On Supermultiplet Twisting and Spin-Statistics

Twisting of off-shell supermultiplets in models with 1+1-dimensional spacetime has been discovered in 1984, and was shown to be a generic feature of off-shell representations in worldline supersymmetry two decades later. It is shown herein that in all supersymmetric models with spacetime of four or more dimensions, this off-shell supermultiplet twisting, if non-trivial, necessarily maps regular (non-ghost) supermultiplets to ghost supermultiplets. This feature is shown to be ubiquitous in all fully off-shell supersymmetric models with (BV/BRST-treated) constraints.Comment: Extended version, including a new section on manifestly off-shell and supersymmetric BRST treatment of gauge symmetry; added reference

State Space Methods in Stata

We illustrate how to estimate parameters of linear state-space models using the Stata program sspace. We provide examples of how to use sspace to estimate the parameters of unobserved-component models, vector autoregressive moving-average models, and dynamic-factor models. We also show how to compute one-step, filtered, and smoothed estimates of the series and the states; dynamic forecasts and their confidence intervals; and residuals.

Nonholomorphic Corrections to the One-Loop N=2 Super Yang-Mills Action

In addition to the familiar contribution from a holomorphic function \FF, the K\"ahler potential of the scalars in the nonabelian $N=2$ vector multiplet receives contributions from a real function \HH. We determine the latter at the one-loop level, taking into account both supersymmetric matter and gauge loops. The function \HH characterizes the four-point coupling of the $N=2$ vector-multiplet vectors for constant values of their scalar superpartners. We discuss the consequences of our results.Comment: 11 pages, Latex, one Postscript figure. Corrections to equation (24): 1 missing term added and one pair of indices interchange

4D, N = 1 Supersymmetry Genomics (I)

Presented in this paper the nature of the supersymmetrical representation theory behind 4D, N = 1 theories, as described by component fields, is investigated using the tools of Adinkras and Garden Algebras. A survey of familiar matter multiplets using these techniques reveals they are described by two fundamental valise Adinkras that are given the names of the cis-Valise (c-V) and the trans-Valise (t-V). A conjecture is made that all off-shell 4D, N = 1 component descriptions of supermultiplets are associated with two integers - the numbers of c-V and t-V Adinkras that occur in the representation.Comment: 53 pages, 19 figures, Report-II of SSTPRS 2008 Added another chapter for clarificatio

Electrochemical deposition of silver crystals aboard Skylab 4

Silver crystals were grown aboard Skylab 4 by an electro-chemical reaction and subsequently returned to earth for comparison with crystals grown at 1- and 5-g. Both the Skylab and earth-grown crystals show a variety of structures. Certain tendencies in structure dependency on gravity level, however, can be discerned. In addition, downward growing dendrite streamers; upward growing chunky crystal streamers; growth along an air/liquid interface; and ribbon, film, and fiber crystal habits were observed in experiments conducted on the ground with solutions of varying concentrations. It was also observed that the crystal structures of space and ground electro-deposited silver crystals were very similar to the structures of germanium selenide and germanium telluride crystals grown in space and on the ground by a vapor transport technique. Consideration of the data leads to the conclusions that: (1) the rate of electrochemical displacement of silver ions from a 5 percent aqueous solution by copper is predominantly diffussion controlled in space and kinetically controlled in 1- and higher-g because of augmentation of mass transport by convection; (2) downward and upward crystal streamers are the result of gravity-driven convection, the flow patterns of which can be delineated. Lateral growths along an air/liquid interface are the result of surface-tension-driven convection, the pattern of which also can be delineated; (3) electrolysis in space or low-g environments can produce either dendritic crystals with more perfect microcrystalline structures or massive, single crystals with fewer defects than those grown on ground or at higher g-levels. Ribbons or films of space-grown silicon crystals would find a ready market for electronic substrate and photocell applications. Space-grown dendritic, metal crystals present the possibility of unique catalysts. Large perfect crystals of various materials are desired for a number of electronic and optical applications; and (4) vapor transport growth of germanium selenide and germanium telluride is affected by convection mechanisms similar to the mechanisms hypothesized for the electrochemical deposition of silver crystals. Evidence and considerations leading to the preceding summaries and conclusions are presented. The implications of the findings and conclusions for technological applications are discussed, and recommendations for further experiments are presented

N=2 Conformal Superspace in Four Dimensions

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.Comment: 43 pages; v2 references added, acknowledgments update

Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories

We present a superspace formulation of the D=3, N=4,5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action, and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new super-potential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4,5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be rederived in our 3-algebra approach. All known N=4,5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie-algebra realization of symplectic 3-algebras.Comment: 37 pages, minor changes, published in PR

Research to develop and define concepts for reliable control sensors - The solid state rate sensors Final report

Solid state device for sensing angular rate by detecting presence of coriolis force

Element-centric clustering comparison unifies overlaps and hierarchy

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically structured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering similarity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community structure of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science