A Nonstochastic Information Theory for Communication and State Estimation

In communications, unknown variables are usually modelled as random variables, and concepts such as independence, entropy and information are defined in terms of the underlying probability distributions. In contrast, control theory often treats uncertainties and disturbances as bounded unknowns having no statistical structure. The area of networked control combines both fields, raising the question of whether it is possible to construct meaningful analogues of stochastic concepts such as independence, Markovness, entropy and information without assuming a probability space. This paper introduces a framework for doing so, leading to the construction of a maximin information functional for nonstochastic variables. It is shown that the largest maximin information rate through a memoryless, error-prone channel in this framework coincides with the block-coding zero-error capacity of the channel. Maximin information is then used to derive tight conditions for uniformly estimating the state of a linear time-invariant system over such a channel, paralleling recent results of Matveev and Savkin

Exploring High Dimensional Free Energy Landscapes: Temperature Accelerated Sliced Sampling

Biased sampling of collective variables is widely used to accelerate rare events in molecular simulations and to explore free energy surfaces. However, computational efficiency of these methods decreases with increasing number of collective variables, which severely limits the predictive power of the enhanced sampling approaches. Here we propose a method called Temperature Accelerated Sliced Sampling (TASS) that combines temperature accelerated molecular dynamics with umbrella sampling and metadynamics to sample the collective variable space in an efficient manner. The presented method can sample a large number of collective variables and is advantageous for controlled exploration of broad and unbound free energy basins. TASS is also shown to achieve quick free energy convergence and is practically usable with ab initio molecular dynamics techniques

Height-length relation of shells in the Indian backwater oyster Crassostrea madrasensis (Preston) of the Cochin harbour

Height-length relationship in Crassostrea madrasensis (Preston) showed an exponential trend and relation in the form, H=ALᴮ. Deviations of actual values from the mean values consequent to the increase in size were noticed. Height and length approximated in oysters of less than 3.5cm in height resulting in orbicular shape. In oyster of shell height 3.5cm to 8cm, increase in height is faster leading to an oval shape. Above 8cm in height, the oysters become further elongated. Height-length relation is non-linear with an index (B value) of 1.1156. A linear relationship also holds good as the B value is not very much different from unity (H=-2.5424+2.0036L)