For a (compact) subset K of a metric space and ε > 0, the covering number N(K, ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In t...

For a (compact) subset K of a metric space and ε > 0, the covering number N(K, ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In t...

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

Families and genera assigned to Tremellomycetes have been mainly circumscribed by morphology and for the yeasts also by biochemical and physiological characteristics. This phenotype-based classification is largely in conflict with molecular phylogenetic analyses. Here a phylogenetic classification framework for the Tremellomycetes is proposed based on the results of phylogenetic analyses from a...

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generat...

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generat...

We develop the geometry of the Cayley graph of the lamplighter group with respect to the generating set rising from its interpretation as an automata group [4]. We find metric behavior with respect to this generating set analogous to the metric behavior in the standard group theoretic generating set. This includes expressions for normal forms and geodesic paths, and families of ‘dead-end’ words...

The paper investigates the strategic behavior of hedge fund families. It focuses on decisions to start and liquidate family-member funds. Hedge fund families tend to liquidate funds that underperform compared to other member funds, and to replace them by new ones. By choosing a launch time after a short period of superior performance by their member funds, families extend the spillover to new f...