Approximation of the Posterior Distribution in a Change-Point Problem

We consider a family of models that arise in connection with sharp change in hazard rate corresponding to high initial hazard rate dropping to a more stable or slowly changing rate at an unknown change-point . Although the Bayes estimates are well behaved and are asymptotically efficient, it is difficult to compute them as the posterior distributions are generally very complicated. We obtain a simple first order asymptotic approximation to the posterior distribution of . The accuracy of the approximation is judged through simulation. The approximation performs quite well. Our method is also applied to analyze a real data set.     

Information and Entropy Flow in the Kalman–Bucy Filter

We investigate the information theoretic properties of Kalman–Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract universe comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman–Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauers Principle.     

Cover Picture

The cover picture shows how thrombosis occurs in the deep veins of the lower limbs. Stasis, which results from slow and turbulent blood flow, combined with hypercoagulation, caused, for example, by a surgical procedure, may result in thrombus formation. The synthetic sulfated pentasaccharide shown in part is a potent antithrombotic compound that exerts its effect by activation of the plasma protein antithrombin III. Conformationally locked monosaccharides have now been synthesized to demonstrate that L-iduronic acid, one part of the pentasaccharide, must adopt an unusual distorted conformation to activate antithrombin III. Such conformational effects might be relevant in explaining the unique biological properties of glycosaminoglycans that contain L-iduronic acid. In the background of the picture, a flight of vampire bats is attracted by the pentasaccharide. Vampire was the name given to South American blood-sucking bats (Latin name: desmodus rotundus) in 1761 by the French naturalist Georges Louis Leclerc Comte de Buffon (1707-1788). These bats are known to attack cattle and, very rarely, sleeping human beings. Although their saliva has been shown to contain an anticoagulant compound, they would also be happy to benefit from the pentasaccharide mentioned above, to suck the blood out of the vein more easily. More details about this compound which would be helpful to vampire bats are reported by Petitou, Sina? et al. on p. 1670 ff.     

An efficient total synthesis of the anticancer agent (+)-spisulosine (ES-285) from Garner’s aldehyde

An efficient total synthesis of (+)-spisulosine (ES-285) was completed in nine steps from (S)-Garner’s aldehyde. The vicinal amino alcohol moiety with anti-configuration was achieved by a highly diastereoselective addition of vinyl magnesium bromide to Garner’s aldehyde. The long hydrocarbon chain of the antitumor natural product was installed via olefin cross metathesis of the benzyl-protected allylic alcohol with an appropriate olefin counterpart followed by hydrogenation.     

Beyond the standard model: Working group report

This report summarises the activities of the working group on ‘Physics beyond the Standard Model’. The results of investigations in incorporatingR-parity in grand unification, the possibility of a light charged Higgs boson in extension of MSSM and radiative generation of neutral vector boson self-couplings within the MSSM are described. Also given is an account of activities in neutrino physics, namely a proposal for a study of the atmospheric muon anomaly in deep underground mines, a field theoretic study of neutrino oscillations and a mechanism to generate appropriate masses of three active plus one sterile neutrino species.     

Conformational fluctuations of a protein-DNA complex and the structure and ordering of water around it

Protein-DNA binding is an important process responsible for the regulation of genetic activities in living organisms. The most crucial issue in this problem is how the protein recognizes the DNA and identifies its target base sequences. Water molecules present around the protein and DNA are also expected to play an important role in mediating the recognition process and controlling the structure of the complex. We have performed atomistic molecular dynamics simulations of an aqueous solution of the protein-DNA complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. The conformational fluctuations of the protein and DNA and the microscopic structure and ordering of water around them in the complex have been explored. In agreement with experimental studies, the calculations reveal conformational immobilization of the terminal segments of the protein on complexation. Importantly, it is discovered that both structural adaptations of the protein and DNA, and the subsequent correlation between them to bind, contribute to the net entropy loss associated with the complex formation. Further, it is found that water molecules around the DNA are more structured with significantly higher density and ordering than that around the protein in the complex.     

Dynamic properties of water around a protein-DNA complex from molecular dynamics simulations

Formation of protein-DNA complex is an important step in regulation of genes in living organisms. One important issue in this problem is the role played by water in mediating the protein-DNA interactions. In this work, we have carried out atomistic molecular dynamics simulations to explore the heterogeneous dynamics of water molecules present in different regions around a complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. It is demonstrated that such heterogeneous water motions around the complex are correlated with the relaxation time scales of hydrogen bonds formed by those water molecules with the protein and DNA. The calculations reveal the existence of a fraction of extraordinarily restricted water molecules forming a highly rigid thin layer in between the binding motifs of the protein and DNA. It is further proved that higher rigidity of water layers around the complex originates from more frequent reformations of broken water-water hydrogen bonds. Importantly, it is found that the formation of the complex affects the transverse and longitudinal degrees of freedom of surrounding water molecules in a nonuniform manner.     

Wiener–Tauberian type theorems for radial sections of homogenous vector bundles on certain rank one Riemannian symmetric spaces of noncompact type

We will show that an uniform treatment yields Wiener–Tauberian type results for various Banach algebras and modules consisting of radial sections of some homogenous vector bundles on rank one Riemannian symmetric spaces G/K of noncompact type. One example of such a vector bundle is the spinor bundle. The algebras and modules we consider are natural generalizations of the commutative Banach algebra of integrable radial functions on G/K. The first set of them are Beurling algebras with analytic weights, while the second set arises due to Kunze–Stein phenomenon for noncompact semisimple Lie groups.     

Polypyrazolylborate analogues without boron: Structural diversity in ligand design and metal complexes

Structural chemistry of organometallic complexes containing pyrazolederived polydentate ligands (without boron) has been reviewed in the context of current results from this laboratory. NCL Communication No. 6137     

Complete Convergence of Martingale Arrays

We study complete convergence of martingale arrays under rather weak conditions. Our results considerably strengthen many of the results available in the literature. As a tool, we establish a martingale analogue of an inequality of Hoffman-Jørgensen which was earlier known only for independent random variables.