Diagram calculus for a type affine CC Temperley--Lieb algebra, I

In this paper, we present an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements (in the sense of Stembridge) of the Coxeter group of type affine $C$. Moreover, we provide an explicit description of a basis for the diagram algebra. In the sequel to this paper, we show that this diagrammatic representation is faithful. The results of this paper and its sequel will be used to construct a Jones-type trace on the Hecke algebra of type affine $C$, allowing us to non-recursively compute leading coefficients of certain Kazhdan--Lusztig polynomials.Comment: Title and content updated to reflect published version. References and contact information updated. 28 pages, 26 figure

Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity

The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free evolution one (used in most numerical approximations) is pointed out. As a generalization, quasi-stationary gauge conditions are also discussed, including numerical experiments with the gauge-waves testbed. The complementary 3+1 approach is also considered, where constraints are related instead with energy and momentum first integrals and the gauge must be provided separately. The relationship between the two formalisms is discussed in a more general framework (Z4 formalism). Different strategies in black hole simulations follow when introducing singularity avoidance as a requirement. More flexible quasi-stationary gauge conditions are proposed in this context, which can be seen as generalizations of the current 'freezing shift' prescriptions.Comment: Talk given at the Spanish Relativity Meeting, Tenerife, September 200

Bacteria as Ovipositional Attractants for \u3ci\u3eAedes Aegypti\u3c/i\u3e (Diptera: Culicidae)

The effectiveness of selected bacterial species as ovipositional attractants for Aedes aegypti was compared. Bacterial washes, in glass containers, were utilized as ovipositional substrates and subsequent egg counts determined the degree of ovipositional attractiveness. Among others, Bacillus cereus and Pseudomonas aeruginosa were noted as being effective attractants. It was concluded that A. aegypti displays discriminatory behavior in selecting individual bacterial species for oviposition

Impartial achievement and avoidance games for generating finite groups

We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. After the development of some general results, we determine the nim-numbers of these games for abelian and dihedral groups. We also present some conjectures based on computer calculations. Our main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple yet intuitive visualizations of these games that capture the complexity of the positions.Comment: 28 pages, 44 figures. Revised in response to comments from refere

What’s Sex (Composition) Got to Do with It? The Importance of Sex Composition of Gangs for Female and Male Members’ Offending and Victimization

Sex composition of groups has been theorized in organizational sociology and found in prior work to structure female and male members’ behaviors and experiences. Peer group and gang literature similarly finds that the sex gap in offending varies across groups of differing sex ratios. Drawing on this and other research linking gang membership, offending, and victimization, we examine whether sex composition of gangs is linked to sex differences in offending in this sample, further assess whether sex composition similarly structures females’ and males’ victimization experiences, and if so, why. Self-report data from gang members in a multi-site, longitudinal study of 3,820 youths are employed. Results support previous findings about variations in member delinquency by both sex and sex composition of the gang and also indicate parallel variations in members’ victimization. These results are further considered within the context of facilitating effects such as gender dynamics, gang characteristics, and normative orientation