The Dynamics of Group Codes: Dual Abelian Group Codes and Systems

Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act as the character groups of the state spaces of C^\perp. The controllability properties of C are the observability properties of C^\perp. In particular, C is (strongly) controllable if and only if C^\perp is (strongly) observable, and the controller memory of C is the observer memory of C^\perp. The controller granules of C act as the character groups of the observer granules of C^\perp. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.Comment: 30 pages, 11 figures. To appear in IEEE Trans. Inform. Theory, 200

Jets in Effective Theory: Summing Phase Space Logs

We demonstrate how to resum phase space logarithms in the Sterman-Weinberg (SW) dijet decay rate within the context of Soft Collinear Effective theory (SCET). An operator basis corresponding to two and three jet events is defined in SCET and renormalized. We obtain the RGE of the two and three jet operators and run the operators from the scale $\mu^2 = Q^2$ to the phase space scale $\mu^2_\delta = \delta^2 Q^2$. This phase space scale, where $\delta$ is the cone half angle of the jet, defines the angular region of the jet. At $\mu^2_{\delta}$ we determine the mixing of the three and two jet operators. We combine these results with the running of the two jet shape function, which we run down to an energy cut scale $\mu^2_{\beta}$. This defines the resumed SW dijet decay rate in the context of SCET. The approach outlined here demonstrates how to establish a jet definition in the context of SCET. This allows a program of systematically improving the theoretical precision of jet phenomenology to be carried out.Comment: 25 pages, 4 figures, V2: Typos fixed, writing clarified, detail on PSRG added. Matching onto jet definition changed to taking place at collinear scal

The gender of the bear

Cet article maintient qu'il existe une relation homologue entre le symbolisme autour de l'ours et la catégorisation du genre chez les Inuit. Dans la première partie de l'article, les vastes implications de la signification de l'ours sont explorées. Les grands débats concernant comment conceptualiser les catégories inuit du genre sont résumés, avec une emphase particulière sur la construction d'un «troisième sexe». Ces deux champs de la pensée sociale apparemment disparates sont alors présentés ensemble pour proposer un modèle qui permet aux chercheurs de comprendre à la fois la signification symbolique des ours et le genre d'une nouvelle façon. Bien que le concept du «troisième sexe» se soit révélé très solide sur le plan théorique, il est inadéquat pour les données provenant d'Inuit qui continuent de maintenir deux catégories distinctes du genre. Mais contrairement à la majorité des autres modèles, il permet un passage connectant les deux genres à travers lequel les gens peuvent passer.This article argues that there is an homological relationship between the symbolism surrounding the polar bear and the categorisation of gender among Inuit. In the first part of the paper, the broad implications of the significance of the bear are explored. The extensive debates around how to conceptualise Inuit gender categories are then summarised, focusing especially on the construction of a "third gender." These two apparently disparate fields of social thought are then brought together to propose a model that allows scholars to understand both the symbolic significance of bears and gender in a new way. Although the concept of a "third gender" has proved to be theoretically very powerful, it is inadequate to the data from Inuit who continue to hold two distinctive categories of gender. But unlike most other models, it allows for a passage connecting the two genres through which people can pass

Bay State Circuit, Sage Park, July 1, 1931

Trott\u27s Official Score Card for the Wednesday, July 1, 1931 Bay State Circuit Races in Windsor, Connecticut published by F. G. Trott, printed by William J. Doyle. The score card contains Guy Kendall\u27s handwritten notes on race day results as well as photos mounted inside by Kendall

Bay State Circuit, Sage Park, July 2, 1931

Trott\u27s Official Score Card for the Thursday, July 2, 1931 Bay State Circuit Races in Windsor, Connecticut published by F. G. Trott, Boston, Mass., printed by William J. Doyle. Contains Guy Kendall\u27s handwritten notes on changes in the race line up and results as well as photos mounted by Kendall inside the score card

Rochester Fair, September 1930

Trott\u27s Official Score Card for the Friday, September 26, 1930 Rochester Fair race at Cold Spring Park, Rochester, N.H. The card includes the names of race officials and Guy Kendall\u27s handwritten notes recording race details, as well as a photo mounted inside the score card. The score card was printed by Frank G. Trott, an agent with Hartford Live Stock Insurance Co., selling insurance coverage for race horses but was also a reporter covering harness racing for The Boston Globe from 1896-1949

Bay State Circuit, Sage Park, July 4, 1931

Trott\u27s Official Score Card for the Saturday, July 4, 1931 Bay State Circuit Races in Windsor, Connecticut published by F. G. Trott, Boston, Massachusetts, printed by William J. Doyle. Contains race day photos taken by Guy Kendall as well as Kendall\u27s handwritten notes on race day results

Bay State Circuit, Sage Park, July 3, 1931

Trott\u27s Official Score Card for the Friday, July 3, 1931 Bay State Circuit Races in Windsor, Connecticut published by F.G. Trott, Boston, Mass., printed by William J. Doyle. Contains race day photos taken by Guy Kendall as well as Kendall\u27s handwritten notes on race day results