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.

Force-free equilibria of magnetized jets

Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.

Changes in the Levels of Free Amino Acids in Various Regions of Cuscuta during Growth

The angiospermous plant parasite Cuscuta derives reduced carbon and nitrogen compounds primarily from its host. Free amino acids along Cuscuta vines in three zones, viz., 0 to 5 cm, 5 to 15 cm, and 15 to 30 cm, which in a broad sense represent the region of cell division, cell elongation and differentiation and vascular tissue differentiation respectively, were quantitatively estimated. The free amino acid content was the highest in the 0 to 5 cm region and progressively decreased along the posterior regions of the vine. The haustorial region showed the lowest content of free amino acids. In general, the free amino acid content in samples collected at 7 p.m. was found to be higher than that in the samples collected at 7 a.m. Three basic amino acids, histidine, the uncommon amino acid γ-hydroxyarginine, and arginine constituted more than 50% of the total free amino acids in all the zones studied except the haustorial region. Aspartic acid and glutamic acid constituted the major portion in the acidic and neutral fraction of amino acids. Glutamine, asparagine, threonine, and serine were eluted together and occurred in substantial amounts. γ-Hydroxyarginine constituted the largest fraction in the cut end exudate of Cuscuta and presumably appeared to be the major form of transport amino acid. γ-Hydroxyarginine was also a major constituent of the basic amino acids in Cuscuta vines parasitizing host plants from widely separated families, suggesting that this amino acid is a biosynthetic product of the parasite rather than that of the hosts. Also, U-14C arginine was converted to γ-hydroxyarginine by cut Cuscuta vines, suggesting that γ-hydroxyarginine is synthesized de novo from arginine by Cuscuta.

A Pd-6 Molecular Cage via Multicomponent Self-Assembly Incorporating Both Neutral and Anionic Linkers

A Pd-6 molecular cage [{(tmen)Pd}(6)(bpy)(3)(tma)2)](NO3)(6) [1; where tmen = N,N,N,N-tetramethylethylene diamine, bpy = 4,4'-bipyridyl,and H(3)tma = trimesic acid] was prepared via the template-free three-component seff-assembly of a cis-blocked palladium(II) acceptorin combination with a tricarboxylate and a dipyridyl donor. Complex 1 represents the first example of a 3D palladium(II) cage of defined shape incorporating anionic and neutral linkers. Guest-induced exclusive formation of this cage was also monitored by an NMR study.

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.

Uracil excision repair in Mycobacterium tuberculosis cell-free extracts

Uracil excision repair is ubiquitous in all domains of life and initiated by uracil DNA glycosylases (UDGs) which excise the promutagenic base, uracil, from DNA to leave behind an abasic site (AP-site). Repair of the resulting AP-sites requires an AP-endonuclease, a DNA polymerase, and a DNA ligase whose combined activities result in either short-patch or long-patch repair. Mycobacterium tuberculosis, the causative agent of tuberculosis, has an increased risk of accumulating uracils because of its G + C-rich genome, and its niche inside host macrophages where it is exposed to reactive nitrogen and oxygen species, two major causes of cytosine deamination (to uracil) in DNA. In vitro assays to study DNA repair in this important human pathogen are limited. To study uracil excision repair in mycobacteria, we have established assay conditions using cell-free extracts of M. tuberculosis and M. smegmatis (a fast-growing mycobacterium) and oligomer or plasmid DNA substrates. We show that in mycobacteria, uracil excision repair is completed primarily via long-patch repair. In addition, we show that M. tuberculosis UdgB, a newly characterized family 5 UDG, substitutes for the highly conserved family 1 UDG, Ung, thereby suggesting that UdgB might function as backup enzyme for uracil excision repair in mycobacteria. (C) 2011 Elsevier Ltd. All rights reserved.

Docking and free energy simulations to predict conformational domains involved in hCG-LH receptor interactions using recombinant antibodies

Single chain fragment variables (ScFvs) have been extensively employed in studying the protein-protein interactions. ScFvs derived from phage display libraries have an additional advantage of being generated against a native antigen, circumventing loss of information on conformational epitopes. In the present study, an attempt has been made to elucidate human chorionic gonadotropin (hCG)-luteinizing hormone (LH) receptor interactions by using a neutral and two inhibitory ScFvs against hCG. The objective was to dock a computationally derived model of these ScFvs onto the crystal structure of hCG and understand the differential roles of the mapped epitopes in hCG-LH receptor interactions. An anti-hCG ScFv, whose epitope was mapped previously using biochemical tools, served as the positive control for assessing the quality of docking analysis. To evaluate the role of specific side chains at the hCG-ScFv interface, binding free energy as well as residue interaction energies of complexes in solution were calculated using molecular mechanics Poisson-Boltzmann/surface area method after performing the molecular dynamic simulations on the selected hCG-ScFv models and validated using biochemical and SPR analysis. The robustness of these calculations was demonstrated by comparing the theoretically determined binding energies with the experimentally obtained kinetic parameters for hCG-ScFv complexes. Superimposition of hCG-ScFv model onto a model of hCG complexed with the 51-266 residues of LH receptor revealed importance of the residues previously thought to be unimportant for hormone binding and response. This analysis provides an alternate tool for understanding the structure-function analysis of ligand-receptor interactions. Proteins 2011;79:3108-3122. (C) 2011 Wiley-Liss, Inc.

Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.

Noise tolerance under risk minimization

In this paper, we explore noise-tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an unobservable training set that is noise free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper, we analyze the noise-tolerance properties of risk minimization (under different loss functions). We show that risk minimization under 0-1 loss function has impressive noise-tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude this paper with some discussion on the implications of these theoretical results.

Making risk minimization tolerant to label noise

In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in the presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the 0-1 loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to nonuniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the 0-1 loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm. (C) 2015 Elsevier B.V. All rights reserved.