Processing and Transmission of Information

Contains reports on three research projects.Lincoln Laboratory, Purchase Order DDL B-00368U. S. ArmyU. S. NavyU. S. Air Force under Air Force Contract AF19(604)-7400National Institutes of Health (Grant MH-04737-03)National Science Foundation (Grant G-16526

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

Computing the broadband vibroacoustic response of arbitrarily thick layered panels by a wave finite element approach

A robust procedure for the prediction of the dynamic response of layered panels within a SEA wave-context approach is proposed hereby. The dispersion characteristics of two dimensional composite orthotropic structures are predicted using a Wave Finite Element method. By manipulating the mass and stiffness matrices of the modelled structural segment a polynomial eigenvalue problem is formed, the solutions of which correspond to the propagation constants of the waves travelling within the structure. The wavenumbers and group velocities for waves comprising out of plane structural displacements can then be calculated. Using the numerically extracted wave propagation data the most important SEA quantities of the structure, namely the modal density and the radiation efficiency of each wave type are calculated. The vibroacoustic response of the structure under a broadband diffused excitation is then computed within a SEA approach. The impact of the symmetric and the antisymmetric vibrational motion of the panel on its sound transmission loss is exhibited and the approach proves robust enough for thin as well as for thick layered structures

Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems

The phenomenon of super-radiance (Dicke effect, coherent spontaneous radiation by a gas of atoms coupled through the common radiation field) is well known in quantum optics. The review discusses similar physics that emerges in open and marginally stable quantum many-body systems. In the presence of open decay channels, the intrinsic states are coupled through the continuum. At sufficiently strong continuum coupling, the spectrum of resonances undergoes the restructuring with segregation of very broad super-radiant states and trapping of remaining long-lived compound states. The appropriate formalism describing this phenomenon is based on the Feshbach projection method and effective non-Hermitian Hamiltonian. A broader generalization is related to the idea of doorway states connecting quantum states of different structure. The method is explained in detail and the examples of applications are given to nuclear, atomic and particle physics. The interrelation of the collective dynamics through continuum and possible intrinsic many-body chaos is studied, including universal mesoscopic conductance fluctuations. The theory serves as a natural framework for general description of a quantum signal transmission through an open mesoscopic system.Comment: 85 pages, 10 figure

Using Multiple Microenvironments to Find Similar Ligand-Binding Sites: Application to Kinase Inhibitor Binding

The recognition of cryptic small-molecular binding sites in protein structures is important for understanding off-target side effects and for recognizing potential new indications for existing drugs. Current methods focus on the geometry and detailed chemical interactions within putative binding pockets, but may not recognize distant similarities where dynamics or modified interactions allow one ligand to bind apparently divergent binding pockets. In this paper, we introduce an algorithm that seeks similar microenvironments within two binding sites, and assesses overall binding site similarity by the presence of multiple shared microenvironments. The method has relatively weak geometric requirements (to allow for conformational change or dynamics in both the ligand and the pocket) and uses multiple biophysical and biochemical measures to characterize the microenvironments (to allow for diverse modes of ligand binding). We term the algorithm PocketFEATURE, since it focuses on pockets using the FEATURE system for characterizing microenvironments. We validate PocketFEATURE first by showing that it can better discriminate sites that bind similar ligands from those that do not, and by showing that we can recognize FAD-binding sites on a proteome scale with Area Under the Curve (AUC) of 92%. We then apply PocketFEATURE to evolutionarily distant kinases, for which the method recognizes several proven distant relationships, and predicts unexpected shared ligand binding. Using experimental data from ChEMBL and Ambit, we show that at high significance level, 40 kinase pairs are predicted to share ligands. Some of these pairs offer new opportunities for inhibiting two proteins in a single pathway

Structural Basis for the Aminoacid Composition of Proteins from Halophilic Archea

In order to survive in highly saline environments, proteins from halophilic archea have evolved with biased amino acid compositions that have the capacity to reduce contacts with the solvent