Nonlinear modeling of oral glucose tolerance test response to evaluate associations with aging outcomes.

As people age, their ability to maintain homeostasis in response to stressors diminishes. Physical frailty, a syndrome characterized by loss of resilience to stressors, is thought to emerge due to dysregulation of and breakdowns in communication among key physiological systems. Dynamical systems modeling of these physiological systems aims to model the underlying processes that govern response to stressors. We hypothesize that dynamical systems model summaries are predictive of age-related declines in health and function. In this study, we analyze data obtained during 75-gram oral-glucose tolerance tests (OGTT) on 1,120 adults older than 50 years of age from the Baltimore Longitudinal Study on Aging. We adopt a two-stage modeling approach. First, we fit OGTT curves with the Ackerman model-a nonlinear, parametric model of the glucose-insulin system-and with functional principal components analysis. We then fit linear and Cox proportional hazards models to evaluate whether usual gait speed and survival are associated with the stage-one model summaries. We also develop recommendations for identifying inadequately-fitting nonlinear model fits in a cohort setting with numerous heterogeneous response curves. These recommendations include: (1) defining a constrained parameter space that ensures biologically plausible model fits, (2) evaluating the relative discrepancy between predicted and observed responses of biological interest, and (3) identifying model fits that have notably poor model fit summary measures, such as [Formula: see text], relative to other fits in the cohort. The Ackerman model was unable to adequately fit 36% of the OGTT curves. The stage-two regression analyses found no associations between Ackerman model summaries and usual gait speed, nor with survival. The second functional principal component score was associated with faster gait speed (p<0.01) and improved survival (p<0.01).

Nonlinearity and anthocyanin colour expression: A mathematical analysis of anthocyanin association kinetics and equilibria.

Anthocyanins are polyphenolic compounds that provide pigmentation in plants as reflected by pH-dependent structural transformations between the red flavylium cation, purple quinonoidal base, blue quinonoidal anion, colourless hemiketal, and pale yellow chalcone species. Thermodynamically stable conditions of hydrated plant cell vacuoles in vivo correspond to the colourless hemiketal, yet anthocyanin colour expression appears in an important variety of hues within plant organs such as flowers and fruit. Moreover, anthocyanin colour from grape berries is significant in red winemaking processes as it plays a crucial role in determining red wine quality. Here, nonlinear ordinary differential equations were developed to represent the evolution in concentration of various anthocyanin species in both monomeric (chemically reactive) and self-associated (temporally stable) forms for the first time, and simulations were verified experimentally. Results indicated that under hydrating conditions, anthocyanin pigmentation is preserved by self-association interactions, based on pigmented monomeric anthocyanins experiencing colour loss whereas colour-stable self-associated anthocyanins increase in concentration nonlinearly over time. In particular, self-association of the flavylium cation and the quinonoidal base was shown to influence colour expression and stability within Geranium sylvaticum flower petals and Vitis vinifera grape skins. This study ultimately characterises fundamental mechanisms of anthocyanin stabilisation and generates a quantitative framework for anthocyanin-containing systems.

Analysing the performance of a health innovation ecosystem in the COVID-19 crisis: complexity and chaos theory perspective.

BACKGROUND: This research delves into the complexity management of collaborative networks and interorganizational systems in the health innovation ecosystem on the basis of a best practice in the coronavirus disease 2019 (COVID-19) crisis. The objective is to offer specific solutions and guidelines to stakeholders in the health innovation ecosystem to control the chaos resulting from unexpected events along the ecosystem development and evolution path. METHODS: For this purpose, the performance of the Health Innovation Ecosystem in Iran (the Every Home is a Health Base plan) has been examined through a detailed and in-depth analysis of events and actions taken using documents, reports and interviews with experts. The practical application of chaos and complex adaptive system features (adaptation, time horizons, edge of chaos, sensitivity to initial conditions, state space and strange attractors) is introduced to identify and manage the transition from a state where the health innovation ecosystem is on the edge of chaos and prone to failure. Data were collected through studying documents, reports and interviews with experts, and then analysed using qualitative content analysis techniques, open and axial coding and metaphors derived from complexity and chaos theories. RESULTS: The findings indicate that to understand and embrace the complexity of the health innovation ecosystem throughout its development and evolution and manage and lead it through the edge of chaos towards successful interorganizational systems performance, it is necessary to use gap analysis to achieve consensus, establish a highly interactive governance structure with key stakeholders of the ecosystem, maintain flexibility to control bifurcations (butterfly effect), prevent transforming emergency solutions into standard routines and ensure the sustainability of the ecosystem against future threats by long-term financial security. CONCLUSIONS: This research provides insights into the dynamics of complex health systems and offers strategies for promoting successful innovation through collaborative networks and interorganizational systems in the development and evolution of the health innovation ecosystem. By embracing complexity and chaos, healthcare professionals, policy-makers and researchers can collaboratively address complex challenges and improve outcomes in health network activities. The conclusion section provides guidelines for successfully managing the complexity of the ecosystem and offers suggestions for further research.

Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm.

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Analyzing solitary wave solutions of the nonlinear Murray equation for blood flow in vessels with non-uniform wall properties.

Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. They have the potential to improve our comprehension of intricate biological systems and help us create novel therapeutic approaches, which is something that researchers are actively investigating. In this study, solitary wave solutions of the nonlinear Murray equation will be discovered using a modified extended direct algebraic method. These solutions represent a uniform variation in blood vessel shape and diameter that can be used to stimulate blood flow in patients with cardiovascular disease. These solutions are newly in the literature, and give researchers an important tool for grasping complex biological systems. To see how the solitary wave solutions behave, graphs are displayed using Matlab.

The effects of ambient temperature on road traffic injuries in Jinan city: a time-stratified case-crossover study based on distributed lag nonlinear model.

Objectives: The impact of climate change, especially extreme temperatures, on health outcomes has become a global public health concern. Most previous studies focused on the impact of disease incidence or mortality, whereas much less has been done on road traffic injuries (RTIs). This study aimed to explore the effects of ambient temperature, particularly extreme temperature, on road traffic deaths in Jinan city. Methods: Daily data on road traffic deaths and meteorological factors were collected among all residents in Jinan city during 2011-2020. We used a time-stratified case-crossover design with distributed lag nonlinear model to evaluate the association between daily mean temperature, especially extreme temperature and road traffic deaths, and its variation in different subgroups of transportation mode, adjusting for meteorological confounders. Results: A total of 9,794 road traffic deaths were collected in our study. The results showed that extreme temperatures were associated with increased risks of deaths from road traffic injuries and four main subtypes of transportation mode, including walking, Bicycle, Motorcycle and Motor vehicle (except motorcycles), with obviously lag effects. Meanwhile, the negative effects of extreme high temperatures were significantly higher than those of extreme low temperatures. Under low-temperature exposure, the highest cumulative lag effect of 1.355 (95% CI, 1.054, 1.742) for pedal cyclists when cumulated over lag 0 to 6 day, and those for pedestrians, motorcycles and motor vehicle occupants all persisted until 14 days, with ORs of 1.227 (95% CI, 1.102, 1.367), 1.453 (95% CI, 1.214, 1.740) and 1.202 (95% CI, 1.005, 1.438), respectively. Under high-temperature exposure, the highest cumulative lag effect of 3.106 (95% CI, 1.646, 5.861) for motorcycle occupants when cumulated over lag 0 to 12 day, and those for pedestrian, pedal cyclists, and motor vehicle accidents all peaked when persisted until 14 days, with OR values of 1.638 (95% CI, 1.281, 2.094), 2.603 (95% CI, 1.695, 3.997) and 1.603 (95% CI, 1.066, 2.411), respectively. Conclusion: This study provides evidence that ambient temperature is significantly associated with the risk of road traffic injuries accompanied by obvious lag effect, and the associations differ by the mode of transportation. Our findings help to promote a more comprehensive understanding of the relationship between temperature and road traffic injuries, which can be used to establish appropriate public health policies and targeted interventions.

Non-trivial relationship between behavioral avalanches and internal neuronal dynamics in a recurrent neural network.

Neuronal activity gives rise to behavior, and behavior influences neuronal dynamics, in a closed-loop control system. Is it possible then, to find a relationship between the statistical properties of behavior and neuronal dynamics? Measurements of neuronal activity and behavior have suggested a direct relationship between scale-free neuronal and behavioral dynamics. Yet, these studies captured only local dynamics in brain sub-networks. Here, we investigate the relationship between internal dynamics and output statistics in a mathematical model system where we have access to the dynamics of all network units. We train a recurrent neural network (RNN), initialized in a high-dimensional chaotic state, to sustain behavioral states for durations following a power-law distribution as observed experimentally. Changes in network connectivity due to training affect the internal dynamics of neuronal firings, leading to neuronal avalanche size distributions approximating power-laws over some ranges. Yet, randomizing the changes in network connectivity can leave these power-law features largely unaltered. Specifically, whereas neuronal avalanche duration distributions show some variations between RNNs with trained and randomized decoders, neuronal avalanche size distributions are invariant, in the total population and in output-correlated sub-populations. This is true independent of whether the randomized decoders preserve power-law distributed behavioral dynamics. This demonstrates that a one-to-one correspondence between the considered statistical features of behavior and neuronal dynamics cannot be established and their relationship is non-trivial. Our findings also indicate that statistical properties of the intrinsic dynamics may be preserved, even as the internal state responsible for generating the desired output dynamics is perturbed.

A multiscale symbolic approach to decoding delta and ripple oscillation bands as biomarkers for epileptiform discharges.

We use a multiscale symbolic approach to study the complex dynamics of temporal lobe refractory epilepsy employing high-resolution intracranial electroencephalogram (iEEG). We consider the basal and preictal phases and meticulously analyze the dynamics across frequency bands, focusing on high-frequency oscillations up to 240 Hz. Our results reveal significant periodicities and critical time scales within neural dynamics across frequency bands. By bandpass filtering neural signals into delta, theta, alpha, beta, gamma, and ripple high-frequency bands (HFO), each associated with specific neural processes, we examine the distinct nonlinear dynamics. Our method introduces a reliable approach to pinpoint intrinsic time lag scales τ within frequency bands of the basal and preictal signals, which are crucial for the study of refractory epilepsy. Using metrics such as permutation entropy (H), Fisher information (F), and complexity (C), we explore nonlinear patterns within iEEG signals. We reveal the intrinsic τmax that maximize complexity within each frequency band, unveiling the nonlinear subtle patterns of the temporal structures within the basal and preictal signal. Examining the H×F and C×F values allows us to identify differences in the delta band and a band between 200 and 220 Hz (HFO 6) when comparing basal and preictal signals. Differences in Fisher information in the delta and HFO 6 bands before seizures highlight their role in capturing important system dynamics. This offers new perspectives on the intricate relationship between delta oscillations and HFO waves in patients with focal epilepsy, highlighting the importance of these patterns and their potential as biomarkers.

On the validity of the state space correspondence strategy based on k-nearest neighbor cross-predictability in assessing directionality in stochastic systems: Application to cardiorespiratory coupling estimation.

We tested the validity of the state space correspondence (SSC) strategy based on k-nearest neighbor cross-predictability (KNNCP) to assess the directionality of coupling in stochastic nonlinear bivariate autoregressive (NBAR) processes. The approach was applied to assess closed-loop cardiorespiratory interactions between heart period (HP) variability and respiration (R) during a controlled respiration (CR) protocol in 19 healthy humans (aged from 27 to 35 yrs, 11 females) and during active standing (STAND) in 25 athletes (aged from 20 to 40 yrs, all men) and 25 non-athletes (aged from 20 to 40 yrs, all men). Over simulated NBAR processes, we found that (i) the SSC approach can detect the correct causal relationship as the direction leads to better KNNCP from the past of the driver to the future state of the target and (ii) simulations suggest that the ability of the method is preserved in any condition of complexity of the interacting series. Over CR and STAND protocols, we found that (a) slowing the breathing rate increases the strength of the causal relationship in both temporal directions in a balanced modality; (b) STAND is more powerful in modulating the coupling strength on the pathway from HP to R; (c) regardless of protocol and experimental condition, the strength of the link from HP to R is stronger than that from R to HP; (d) significant causal relationships in both temporal directions are found regardless of the level of complexity of HP variability and R. The SSC strategy is useful to disentangle closed-loop cardiorespiratory interactions.

Chaotic behavior in Lotka-Volterra and May-Leonard models of biodiversity.

Quantification of chaos is a challenging issue in complex dynamical systems. In this paper, we discuss the chaotic properties of generalized Lotka-Volterra and May-Leonard models of biodiversity, via the Hamming distance density. We identified chaotic behavior for different scenarios via the specific features of the Hamming distance and the method of q-exponential fitting. We also investigated the spatial autocorrelation length to find the corresponding characteristic length in terms of the number of species in each system. In particular, the results concerning the characteristic length are in good accordance with the study of the chaotic behavior implemented in this work.

Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis.

In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity. Additionally, we briefly investigate the Hamiltonian function and the stability of the model using a planar dynamical system approach. This involves examining trajectories, isoclines, and nullclines to illustrate stable solution paths for the wave variables. Numerical results demonstrate that these methods are reliable, straightforward, and potent tools for analyzing various nonlinear evolution equations found in physics, applied mathematics, and engineering.

Neurovascular Coupling Analysis Based on Multivariate Variational Gaussian Process Convergent Cross-Mapping.

Neurovascular coupling (NVC) provides important insights into the intricate activity of brain functioning and may aid in the early diagnosis of brain diseases. Emerging evidences have shown that NVC could be assessed by the coupling between electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS). However, this endeavor presents significant challenges due to the absence of standardized methodologies and reliable techniques for coupling analysis of these two modalities. In this study, we introduced a novel method, i.e., the collaborative multi-output variational Gaussian process convergent cross-mapping (CMVGP-CCM) approach to advance coupling analysis of EEG and fNIRS. To validate the robustness and reliability of the CMVGP-CCM method, we conducted extensive experiments using chaotic time series models with varying noise levels, sequence lengths, and causal driving strengths. In addition, we employed the CMVGP-CCM method to explore the NVC between EEG and fNIRS signals collected from 26 healthy participants using a working memory (WM) task. Results revealed a significant causal effect of EEG signals, particularly the delta, theta, and alpha frequency bands, on the fNIRS signals during WM. This influence was notably observed in the frontal lobe, and its strength exhibited a decline as cognitive demands increased. This study illuminates the complex connections between brain electrical activity and cerebral blood flow, offering new insights into the underlying NVC mechanisms of WM.

The impact of meteorological parameters on the scrub typhus incidence in Baoshan City, western Yunnan, China.

Background: Scrub typhus has become widespread across various regions in China in recent decades, causing a considerable burden on residents. While meteorological variables significantly impact the spread of scrub typhus, there is insufficient quantitative evidence illustrating this association in known high-endemic areas. Methods: A distributed lag non-linear model was applied to explore the relationship between meteorological parameters and scrub typhus incidence from 2010 to 2019 in Baoshan City, western Yunnan Province, China. Results: High monthly mean (20°C) and maximum (30°C) temperatures were associated with a peak risk of scrub typhus in the current month. Higher minimum temperatures and higher relative humidity were followed by increasing cumulative risks over the ensuing 3 months. Higher precipitation was followed by increasing cumulative risk over the ensuing 2-month period, peaking at around 30 cm. Conclusion: The non-linear lag associations between meteorological parameters and scrub typhus incidence suggest that higher monthly minimum temperature and relative humidity could be associated with an increased risk of scrub typhus in the subsequent several months, while warm temperature is more likely to impact the occurrence of scrub typhus in the current month.

Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization.

By using the power-exponential function method and the extended hyperbolic auxiliary equation method, we present the explicit solutions of the subsidiary elliptic-like equation. With the aid of the subsidiary elliptic-like equation and a simple transformation, we obtain the exact solutions of Hirota equation which include bright solitary wave, dark solitary wave, bell profile solitary wave solutions and Jacobian elliptic function solutions. Some of these solutions are found for the first time, which may be useful for depicting nonlinear physical phenomena. This approach can also be applied to solve the other nonlinear partial differential equations.

Validity and Impact of Methods for Collecting Training Data for Myoelectric Prosthetic Control Algorithms.

Intuitive regression control of prostheses relies on training algorithms to correlate biological recordings to motor intent. The quality of the training dataset is critical to run-time regression performance, but accurately labeling intended hand kinematics after hand amputation is challenging. In this study, we quantified the accuracy and precision of labeling hand kinematics using two common training paradigms: 1) mimic training, where participants mimic predetermined motions of a prosthesis, and 2) mirror training, where participants mirror their contralateral intact hand during synchronized bilateral movements. We first explored this question in healthy non-amputee individuals where the ground-truth kinematics could be readily determined using motion capture. Kinematic data showed that mimic training fails to account for biomechanical coupling and temporal changes in hand posture. Additionally, mirror training exhibited significantly higher accuracy and precision in labeling hand kinematics. These findings suggest that the mirror training approach generates a more faithful, albeit more complex, dataset. Accordingly, mirror training resulted in significantly better offline regression performance when using a large amount of training data and a non-linear neural network. Next, we explored these different training paradigms online, with a cohort of unilateral transradial amputees actively controlling a prosthesis in real-time to complete a functional task. Overall, we found that mirror training resulted in significantly faster task completion speeds and similar subjective workload. These results demonstrate that mirror training can potentially provide more dexterous control through the utilization of task-specific, user-selected training data. Consequently, these findings serve as a valuable guide for the next generation of myoelectric and neuroprostheses leveraging machine learning to provide more dexterous and intuitive control.

Nonlinear association of fibrinogen levels with functional prognosis in patients with acute ischemic stroke: a prospective cohort study.

OBJECTIVE: Fibrinogen, essential in primary hemostasis, platelet aggregation, and leukocyte-endothelial interactions, is also associated with a heightened risk of acute ischemic stroke (AIS). However, its influence on AIS patient outcomes is unclear. This study examines the correlation between fibrinogen levels and the risk of unfavorable outcomes three months post-AIS. METHODS: This is a secondary analysis of a prospective cohort study conducted in Korea. The sample consisted of 1851 AIS patients who received treatment at a Korean hospital between January 2010 and December 2016. Statistical models were established to understand the relationship between fibrinogen levels(mg/dL) and unfavorable outcomes(mRs ≥ 3), including logistic regression models, Generalized Additive Models (GAM), and smooth curve fitting (penalized splines). The log-likelihood ratio test has been utilized to evaluate the best fit. To ensure the robustness of the results, sensitivity analyses were conducted by reanalyzing the relationship after excluding participants with TG > 200 mg/dl and BMI > 25 kg/m2. Subgroup analyses were also performed to assess whether influencing factors modify the association between fibrinogen levels and unfavorable outcomes. RESULTS: After adjusting for multiple covariates including age, BMI, sex, LDL-c, TG, HGB, HDL-c, BUN, FPG, ALB, PLT, AF, hypertension, smoking, DM, mRs score at admission, the binary logistic regression model demonstrated revealed a significant positive association between fibrinogen levels and the risk of unfavorable outcomes in AIS patients (OR = 1.215, 95% CI: 1.032-1.429, p = 0.019). Sensitivity analyses supported these findings, with similar ORs observed in subsets of patients with TG < 200 mg/dL (OR = 1.221, 95% CI: 1.036-1.440) and BMI < 25 kg/m2 (OR = 1.259, 95% CI: 1.051-1.509). Additionally, the relationship between fibrinogen levels and outcomes was nonlinear, with a critical threshold of 2.74 g/L. Below the inflection point, the OR for unfavorable outcomes was 0.666 ((95% CI: 0.360, 1.233, p = 0.196), whereas above it, the OR increased to 1.374 (95% CI: 1.138, 1.659). CONCLUSIONS: This study has provided evidence of a positive and nonlinear correlation between fibrinogen levels and 3-month poor functional outcomes in patients with AIS. When fibrinogen levels exceeded 2.74 g/L, a significant and positive association was observed with the risk of poor outcomes. This study provides a further reference for optimizing rehabilitation exercises and facilitating clinical counseling in patients with acute ischemic stroke.

Classification of motor imagery using chaotic entropy based on sub-band EEG source localization.

Objective.Electroencephalography (EEG) has been widely used in motor imagery (MI) research by virtue of its high temporal resolution and low cost, but its low spatial resolution is still a major criticism. The EEG source localization (ESL) algorithm effectively improves the spatial resolution of the signal by inverting the scalp EEG to extrapolate the cortical source signal, thus enhancing the classification accuracy.Approach.To address the problem of poor spatial resolution of EEG signals, this paper proposed a sub-band source chaotic entropy feature extraction method based on sub-band ESL. Firstly, the preprocessed EEG signals were filtered into 8 sub-bands. Each sub-band signal was source localized respectively to reveal the activation patterns of specific frequency bands of the EEG signals and the activities of specific brain regions in the MI task. Then, approximate entropy, fuzzy entropy and permutation entropy were extracted from the source signal as features to quantify the complexity and randomness of the signal. Finally, the classification of different MI tasks was achieved using support vector machine.Main result.The proposed method was validated on two MI public datasets (brain-computer interface (BCI) competition III IVa, BCI competition IV 2a) and the results showed that the classification accuracies were higher than the existing methods.Significance.The spatial resolution of the signal was improved by sub-band EEG localization in the paper, which provided a new idea for EEG MI research.

Nonlinear Fourier classification of 663 rogue waves measured in the Philippine Sea.

Rogue waves are sudden and extreme occurrences, with heights that exceed twice the significant wave height of their neighboring waves. The formation of rogue waves has been attributed to several possible mechanisms such as linear superposition of random waves, dispersive focusing, and modulational instability. Recently, nonlinear Fourier transforms (NFTs), which generalize the usual Fourier transform, have been leveraged to analyze oceanic rogue waves. Next to the usual linear Fourier modes, NFTs can additionally uncover nonlinear Fourier modes in time series that are usually hidden. However, so far only individual oceanic rogue waves have been analyzed using NFTs in the literature. Moreover, the completely different types of nonlinear Fourier modes have been observed in these studies. Exploiting twelve years of field measurement data from an ocean buoy, we apply the nonlinear Fourier transform (NFT) for the nonlinear Schrödinger equation (NLSE) (referred to NLSE-NFT) to a large dataset of measured rogue waves. While the NLSE-NFT has been used to analyze rogue waves before, this is the first time that it is systematically applied to a large real-world dataset of deep-water rogue waves. We categorize the measured rogue waves into four types based on the characteristics of the largest nonlinear mode: stable, small breather, large breather and (envelope) soliton. We find that all types can occur at a single site, and investigate which conditions are dominated by a single type at the measurement site. The one and two-dimensional Benjamin-Feir indices (BFIs) are employed to examine the four types of nonlinear spectra. Furthermore, we verify on a part of the data set that for the localized types, the largest nonlinear Fourier mode can be attributed directly to the rogue wave, and investigate the relation between the height of the rogue waves and that of the dominant nonlinear Fourier mode. While the dominant nonlinear Fourier mode in general only contributes a small fraction of the rogue wave, we find that soliton modes can contribute up to half of the rogue wave. Since the NLSE does not account for directional spreading, the classification is repeated for the first quartile with the lowest directional spreading for each type. Similar results are obtained.

Extraction of new solitary wave solutions in a generalized nonlinear Schrödinger equation comprising weak nonlocality.

This article delves into examining exact soliton solutions within the context of the generalized nonlinear Schrödinger equation. It covers higher-order dispersion with higher order nonlinearity and a parameter associated with weak nonlocality. To tackle this equation, two reputable methods are harnessed: the sine-Gordon expansion method and the [Formula: see text]-expansion method. These methods are employed alongside suitable traveling wave transformation to yield novel, efficient single-wave soliton solutions for the governing model. To deepen our grasp of the equation's physical significance, we utilize Wolfram Mathematica 12, a computational tool, to produce both 3D and 2D visual depictions. These graphical representations shed light on diverse facets of the equation's dynamics, offering invaluable insights. Through the manipulation of parameter values, we achieve an array of solutions, encompassing kink-type, dark soliton, and solitary wave solutions. Our computational analysis affirms the effectiveness and versatility of our methods in tackling a wide spectrum of nonlinear challenges within the domains of mathematical science and engineering.

Estimation of instantaneous peak flows in Canadian rivers: an evaluation of conventional, nonlinear regression, and machine learning methods.

Instantaneous peak flows (IPFs) are often required to derive design values for sizing various hydraulic structures, such as culverts, bridges, and small dams/levees, in addition to informing several water resources management-related activities. Compared to mean daily flows (MDFs), which represent averaged flows over a period of 24 h, information on IPFs is often missing or unavailable in instrumental records. In this study, conventional methods for estimating IPFs from MDFs are evaluated and new methods based on the nonlinear regression framework and machine learning architectures are proposed and evaluated using streamflow records from all Canadian hydrometric stations with natural and regulated flow regimes. Based on a robust model selection criterion, it was found that multiple methods are suitable for estimating IPFs from MDFs, which precludes the idea of a single universal method. The performance of machine learning-based methods was also found reasonable compared to conventional and regression-based methods. To build on the strengths of individual methods, the fusion modeling concept from the machine learning area was invoked to synthesize outputs of multiple methods. The study findings are expected to be useful to the climate change adaptation community, which currently heavily relies on MDFs simulated by hydrologic models.