The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in epsilon. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series

Discrete breathers in polyethylene chain

The existence of discrete breathers (DBs), or intrinsic localized modes (localized periodic oscillations of transzigzag) is shown. In the localization region periodic contraction-extension of valence C-C bonds occurs which is accompanied by decrease-increase of valence angles. It is shown that the breathers present in thermalized chain and their contribution dependent on temperature has been revealed.Comment: 5 pages, 6 figure

The stability of capillary waves on fluid sheets

The linear stability of finite amplitude capillary waves on inviscid sheets of fluid is investigated. A method similar to that recently used by Tiron & Choi (2012) to determine the stability of Crapper waves on fluid of infinite depth is developed by extending the conformal mapping technique of Dyachenko et al. (1996a) to a form capable of capturing general periodic waves on both the upper and the lower surface of the sheet, including the symmetric and antisymmetric waves studied by Kinnersley (1976). The primary, surprising result is that both symmetric and antisymmetric Kinnersley waves are unstable to small superharmonic disturbances. The waves are also unstable to subharmonic perturbations. Growth rates are computed for a range of steady waves in the Kinnersley family, and also waves found along the bifurcation branches identified by Blyth & Vanden-Broeck (2004). The instability results are corroborated by time integration of the fully nonlinear unsteady equations. Evidence is presented for superharmonic instability of nonlinear waves via a collision of eigenvalues on the imaginary axis which appear to have the same Krein signature

A detailed binding free energy study of 2 : 1 ligand–DNA complex formation by experiment and simulation

In 2004, we used NMR to solve the structure of the minor groove binder thiazotropsin A bound in a 2 : 1 complex to the DNA duplex, d(CGACTAGTCG)2. In this current work, we have combined theory and experiment to confirm the binding thermodynamics of this system. Molecular dynamics simulations that use polarizable or non-polarizable force fields with single and separate trajectory approaches have been used to explore complexation at the molecular level. We have shown that the binding process invokes large conformational changes in both the receptor and ligand, which is reflected by large adaptation energies. This is compensated for by the net binding free energy, which is enthalpy driven and entropically opposed. Such a conformational change upon binding directly impacts on how the process must be simulated in order to yield accurate results. Our MM-PBSA binding calculations from snapshots obtained from MD simulations of the polarizable force field using separate trajectories yield an absolute binding free energy (-15.4 kcal mol-1) very close to that determined by isothermal titration calorimetry (-10.2 kcal mol-1). Analysis of the major energy components reveals that favorable non-bonded van der Waals and electrostatic interactions contribute predominantly to the enthalpy term, whilst the unfavorable entropy appears to be driven by stabilization of the complex and the associated loss of conformational freedom. Our results have led to a deeper understanding of the nature of side-by-side minor groove ligand binding, which has significant implications for structure-based ligand development

Stability of non-time-reversible phonobreathers

Non-time reversible phonobreathers are non-linear waves that can transport energy in coupled oscillator chains by means of a phase-torsion mechanism. In this paper, the stability properties of these structures have been considered. It has been performed an analytical study for low-coupling solutions based upon the so called {\em multibreather stability theorem} previously developed by some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms the analytical predictions and gives a detailed picture of the existence and stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010

Surface-plasmon-polariton wave propagation supported by anisotropic materials: multiple modes and mixed exponential and linear localization characteristics

The canonical boundary-value problem for surface-plasmon-polariton (SPP) waves guided by the planar interface of a dielectric material and a plasmonic material was solved for cases wherein either partnering material could be a uniaxial material with optic axis lying in the interface plane.Numerical studies revealed that two different SPP waves, with different phase speeds, propagation lengths, and penetration depths, can propagate in a given direction in the interface plane; in contrast, the planar interface of isotropic partnering materials supports only one SPP wave for each propagation direction. Also, for a unique propagation direction in each quadrant of the interface plane, it was demonstrated that a new type of SPP wave--called a surface-plasmon-polariton-Voigt (SPP-V) wave--can exist. The fields of these SPP-V waves decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic partnering material; in contrast, the fields of conventional SPP waves decay only exponentially with distance from the interface. Explicit analytic solutions of the dispersion relation for SPP-V waves exist and help establish constraints on the constitutive-parameter regimes for the partnering materials that support SPP-V-wave propagation

The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.Comment: 35 pages, 4 figure

Tomography increases key rates of quantum-key-distribution protocols

We construct a practically implementable classical processing for the BB84 protocol and the six-state protocol that fully utilizes the accurate channel estimation method, which is also known as the quantum tomography. Our proposed processing yields at least as high key rate as the standard processing by Shor and Preskill. We show two examples of quantum channels over which the key rate of our proposed processing is strictly higher than the standard processing. In the second example, the BB84 protocol with our proposed processing yields a positive key rate even though the so-called error rate is higher than the 25% limit.Comment: 13 pages, 1 figure, REVTeX4. To be published in PRA. Version 2 adds many references, a closed form key rate formula for unital channels, and a procedure for the maximum likelihood channel estimatio