Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

Dynamics of earthquake nucleation process represented by the Burridge-Knopoff model

Dynamics of earthquake nucleation process is studied on the basis of the one-dimensional Burridge-Knopoff (BK) model obeying the rate- and state-dependent friction (RSF) law. We investigate the properties of the model at each stage of the nucleation process, including the quasi-static initial phase, the unstable acceleration phase and the high-speed rupture phase or a mainshock. Two kinds of nucleation lengths L_sc and L_c are identified and investigated. The nucleation length L_sc and the initial phase exist only for a weak frictional instability regime, while the nucleation length L_c and the acceleration phase exist for both weak and strong instability regimes. Both L_sc and L_c are found to be determined by the model parameters, the frictional weakening parameter and the elastic stiffness parameter, hardly dependent on the size of an ensuing mainshock. The sliding velocity is extremely slow in the initial phase up to L_sc, of order the pulling speed of the plate, while it reaches a detectable level at a certain stage of the acceleration phase. The continuum limits of the results are discussed. The continuum limit of the BK model lies in the weak frictional instability regime so that a mature homogeneous fault under the RSF law always accompanies the quasi-static nucleation process. Duration times of each stage of the nucleation process are examined. The relation to the elastic continuum model and implications to real seismicity are discussed.Comment: Title changed. Changes mainly in abstract and in section 1. To appear in European Physical Journal

SUMOylation Is Required for Glycine-Induced Increases in AMPA Receptor Surface Expression (ChemLTP) in Hippocampal Neurons

yesMultiple pathways participate in the AMPA receptor trafficking that underlies long-term potentiation (LTP) of synaptic transmission. Here we demonstrate that protein SUMOylation is required for insertion of the GluA1 AMPAR subunit following transient glycine-evoked increase in AMPA receptor surface expression (ChemLTP) in dispersed neuronal cultures. ChemLTP increases co-localisation of SUMO-1 and the SUMO conjugating enzyme Ubc9 and with PSD95 consistent with the recruitment of SUMOylated proteins to dendritic spines. In addition, we show that ChemLTP increases dendritic levels of SUMO-1 and Ubc9 mRNA. Consistent with activity dependent translocation of these mRNAs to sites near synapses, levels of the mRNA binding and dendritic transport protein CPEB are also increased by ChemLTP. Importantly, reducing the extent of substrate protein SUMOylation by overexpressing the deSUMOylating enzyme SENP-1 or inhibiting SUMOylation by expressing dominant negative Ubc9 prevent the ChemLTP-induced increase in both AMPAR surface expression and dendritic SUMO-1 mRNA. Taken together these data demonstrate that SUMOylation of synaptic protein(s) involved in AMPA receptor trafficking is necessary for activity-dependent increases in AMPAR surface expression.Medical Research Council, the European Research Council and the Wellcome Trus

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Serum antioxidants as predictors of the adult respiratory distress syndrome in septic patients

Adult respiratory distress syndrome (ARDS) can develop as a complication of various disorders, including sepsis, but it has not been possible to identify which of the patients at risk will develop this serious disorder. We have investigated the ability of six markers, measured sequentially in blood, to predict development of ARDS in 26 patients with sepsis. At the initial diagnosis of sepsis (6-24 h before the development of ARDS), serum manganese superoxide dismutase concentration and catalase activity were higher in the 6 patients who subsequently developed ARDS than in 20 patients who did not develop ARDS. These changes in antioxidant enzymes predicted the development of ARDS in septic patients with the same sensitivity, specificity, and efficiency as simultaneous assessments of serum lactate dehydrogenase activity and factor VIII concentration. By contrast, serum glutathione peroxidase activity and α1Pi-elastase complex concentration did not differ at the initial diagnosis of sepsis between patients who did and did not subsequently develop ARDS, and were not as effective in predicting the development of ARDS. Measurement of manganese superoxide dismutase and catalase, in addition to the other markers, should facilitate identification of patients at highest risk of ARDS and allow prospective treatment

The universe formation by a space reduction cascade with random initial parameters

In this paper we discuss the creation of our universe using the idea of extra dimensions. The initial, multidimensional Lagrangian contains only metric tensor. We have found many sets of the numerical values of the Lagrangian parameters corresponding to the observed low-energy physics of our universe. Different initial parameters can lead to the same values of fundamental constants by the appropriate choice of a dimensional reduction cascade. This result diminishes the significance of the search for the 'unique' initial Lagrangian. We also have obtained a large number of low-energy vacua, which is known as a 'landscape' in the string theory.Comment: 17 pages, 1 figur

Correlations and scaling in one-dimensional heat conduction

We examine numerically the full spatio-temporal correlation functions for all hydrodynamic quantities for the random collision model introduced recently. The autocorrelation function of the heat current, through the Kubo formula, gives a thermal conductivity exponent of 1/3 in agreement with the analytical prediction and previous numerical work. Remarkably, this result depends crucially on the choice of boundary conditions: for periodic boundary conditions (as opposed to open boundary conditions with heat baths) the exponent is approximately 1/2. This is expected to be a generic feature of systems with singular transport coefficients. All primitive hydrodynamic quantities scale with the dynamic critical exponent predicted analytically.Comment: 7 pages, 11 figure

Onsager coefficients of a Brownian Carnot cycle

We study a Brownian Carnot cycle introduced by T. Schmiedl and U. Seifert [Europhys. Lett. \textbf{81}, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the information of the protocol shape and they satisfy the tight-coupling condition irrespective of whatever protocol shape we choose. These properties may give an explanation why the Curzon-Ahlborn efficiency often appears in the finite-time heat engines