Weak Convergence to Stochastic Integrals for Econometric Applications

Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications in econometrics involve a cointegration framework where endogeneity and nonlinearity play a major role and lead to complications in the limit theory. This paper explores weak convergence limit theory to stochastic integral functionals in such settings. We use a novel decomposition of sample covariances of functions of I(1) and I(0) time series that simplifies the asymptotic development and we provide limit results for such covariances when linear process, long memory, and mixing variates are involved in the innovations. The limit results extend earlier findings in the literature, are relevant in many econometric applications, and involve simple conditions that facilitate implementation in practice. A nonlinear extension of FM regression is used to illustrate practical application of the methods

Black hole thermodynamics with generalized uncertainty principle

In the standard viewpoint, the temperature of a stationary black hole is proportional to its surface gravity, $T_H=\hbar\kappa/2\pi$. This is a semiclassical result and the quantum gravity effects are not taken into consideration. This Letter explores a unified expression for the black hole temperature in the sense of a generalized uncertainty principle(GUP). Our discussion involves a heuristic analysis of a particle which is absorbed by the black hole. Besides a class of static and spherically symmetric black holes, an axially symmetric Kerr-Newman black hole is considered. Different from the existing literature, we suggest that the black hole's irreducible mass represent the characteristic size in the absorption process. The information capacity of a remnant is also discussed by Bousso's D-bound in de Sitter spacetime.Comment: 18 pages, great improvement on the first version; a Kerr-Newman black hole is considere

Active Amplification of the Terrestrial Albedo to Mitigate Climate Change: An Exploratory Study

This study explores the potential to enhance the reflectance of solar insolation by the human settlement and grassland components of the Earth's terrestrial surface as a climate change mitigation measure. Preliminary estimates derived using a static radiative transfer model indicate that such efforts could amplify the planetary albedo enough to offset the current global annual average level of radiative forcing caused by anthropogenic greenhouse gases by as much as 30 percent or 0.76 W/m2. Terrestrial albedo amplification may thus extend, by about 25 years, the time available to advance the development and use of low-emission energy conversion technologies which ultimately remain essential to mitigate long-term climate change. However, additional study is needed to confirm the estimates reported here and to assess the economic and environmental impacts of active land-surface albedo amplification as a climate change mitigation measure.Comment: 21 pages, 3 figures. In press with Mitigation and Adaptation Strategies for Global Change, Springer, N

Propagation and blocking in periodically hostile environments

We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the existence of a minimal nonnegative nontrivial stationary solution and study the large-time behavior of the solution of the initial boundary value problem. To the main goal, we then study a sequence of approximated problems in the whole space with reaction terms which are with very negative growth rates outside the domain under investigation. Finally, for a given unit vector, by using the information of the minimal speeds of approximated problems, we provide a simple geometric condition for the blocking of propagation and we derive the asymptotic behavior of the approximated pulsating travelling fronts. Moreover, for the case of constant diffusion matrix, we provide two conditions for which the limit of approximated minimal speeds is positive

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Spin-Charge Separation in the t−Jt-J Model: Magnetic and Transport Anomalies

A real spin-charge separation scheme is found based on a saddle-point state of the $t-J$ model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed-point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at {\em finite doping} so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic {\em residual} couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at ($\pi/a$, $\pi/a$) with a doping-dependent width ($\propto \sqrt{\delta}$, $\delta$ is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exits a characteristic temperature scale below which a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a {\em finite} energy regime. In transport, a strong short-range phase interference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-$T$ resistivity and $T^2$ Hall-angle. We discuss the striking similarities of these theoretical features with those found in the high-$T_c$ cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request; minor revisions in the text and references have been made; To be published in July 1 issue of Phys. Rev. B52, (1995

Metabolites related to purine catabolism and risk of type 2 diabetes incidence; modifying efects of the TCF7L2-rs7903146 polymorphism

Studies examining associations between purine metabolites and type 2 diabetes (T2D) are limited. We prospectively examined associations between plasma levels of purine metabolites with T2D risk and the modifying effects of transcription factor-7-like-2 (TCF7L2) rs7903146 polymorphism on these associations. This is a case-cohort design study within the PREDIMED study, with 251 incident T2D cases and a random sample of 694 participants (641 non-cases and 53 overlapping cases) without T2D at baseline (median follow-up: 3.8 years). Metabolites were semi-quantitatively profiled with LC-MS/MS. Cox regression analysis revealed that high plasma allantoin levels, including allantoin-to-uric acid ratio and high xanthine-to-hypoxanthine ratio were inversely and positively associated with T2D risk, respectively, independently of classical risk factors. Elevated plasma xanthine and inosine levels were associated with a higher T2D risk in homozygous carriers of the TCF7L2-rs7903146 T-allele. The potential mechanisms linking the aforementioned purine metabolites and T2D risk must be also further investigated

Circulating citric acid cycle metabolites and risk of cardiovascular disease in the PREDIMED study

Background and aim Plasma citric acid cycle (CAC) metabolites might be likely related to cardiovascular disease (CVD). However, studies assessing the longitudinal associations between circulating CAC-related metabolites and CVD risk are lacking. The aim of this study was to evaluate the association of baseline and 1-year levels of plasma CAC-related metabolites with CVD incidence (a composite of myocardial infarction, stroke or cardiovascular death), and their interaction with Mediterranean diet interventions. Methods and results Case-cohort study from the PREDIMED trial involving participants aged 55–80 years at high cardiovascular risk, allocated to MedDiets or control diet. A subcohort of 791 participants was selected at baseline, and a total of 231 cases were identified after a median follow-up of 4.8 years. Nine plasma CAC-related metabolites (pyruvate, lactate, citrate, aconitate, isocitrate, 2-hydroxyglutarate, fumarate, malate and succinate) were measured using liquid chromatography-tandem mass spectrometry. Weighted Cox multiple regression was used to calculate hazard ratios (HRs). Baseline fasting plasma levels of 3 metabolites were associated with higher CVD risk, with HRs (for each standard deviation, 1-SD) of 1.46 (95%CI:1.20–1.78) for 2-hydroxyglutarate, 1.33 (95%CI:1.12–1.58) for fumarate and 1.47 (95%CI:1.21–1.78) for malate (p of linear trend <0.001 for all). A higher risk of CVD was also found for a 1-SD increment of a combined score of these 3 metabolites (HR = 1.60; 95%CI: 1.32–1.94, p trend <0.001). This result was replicated using plasma measurements after one-year. No interactions were detected with the nutritional intervention. Conclusion Plasma 2-hydroxyglutarate, fumarate and malate levels were prospectively associated with increased cardiovascular risk

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics