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It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of dimensionality and thus solving it directly is not feasible for most realistic problems. In this paper we propose a dynamical low-rank algorithm for the CME that reduces the dimensionality of the problem by dividing the reaction network into partitions. Only reactions that cross partitions are subject to an approximation error (everything else is computed exactly). This approach, compared to the commonly used stochastic simulation algorithm (SSA, a Monte Carlo method), has the advantage that it is completely noise-free. This is particularly important if one is interested in resolving the tails of the probability distribution. We show that in some cases (e.g. for the lambda phage) the proposed method can drastically reduce memory consumption and run time and provide better accuracy than SSA. • We propose a low-rank algorithm that does not rely on single orbital basis functions. • The proposed approach is better suited for biological/chemical reaction networks. • We demonstrate better accuracy and improved efficiency compared to SSA for some problems. • The proposed complexity reduction algorithm is noise free (in contrast to SSA). • We demonstrate that our algorithm accurately resolves the tails of the distribution (in contrast to SSA). [ABSTRACT FROM AUTHOR]

The First Passage Time (FPT) of a given signal is the time required to reach a level X f for the first time, when starting from a level X 0. For a given set (X 0 , X f) , this time can be obtained by moving along the given signal and clocking the time on when passing through level X 0 , then off when passing through level X f for the first time. For random signals, the FPT is a random variable. Several samples of the first passage time are collected while moving along the given signal to compute the corresponding statistical moments and probability density function. The FPT map associates each statistical moment with every couple (X 0 , X f). A map is constructed for every desired moment. A naive implementation of the signal processing method to compute the FPT map would require to move along the signal as many times as the desired pairs (X 0 , X f). Instead, this paper introduces a new and optimized algorithm to establish the FPT maps of any statistical moment and, optionally, of the whole probability distribution. This algorithm combines different features to produce a computationally effective and memory-efficient method. The algorithm estimates the entire map by iterating only once across the signal. The accuracy of the algorithm has been assessed with particular cases where theoretical solutions exist as well as for lab data. Furthermore the algorithm's performance has also been evaluated in terms of computational burden. A specific attention is given to the computation time scaling for the evaluation of an FPT map, with respect to the signal size. • First passage times are determined for signals from experimental or synthetic data. • Both their statistical moments and, optionally, distributions are computed. • The proposed algorithm runs much faster than an elementary implementation. • The crucial detail of the proposed method is the backward processing of the signal. [ABSTRACT FROM AUTHOR]

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, the tool for the evaluation of Bayesian inference problems that yield non-standard posterior distributions. In recent years, however, it has become apparent that Sequential Monte Carlo (SMC) samplers have the potential to outperform MCMC in several ways. SMC samplers are better suited to highly parallel computing architectures and also feature various tuning parameters that are not available to MCMC. One such parameter – the 'L-kernel' – is a user-defined probability distribution that can be used to influence the efficiency of the sampler. In the current paper, the authors explain how to derive an expression for the L-kernel that minimises the variance of the estimates realised by an SMC sampler. Various approximation methods are then proposed to aid the implementation of the proposed L-kernel. The improved performance of the resulting algorithm is demonstrated in multiple scenarios. For the examples shown in the current paper, the use of an approximately optimal L-kernel has reduced the variance of the SMC estimates by up to 99 % while also reducing the number of times that resampling was required by between 65% and 70%. Python code and code tests accompanying this manuscript are available through the Github repository https://github.com/plgreenLIRU/SMC_approx_optL. [ABSTRACT FROM AUTHOR]

[Display omitted] • We derive an algorithm to detect and segment contaminations in cryo-EM micrographs. • The only parameter required by the algorithm is an estimate of the particle size. • We demonstrate the performance of our algorithm on various experimental datasets. Particle picking is currently a critical step in the cryo-electron microscopy single particle reconstruction pipeline. Contaminations in the acquired micrographs severely degrade the performance of particle pickers, resulting in many "non-particles" in the collected stack of particles. In this paper, we present ASOCEM (Automatic Segmentation Of Contaminations in cryo-EM), an automatic method to detect and segment contaminations, which requires as an input only the approximate particle size. In particular, it does not require any parameter tuning nor manual intervention. Our method is based on the observation that the statistical distribution of contaminated regions is different from that of the rest of the micrograph. This nonrestrictive assumption allows to automatically detect various types of contaminations, from the carbon edges of the supporting grid to high contrast blobs of different sizes. We demonstrate the efficiency of our algorithm using various experimental data sets containing various types of contaminations. ASOCEM is integrated as part of the KLT picker (Eldar et al., 2020) and is available at https://github.com/ShkolniskyLab/kltpicker2. [ABSTRACT FROM AUTHOR]

Conventional linear mixed-effects modeling is routinely challenging when the validity of necessary assumptions is suspicious. In particular, robustifying model fitting is appealing in the presence of potential outlying points. This paper introduces a robust regression methodology in a parametric setting by constructing a novel multivariate skew-Huber distribution for longitudinal data with heavy-tails and skewed structures. Unlike preceding studies, our model allows for jointly estimating the tuning parameter, which controls the impact of outliers, with all other parameters using an undemanding computational algorithm. Moreover, by promoting an unconstrained parameterization through the modified Cholesky decomposition, the estimate of variance–covariance components can be merely accessible. We also present a spline mixed model to account for the covariate effect. To highlight the usefulness of our methodology, we conducted a simulation study and analyzed a data set collected on type 2 diabetic patients with microalbuminuria over a 6-year prospective cohort study. Findings show that our proposed robust model leads to convincing conclusions in empirical studies. • Introduces the multivariate Huber distribution and studies its main properties. • Presents a robust regression mixed model to analyze correlated data when outliers exist. • Provides case weight for each subject through the tuning parameter estimate. • Offers an easy algorithm for jointly estimate the tuning parameter, variance–covariance components, and fixed effects. • Delivers direct parameterization by utilizing the modified Cholesky decomposition technique. We consider various correlation structures to the model specification. [ABSTRACT FROM AUTHOR]

Fiber-wireless (FiWi) access networks smartly integrate the mobility, robustness, and ubiquity of wireless networks and the high capacity of fiber networks. A demanding task in FiWi networks is to find the optimal placement of optical network units (ONUs), which leads to resource, throughput, and cost optimization. Several studies have been carried out to solve the ONU placement problem. Most approaches achieve encouraging results; however, they suffer from trapping in local optima, and their performance is far from the ideal state. This paper introduces a chaotic local search-based levy flight distribution (CLS-LFD) algorithm to optimize the position of ONUs in the FiWi network. The proposed algorithm models the ONU placement as a constraint multi-modal optimization problem. The objective is to minimize the overall average distance between ONUs and users. With a test on four ONU placement benchmarks, the proposed CLS-LFD algorithm has shown significant improvement over the canonical LFD algorithm and several counterpart algorithms in terms of convergence performance and cost value. [ABSTRACT FROM AUTHOR]

In water distribution system (WDS), chlorine is often injected as disinfectant to control the growth of microorganism in WDS. However, the chlorine reacts with organism to form disinfectant byproduct, which can bring risk to human health. As such, the chlorine at nodes in WDS should be kept between acceptable range, which is simulated based on the response at nodes corresponding to unit injection mass at boosters. To deal with the uncertainty in chlorine decay process and lower and upper chlorine concentration limits, an inexact left-hand-side chance-constrained programming (ILCCP) model was proposed in this paper and applied to two WDSs. The response coefficients matrix was expressed as random variables with normal probability distribution in the constraints of lower and upper limits, which was obtained through Monte Carlo simulation by linking with EPANET software. The intervals of injection mass were obtained by solving the ILCCP model with a two-step algorithm. Moreover, the effects of random bulk decay coefficients and interval of chlorine limits on the injection mass were analyzed and compared. The results indicated that the lower bounds of optimal injection mass increased with the rise of probability lever for lower limits, while the upper bounds decreased with the rise of the probability level for upper limits. The results can help managers determine the chlorine injection mass under uncertain scenarios, and can be applied to more complicated WDS to obtain meaningful results. • An inexact left-hand-side chance-constrained programming model was proposed. • Response coefficients were expressed as random variables with normal distribution. • Effects of decay coefficients and limits on the injection mass were analyzed. [ABSTRACT FROM AUTHOR]

Variable selection for multi-sample problems is of great interest in statistics. Existing methods for addressing this problem have some limits or disadvantages. In this paper, we propose distance-based variable importance measures to deal with these problems, which are inspired by the Multi-response permutation procedure (MRPP), Energy distance (ED) and Distance components (DISCO) analysis. The proposed variable importance assessments can effectively measure the importance of an individual dimension by quantifying its influence on the differences between multivariate distributions across treatment groups. An importance-measure-based backward selection (IM-BWS) algorithm is developed that can be used in variable selection for multi-sample problems to discover important variables. We propose a modified MRPP based on the IM-BWS procedure for improving the power performance of the original MRPP. Our proposed methods are model-free, work for high-dimensional data, and can capture important variables under different models. Both simulations and real data applications demonstrate that our proposed method enjoys good properties and has advantages over other existing methods. [ABSTRACT FROM AUTHOR]

Structural repairs alter the physical properties of a structure, changing its responses, both in terms of its normal condition and of its different damage states. This difference in responses manifests itself as a shift between the pre- and post-repair data distributions, which can be problematic for conventional data-driven approaches to structural health monitoring (SHM), and limits their effectiveness in industrial applications. This limitation occurs typically because approaches assume that the data distribution is the same in training as appears in testing; with an algorithm failing to generalise when this assumption is not true; that is, pre-repair labels no longer apply to the post-repair data. Transfer learning, in the form of domain adaptation, proposes a solution to this issue, by mapping the pre- and post-repair data distributions onto a shared latent space where their distributions are approximately equal, allowing pre-repair label knowledge to be used to classify the post-repair data. This paper demonstrates the applicability of domain adaptation as a method for overcoming the problem of repair on a dataset from a Gnat trainer aircraft. In addition, a novel modification to an existing domain adaptation technique – joint distribution adaptation – is proposed, which seeks to improve the semi-supervised learning phase of the algorithm by considering a metric-informed procedure. The metric-informed joint distribution adaptation algorithm is benchmarked against, and shown to outperform, both conventional data-based approaches and other domain adaptation techniques. • Proposes, for the first time, the application of domain adaptation to overcome the problem of repair in data-based structural health monitoring. • A novel modification to joint domain adaptation, named metric-informed joint domain adaptation , improves initial pseudo-label estimates for the target dataset. • Demonstrates existing and proposed domain adaptation techniques on a repair problem for a Gnat trainer aircraft wing. [ABSTRACT FROM AUTHOR]

Expectiles are the solution to an asymmetric least squares minimization problem for univariate data. They resemble the quantiles, and just like them, expectiles are indexed by a level α in the unit interval. In the present paper, we introduce and discuss the main properties of the (multivariate) expectile regions, a nested family of sets, whose instance with level 0 < α ≤ 1 ∕ 2 is built up by all points whose univariate projections lie between the expectiles of levels α and 1 − α of the projected dataset. Such level is interpreted as the degree of centrality of a point with respect to a multivariate distribution and therefore serves as a depth function. We propose here algorithms for determining all the extreme points of the bivariate expectile regions as well as for computing the depth of a point in the plane. We also study the convergence of the sample expectile regions to the population ones and the uniform consistency of the sample expectile depth. Finally, we present some real data examples for which the Bivariate Expectile Plot (BExPlot) is introduced. [ABSTRACT FROM AUTHOR]