Substitute valuations (in some contexts called gross substitute valuations) are prominent in combinatorial auction theory. An algorithm is given in this paper for generating a substitute valuation through Monte Carlo simulation. In addition, the geometry of the set of all substitute valuations for a fixed number of goods K is investigated. The set consists of a union of polyhedrons, and the max...

Let G be a connected linear semisimple Lie group having a Holomorphic Discrete Series representation π. Let H be a connected reductive subgroupof G so that the global symmetric space attached to H is a real form of the Hermitian symmetric space associated to G. Fix a maximal compact subgroup K of G so that H ∩ K is a maximal compact subgroup for H. Let τ be the lowest K−type for π and let τ? de...

Peter Gacs showed [1] that for every n there exists a bit string x of length n whose plain complexity C (x) has almost maximal conditional complexity relative to x, i.e., C (C (x)|x) ≥ log n− log n−O(1). Here log(i) = log log i etc. Following Elena Kalinina [3], we provide a gametheoretic proof of this result; modifying her argument, we get a better (and tight) bound log n − O(1). We also show ...

We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the basic separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly,...

Theorem 0.1. Let K be an abstract elementary class (AEC) with amalgamation and no maximal models. Let λ > LS(K). If K is categorical in λ, then the model of cardinality λ is Galois-saturated. This answers a question asked independently by Baldwin and Shelah. We deduce several corollaries: K has a unique limit model in each cardinal below λ, (when λ is big-enough) K is weakly tame below λ, and t...

If a two-player social welfare maximization problem does not admit a PTAS, we prove that any maximal-in-range truthful mechanism that runs in polynomial time cannot achieve an approximation factor better than 1/2. Moreover, for the k-player version of the same problem, the hardness of approximation improves to 1/k under the same two-player hardness assumption. (We note that 1/k is achievable by...

The maximal pattern complexity of one-dimensional words has been studied in several papers [T. Kamae, L. Zamboni, Sequence entropy and the maximal pattern complexity of infinite words, Ergodic Theory Dynam. Systems 22(4) (2002) 1191–1199; T. Kamae, L. Zamboni,Maximal pattern complexity for discrete systems, Ergodic Theory Dynam. Systems 22(4) (2002) 1201–1214; T. Kamae, H. Rao, Pattern Complexi...

We study the persistent homology of an Erdős–Rényi random clique complex filtration on n vertices. Here, each edge e appears independently at a uniform time $$p_e \in [0,1]$$ , and persistence cycle $$\sigma $$ is defined as $$p_2(\sigma ) / p_1(\sigma )$$ where $$p_1(\sigma are birth death times . show that if $$k \ge 1$$ fixed, then with high probability maximal k-cycle order $$n^{1/k(k+1)}$$

We re-fit for the neutrino mass-squared difference ∆m2 in the threefold maximal (ie. tri-maximal) mixing scenario using recent CHOOZ and SUPER-K data, taking account of matter effects in the Earth. While matter effects have little influence on reactor experiments and proposed long-baseline accelerator experiments with L ∼ 1000 km, they are highly significant for atmospheric experiments, suppres...

The core is the unique homorphically minimal subgraph of a graph A triangle free graph with minimum degree n is called dense It was observed by many authors that dense triangle free graphs share strong structural properties and that the natural way to describe the structure of these graphs is in terms of graph homomorphisms One in nite sequence of cores of dense maximal triangle free graphs was...