Matteo Palassini

Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two‐state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small‐loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two‐state kinetics, and it predicts well the average Φ‐values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.

Monte Carlo simulations of spin glasses at low temperatures

We report the results of Monte Carlo simulations on several spin-glass models at low temperatures. By using the parallel tempering (exchange Monte Carlo) technique we are able to equilibrate down to low temperatures, for moderate sizes, and hence the data should not be affected by critical fluctuations. Our results for short-range models are consistent with a picture proposed earlier that there are large-scale excitations which cost only a finite energy in the thermodynamic limit, and these excitations have a surface whose fractal dimension is less than the space dimension. For the infinite range Viana-Bray model, our results obtained for a similar number of spins, are consistent with standard replica symmetry breaking.

Nature of the spin glass state.

The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range Sherrington-Kirkpatrick (SK) and Viana-Bray models. Our results for the SK and Viana-Bray models agree with the replica symmetry breaking picture. The data for the short range models fit naturally a picture in which there are large scale excitations which cost a finite energy but whose surface has a fractal dimension, d(s), less than the space dimension d. We also discuss the possible crossover to other behavior at larger length scales than the sizes studied.

Universal Finite-Size Scaling Functions in the 3D Ising Spin Glass

We study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Monte Carlo data are extrapolated to infinite volume with an iterative procedure up to correlation lengths xi \approx 140. The infinite volume data are consistent with a conventional power law singularity at finite temperature Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015, nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an exponential singularity at finite Tc, but not with an exponential singularity at zero temperature.

Improving free-energy estimates from unidirectional work measurements: theory and experiment.

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the random energy model in a suitable scaling limit parametrized by (logN)/μ, where μ measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (logN)/μ. We show that these expressions describe accurately the bias for a wide class of work distributions and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding and refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.

Landscape of Solutions in Constraint Satisfaction Problems

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.

Triviality of the Ground State Structure in Ising Spin Glasses

We investigate the ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory. Similar results are also obtained in two dimensions. PACS numbers: 75.50.Lk, 05.70.Jk, 75.40.Mg, 77.80.Bh Controversy remains over the nature of ordering in spin glasses below the transition temperature, Tc, and two scenarios have been extensively discussed. In the “droplet model” proposed by Fisher and Huse [1] (see also Refs. [2 ‐ 5]), the structure of “pure states” is predicted to be trivial. This means that there is a unique state [6] in the sense that correlations of the spins in a region far from the boundaries are independent of the boundary conditions imposed. As a consequence, the order parameter distribution function [7‐ 9], Pq, is also trivial, i.e., is a pair of delta functions at q 6qEA where qEA is the Edwards-Anderson order parameter. In the alternative approach, one assumes that the basic structure of the Parisi [7 ‐ 9] solution of the infinite range model applies also to realistic short range systems. In this picture, Pq is a nontrivial function because many thermodynamic states contribute to the partition function; i.e., the pure state structure is nontrivial. Monte Carlo simulations on short range models on small lattices [10 ‐13] find a nontrivial Pq with a weight at q 0 which is independent of system size (for the range of sizes studied ), as predicted by the Parisi theory. Most numerical work has concentrated on Pq .B y contrast, here we attempt to determine the pure state structure by investigating whether spin correlation functions in a finite region [5] far from the boundary, change when the boundary conditions are changed. It is interesting to investigate this question even at T 0, where there are efficient algorithms for determining ground states, even though Pq is trivial in this limit (for a continuous bond distribution). Here we show that the Ising spin glass in three dimensions, which has a finite transition temperature [14 ‐17] Tc, has a trivial ground state structure. We also find a trivial ground state structure in the twodimensional Ising spin glass which has a transition at zero temperature with long range order at T 0. Some of our results in two dimensions have also been reported elsewhere, Palassini and Young (PY) [18]. Similar results for two dimensions, as well as results for some threedimensional models ( but none for a spin glass with a finite Tc), have also been found by Middleton [19]. The Hamiltonian is given by H 2 X i,j JijSiSj , (1)

Evidence for a trivial ground-state structure in the two-dimensional Ising spin glass

We study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from the boundary goes to zero with the (linear) size of the system L like L^{-lambda}, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to d-d_f where d (=2) is the dimension of the system and d_f is the fractal dimension of a domain wall induced by changes in the boundary conditions. Our value for d_f is consistent with earlier estimates. These results show that, at zero temperature, there is only a single pure state (plus the state with all spins flipped) in agreement with the predictions of the droplet model.

Ground state of the Bethe lattice spin glass and running time of an exact optimization algorithm

We study the Ising spin glass on random graphs with fixed connectivity z and with a Gaussian distribution of the couplings, with mean

Elementary excitations and avalanches in the Coulomb glass

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