Consider a setting where selfish agents are to be assigned to coalitions or projects from a set P. Each project k ∈ P is characterized by a valuation function; vk(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: “how should the agents divide the value that they collectively create?”. One traditional approach in cooperat...

We study a generalization of the Steiner tree problem, where we are given a weighted network G together with a collection of k subsets of its vertices and a root r. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simultan...

A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Λ-coalescents) is provided. This recursion is used to derive asymptotic results as the sample size n tends to infinity for the joint moments of the external branch lengths and for the moments of the total external branch length of the Bolthausen–Sznitman coalescent. These asymptotic result...

I Coherent Sequences 3 by Stevo Todorcevic 1 The Space of Countable Ordinals . . . . . . . . . . . . . . . . . . 4 2 Subadditive Functions . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Steps and Coherence . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 The Trace and the Square-Bracket Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5 A Square-Bracket Ope...

The effects of vincristine (VCR) in combination with methotrexate (MTX) and other antitumor agents were evaluated by cell growth inhi bition assay using a human acute lymphoblastic leukemia cell line (MOLT-3). The data were analyzed with the aid of an isobologram using the concept of an envelope of additivity (G. G. Steel and M. J. Peckman, Int. J. Radiât.Oncol., 5: 85-91, 1979). Simultaneous ...

In this paper, we define the topological pressure for subadditive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.

The entropy of irreducible stochastic matrix measures its mixing properties. We show that this quantity is subadditive and strongly subadditive. 1Instytut Matematyki Uniwersytet Jagielloński Reymonta 4, 30-059 Kraków, Poland mail: [email protected] 1 1 Preliminaries Let N ∈ N. We denote the simplex of probability vectors (finite probability distributions) by ∆N = { p ∈ R : pi ≥ 0 for i = 1,...