Microscopic Theory of Protein Folding Rates.I: Fine Structure of the Free Energy Profile and Folding Routes from a Variational Approach

A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G. Wolynes, Phys. Rev. Lett. {\bf 81}, 5237 (1998)]. We choose the $\lambda$-repressor protein as an illustrative example and focus on how the polymer chain statistics influence free energy profiles and partially ordered ensembles of structures. In particular, we investigate the role of chain stiffness on the free energy profile and folding routes. We evaluate the applicability of simpler approximations in which the conformations of the protein molecule along the folding route are restricted to have residues that are either entirely folded or unfolded in contiguous stretches. We find that the folding routes obtained from only one contiguous folded region corresponds to a chain with a much greater persistence length than appropriate for natural protein chains, while the folding route obtained from two contiguous folded regions is able to capture the relatively folded regions calculated within the variational approach. The free energy profiles obtained from the contiguous sequence approximations have larger barriers than the more microscopic variational theory which is understood as a consequence of partial ordering.Comment: 16 pages, 11 figure

High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.Comment: 15 pages, 9 figures, uses revte

Quantum annealing and the Schr\"odinger-Langevin-Kostin equation

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schr\"odinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.Comment: 5 pages, 4 figures. To appear on Physical Review

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.

The double mass hierarchy pattern: simultaneously understanding quark and lepton mixing

The charged fermion masses of the three generations exhibit the two strong hierarchies m_3 >> m_2 >> m_1. We assume that also neutrino masses satisfy m_{nu 3} > m_{nu 2} > m_{nu 1} and derive the consequences of the hierarchical spectra on the fermionic mixing patterns. The quark and lepton mixing matrices are built in a general framework with their matrix elements expressed in terms of the four fermion mass ratios m_u/m_c, m_c/m_t, m_d/m_s, and m_s/m_b and m_e/m_mu, m_mu/m_tau, m_{nu 1}/m_{nu 2}, and m_{nu 2}/m_{nu 3}, for the quark and lepton sector, respectively. In this framework, we show that the resulting mixing matrices are consistent with data for both quarks and leptons, despite the large leptonic mixing angles. The minimal assumption we take is the one of hierarchical masses and minimal flavour symmetry breaking that strongly follows from phenomenology. No special structure of the mass matrices has to be assumed that cannot be motivated by this minimal assumption. This analysis allows us to predict the neutrino mass spectrum and set the mass of the lightest neutrino well below 0.01 eV. The method also gives the 1 sigma allowed ranges for the leptonic mixing matrix elements. Contrary to the common expectation, leptonic mixing angles are found to be determined solely by the four leptonic mass ratios without any relation to symmetry considerations as commonly used in flavor model building. Still, our formulae can be used to build up a flavor model that predicts the observed hierarchies in the masses---the mixing follows then from the procedure which is developed in this work.Comment: 28 pages, 3 figures, 4 tables; v2: references added, Appendix C added, additional clarification and explanations in Sec. 2; matches version accepted by Nucl. Phys.

Quantum Cognition based on an Ambiguous Representation Derived from a Rough Set Approximation

Over the last years, in a series papers by Arrechi and others, a model for the cognitive processes involved in decision making has been proposed and investigated. The key element of this model is the expression of apprehension and judgement, basic cognitive process of decision making, as an inverse Bayes inference classifying the information content of neuron spike trains. For successive plural stimuli, it has been shown that this inference, equipped with basic non-algorithmic jumps, is affected by quantum-like characteristics. We show here that such a decision making process is related consistently with ambiguous representation by an observer within a universe of discourse. In our work ambiguous representation of an object or a stimuli is defined by a pair of maps from objects of a set to their representations, where these two maps are interrelated in a particular structure. The a priori and a posteriori hypotheses in Bayes inference are replaced by the upper and lower approximation, correspondingly, for the initial data sets each derived with respect to a map. We show further that due to the particular structural relation between the two maps, the logical structure of such combined approximations can only be expressed as an orthomodular lattice and therefore can be represented by a quantum rather than a Boolean logic. To our knowledge, this is the first investigation aiming to reveal the concrete logic structure of inverse Bayes inference in cognitive processes.Comment: 23 pages, 8 figures, original research pape