Comment on "Chain Length Scaling of Protein Folding Time", PRL 77, 5433 (1996)

In a recent Letter, Gutin, Abkevich, and Shakhnovich (GAS) reported on a series of dynamical Monte Carlo simulations on lattice models of proteins. Based on these highly simplified models, they found that four different potential energies lead to four different folding time scales tau_f, where tau_f scales with chain length as N^lambda (see, also, Refs. [2-4]), with lambda varying from 2.7 to 6.0. However, due to the lack of microscopic models of protein folding dynamics, the interpretation and origin of the data have remained somewhat speculative. It is the purpose of this Comment to point out that the application of a simple "mesoscopic" model (cond-mat/9512019, PRL 77, 2324, 1996) of protein folding provides a full account of the data presented in their paper. Moreover, we find a major qualitative disagreement with the argumentative interpretation of GAS. Including, the origin of the dynamics, and size of the critical folding nucleus.Comment: 1 page Revtex, 1 fig. upon request. Submitted to PR

A Criterion That Determines Fast Folding of Proteins: A Model Study

We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular ($T_\theta$) and the folding ($T_f$) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as $\tau_f\sim F(M)\exp(\sigma/\sigma_0)$, where $\sigma=1-T_f/T_\theta$, $M$ is the number of residues, and $F(M)$ scales algebraically with $M$. We argue that $T_f$ scales linearly with the inverse of entropy of low energy non-native states, whereas $T_\theta$ is almost independent of it. As $\sigma\rightarrow 0$, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on {\it accessible} information, $\sigma$ can be used to predict sequences that fold rapidly.Comment: 10 pages, latex, figures upon reques

Quantum nondemolition measurements of a particle in electric and gravitational fields

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields are commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.Comment: Accepted in International Journal of Modern Physics D, 14 page

Spontaneous patterns in coherently driven polariton microcavities

We consider a polariton microcavity resonantly driven by two external lasers which simultaneously pump both lower and upper polariton branches at normal incidence. In this setup, we study the occurrence of instabilities of the pump-only solutions towards the spontaneous formation of patterns. Their appearance is a consequence of the spontaneous symmetry breaking of translational and rotational invariance due to interaction induced parametric scattering. We observe the evolution between diverse patterns which can be classified as single-pump, where parametric scattering occurs at the same energy as one of the pumps, and as two-pump, where scattering occurs at a different energy. For two-pump instabilities, stripe and chequerboard patterns become the dominant steady-state solutions because cubic parametric scattering processes are forbidden. This contrasts with the single-pump case, where hexagonal patterns are the most common arrangements. We study the possibility of controlling the evolution between different patterns. Our results are obtained within a linear stability analysis and are confirmed by finite size full numerical calculations.Comment: 15 pages, 9 figure

Low-distortion slow light using two absorption resonances

We consider group delay and broadening using two strongly absorbing and widely spaced resonances. We derive relations which show that very large pulse bandwidths coupled with large group delays and small broadening can be achieved. Unlike single resonance systems, the dispersive broadening dominates the absorptive broadening which leads to a dramatic increase in the possible group delay. We show that the double resonance systems are excellent candidates for realizing all-optical delay lines. We report on an experiment which achieved up to 50 pulse delays with 40% broadening.Comment: 4 pages 4 figure

Rapidly reconfigurable slow-light system based on off-resonant Raman absorption

We present a slow-light system based on dual Raman absorption resonances in warm rubidium vapor. Each Raman absorption resonance is produced by a control beam in an off-resonant Λ system. This system combines all optical control of the Raman absorption and the low-dispersion broadening properties of the double Lorentzian absorption slow light. The bandwidth, group delay, and central frequency of the slow-light system can all be tuned dynamically by changing the properties of the control beam. We demonstrate multiple pulse delays with low distortion and show that such a system has fast switching dynamics and thus fast reconfiguration rates

From Collapse to Freezing in Random Heteropolymers

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N_H (out ofN) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho_H=N_H/N. The average chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H --> 0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H < 1, entropy approaches zero as N --> infty (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R ~ N^nu) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.Comment: 4 pages, Revtex, figs upon request. New interpretation and emphasis. Submitted to Europhys.Let

A New Approach for Guaranteed State Estimation by Zonotopes

18th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2This paper proposes a methodology for guaranteed state estimation of linear discrete-time systems in the presence of bounded disturbances and noises. This aims at computing an outer approximation of the state estimation domain represented by a zonotope. A new criterion is used to reduce the size of the zonotope at each sample time. An illustrative example is analyzed in order to highlight the advantages of the proposed algorithm