Informed Consent Versus Presumed Consent The Role of the Family in Organ Donations

Two types of legislation underlie cadaveric organ donations: presumed consent (PC) and informed consent (IC). In informed consent countries, people are only donors when deceased if they registered to do so while alive. Conversely, in presumed consent countries, anybody is a potential donor when deceased. People have thus to register if they do not want to donate their body. PC has always been perceived as the “best” system for society in terms of organ donations whereas IC is supposed to be more ethical. However, in both systems, the family has a say, especially for the deceased who did not sign anything while alive. Taking the family decision into account, we show that the previous results may be reversed. The difference between both systems resides in the way an individual can commit to his/her will, eventually against the opinion of his/her family. IC can dominate PC in terms of organ donations whereas PC can be a more ethical system. In the general case, two opposite effects are at stake and the result depends on the extent to which people stay in the default situation. We discuss several causes of inactions (death taboo, procrastination, anticipated regret,...) and their impact on both the individual and the family.

On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations

This paper studies the stability properties of a two dimensional relative velocity scheme for the Navier-Stokes equations. This scheme inspired by the cascaded scheme has the particularity to relax in a frame moving with a velocity field function of space and time. Its stability is studied first in a linear context then on the non linear test case of the Kelvin-Helmholtz instability. The link with the choice of the moments is put in evidence. The set of moments of the cascaded scheme improves the stability of the d'Humi\`eres scheme for small viscosities. On the contrary, a relative velocity scheme with the usual set of moments deteriorates the stability

Lattice Boltzmann schemes with relative velocities

In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d'Humi\`eres. They extend also the Geier's cascaded method. The relaxation phase takes place in a moving frame involving a set of moments depending on a given relative velocity field. We establish with the Taylor expansion method that the equivalent partial differential equations are identical to the ones obtained with the multiple relaxation times method up to the second order accuracy. The method is then performed to derive the equivalent equations up to third order accuracy

Convolution powers in the operator-valued framework

We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers with respect to free additive convolution and with respect to Boolean convolution, where the exponent considered in the power is a suitably chosen linear map \eta from B to B, instead of being a non-negative real number. More precisely, the Boolean convolution power is defined whenever \eta is completely positive, while the free additive convolution power is defined whenever \eta - 1 is completely positive (where 1 stands for the identity map on B). In connection to these convolution powers we define an evolution semigroup related to the Boolean Bercovici-Pata bijection. We prove several properties of this semigroup, including its connection to the B-valued free Brownian motion. We also obtain two results on the operator-valued analytic function theory related to the free additive convolution powers with exponent \eta. One of the results concerns analytic subordination for B-valued Cauchy-Stieltjes transforms. The other gives a B-valued version of the inviscid Burgers equation, which is satisfied by the Cauchy-Stieltjes transform of a B-valued free Brownian motion.Comment: 33 pages, no figure

Exploratory Data Analysis on Race & Doctor Visits

Our study will look at the race of a child and if they have had a visit with their primary care-provider within the last 12 months. We obtained our information from the National Survey of Children’s health. The data set sample is 42,777 children aged 1-17 and the data set includes 831 variables. this data is from the year 2020, Between June 2020 and January 2021. Even though the data sets include a plethora of information on factors affecting children, we specifically are looking at if the children are part of the majority (white) or if they are a minority, and a yearly doctor visit. Doctor visit are essential for children at least once a year because they asses their physical and emotional needs, support their growth and development, and overall make sure everything is okay in the child’s life. Minority children are more likely to have a language barrier, experience implicit bias and not have the correct insurance, all factors that affect visiting the doctor. While at the doctor minority children are also less likely to be screened for disorders such as mental illnesses. Other variables that we will include are the sex of the child and if they have experienced a negative experience (outside the doctor office), due to their race. The research question for our study is Does the race of a child have an impact on whether they see their primary-care giver at least once a year. The main variables of the study are race (SC_RACE_R) and doctor visit in 12 months (S4Q01). We choose this variables as well as the alternative variables because we believe that the race of a child somewhat affects their amount of doctor visits

FLUCTUATIONS OF LINEAR SPECTRAL STATISTICS OF DEFORMED WIGNER MATRICES

We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W_N$ deformed by a deterministic diagonal perturbation $D_N$, around a deterministic equivalent which can be expressed in terms of the free convolution between a semicircular distribution and the empirical spectral measure of $D_N$. We obtain Gaussian fluctuations for test functions in $\mathcal{C}_c^7(\R)$ ($\mathcal{C}_c^2(\R)$ for fluctuations around the mean). Furthermore, we provide as a tool a general method inspired from Shcherbina and Johansson to extend the convergence of the bias if there is a bound on the bias of the trace of the resolvent of a random matrix. Finally, we state and prove an asymptotic infinitesimal freeness result for independent GUE matrices together with a family of deterministic matrices, generalizing the main result from [Shl18]