Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed

Biology, Genetics, and Environment: Underlying Factors Influencing Alcohol Metabolism.

Gene variants encoding several of the alcohol-metabolizing enzymes, alcohol dehydrogenase (ADH) and aldehyde dehydrogenase (ALDH), are among the largest genetic associations with risk for alcohol dependence. Certain genetic variants (i.e., alleles)--particularly the ADH1B*2, ADH1B*3, ADH1C*1, and ALDH2*2 alleles--have been associated with lower rates of alcohol dependence. These alleles may lead to an accumulation of acetaldehyde during alcohol metabolism, which can result in heightened subjective and objective effects. The prevalence of these alleles differs among ethnic groups; ADH1B*2 is found frequently in northeast Asians and occasionally Caucasians, ADH1B*3 is found predominantly in people of African ancestry, ADH1C*1 varies substantially across populations, and ALDH2*2 is found almost exclusively in northeast Asians. Differences in the prevalence of these alleles may account at least in part for ethnic differences in alcohol consumption and alcohol use disorder (AUD). However, these alleles do not act in isolation to influence the risk of AUD. For example, the gene effects of ALDH2*2 and ADH1B*2 seem to interact. Moreover, other factors have been found to influence the extent to which these alleles affect a person's alcohol involvement, including developmental stage, individual characteristics (e.g., ethnicity, antisocial behavior, and behavioral undercontrol), and environmental factors (e.g., culture, religion, family environment, and childhood adversity)

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed

Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.Comment: 10 page

Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol

The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal

The FKBP5 Gene Affects Alcohol Drinking in Knockout Mice and Is Implicated in Alcohol Drinking in Humans

FKBP5 encodes FK506-binding protein 5, a glucocorticoid receptor (GR)-binding protein implicated in various psychiatric disorders and alcohol withdrawal severity. The purpose of this study is to characterize alcohol preference and related phenotypes in Fkbp5 knockout (KO) mice and to examine the role of FKBP5 in human alcohol consumption. The following experiments were performed to characterize Fkpb5 KO mice. (1) Fkbp5 KO and wild-type (WT) EtOH consumption was tested using a two-bottle choice paradigm; (2) The EtOH elimination rate was measured after intraperitoneal (IP) injection of 2.0 g/kg EtOH; (3) Blood alcohol concentration (BAC) was measured after 3 h limited access of alcohol; (4) Brain region expression of Fkbp5 was identified using LacZ staining; (5) Baseline corticosterone (CORT) was assessed. Additionally, two SNPs, rs1360780 (C/T) and rs3800373 (T/G), were selected to study the association of FKBP5 with alcohol consumption in humans. Participants were college students (n = 1162) from 21–26 years of age with Chinese, Korean or Caucasian ethnicity. The results, compared to WT mice, for KO mice exhibited an increase in alcohol consumption that was not due to differences in taste sensitivity or alcohol metabolism. Higher BAC was found in KO mice after 3 h of EtOH access. Fkbp5 was highly expressed in brain regions involved in the regulation of the stress response, such as the hippocampus, amygdala, dorsal raphe and locus coeruleus. Both genotypes exhibited similar basal levels of plasma corticosterone (CORT). Finally, single nucleotide polymorphisms (SNPs) in FKBP5 were found to be associated with alcohol drinking in humans. These results suggest that the association between FKBP5 and alcohol consumption is conserved in both mice and humans

Diverse perspectives on interdisciplinarity from the Members of the College of the Royal Society of Canada

Various multiple-disciplinary terms and concepts (although most commonly “interdisciplinarity”, which is used herein) are used to frame education, scholarship, research, and interactions within and outside academia. In principle, the premise of interdisciplinarity may appear to have many strengths; yet, the extent to which interdisciplinarity is embraced by the current generation of academics, the benefits and risks for doing so, and the barriers and facilitators to achieving interdisciplinarity represent inherent challenges. Much has been written on the topic of interdisciplinarity, but to our knowledge there have been few attempts to consider and present diverse perspectives from scholars, artists, and scientists in a cohesive manner. As a team of 57 members from the Canadian College of New Scholars, Artists, and Scientists of the Royal Society of Canada (the College) who self-identify as being engaged or interested in interdisciplinarity, we provide diverse intellectual, cultural, and social perspectives. The goal of this paper is to share our collective wisdom on this topic with the broader community and to stimulate discourse and debate on the merits and challenges associated with interdisciplinarity. Perhaps the clearest message emerging from this exercise is that working across established boundaries of scholarly communities is rewarding, necessary, and is more likely to result in impact. However, there are barriers that limit the ease with which this can occur (e.g., lack of institutional structures and funding to facilitate cross-disciplinary exploration). Occasionally, there can be significant risk associated with doing interdisciplinary work (e.g., lack of adequate measurement or recognition of work by disciplinary peers). Solving many of the world’s complex and pressing problems (e.g., climate change, sustainable agriculture, the burden of chronic disease, and aging populations) demand thinking and working across long-standing, but in some ways restrictive, academic boundaries. Academic institutions and key support structures, especially funding bodies, will play an important role in helping to realize what is readily apparent to all who contributed to this paper—that interdisciplinarity is essential for solving complex problems; it is the new norm. Failure to empower and encourage those doing this research will serve as a great impediment to training, knowledge, and addressing societal issues

ALDH2, ADH1B, and ADH1C genotypes in Asians: a literature review.

Variants of three genes encoding alcohol-metabolizing enzymes, the aldehyde dehydrogenase gene ALDH2 and the alcohol dehydrogenase genes ADH1B and ADH1C, have been associated with reduced rates of alcohol dependence. The genotype prevalence of these genes varies in general samples of different Asian ethnic groups. The ALDH2*2 allele appears to be most prevalent in Chinese-American, Han Chinese and Taiwanese, Japanese, and Korean samples. Much lower rates have been reported in Thais, Filipinos, Indians, and Chinese and Taiwanese aborigines. ADH1B*2 is highly prevalent among Asians, with the exception of Indians. ADH1C*1 also is highly prevalent in Asians, but has only been examined in a few studies of Chinese and Korean samples