General combination rules for qualitative and quantitative beliefs

Martin and Osswald \cite{Martin07} have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural language with linguistic labels, Smarandache and Dezert \cite{Li07} have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs

Combination Rules, Charge Symmetry, and Hall Effect in Cuprates

The rule relating the observed Hall coefficient to the spin and charge responses of the uniform doped Mott insulator is derived. It is essential to include the contribution of holon and spinon three-current correlations to the effective action of the gauge field. In the vicinity of the Mott insulating point the Hall coefficient is holon dominated and weakly temperature dependent. In the vicinity of a point of charge conjugation symmetry the holon contribution to the observed Hall coefficient is small: the Hall coefficient follows the temperature dependence of the diamagnetic susceptibility with a sign determined by the Fermi surface shape. NOTE: document prepared using REVTEX. (3 Figs, not included, available on request from: [email protected])Comment: 8 page

The Lending-Limit Combination Rules: Regulation by Enforcement at the OCC

The regulation-by-enforcement critique has made an impact at the Securities and Exchange Commission, and scholars are beginning to turn this critique against other agencies. Using this critique, this Note demonstrates that the federal combination rules for the lending-limit law should be rewritten. Under the lending-limit law, national banking associations may lend only a certain percentage of their unimpaired capital and unimpaired surplus to any one borrower. Although the combination rules include several per se rules pursuant to which loans made to two borrowers will be aggregated, they also grant the Office of the Comptroller of the Currency (OCC) the power to determine ad hoc whether to aggregate two loans. This power to determine on an ad hoc and even on a post hoc basis whether a violation of the law has occurred is an affront to the rule of law and is unfair to the industry. The combination rules should be amended to remove the OCC\u27s power to make ad hoc determinations

Allocentric coding: spatial range and combination rules

International audienceWhen a visual target is presented with neighboring landmarks, its location can be determined both relative to the self (egocentric coding) and relative to these landmarks (allocentric coding). In the present study, we investigated (1) how allocentric coding depends on the distance between the targets and their surrounding landmarks (i.e. the spatial range) and (2) how allocentric and egocentric coding interact with each other across targets-landmarks distances (i.e. the combination rules). Subjects performed a memory-based pointing task toward previously gazed targets briefly superimposed (200ms) on background images of cluttered city landscapes. A variable portion of the images was occluded in order to control the distance between the targets and the closest potential landmarks within those images. The pointing responses were performed after large saccades and the reappearance of the images at their initial location. However, in some trials, the images' elements were slightly shifted (±3°) in order to introduce a subliminal conflict between the allocentric and egocentric reference frames. The influence of allocentric coding in the pointing responses was found to decrease with increasing target-landmarks distances, although it remained significant even at the largest distances (⩾10°). Interestingly, both the decreasing influence of allocentric coding and the concomitant increase in pointing responses variability were well captured by a Bayesian model in which the weighted combination of allocentric and egocentric cues is governed by a coupling prior

Factors affecting the perception of transparent motion

It is possible to create a perception of transparency by combining patterns having different motions. Two particular combination rules, have specific interpretations in terms of physical phenomena: additive (specular reflection) and multiplicative (shadow illumination). Arbitrary combination rules applied to random patterns generate percepts in which the motions of the two patterns are visible, but have super-imposed noise. It is also possible to combine the patterns (using an exclusive-OR rule) so that only noise is visible. Within a one-dimensional family of combination rules which include addition and multiplication, there is a range where smooth motions are seen with no superimposed noise; this range is centered about the additive combination. This result suggests that the motion system deals with a linear representation of luminance, and is consistent with the analysis of motion by linear sensors. This research gives tentative validation the use in beam splitters (which combine images additively) in the construction of heads-up aviation displays. Further work is needed to determine if the superiority of additive combination generalizes to the case of full-color imagery (there are results in the literature suggesting that subtractive color mixture yields the best legibility of overlapping alphanumerics)

Aspects of Defect Topology in Smectic Liquid Crystals

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmetry of the smectic confers a path dependence on the result of defect addition.Comment: 19 pages, 13 figure