Rate Of Divergence Research Articles

Neural Networks as Geometric Chaotic Maps.

The use of artificial neural networks (NNs) as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how NNs learn chaos is lacking. Here, we employ a geometric perspective to show that NNs can efficiently model chaotic dynamics by becoming structurally chaotic themselves. We first confirm NN's efficiency in emulating chaos by showing that a parsimonious NN trained only on few data points can reconstruct strange attractors, extrapolate outside training data boundaries, and accurately predict local divergence rates. We then posit that the trained network's map comprises sequential geometric stretching, rotation, and compression operations. These geometric operations indicate topological mixing and chaos, explaining why NNs are naturally suitable to emulate chaotic dynamics.

Data-Driven Self-Triggering Mechanism for State Feedback Control

This paper presents a novel approach for data-driven self-triggered state feedback control of unknown linear systems using noisy data gathered offline. The self-triggering mechanism determines the next triggering time by checking whether the difference between the predicted state and the current state is significant or not. However, when the system matrices are unknown, the challenge lies in characterizing the distance between future states and the current state using only data. To address this, we put forth a data-driven online optimization problem for trajectory prediction by using noisy input-state data. Its optimal solution, together with another unknown parameter that reflects the open-loop divergence rate, is shown sufficient for explicitly quantifying the distance. Moreover, a data-driven set-based over-approximating algorithm using matrix zonotopes is subsequently proposed to upper-bound the open-loop divergence rate. Leveraging the optimal solution and the upper bound, a self-triggering mechanism is devised for state feedback control systems, which is proven to ensure input-to-state stability. Numerical examples are presented to validate the effectiveness of the proposed method.

Genomic divergence and introgression among three Populus species

Genomic divergence with gene flow is very common in both plants and animals. However, divergence and gene flow are two counteracting factors during speciation. Identifying the types of genes that are likely to be introgressed and what genetic factors restrict further effective reproduction of interspecific hybrids is of great interest to biologists. We aimed to address these issues using three related tree species, Populus alba (Pa), P. tremula (Pt), and P. tremuloides (Ps), and the interspecific hybrid of the former two species, P. × canescens (Pc). We collected 105 genomes for these four poplar lineages, including 28 Pa, 38Pt, 21 Ps, and 18 Pc individuals, to reconstruct their evolutionary histories. Our coalescence-based simulations indicated that Pa diverged earliest from Ps and Pt, and asymmetrical gene flow existed between any two lineages, with especially large ancient gene flow occurring between Pa and Pt. The genomic landscape of divergence between pairs of the three species are highly heterogeneous, which may have arisen through both divergent sorting of ancient polymorphisms and ongoing gene flow. We found that extant regions of the genome with introgressed ancestry reduced genetic divergence but elevated recombination rates and accounted for 5.76 % of the total genome. Introgressed genes were functionally associated with stress resistance, including innate immune response, anti-adversity response, and programmed cell death. However, candidate genes underlying postmating barriers of Pc were homozygous and resistant to introgression due to the incompatibility of alleles between loci after hybridization and were associated with endosperm and gamete formation and disease resistance. Our study revealed genomic dynamics during speciation with gene flow and identified regions of the genome that were likely introgressed and adaptive as well as candidate loci responsible for hybrid incompatibility that resulted in the formation of postmating barriers after hybridization.

Divergence of a speciation trait through artificial selection: Insights into constraints, by-product effects and sexual isolation.

Speciation and sexual isolation often occur when divergent female mating preferences target male secondary sexual traits. Despite the importance of such male signals, little is known about their evolvability and genetic linkage to other traits during speciation. To answer these questions, we imposed divergent artificial selection for 10 non-overlapping generations on the Inter-Pulse-Interval (IPI) of male courtship songs; which has been previously shown to be a major species recognition trait for females in the Drosophila athabasca species complex. Focusing on one of the species, Drosophila mahican (previously known as EA race), we examined IPI's: (1) rate of divergence, (2) response to selection in different directions, (3) genetic architecture of divergence and (4) by-product effects on other traits that have diverged in the species complex. We found rapid and consistent response for higher IPI but less response to lower IPI; implying asymmetrical constraints. Genetic divergence in IPI differed from natural species in X versus autosome contribution and in dominance, suggesting that evolution may take different paths. Finally, selection on IPI did not alter other components of male songs, or other ecological traits, and did not cause divergence in female preferences, as evidenced by lack of sexual isolation. This suggests that divergence of male courtship song IPI is unconstrained by genetic linkage with other traits in this system. This lack of linkage between male signals and other traits implies that female preferences or ecological selection can co-opt and mould specific male signals for species recognition free of genetic constraints from other traits.

The Satellite DNA Catalogues of Two Serrasalmidae (Teleostei, Characiformes): Conservation of General satDNA Features over 30 Million Years.

Satellite DNAs (satDNAs) are tandemly repeated sequences that are usually located on the heterochromatin, and the entire collection of satDNAs within a genome is called satellitome. Primarily, these sequences are not under selective pressure and evolve by concerted evolution, resulting in elevated rates of divergence between the satDNA profiles of reproductive isolated species/populations. Here, we characterized two additional satellitomes of Characiformes fish (Colossoma macropomum and Piaractus mesopotamicus) that diverged approximately 30 million years ago, while still retaining conserved karyotype features. The results we obtained indicated that several satDNAs (50% of satellite sequences in P. mesopotamicus and 43% in C. macropomum) show levels of conservation between the analyzed species, in the nucleotide and chromosomal levels. We propose that long-life cycles and few genomic changes could slow down rates of satDNA differentiation.

Responsiveness of Daily Life Gait Quality Characteristics over One Year in Older Adults Who Experienced a Fall or Engaged in Balance Exercise

Gait quality characteristics obtained from daily-life accelerometry are clinically relevant for fall risk in older adults but it is unknown whether these characteristics are responsive to changes in gait quality. We aimed to test whether accelerometry-based daily-life gait quality characteristics are reliable and responsive to changes over one year in older adults who experienced a fall or an exercise intervention. One-week trunk acceleration data were collected from 522 participants (65-97 years), at baseline and after one year. We calculated median values of walking speed, regularity (sample entropy), stability (logarithmic rate of divergence per stride), and a gait quality composite score, across all 10-s gait epochs derived from one-week gait episodes. Intraclass correlation coefficients (ICC) and limits of agreement (LOA) were determined for 198 participants who did not fall nor participated in an exercise intervention during follow-up. For responsiveness to change, we determined the number of participants who fell (n = 209) or participated in an exercise intervention (n = 115) that showed a change beyond the LOA. ICCs for agreement between baseline and follow-up exceeded 0.70 for all gait quality characteristics except for vertical gait stability (ICC = 0.69, 95% CI [0.62, 0.75]) and walking speed (ICC = 0.68, 95% CI [0.62, 0.74]). Only walking speed, vertical and mediolateral gait stability changed significantly in the exercisers over one year but effect sizes were below 0.2. The characteristic associated with most fallers beyond the LOA was mediolateral sample entropy (4.8% of fallers). For the exercisers, this was gait stability in three directions and the gait quality composite score (2.6% of exercisers). The gait quality characteristics obtained by median values over one week of trunk accelerometry were not responsive to presumed changes in gait quality after a fall or an exercise intervention in older people. This is likely due to large (within subjects) differences in gait behaviour that participants show in daily life.

Dermacentor reticulatus – a tick on its way from glacial refugia to a panmictic Eurasian population

The ornate dog tick (Dermacentor reticulatus) shows a recently expanding geographic distribution. Knowledge on its intraspecific variability, population structure, rate of genetic diversity and divergence, including its evolution and geographic distribution, is crucial to understand its dispersal capacity. All such information would help to evaluate the potential risk of future spread of associated pathogens of medical and veterinary concern. A set of 865 D. reticulatus ticks was collected from 65 localities across 21 countries, from Portugal in the west to Kazakhstan and southern Russia in the east. Cluster analyses of 16 microsatellite loci were combined with nuclear (ITS2, 18S) and mitochondrial (12S, 16S, COI) sequence data to uncover the ticks’ population structures and geographical patterns. Approximate Bayesian computation was applied to model evolutionary relationships among the found clusters. Low variability and a weak phylogenetic signal showing an east–west cline were detected both for mitochondrial and nuclear sequence markers. Microsatellite analyses revealed three genetic clusters, where the eastern and western cluster gradient was supplemented by a third, northern cluster. Alternative scenarios could explain such a tripartite population structure by independent formation of clusters in separate refugia, limited gene flow connected with isolation by distance causing a “bipolar pattern”, and the northern cluster deriving from admixture between the eastern and western populations. The best supported demographic scenario of this tick species indicates that the northern cluster derived from admixture between the eastern and western populations 441 (median) to 224 (mode) generations ago, suggesting a possible link with the end of the Little Ice Age in Europe.

Digest: Parks aren't just for us: city parks as archipelagos for the study of rapid evolution.

Can city parks provide adequate environments for studying rapid evolution? Jackson et al. (2022) found divergent selection is contributing to significant rates of phenotypic divergence across city populations of the eastern water dragon (Intellagama lesueurii), suggesting city green spaces may be ideal for the study of rapid evolution in urban populations.

Exploring clade differentiation of the Faecalibacterium prausnitzii complex.

Faecalibacterium prausnitzii is one of the most prevalent and abundant polyphyletic health-promoting components of the human gut microbiome with a propensity for dysbiotic decreases. To better understand its biology in the human gut, we specifically explored the divergence pressures acting on F.prausnitzii clades on a global scale. Five F.prausnitzii clades were de novo identified from 55 publicly available genomes and 92 high-quality metagenome assembled genomes. Divergence rate indices were constructed and validated to compare the divergence rates among the different clades and between each of the diverging genes. For each clade we identified specific patterns of diverging functionalities, probably reflecting different ecological propensities, in term of inter-host dispersion capacity or exploitation of different substrates in the gut environment. Finally, we speculate that these differences may explain, at least in part, the observed differences in the overall divergence rates of F.prausnitzii clades in human populations.

Improving convergence properties of autonomous demand side management algorithms

For implementing Autonomous Demand Side Management (ADSM) in the smart grid, when there is a large number of consumers, there are some problems like low convergence speed and large volume of calculation for finding the optimal amount of energy consumption in any time slot. In this paper, we propose a new method to speed up the convergence of ADSM algorithms and to reduce the volume of computations. When the consumers try to calculate their energy consumption individually in parallel, a problem of peak shifting will be appeared, which causes divergence or slow convergence rate in the ADSM algorithm. Therefore, we modify the ADSM algorithm such that the consumers can avoid peak shifting while making decisions in parallel. The proposed algorithm increases the convergence rate via solving a primal problem instead of the main problem, and decomposing it for each consumer to solve it in parallel. The proposed algorithm is compared with the ADSM algorithms suggested for the same system model in the literature. Our results show a significant improvement in convergence rate and computation volume. In summary, the proposed algorithm is more than 7.5 times faster than the existing algorithms and reduces the number of required operations by more than 2.8 times.

Numerical Simulation of Single-Mode 3D Rayleigh-Taylor Instability

Rayleigh-Taylor instability (RTI) is analyzed theoretically by Taylor, and 2-dimensional experimental results are obtained by Lewis in 1950. Over the 72 years, several experiments and theories are developed with the shock-driven Ritchmyer-Meshkov instability (RMI) and the shear-driven Kelvin-Helmholtz instability (KHI). Here, we emphasize the single-mode Rayleigh-Taylor instability (RTI) mixing simulation with a surface area in 3 dimensions. The simulation uses concentration equations and nonzero transport. We observed chaotic interface behavior even for this single-mode simulation, in the sense that the interface appears to have an area proportional to Δ x − 1 , with respect to its mesh (non)convergence (i.e., rate of divergence) properties.

Exploring Special Education and Center for Independent Living Professional Beliefs on Collaboration and the Value-Based Principles That Drive Secondary Transition Service Delivery

The importance of interagency collaboration to support the postschool outcomes of youth with disabilities is underscored in many ways. Perhaps one of the most important among them is the place of interagency collaboration as an evidence-based predictor of postschool success. Although Centers for Independent Living (CILs) receive U.S. federal funding to serve people with disabilities across the lifespan, little research exists to map the nature of their collaboration with local education agencies (LEAs) to this end. The current survey-based study examined perceptions of professionals in both settings (i.e., LEAs and CILs) on their current level of collaboration with one another and the value-based principles they believe influence their work as they support transition-age youth with disabilities ( n = 581). Findings indicate a widespread belief in the importance of CILs in youth transition service delivery, a stark contrast between CIL and school-based transition professional perceptions of current collaboration, and a dynamic landscape of shared and divergent ratings of importance across value-based principles of transition practice. Practical implications are outlined to inform CIL and LEA collaboration to support youth with disabilities alongside directions for future research.

Mobilising the Market: An Empirical Analysis of Crowdfunding for Judicial Review Litigation

This article provides an analysis of 413 crowdfunding campaigns raising funds for judicial review cases. In doing so, it empirically captures the judicial review crowdfunding landscape for the first time, drawing attention to the divergent rates of funding and generating a profile of the actors using the resource based on their geographic scope and their litigation experience. Noting the proliferation of campaigns seeking social goals beyond the immediate litigation, it argues that crowdfunding reveals, and gives rise to, an important reality of legal mobilisation that has received insufficient recognition – the use of law for social change by groups that are inexperienced or locally‐oriented. It therefore constructs a typology for understanding these broader patterns of legal mobilisation, accounting for the dimensions of scale and litigation experience.

Arctic charr phenotypic responses to abrupt generational scale temperature change: an insight into how cold-water fish could respond to extreme climatic events

Phenotypic plasticity, the ability of an organism to express multiple phenotypes in response to the prevailing environmental conditions without genetic change, may result in a response to anthropogenic environmental change. Given that increasing climate variability is predicted to pose a greater risk than directional climate change, we tested the effect of a water temperature differential of 4 °C on the Arctic charr phenotypic within a single generation. We demonstrate that Arctic charr phenotype can respond rapidly and markedly to an environmental temperature cue. The plastic response to different temperature regimes comprised a shift in the mean expressed phenotype but also coupled with a reduction in the between-individual phenotypic variation in the expressed head shape. The magnitude of shape difference between temperature conditions was cumulative over time but the rate of divergence diminished as fish became larger. Overall, individuals raised in the elevated temperature treatment expressed a phenotype analogous to a benthivorous ecotype of this species, rather than that of the parental pelagic feeding form. The response of cold-water freshwater species to temperature change is likely to be an interaction between the capacity of the organism for phenotypic plasticity, the mean speed of change in the environment, and the degree of short interval variation in the environment.

The Hierarchical Sequence Requirements of the H1 Subtype-Specific Noncoding Regions of Influenza A Virus.

The genome of influenza A virus consists of eight single-stranded viral RNA (vRNA) segments. The nonconserved noncoding regions (NCRs) at the 3' and 5' termini of each segment show extremely low divergence and mutation rate. They appear as segment specific among the eight segments and also subtype specific among different subtype-determinant hemagglutinin (HA) and neuraminidase (NA) segments. In order to acquire in-depth knowledge on the sequence requirements of the segment-specific or subtype-specific NCRs (ssNCRs), we, in the context of WSN (H1N1) reverse genetics, designed a virus random nucleotide selection assay (vRNSA) in which we generated pHW2000-HA plasmid libraries with random nucleotides in each grouped nucleotide positions in the 3' and 5' H1-ssNCRs, followed by virus rescue, serial passage, and deep sequencing. The resulting sequence logos present a visualized dynamic overview of the hierarchical sequence requirements of the 3' and 5' H1-ssNCRs. It showed that, in the process of continuous passage, the 3' H1-ssNCR, in general, stabilized more quickly than the 5' H1-ssNCR. The nucleotides close to the highly conserved 3' and 5' promoter regions showed higher sequence stringency than nucleotides away from the promoter regions. All stabilized sequences displayed a common feature of high A/U ratios. Especially with our mutational function analyses, we demonstrate that the 3' promoter-proximal nucleotides could cooperatively exert a direct effect on the transcription and replication of the HA segment. Together, these results provide in-depth knowledge for understanding the NCRs of influenza A virus. IMPORTANCE The segment-specific and subtype-specific nonconserved noncoding regions (ssNCRs) at both 3' and 5' ends of viral RNA segments of influenza A virus are largely conserved among the same segments of different viruses. However, the function-related sequence requirements of these ssNCRs remain unclear. In this study, through a novel self-designed vRNSA approach, we present a visualized dynamic overview diagram directly reflecting the hierarchical sequence requirements within and between the 3' and 5' H1-ssNCRs. The in-depth functional mutagenesis analyses further revealed that specific nucleotides in the 3' promoter-proximal region could cooperatively exert a direct effect on viral RNA transcription and replication. This work further advanced our knowledge in understanding the nonconserved noncoding regions of influenza A viruses.

Asymptotic and finite sample properties of Hill-type estimators in the presence of errors in observations

We establish asymptotic and finite sample properties of the Hill and Harmonic Moment estimators applied to heavy-tailed data contaminated by errors. We formulate conditions on the errors and the number of upper order statistics under which these estimators continue to be asymptotically normal. We specify analogous conditions which must hold in finite samples for the confidence intervals derived from the asymptotic normal distribution to be reliable. In the large sample analysis, we specify conditions related to second-order regular variation and divergence rates for the number of upper order statistics, k, used to compute the estimators. In the finite sample analysis, we examine several data-driven methods of selecting k, and determine which of them are most suitable for confidence interval inference. The results of these investigations are applied to interarrival times of internet traffic anomalies, which are available only with a round-off error.

Deep learning-based AMP for massive MIMO detection

Low-complexity detectors play an essential role in massive multiple-input multiple-output (MIMO) transmissions. In this work, we discuss the perspectives of utilizing approximate message passing (AMP) algorithm to the detection of massive MIMO transmission. To this end, we need to efficiently reduce the divergence occurrence in AMP iterations and bridge the performance gap that AMP has from the optimum detector while making use of its advantage of low computational load. Our solution is to build a neural network to learn and optimize AMP detection with four groups of specifically designed learn-able coefficients such that divergence rate and detection mean squared error (MSE) can be significantly reduced. Moreover, the proposed deep learning-based AMP has a much faster converging rate, and thus a much lower computational complexity than conventional AMP, providing an alternative solution for the massive MIMO detection. Extensive simulation experiments are provided to validate the advantages of the proposed deep learning-based AMP.

Conditions for Reliable Divergence Estimates from Drifter Triplets

Abstract Horizontal velocity gradients of a flow field and the related kinematic properties (KPs) of divergence, vorticity, and strain rate can be estimated from dense drifter deployments, e.g., the spatiotemporal average divergence (and other KPs) over a triangular area defined by three drifters and over a given time interval can be computed from the initial and final areas of said triangle. Unfortunately, this computation can be subject to large errors, especially when the triangle shape is far from equilateral. Therefore, samples with small aspect ratios are generally discarded. Here we derive the thresholds on two shape metrics that optimize the balance between retention of good and removal of bad divergence estimates. The primary tool is a high-resolution regional ocean model simulation, where a baseline for the average divergence can be established, so that actual errors are available. A value of 0.2 for the scaled aspect ratio Λ and a value of 0.86π for the largest interior angle θ are found to be equally effective thresholds, especially at scales of 5 km and below. While discarding samples with low Λ or high θ values necessarily biases the distribution of divergence estimates slightly toward positive values, this bias is small compared to (and in the opposite direction of) the Lagrangian sampling bias due to drifters preferably sampling convergence regions. Errors due to position uncertainty are suppressed by the shape-based subsampling. The subsampling also improves the identification of the areas of extreme divergence or convergence. An application to an observational dataset demonstrates that these model-derived thresholds can be effectively used on actual drifter data. Significance Statement Divergence in the ocean indicates how fast floating objects in the ocean spread apart, while convergence (negative divergence) captures how fast they accumulate. Measuring divergence in the ocean, however, remains challenging. One method is to estimate divergence from the trajectories of drifting buoys. This study provides guidance under what circumstances these estimates should be discarded because they are too likely to have large errors. The criteria proposed here are less stringent than some of the ad hoc criteria previously used. This will allow users to retain more of their estimates. We consider how position uncertainty affects the reliability of the divergence estimates. An observational dataset collected in the Mediterranean is used to illustrate an application of these reliability criteria.

A common mechanism drives the alignment between the micro- and macroevolution of primate molars.

A central challenge for biology is to reveal how different levels of biological variation interact and shape diversity. However, recent experimental studies have indicated that prevailing models of evolution cannot readily explain the link between micro- and macroevolution at deep timescales. Here, we suggest that this paradox could be the result of a common mechanism driving a correlated pattern of evolution. We examine the proportionality between genetic variance and patterns of trait evolution in a system whose developmental processes are well understood to gain insight into how such alignment between morphological divergence and genetic variation might be maintained over macroevolutionary time. Primate molars present a model system by which to link developmental processes to evolutionary dynamics because of the biased pattern of variation that results from the developmental architecture regulating their formation. We consider how this biased variation is expressed at the population level, and how it manifests through evolution across primates. There is a strong correspondence between the macroevolutionary rates of primate molar divergence and their genetic variation. This suggests a model of evolution in which selection is closely aligned with the direction of genetic variance, phenotypic variance, and the underlying developmental architecture of anatomical traits.

Uncertainty maps for motion around binary asteroids

In this work, two novel dynamics indicators are introduced and used to characterise the uncertain dynamics around a binary asteroid. These indicators are derived from the propagated expansion of the states in polynomial series of the uncertainty in initial conditions and dynamical model parameters. Thus, each indicator encapsulates in a single scalar the effect of the uncertainty in multiple model parameters. The first indicator directly calculates the second statistical moment of the propagated uncertainty set. This indicator gives a measure of the rate of divergence of an ensemble of trajectories in phase space. The second indicator estimates the approximation error of the polynomial expansion. Hence, it captures the nonlinearity in the distribution of the propagated states that is induced by the uncertainty. The two indicators are then used to create a map in phase space, which relates initial conditions to the sensitivity of the state over time to multiple realisation of the uncertain parameters. The case of the a spacecraft orbiting the binary asteroid system Didymos is considered in this paper. The uncertainty maps proposed in this paper are shown to reveal the characteristics of the motion around Didymos under uncertainty in the masses of both bodies.