sphere of e attaining their norm at a unique compact tripotent in e in particular every proper weak closed face of the closed unit ball e 1 is weak semi exposed this result provides an affirmative answer to a conjecture posed over 20 years ago

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

the spectrum of coupled random matrices the study of the spectrum of coupled random matrices has received rather little attention to the best of our knowledge coupled random matrices have been studied to some extent by mehta in this work we explain how the integrable technology can be brought to bear to gain insight into the nature of the distribution of the spectrum of coupled hermitean random matrices and the equations the associated probabilities satisfy in particular the two toda lattice its algebra of symmetries and its vertex operators will play a prominent role in this interaction namely the method is to introduce time parameters in an artificial way and to dress up a certain matrix integral with a vertex integral operator for which we find virasoro like differential equations these methods lead to very simple nonlinear third order partial differential equations for the joint statistics of the spectra of two coupled gaussian random matrices comment 56 pages published version abstract added in migration

an optimal algorithm for intersecting line segments in the plane the main contribution of this work is an o n log n k time algorithm for computing all k intersections among n line segments in the plane this time complexity is easily shown to be optimal within the same asymptotic cost our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment if any lies right above or below each intersection and each endpoint the algorithm has been implemented and performs very well the storage requirement is on the order of n k in the worst case but it is considerably lower in practice to analyze the complexity of the algorithm an amortization argument based on a new combinatorial theorem on line arrangements is used

tingley s problem for spaces of trace class operators abstract we prove that every surjective isometry between the unit spheres of two trace class spaces admits a unique extension to a surjective complex linear or conjugate linear isometry between the spaces this provides a positive solution to tingley s problem in a new class of operator algebras

convex decomposition of polyhedra and robustness this paper presents a simple algorithm to compute a convex decomposition of a nonconvex polyhedron of arbitrary genus handles and shells internal voids for such a polyhedron s with n edges and rnotches features causing nonconvexity in polyhedra the algorithm produces a worst case optimal o r 2 number of convex polyhedra s i with u i 1 k s i s in o nr 2 r 7 2 time and o nr r 5 2 space recently chazelle and palios have given a fast o n r 2 log r time and o n r 2 space algorithm to tetrahedralize a nonconvex polyhedron their algorithm however works for a simple polyhedron of genus zero and with no shells internal voids the algorithm presented here is based on the simple cut and split paradigm of chazelle with the help of zone theorems on arrangements it is shown that this cut and split method is quite efficient the algorithm is extended to work for a certain class of nonmanifold polyhedra also presented is an algorithm for the same problem

the soft heap an approximate priority queue with optimal error rate a simple variant of a priority queue called a soft heap is introduced the data structure supports the usual operations insert delete meld and findmin its novelty is to beat the logarithmic bound on the complexity of a heap in a comparison based model to break this information theoretic barrier the entropy of the data structure is reduced by artifically raising the values of certain keys given any mixed sequence of n operations a soft heap with error rate e for any 0 en of its items have their keys raised the amortized complexity of each operation is constant except for insert which takes 0 log 1 e time the soft heap is optimal for any value of e in a comparison based model the data structure is purely pointer based no arrays are move items across the data structure not individually as is customary but in groups in a data structuring equivalent of car pooling keys must be raised as a result in order to preserve the heap ordering of the data structure the soft heap can be used to compute exact or approximate medians and percentiles optimally it is also useful for approximate sorting and for computing minimum spanning trees of general graphs

su n meander determinants we propose a generalization of meanders i e configurations of non self intersecting loops crossing a line through a given number of points to su n this uses the reformulation of meanders as pairs of reduced elements of the temperley lieb algebra a su 2 related quotient of the hecke algebra with a natural generalization to su n we also derive explicit formulas for su n meander determinants defined as the gram determinants of the corresponding bases of the hecke algebra

a study on splay trees abstract we study the dynamic optimality conjecture which predicts that splay trees are a form of universally efficient binary search tree for any access sequence we reduce this claim to a regular access bound which seems plausible and might be easier to prove this approach may be useful to establish dynamic optimality

self adjusting binary search trees the splay tree a self adjusting form of binary search tree is developed and analyzed the binary search tree is a data structure for representing tables and lists so that accessing inserting and deleting items is easy on an n node splay tree all the standard search tree operations have an amortized time bound of o log n per operation where by amortized time is meant the time per operation averaged over a worst case sequence of operations thus splay trees are as efficient as balanced trees when total running time is the measure of interest in addition for sufficiently long access sequences splay trees are as efficient to within a constant factor as static optimum search trees the efficiency of splay trees comes not from an explicit structural constraint as with balanced trees but from applying a simple restructuring heuristic called splaying whenever the tree is accessed extensions of splaying give simplified forms of two other data structures lexicographic or multidimensional search trees and link cut trees

tingley s problem through the facial structure of operator algebras abstract tingley s problem asks whether every surjective isometry between the unit spheres of two banach spaces admits an extension to a real linear surjective isometry between the whole spaces in this paper we give an affirmative answer to tingley s problem when both spaces are preduals of von neumann algebras the spaces of self adjoint operators in von neumann algebras or the spaces of self adjoint normal functionals on von neumann algebras we also show that every surjective isometry between the unit spheres of unital c algebras restricts to a bijection between their unitary groups in addition we show that every surjective isometry between the normal state spaces or the normal quasi state spaces of two von neumann algebras extends to a linear surjective isometry

biased search trees we consider the problem of storing items from a totally ordered set in a search tree so that the access time for a given item depends on a known estimate of the access frequency of the item we describe two related classes of biased search trees whose average access time is within a constant factor of the minimum and that are easy to update under insertions deletions and more radical update operations we present and analyze efficient update algorithms for biased search trees we list several applications of such trees

a geometric spectral theory for n tuples of self adjoint operators in finite von neumann algebras abstract suppose b 1 b n are self adjoint elements in a finite von neumann algebra m with trace and define a map from m to complex n 1 space by the formula x x b 1 x b n x next let b denote the image of the positive unit ball of m under the map b is called the spectral scale of b 1 b n it is clearly compact and convex the main theme of this work is that the geometry of the spectral scale b reflects spectral data for the b i s for example in the finite dimensional case the operators commute if and only if the spectral scale is a polytope thus one can see that the operators commute from the shape of spectral scale in the case of a single operator where the scale lies in the plane the slopes of the boundary fill out the spectrum of the operator corners correspond to gaps in the spectrum and flat sports indicate eigenvalues analogous results hold when there is more than one operator in the commutative setting the spectral scale determines the n 1 tuple b 1 b n however an example is given that shows this is not generally true in the noncommutative case finally a matricial version of the spectral scale is shown to be sufficient to completely determine the n 1 tuple b 1 b n

duality biorthogonal polynomials and multi matrix models the statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized christoffel darboux form constructed from sequences of biorthogonal polynomials for measures involving exponentials of a pair of polynomials v1 v2 in two different variables these kernels may be expressed in terms of finite dimensional windows spanned by finite subsequences having length equal to the degree of one or the other of the polynomials v1 v2 the vectors formed by such subsequences satisfy dual pairs of first order systems of linear differential equations with polynomial coefficients having rank equal to one of the degrees of v1 or v2 and degree equal to the other they also satisfy recursion relations connecting the consecutive windows and deformation equations determining how they change under variations in the coefficients of the polynomials v1 and v2 viewed as overdetermined systems of linear difference differential deformation equations these are shown to be compatible and hence to admit simultaneous fundamental systems of solutions the main result is the demonstration of a spectral duality property namely that the spectral curves defined by the characteristic equations of the pair of matrices defining the dual differential systems are equal upon interchange of eigenvalue and polynomial parameters

a study of exponential neighborhoods for the travelling salesman problem and for the quadratic assignment problem this paper deals with exponential neighborhoods for combinatorial optimization problems exponential neighborhoods are large sets of feasible solutions whose size grows exponentially with the input length we are especially interested in exponential neighborhoods over which the tsp respectively the qap can be solved in polynomial time and we investigate combinatorial and algorithmical questions related to such neighborhoods first we perform a careful study of exponential neighborhoods for the tsp we investigate neighborhoods that can be defined in a simple way via assignments matchings in bipartite graphs partial orders trees and other combinatorial structures we identify several properties of these combinatorial structures that lead to polynomial time optimization algorithms and we also provide variants that slightly violate these properties and lead to np complete optimization problems whereas it is relatively easy to find exponential neighborhoods over which the tsp can be solved in polynomial time the corresponding situation for the qap looks pretty hopeless every exponential neighborhood that is considered in this paper provably leads to an np complete optimization problem for the qap

meanders and the temperley lieb algebra the statistics of meanders is studied in connection with the temperley lieb algebra each multi component meander corresponds to a pair of reduced elements of the algebra the assignment of a weightq per connected component of meander translates into a bilinear form on the algebra with a gram matrix encoding the fine structure of meander numbers here we calculate the associated gram determinant as a function ofq and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks

spherical isometries of finite dimensional c algebras abstract in this paper it is shown that every surjective isometry between the unit spheres of two finite dimensional c algebras extends to a real linear jordan isomorphism followed by multiplication operator by a fixed unitary element this gives an affirmative answer to tingley s problem between two finite dimensional c algebras moreover we show that if two finite dimensional c algebras have isometric unit spheres then they are isomorphic

matrices coupled in a chain i eigenvalue correlations the general correlation function for the eigenvalues of p complex hermitian matrices coupled in a chain is given as a single determinant for this we use a slight generalization of a theorem of dyson

facial structure in operator algebra theory we give a complete description of the closed faces in twelve kinds of convex sets that appear in operator algebra theory these consist of positive parts of unit balls for c algebras and their dual spaces and for von neumann algebras and their pre duals of self adjoint parts of unit balls in the same four classes and finally of general unit balls in the four classes all these faces are shown to be semi exposed and naturally paired with a polar face in the dual or pre dual space

a transfer matrix approach to the enumeration of plane meanders a closed plane meander of order n is a closed self avoiding curve intersecting an infinite line 2n times meanders are considered distinct up to any smooth deformation leaving the line fixed we have developed an improved algorithm based on transfer matrix methods for the enumeration of plane meanders while the algorithm has exponential complexity its rate of growth is much smaller than that of previous algorithms the algorithm is easily modified to enumerate various systems of closed meanders semi meanders open meanders and many other geometries

robust balancing in b trees robust balancing is a technique that substantially decreases the worst case cost of rebalancing b trees when intermixed insertions and deletions occur from theta k log k to 0 k for k insertions and deletions it requires a slight extension to the standard data structure robust b trees but it uses the same simple operations as the standard algorithm to rebalance robust and standard b tree algorithms have identical behavior and 0 k cost when only insertions occur on intermixed insertions and deletions a robust algorithm substantially decreases rebalancing cost and increases space utilization and search cost slightly this is most significant when the cost of rebalancing dominates the total cost as in applications with localized accesses and finger access points in the active localities in applications that use top down searching search cost and total cost are 0 k log k and a robust algorithm improves total cost by a large constant factor because of the larger coefficient for rebalancing than for searching this dissertation makes a thorough study of robust balancing and its impact on maintenance cost we examine the choices for rebalancing that robust b trees introduce and define new algorithms to exploit these choices we develop powerful and uniform techniques for deriving upper bounds on rebalancing cost using the bank account paradigm a method for analyzing the cost of a sequence of operations the power of these techniques is demonstrated by strong lower bounds including several tight bounds and by simple extensions which show the dependence of rebalancing cost on different types of operations the mix of insertions and deletions and the height of rebalancing further refinements show strong bounds on subasymptotic rebalancing cost in a nonempty initial tree and on rebalancing cost in b trees a b tree generalization with improved space utilization robust algorithms for b trees can significantly improve rebalancing cost and total cost even when only insertions occur we use this analysis to find the best algorithms for several applications these include some algorithms whose rebalancing cost is sublinear in the sense of having maximum cost k c for some c 1 previous work done independently by this author mehlhorn and maier and salveter considered only one robust algorithm with a linear rebalancing cost our original contributions include new algorithms for robust b trees and b trees development of the accounting techniques and their use in identifying the best algorithms

efficient simulation of the random cluster model the simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down a number of cluster algorithms usually based on the fortuin kasteleyn representation of the potts model and suitable generalizations for continuous spin models have been used to increase simulation efficiency the first algorithm making use of this representation suggested by sweeny in 1983 has not found widespread adoption due to problems in its implementation however it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well known algorithm due to swendsen and wang here we present an efficient implementation of sweeny s approach for the random cluster model using recent algorithmic advances in dynamic connectivity algorithms

ordered c ast modules in this first part of a study of ordered operator spaces we develop the basic theory of ordered c bimodules a crucial role is played by open tripotents a jb triple variant of akemann s notion of open projection

shortest curves in planar regions with curved boundary abstract a general framework is presented for describing shortest curve algorithms and their time complexity in regions of the plane whose boundaries may be curved an algorithm that accepts curved boundary jordan regions along with given start and end points and produces the shortest curve between them is presented its time complexity is bounded by the product of the complexity of the region s boundary and that of the output shortest curve when the region is a simple polygon with n vertices the time bound is o nk where k is the number of vertices in the shortest curve a second algorithm produces shortest curves in multiply connected regions with possibly curved boundary

on the extension of isometries between the unit spheres of von neumann algebras abstract we prove that every surjective isometry between the unit spheres of two von neumann algebras admits a unique extension to a surjective real linear isometry between these two algebras

tingley s problem through the facial structure of an atomic jbw triple abstract we prove that every surjective isometry between the unit spheres of two atomic jbw triples e and b admits a unit extension to a surjective real linear isometry from e into b this result constitutes a new positive answer to tingley s problem in the jordan setting

pdes for the joint distributions of the dyson airy and sine processes in a celebrated paper dyson shows that the spectrum of an n x n random hermitian matrix diffusing according to an ornstein uhlenbeck process evolves as n noncolliding brownian motions held together by a drift term the universal edge and bulk scalings for hermitian random matrices applied to the dyson process lead to the airy and sine processes in particular the airy process is a continuous stationary process describing the motion of the outermost particle of the dyson brownian motion when the number of particles gets large with space and time appropriately rescaled in this paper we answer a question posed by kurt johansson to find a pde for the joint distribution of the airy process at two different times similarly we find a pde satisfied by the joint distribution of the sine process this hinges on finding a pde for the joint distribution of the dyson process which itself is based on the joint probability of the eigenvalues for coupled gaussian hermitian matrices the pde for the dyson process is then subjected to an asymptotic analysis consistent with the edge and bulk rescalings the pdes enable one to compute the asymptotic behavior of the joint distribution and the correlation for these processes at different times t 1 and t 2 when t 2 t 1 infinity as illustrated in this paper for the airy process this paper also contains a rigorous proof that the extended hermite kernel governing the joint probabilities for the dyson process converges to the extended airy and sine kernels after the appropriate rescalings

optimal expected case planar point location point location is the problem of preprocessing a planar polygonal subdivision s of size n into a data structure in order to determine efficiently the cell of the subdivision that contains a given query point we consider this problem from the perspective of expected query time we are given the probabilities p z that the query point lies within each cell z in s the entropy h of the resulting discrete probability distribution is the dominant term in the lower bound on the expected case query time we show that it is possible to achieve query time h o sqrt h 1 with space o n which is optimal up to lower order terms in the query time we extend this result to subdivisions with convex cells assuming a uniform query distribution within each cell in order to achieve space efficiency we introduce the concept of entropy preserving cuttings

tingley s problem on finite von neumann algebras abstract in this paper we give an affirmative answer to tingley s problem between finite von neumann algebras to do this we see that every norm closed proper face of the unit ball of a unital c algebra can be represented as the intersection of a family of maximal proper faces

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

sorting jordan sequences in linear time using level linked search trees for a jordan curve c in the plane nowhere tangent to the x axis let x1 x2 xn be the abscissas of the intersection points of c with the x axis listed in the order the points occur on c we call x1 x2 xn a jordan sequence in this paper we describe an o n time algorithm for recognizing and sorting jordan sequences the problem of sorting such sequences arises in computational geometry and computational geography our algorithm is based on a reduction of the recognition and sorting problem to a list splitting problem to solve the list splitting problem we use level linked search trees

brownian motion ensembles correlation functions of determinantal processes we calculate the n point correlation function for a large class of brownian motion ensembles of random matrix theory the corresponding fokker planck equation describes a determinantal process in the theory of matrix valued stochastic differential equations and can be mapped onto a schodinger equation of non interacting electrons in one dimension the correlation functions are obtained explicitly via a suitable generalization of the method of biorthogonal functions

operator algebras with contractive approximate identities ii abstract we make several contributions to our recent program investigating structural properties of algebras of operators on a hilbert space for example we make substantial contributions to the noncommutative peak interpolation program begun by hay and the first author hay and neal another sample result an operator algebra has a contractive approximate identity iff the linear span of the elements with positive real part is dense we also extend the theory of compact projections to the most general case despite the title our algebras are often allowed to have no approximate identity

differential equations for dyson processes we call a dyson process any process on ensembles of matrices in which the entries undergo diffusion we are interested in the distribution of the eigenvalues or singular values of such matrices in the original dyson process it was the ensemble of n n hermitian matrices and the eigenvalues describe n curves given sets x1 xm the probability that for each k no curve passes through xk at time k is given by the fredholm determinant of a certain matrix kernel the extended hermite kernel for this reason we call this dyson process the hermite process similarly when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the laguerre process for which there is a corresponding extended laguerre kernel scaling the hermite process at the edge leads to the airy process which was introduced by prahofer and spohn as the limiting stationary process for a polynuclear growth model and in the bulk to the sine process scaling the laguerre process at the edge leads to the bessel process

critical exponents of plane meanders meanders form a set of combinatorial problems concerned with the enumeration of self avoiding loops crossing a line through a given number of points n meanders are considered distinct up to any smooth deformation leaving the line fixed we use a recently developed algorithm based on transfer matrix methods to enumerate plane meanders this allows us to calculate the number of closed meanders up to n 48 the number of open meanders up to n 43 and the number of semi meanders up to n 45 the analysis of the series yields accurate estimates of both the critical point and critical exponent and shows that a recent conjecture for the exact value of the semi meander critical exponent is unlikely to be correct while the conjectured exponent value for closed and open meanders is not inconsistent with the results from the analysis

inner ideals and facial structure of the quasi state space of a jb algebra abstract in this paper we relate the geometric structure of the quasi state space a 1 of a jb algebra a to the algebraic structure of a we prove that each non empty w closed face f of a 1 coincides with the set of elements of a that attain their norms at a closed projection p in a uniquely determined by f when a is unital we establish an order anti isomorphism between the complete lattice of w closed faces of a 1 and the complete lattice of norm closed inner ideals of a these results are known for the special case when a is the self adjoint part of a c algebra the proofs use associative techniques and the gelfand naimark representation in the general case such techniques are not available and it is necessary to introduce new techniques including the use of a new inequality of cauchy schwarz type for elements of a

self adjusting heaps in this paper we explore two themes in data structure design amortized computational complexity and self adjustment we are motivated by the following observations in most applications of data structures we wish to perform not just a single operation but a sequence of operations possibly having correlated behavior by averaging the running time per operation over a worst case sequence of operations we can sometimes obtain an overall time bound much smaller than the worst case time per operation multiplied by the number of operations we call this kind of averaging amortization standard kinds of data structures such as the many varieties of balanced trees are specifically designed so that the worst case time per operation is small such efficiency is achieved by imposing an explicit structural constraint that must be maintained during updates at a cost of both running time and storage space however if amortized running time is the complexity measure of interest we can guarantee efficiency withou

perturbation of ell_1 copies in preduals of jbw triples abstract it is known that two normal functionals on a jbw triple are orthogonal i e they have orthogonal support tripotents if and only if they are l orthogonal meaning that they span an isometric copy of l 1 2 this is shown to be stable under small norm perturbations in the following sense if the linear span of the two functionals is isometric up to 0 to l 1 2 then the functionals are less far in norm than e 0 from two orthogonal functionals where e 0 as 0 analogous statements for finitely and even infinitely many functionals hold as well and so does a corresponding statement for non normal functionals

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result

universal structure and universal equations pde for unitary ensembles random matrix ensembles with unitary invariance of measure ue are described in a unified way using a combination of tracy widom tw and adler shiota van moerbeke approaches to the derivation of partial differential equations pdes for spectral gap probabilities first general three term recurrence relations for ue restricted to subsets of real line or in other words for functions in the resolvent kernel are obtained using them simple universal relations between all tw dependent variables and one dimensional toda lattice functions are found a universal system of pde for ue is derived from previous relations which leads also to a single independent pde for spectral gap probability of various ue thus orthogonal function bases and toda lattice are seen at the core of correspondence of different approaches moreover toda akns system provides a common structure of pde for unitary ensembles interestingly this structure can be seen in two very different forms one arises from orthogonal functi

non commutative generalisations of urysohn s lemma and hereditary inner ideals abstract we establish several generalisations of urysohn s lemma in the setting of jb triples which provide full answers to problems 1 12 and 1 13 in fernandez polo and peralta 2007 22 these results extend the previous generalisations obtained by c a akemann g k pedersen and l g brown in the setting of c algebras a generalised kadison s transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in jbw triples we introduce the notion of positively open tripotent in the bidual of a jb triple as an extension of a concept which was already considered in the setting of ternary rings of operators we investigate the connections appearing between positively open tripotents and hereditary inner ideals