The Degrees of Freedom of Partial Least Squares Regression

The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of Partial Least Squares Regression. Our contribution is an unbiased estimate of its Degrees of Freedom. It is defined as the trace of the first derivative of the fitted values, seen as a function of the response. We establish two equivalent representations that rely on the close connection of Partial Least Squares to matrix decompositions and Krylov subspace techniques. We show that the Degrees of Freedom depend on the collinearity of the predictor variables: The lower the collinearity is, the higher the Degrees of Freedom are. In particular, they are typically higher than the naive approach that defines the Degrees of Freedom as the number of components. Further, we illustrate how the Degrees of Freedom approach can be used for the comparison of different regression methods. In the experimental section, we show that our Degrees of Freedom estimate in combination with information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio

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

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.

Selective Constraints on Amino Acids Estimated by a Mechanistic Codon Substitution Model with Multiple Nucleotide Changes

Empirical substitution matrices represent the average tendencies of substitutions over various protein families by sacrificing gene-level resolution. We develop a codon-based model, in which mutational tendencies of codon, a genetic code, and the strength of selective constraints against amino acid replacements can be tailored to a given gene. First, selective constraints averaged over proteins are estimated by maximizing the likelihood of each 1-PAM matrix of empirical amino acid (JTT, WAG, and LG) and codon (KHG) substitution matrices. Then, selective constraints specific to given proteins are approximated as a linear function of those estimated from the empirical substitution matrices. Akaike information criterion (AIC) values indicate that a model allowing multiple nucleotide changes fits the empirical substitution matrices significantly better. Also, the ML estimates of transition-transversion bias obtained from these empirical matrices are not so large as previously estimated. The selective constraints are characteristic of proteins rather than species. However, their relative strengths among amino acid pairs can be approximated not to depend very much on protein families but amino acid pairs, because the present model, in which selective constraints are approximated to be a linear function of those estimated from the JTT/WAG/LG/KHG matrices, can provide a good fit to other empirical substitution matrices including cpREV for chloroplast proteins and mtREV for vertebrate mitochondrial proteins. The present codon-based model with the ML estimates of selective constraints and with adjustable mutation rates of nucleotide would be useful as a simple substitution model in ML and Bayesian inferences of molecular phylogenetic trees, and enables us to obtain biologically meaningful information at both nucleotide and amino acid levels from codon and protein sequences.Comment: Table 9 in this article includes corrections for errata in the Table 9 published in 10.1371/journal.pone.0017244. Supporting information is attached at the end of the article, and a computer-readable dataset of the ML estimates of selective constraints is available from 10.1371/journal.pone.001724

Fast stable direct fitting and smoothness selection for Generalized Additive Models

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of models, with failure being particularly frequent in the presence of concurvity. If smoothness selection is performed by optimizing `whole model' criteria these problems disappear, but until now attempts to do this have employed finite difference based optimization schemes which are computationally inefficient, and can suffer from false convergence. This paper develops the first computationally efficient method for direct GAM smoothness selection. It is highly stable, but by careful structuring achieves a computational efficiency that leads, in simulations, to lower mean computation times than the schemes based on working-model smoothness selection. The method also offers a reliable way of fitting generalized additive mixed models

Modulation of glycinergic transmission in the rat spinal dorsal commissural nucleus by ginkgolide B

The action of ginkgolide B (GB), the powerful compound of Ginkgo biloba extract, on glycinemediated spontaneous currents in rat spinal sacral dorsal commissural nucleus (SDCN) neurons was examined. IPSCs evoked in spinal cord slices were inhibited in a dose-dependent manner by the addition of GB to the superfusion solution. The amplitude of eIPSCs was reduced to 61 ± 6.4% by 10 μM GB, with acceleration of the kinetics of the currents indicating the effect of GB on channel pores. Both the amplitude and success ratio (Rsuc) of eIPSC induced by electrical focal stimulation of single glycinergic nerve endings (boutons) also decreased in the presence of 1 μM GB. These data suggest that GB modulates not only post-synaptic glycine receptors but also the pre-synaptic glycine release mac hinery.Вплив гінкголіду В (GB) – діючої сполуки екстракту з гінкго дволопатевого (Ginkgo biloba) на гліцинопосередковані синаптичні струми вивчався на нейронах спінального сакрального дорсального комісурального ядра (SDCN) щурів. Гальмівні постсинаптичні струми (ГПСС), викликані в препаратах зрізів спинного мозку, дозозалежно зменшувалися при аплікації GB. Амплітуда викликаних ГПСС під дією 10 мкМ GB падала до 61 ± 6.4 % з одночасним прискоренням кінетики струмів, що свідчило про наявність впливу на канальні пори. Як амплітуда, так і відносна кількість синаптичних подій (викликаних ГПСС), індукованих електричною фокальною стимуляцією поодиноких гліцинергічних нервових закінчень (бутонів), також зменшувались у присутності 1 мкМ GB. Ці результати свідчать, що GB не тільки модулює постсинаптичні гліцинові рецептори, але й впливає на пре синаптичні механізми вивільнення гліцину

Forecasting Player Behavioral Data and Simulating in-Game Events

Understanding player behavior is fundamental in game data science. Video games evolve as players interact with the game, so being able to foresee player experience would help to ensure a successful game development. In particular, game developers need to evaluate beforehand the impact of in-game events. Simulation optimization of these events is crucial to increase player engagement and maximize monetization. We present an experimental analysis of several methods to forecast game-related variables, with two main aims: to obtain accurate predictions of in-app purchases and playtime in an operational production environment, and to perform simulations of in-game events in order to maximize sales and playtime. Our ultimate purpose is to take a step towards the data-driven development of games. The results suggest that, even though the performance of traditional approaches such as ARIMA is still better, the outcomes of state-of-the-art techniques like deep learning are promising. Deep learning comes up as a well-suited general model that could be used to forecast a variety of time series with different dynamic behaviors