Phylogenetics, the inference of evolutionary trees from molecular sequence data such as DNA, is an enterprise that yields valuable evolutionary understanding of many biological systems. Bayesian phylogenetic algorithms, which approximate a posterior distribution on trees, have become a popular if computationally expensive means of doing phylogenetics. Modern data collection technologies are quickly adding new sequences to already substantial databases. With all current techniques for Bayesian phylogenetics, computation must start anew each time a sequence becomes available, making it costly to maintain an up-to-date estimate of a phylogenetic posterior. These considerations highlight the need for an online Bayesian phylogenetic method which can update an existing posterior with new sequences. Here, we provide theoretical results on the consistency and stability of methods for online Bayesian phylogenetic inference based on Sequential Monte Carlo (SMC) and Markov chain Monte Carlo. We first show a consistency result, demonstrating that the method samples from the correct distribution in the limit of a large number of particles. Next, we derive the first reported set of bounds on how phylogenetic likelihood surfaces change when new sequences are added. These bounds enable us to characterize the theoretical performance of sampling algorithms by bounding the effective sample size (ESS) with a given number of particles from below. We show that the ESS is guaranteed to grow linearly as the number of particles in an SMC sampler grows. Surprisingly, this result holds even though the dimensions of the phylogenetic model grow with each new added sequence.
Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy.
The previously described optimized binary compressive detection (OB-CD) strategy enables fast hyperspectral Raman (and fluorescence) spectroscopic analysis of systems containing two or more chemical components. However, each OB-CD filter collects only a fraction of the scattered photons and the remainder of the photons are lost. Here, we present a refinement of OB-CD, the OB-CD2 strategy, in which all of the collected Raman photons are detected using a pair of complementary binary optical filters that direct photons of different colors to two photon counting detectors. The OB-CD2 filters are generated using a new optimization algorithm described in this work and implemented using a holographic volume diffraction grating and a digital micromirror device (DMD) whose mirrors are programed to selectively direct photons of different colors either to one or the other photon-counting detector. When applied to pairs of pure liquids or two-component solid powder mixtures, the resulting OB-CD2 strategy is shown to more accurately estimate Raman scattering rates of each chemical component, when compared to the original OB-CD, thus facilitating chemical classification at speeds as fast as 3 μs per measurement and the collection of Raman images in under a second.
A robust control strategy for stabilizing nonlinear systems in the presence of additive bounded disturbances is proposed. The proposed control architecture is a novel combination of explicit nonlinear model predictive control (EMPC) and integral sliding mode control (ISMC). Feasibility analysis of a finite-horizon optimal control problem involved in deriving the EMPC control action is performed over a polytope of interest in the state space. A sparse sampling-based boundary detection algorithm is employed to compute an approximating polynomial bounding the feasible region. A sparse-grid based interpolation scheme with Chebyshev-Gauss-Lobatto nodes and Legendre-basis polynomials are used to design the stabilizing EMPC surface. The proposed method is appealing because of the simplicity of the controller construction in conjunction with its applicability to higher-dimensional problems, which stems from the scale-ability property of sparse-grids. Robustness to the designed EMPC is provided by the ISMC. A simulated example is provided to illustrate the efficacy and performance of the proposed control strategy for the stabilization of an uncertain nonlinear dynamical system.Index Terms-Explicit model predictive control, Integral sliding mode control, sparse grid interpolation, feasibility analysis.
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