Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure

Volumetric spatial behaviour in rats reveals the anisotropic organisation of navigation

We investigated how access to the vertical dimension influences the natural exploratory and foraging behaviour of rats. Using high-accuracy three-dimensional tracking of position in two- and three-dimensional environments, we sought to determine (i) how rats navigated through the environments with respect to gravity, (ii) where rats chose to form their home bases in volumetric space, and (iii) how they navigated to and from these home bases. To evaluate how horizontal biases may affect these behaviours, we compared a 3D maze where animals preferred to move horizontally to a different 3D configuration where all axes were equally energetically costly to traverse. Additionally, we compared home base formation in two-dimensional arenas with and without walls to the three-dimensional climbing mazes. We report that many behaviours exhibited by rats in horizontal spaces naturally extend to fully volumetric ones, such as home base formation and foraging excursions. We also provide further evidence for the strong differentiation of the horizontal and vertical axes: rats showed a horizontal movement bias, they formed home bases mainly in the bottom layers of both mazes and they generally solved the vertical component of return trajectories before and faster than the horizontal component. We explain the bias towards horizontal movements in terms of energy conservation, while the locations of home bases are explained from an information gathering view as a method for correcting self-localisation

Ammonia-Nitrogen Recovery from Synthetic Solution using Agricultural Waste Fibers

In this study, modification of Empty Fruit Bunch (EFB) fibers as a means to recover ammonianitrogen from a synthetic solution was investigated. Methods: The EFB fiber was modified using sodium hydroxide.Adsorption-desorption studies of ammonia nitrogen into the modified EFB fiber were investigated Findings: Theincrease in adsorption capacity was found to be proportional with the increase of pH up to 7, temperature and ammoniaconcentration. The maximum adsorption capacity is 0.53-10.89 mg/g. The attachment of ammonia nitrogen involves ionexchange-chemisorption. The maximum desorption capacity of 0.0999 mg/g. Applications: This study can be used as abaseline for designing a low cost adsorbent system for ammonia nitrogen recovery drainage and industrial wastewater aswell as EFBs-palm oil mill effluent composting

A spatial interaction model for deriving joint space maps of bundle compositions and market segments from pick-any/J data: An application to new product options

We propose an approach for deriving joint space maps of bundle compositions and market segments from three-way (e.g., consumers x product options/benefits/features x usage situations/scenarios/time periods) pick-any/J data. The proposed latent structure multidimensional scaling procedure simultaneously extracts market segment and product option positions in a joint space map such that the closer a product option is to a particlar segment, the higher the likelihood of its being chosen by that segment. A segment-level threshold parameter is estimated that spatially delineates the bundle of product options that are predicted to be chosen by each segment. Estimates of the probability of each consumer belonging to the derived segments are simultaneously obtained. Explicit treatment of product and consumer characteristics are allowed via optional model reparameterizations of the product option locations and segment memberships. We illustrate the use of the proposed approach using an actual commercial application involving pick-any/J data gathered by a major hi-tech firm for some 23 advanced technological options for new automobiles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47207/1/11002_2004_Article_BF00434905.pd

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45748/1/11336_2005_Article_BF02294463.pd

A stochastic multidimensional scaling vector threshold model for the spatial representation of “pick any/ n ” data

This paper presents a new stochastic multidimensional scaling vector threshold model designed to analyze “pick any/ n ” choice data (e.g., consumers rendering buy/no buy decisions concerning a number of actual products). A maximum likelihood procedure is formulated to estimate a joint space of both individuals (represented as vectors) and stimuli (represented as points). The relevant psychometric literature concerning the spatial treatment of such binary choice data is reviewed. The nonlinear probit type model is described, as well as the conjugate gradient procedure used to estimate parameters. Results of Monte Carlo analyses investigating the performance of this methodology with synthetic choice data sets are presented. An application concerning consumer choices for eleven competitive brands of soft drinks is discussed. Finally, directions for future research are presented in terms of further applications and generalizing the model to accommodate three-way choice data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45743/1/11336_2005_Article_BF02294452.pd

A maximum likelihood method for latent class regression involving a censored dependent variable

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45751/1/11336_2005_Article_BF02294647.pd

A stochastic multidimensional scaling procedure for the spatial representation of three-mode, three-way pick any/ J data

This paper presents a new stochastic multidimensional scaling procedure for the analysis of three-mode, three-way pick any/ J data. The method provides either a vector or ideal-point model to represent the structure in such data, as well as “floating” model specifications (e.g., different vectors or ideal points for different choice settings), and various reparameterization options that allow the coordinates of ideal points, vectors, or stimuli to be functions of specified background variables. A maximum likelihood procedure is utilized to estimate a joint space of row and column objects, as well as a set of weights depicting the third mode of the data. An algorithm using a conjugate gradient method with automatic restarts is developed to estimate the parameters of the models. A series of Monte Carlo analyses are carried out to investigate the performance of the algorithm under diverse data and model specification conditions, examine the statistical properties of the associated test statistic, and test the robustness of the procedure to departures from the independence assumptions. Finally, a consumer psychology application assessing the impact of situational influences on consumers' choice behavior is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45749/1/11336_2005_Article_BF02294486.pd

Clustering at the movies

Weekly box office revenues for approximately 100 successful motion pictures are analyzed by use of a finite mixture regression technique to determine if regular sales patterns emerge. Based on an exponential decay model applied to market share data, four clusters of movies, varying in opening strength and decay rate, are found. Characteristics of the clusters and implications for future research are discussed