Varying Parameter Values Research Articles

A brain-wide solute transport model of the glymphatic system.

Brain waste is largely cleared via diffusion and advection in cerebrospinal fluid (CSF). CSF flows through a pathway referred to as the glymphatic system, which is also being targeted for delivering drugs to the brain. Despite the importance of solute transport, no brain-wide models for predicting clearance and delivery through perivascular pathways and adjacent parenchyma existed. We devised such a model by upgrading an existing model of CSF flow in the mouse brain to additionally solve advection-diffusion equations, thereby estimating solute transport. We simulated steady-state transport of 3 kDa dextran injected proximal to the perivascular space (PVS) of the middle cerebral artery, mimicking in vivo experiments. We performed a sensitivity analysis of 11 biological properties of PVSs and brain parenchyma by repeatedly simulating solute transport with varying parameter values. Parameter combinations that led to a large total pressure gradient, poor CSF perfusion or a steep solute gradient were deemed unrealistic. Solute concentrations in parenchyma were most sensitive to changes in pial PVS size, as this parameter linearly affects volume flow rates. We also found that realistic transport requires both highly permeable penetrating PVSs and high-resistance parenchyma. This study highlights the potential of brain-wide models to provide insights into solute transport processes.

Density dependent survival drives variation in density dependent population growth of an insect pest

Several ecological processes – from population dynamics to species co‐existence – are driven by density dependence (DD) in population growth rate. Thus, to predict and manage ecological outcomes, we need a deep understanding of which factors and demographic traits drive variation in DD. In the insect pest Tribolium castaneum, we found large variation in DD across habitats but not across source populations. We modeled DD in population growth as the product of DD in fecundity and survival, experimentally estimating each parameter. Across habitats, survival parameters varied more than fecundity, including in simulations with varying parameter values. Thus, DD in survival drives variation in density‐dependent population growth. Hence, under strong density‐dependent selection, we expect evolutionary change in density‐dependent survival, provided sufficient genetic variance. Our general framework combining detailed experiments and simulations with a simple model can be used for other species to better understand the causes and consequences of density dependent population growth.

Frequency switching leads to distinctive fast–slow behaviors in Duffing system

The slowly forced Duffing system has been found to exhibit unique fast–slow behaviors in descending frequency switching scheme, the typical of which is the sliding bursting, which is instructive for understanding the dynamics of ubiquitous frequency switching systems in scientific research and practical engineering. This paper is devoted to further refining the fast–slow dynamics of the slowly forced Duffing system with another commonly encountered frequency switching scheme, i.e., the ascending frequency switching, characterized by switching the frequency synchronously according to the increase or decrease of state variable values. Taking the forcing amplitude as an example, this paper provides a theoretical way to fully summarize the fast–slow behaviors in frequency switching systems with the variation of parameter values based on the proposed superposition analysis of one- and two-parameter bifurcations of subsystems. As a result, two typical bifurcation structures and eight threshold windows with distinct switching vector fields therein are identified, inducing up to ten different bursting patterns. Among them, several novel fast–slow dynamics, such as multiple jumps hysteresis loop formed by boundary equilibrium bifurcations and the switching failure phenomena, are presented and investigated. In particular, the underlying mechanism of threshold modulation, i.e., the evolution of unconventional bifurcations, is also found. These findings contribute to complementing and contrasting the existing studies on the fast–slow dynamics of frequency switching systems.

The use of an imperfect vaccination and awareness campaign in the control of antibiotic resistant gonorrhoea infection: A mathematical modelling perspective

The multi drug-resistant Neisseria gonorrhoeae has been classified by the World Health Organisation (WHO) as a high-priority global public health problem. This underlines the need for better understanding of the transmission dynamics and proposing an optimal intervention strategy to control the disease. In this article, a deterministic mathematical model for the transmission dynamics of gonorrhoea as an antibiotic resistant disease in a population with an imperfect vaccination is proposed and analysed. The model incorporates the classes of vaccinated individuals and individuals equipped with self protection interventions to reduce antibiotic resistant cases. The threshold parameter R0, the basic reproduction number, for the analysis of the model is calculated. In the given setting, the model exhibits a backward bifurcation for R0<1. However, if the efficacy of the vaccine is 100% without a waning effect, the model is shown to be without a backward bifurcation and the disease-free equilibrium is globally asymptotically stable whenever R0<1. The global sensitivity analysis of the model to variations in parameter values is also performed to determine the most influential parameters on the disease transmission. Moreover, the optimal control analysis of the full model is presented and the optimal intervention strategies are proposed. The proposed intervention strategies are shown to be able to control the disease within a relatively shorter period of time. Finally, numerical experiments are presented to support the theoretical analysis of the model.

Design Parameter Values for Planning Mediation Studies with Teacher and Student Mathematics Outcomes

Despite the widespread use of mediation analyses to test and unpack program effects across areas of education research, scant empirical literature is available to guide the effective and efficient prospective design of mediation studies. We contribute to this gap by developing an initial collection of empirical estimates of design parameter values for mediation studies drawing on teacher mediators and student outcomes within a three-level structure context: students nested in teachers nested in schools. Our analyses significantly expanded the scope and breadth of prior work by investigating design parameter values across a broad range of contexts (e.g., academic year, summer programs), modes (e.g., surveys, observations, assessments), mediator types (e.g., knowledge, instruction, affect, beliefs, perceptions, attitudes, climate, program implementation), instruments (e.g., MKT, CLASS, MQI, CLE, TIPS), and domains (e.g., algebra, geometry, classroom management). The results demonstrate substantial variability in parameter values across mediators and outcomes and highlight the potential value of collecting pretreatment assessments of mediators (and outcomes) in increasing statistical power. Collectively, the results underscore the significance of drawing on mediator- and outcome-specific design parameter estimates when planning studies.

Interspecies diversity in morphological responses to water stress: Study on a panel of weed and crop species

Climate change modifies the dynamics and the quantity of plant water supply, and plant morphological response to environmental factors plays a key role in crop-weed interactions. This study investigated the interspecies diversity related to the morphological responses of annual herbaceous species to water stress. Key morphological traits were measured at two growth stages on five weed and two crop (soft wheat, rapeseed) species grown on a gradient of water availability in a greenhouse experiment. For each trait, response curves to water stress were defined, and their parameters were used to quantify interspecies diversity. Generic morphological response patterns were identified across all species and plant stages. Water stress reduced leaf area per unit leaf biomass (SLA, lowering water demand) and increased the ratio of plant height to aboveground biomass for all species (HBR, keeping access to light). In most situations, the ratio of root biomass over total biomass (RBR) increased (improving water uptake). Variability in parameter values of morphological traits was primarily explained by the species, followed by growth stage. Geranium dissectum L. and Abutilon theophrasti Medik. were the most responsive species to water stress, especially at the flowering stage, with strong RBR and HBR increase and slight SLA decrease. Species differences were not related to clade (monocotyledonous/dicotyledonous) nor status (weed/crop), despite a near-significant clade effect on allocation of aboveground biomass, with grass species allocating more biomass to stems (vs leaves), while no general tendency was observed in broadleaved species. These findings provide new insights on comparative ecology of weed and crop species response to water limitation, and more research is expected to cover a wider range of weed and crop species.

Artificial Neural Network Modeling in the Presence of Uncertainty for Predicting Hydrogenation Degree in Continuous Nitrile Butadiene Rubber Processing

The transition from batch to continuous production in the catalytic hydrogenation of nitrile butadiene rubber (NBR) into hydrogenated NBR (HNBR) marks a significant advance for applications under demanding conditions. This study introduces a continuous process utilizing a static mixer (SM) reactor, which notably achieves a hydrogenation conversion rate exceeding 97%. We thoroughly review a mechanistic model of the SM reactor to elucidate the internal dynamics governing the hydrogenation process and address the inherent uncertainties in key parameters such as the Peclet number (Pe), dimensionless time (θτ), reaction coefficient (R), and flow rate coefficient (q). A comprehensive dataset generated from varied parameter values serves as the basis for training an artificial neural network (ANN), which is then compared against traditional models including linear regression, decision tree, and random forest in terms of efficacy. Our results clearly demonstrate the ANN’s superiority in predicting the degree of hydrogenation, achieving the lowest root mean squared error (RMSE) of 3.69 compared to 21.90 for linear regression, 4.94 for decision tree, and 7.51 for random forest. The ANN’s robust capability for modeling complex nonlinear relationships and dynamics significantly enhances decision-making, planning, and optimization of the reactor, reducing computational demands and operational costs. In other words, this approach allows users to rely on a single ML-based model instead of multiple mechanistic models for reflecting the effects of possible uncertainties. Additionally, a feature importance study validates the critical impact of time and element number on the hydrogenation process, further supporting the ANN’s predictive accuracy. These findings underscore the potential of ML-based models in streamlining and enhancing the efficiency of chemical production processes.

Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimating the scale parameter of the Weibull distribution. To evaluate their performance, we generate simulated datasets with different sample sizes and varying parameter values. A technique for pre-estimation shrinkage is suggested to enhance the precision of estimation. Simulation experiments proved that the Bayesian shrinkage estimator and shrinkage pre-estimation under the squared loss function method are better than the other methods because they give the least mean square error. Overall, our findings highlight the advantages of shrinkage Bayesian estimation methods for the proposed distribution. Researchers and practitioners in fields reliant on extreme value analysis can benefit from these findings when selecting appropriate Bayesian estimation techniques for modeling extreme events accurately and efficiently.

Economic impact analysis of a minimally invasive temperature-controlled radiofrequency device versus nasal surgery for the treatment of nasal airway obstruction in the United States

Objective To determine the economic impact of a minimally invasive temperature-controlled radiofrequency (TCRF) device for treating nasal airway obstruction (NAO). Methods A budget impact model was developed for two scenarios: a reference scenario of functional rhinoplasty surgery with concomitant septoplasty and inferior turbinate reduction (ITR) performed in the hospital outpatient department where TCRF is not an available treatment option and a new scenario consisting of in-office TCRF treatment of the nasal valve and ITR. A payor perspective was adopted with a hypothetical population plan size of one million members. Costs were estimated over a time horizon of 4 years. The eligible population included patients with severe/extreme NAO and nasal valve collapse (NVC) as the primary cause or significant contributor. Data inputs were sourced from targeted literature reviews. Uncertainty within the model structure and input parameters was assessed using one-way sensitivity analysis. Results The introduction of a TCRF device resulted in population-level cost savings of $20,015,123 and per-responder average cost savings of $3531 through a 4-year time horizon due to lower procedure costs and complication rates of the device relative to the surgical comparator. Results were robust when varying parameter values in sensitivity analyses, with cost savings being most sensitive to the prevalence of NAO and estimated response rates to functional rhinoplasty and TCRF. Conclusions In patients with severe/extreme NAO, with NVC as the primary or major contributor, introducing TCRF with ITR as a treatment option demonstrates the potential for significant cost savings over functional rhinoplasty with septoplasty and ITR.

Renewable Energy Real-Time Carrying Capacity Assessment Method and Response Strategy under Typhoon Weather

Currently, the integration of distributed power supply into the power grid is steadily increasing. The grid’s carrying capacity serves as a crucial metric for evaluating the grid’s resilience following the widespread integration of distributed power supply. During typhoon conditions, if the power grid experiences line breakage and load loss faults, the grid’s framework is altered, rendering the conventional carrying capacity assessment method obsolete. This study introduces a method for assessing the risk of line carrying capacity and an index for line overload probability under typhoon conditions, integrating line and transformer capacity constraints to evaluate the grid’s carrying capacity risk. The probability of line failure is modeled during typhoon events, and a modified IEEE39 node example is employed to simulate a high-penetration grid in a typhoon scenario. Addressing the issue of inadequate intraday dispatch capability under insufficient carrying capacity, we propose a multi-timescale dispatch method and derive the optimal grid dispatch strategy using the viscous bacteria algorithm. The efficacy of the multi-timescale dispatch strategy in addressing the grid’s carrying capacity risk is validated through simulation, while the economic cost of mitigating the grid’s carrying capacity risk and the line overload probability is assessed across varying parameter values.

Data-Driven Modeling of the Nonlinear Dynamics of Passive Lower-Limb Prosthetic Systems

Abstract Modeling the nonlinear dynamics of prosthetic feet is an important tool for linking prosthesis mechanical properties to end-user outcomes. There has been a renewed interest in data-driven modeling of dynamical systems, with the development of the Extended Dynamic Mode Decomposition with control (eDMDc) and the Sparse Identification of Nonlinear Dynamics with Control (SINDYc). These algorithms do not require prior information about the system, including mechanical configuration, and are data-driven. The aim of this study was to assess the feasibility and accuracy of applying these data-driven algorithms to model prosthesis nonlinear load response dynamics. Different combinations of a dynamic response foot, a hydraulic ankle unit, and three shock-absorbing pylons of varying resistance were tested loaded and unloaded at three orientations reflecting critical positions during the stance phase of walking. We tested two different data-driven algorithms, the eDMDc, with two different kernels, and the SINDYc, which regresses the coefficients for a nonlinear ordinary differential equation. Each algorithm was able to model the nonlinear prosthesis dynamics, but the SINDYc outperformed the eDMDc methods with a root mean square error across orientations &amp;lt; 1.50 mm and a maximum error in peak displacement of 1.28 mm or 4% relative error. From the estimated SINDYc governing equation of the system dynamics, we were able to simulate different mechanical behavior by systematically varying parameter values, which offers a novel foundation for designing, controlling, and classifying prosthetic systems ultimately aimed at improving prosthesis user outcomes.

Controller Design for Congestion Avoidance Based on Several Optimization Techniques

The world has become more like a small community thanks to the internet, which connects millions of people, businesses, and pieces of technology for a variety of uses. Because of the significant influence these networks have on our lives, maintaining their efficiency is important, which necessitates addressing issues like congestion. In this study, PI-controller gains are adjusted using a variety of optimization strategies to regulate the nonlinear TCPAQM model. This controller commits controlled pressured signaling characteristics and modifies computer network congestion. First manual tune PI-Controller are used; then several optimization techniques were used to tune PI-controller gains (Particle Swarm Optimization (PSO), Ant-Colony Optimization (ACO) and Simulated Annealing algorithm (SA)) and then Linear Quadratic Regulator theory are used. To test the reliability and effectiveness of each of the suggested controllers, several tests utilizing varied network parameter values, different queue sizes, and extra disturbances were conducted. MATLAB was used for all experiments., the results show the superiority of the LQR controller over PI controller with both manual and optimal tuning techniques.

Numerical investigation of a typhoid disease model in fuzzy environment

Salmonella Typhi, a bacteria, is responsible for typhoid fever, a potentially dangerous infection. Typhoid fever affects a large number of people each year, estimated to be between 11 and 20 million, resulting in a high mortality rate of 128,000 to 161,000 deaths. This research investigates a robust numerical analytic strategy for typhoid fever that takes infection protection into consideration and incorporates fuzzy parameters. The use of fuzzy parameters acknowledges the variation in parameter values among individuals in the population, which leads to uncertainties. Because of their diverse histories, different age groups within this community may exhibit distinct customs, habits, and levels of resistance. Fuzzy theory appears as the most appropriate instrument for dealing with these uncertainty. With this in mind, a model of typhoid fever featuring fuzzy parameters is thoroughly examined. Two numerical techniques are developed within a fuzzy framework to address this model. We employ the non-standard finite difference (NSFD) scheme, which ensures the preservation of essential properties like dynamic consistency and positivity. Additionally, we conduct numerical simulations to illustrate the practical applicability of the developed technique. In contrast to many classical methods commonly found in the literature, the proposed approach exhibits unconditional convergence, solidifying its status as a dependable tool for investigating the dynamics of typhoid disease.

Conserved quantities and sensitivity analysis influence of damping effect in ferrites materials

In this paper, we investigate the Kraenkel-Manna-Merle (KMM) system, which explains the nonlinear propagation of ultra-short wave pulses in specific saturated ferromagnetic materials. Ferromagnetic materials play a crucial role in data storage, manipulation, and telecommunications applications. Lie symmetry invariance analysis was conducted to identify infinitesimal generators of symmetries, and the adjoint representation was utilized to formulate an optimal system based on the identified Lie vectors. We obtained the analytical solution using the powerful power series method. To assess the impact of damping on the nonlinear Kraenkel-Manna-Merle (KMM) system, we evaluated its stability based on modulation instability criteria. Furthermore, we visually depicted wave solutions obtained by applying damping with varying parameter values. Additionally, we computed conserved quantities for the nonlinear KMM equation using the multiplier technique.

Economic production quantity for a decaying item with stochastic demand and positive lead time

This paper considers a single-item, single-location production-inventory system subject to decay and random demand. Production occurs on a single machine at a constant and finite production rate. Shortages are allowed and partially backordered, while the other fraction of unmet demand is lost. A continuous review, lot size-reorder point policy is implemented to determine the size and the timing of production orders. The typical zero-lead time assumption made in existing economic production quantity models for a decaying inventory with random demand is relaxed here: when a production order is issued, a positive lead time is required before production starts. The long-run expected total cost per time unit is derived characterizing the stock dynamics as an Itō diffusion. Several properties concerning the inventory dynamics and the cost function are demonstrated, and an optimization procedure that finds the optimal solution for the developed cost function is presented. Numerical experiments are carried out with a twofold objective: (i) to validate the inventory model through simulation, and (ii) to evaluate the model sensitivity with respect to variations in parameter values.

Modified α -Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation

In this article, we present a novel enhancement to the α -parameterized differential transform method (PDTM) for solving nonlinear boundary value problems. The proposed method is applied to solve the generalized Gardner equation by utilizing genetic algorithms to obtain optimal parameter values. Our proposed approach extends the general differential transformation method, allowing for the use of various values for the coefficient α . Our solution procedure offers a distinct advantage by allowing the original differential transformation method to be divided into multiple steps, thereby illustrating specific solution properties for nonlinear boundary value problems. Additionally, possible alternative solutions based on varying parameter values are also explored and discussed. The results with those obtained through the DTM method and exact solutions are compared to confirm the accuracy of our method and its efficiency in reaching the exact solution quickly.

Transmuted Modified Weibull Distribution for Modeling Skewed Lifetime Dataset; Properties and Application

A new five parameter model called Generalized Modified Weibull distribution is proposed and studied. The new distribution generalizes the Modified Weibull Distribution introduced by Lai et al. (2003) using transformed – Transformer framework of Alzaatreh et al. (2014) which resulted to a distribution capable of modeling skewed data (positively or negatively skewed data), as well as, symmetric data. Property of a proper probability density function was used to ascertain that the resulting function is a proper probability density function. Statistical properties of the newly generated distribution were studied. Graph of probability density function of the distribution was used to show that it is capable of modeling skewed data. Graph of cumulative density functions of the distribution was plotted using varying parameter values. Monte Carlo simulation approach was used for the test of homogeneity of the distribution and it was observed that the parameters in the distribution approach the true values as sample size increases. Maximum likelihood Estimation method was used for estimation of the model parameters. Real life dataset was used for model comparison as well as demonstration of its application.

Dynamical analysis of a discrete-time plant–herbivore model

In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system’s dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems.

Assessment of the ultimate strength of stiffened panels of ships considering uncertainties in geometrical aspects: Finite element approach and simplified formula

The development of reliability-based assessments has improved the safety design of ship structures by considering the stochastic behaviour of structural components such as stiffened panels. However, previous studies generally considered the variation in the initial geometric imperfection of a stiffened panel as a single deterministic value. To enhance the analysis, in this study, a series of ultimate strength analyses of stiffened panels were carried out by varying and combining the stiffened panel parameters, including variations in the initial geometric imperfection (2.5%, 25%, 50%, 75%, and 100% of the maximum value), modes of the imperfection (column, local, and torsional imperfection modes), slenderness ratios (plate and web slenderness), and span-to-bay ratios (3 and 6). A total of 750 stiffened panel configurations were investigated through a nonlinear finite element method (FEM) analysis using ANSYS APDL incorporated with a code in MATLAB to model the imperfections based on idealised models. The obtained ultimate strength values were then formulated using a nonlinear correlation between the variables in the regression method to yield a new formula for predicting the ultimate strength of the stiffened panel. The results showed that combining the varied parameter values significantly affected the ultimate strength of the stiffened panel and collapse modes. The newly derived formula provided good accuracy with a standard error of only 2.08% when compared with the FEM results of stiffened panels having a significant disparity with the configuration of the idealised models. This confirms the validity of the formula as a reference for evaluating the ultimate strength value with the influence of an initial geometric imperfection.

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise and uncertain parameters. By sampling techniques and robust analysis, we capture both aleatoric and epistemic uncertainty, with a user-specified confidence level, in the transition probability intervals of a so-called interval Markov decision process (iMDP). We synthesize an optimal policy on this iMDP, which translates (with the specified confidence level) to a feedback controller for the continuous model with the same performance guarantees. Our experimental benchmarks confirm that accounting for epistemic uncertainty leads to controllers that are more robust against variations in parameter values.