Cycle Bases of Reduced Powers of Graphs

We define what appears to be a new construction. Given a graph G and a positive integer k, the reduced kth power of G, denoted G(k), is the configuration space in which k indistinguishable tokens are placed on the vertices of G, so that any vertex can hold up to k tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex. We present propositions related to the structural properties of reduced graph powers and, most significantly, provide a construction of minimum cycle bases of G(k). The minimum cycle basis construction is an interesting combinatorial problem that is also useful in applications involving configuration spaces. For example, if G is the state-transition graph of a Markov chain model of a stochastic automaton, the reduced power G(k) is the state-transition graph for k identical (but not necessarily independent) automata. We show how the minimum cycle basis construction of G(k) may be used to confirm that state-dependent coupling of automata does not violate the principle of microscopic reversibility, as required in physical and chemical applications

Eulerian 2-Complexes

It is shown that Euler's theorem for graphs can be generalized for 2-complexes. Two notions that generalize cycle and Eulerian tour are introduced (``circlet'' and ``Eulerian cover''), and we show that for a strongly-connected, pure 2-complex, the following are equivalent: (i) each edge meets a positive even number of 2-cells (faces), (ii) the complex can be decomposed as the face-disjoint union of circlets, and (iii) the complex has an Eulerian cover. A number of examples are provided.Comment: 13 pages, 15 figure

A new view of hypercube genus

Beineke, Harary and Ringel discovered a formula for the minimum genus of a torus in which the $n$-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this surface as a union of certain faces in the hypercube's 2-skeleton. For odd dimension $n$, the entire 2-skeleton decomposes into $(n-1)/2$ copies of the surface, and the intersection of any two copies is the hypercube graph.Comment: 8 pages, 6 figure

Euler's Theorem for Regular CW-Complexes

For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and traversability.Comment: 15 pages, 3 figures, to appear in Combinatorica, 202

The Qualitative Interview in Psychology and the Study of Social Change: Sexual Identity Development, Minority Stress, and Health in the Generations Study.

Interviewing is considered a key form of qualitative inquiry in psychology that yields rich data on lived experience and meaning making of life events. Interviews that contain multiple components informed by specific epistemologies have the potential to provide particularly nuanced perspectives on psychological experience. We offer a methodological model for a multi-component interview that draws upon both pragmatic and constructivist epistemologies to examine generational differences in the experience of identity development, stress, and health among contemporary sexual minorities in the United States. Grounded in theories of life course, narrative, and intersectionality, we designed and implemented a multi-component protocol that was administered among a diverse sample of three generations of sexual minority individuals. For each component, we describe the purpose and utility, underlying epistemology, foundational psychological approach, and procedure, and we provide illustrative data from interviewees. We discuss procedures undertaken to ensure methodological integrity in process of data collection, illustrating the implementation of recent guidelines for qualitative inquiry in psychology. We highlight the utility of this qualitative multi-component interview to examine the way in which sexual minorities of distinct generations have made meaning of significant social change over the past half-century

On Cartesian skeletons of graphs,

Abstract Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a notion of a Cartesian skeleton which transfers their multiplication properties to the Cartesian product. The present article introduces simplified definitions of Cartesian skeletons for the direct and strong products, and provides new, fast and transparent algorithms for their construction. Since the complexity of the prime factorization of the direct and the strong product is determined by the complexity of the construction of the Cartesian skeleton, the new algorithms also improve the complexity of the prime factorizations of graphs with respect to the direct and the strong product. We indicate how these simplifications fit into the existing literature

Instrument manual for the retarding ion mass spectrometer on Dynamics Explorer-1

The retarding ion mass spectrometer (RIMS) for Dynamics Explorer-1 is an instrument designed to measure the details of the thermal plasma distribution. It combines the ion temperature determining capability of the retarding potential analyzer with the compositional capabilities of the mass spectrometer and adds multiple sensor heads to sample all directions relative to the spacecraft ram direction. This manual provides a functional description of the RIMS, the instrument calibration, and a description of the commands which can be stored in the instrument logic to control its operation

Can the Benjamin-Feir instability spawn a rogue wave?

Abstract. Recent work by our research group has shown that wave damping can have a surprisingly strong effect on the evolution of waves in deep water, even when the damping is weak. Whether damping is or is not included in a theoretical model can change the outcome in terms of both stability of wave patterns and frequency downshifting. It is conceivable that it might affect the early development of rogue waves as well

Trapping of Cold Excitons with Laser Light

Optical trapping and manipulation of neutral particles has led to a variety of experiments from stretching DNA-molecules to trapping and cooling of neutral atoms. An exciting recent outgrowth of the technique is an experimental implementation of atom Bose-Einstein condensation. In this paper, we propose and demonstrate laser induced trapping for a new system--a gas of excitons in quantum well structures. We report on the trapping of a highly degenerate Bose gas of excitons in laser induced traps.Comment: 9 pages, 3 figure