Utility of su(1,1)-Algebra in a Schematic Nuclear su(2)-Model

The su(2)-algebraic model interacting with an environment is investigated from a viewpoint of treating the dissipative system. By using the time-dependent variational approach with a coherent state and with the help of the canonicity condition, the time-evolution of this quantum many-body system is described in terms of the canonical equations of motion in the classical mechanics. Then, it is shown that the su(1,1)-algebra plays an essential role to deal with this model. An exact solution with appropriate initial conditions is obtained by means of Jacobi's elliptic function. The implication to the dissipative process is discussed.Comment: 14 pages using PTPTeX.st

Fermi level pinning induced electrostatic fields and band bending at organic heterojunctions

The energy level alignment at interfaces between organic semiconductors is of direct relevance to understand charge carrier generation and recombination in organic electronic devices. Commonly, work function changes observed upon interface formation are interpreted as interface dipoles. In this study, using ultraviolet and X ray photoelectron spectroscopy, complemented by electrostatic calculations, we find a huge work function decrease of up to 1.4 amp; 8201;eV at the C60 bottom layer zinc phthalocyanine ZnPc, top layer interface prepared on a molybdenum trioxide MoO3 substrate. However, detailed measurements of the energy level shifts and electrostatic calculations reveal that no interface dipole occurs. Instead, upon ZnPc deposition, a linear electrostatic potential gradient is generated across the C60 layer due to Fermi level pinning of ZnPc on the high work function C60 MoO3 substrate, and associated band bending within the ZnPc layer. This finding is generally of importance for understanding organic heterojunctions when Fermi level pinning is involved, as induced electrostatic fields alter the energy level alignment significantl

GABA(A) receptor phospho-dependent modulation is regulated by phospholipase C-related inactive protein type 1, a novel protein phosphatase 1 anchoring protein

GABA(A) receptors are critical in controlling neuronal activity. Here, we examined the role for phospholipase C-related inactive protein type 1 (PRIP-1), which binds and inactivates protein phosphatase 1alpha (PP1alpha) in facilitating GABA(A) receptor phospho-dependent regulation using PRIP-1(-/-) mice. In wild-type animals, robust phosphorylation and functional modulation of GABA(A) receptors containing beta3 subunits by cAMP-dependent protein kinase was evident, which was diminished in PRIP-1(-/-) mice. PRIP-1(-/-) mice exhibited enhanced PP1alpha activity compared with controls. Furthermore, PRIP-1 was able to interact directly with GABA(A) receptor beta subunits, and moreover, these proteins were found to be PP1alpha substrates. Finally, phosphorylation of PRIP-1 on threonine 94 facilitated the dissociation of PP1alpha-PRIP-1 complexes, providing a local mechanism for the activation of PP1alpha. Together, these results suggest an essential role for PRIP-1 in controlling GABA(A) receptor activity via regulating subunit phosphorylation and thereby the efficacy of neuronal inhibition mediated by these receptors

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

Probability Models for Degree Distributions of Protein Interaction Networks

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad-hoc fashion, with clear power-law like behaviour often only extending over a limited range of connectivities. Here we apply formal model selection techniques to decide which probability distribution best describes the degree distributions of protein interaction networks. Contrary to previous studies this well defined approach suggests that the degree distribution of many molecular networks is often better described by distributions other than the popular power-law distribution. This, in turn, suggests that simple, if elegant, models may not necessarily help in the quantitative understanding of complex biological processes.

Model selection in High-Dimensions: A Quadratic-risk based approach

In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a nonnegative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a quick-to-compute approximation for the risk function. Its derivation is analogous to the Akaike Information Criterion (AIC), but unlike AIC, the quadratic risk is a global comparison tool. The method does not require resampling, a great advantage when point estimators are expensive to compute. The method is illustrated using the problem of selecting the number of components in a mixture model, where it is shown that, by using an appropriate kernel, the method is computationally straightforward in arbitrarily high data dimensions. In this same context it is shown that the method has some clear advantages over AIC and BIC.Comment: Updated with reviewer suggestion

Prediction and Generation of Binary Markov Processes: Can a Finite-State Fox Catch a Markov Mouse?

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.Comment: 12 pages, 12 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/gmc.ht

Information criteria for inhomogeneous spatial point processes

The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For inhomogeneous Poisson processes we consider Akaike information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of sample size needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.Comment: 6 figure

Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

Large-scale structure of time evolving citation networks

In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers, patents, or court cases. We describe three different methods of analysis, one based on an expectation-maximization algorithm, one based on modularity optimization, and one based on eigenvector centrality. Using the network of citations between opinions of the United States Supreme Court as an example, we demonstrate how each of these methods can reveal significant structural divisions in the network, and how, ultimately, the combination of all three can help us develop a coherent overall picture of the network's shape.Comment: 10 pages, 6 figures; journal names for 4 references fixe