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We study a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbations via an additive Gaussian noise. We show that for a broad class of non-linear potentials, the system always admits invariant probability measures. However, the presence of memory effects precludes access to compactness in a typical fashion. In this paper, this obstacle is overcome by introducing functional spaces adapted to the memory kernels, thereby allowing one to recover compactness. Under the assumption of sufficiently smooth noise, it is then shown that the statistically stationary states possess higher-order regularity properties dictated by the structure of the nonlinearity. This is established through a control argument that asymptotically transfers regularity onto the solution by exploiting the underlying Lyapunov structure of the system in a novel way. 

Delta blue intensity is a commonly used method to correct for the heartwood-sapwood color change in blue intensity (BI) measurements. It is based on the assumption that the heartwood-sapwood color change is similar in both earlywood and latewood. This assumption has not been supported physiologically. Furthermore, delta BI may confound the climate signals in earlywood and latewood BI as it is technically a linear combination of the other two. Here, instead of using delta BI, we used change point detection to identify the heartwood-sapwood transition, and corrected for the color change by rescaling the mean and variance of BI measurements after the transition to those immediately before. We tested three different change point detection methods and found that they agreed well with one another. Importantly, our approach preserves the climate signals in both earlywood and latewood BI data, while delta BI causes a total loss of climate signals in our test case. Therefore, we suggest that change point detection should be used instead of delta BI to account for the heartwood-sapwood color change. 

Abstract We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential. 

Abstract This manuscript describes the development of a resource module that is part of a learning platform named ‘NIGMS Sandbox for Cloud-based Learning’ (https://github.com/NIGMS/NIGMS-Sandbox). The module delivers learning materials on Cloud-based Consensus Pathway Analysis in an interactive format that uses appropriate cloud resources for data access and analyses. Pathway analysis is important because it allows us to gain insights into biological mechanisms underlying conditions. But the availability of many pathway analysis methods, the requirement of coding skills, and the focus of current tools on only a few species all make it very difficult for biomedical researchers to self-learn and perform pathway analysis efficiently. Furthermore, there is a lack of tools that allow researchers to compare analysis results obtained from different experiments and different analysis methods to find consensus results. To address these challenges, we have designed a cloud-based, self-learning module that provides consensus results among established, state-of-the-art pathway analysis techniques to provide students and researchers with necessary training and example materials. The training module consists of five Jupyter Notebooks that provide complete tutorials for the following tasks: (i) process expression data, (ii) perform differential analysis, visualize and compare the results obtained from four differential analysis methods (limma, t-test, edgeR, DESeq2), (iii) process three pathway databases (GO, KEGG and Reactome), (iv) perform pathway analysis using eight methods (ORA, CAMERA, KS test, Wilcoxon test, FGSEA, GSA, SAFE and PADOG) and (v) combine results of multiple analyses. We also provide examples, source code, explanations and instructional videos for trainees to complete each Jupyter Notebook. The module supports the analysis for many model (e.g. human, mouse, fruit fly, zebra fish) and non-model species. The module is publicly available at https://github.com/NIGMS/Consensus-Pathway-Analysis-in-the-Cloud. This manuscript describes the development of a resource module that is part of a learning platform named ``NIGMS Sandbox for Cloud-based Learning'' https://github.com/NIGMS/NIGMS-Sandbox. The overall genesis of the Sandbox is described in the editorial NIGMS Sandbox [1] at the beginning of this Supplement. This module delivers learning materials on the analysis of bulk and single-cell ATAC-seq data in an interactive format that uses appropriate cloud resources for data access and analyses. 

Repeat RNA sequences self-associate to form condensates. Simulations of a coarse-grained single-interaction site model for (CAG)n (n = 30 and 31) show that the salt-dependent free energy gap, ΔGS, between the ground (perfect hairpin) and the excited state (slipped hairpin (SH) with one CAG overhang) of the monomer for (n even) is the primary factor that determines the rates and yield of self-assembly. For odd n, the free energy (GS) of the ground state, which is an SH, is used to predict the self-association kinetics. As the monovalent salt concentration, CS, increases, ΔGS and GS increase, which decreases the rates of dimer formation. In contrast, ΔGS for shuffled sequences, with the same length and sequence composition as (CAG)31, is larger, which suppresses their propensities to aggregate. Although demonstrated explicitly for (CAG) polymers, the finding of inverse correlation between the free energy gap and RNA aggregation is general. 

Abstract Identifying impacted pathways is important because it provides insights into the biology underlying conditions beyond the detection of differentially expressed genes. Because of the importance of such analysis, more than 100 pathway analysis methods have been developed thus far. Despite the availability of many methods, it is challenging for biomedical researchers to learn and properly perform pathway analysis. First, the sheer number of methods makes it challenging to learn and choose the correct method for a given experiment. Second, computational methods require users to be savvy with coding syntax, and comfortable with command‐line environments, areas that are unfamiliar to most life scientists. Third, as learning tools and computational methods are typically implemented only for a few species (i.e., human and some model organisms), it is difficult to perform pathway analysis on other species that are not included in many of the current pathway analysis tools. Finally, existing pathway tools do not allow researchers to combine, compare, and contrast the results of different methods and experiments for both hypothesis testing and analysis purposes. To address these challenges, we developed an open‐source R package for Consensus Pathway Analysis (RCPA) that allows researchers to conveniently: (1) download and process data from NCBI GEO; (2) perform differential analysis using established techniques developed for both microarray and sequencing data; (3) perform both gene set enrichment, as well as topology‐based pathway analysis using different methods that seek to answer different research hypotheses; (4) combine methods and datasets to find consensus results; and (5) visualize analysis results and explore significantly impacted pathways across multiple analyses. This protocol provides many example code snippets with detailed explanations and supports the analysis of more than 1000 species, two pathway databases, three differential analysis techniques, eight pathway analysis tools, six meta‐analysis methods, and two consensus analysis techniques. The package is freely available on the CRAN repository. © 2024 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Processing Affymetrix microarrays Basic Protocol 2: Processing Agilent microarrays Support Protocol: Processing RNA sequencing (RNA‐Seq) data Basic Protocol 3: Differential analysis of microarray data (Affymetrix and Agilent) Basic Protocol 4: Differential analysis of RNA‐Seq data Basic Protocol 5: Gene set enrichment analysis Basic Protocol 6: Topology‐based (TB) pathway analysis Basic Protocol 7: Data integration and visualization 

Abstract Single-cell RNA sequencing (scRNA-Seq) is a recent technology that allows for the measurement of the expression of all genes in each individual cell contained in a sample. Information at the single-cell level has been shown to be extremely useful in many areas. However, performing single-cell experiments is expensive. Although cellular deconvolution cannot provide the same comprehensive information as single-cell experiments, it can extract cell-type information from bulk RNA data, and therefore it allows researchers to conduct studies at cell-type resolution from existing bulk datasets. For these reasons, a great effort has been made to develop such methods for cellular deconvolution. The large number of methods available, the requirement of coding skills, inadequate documentation, and lack of performance assessment all make it extremely difficult for life scientists to choose a suitable method for their experiment. This paper aims to fill this gap by providing a comprehensive review of 53 deconvolution methods regarding their methodology, applications, performance, and outstanding challenges. More importantly, the article presents a benchmarking of all these 53 methods using 283 cell types from 30 tissues of 63 individuals. We also provide an R package named DeconBenchmark that allows readers to execute and benchmark the reviewed methods (https://github.com/tinnlab/DeconBenchmark). 

Low-complexity nucleotide repeat sequences, which are implicated in several neurological disorders, undergo liquid–liquid phase separation (LLPS) provided the number of repeat units, n , exceeds a critical value. Here, we establish a link between the folding landscapes of the monomers of trinucleotide repeats and their propensity to self-associate. Simulations using a coarse-grained Self-Organized Polymer (SOP) model for (CAG) n repeats in monovalent salt solutions reproduce experimentally measured melting temperatures, which are available only for small n . By extending the simulations to large n , we show that the free-energy gap, ΔG S , between the ground state (GS) and slipped hairpin (SH) states is a predictor of aggregation propensity. The GS for even n is a perfect hairpin (PH), whereas it is a SH when n is odd. The value of ΔG S (zero for odd n ) is larger for even n than for odd n . As a result, the rate of dimer formation is slower in (CAG) 30 relative to (CAG) 31 , thus linking ΔG S to RNA–RNA association. The yield of the dimer decreases dramatically, compared to the wild type, in mutant sequences in which the population of the SH decreases substantially. Association between RNA chains is preceded by a transition to the SH even if the GS is a PH. The finding that the excitation spectrum—which depends on the exact sequence, n , and ionic conditions—is a predictor of self-association should also hold for other RNAs (mRNA for example) that undergo LLPS. 

Flow-based manipulation of particles is an essential tool for studying soft materials, but prior work has nearly exclusively relied on using two-dimensional (2D) flows generated in planar microfluidic geometries. In this work, we demonstrate 3D trapping and manipulation of freely suspended particles, droplets, and giant unilamellar vesicles in 3D flow fields using automated flow control. Three-dimensional flow fields including uniaxial extension and biaxial extension are generated in 3D-printed fluidic devices combined with active feedback control for particle manipulation in 3D. Flow fields are characterized using particle tracking velocimetry complemented by finite-element simulations for all flow geometries. Single colloidal particles (3.4 μm diameter) are confined in low viscosity solvent (1.0 mPa s) near the stagnation points of uniaxial and biaxial extensional flow for long times (≥10 min) using active feedback control. Trap stiffness is experimentally determined by analyzing the power spectral density of particle position fluctuations. We further demonstrate precise manipulation of colloidal particles along user-defined trajectories in three dimensions using automated flow control. Newtonian liquid droplets and GUVs are trapped and deformed in precisely controlled uniaxial and biaxial extensional flows, which is a new demonstration for 3D flow fields. Overall, this work extends flow-based manipulation of particles and droplets to three dimensions, thereby enabling quantitative analysis of colloids and soft materials in complex nonequilibrium flows.