ADVANCED MEMRISTOR MODEL WITH A MODIFIED BIOLEK WINDOW AND A VOLTAGE-DEPENDENT VARIABLE EXPONENT

The main idea of the present research is to propose a new nonlinear ionic drift memristor model suitable for computer simulations of memristor elements for different voltages. For this purpose, a modified Biolek window function with a voltage-dependent exponent is applied. The proposed modified memristor model is based on Biolek model and due to this and to the use of a voltage-dependent positive integer exponent in the modified Biolek window function it has a new improved property - changing the model nonlinearity extent dependent on the integer exponent in accordance with the memristor voltage. Several computer simulations were made for soft-switching and hard-switching modes and also for pseudo-sinusoidal alternating voltage with an exponentially increasing amplitude and the respective basic important time diagrams, state-flux and i-v relationships are established.

Beyond non-integer Hill coefficients: A novel approach to analyzing binding data, applied to Na+-driven transporters

Prokaryotic and eukaryotic Na+-driven transporters couple the movement of one or more Na+ ions down their electrochemical gradient to the active transport of a variety of solutes. When more than one Na+ is involved, Na+-binding data are usually analyzed using the Hill equation with a non-integer exponent n. The results of this analysis are an overall Kd-like constant equal to the concentration of ligand that produces half saturation and n, a measure of cooperativity. This information is usually insufficient to provide the basis for mechanistic models. In the case of transport using two Na+ ions, an n < 2 indicates that molecules with only one of the two sites occupied are present at low saturation. Here, we propose a new way of analyzing Na+-binding data for the case of two Na+ ions that, by taking into account binding to individual sites, provides far more information than can be obtained by using the Hill equation with a non-integer coefficient: it yields pairs of possible values for the Na+ affinities of the individual sites that can only vary within narrowly bounded ranges. To illustrate the advantages of the method, we present experimental scintillation proximity assay (SPA) data on binding of Na+ to the Na+/I− symporter (NIS). SPA is a method widely used to study the binding of Na+ to Na+-driven transporters. NIS is the key plasma membrane protein that mediates active I− transport in the thyroid gland, the first step in the biosynthesis of the thyroid hormones, of which iodine is an essential constituent. NIS activity is electrogenic, with a 2:1 Na+/I− transport stoichiometry. The formalism proposed here is general and can be used to analyze data on other proteins with two binding sites for the same substrate.

Pair correlation for fractional parts of αn2

It was proved by Weyl [8] in 1916 that the sequence of values of αn2 is uniformly distributed modulo 1, for any fixed real irrational α. Indeed this result covered sequences αnd for any fixed positive integer exponent d. However Weyl's work leaves open a number of questions concerning the finer distribution of these sequences. It has been conjectured by Rudnick, Sarnak and Zaharescu [6] that the fractional parts of αn2 will have a Poisson distribution provided firstly that α is “Diophantine”, and secondly that if a/q is any convergent to α then the square-free part of q is q1+o(1). Here one says that α is Diophantine if one has (1.1) for every rational number a/q and any fixed ϵ > 0. In particular every real irrational algebraic number is Diophantine. One would predict that there are Diophantine numbers α for which the sequence of convergents pn/qn contains infinitely many squares amongst the qn. If true, this would show that the second condition is independent of the first. Indeed one would expect to find such α with bounded partial quotients.