Modelling the Biomacromolecular Structure with Selected Combinatorial Optimization Techniques

Modern approaches to the search of Relative and Global minima of potential energy function of Biomacromolecular structures include techniques of combinatorial optimization like the study of Steiner Points and Steiner Trees. These methods have been successfully applied to the problem of modelling the configurations of the average atomic positions when they are disposed in the usual sequence of evenly spaced points along right circular helices. In the present contribution, we intend to show how these methods can be adapted for explaining the advantages of introducing the concept of a Steiner Ratio Function (SRF). We also show how this new concept is adequate for fitting the results obtained by computing experiments and for providing an improvement to these results if we use the restriction of working with Full Steiner Trees.Comment: 12 pages, 5 figures; typo correcte

A Combinatorial Optimization Approach to the Stability of Biomacromolecular Structures

The application of optimization techniques derived from the study of Euclidean full Steiner Trees to macromolecules like proteins is reported in the present work. We shall use the concept of Euclidean Steiner Ratio Function (SRF) as a good Lyapunov function in order to perform an elementary stability analysis.Comment: 13 pages, 4 figure

Magnetic and metal-insulator transitions in coupled spin-fermion systems

We use quantum Monte Carlo to determine the magnetic and transport properties of coupled square lattice spin and fermionic planes as a model for a metal-insulator interface. Specifically, layers of Ising spins with an intra-layer exchange constant $J$ interact with the electronic spins of several adjoining metallic sheets via a coupling $J_H$. When the chemical potential cuts across the band center, that is, at half-filling, the N\'eel temperature of antiferromagnetic ($J>0$) Ising spins is enhanced by the coupling to the metal, while in the ferromagnetic case ($J<0$) the metallic degrees of freedom reduce the ordering temperature. In the former case, a gap opens in the fermionic spectrum, driving insulating behavior, and the electron spins also order. This induced antiferromagnetism penetrates more weakly as the distance from the interface increases, and also exhibits a non-monotonic dependence on $J_H$. For doped lattices an interesting charge disproportionation occurs where electrons move to the interface layer to maintain half-filling there.Comment: 12 pages, 15 figure

Dynamical localization and the effects of aperiodicity in Floquet systems

We study the localization aspects of a kicked non-interacting one-dimensional (1D) quantum system subject to either time-periodic or non-periodic pulses. These are reflected as sudden changes of the onsite energies in the lattice with different modulations in real space. When the modulation of the kick is incommensurate with the lattice spacing, and the kicks are periodic, a well known dynamical localization in real space is recovered for large kick amplitudes and frequencies. We explore the universality class of this transition and also test the robustness of localization under deviations from the perfect periodic case. We show that delocalization ultimately sets in and a diffusive spreading of an initial wave packet is obtained when the aperiodicity of the driving is introduced.Comment: 9 pages, 8 figures, as publishe

The Protein Family Classification in Protein Databases via Entropy Measures

In the present work, we review the fundamental methods which have been developed in the last few years for classifying into families and clans the distribution of amino acids in protein databases. This is done through functions of random variables, the Entropy Measures of probabilities of occurrence of the amino acids. An intensive study of the Pfam databases is presented with restrictions to families which could be represented by rectangular arrays of amino acids with m rows (protein domains) and n columns (amino acids). This work is also an invitation to scientific research groups worldwide to undertake the statistical analysis with different numbers of rows and columns since we believe in the mathematical characterization of the distribution of amino acids as a fundamental insight on the determination of protein structure and evolution

Determinant Quantum Monte Carlo Study of the Enhancement of d-wave Pairing by Charge Inhomogeneity

Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO_2 planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two dimensional Hubbard Hamiltonian. In this paper we use determinant Quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the d-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearence of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a \pi-phase shift in the magnetic order.Comment: 10 pages, 16 figures To appear in Phys. Rev.

Eigenstate thermalization in the two-dimensional transverse field Ising model

We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two non-equivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. A finite size scaling analysis reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.Comment: 10 pages, 10 figures, as publishe

Determinant Quantum Monte Carlo Study of d-wave pairing in the Plaquette Hubbard Hamiltonian

Determinant Quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters -a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping $t$ and on-site repulsion $U$ coupled by an inter-plaquette hopping $t' \leq t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For $U/t=4$, DQMC indicates an optimal $t'/t \approx 0.4$ at which the pairing vertex is most attractive. The optimal $t'/t$ increases with $U/t$. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO$_2$ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.Comment: 13 pages, 19 figure

Viral Evolution and Adaptation as a Multivariate Branching Process

In the present work we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process in close relation with the branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. We show that in the absence of beneficial forces the model is exactly solvable. As a result it is possible to prove several key results directly related to known typical properties of these systems like (i) proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939); (ii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation and (iii) the quantitative description of the evolution of the expected values in four distinct regimes: transient, "stationary" equilibrium, extinction threshold and lethal mutagenesis. Moreover, new insights on the dynamics of evolving virus populations can be foreseen.Comment: 39 pages, 3 figures. International Symposium on Mathematical and Computational Biology, Tempe, Arizona, USA, 6 - 10 November 2012. Fernando Antoneli, Francisco Bosco, Diogo Castro, And Luiz Mario Janini (2013) Viral Evolution and Adaptation as a Multivariate Branching Process. Biomat 2012: pp. 217-243. Ed.: R. P. Mondaini. World Scientific, Singapor

Intramolecular Structure of Proteins as driven by Steiner Optimization Problems

In this work we intend to report on some results obtained by an analytical modelling of biomacromolecular structures as driven by the study of Steiner points and Steiner trees with an Euclidean definition of distance.Comment: 2 page