Minority opinion spreading in random geometry

The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry shaped by social life (offices, houses, bars, and restaurants). A perfect world is considered with no advantage to the minority. A one person-one argument principle is applied to determine locally individual mind changes. In case of equality, a collective doubt is evoked which in turn favors the Status Quo. Starting from a large in favor of the proposal initial majority, repeated random size local discussions are found to drive the majority reversal along the minority hostile view. Total opinion refusal is completed within few days. Recent national collective issues are revisited. The model may apply to rumor and fear propagation. Received 23 January 2002     

The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions.     

可能性概念与可靠性分析

本文讨论了可能性概念在大系统特别是人－机混合系统的可靠性分析的应用，依据Ｚａｄｅｈ的原始思想，人为差错率应该用可能性分析与概率分析来描述，前者描述差错的潜在可能性而后者描述差错发生的实际可能性。这一点，在大型灾害性事故的分析中具有特殊重要意义。     

直径为4的整树

本文给出了直径为4的整树的一个充分条件，并由此给出了直径为4的整树的许多新类．最后提出一些基本的公开问题．     

Cycle Action on Treelike Structures

The purpose of this paper is to study the action on cycles of several known classes of oligomorphic groups, that is, infinite permutation groups of countable degree having only finitely many orbits on k-sets for each k. The groups studied here are all related to trees and treelike relational structures. The sequence whose k-th term is the number of orbits in the action on k-cycles is called Parker sequence. It turns out that, if we are dealing with the automorphism group of a suitable relational structure, this sequence counts also the finite substructures admitting a cyclic automorphism; in calculating these sequences for various groups, we shall thus describe and enumerate such substructures.Di più dirò: ch’a gli alberi dà vita [I shall say more: the trees are given life spirito uman che sente e che ragiona. by a human spirit that perceives and reasons.Di più dirò: ch’a gli alberi dà vita spirito uman che sente e che ragiona. Per prova sollo; io n’ho la voce udita che nel cor flebilmente anco mi suona.[I shall say more: the trees are given life by a human spirit that perceives and reasons. I know it by experience: I heard their voice and it still resounds faintly in my heart.]Torquato Tasso, Gerusalemme liberata, XIII, 49     

Phase diagrams of Ising models on Husimi trees II. Pair Wand multisite interaction systems

We continue an earlier study of multisite interaction Ising spin models on Husimi trees. In particular, attention is given to systems with both a nearestneighbor pair interaction and three-site interactions. We use our calculations of the phase diagrams of the systems on Husimi trees as approximations of systems with the same interactions but on a regular lattice, e.g., the triangle lattice. Specific models where exact results are available are used as test cases. All of the work involves computation of quantities, such as the magnetization, by iterative processes. Hence we are dealing with a discrete map and for certain values of the interaction strengths we obtain for the magnetization diagram results involving period doubling, chaos, period-three windows, etc., all phenomena of recent interest in connection with dynamical systems and now associated with certain Ising spin systems.     

Trees with Equal Domination and Restrained Domination Numbers

Let G = (V,E) be a graph and let S V. The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), is the minimum cardinality of a DS of G, while the restrained domination number of G, denoted by γ_r(G), is the minimum cardinality of a RDS of G. The graph G is γ-excellent if every vertex of G belongs to some minimum DS of G. A constructive characterization of trees with equal domination and restrained domination numbers is presented. As a consequence of this characterization we show that the following statements are equivalent: (i) T is a tree with γ(T)=γ_r(T); (ii) T is a γ-excellent tree and T ≠ K₂; and (iii) T is a tree that has a unique maximum packing and this set is a dominating set of T. We show that if T is a tree of order n with ℓ leaves, then γ_r(T) ≤ (n + ℓ + 1)/2, and we characterize those trees achieving equality.     

A Class of Trees and its Wiener Index

In this paper, we will consider the Wiener index for a class of trees that is connected to partitions of integers. Our main theorem is the fact that every integer is the Wiener index of a member of this class. As a consequence, this proves a conjecture of Lepović and Gutman. The paper also contains extremal and average results on the Wiener index of the studied class.This work was supported by Austrian Science Fund project no. S-8307-MAT.     

Comovements in government bond markets: A minimum spanning tree analysis

The concept of a minimum spanning tree (MST) is used to study patterns of comovements for a set of twenty government bond market indices for developed North American, European, and Asian countries. We show how the MST and its related hierarchical tree evolve over time and describe the dynamic development of market linkages. Over the sample period, 1993-2008, linkages between markets have decreased somewhat. However, a subset of European Union (EU) bond markets does show increasing levels of comovements. The evolution of distinct groups within the Eurozone is also examined. The implications of our findings for portfolio diversification benefits are outlined.