From Structure to Function in Open Ionic Channels

We consider a simple working hypothesis that all permeation properties of open ionic channels can be predicted by understanding electrodiffusion in fixed structures, without invoking conformation changes, or changes in chemical bonds. We know, of course, that ions can bind to specific protein structures, and that this binding is not easily described by the traditional electrostatic equations of physics textbooks, that describe average electric fields, the so-called `mean field'. The question is which specific properties can be explained just by mean field electrostatics and which cannot. I believe the best way to uncover the specific chemical properties of channels is to invoke them as little as possible, seeking to explain with mean field electrostatics first. Then, when phenomena appear that cannot be described that way, by the mean field alone, we turn to chemically specific explanations, seeking the appropriate tools (of electrochemistry, Langevin, or molecular dynamics, for example) to understand them. In this spirit, we turn now to the structure of open ionic channels, apply the laws of electrodiffusion to them, and see how many of their properties we can predict just that way.Comment: Nearly final version of publicatio

Solution of the minimum modulus problem for covering systems

We answer a question of Erd\H{o}s by showing that the least modulus of a distinct covering system of congruences is no larger than $10^{18}$.Comment: Submitted version, comments welcom

Reasons for Reliabilism

One leading approach to justification comes from the reliabilist tradition, which maintains that a belief is justified provided that it is reliably formed. Another comes from the ‘Reasons First’ tradition, which claims that a belief is justified provided that it is based on reasons that support it. These two approaches are typically developed in isolation from each other; this essay motivates and defends a synthesis. On the view proposed here, justification is understood in terms of an agent’s reasons for belief, which are in turn analyzed along reliabilist lines: an agent's reasons for belief are the states that serve as inputs to their reliable processes. I show that this synthesis allows each tradition to profit from the other's explanatory resources. In particular, it enables reliabilists to explain epistemic defeat without abandoning their naturalistic ambitions. I go on to compare my proposed synthesis with other hybrid versions of reliabilism that have been proposed in the literature

HELIN Consortium LORI Grant Final Report HELIN

Final report to the RI Office of Library and Information Services on the work accomplished with the LORI grant received from that agency