Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS₅ braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact five-dimensional warped solutions which are associated with conformal bulk fields of weight –4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.     

Abelian Ward identity from the background field dependence of the effective action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We show that for Abelian theories the Ward identity follows from the more general background field identity. This observation is relevant for the formulation of effective actions with an infrared cutoff since the solution of exact flow equations must obey an anomalous Ward identity.     

A highly specific polyclonal antiserum to the environmental contaminant 1,1,1-trichloro-2,2-bis-(4-chlorophenyl)-ethane (p,p′-DDT)

A very selective polyclonal antiserum against 1,1,1-trichloro-2,2-bis-(4-chlorophenyl)-ethane (p,p′-DDT) was obtained by a careful choice of the haptenic structure (2,2-bis(4-chlorophenyl)-ethanol hemisuccinate). This hapten was conjugated to BSA to prepare the immunogen. The effects of different types of solid phases on the equilibrium reaction between the hapten on solid phase and the polyclonal antiserum were evaluated to obtain a fine tuning of the antiserum performances in terms of specificity for p,p′-DDT and sensitivity to low levels of this pesticide. The calibration curves obtained show that it is possible to set up a sensitive assay for p,p′-DDT, employing a p,p′-dichlorodiphenylacetic acid-based solid phase, with a detection limit of 0.12 ng/mL and a working range of about 0.21–40 ng/mL. Selectivity towards several p,p′-DDT-related substances was good (o,p-DDT 17%, p,p′-DDD 1.2% o,p-DDD 6.3%, p,p′-DDE 6.7%).     

Automorphism groups of compact planar Klein surfaces

By a compact Klein surface X, we shall mean a compact surface together with a dianalytic structure on X [1]. A dianalytic homeomorphism of X onto itself will be called an automorphism of X, and we call the automorphism group of X, the full group of automorphisms of X.In this paper we calculate all groups that are the automorphism group of a compact planar Klein surface of algebraic genus p2. As a consequence of the equivalence between compact bordered Klein surfaces and real algebraic curves, we calculate all groups that are the automorphism group of an M-real algebraic curve. Some results on automorphism groups of Riemann surfaces of M-curves were obtained by Natanzon in [14].Partially supported by CAICYT (2280/83)     

Temperature weighted histogram analysis method, replica exchange, and transition paths

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.