Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution

The absorption spectrum of the MnO$_{4}$$^{-}$ ion has been a test-bed for quantum-chemical methods over the last decades. Its correct description requires highly-correlated multiconfigurational methods, which are incompatible with the inclusion of finite-temperature and solvent effects due to their high computational demands. Therefore, implicit solvent models are usually employed. Here we show that implicit solvent models are not sufficiently accurate to model the solvent shift of MnO$_{4}$$^{-}$, and we analyze the origins of their failure. We obtain the correct solvent shift for MnO$_{4}$$^{-}$ in aqueous solution by employing the polarizable embedding (PE) model combined with a range-separated complete active space short-range density functional theory method (CAS-srDFT). Finite-temperature effects are taken into account by averaging over structures obtained from ab initio molecular dynamics simulations. The explicit treatment of finite-temperature and solvent effects facilitates the interpretation of the bands in the low-energy region of the MnO$_{4}$$^{-}$ absorption spectrum, whose assignment has been elusive.Comment: 15 pages, 3 tables, 1 Figur

Warm Inflation and its Microphysical Basis

The microscopic quantum field theory origins of warm inflation dynamics are reviewed. The warm inflation scenario is first described along with its results, predictions and comparison with the standard cold inflation scenario. The basics of thermal field theory required in the study of warm inflation are discussed. Quantum field theory real time calculations at finite temperature are then presented and the derivation of dissipation and stochastic fluctuations are shown from a general perspective. Specific results are given of dissipation coefficients for a variety of quantum field theory interaction structures relevant to warm inflation, in a form that can readily be used by model builders. Different particle physics models realising warm inflation are presented along with their observational predictions.Comment: 34 pages, 8 figures. Invited review article for Reports on Progress in Physics, In Press 200

Kinetic model of DNA replication in eukaryotic organisms

We formulate a kinetic model of DNA replication that quantitatively describes recent results on DNA replication in the in vitro system of Xenopus laevis prior to the mid-blastula transition. The model describes well a large amount of different data within a simple theoretical framework. This allows one, for the first time, to determine the parameters governing the DNA replication program in a eukaryote on a genome-wide basis. In particular, we have determined the frequency of origin activation in time and space during the cell cycle. Although we focus on a specific stage of development, this model can easily be adapted to describe replication in many other organisms, including budding yeast.Comment: 10 pages, 6 figures: see also cond-mat/0306546 & physics/030615

Pascal’s wager and the origins of decision theory: decision-making by real decision-makers

Pascal’s Wager does not exist in a Platonic world of possible gods, abstract probabilities and arbitrary payoffs. Real decision-makers, such as Pascal’s “man of the world” of 1660, face a range of religious options they take to be serious, with fixed probabilities grounded in their evidence, and with utilities that are fixed quantities in actual minds. The many ingenious objections to the Wager dreamed up by philosophers do not apply in such a real decision matrix. In the situation Pascal addresses, the Wager is a good bet. In the situation of a modern Western intellectual, the reasoning of the Wager is still powerful, though the range of options and the actions indicated are not the same as in Pascal’s day

Origins of the Combinatorial Basis of Entropy

The combinatorial basis of entropy, given by Boltzmann, can be written $H = N^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy, $N$ is the number of entities and $\mathbb{W}$ is number of ways in which a given realization of a system can occur (its statistical weight). This can be broadened to give generalized combinatorial (or probabilistic) definitions of entropy and cross-entropy: $H=\kappa (\phi(\mathbb{W}) +C)$ and $D=-\kappa (\phi(\mathbb{P}) +C)$, where $\mathbb{P}$ is the probability of a given realization, $\phi$ is a convenient transformation function, $\kappa$ is a scaling parameter and $C$ an arbitrary constant. If $\mathbb{W}$ or $\mathbb{P}$ satisfy the multinomial weight or distribution, then using $\phi(\cdot)=\ln(\cdot)$ and $\kappa=N^{-1}$, $H$ and $D$ asymptotically converge to the Shannon and Kullback-Leibler functions. In general, however, $\mathbb{W}$ or $\mathbb{P}$ need not be multinomial, nor may they approach an asymptotic limit. In such cases, the entropy or cross-entropy function can be {\it defined} so that its extremization ("MaxEnt'' or "MinXEnt"), subject to the constraints, gives the ``most probable'' (``MaxProb'') realization of the system. This gives a probabilistic basis for MaxEnt and MinXEnt, independent of any information-theoretic justification. This work examines the origins of the governing distribution $\mathbb{P}$.... (truncated)Comment: MaxEnt07 manuscript, version 4 revise