Lower Bounds on the Rate of Convergence for Accept-Reject-Based Markov Chains

Practitioners are often left tuning Metropolis-Hastings algorithms by trial and error or using optimal scaling guidelines to avoid poor empirical performance. We develop lower bounds on the convergence rates of geometrically ergodic accept-reject-based Markov chains (i.e. Metropolis-Hastings, non-reversible Metropolis-Hastings) to study their computational complexity. If the target density concentrates with a parameter $n$ (e.g. Bayesian posterior concentration, Laplace approximations), we show the convergence rate can tend to $1$ exponentially fast if the tuning parameters do not depend carefully on $n$. We show this is the case for random-walk Metropolis in Bayesian logistic regression with Zellner's g-prior when the dimension and sample size $d/n \to \gamma \in (0, 1)$. We focus on more general target densities using a special class of Metropolis-Hastings algorithms with a Gaussian proposal (e.g. random walk and Metropolis-adjusted Langevin algorithms) where we give more general conditions. An application to flat prior Bayesian logistic regression as $n \to \infty$ is studied. We also develop lower bounds in the Wasserstein distances which have become popular in the convergence analysis of high-dimensional MCMC algorithms with similar conclusions

Observable essential fatty acid deficiency markers and autism spectrum disorder

Autism Spectrum Disorder (ASD) has been associated with essential fatty acid (EFA) deficiencies, with some researchers theorising that dysregulation of phospholipid metabolism may form part of the biological basis for ASD. This pilot study compared observable signs of fatty acid status of 19 children with an ASD diagnosis to 23 of their typically developing siblings. A pregnancy, birth and breastfeeding history was also obtained from their parents, which included a measure of infant intake of fatty acid rich colostrum immediately post-partum. When considered within their family group, those infants not breastfed (with colostrum) within the first hour of life and who had a history of fatty acid deficiency symptoms were more likely to have an ASD diagnosis. Other variables such as formula use, duration of breastfeeding, gestational age and Apgar scores were not associated with group membership. The results of this study are consistent with previous research showing a relationship between fatty acid metabolism, breastfeeding and ASD such that early infant feeding practices and the influence this has on the fatty acid metabolism of the child may be a risk factor for ASD

MEC-2 and MEC-6 in the Caenorhabditis elegans Sensory Mechanotransduction Complex: Auxiliary Subunits that Enable Channel Activity

The ion channel formed by the homologous proteins MEC-4 and MEC-10 forms the core of a sensory mechanotransduction channel in Caenorhabditis elegans. Although the products of other mec genes are key players in the biophysics of transduction, the mechanism by which they contribute to the properties of the channel is unknown. Here, we investigate the role of two auxiliary channel subunits, MEC-2 (stomatin-like) and MEC-6 (paraoxonase-like), by coexpressing them with constitutively active MEC-4/MEC-10 heteromeric channels in Xenopus oocytes. This work extends prior work demonstrating that MEC-2 and MEC-6 synergistically increase macroscopic current. We use single-channel recordings and biochemistry to show that these auxiliary subunits alter function by increasing the number of channels in an active state rather than by dramatically affecting either single-channel properties or surface expression. We also use two-electrode voltage clamp and outside-out macropatch recording to examine the effects of divalent cations and proteases, known regulators of channel family members. Finally, we examine the role of cholesterol binding in the mechanism of MEC-2 action by measuring whole-cell and single-channel currents in MEC-2 mutants deficient in cholesterol binding. We suggest that MEC-2 and MEC-6 play essential roles in modulating both the local membrane environment of MEC-4/MEC-10 channels and the availability of such channels to be gated by force in vivo

Gain-of-Function Mutations in the MEC-4 DEG/ENaC Sensory Mechanotransduction Channel Alter Gating and Drug Blockade

MEC-4 and MEC-10 are the pore-forming subunits of the sensory mechanotransduction complex that mediates touch sensation in Caenorhabditis elegans (O'Hagan, R., M. Chalfie, and M.B. Goodman. 2005. Nat. Neurosci. 8:43–50). They are members of a large family of ion channel proteins, collectively termed DEG/ENaCs, which are expressed in epithelial cells and neurons. In Xenopus oocytes, MEC-4 can assemble into homomeric channels and coassemble with MEC-10 into heteromeric channels (Goodman, M.B., G.G. Ernstrom, D.S. Chelur, R. O'Hagan, C.A. Yao, and M. Chalfie. 2002. Nature. 415:1039–1042). To gain insight into the structure–function principles that govern gating and drug block, we analyzed the effect of gain-of-function mutations using a combination of two-electrode voltage clamp, single-channel recording, and outside-out macropatches. We found that mutation of A713, the d or degeneration position, to residues larger than cysteine increased macroscopic current, open probability, and open times in homomeric channels, suggesting that bulky residues at this position stabilize open states. Wild-type MEC-10 partially suppressed the effect of such mutations on macroscopic current, suggesting that subunit–subunit interactions regulate open probability. Additional support for this idea is derived from an analysis of macroscopic currents carried by single-mutant and double-mutant heteromeric channels. We also examined blockade by the diuretic amiloride and two related compounds. We found that mutation of A713 to threonine, glycine, or aspartate decreased the affinity of homomeric channels for amiloride. Unlike the increase in open probability, this effect was not related to size of the amino acid side chain, indicating that mutation at this site alters antagonist binding by an independent mechanism. Finally, we present evidence that amiloride block is diffusion limited in DEG/ENaC channels, suggesting that variations in amiloride affinity result from variations in binding energy as opposed to accessibility. We conclude that the d position is part of a key region in the channel functionally and structurally, possibly representing the beginning of a pore-forming domain

Environmental geologic atlas of the Texas coastal zone : Brownsville-Harlingen area

UT Librarie

Adolescent Experiences with Self-Asphyxial Behaviors and Problematic Drinking in Emerging Adulthood

Self-asphyxial behavior to achieve a euphoric high (The Choking Game; TCG), occurs most often during early adolescence. Participants in TCG often engage in other risky behaviors. This study investigated the relationship between prior experience with TCG and problematic drinking behaviors in emerging adulthood. Emerging adults, 18 to 25 years old (N = 1248), 56% female, and 78% Caucasian completed an online survey regarding knowledge of and prior engagement in TCG and current drinking behaviors. Participants who personally engaged in TCG during childhood/adolescence or were familiar with TCG reported significantly more problematic drinking behaviors during emerging adulthood. Those present when others engaged in TCG but resisted participation themselves reported significantly less current problematic drinking behaviors than those who participated, but significantly more current problematic drinking behaviors than those never present. Emerging adults with increased social familiarity with TCG during adolescence endorsed greater problematic drinking behaviors. Results suggest resistance skills may generalize across time/activities

The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems

The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time for the Gaussian orthogonal ensemble. The correlation function is found to be dominated by the nearest neighbor level spacings. It was calculated for a variety of nearest neighbor level spacing distributions, including ones that do not originate from RMT ensembles. The various approximate formulas obtained are tested numerically in RMT. The results shed light on the quantum to classical crossover for chaotic systems. The implications on the possibility to experimentally observe deterministic friction are discussed.Comment: 26 pages, including 6 figure