Combining the strengths of inverse-variance weighting and Egger regression in Mendelian randomization using a mixture of regressions model

With the increasing availability of large-scale GWAS summary data on various traits, Mendelian randomization (MR) has become commonly used to infer causality between a pair of traits, an exposure and an outcome. It depends on using genetic variants, typically SNPs, as instrumental variables (IVs). The inverse-variance weighted (IVW) method (with a fixed-effect meta-analysis model) is most powerful when all IVs are valid; however, when horizontal pleiotropy is present, it may lead to biased inference. On the other hand, Egger regression is one of the most widely used methods robust to (uncorrelated) pleiotropy, but it suffers from loss of power. We propose a two-component mixture of regressions to combine and thus take advantage of both IVW and Egger regression; it is often both more efficient (i.e. higher powered) and more robust to pleiotropy (i.e. controlling type I error) than either IVW or Egger regression alone by accounting for both valid and invalid IVs respectively. We propose a model averaging approach and a novel data perturbation scheme to account for uncertainties in model/IV selection, leading to more robust statistical inference for finite samples. Through extensive simulations and applications to the GWAS summary data of 48 risk factor-disease pairs and 63 genetically uncorrelated trait pairs, we showcase that our proposed methods could often control type I error better while achieving much higher power than IVW and Egger regression (and sometimes than several other new/popular MR methods). We expect that our proposed methods will be a useful addition to the toolbox of Mendelian randomization for causal inference.

Handling Measurement Delay in Iterative Real-Time Optimization Methods

This paper is concerned with the real-time optimization (RTO) of chemical plants, i.e., the optimization of the steady-state operating points during operation, based on inaccurate models. Specifically, modifier adaptation is employed to cope with the plant-model mismatch, which corrects the plant model and the constraint functions by bias and gradient correction terms that are computed from measured variables at the steady-states of the plant. This implies that the sampling time of the iterative RTO scheme is lower-bounded by the time to reach a new steady-state after the previously computed inputs were applied. If analytical process measurements (PAT technology) are used to obtain the steady-state responses, time delays occur due to the measurement delay of the PAT device and due to the transportation delay if the samples are transported to the instrument via pipes. This situation is quite common because the PAT devices can often only be installed at a certain distance from the measurement location. The presence of these time delays slows down the iterative real-time optimization, as the time from the application of a new set of inputs to receiving the steady-state information increases further. In this paper, a proactive perturbation scheme is proposed to efficiently utilize the idle time by intelligently scheduling the process inputs taking into account the time delays to obtain the steady-state process measurements. The performance of the proposed proactive perturbation scheme is demonstrated for two examples, the Williams–Otto reactor benchmark and a lithiation process. The simulation results show that the proposed proactive perturbation scheme can speed up the convergence to the true plant optimum significantly.

An Adaptive Refined Grid Search Strategy for Assessing Operational Flexibility and Application on Refrigerant Selection

A novel adaptive refined grid search strategy is developed for representative characterization of process feasible region boundaries and accurate estimation of its hypervolume. In particular, a linked list data structure adopted from the field of computer science is used to maintain the grid connectivity information. A uniform perturbation scheme is used to refine the search only near boundaries. The volumetric flexibility index FI_V is calculated directly from a summation of feasible hypercubes in the grid, without the need to apply shape reconstruction techniques. The proposed adaptive grid search strategy can capture complex region shapes with reduced sampling costs and without randomness for better reproducibility. Operational flexibility is optimized traditionally at a process scale. A case study on refrigerant selection is presented to demonstrated that the developed strategy could be combined within a computer-aided molecular design framework for operational flexibility optimization in molecular scale.

Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation

Ringdown gravitational waves of compact object binaries observed by ground-based gravitational-wave detectors encapsulate rich information to understand remnant objects after the merger and to test general relativity in the strong field. In this work, we investigate the ringdown gravitational waves in detail to better understand their property, assuming that the remnant objects are black holes. For this purpose, we perform numerical simulations of post-merger phase of binary black holes by using the black hole perturbation scheme with the initial data given under the close-limit approximation, and we generate data of ringdown gravitational waves with smaller numerical errors than that associated with currently available numerical relativity simulations. Based on the analysis of the data, we propose an orthonormalization of the quasinormal mode functions describing the fundamental tone and overtones to model ringdown gravitational waves. Finally, through some demonstrations of the proposed model, we briefly discuss the prospects for ringdown gravitational-wave data analysis including the overtones of quasinormal modes.

Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.

SEGMENT RANDOM INSERTION PERTURBATION SCHEME (SRIPS) GENETIC ALGORITHM FOR MANUFACTURING INDUSTRY

This paper lays down a formal framework for simultaneous scheduling of machines- automated guided vehicles (AGVs) and tools in a multi-machine flexible manufacturing system (FMS) while accounting for transport times of parts to minimise makespan. To minimize tooling costs- a central tool magazine (CTM) is suggested so that the tools are ‘shared’. AGVs and tool transporter (TT) carry jobs and tools between machines. The complexity of including sequencing of job operations on machines- assignment of AGVs and tools to job operations and corresponding trip operations such as the empty trip and loaded trip times of AGVs and a CTM in scheduling is greater. The scope of this paper is to propose a nonlinear Mixed Integer Programming (MIP) model to minimize makespan. Since the problem is known to be NP hard- it is conjectured and then verified that the intelligent behaviour of chromosomes and genes can be effectively used to lay down a metaheuristic algorithm known as a segment random insertion perturbation scheme genetic algorithm (SRIPSGA) suitable for the problem at hand- and the results have been tabulated and analyzed.

Impact of f(R,T) gravity in evolution of charged viscous fluids

In this work, the evolution of spherically symmetric charged anisotropic viscous fluids is discussed in framework of [Formula: see text] gravity. In order to conduct the analysis, modified Einstein Maxwell field equations are constructed. Nonzero divergence of modified energy momentum tensor is taken that implicates dynamical equations. The perturbation scheme is applied to dynamical equations for stability analysis. The stability analysis is carried out in Newtonian and post-Newtonian limits. It is observed that charge, fluid distribution, electromagnetic field, viscosity and mass of the celestial objects greatly affect the collapsing process as well as stability of stars.

SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

I construct infinitely many nondiffeomorphic examples of $5$ -dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces, as outlined in [23, 24], as a prequel to [30].