on the topological 4 genus of torus knots we prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus as an application we derive the best possible linear estimate of the topological slice genus for torus knots with non maximal signature invariant

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

curvature diameter homotopy groups and cohomology rings we establish two topological results a if m is a 1 connected compact n manifold and q 2 then the minimal number of generators for the qth homotopy group q m mng q m is bounded above by a number depending only on mng h m and q where h m is the homology group c let mathscr m n y be the collection of compact orientable n manifolds whose oriented bundles admit so n invariant fibrations over y with fiber compact nilpotent manifolds such that the induced so n actions on y are equivalent then q m finitely generated m mathscr m n y contains only finite isomorphism classes depending only on n y q together with the results of cg and gr1 from a we conclude that i if m is a complete n manifold of nonnegative curvature then mng q m is bounded above by a number depending only on n and q 2 together with the results of ch and cfg from c we conclude that ii if m is a compact n manifold whose sectional curvature and diameter satisfy secm and diamm d then q m has a finite number of possible isomorphism classes depending on n d q 2 provided q m is finitely generated we also show that b if m is a compact n manifold with secm and diam m d then the cohomology ring h m may have infinitely many isomorphism classes in particular b answers some questions raised by k grove gro

a controlled plus construction for crumpled laminations given a closed n manifold m n 4 and a finitely generated perfect subgroup p of it1 m we previously developed a controlled version of quillen s plus construction namely a cobordism w m n with the inclusion j n f w a homotopy equivalence and kernel of i i1 m f it1 w equalling the smallest normal subgroup of xl1 m containing p together with a closed map p w 0 1 such that p l t is a closed n manifold for every t e 0 1 and in particular m p 1 o and n p l l we accomplished this by constructing an acyclic map of manifolds f m f n having the right fundamental groups and w arose as the mapping cylinder of f with a collar attached along n the main result here presents a condition under which the desired controlled plus construction can still be accomplished in many cases even when it1 m contains no finitely generated perfect subgroups by products of these results include a new method for constructing wild embeddings of codimension one manifolds and a better understanding of perfect subgroups of finitely presented groups

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

dissolving four manifolds and positive scalar curvature we prove that many simply connected symplectic four manifolds dissolve after connected sum with only one copy of s2 s2 for any finite group g that acts freely on the three sphere we construct closed smooth four manifolds with fundamental group g which do not admit metrics of positive scalar curvature but whose universal covers do admit such metrics

the full ward takahashi identity for colored tensor models colored tensor models ctm is a random geometrical approach to quantum gravity we scrutinize the structure of the connected correlation functions of general ctm interactions and organize them by boundaries of feynman graphs for rank d interactions including but not restricted to all melonic varphi 4 vertices to wit solely those quartic vertices that can lead to dominant spherical contributions in the large n expansion the aforementioned boundary graphs are shown to be precisely all possibly disconnected vertex bipartite regularly edge d colored graphs the concept of ctm compatible boundary graph automorphism is introduced and an auxiliary graph calculus is developed with the aid of these constructs certain u invariance of the path integral measure is fully exploited in order to derive a strong ward takahashi identity for ctms with a symmetry breaking kinetic term for the rank 3 varphi 4 theory we get the exact integral like equation for the 2 point function similarly exact equations for higher multipoint functions can be readily obtained departing from this full ward takahashi identity our results hold for some group field theories as well altogether our non perturbative approach trades some graph theoretical methods for analytical ones we believe that these tools can be extended to tensorial syk models

whitehead 3 is a slice link we show that the whitehead double t wh l of a two component link l is topologically flat slice if and only if the linking number of l is zero when they exist the slices may be chosen so that the complement b slices is homotopy equivalent to a wedge of two circles s 1 v s 1 with certain meridinal loops of wh l freely generating b4 slices compare this with if1 where it is shown that the whitehead double of boundary links are slice this is consistent with the surgery conjecture but seems not to illuminate the key 3component case see i f2 in particular wh3 wh who is slice we will describe the argument quite explicitly for this case and indicate in closing remarks what modifications are needed for the general result first we deal with non existence let s be the obvious two component seifert surface for wh l a component of s is obtained by composing either of the two punctured tori tz cslx d 2 pictured below with an untwisted identification of s i 2 with a neighborhood of a component of l add a band to s s su band so that s becomes the seifert surface for some knot k the seifert forms for s and s are identical and in a natural basis will be

simply connected 4 manifolds with a given boundary let m be a closed oriented connected 3 manifold for each bilinear symmetric pairing zn l our goal is to calculate the set vl m of all oriented homeomorphism types of compact 1 connected oriented 4manifolds with boundary m and intersection pairing isomorphic to zn l for each pair zn l which presents h m we construct a double coset space bl m and a function ct vl m bl m the set bt m is the quotient of the group of all link pairing preserving isomorphisms of the torsion subgroup of h1 m by two naturally occuring subgroups when zn l is an even pairing we construct another double coset space bl m a function 6l vl m b fl m and a projection p2 bl m bl m such that p2 c l ct our main result states that when zn l is even the function c l is injective as is the function c x a vl m bl m x z 2 when z l is odd here a is a kirby siebenmann obstruction to smoothing it follows that the sets vl m are finite and of an order bounded above by a constant depending only on h1 m we also show that when hi m q 0 and z l is even ct p2 c 6l is injective it seems likely that via the functions cl x a and 6l the sets bl m x z 2 and bl m calculate vl m when zn l is respectively odd and even we verify this in several cases most notably when h1 m is free abelian the results above are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between two 1connected 4 manifolds extending a given homeomorphism of their boundaries the theory developed is then applied to show that there is an m 0 depending only on h1 m such that for any self homeomorphism f of m fm extends to a self homeomorphism of any 1 connected compact 4 manifold with boundary m introduction in m freedman s fundamental paper fr he classified closed simply connected oriented 4 manifolds up to orientation preserving homeomorphism he showed that modulo the kirby siebenmann invariant these manifolds are in bijective correspondence through their intersection pairings with the set of unimodular bilinear symmetric pairings over z see theorem 1 5 of fr and corollary 2 2 3 of q in this paper we begin a classification of simply connected 4 manifolds with connected boundary our results with regard to this problem are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between 1 connected 4 manifolds extending a given homeomorphism of their boundaries received by the editors september 19 1985 1980 mathematics subject classification 1985 revision primary 57n15 research supported by an nserc canada post doctoral fellowship 1986 american mathematical society 0002 9947 86 1 00 25 per page

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

generalized pointwise bias error bounds for response surface approximations this paper proposes a generalized pointwise bias error bounds estimation method for polynomial based response surface approximations when bias errors are substantial a relaxation parameter is introduced to account for inconsistencies between the data and the assumed true model the method is demonstrated with a polynomial example where the model is a quadratic polynomial while the true function is assumed to be cubic polynomial the effect of relaxation parameter is studied it is demonstrated that when bias errors dominate the bias error bounds characterize the actual error field better than the standard error the bias error bound estimates also help to identify regions in the design space where the accuracy of the response surface approximations is inadequate it is demonstrated that this information can be utilized for adaptive sampling in order to improve accuracy in such regions copyright 2005 john wiley sons ltd

heegaard floer homology of matsumoto s manifolds abstract we consider a homology sphere m n k 1 k 2 presented by two knots k 1 k 2 with linking number 1 and framing 0 n we call the manifold matsumoto s manifold we show that m n t 2 3 k 2 never bounds any contractible 4 manifold if n 2 k 2 holds we also give a formula of ozsvath szabo s invariant as the total sum of the euler numbers of the reduced filtration we compute the invariants of the twisted whitehead doubles of torus knots and correction terms of the branched covers of the whitehead doubles by using owens and strle s obstruction we show that the 12 twisted whitehead double of the 2 7 torus knot and the 20 twisted whitehead double of the 3 7 torus knot are not slice but the double branched covers bound rational homology 4 balls these are new examples having a gap between what a knot is slice and what a double branched cover bounds a rational homology 4 ball

casson towers and slice links we prove that a casson tower of height 4 contains a flat embedded disc bounded by the attaching circle and we prove disc embedding results for height 2 and 3 casson towers which are embedded into a 4 manifold with some additional fundamental group assumptions in the proofs we create a capped grope from a casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps data which is sufficient for a topological disc to exist with the desired boundary as applications we present new slice knots and links by giving direct applications of the disc embedding theorem to produce slice discs without first constructing a complementary 4 manifold in particular we construct a family of slice knots which are potential counterexamples to the homotopy ribbon slice conjecture

homotopy invariants of links this paper answers a question originally asked by john milnor in 1957 it offers significant progress toward another question from that paper in m 1 an m 2 john milnor defined a collection of isotopy invariants of links stallings showed these were actually concordance i variants of the ink stallings work suggested that milnor s invariants were related to other algebraically defined invariants the massey products in the exterior of the link a connection made precise in tu and p thus the results in this paper can be reinterpreted as results about massey products in the link exterior recently mike freedman has suggested that some of these invariants may be the obstructions to the topological surgery theorem in dimension four f i if2 fl in this paper the approach to studying higher dimensional link concordance presented in o 1 is extended to the study of links in the 3 sphere a collection of new link invariants is defined and related to milnor s invariants one fundamental advantage of this approach is that these new invariants make explicit use of the three sphere containing the link the link exterior contains all the relations among milnor s invariants by accounting for the ambient sphere our invariants eliminate redundancy see theorem 15 we answer this question originally asked by milnor 1 to what extent are milnor s invariants independent of each other theorem 15 milnor also asked this question 2 can one extract invariants from the group rc n where 7r is the link group and n is the intersection of the lower central series of the link group theorem 15 answers question 1 partial results can be found in c 1 ma i on and t the only previously known results for two component links were k 2 8 where the number of linearly independent invariants are 0 1 0 5 0 6 and 4 respectively for links with three or more components tess was known

nonlocally smoothable topological symmetries of four manifolds il existe une infinite de varietes a 4 dimensions simplement connexes closes qui n admettent pas d involutions localement regularisables mais qui en admet des topologiques

entropy limit theorems and variational principles for disordered lattice systems we study infinite volume limits and gibbs states of disordered lattice systems with bounded and continuous potentials our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes we find that many familiar results of invariant potentials such as large deviation theorems variational principles and equivalence of ensembles continue to hold for disordered models with suitably modified statements

pitfalls of using a single criterion for selecting experimental designs for surrogate construction a good experimental design ed is essential to simultaneously reduce the effect of noise and bias errors however most eds cater to a single criterion and may lead to small gains in that criterion at the expense of large deteriorations in other criteria we use multiple criteria to assess the performance of different popular eds we demonstrate that these eds offer different trade offs and that use of a single criterion is indeed risky in addition we show that popular eds such as latin hypercube sampling lhs and d optimal designs often leave large regions of the design space unsampled even for moderate dimensions we discuss a few possible strategies to combine multiple criteria and illustrate them with examples we show that complementary criteria e g bias handling criterion for variance based designs and vice versa can be combined to improve the performance of eds we demonstrate improvements in the trade offs between noise and bias error by combining a model based criterion like the d optimality criterion and a geometry based criterion like lhs next we demonstrate that selecting an ed from three candidate eds using a suitable error based criterion helped eliminate potentially poor designs finally we show benefits from combining the multiple criteria based strategies that is generation of multiple eds using the d optimality and lhs criteria and selecting one design using a pointwise bias error criterion the encouraging results from the examples indicate that it may be worthwhile studying these strategies more rigorously and in more detail copyright 2007 john wiley sons ltd

4 manifold topology ii dwyer s filtration and surgery kernels even when the fundamental group is intractable i e not good many interesting 4 dimensional surgery problems have topological solutions we unify and extend the known examples and show how they compare to the presumed counterexamples by reference to dwyer s filtration on second homology the development brings together many basic results on the nilpotent theory of links as a special case a class of links only slightly smaller than homotopically trivial links is shown to have free slices on their whitehead doubles

surgery in dimension four and noncompact 5 manifolds this paper describes a precise relationship between the problems of completing surgery in dimension four and finding boundaries for noncompact 5 manifolds two outstanding problems of low dimensional topology are completing 4 dimensional surgery and finding boundaries for noncompact 5 dimensional manifolds although no complete theory is known for either problem some interesting results have been found see 1 4 5 10 and addendum in this paper we describe a complete relationship between these two problems consequently knowledge of 4 dimensional surgery yields information about noncompact 5 manifolds and conversely all manifolds and maps in this paper are assumed to be smooth each manifold is provided with a basepoint and when appropriate basepaths will be chosen to given 2 spheres without explicit mention i wish to thank gerald a anderson and frank quinn for helpful discussions also i wish to thank patrick gilmer for his advice and encouragement during this project 1 statement of results let f b m am y x be a degree one normal map in the sense of wall 11 where m is a compact connected 4 manifold and y x is a poincare pair not necessarily simple if x 0 then we require that f jam am x induces an isomorphism of homology groups with a z vi y coefficients also we assume that f is 2 connected k2 m is a free a module and the surgery obstruction a f b e lh 7 c is zero if h c k2 m is a subkernel we will say that h is representable in m if we can find disjoint framed embedded 2 spheres si sr c int m such that the inclusion m ui si m induces an isomorphism of fundamental groups and the classes of sl sr in h2 m a 7t2 m form a basis over a for h the subkernel h is stably representable if for some integer k 0 h ed kei ek is representable in m k s2 x s2 here ei denotes the class of s2 x 1 c ith summand s2 x s2 and e1 ek is the submodule generated by el ek we regard h ed ke ek as received by the editors august 10 1982 1980 mathematics subject classification primary 57r65 secondary 57m99 1985 american mathematical society 0002 9947 85 1 00 25 per page

on the diffeomorphism groups of elliptic surfaces in this paper we determine for relatively minimal elliptic surfaces with positive euler number the image of the natural representation of the group of orientation preserving self diffeomorphisms on h the second homology group reduced modulo torsion to this end we construct as many embedded spheres of square 2 such that an isometry not induced from any combination of reflections at such spheres or from complex conjugation can be shown not to be induced from some diffeomorphism at all this is done with the help of seiberg witten invariants

theory of ordered spaces this is the first of a planned series of investigations on the theory of ordered spaces based upon four axioms two of these the order i 1 1 and the local structure ii 5 1 axioms provide the structure of the theory and the other two the identification i 1 11 and cone i 2 7 axioms eliminate pathologies or excessive generality in the present paper the axioms are supplemented by the nontriviality conditions i 1 9 and a regularity property ii 4 2

evaluation of convergence behavior of metamodeling techniques for bridging scales in multi scale multimaterial simulation the effectiveness of several metamodeling techniques viz the polynomial stochastic collocation method adaptive stochastic collocation method a radial basis function neural network a kriging method and a dynamic kriging method is evaluated this is done with the express purpose of using metamodels to bridge scales between micro and macro scale models in a multi scale multimaterial simulation the rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied for sufficiently large number of training points stochastic collocation methods generally converge faster than the other metamodeling techniques while the dkg method converges faster when the number of input points is less than 100 in a two dimensional parameter space because the input points correspond to computationally expensive micro meso scale computations the dkg is favored for bridging scales in a multi scale solver

a mean squared error criterion for the design of experiments in estimating a response surface over a design region of interest mean squared error can arise both from sampling variance and bias introduced by model inadequacy the criterion adopted here for experimental design attempts to protect against bias resulting from a large class of deviations from the assumed model two algorithms are proposed for the construction of either approximate or exact designs and an example is given

the global structure of simple space times according to a standard definition of penrose a space time admitting well defined future and past null infinitiesi andi is asymptotically simple if it has no closed timelike curves and all its endless null geodesics originate fromi and terminate ati the global structure of such space times has previously been successfully investigated only in the presence of additional constraints the present paper deals with the general case it is shown thati is diffeomorphic to the complement of a point in some contractible open 3 manifold the strongly causal regioni0 ofi is diffeomorphic to mathbb s 2 times mathbb r and every compact connected spacelike 2 surface ini is contained ini0 and is a strong deformation retract of bothi0 andi moreover the space time must be globally hyperbolic with cauchy surfaces which subject to the truth of the poincare conjecture are diffeomorphic to 3

fundamental groups of positively curved manifolds with symmetry we obtain a classification for the fundamental groups of closed n manifolds of positive sectional curvature which admit an isometric t k action with k ge frac n 6 1 n ne 11 15

stein structures and holomorphic mappings we prove that every continuous map from a stein manifold x to a complex manifold y can be made holomorphic by a homotopic deformation of both the map and the stein structure on x in the absence of topological obstructions the holomorphic map may be chosen to have pointwise maximal rank the analogous result holds for any compact hausdorff family of maps but it fails in general for a noncompact family our main results are actually proved for smooth almost complex source manifolds x j with the correct handlebody structure the paper contains another proof of eliashberg s int j math 1 29 46 1990 homotopy characterization of stein manifolds and a slightly different explanation of the construction of exotic stein surfaces due to gompf ann math 148 2 619 693 1998 j symplectic geom 3 565 587 2005

self affine manifolds abstract this paper studies closed 3 manifolds which are the attractors of a system of finitely many affine contractions that tile r 3 such attractors are called self affine tiles effective characterization and recognition theorems for these 3 manifolds as well as theoretical generalizations of these results to higher dimensions are established the methods developed build a bridge linking geometric topology with iterated function systems and their attractors a method to model self affine tiles by simple iterative systems is developed in order to study their topology the model is functorial in the sense that there is an easily computable map that induces isomorphisms between the natural subdivisions of the attractor of the model and the self affine tile it has many beneficial qualities including ease of computation allowing one to determine topological properties of the attractor of the model such as connectedness and whether it is a manifold the induced map between the attractor of the model and the self affine tile is a quotient map and can be checked in certain cases to be monotone or cell like deep theorems from geometric topology are applied to characterize and develop algorithms to recognize when a self affine tile is a topological or generalized manifold in all dimensions these new tools are used to check that several self affine tiles in the literature are 3 balls an example of a wild 3 dimensional self affine tile is given whose boundary is a topological 2 sphere but which is not itself a 3 ball the paper describes how any 3 dimensional handlebody can be given the structure of a self affine 3 manifold it is conjectured that every self affine tile which is a manifold is a handlebody

a decomposition theorem for h cobordant smooth simply connected compact 4 manifolds theorem let m and n be smooth h cobordant compact 1 connected 4 manifolds there exist decompositions m m0 m1 and n n0 n1 where m0 and n0 are smooth compact contractible 4 manifolds with boundary so that m1 and n1 are dieomorphic if m and n are closed then we may further arrange that m1 and n1 are 1 connected in fact if w is an h cobordism connecting m and n then w can be written w w0 i w1 where w0 m0 n0 is an often nontrivial h cobordism and w1 m1 n1 is smoothly the product h cobordism m1 i m1 f0 g m1 f1 g this theorem lies in the mainstream of combinatorial 4 manifold theory circa 1975 but oddly the result was overlooked it now ts into a rich context donaldson theory and raises new questions when compared with the known examples in 1988 akbulut a showed that a manifold x homotopy equivalent to a k3 surface could after blowing up a point be transformed into a rational surface q by cutting out and regluing a certain contractible mazur manifold by an involution of its boundary at the time a rather delicate argument of fintushel and stern relying on the observed presence of the homology sphere 2 3 7 x showed that certain donaldson invariants of x and its blow up x were nontrivial this distinguished x from the h cobordant manifold q in retrospect this was the rst nontrivial example of our theorem the result was a surprise the donaldson invariant which derives from the second homology had been localized on a contractible piece recently bizaca and gompf bg have shown that x is in fact dieomorphic to k3 allowing a more direct analysis of its donaldson invariant see e g qk or km they also nd an innite family of examples

a family of freely slice good boundary links we show that every good boundary link with a pair of derivative links on a seifert surface satisfying a homotopically trivial plus assumption is freely slice this subsumes all previously known methods for freely slicing good boundary links with two or more components and provides new freely slice links

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

higher order alexander invariants and filtrations of the knot concordance group we establish certain nontriviality results for several filtrations of the smooth and topological knot concordance groups first as regards the n solvable filtration of the topological knot concordance group c defined by k orr p teichner and the first author 0 f n 5 f n f 1 5 f 1 0 f 0 5 f 0 c we refine the recent nontriviality results of cochran and teichner by including information on the alexander modules these results also extend those of c livingston and the second author we exhibit similar structure in the closely related symmetric grope filtration ofc we also show that the grope filtration of the smooth concordance group is nontrivial using examples that cannot be distinguished by the ozsvath szabo invariant nor by j rasmussen s s invariant our broader contribution is to establish in the relative case the key homological results whose analogues cochran orr teichner established in the absolute case we say two knots k 0 and k 1 are concordant modulo n solvability if k o k 1 f n our main result is that for any knot k whose classical alexander polynomial has degree greater than 2 and for any positive integer n there exist infinitely many knots k i that are concordant to k modulo n solvability but are all distinct modulo n 5 solvability moreover the k i and k share the same classical seifert matrix and alexander module as well as sharing the same higher order alexander modules and seifert presentations up to order n 1

heegaard floer homology and concordance bounds on the thurston norm we prove that twisted correction terms in heegaard floer homology provide lower bounds on the thurston norm of certain cohomology classes determined by the strong concordance class of a 2 component link l in s 3 we then specialise this procedure to knots in s 2 times s 1 and obtain a lower bound on their geometric winding number furthermore we produce an obstruction for a knot in s 3 to have untwisting number 1 we then provide an infinite family of null homologous knots with increasing geometric winding number on which the bound is sharp

pointwise bias error bounds and min max design for response surface approximations bounds on response surface approximation errors as a result of model inadequacy bias error are presented and a design of experiments minimizing the maximal bias error is proposed the bias error bounds are considered as a tool to identify locations in the design space where the accuracy of the approximation fitted on a given design of experiments might be poor two approaches to characterize the bias error assume that the functional form of the true model is known and seek at each point in design space worst case bounds on the absolute error the first approach is implemented before data generation this data independent error bound can easily be implemented in a search for a design of experiments that minimize the bias error bound as it requires very little computation the second approach is to be used posterior to the data generation and provides tightened error bound consistent with the data this data dependent error bound requires the solution of two linear programming problems at each point the data independent error bound for design of experiments of two variable examples is demonstrated randomly generated polynomials in two variables are then used to validate the data dependent bias error bound distribution although the two approaches are used in conjunction in the given examples the data independent error bound design of experiment is not a prerequisite for the application of the data dependent error bounds in search for the high bias error regions

stable mapping class groups of 4 manifolds with boundary we give a complete algebraic description of the mapping class groups of compact simply connected 4 manifolds with boundary up to connected sum with copies of s 2 s 2

locally flat 2 knots in with the same fundamental group we consider a locally flat 2 sphere in s x s2 representing a primitive homology class 4 which is referred to as a 2 knot in s x s2 representing 4 then for any given primitive class there exists a 2 knot in s2 x s2 representing 4 with simply connected complement in this paper we consider the classification of 2 knots in s2 x s2 whose complements have a fixed fundamental group we show that if the complement of a 2 knot s in s2 x s2 is simply connected then the ambient isotopy type of s is determined in the case of nontrivial 7r1 however we show that the ambient isotopy type of a 2 knot in s2 x s2 with nontrivial 71 is not always determined by 71

metabelian representations twisted alexander polynomials knot slicing and mutation given a knot complement x and its p fold cyclic cover x p x we identify twisted polynomials associated to gl 1 left bf f t pm 1 right representations of 1 x p with twisted polynomials associated to related gl p left bf f t pm 1 right representations of 1 x which factor through metabelian representations this provides a simpler and faster algorithm to compute these polynomials allowing us to prove that 16 of 18 previously unknown algebraically slice knots of 12 or fewer crossings are not slice we also use this improved algorithm to prove that the 24 mutants of the pretzel knot p 3 7 9 11 15 corresponding to permutations of 7 9 11 15 represent distinct concordance classes

link concordance invariants and homotopy theory we show that each of a sequence of concordance invariants for codimension two links of spheres ins n 2 defined by kent orr is identically zero forn 1 for classical links n 1 the same proof shows that these invariants vanish if and only if milnor s bar mu vanish a result obtained independently and earlier by orr himself we offer sufficient conditions for the vanishing of orr s invariant not covered by the above we discuss how this relates to positive results

an algorithm for fast optimal latin hypercube design of experiments citation viana f a c venter g balabanov v 2010 an algorithm for fast optimal latin hypercube design of experiments international journal for numerical methods in engineering 82 2 135 156 doi 10 1002 nme 2750

orthogonal array based latin hypercubes abstract in this article we use orthogonal arrays oa s to construct latin hypercubes besides preserving the univariate stratification properties of latin hypercubes these strength r oa based latin hypercubes also stratify each r dimensional margin therefore such oa based latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes we prove that when used for integration the sampling scheme with oa based latin hypercubes offers a substantial improvement over latin hypercube sampling

rigidity theorems for right angled reflection groups let t be a right angled reflection group let m and m be coxeter manifolds then any t map f m fm is t homotopic to a homeo morphism introduction this paper contains the results given in the author s ph d the sis davis in 9 showed that in every dimension 4 there exists a cocompact reflection group on a contractible manifold not homeomorphic to an euclidean space also he gave the first example of a closed aspherical manifold not covered by euclidean space davis construction provides an infinite coxeter group acting locally smoothly effectively and properly discontinuously on a contractible manifold with compact quotient

topologically invariant chern numbers of projective varieties abstract we prove that a rational linear combination of chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the euler and pontryagin numbers in dimension at least three we prove that only multiples of the top chern number which is the euler characteristic are invariant under diffeomorphisms that are not necessarily orientation preserving these results solve a long standing problem of hirzebruch s we also determine the linear combinations of chern numbers that can be bounded in terms of betti numbers

a new technique for the link slice problem the conjectures that the 4 dimensional surgery theorem and 5 dimensional s cobordism theorem hold without fundamental group restriction in the topological category are equivalent to assertions that certain atomic links are slice this has been reported in cf f2 f4 and fq the slices must be topologically flat and obey some side conditions for surgery the condition is a s 3 slice rq b 4 slice must be an epimorphism i e the slice should be homotopically ribbon for the s cobordism theorem the slice restricted to a certain trivial sublink must be standard there is some choice about what the atomic links are the current favorites are built from the simple hopf link by a great deal of bing doubling and just a little whitehead doubling a link typical of those atomic for surgery is illustrated in fig 1 links atomic for both s cobordism and surgery are slightly less symmetrical there has been considerable interplay between the link theory and the equivalent abstract questions the link theory has been of two sorts algebraic invariants of finite links and the limiting geometry of infinitely iterated links our object here is to solve a class of free group surgery problems specifically to construct certain slices for the class of links where d l ecg if and only if d l is an untwisted whitehead double of a boundary link l unfortunately appears not to be atomic for surgery or s cobordism however our technique is quite different from the earlier extension f4 of simply connected methods and may prove helpful in establishing the limits of the nonsimply connected theory an n component link is a topological imbedding i si c l 3 of n circles i 1 in the 3 sphere it is slice if and only if there is a topological imbedding l dotted arrow making the diagram

construction of group actions on four manifolds it is shown that any cyclic group of odd prime order acts on any closed simply connected topological 4 manifold inducing the identity on integral homology the action is locally linear except perhaps at one isolated fixed point in the case of primes greater than three a more careful argument is used to show that the action can be constructed to be locally linear introduction in this paper we shall show that every closed simply connected topological 4 manifold m4 admits an action of any cyclic group zp of odd prime order p the action will be homologically trivial that is induce the identity on integral homology be pseudofree that is have only isolated fixed points except in certain cases when p 3 and be locally linear except perhaps at one isolated fixed point when p 2 and the intersection form of m4 has even type then the same conclusion holds this is also due to s kwasik and p vogel 1985 by a somewhat different proof if p 2 and the intersection form of m has odd type however then an action of z2 which is homologically trivial must have a fixed point set containing two dimensional components see 7 further it is harder to control the kirby siebenmann triangulation obstruction which is then not determined by the intersection form it is interesting to ask whether these actions can be locally linear or smooth when m4 is smooth the existence of a locally linear z2 action implies the vanishing of the kirby siebenmann obstruction see kwasik and vogel 1984 we shall show however that for p 3 in general these actions can be constructed to be locally linear in a recent preprint kwasik has shown that this is the case for the fake cp2 when p is odd by a rather different proof these actions are homologically trivial and have only isolated fixed points except sometimes when p 3 the g signature theorem shows that not every simply connected 4 manifold admits pseudofree locally linear actions when p 3 we shall see for example that neither the e8 manifold the kummer surface nor a nontrivial connected sum of copies of cp2 admits such an action for p 3 in broad outline our construction goes as follows let a closed oriented simply connected 4 manifold m be given by studying equivariant framed links we construct a compact smooth 4 manifold with boundary having the intersection form of m and admitting a smooth zp action which is pseudofree and homologically trivial the action is free on the boundary homology sphere e in a paper primarily focused on equivariant plumbing diagrams for high dimensional highly connected manifolds with even intersection forms weintraub 1975 carried out most of this we give an independent development because we need to be able to better control received by the editors october 16 1985 and in revised form january 7 1986 1980 mathematics subject classification 1985 revision primary 57s17 57s25 57n15 research supported in part by a grant from the national science foundation 1987 american mathematical society 0002 9947 87 1 00 25 per page

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

orthogonal column latin hypercubes and their application in computer experiments abstract latin hypercubes have been frequently used in conducting computer experiments in this paper a class of orthogonal latin hypercubes that preserves orthogonality among columns is proposed applying an orthogonal latin hypercube design to a computer experiment benefits the data analysis in two ways first it retains the orthogonality of traditional experimental designs the estimates of linear effects of all factors are uncorrelated not only with each other but also with the estimates of all quadratic effects and bilinear interactions second it can facilitate nonparametric fitting procedures because one can select good space filling designs within the class of orthogonal latin hypercubes according to selection criteria

a surgery sequence in dimension four the relations with knot concordance we present a systematic treatment of the classification problem for compact smooth 4 manifolds m it is modeled on the surgery exact sequence the central theorem in the classification of n manifolds n 5 the price for the extension to dimension 4 is a hole in m where a homotopy 1 skeleton should be there is no homotopy theoretic or surgical obstruction to complet ing m with a wedge of circles so that the completion has the topology of a compact smooth manifold this point set problem is all that stands between 4 manifolds and the tranquility that prevails in higher dimensions when m is simply connected only a point is missing from the model the applications of this are discussed in f and fq 1 the general theory has application to knot and link theory in particular knots with alexander polynomial 1 are characterized geometrically as knots admitting a certain

linking and causality in globally hyperbolic space times the classical linking number lk is defined when link components are zero homologous in 15 we constructed the affine linking invariant alk generalizing lk to the case of linked submanifolds with arbitrary homology classes here we apply alk to the study of causality in lorentzian manifolds

statistics and meta statistics in the concept of complexity abstract a crucial distinction between different classes of complexity measures is found to consist in their statistical structure while first order statistics always provides one or another kind of a measure of randomness second order meta statistics provides more subtle measures of complexity an example of a second order measure is constructed and applied to specific cases some formal and conceptual issues concerning the general relevance of meta statistical concepts of complexity are pointed out

a diffeomorphism classification of manifolds which are like projective planes we give a complete diffeomorphism classification of 1 connected closed manifolds m with integral homology h m z z z provided that dim m 6 4

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4