Calculation of the Stability Index in Parameter-Dependent Calculus of Variations Problems: Buckling of a Twisted Elastic Strut

We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler--Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting conjugate points, with local minima corresponding to equilibria with no conjugate points. These conjugate points are arclength values $\sigma \le 1$ at which a second ODE (the Jacobi equation) has a solution vanishing at $0$ and $\sigma$. Finding conjugate points normally involves the numerical solution of a set of initial value problems for the Jacobi equation. For problems involving a parameter $\lambda$, such as the force or twist angle in the elastic strut, this computation must be repeated for every value of $\lambda$ of interest. Here we present an alternative approach that takes advantage of the presence of a parameter $\lambda$. Rather than search for conjugate points $\sigma \le 1$ at a fixed value of $\lambda$, we search for a set of special parameter values $\lambda_m$ (with corresponding Jacobi solution \bfzeta^m) for which $\sigma=1$ is a conjugate point. We show that, under appropriate assumptions, the index of an equilibrium at any $\lambda$ equals the number of these \bfzeta^m for which \langle \bfzeta^m, \Op \bfzeta^m \rangle < 0, where \Op is the Jacobi differential operator at $\lambda$. This computation is particularly simple when $\lambda$ appears linearly in \Op. We apply this approach to the elastic strut, in which the force appears linearly in \Op, and, as a result, we locate the conjugate points for any twisted unbuckled rod configuration without resorting to numerical solution of differential equations. In addition, we numerically compute two-dimensional sheets of buckled equilibria (as the two parameters of force and twist are varied) via a coordinated family of one-dimensional parameter continuation computations. Conjugate points for these buckled equilibria are determined by numerical solution of the Jacobi ODE

Multi-Objective Reinforcement Learning for Cognitive Radio-Based Satellite Communications

Previous research on cognitive radios has addressed the performance of various machine-learning and optimization techniques for decision making of terrestrial link properties. In this paper, we present our recent investigations with respect to reinforcement learning that potentially can be employed by future cognitive radios installed onboard satellite communications systems specifically tasked with radio resource management. This work analyzes the performance of learning, reasoning, and decision making while considering multiple objectives for time-varying communications channels, as well as different cross-layer requirements. Based on the urgent demand for increased bandwidth, which is being addressed by the next generation of high-throughput satellites, the performance of cognitive radio is assessed considering links between a geostationary satellite and a fixed ground station operating at Ka-band (26 GHz). Simulation results show multiple objective performance improvements of more than 3.5 times for clear sky conditions and 6.8 times for rain conditions

Dimensionally reduced machine learning model for predicting single component octanol–water partition coefficients

Abstract MF-LOGP, a new method for determining a single component octanol–water partition coefficients ( $$LogP$$ LogP ) is presented which uses molecular formula as the only input. Octanol–water partition coefficients are useful in many applications, ranging from environmental fate and drug delivery. Currently, partition coefficients are either experimentally measured or predicted as a function of structural fragments, topological descriptors, or thermodynamic properties known or calculated from precise molecular structures. The MF-LOGP method presented here differs from classical methods as it does not require any structural information and uses molecular formula as the sole model input. MF-LOGP is therefore useful for situations in which the structure is unknown or where the use of a low dimensional, easily automatable, and computationally inexpensive calculations is required. MF-LOGP is a random forest algorithm that is trained and tested on 15,377 data points, using 10 features derived from the molecular formula to make $$LogP$$ LogP predictions. Using an independent validation set of 2713 data points, MF-LOGP was found to have an average $$RMSE$$ RMSE = 0.77 ± 0.007, $$MAE$$ MAE = 0.52 ± 0.003, and $${R}^{2}$$ R 2 = 0.83 ± 0.003. This performance fell within the spectrum of performances reported in the published literature for conventional higher dimensional models ( $$RMSE$$ RMSE = 0.42–1.54, $$MAE$$ MAE = 0.09–1.07, and $${R}^{2}$$ R 2 = 0.32–0.95). Compared with existing models, MF-LOGP requires a maximum of ten features and no structural information, thereby providing a practical and yet predictive tool. The development of MF-LOGP provides the groundwork for development of more physical prediction models leveraging big data analytical methods or complex multicomponent mixtures. Graphical Abstrac

Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

Single-particle tracking (SPT) has been extensively used to obtain information about diffusion and directed motion in a wide range of biological applications. Recently, new methods have appeared for obtaining precise (10s of nm) spatial information in three dimensions (3D) with high temporal resolution (measurements obtained every 4 ms), which promise to more accurately sense the true dynamical behavior in the natural 3D cellular environment. Despite the quantitative 3D tracking information, the range of mathematical methods for extracting information about the underlying system has been limited mostly to mean-squared displacement analysis and other techniques not accounting for complex 3D kinetic interactions. There is a great need for new analysis tools aiming to more fully extract the biological information content from in vivo SPT measurements. High-resolution SPT experimental data has enormous potential to objectively scrutinize various proposed mechanistic schemes arising from theoretical biophysics and cell biology. At the same time, methods for rigorously checking the statistical consistency of both model assumptions and estimated parameters against observed experimental data (i.e., goodness-of-fit tests) have not received great attention. We demonstrate methods enabling (1) estimation of the parameters of 3D stochastic differential equation (SDE) models of the underlying dynamics given only one trajectory; and (2) construction of hypothesis tests checking the consistency of the fitted model with the observed trajectory so that extracted parameters are not overinterpreted (the tools are applicable to linear or nonlinear SDEs calibrated from nonstationary time series data). The approach is demonstrated on high-resolution 3D trajectories of single <i>ARG</i>3 mRNA particles in yeast cells in order to show the power of the methods in detecting signatures of transient directed transport. The methods presented are generally relevant to a wide variety of 2D and 3D SPT tracking applications

Graphene Nanoplatelet-Polymer Chemiresistive Sensor Arrays for the Detection and Discrimination of Chemical Warfare Agent Simulants

A cross-reactive array of semiselective chemiresistive sensors made of polymer-graphene nanoplatelet (GNP) composite coated electrodes was examined for detection and discrimination of chemical warfare agents (CWA). The arrays employ a set of chemically diverse polymers to generate a unique response signature for multiple CWA simulants and background interferents. The developed sensors’ signal remains consistent after repeated exposures to multiple analytes for up to 5 days with a similar signal magnitude across different replicate sensors with the same polymer-GNP coating. An array of 12 sensors each coated with a different polymer–GNP mixture was exposed 100 times to a cycle of single analyte vapors consisting of 5 chemically similar CWA simulants and 8 common background interferents. The collected data was vector normalized to reduce concentration dependency, <i>z</i>-scored to account for baseline drift and signal-to-noise ratio, and Kalman filtered to reduce noise. The processed data was dimensionally reduced with principal component analysis and analyzed with four different machine learning algorithms to evaluate discrimination capabilities. For 5 similarly structured CWA simulants alone 100% classification accuracy was achieved. For all analytes tested 99% classification accuracy was achieved demonstrating the CWA discrimination capabilities of the developed system. The novel sensor fabrication methods and data processing techniques are attractive for development of sensor platforms for discrimination of CWA and other classes of chemical vapors