Bars in galaxies are mainly supported by particles trapped around stable periodic orbits. These orbits represent oscillatory motion with only one frequency, which is the bar driving frequency, and miss free oscillations. We show that a similar situation takes place in double bars: particles get trapped around parent orbits, which in this case represent oscillatory motion with two frequencies of...

The enumeration of independent sets in graphs with various restrictions has been a topic of much interest of late. Let i(G) be the number of independent sets in a graph G and let it(G) be the number of independent sets in G of size t. Kahn used entropy to show that if G is an r-regular bipartite graph with n vertices, then i(G) 6 i(Kr,r). Zhao used bipartite double covers to extend this bound t...

We consider the problem of stabilizing sets parametrized by a single variable. Our approach is based on the solution to the maneuvering problem. In this problem, the state of the system is driven to a path that coincides with the set, and the particular location on the path is determined dynamically from the value of the state. Within this control structure, we induce a separation of time scale...

Unavoidable subgraphs have been widely studied in the context of Ramsey Theory. The research in this area focuses on highly structured graphs such as cliques, cycles, paths, stars, trees, and wheels. We propose to study maximum unavoidable subgraphs measuring the size in the number of edges. We computed maximum unavoidable subgraphs for graphs up to order nine via SAT solving and observed that ...

We characterize the edge-signed graphs in which every 'significant' positive closed walk (or combination of walks) has even length, under seven different criteria for significance, and also those edge-signed graphs whose double covering graph is bipartite. If the property of even length is generalized to positivity in a second edge signing, the characterizations generalize as well. We also char...

The protein barnase folds from the denatured state into its native conformation via a high-energy intermediate. Using I-values determined experimentally from single-point mutations as restraints in all-atom molecular dynamics simulations, we have determined ensembles of structures corresponding to the transition states for the formation of the folding intermediate and its conversion into the na...

At the 16th British Combinatorial Conference (1997), Cameron introduced a new concept called 2-simultaneous coloring. He used this concept to reformulate a conjecture of Keedwell (1994) on the existence of critical partial latin squares of a given type. Using computer programs, we have veri ed the truth of the above conjecture (the SE conjecture) for all graphs having less than 29 edges. In thi...

Fleischner [3] has proposed a novel approach to several deep graph-theoretic conjectures, such as the Cycle Double Cover Conjecture [9,10] or the 5-Flow Conjecture of Tutte [12]. A key ingredient in this approach is the Bipartizing Matchings Conjecture (Conjecture 1.2 below, abbreviated BM Conjecture). In this paper, we introduce the notion of an Eulerian coloring of a trigraph, providing a set...

Given a bipartite graph G(U ∪ V, E) with n vertices on each side, an independent set I ∈ G such that |U ⋂ I| = |V ⋂ I| is called a balanced bipartite independent set. A balanced coloring of G is a coloring of the vertices of G such that each color class induces a balanced bipartite independent set in G. If graph G has a balanced coloring we call it colorable. The coloring number χB(G) is the mi...