the coordinate exchange algorithm for constructing exact optimal experimental designs we describe the cyclic coordinate exchange algorithm for constructing d optimal and linear optimal experimental designs the algorithm uses a variant of the gauss southwell cyclic coordinate descent algorithm within the k exchange algorithm to achieve substantive reductions in required computing among its advantages are the following candidate sets which grow exponentially in the number of factors need not be explicitly constructed or enumerated convex design spaces or mixed convex by discrete design spaces are handled directly without the need for sophisticated nonlinear programming routines or candidate set adjustment for design problems having 10 or more factors the reductions in execution time are typically two or more orders of magnitude when compared to standard candidateset based procedures such as k exchange yet the designs produced exhibit no loss of efficiency

construction of two level nonregular designs of strength three with large run sizes abstracttwo level orthogonal arrays of strength 3 permit the study of the main effects and the two factor interactions of the experimental factors these arrays are classified into regular and nonr

rigidity of coxeter groups let w be a coxeter group acting properly discontinuously and cocompactly on manifolds n and m 9m 0 such that the fixed point sets of finite subgroups are contractible let f n n mx dk m xsk1 be a w homotopy equivalence which restricts to a w homeomorphism on the boundary under an assumption on the three dimensional fixed point sets we show that then f is w homotopic to a w homeomorphism

on a numerical characterization of non simple principally polarized abelian varieties to every abelian subvariety of a principally polarized abelian variety a mathcal l we canonically associate a numerical class in the neron severi group of a we prove that these classes are characterized by their intersection numbers with mathcal l moreover the cycle class induced by an abelian subvariety in the chow ring of a modulo algebraic equivalence can be described in terms of its numerical divisor class over the field of complex numbers this correspondence gives way to an explicit description of the coarse moduli space that parametrizes non simple principally polarized abelian varieties with a fixed numerical class

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

efficient designs with minimal aliasing for some experimenters a disadvantage of the standard optimal design approach is that it does not consider explicitly the aliasing of specified model terms with terms that are potentially important but are not included in the model for example when constructing an optimal design for a first order model aliasing of main effects and interactions is not considered this can lead to designs that are optimal for estimation of the primary effects of interest yet have undesirable aliasing structures in this article we construct exact designs that minimize the squared norm of the alias matrix subject to constraints on design efficiency we demonstrate use of the method for the construction of screening and response surface designs

bipolar coxeter groups we consider the class of those coxeter groups for which removing from the cayley graph any tubular neighbourhood of any wall leaves exactly two connected components we call these coxeter groups bipolar they include the virtually poincare duality coxeter groups the pseudo manifold coxeter groups and the infinite irreducible 2 spherical ones we show in a geometric way that a bipolar coxeter group admits a unique conjugacy class of coxeter generating sets moreover we provide a characterisation of bipolar coxeter groups in terms of the associated coxeter diagram

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

model robust two level designs using coordinate exchange algorithms and a maximin criterion we propose a candidate list free exchange algorithm that facilitates construction of exact model robust two level experiment designs in particular we investigate two model spaces previously considered in the literature the first assumes that all main effects and an unknown subset of two factor interactions are active but that the experimenter knows the number of active interactions the second assumes that an unknown subset of the main effects and all associated two factor interactions are active previous literature uses two criteria for design construction first maximize the number of estimable models then differentiate between designs equivalent in estimability by choosing the design with the highest average efficiency we adopt a similar strategy but 1 do not impose orthogonality or factor level balance constraints resulting in generally equal or larger numbers of estimable models and 2 use a flexible secondary criterion that maximizes the minimum efficiency we provide results fo

dominant k theory and integrable highest weight representations of kac moody groups we give a topological interpretation of the highest weight representations of kac moody groups given the unitary form g of a kac moody group over c we define a version of equivariant k theory kg on the category of proper g cw complexes we then study kac moody groups of compact type in detail see section 2 for definitions in particular we show that the grothendieck group of integrable highest weight representations of a kac moody group g of compact type maps isomorphically onto k g eg where eg is the classifying space of proper g actions for the affine case this agrees very well with recent results of freed hopkins teleman we also explicitly compute kg eg for kac moody groups of extended compact type which includes the kac moody group e10

topology of homology manifolds anr homology n manifolds are nite dimensional absolute neighborhood retracts x with the property that for every x 2 x hi x x fxg is 0 for i 6 n and z for i n topological manifolds are natural examples of such spaces to obtain nonmanifold examples we can take a manifold whose boundary consists of a union of integral homology spheres and glue on the cone on each one of the boundary components the resulting space is not a manifold if the fundamental group of any boundary component is a nontrivial perfect group it is a consequence of the double suspension theorem of cannon and edwards that as in the examples above the singularities of polyhedral anr homology manifolds are isolated there are however many examples of anr homology manifolds which have no manifold points whatever see 12 for a good exposition of the relevant theory the purpose of this paper is to begin a surgical classi cation of anr homology manifolds sometimes referred to in the sequel simply as homology manifolds one way to approach this circle of ideas is via the problem of characterizing topological manifolds among anr homology manifolds in cannon s work on the double suspension problem 6 it became clear that in dimensions greater than 4 the right transversality hypothesis is the following weak form of general position

two level designs to estimate all main effects and two factor interactions we study the design of two level experiments with n runs and n factors large enough to estimate the interaction model which contains all the main effects and all the two factor interactions yet an effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two factor interactions orthogonal arrays oas favor main effect estimation however complete enumeration becomes infeasible for cases relevant for practitioners we develop a partial enumeration procedure for these cases and we establish upper bounds on the d efficiency for the interaction model based on arrays that have not been generated by the partial enumeration we also propose an optimal design procedure that favors main effect estimation designs created with this procedure have smaller d efficiencies for the interaction model than d optimal designs but standard errors for the main effects in this model are improved generated oas for 7 10 factors and 32 72 runs are smaller or have a higher d efficiency than the smallest oas from the literature designs obtained with the new optimal design procedure or strength 3 oas which have main effects that are not correlated with two factor interactions are recommended if main effects unbiased by possible two factor interactions are of primary interest d optimal designs are recommended if interactions are of primary interest supplementary materials for this article are available online 2017 american statistical association and the american society for quality

two level orthogonal screening designs with 24 28 32 and 36 runs abstractthe potential of two level orthogonal designs to fit models with main effects and two factor interaction effects is commonly assessed through the correlation between contrast vectors involving these effects we study the complete catalog of nonisomorphic orthogonal two level 24 run designs involving 3 23 factors and we identify the best few designs in terms of these correlations by modifying an existing enumeration algorithm we identify the best few 28 run designs involving 3 14 factors and the best few 36 run designs in 3 18 factors as well based on a complete catalog of 7570 designs with 28 runs and 27 factors we also seek good 28 run designs with more than 14 factors finally starting from a unique 31 factor design in 32 runs that minimizes the maximum correlation among the contrast vectors for main effects and two factor interactions we obtain 32 run designs that have low values for this correlation to demonstrate the added value of our work we provide a detailed comparison of our desi

finiteness conditions and pd r group covers of pd n complexes we show that an infinite cyclic covering space m of a pdn complex m is a pdn 1 complex if and only if m 0 m is homotopy equivalent to a complex with finite n 1 2 skeleton and 1 m is finitely presentable this is best possible in terms of minimal finiteness assumptions on the covering space we give also a corresponding result for covering spaces m with covering group a pdr group under a slightly stricter finiteness condition

on of truncated polynomial rings group homology spectral sequences are used to investigate k of truncated polynomial rings if f is a finite field of odd characteristic we show that relative k of the pair formula presented which has been identified by van der kallen and stienstra is isomorphic to formula presented when q is sufficiently large we also show that formula presented and is isomorphic to the associated k group modulo an elementary abelian 2 group