Voltage dependence of Hodgkin-Huxley rate functions for a multi-stage K channel voltage sensor within a membrane

The activation of a $K^+$ channel sensor in two sequential stages during a voltage clamp may be described as the translocation of a Brownian particle in an energy landscape with two large barriers between states. A solution of the Smoluchowski equation for a square-well approximation to the potential function of the S4 voltage sensor satisfies a master equation, and has two frequencies that may be determined from the forward and backward rate functions. When the higher frequency terms have small amplitude, the solution reduces to the relaxation of a rate equation, where the derived two-state rate functions are dependent on the relative magnitude of the forward rates ($\alpha$ and $\gamma$) and the backward rates ($\beta$ and $\delta$) for each stage. In particular, the voltage dependence of the Hodgkin-Huxley rate functions for a $K^+$ channel may be derived by assuming that the rate functions of the first stage are large relative to those of the second stage - $\alpha \gg \gamma$ and $\beta \gg \delta$. For a {\em Shaker} IR $K^+$ channel, the first forward and backward transitions are rate limiting ($\alpha < \gamma$ and $\delta \ll \beta$), and for an activation process with either two or three stages, the derived two-state rate functions also have a voltage dependence that is of a similar form to that determined for the squid axon. The potential variation generated by the interaction between a two-stage $K^+$ ion channel and a noninactivating $Na^+$ ion channel is determined by the master equation for $K^+$ ion channel activation and the ionic current equation when the $Na^+$ ion channel activation time is small, and if $\beta \ll \delta$ and $\alpha \ll \gamma$, the system may exhibit a small amplitude oscillation between spikes, or mixed-mode oscillation.Comment: 31 pages, 14 figure

Lost Lives: Miscarriages of Justice in Capital Cases

Gross discusses the incidence of erroneous convictions for capital murder, which are systematic consequences of the natuere of homicide prosection in general and capital prosecution in particular

ListOps: A Diagnostic Dataset for Latent Tree Learning

Latent tree learning models learn to parse a sentence without syntactic supervision, and use that parse to build the sentence representation. Existing work on such models has shown that, while they perform well on tasks like sentence classification, they do not learn grammars that conform to any plausible semantic or syntactic formalism (Williams et al., 2018a). Studying the parsing ability of such models in natural language can be challenging due to the inherent complexities of natural language, like having several valid parses for a single sentence. In this paper we introduce ListOps, a toy dataset created to study the parsing ability of latent tree models. ListOps sequences are in the style of prefix arithmetic. The dataset is designed to have a single correct parsing strategy that a system needs to learn to succeed at the task. We show that the current leading latent tree models are unable to learn to parse and succeed at ListOps. These models achieve accuracies worse than purely sequential RNNs.Comment: 8 pages, 4 figures, 3 tables, NAACL-SRW (2018

Melodia : A Comprehensive Course in Sight-Singing (Solfeggio)

Melodia is a 1904 book designed to teach sight-singing. The educational plan is by Samuel W. Cole; the exercises were written and selected by Leo R. Lewis. Melodia is presented here as a complete edition and has also been divided into its four separate books.https://scholarworks.sjsu.edu/oer/1000/thumbnail.jp