Cumulative prospect theory and gambling

Whilst Cumulative Prospect theory (CPT) provides an explanation of gambling on longshots at actuarially unfair odds, it cannot explain why people might bet on more favoured outcomes. This paper shows that this is explicable if the degree of loss aversion experienced by the agent is reduced for small-stake gambles (as a proportion of wealth), and probability distortions are greater over losses than gains. If the utility or value function is assumed to be bounded, the degree of loss aversion assumed by Kahneman and Tversky leads to absurd predictions, reminiscent of those pointed out by Rabin (2000), of refusal to accept infinite gain bets at low probabilities. Boundedness of the value function in CPT implies that the indifference curve between expected-return and win-probability will typically exhibit both an asymptote (implying rejection of an infinite gain bet) and a minimum at low probabilities, as the shape of the value function dominates the probability weighting function. Also the high probability section of the indifference curve will exhibit a maximum. These implications are consistent with outcomes observed in gambling markets.

Cost comparison of asthma treatments in 12-week study : caution about matching and short observational follow-up

This review was funded by Observational and Pragmatic Research Institute Pte Ltd.Peer reviewedPublisher PD

Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.Comment: 12 files,6 figure

The inner structure and kinematics of the Sagittarius dwarf galaxy as a product of tidal stirring

The tidal stirring model envisions the formation of dwarf spheroidal (dSph) galaxies in the Local Group via the tidal interaction of disky dwarf systems with a larger host galaxy like the Milky Way. These progenitor disks are embedded in extended dark halos and during the evolution both components suffer strong mass loss. In addition, the disks undergo the morphological transformation into spheroids and the transition from ordered to random motion of their stars. Using collisionless N-body simulations we construct a model for the nearby and highly elongated Sagittarius (Sgr) dSph galaxy within the framework of the tidal stirring scenario. Constrained by the present known orbit of the dwarf, the model suggests that in order to produce the majority of tidal debris observed as the Sgr stream, but not yet transform the core of the dwarf into a spherical shape, Sgr must have just passed the second pericenter of its current orbit around the Milky Way. In the model, the stellar component of Sgr is still very elongated after the second pericenter and morphologically intermediate between the strong bar formed at the first pericenter and the almost spherical shape existing after the third pericenter. This is thus the first model of the evolution of the Sgr dwarf that accounts for its observed very elliptical shape. At the present time there is very little intrinsic rotation left and the velocity gradient detected along the major axis is almost entirely of tidal origin. We model the recently measured velocity dispersion profile for Sgr assuming that mass traces light and estimate its current total mass within 5 kpc to be 5.2 x 10^8 M_sun. To have this mass at present, the model requires that the initial virial mass of Sgr must have been as high as 1.6 x 10^10 M_sun, comparable to that of the Large Magellanic Cloud, which may serve as a suitable analog for the pre-interaction, Sgr progenitor.Comment: 14 pages, 14 figures, minor changes to match the version published in Ap

Wild at Heart:-The Particle Astrophysics of the Galactic Centre

We treat of the high-energy astrophysics of the inner ~200 pc of the Galaxy. Our modelling of this region shows that the supernovae exploding here every few thousand years inject enough power to i) sustain the steady-state, in situ population of cosmic rays (CRs) required to generate the region's non-thermal radio and TeV {\gamma}-ray emis-sion; ii) drive a powerful wind that advects non-thermal particles out of the inner GC; iii) supply the low-energy CRs whose Coulombic collisions sustain the temperature and ionization rate of the anomalously warm, envelope H2 detected throughout the Cen-tral Molecular Zone; iv) accelerate the primary electrons which provide the extended, non-thermal radio emission seen over ~150 pc scales above and below the plane (the Galactic centre lobe); and v) accelerate the primary protons and heavier ions which, advected to very large scales (up to ~10 kpc), generate the recently-identified WMAP haze and corresponding Fermi haze/bubbles. Our modelling bounds the average magnetic field amplitude in the inner few degrees of the Galaxy to the range 60 < B/microG < 400 (at 2 sigma confidence) and shows that even TeV CRs likely do not have time to penetrate into the cores of the region's dense molecular clouds before the wind removes them from the region. This latter finding apparently disfavours scenarios in which CRs - in this star-burst-like environment - act to substantially modify the conditions of star-formation. We speculate that the wind we identify plays a crucial role in advecting low-energy positrons from the Galactic nucleus into the bulge, thereby explaining the extended morphology of the 511 keV line emission. (abridged)Comment: One figure corrected. Accepted for publication in MNRAS. 29 pages, 14 figure

Downward Flame Spread over PMMA Spheres

Experiments were conducted to measure downward flame spread over PMMA spheres, and an underpinning theoretical basis was developed to explain the relevant mechanisms governing flame spread over spherical geometries. Flame spread over a sphere was classified into two distinct regimes, that being spread over the upper and lower hemispheres. Experiments were conducted using cast PMMA spheres 40 and 50 mm in diameter. Samples were ignited at the top of the sphere and the progression of the flame front was determined using video analysis. The time resolved flame spread rate was found to increase nearly linearly in time while the flame spread across the upper hemisphere of the sample (at rates ranging from approximately 2.0–3.5 mm/min). Flame spread on the lower hemisphere was observed to accelerate nonlinearly reaching instantaneous flame spread rates greater than 15 mm/min. The flame spread rates were found to be unsteady (i.e., continuously increasing) throughout each experiment. A Stokes flow solution was found to adequately characterize the opposed flame spread rate over the upper hemisphere with respect to the induced buoyant flow. Flame spread rates in the lower hemisphere were found to be controlled by a combination of increasing velocity of the ambient flow and increased heat transfer through the interior of the solid. Flame spread rates for each diameter tested were normalized and presented as a function of the relative angle of inclination at the flame front, . Thus, the two regimes of flame spread identified in this work are largely independent across sphere size for the diameters used in this study. The study of flame spread over spheres provides a unique condition to observe the transition from spread dictated by a well-defined flow condition to one in which heat transfer effects through the solid become increasingly significant