Visualizing Probabilistic Proof

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus problem. In addition, the author expresses his solutions in standard and visual formats, i.e. in terms of probabilities and natural frequencies

Does the Prisoner's Dilemma Refute the Coase Theorem?

Two of the most important ideas in the philosophy of law are the “Coase Theorem” and the “Prisoner’s Dilemma.” In this paper, the authors explore the relation between these two influential models through a creative thought-experiment. Specifically, the paper presents a pure Coasean version of the Prisoner’s Dilemma, one in which property rights are well-defined and transactions costs are zero (i.e. the prisoners are allowed to openly communicate and bargain with each other), in order to test the truth value of the Coase Theorem. In addition, the paper explores what effect (a) uncertainty, (b) exponential discounting, (c) and elasticity have on the behavior of the prisoners in the Coasean version of the dilemma. Lastly, the paper considers the role of the prosecutor (and third-parties generally) in the Prisoner’s Dilemma and closes with some parting thoughts about the complexity of the dilemma. The authors then conclude by identifying the conditions under which the Prisoner’s Dilemma refutes the Coase Theorem

Response for light scattered in the ocular fundus from double-pass and Hartmann–Shack estimations

Double-pass (DP) and Hartmann--Shack (HS) are complementary techniques based on reflections of light in the ocular fundus that may be used to estimate the optical properties of the human eye. Under conventional data processing, both of these assessment modes provide information on aberrations. In addition, DP data contain the effects of scattering. In the ocular fundus, this phenomenon may arise from the interaction of light with not only the retina, but also deeper layers up to which certain wavelengths may penetrate. In this work, we estimate the response of the ocular fundus to incident light by fitting the deviations between DP and HS estimations using an exponential model. In measurements with negligible intraocular scattering, such differences may be related to the lateral spreading of light that occurs in the ocular fundus due to the diffusive properties of the media at the working wavelength. The proposed model was applied in young healthy eyes to evaluate the performance of scattering in such a population. Besides giving a parameter with information on the ocular fundus, the model contributes to the understanding of the differences between DP and HS estimations.Postprint (author's final draft

Speckle reduction in double-pass retinal images using variable-focus lenses

Speckle arises in double-pass images when coherent light is scattered by the retina. Since this noise degrades the images that are used to characterize the eye, there is special attention in reducing speckle when working with instruments based on retina reflections. In this work, we present a method for speckle reduction in double-pass retinal images by producing minor periodic variations in the vergence of the beam entering the eye with a variable-focus lens during image recording. Measurements in an artificial and a real eye following the implementation of the method corroborate the speckle reduction.Postprint (published version

Tear film stability assessment by corneal reflex image degradation

Postprint (published version

Quantification of forward scattering based on the analysis of double-pass images in the frequency domain

Preprin

Influence of power and the time of application of fogging lenses on accommodation

Fogging is a non-invasive technique based on the use of positive spherical power lenses to relax accommodation during refraction that is commonly used as an alternative to cycloplegic drugs. Although the mechanism of the fogging technique has been described, some aspects of its methodology remain unclear. The main purpose of this work was to determine which lens power and time of application are more suitable for achieving a successful relaxation of accommodation by analyzing the changes in accommodation when fogging lenses of different powers were placed in front of the participants’ eye for a certain timespan. The results of this analysis showed, in general, that low-power lenses and timespans of less than half a minute provided the highest relaxation of accommodation. However, high inter-subject variability was found in the two variables (power and time).Universitat Politècnica de Catalunya (FPI-UPC Grant); Banco Santander (FPI-UPC Grant); Agencia Estatal de Investigación (MCIN/AEI/10.13039/501100011033, PID2020-112527RB-I00).Peer ReviewedPostprint (published version

Implementation of the frequency scatter index in clinical commercially available double-pass systems

A previous work has reported a methodology to quantify intraocular scattering using a high sensitivity double-pass instrument with a robust index, the frequency scatter index. The purpose of our study was to evaluate an adaptation of the frequency scatter index for use in clinical double-pass systems. A prospective observational study was carried out in a group of patients with nuclear cataracts (n = 52) and in a control group (n = 11) using conventional double-pass systems. The frequency scatter index and the objective scatter index were used to assess the scattering. The Spearman coefficient was calculated to assess the correlation between both indexes, obtained from the double-pass images. Simultaneous measurements were performed with a double-pass and with a Hartmann-Shack wavefront sensor in the control group. The root-mean-square wavefront error and the full width at half maximum of the double-pass image were used to quantify the residual aberrations introduced by the variations in pupil size and retinal eccentricity. Measurement in eyes with different grades of cataracts shows a strong correlation (¿ = 0.929, p .05). We have introduced and evaluated an adaptation of a methodology proposed recently for the measurement of intraocular scattering using the double-pass technique with a robust index, which is less affected by ocular aberrations. The frequency scatter index can be applied to conventional double-pass instruments available in clinical environments.Peer ReviewedPostprint (updated version