Protein Folding & Self-Organized Criticality

Proteins are known to fold into tertiary structures that determine their functionality in living organisms. However, the complex dynamics of protein folding and the way they consistently fold into the same structures is unknown. Self-organized criticality (SOC) has provided a framework for understanding complex systems in various scientific disciplines through scale invariance and the associated fractal power law behavior. In this research, we use a simple hydrophobic-polar lattice-bound computational model to investigate self-organized criticality as a possible mechanism for generating complexity in protein folding

Occurrence of Hysteresis like behavior of resistance of Sb2Te3Sb_2 Te_3 film in heating-cooling cycle

Experimental observations of a peculiar behavior observed on heating and cooling ${\rm Sb_2Te_3}$ films at different heating and cooling rate are detailed. The film regained its original resistance, forming a closed loop, on the completion of the heating-cooling cycle which was reproducible for identical conditions of heating and cooling. The area enclosed by the loop was found to depend on (i) the thickness of the film, (ii) the heating rate, (iii) the maximum temperature to which film was heated and (iv) the cooling rate. The observations are explained on basis of model which considers the film to be a resultant of parallel resistances. The film's finite thermal conductivity gives rise to a temperature gradient along the thickness of the film, due to this and the temperature coefficient of resistance, the parallel combination of resistance changes with temperature. Difference in heating and cooling rates give different temperature gradient, which explains the observed hysteresis.Comment: 21 pages and 10 figure

A Morse theoretic description of the Goresky-Hingston product

The Goresky-Hingston coproduct was first introduced by D. Sullivan and later extended by M. Goresky and N. Hingston. In this article we give a Morse theoretic description of the coproduct. Using the description we prove homotopy invariance property of the coproduct. We describe a connection between our Morse theoretic coproduct and a coproduct on Floer homology of cotangent bundle.Comment: 32 pages, 2 figure

The closed geodesic problem and the string products

In this paper, we show that the Chas-Sullivan product (respectively the Goresky-Hingston product) on level homology detects isolated closed geodesic with slowest (resp. fastest) possible index growth rate. We discuss how string topology along with this result gives a new perspective on questions of the existence of closed geodesics.Comment: 9 page

The Merton Problem with a Drawdown Constraint on Consumption

In this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In terms of economic motivation, this constraint represents a type of habit formation where the investor is reluctant to let his standard of living fall too far from the maximum standard achieved to date. We use techniques from stochastic optimal control and duality theory to obtain our candidate value function and optimal controls, which are then verified