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.

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.

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.

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 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.

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.

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.

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.

Learning spiking neuronal networks with artificial neural networks: neural oscillations.

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.

Physiological and chaos effect on dynamics of neurological disorder with memory effect of fractional operator: A mathematical study.

BACKGROUND AND OBJECTIVE: To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases that are spread worldwide. The main objective of our work is to examine neurological disorders by early detection and treatment by taking asymptomatic. The central nervous system (CNS) is impacted by the prevalent neurological condition known as multiple sclerosis (MS), which can result in lesions that spread across time and place. It is widely acknowledged that multiple sclerosis (MS) is an unpredictable disease that can cause lifelong damage to the brain, spinal cord, and optic nerves. The use of integral operators and fractional order (FO) derivatives in mathematical models has become popular in the field of epidemiology. METHOD: The model consists of segments of healthy or barian brain cells, infected brain cells, and damaged brain cells as a result of immunological or viral effectors with novel fractal fractional operator in sight Mittag Leffler function. The stability analysis, positivity, boundedness, existence, and uniqueness are treated for a proposed model with novel fractional operators. RESULTS: Model is verified the local and global with the Lyapunov function. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium so that solutions are bounded in the feasible domain. To ensure the existence and uniqueness of the solutions to the suggested model, it makes use of Banach's fixed point and the Leray Schauder nonlinear alternative theorem. For numerical simulation and results the steps Lagrange interpolation method at different fractional order values and the outcomes are compared with those obtained using the well-known FFM method. CONCLUSION: Overall, by offering a mathematical model that can be used to replicate and examine the behavior of disease models, this research advances our understanding of the course and recurrence of disease. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

Reflective optical imaging for scattering medium using chaotic laser.

Significance: Optical imaging is a non-invasive imaging technology that utilizes near-infrared light, allows for the image reconstruction of optical properties like diffuse and absorption coefficients within the tissue. A recent trend is to use signal processing techniques or new light sources and expanding its application. Aim: We aim to develop the reflective optical imaging using the chaotic correlation technology with chaotic laser and optimize the quality and spatial resolution of reflective optical imaging. Approach: Scattering medium was measured using reflective configuration in different inhomogeneous regions to evaluate the performance of the imaging system. The accuracy of the recovered optical properties was investigated. The reconstruction errors of absorption coefficients and geometric centers were analyzed, and the feature metrics of the reconstructed images were evaluated. Results: We showed how chaotic correlation technology can be utilized for information extraction and image reconstruction. This means that a higher signal-to-noise ratio and image reconstruction of inhomogeneous phantoms under different scenarios successfully were achieved. Conclusions: This work highlights that the peak values of correlation of chaotic exhibit smaller reconstruction error and better reconstruction performance in optical imaging compared with reflective optical imaging with the continuous wave laser.

Spatial Bayesian distributed lag non-linear models (SB-DLNM) for small-area exposure-lag-response epidemiological modelling.

BACKGROUND: Distributed lag non-linear models (DLNMs) are the reference framework for modelling lagged non-linear associations. They are usually used in large-scale multi-location studies. Attempts to study these associations in small areas either did not include the lagged non-linear effects, did not allow for geographically-varying risks or downscaled risks from larger spatial units through socioeconomic and physical meta-predictors when the estimation of the risks was not feasible due to low statistical power. METHODS: Here we proposed spatial Bayesian DLNMs (SB-DLNMs) as a new framework for the estimation of reliable small-area lagged non-linear associations, and demonstrated the methodology for the case study of the temperature-mortality relationship in the 73 neighbourhoods of the city of Barcelona. We generalized location-independent DLNMs to the Bayesian framework (B-DLNMs), and extended them to SB-DLNMs by incorporating spatial models in a single-stage approach that accounts for the spatial dependence between risks. RESULTS: The results of the case study highlighted the benefits of incorporating the spatial component for small-area analysis. Estimates obtained from independent B-DLNMs were unstable and unreliable, particularly in neighbourhoods with very low numbers of deaths. SB-DLNMs addressed these instabilities by incorporating spatial dependencies, resulting in more plausible and coherent estimates and revealing hidden spatial patterns. In addition, the Bayesian framework enriches the range of estimates and tests that can be used in both large- and small-area studies. CONCLUSIONS: SB-DLNMs account for spatial structures in the risk associations across small areas. By modelling spatial differences, SB-DLNMs facilitate the direct estimation of non-linear exposure-response lagged associations at the small-area level, even in areas with as few as 19 deaths. The manuscript includes an illustrative code to reproduce the results, and to facilitate the implementation of other case studies by other researchers.

Spatially modulated ablation driven by chaotic attractors in human lung epithelial cancer cells.

A significant modification in photoinduced energy transfer in cancer cells is reported by the assistance of a dynamic modulation of the beam size of laser irradiation. Human lung epithelial cancer cells in monolayer form were studied. In contrast to the quantum and thermal ablation effect promoted by a standard focused Gaussian beam, a spatially modulated beam can caused around 15% of decrease in the ablation threshold and formation of a ring-shaped distribution of the photothermal transfer effect. Optical irradiation was conducted in A549 cells by a 532 nm single-beam emerging from a Nd:YVO4 system. Ablation effects derived from spatially modulated convergent waves were controlled by an electrically focus-tunable lens. The proposed chaotic behavior of the spatial modulation followed an Arneodo chaotic oscillator. Fractional dynamic thermal transport was analyzed in order to describe photoenergy in propagation through the samples. Immediate applications of chaos theory for developing phototechnology devices driving biological functions or phototherapy treatments can be considered.

Modeling Nonlinear Dynamics of Functionalization Layers: Enhancing Gas Sensor Sensitivity for Piezoelectrically Driven Microcantilever.

This article presents a parametrized response model that enhances the limit of detection (LOD) of piezoelectrically driven microcantilever (PD-MC) based gas sensors by accounting for the adsorption-induced variations in elastic properties of the functionalization layer (binder) and the nonlinear motional dynamics of the PD-MC. The developed model is demonstrated for quantifying cadaverine, a volatile biogenic diamine whose concentration is used to assess the freshness of meat. At low concentrations of cadaverine, an increase in the resonance frequency is observed, contrary to the expected reduction due to mass added by adsorption. The study explores the variations in the elastic modulus vis-à-vis the adsorbed mass of cadaverine and derives the resonance frequency to the adsorbed mass response function. We advance a blended technique involving the analysis of atomic force microscopy (AFM) force-distance (f-d) curves and fitting of the quartz crystal microbalance (QCM) impedance response spectrum to deduce the adsorption-induced changes in the viscoelastic properties of the functionalization layer. The findings obtained are subsequently employed in modeling the response function for a structurally nonhomogenous PD-MC, highlighting the significance of the functionalization layer to the global elastic properties. The structural composition of the PD-MC beam adopted herein features a trapezoidal base hosting the actuating piezoelectric stratum and a rectangular free end with a functionalization layer. The Euler-Bernoulli beam theory coupled with Hamilton's principle is used to develop the equation of motion, which is subsequently discretized into a set of nonlinear ordinary differential equations via Galerkin expansion, and the solutions to the first fundamental mode of vibration are determined using the method of multiple scales. The obtained solutions provide a basis for deducing the nonlinear response function model to the adsorbed mass. The derived model is validated by recorded resonance frequency changes resulting from exposure to known concentrations of cadaverine. We demonstrate that the increase in resonance frequency for low concentrations of cadaverine is due to the dominance of the variation of the elastic modulus of the functionalization layer originating from the initial binder-analyte interactions over damping due to added mass. It is concluded that the developed nonlinear response function model can reliably be used to quantify the cadaverine concentration at low concentrations with an elevated Limit of Detection.

A variety of soliton solutions of time M-fractional: Non-linear models via a unified technique.

This work explores diverse novel soliton solutions of two fractional nonlinear models, namely the truncated time M-fractional Chafee-Infante (tM-fCI) and truncated time M-fractional Landau-Ginzburg-Higgs (tM-fLGH) models. The several soliton waves of time M-fractional Chafee-Infante model describe the stability of waves in a dispersive fashion, homogeneous medium and gas diffusion, and the solitary waves of time M-fractional Landau-Ginzburg-Higgs model are used to characterize the drift cyclotron movement for coherent ion-cyclotrons in a geometrically chaotic plasma. A confirmed unified technique exploits soliton solutions of considered fractional models. Under the conditions of the constraint, fruitful solutions are gained and verified with the use of the symbolic software Maple 18. Keeping special values of the constraint, this inquisition achieved kink shape, the collision of kink type and lump wave, the collision of lump and bell type, periodic lump wave, bell shape, some periodic soliton waves for time M-fractional Chafee-Infante and periodic lump, and some diverse periodic and solitary waves for time M-fractional Landau-Ginzburg-Higgs model successfully. The required solutions in this work have many constructive descriptions, and corporal behaviors have been incorporated through some abundant 3D figures with density plots. We compare the m-fractional derivative with the beta fractional derivative and the classical form of these models in two-dimensional plots. Comparisons with others' results are given likewise.