a differential complex for cat 0 cubical spaces abstract in the 1980 s pierre julg and alain valette and also tadeusz pytlik and ryszard szwarc constructed and studied a certain fredholm operator associated to a simplicial tree the operator can be defined in at least two ways from a combinatorial flow on the tree similar to the flows in forman s discrete morse theory or from the theory of unitary operator valued cocycles there are applications of the theory surrounding the operator to c algebra k theory to the theory of completely bounded representations of groups that act on trees and to the selberg principle in the representation theory of p adic groups the main aim of this paper is to extend the constructions of julg and valette and pytlik and szwarc to cat 0 cubical spaces a secondary aim is to illustrate the utility of the extended construction by developing an application to operator k theory and giving a new proof of k amenability for groups that act properly on finite dimensional cat 0 cubical spaces

bmo spaces associated with semigroups of operators we study bmo spaces associated with semigroup of operators on noncommutative function spaces i e von neumann algebras and apply the results to boundedness of fourier multipliers on non abelian discrete groups we prove an interpolation theorem for bmo spaces and prove the boundedness of a class of fourier multipliers on noncommutative lp spaces for all 1 p with optimal constants in p

free group representations from vector valued multiplicative functions ii let gamma be a non commutative free group on finitely many generators in a previous work two of the authors have constructed the class of multiplicative representations of gamma and proved them irreducible as representation of gamma ltimes lambda c omega in this paper we analyze multiplicative representations as representations of gamma and we prove a criterium for irreducibility based on the growth of their matrix coefficients

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

semigroups of herz schur multipliers abstract in order to investigate the relationship between weak amenability and the haagerup property for groups we introduce the weak haagerup property and we prove that having this approximation property is equivalent to the existence of a semigroup of herz schur multipliers generated by a proper function see theorem 1 2 it is then shown that a not necessarily proper generator of a semigroup of herz schur multipliers splits into a positive definite kernel and a conditionally negative definite kernel we also show that the generator has a particularly pleasant form if and only if the group is amenable in the second half of the paper we study semigroups of radial herz schur multipliers on free groups we prove that a generator of such a semigroup is linearly bounded by the word length function see theorem 1 6

kinetics of diffusing polymer encounter in confined cellular microdomains we study the mean first time that two monomers located on the same polymer encounter in a confined microdomain approximating the confined geometry by a harmonic potential well we obtain an asymptotic expression for the mean first encounter time mfetc as a function of the radius e around one monomer by studying the end to end distance of the polymer in a ball using the edwards formalism we derive an other estimation of the mfetc we validate the asymptotic formulas using brownian simulations and derive their range of validity in terms of the polymer length we apply the present models to compute the mean time for a gene located far away from a promoter site to be activated during looping in confined genomic territories

measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming one way of solving multiple objective mathematical programming problems is finding discrete representations of the efficient set a modified goal of finding good discrete representations of the efficient set would contribute to the practicality of vector maximization algorithms we define coverage uniformity and cardinality as the three attributes of quality of discrete representations and introduce a framework that includes these attributes in which discrete representations can be evaluated compared to each other and judged satisfactory or unsatisfactory by a decision maker we provide simple mathematical programming formulations that can be used to compute the coverage error of a given discrete representation our formulations are practically implementable when the problem under study is a multiobjective linear programming problem we believe that the interactive algorithms along with the vector maximization methods can make use of our framework and its tools

the similarity problem for fourier algebras and corepresentations of group von neumann algebras let g be a locally compact group and let a g and vn g be its fourier algebra and group von neumann algebra respectively in this paper we consider the similarity problem for a g is every bounded representation of a g on a hilbert space h similar to a representation we show that the similarity problem for a g has a negative answer if and only if there is a bounded representation of a g which is not completely bounded for groups with small invariant neighborhoods i e sin groups we show that a representation a g b h is similar to a representation if and only if it is completely bounded this in particular implies that corepresentations of vn g associated to non degenerate completely bounded representations of a g are similar to unitary corepresentations we also show that if g is a sin maximally almost periodic or totally disconnected group then a representation of a g is a representation if and only if it is a complete contraction these results partially answer questions posed in effros and ruan 2003 7 and spronk 2002 25

uniformly bounded representations of sl 2 r abstract we compute the norm of irreducible uniformly bounded representations of sl 2 r we show that the kunze stein version of the uniformly bounded representations has minimal norm in its similarity class of uniformly bounded representations

computation of the mean first encounter time between the ends of a polymer chain using a novel theoretical approach we study the mean first encounter time mfet between the two ends of a polymer previous approaches used various simplifications that reduced the complexity of the problem leading however to incompatible results we construct here for the first time a general theory that allows us to compute the mfet the method is based on estimating the mean time for a brownian particle to reach a narrow domain in the polymer configuration space in dimension two and three we find that the mfet depends mainly on the first eigenvalue of the associated fokker planck operator and provide precise estimates that are confirmed by brownian simulations interestingly although many time scales are involved in the encounter process its distribution can be well approximated by a single exponential which has several consequences for modeling chromosome dynamics in the nucleus another application of our result is computing the mean time for a dna molecule to form a closed loop when its two ends meet for the first time

tent spaces associated with semigroups of operators abstract we study tent spaces on general measure spaces we assume that there exists a semigroup of positive operators on l p satisfying a monotone property but do not assume any geometric metric structure on the semigroup plays the same role as integrals on cones and cubes in euclidean spaces we then study bmo spaces on general measure spaces and get an analogue of fefferman s h 1 bmo duality theory we also get a h 1 bmo duality inequality without assuming the monotone property all the results are proved in a more general setting namely for noncommutative l p spaces

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

the poisson transform and representations of a free group abstract let g be a free group with r generators 1 r g which plays the same role of the laplace beltrami operator on semisimple lie groups are characterized furthermore an analytic family of representations z of g on functions on the boundary is considered defined by z x p z x x 1 where p x is the poisson kernel relative to the action of g on it is proved that for 0 s re z z is uniformly bounded on an appropriate hilbert space h s finally the uniform boundedness of other special representations of g obtained by considering the free group either as a subgroup of the group of all isometries of a tree or as a subgroup of gl 2 q p is proved

a radial boundary intersection aided interior point method for multi objective optimization abstract we propose a novel multi objective optimization technique combining non convex radial boundary intersection based decomposition with an interior point method which utilizes both line search and trust region steps suitable for non convex nonlinear optimization radial boundary intersection decomposes the multi objective optimization problem into subproblems which are concerned with finding the solutions closest to a reference point along equally spaced lines emanating radially outwards from the latter point the proposed approach is found to be able to generate good approximations of the pareto front including the periphery by generating a sufficiently diverse set of pareto optimal solutions the proposed method is extensively tested on a large number of recent benchmark problems and real world problems and the performance is found to be favorable in comparison to those of some of the cutting edge stochastic evolutionary optimization algorithms that are commonly used to solve non convex multi objective optimization problems

a derivative free trust region method for biobjective optimization we consider unconstrained black box biobjective optimization problems in which analytic forms of the objective functions are not available and function values can be obtained only through computationally expensive simulations we propose a new algorithm to approximate the pareto optimal solutions of such problems based on a trust region approach at every iteration we identify a trust region then sample and evaluate points from it to determine nondominated solutions in the trust region we employ a scalarization method to convert the two objective functions into one we construct and optimize quadratic regression models for the two original objectives and the converted single objective we then remove dominated points from the current pareto approximation and construct a new trust region around the most isolated point in order to explore areas that have not been visited we prove convergence of the method under general regularity conditions and present numerical results suggesting that the method effic

complete boundedness of heat semigroups on the von neumann algebra of hyperbolic groups we prove that lambda g mapsto e t g r lambda g t 0 defines a completely bounded semigroup of multipliers on the von neuman algebra of hyperbolic groups for all real number r one ingredient in the proof is the observation that a construction of ozawa allows to characterize the radial multipliers that are bounded on every hyperbolic graph partially generalizing results of haagerup steenstrup szwarc and wysocza nski another ingredient is an upper estimate of trace class norms for hankel matrices which is based on peller s characterization of such norms

quantitative comparison of approximate solution sets for multicriteria optimization problems with weighted tchebycheff preference function we consider the problem of evaluating the quality of solution sets generated by heuristics for multiple objective combinatorial optimization problems we extend previous research on the integrated preference functional ipf which assigns a scalar value to a given discrete set of nondominated points so that the weighted tchebycheff function can be used as the underlying implicit value function this extension is useful because modeling the decision maker s value function with the weighted tchebycheff function reflects the impact of unsupported points when evaluating sets of nondominated points we present an exact calculation method for the ipf measure in this case for an arbitrary number of criteria we show that every nondominated point has its optimal weight interval for the weighted tchebycheff function accordingly all nondominated points and not only the supported points in a set contribute to the value of the ipf measure when using the weighted tchebycheff function two and three criteria numerical examples illustrate the desirable properties of the weighted tchebycheff function providing a richer measure than the original ipf based on a convex combination of objectives

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

spherical functions and harmonic analysis on free groups let f r 1 be a free group with r generators in this paper we study a principal series and a complementary series of irreducible unitary representations of f which are defined through the action of f on its poisson boundary relative to a simple random walk we show that the regular representation of f can be written as a direct integral of the representations of the principal series and that the resulting harmonic analysis on the free group bears a close resemblance with the harmonic analysis of sl 2 ir

h calculus for semigroup generators on bmo abstract we prove that the negative generator l of a semigroup of positive contractions on l has bounded h s calculus on the associated poisson semigroup bmo space for any angle 2 provided l satisfies bakry emery s 2 0 criterion our arguments only rely on the properties of the underlying semigroup and work well in the noncommutative setting a key ingredient of our argument is a type of quasi monotone properties for the subordinated semigroup t t e t l 0 1 that is proved in the first part of this article

radial multipliers on reduced free products of operator algebras let ai be a family of unital c algebras respectively of von neumann algebras and n0 c we show that if a hankel matrix related to is trace class then there exists a unique completely bounded map m on the reduced free product of the ai which acts as a radial multiplier hereby we generalize a result of wysoczanski for herz schur multipliers on reduced group c algebras for free products of groups

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

nonsmooth optimization via quasi newton methods we investigate the behavior of quasi newton algorithms applied to minimize a nonsmooth function f not necessarily convex we introduce an inex act line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the armijo and wolfe conditions if f is absolutely continuous along the line furthermore the line search is guaranteed to terminate if f is semi algebraic it seems quite difficult to establish a convergence theorem for quasi newton methods applied to such general classes of functions so we give a care ful analysis of a special but illuminating case the euclidean norm in one variable using the inexact line search and in two variables assuming that the line search is exact in practice we find that when f is locally lipschitz and semi algebraic with bounded sublevel sets the bfgs broyden fletcher goldfarb shanno method with the inexact line search almost always generates sequences whose cluster points are clarke stationary and with function values converging r linearly to a clarke station ary value we give references documenting the successful use of bfgs in a variety of nonsmooth applications particularly the design of low order controllers for linear dynamical systems we conclude with a challenging open question

radial functions on free groups and a decomposition of the regular representation into irreducible components this opens a possibility of using methods of commutative harmonic analysis to study certain convolution algebras of radial functions on g the fist who considered the subalgebra of radial functions in the regular c algebra of g was j m cohen 1 he proved that it is isomorphic to c 2 2 the algebra of continuous functions on the interval 2 2 where 2k 1 and k is the number of free generators in g in the paper we study other such algebras one of our results is theorem 2 1 that the algebra r g of radial functions in 1 g has the ellipse

mean first passage times in confined media from markovian to non markovian processes we review recent theoretical works that enable the accurate evaluation of the mean first passage time mfpt of a random walker to a target in confinement for markovian memory less and non markovian walkers for the markovian problem we present a general theory which allows one to accurately evaluate the mfpt and its extensions to related first passage observables such as splitting probabilities and occupation times we show that this analytical approach provides a universal scaling dependence of the mfpt on both the volume of the confining domain and the source target distance in the case of general scale invariant processes this analysis is applicable to a broad range of stochastic processes characterized by length scale invariant properties and reveals the key role that can be played by the starting position of the random walker we then present an extension to non markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement we show that the mfpt can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for markovian walks finally we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain and review the various theoretical approaches of this nonmarkovian problem

an analytic family of uniformly bounded representations of free groups harmonic analysis on a free group f has attracted considerable attention in the last ten years or so there seem to be two reason for that one is the discovery of deep analogy of certain aspects of harmonic analysis on a free group and harmonic analysis on sl 2 r cf e g fundamental works of p cartier 4 a figa talamanca and m a picardello 8 the other being the interest in the c algebra generated by the regular representation of f cf a connes 5 j cuntz 6 u haagerup 10 m pimsner and d voiculescu 14

a characterization of radial herz schur multipliers on free products of discrete groups a characterization of radial herz schur multipliers on groups which are free products g ni 1gi of subgroups of the same order finite or infinite is given the multiplier norm is computed in terms of trace norms of appropriate trace operators this applies in particular to free groups fn ni 1 z with block length this method also applies to characterizing radial multipliers of free product groups of distinct orders all greater than 2 but in this case we can compute only the multiplier norm up to some constant

groups acting on trees and approximation properties of the fourier algebra let be a tree and g a locally compact group acting on by isometries with respect to the natural metric on we construct the series of representations of g parametrized by the complex unit disc associated canonically with the distance on via the matrix coefficients we apply this series to prove that for any group g acting on a tree in such a way that the stabilizer of a vertex is a compact subgroup of g the fourier algebra a g admits an approximate unit bounded in the multiplier norm on a g for the special case of semihomogeneous trees and the full group aut of isometries of we decompose the constructed representations obtaining finally an analytic continuation of the principal series of aut