Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence

Belief revision characterizes the process of revising an agent’s beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation
is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster
rule of combination, just like revision in the sense of Alchourron, Gardenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey’s rule of updating, Dempster rule of conditioning and a form of AGM revision.

Classical novae from the POINT-AGAPE microlensing survey of M31 - II. Rate and statistical characteristics of the nova population

The POINT-AGAPE (Pixel-lensing Observations with the Isaac Newton Telescope-Andromeda Galaxy Amplified Pixels Experiment) survey is an optical search for gravitational microlensing events towards the Andromeda galaxy (M31). As well as microlensing, the survey is sensitive to many different classes of variable stars and transients. In our first paper of this series, we reported the detection of 20 classical novae (CNe) observed in Sloan r' and i' passbands.

Classical novae from the POINT-AGAPE microlensing survey of M31 - I. The nova catalogue

The POINT-AGAPE (Pixel-lensing Observations with the Isaac Newton Telescope-Andromeda Galaxy Amplified Pixels Experiment) survey is an optical search for gravitational microlensing events towards the Andromeda galaxy (M31). As well as microlensing, the survey is sensitive to many different classes of variable stars and transients. Here we describe the automated detection and selection pipeline used to identify M31 classical novae (CNe) and we present the resulting catalogue of 20 CN candidates observed over three seasons. CNe are observed both in the bulge region as well as over a wide area of the M31 disc. Nine of the CNe are caught during the final rise phase and all are well sampled in at least two colours. The excellent light-curve coverage has allowed us to detect and classify CNe over a wide range of speed class, from very fast to very slow. Among the light curves is a moderately fast CN exhibiting entry into a deep transition minimum, followed by its final decline. We have also observed in detail a very slow CN which faded by only 0.01 mag d(-1) over a 150-d period. We detect other interesting variable objects, including one of the longest period and most luminous Mira variables. The CN catalogue constitutes a uniquely well-sampled and objectively-selected data set with which to study the statistical properties of CNe in M31, such as the global nova rate, the reliability of novae as standard-candle distance indicators and the dependence of the nova population on stellar environment. The findings of this statistical study will be reported in a follow-up paper.

Heritability of the spatial distribution and peak density of macular pigment:a classical twin study

Purpose: To elucidate the heritability of peak density and spatial width of macular pigment (MP) using a Classical Twin Study.

Methods: Fundus autofluorescence images were obtained at 488?nm from 86 subjects or 43 twin pairs (21 monozygotic (MZ) and 22 dizygotic (DZ)) (27 male, 59 female) aged from 55 to 76 years (mean 62.2±5.3 years). The relative topographic distribution of MP was measured using a grey scale of intensity (0-255 units) in a 7° eccentricity around the fovea. Relative peak MP density (rPMPD) and relative spatial distribution of MP (rSDMP) were used as the main outcome measure in the statistical analysis.

Results: A significantly higher correlation was found within MZ pairs as compared with that within DZ pairs for rPMPD, (r=0.99, 95% confidence interval (95% CI) 0.93 to 1.00) and 0.22, 95% CI -0.34 to 0.71), respectively, suggesting strong heritability of this trait. When rSDMP was compared, there was no significant difference between the correlations within MZ pairs (r=0.48, 95% CI -0.02 to 0.83) and DZ pairs (r=0.63, 95% CI 0.32 to 0.83), thus rSDMP is unlikely to have a considerable heritable component. In addition, there was no difference between any MP parameter when normal maculae were compared with early age-related macular degeneration (AMD) (rPMPD 0.36 vs 0.34, t=1.18 P=0.243, rSDMP 1.75 vs 1.75, t=0.028 P=0.977).ConclusionsrPMPD is a strongly heritable trait whereas rSDMP has minimal genetic influence and a greater influence by environmental factors. The presence of macular changes associated with early AMD did not appear to influence any of these pigment parameters. © 2012 Macmillan Publishers Limited All rights reserved 0950-222X/12

Sudden Transition between Classical and Quantum Decoherence

We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t < <(t)over bar>. In this initial time interval classical correlations decay. For t > (t) over bar, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time (t) over bar the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.

Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

From Frank Miller to Zack Snyder, and Return: Contemporary Superhero Comics and Post-Classical Hollywood

Film adaptations of superhero comic-books offer a particularly rich case study to analyse narrative strategies of contemporary Hollywood cinema. The serial structures adopted by the comics they are based on, as well as their use of the spectacular potential of the image, provide a successful model for current audiovisual productions. Without completely abandoning classical techniques, these adaptations try to find a new balance between narrative and digital phantasmagoria. This paper discusses some significant examples of this genre, including adaptations of classical DC and Marvel franchises and more recent series, as well as other comic-book influenced films such as The Matrix and Unbreakable.