A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

The cis-Diammineplatinum(II) Complex of Curcumin: A Dual Action DNA Crosslinking and Photochemotherapeutic Agent

Pt(cur)(NH3)(2)](NO3) (1), a curcumin-bound cis-diammineplatinum(II) complex, nicknamed Platicur, as a novel photoactivated chemotherapeutic agent releases photoactive curcumin and an active platinum(II) species upon irradiation with visible light. The hydrolytic instability of free curcumin reduces upon binding to platinum(II). Interactions of 1 with 5'-GMP and ct-DNA indicated formation of platinum-bound DNA adducts upon exposure to visible light (lambda = 400-700 nm). It showed apoptotic photocytotoxicity in cancer cells (IC50 approximate to 15 mu M), thus forming (OH)-O-center dot, while remaining passive in the darkness (IC50 > 200 mu M). A comet assay and platinum estimation suggest Pt-DNA crosslink formation. The fluorescence microscopic images showed cytosolic localization of curcumin, thus implying possibility of dual action as a chemo-and phototherapeutic agent.

Action of Hopf on the twisted modular Hecke operator

Let Gamma subset of SL2(Z) be a principal congruence subgroup. For each sigma is an element of SL2(Z), we introduce the collection A(sigma)(Gamma) of modular Hecke operators twisted by sigma. Then, A(sigma)(Gamma) is a right A(Gamma)-module, where A(Gamma) is the modular Hecke algebra introduced by Connes and Moscovici. Using the action of a Hopf algebra h(0) on A(sigma)(Gamma), we define reduced Rankin-Cohen brackets on A(sigma)(Gamma). Moreover A(sigma)(Gamma) carries an action of H 1, where H 1 is the Hopf algebra of foliations of codimension 1. Finally, we consider operators between the levels A(sigma)(Gamma), sigma is an element of SL2(Z). We show that the action of these operators can be expressed in terms of a Hopf algebra h(Z).