We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of large network dynamics is usually quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of bin...

This paper surveys certain developments in the use of probabilistic techniques for the modelling of generalization in machine learning. Building on ‘uniform convergence’ results in probability theory, a number of approaches to the problem of quantifying generalization have been developed in recent years. Initially these models addressed binary classification, and as such were applicable, for ex...

Sodium measurement during hemodialysis treatment is important to preserve the patient from clinical events related to hypo- or hyper-natremia Usually, sodium measurement is performed through laboratory equipment which is typically expensive, and requires manual intervention. We propose a new method, based on conductivity measurement after treatment of dialysate solution through ion-exchange res...

Aggregation of amyloid-β (Aβ) protein plays a central role in Alzheimer's disease. Because protein aggregation is a concentration-dependent process, rigorous investigations require accurate concentration measurements. Owing to the high aggregation propensity of Aβ protein, working solutions of Aβ are typically in the low micromolar range. Therefore, an ideal Aβ quantification method requires hi...

Drop size distribution in a mixer-settler is an essential design parameter, as obtaining drop size distribution will result in optimum performance of equipment. In this paper for obtaining drop size, several experiments have been performed with a single stage horizontal mixer-settler. A video technique has been used in order to measure the drop size in the mixer-settler with the help of a digit...

Iron is ubiquitous in natural water sources used around the world for drinking and cooking. The health impact of chronic exposure to iron through water, which in groundwater sources can reach well above the World Health Organization's defined aesthetic limit of 0.3 mg/L, is not currently understood. To quantify the impact of consumption of iron in groundwater on nutritional status, it is import...

Suppose A is a finite set, let P be a discrete probability distribution on A, and let M be an arbitrary “mass” function on A. We give a precise characterization of the most efficient way in which An can be almost-covered using spheres of a fixed radius. An almost-covering is a subset Cn of A n, such that the union of the spheres centered at the points of Cn has probability close to one with res...

This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base measure itself is endowed with another Dirichlet prior, a construction known as the hierarchical Dirichlet processes (Teh et al. [J. Amer. Statist. Assoc. 101 (200...

Theoretical analysis of randomized, compressive operators often depends on a concentration of measure inequality for the operator in question. Typically, such inequalities quantify the likelihood that a random matrix will preserve the norm of a signal after multiplication. When this likelihood is very high for any signal, the random matrices have a variety of known uses in dimensionality reduct...