Equation Approach Research Articles

Variational approach for time-space fractal Bogoyavlenskii equation

In this paper, we apply the variational approach for solving the time-space fractal Bogoyavlenskii equation. By the two-scale fractal complex transformation, the fractal modification of Bogoyarlenskii equation is equivalently rewritten as the original Bogoyavlenskii equation. By variational principle, different type solutions including fractal bright soliton solution, fractal bright-like soliton solution, fractal kinky-bright soliton solution and fractal periodic wave solution are provided, which are not touched in the existing literature. Numerical results are presented to show the propagation behaviours.

Robust asset-liability management games for n players under multivariate stochastic covariance models

This paper investigates a non-zero-sum stochastic differential game among n competitive CARA asset-liability managers, who are concerned about the potential model ambiguity and aim to seek the robust investment strategies. The ambiguity-averse managers are subject to uncontrollable and idiosyncratic random liabilities driven by generalized drifted Brownian motions and have access to an incomplete financial market consisting of a risk-free asset, a market index and a stock under a multivariate stochastic covariance model. The market dynamics permit not only stochastic correlation between the risky assets but also path-dependent and time-varying risk premium and volatility, depending on two affine-diffusion factor processes. The objective of each manager is to maximize the expected exponential utility of his terminal surplus relative to the average among his competitors under the worst-case scenario of the alternative measures. We manage to solve this robust non-Markovian stochastic differential game by using a backward stochastic differential equation approach. Explicit expressions for the robust Nash equilibrium investment policies, the density generator processes under the well-defined worst-case probability measures and the corresponding value functions are derived. Conditions for the admissibility of the robust equilibrium strategies are provided. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium investment strategies and draw some economic interpretations from these results.

Current dependence of the low bias resistance of small capacitance Josephson junctions

The dc current-voltage characteristics of small Josephson junctions reveal features that are not observed in larger junctions, in particular, a switch to the finite voltage state at current values much less than the expected critical current of the junction and a finite resistance in the nominally superconducting regime. Both phenomena are due to the increased sensitivity to noise associated with the small capacitance of the Josephson junction and have been extensively studied a few decades ago. Here I focus on the current bias dependence of the differential resistance of the junction at low current bias in the nominally superconducting regime, using a quantum Langevin equation approach that enables a physically transparent incorporation of the noise environment of the junction. A similar approach might be useful in modeling the sensitivity of superconducting qubits to noise in the microwave regime.

Exploring the effects of temperature on demersal fish communities in the Central Mediterranean Sea using INLA-SPDE modeling approach

Climate change significantly impacts marine ecosystems worldwide, leading to alterations in the composition and structure of marine communities. In this study, we aim to explore the effects of temperature on demersal fish communities in the Central Mediterranean Sea, using data collected from a standardized monitoring program over 23 years. Computationally efficient Bayesian inference is performed using the integrated nested Laplace approximation and the stochastic partial differential equation approach to model the spatial and temporal dynamics of the fish communities. We focused on the mean temperature of the catch (MTC) as an indicator of the response of fish communities to changes in temperature. Our results showed that MTC decreased significantly with increasing depth, indicating that deeper fish communities may be composed of colder affinity species, more vulnerable to future warming. We also found that MTC had a step-wise rather than linear increase with increasing water temperature, suggesting that fish communities may be able to adapt to gradual changes in temperature up to a certain threshold before undergoing abrupt changes. Our findings highlight the importance of considering the non-linear dynamics of fish communities when assessing the impacts of temperature on marine ecosystems and provide important insights into the potential impacts of climate change on demersal fish communities in the Central Mediterranean Sea.

Modal analysis of a submerged elastic disk: A hypersingular integral equation approach

A method based on the hypersingular integral equation approach and the modal analysis is presented to consider the effects of the motion of a submerged elastic disk on the incoming waves. Initially, the governing boundary value problem is reduced to a two-dimensional integral equation with a hypersingular kernel. This integral equation is further reduced to a one-dimensional Fredholm integral equation of the second kind with the help of Fourier series expansions and a newly defined function. As a part of modal analysis, eigenfunction expansion based on natural modes of structural motion is considered to describe the motion of a thin circular elastic disk. Physical quantities, such as hydrodynamic force, added mass, damping coefficient, and surface elevation, are numerically evaluated. The computed numerical results are verified by comparing them with those for the rigid disk horizontally submerged in deep water. Apart from this, as a part of the analytical verification of our present analysis, the reciprocity relation has been included. The effects of different parameters (disk's rigidity, radius, submergence depth, and mode of vibrations) on the aforementioned physical quantities have been studied. The maximum hydrodynamic force occurs around Ka = 0.5, while the maximum added mass and damping coefficient occur around the wavenumber Ka = 0.3 and Ka = 0.5, respectively. The peaks of the hydrodynamic force and free surface elevation become sharper with the increasing values of the disk's size. The numerical results emphasize that the wave focusing can be controlled by changing the submergence depth, size, and rigidity of the disk.

Implementation of an intervention aimed at deprescribing benzodiazepines in a large US healthcare system using patient education materials: a pre/post-observational study with a control group

ObjectivesLong-term benzodiazepine use is common despite known risks. In the original Eliminating Medications Through Patient Ownership of End Results (EMPOWER) Study set in Canada, patient education led to increased rates...

Comparing spatiotemporal species distribution models: A case study of a Scotian Shelf sea cucumber (Cucumaria frondosa)

AbstractNumerous spatiotemporal species distribution modeling frameworks are now available to the ecological practitioner. This study compared three such frameworks accessible in the R programming language: generalized additive models with spatiotemporal smooths as implemented by mgcv, spatiotemporal generalized linear mixed models based on nearest neighbor Gaussian processes as implemented by starve, and spatiotemporal generalized linear mixed models based on the stochastic partial differential equations approach as implemented by sdmTMB. The primary focus was to compare the inferences obtained from applying these frameworks to the case study of the orange‐footed sea cucumber, Cucumaria frondosa, on the Scotian Shelf off Nova Scotia, Canada. Each model was fit to catch data (2000–2019) from Fisheries and Oceans Canada's annual Research Vessel and Snow Crab surveys. Environmental covariates were sourced from high‐resolution data layers, including physical oceanographic, bathymetric, and seafloor morphometric datasets. The three models captured variability in sea cucumber distribution that would have been overlooked without a spatiotemporal approach. Although their predictions were similar, including within C. frondosa spatial reserves, the models provided different inferences regarding covariate effects. This suggests that while practitioners primarily interested in mapping species distributions need only apply the most familiar framework, those most concerned with identifying predictive environmental covariates may benefit from comparing the output from multiple approaches. Employing multiple approaches can also serve as a validation technique.

Capturing The Dynamics of Environmental Degradation and Economic Growth in Selected Developing Countries: Using Simultaneous Equation Approach

The current study aims to investigate the dynamic nexus between environmental degradation and economic growth in selected developing countries. To analyze the impact of control of corruption as a measure of governance, FDI, renewable energy and urbanization on economic growth and carbon emissions, the simultaneous equation modeling is applied. A panel of 18 selected developing countries for the time period 1995-2022 is taken for empirical verification of the relationship. This study employs descriptive analysis and for diagnostic checking the normality of residual is also tested for the possibility of any model misspecification. Correlation matrix is used to check the degree of multicollinearity among the independent variables. The nature of study indicate the use of simultaneous equation model where economic growth and carbon emission, as a measure of environmental degradation are indigenous variables. The statistical package EVIEWS is used in estimation and obtaining results. In the long run estimation model of CE, URBAN and PG are positively correlated with CE, and GDP, REEC, COC are inversely related to CE in selected developing countries. In model of GDP, CE, FDI and COC are positively correlating with GDP and REEC and PG are negatively affecting the GDP.

Effective Measures of Thickness Evolution of the Solid Electrolyte Interphase of Graphite Anodes for Li-Ion Batteries.

Upon forming, the intensity or thickness of the solid electrolyte interphase (SEI) in a Li-ion battery (LIB) evolves to various states depending on the cell materials and operation conditions. Despite a crucial role in comprehending the behaviors of an LIB, its quantitative measure is far from satisfactory mainly because of the undue complexity of the concentration profiles of the comprising chemical species. Here, we calculate the depth profiles of atomic mole fractions of C and F and their ratio as RC/F = C/F of graphite anodes for LIBs in comparison to an X-ray photoelectron spectroscopy (XPS) experiment. To this end, we take a differential equation approach to dC/dt*, where t* is the reduced XPS etching time for depth. As a result, the respective analytical expression derived for C, F, and RC/F(t*) is verified to accurately account for the experiment. Moreover, we show that RC/F(t*) in the j state can be practically expressed in , where γ is a constant for a given anode. Based on this, we suggest ξj* = (αi + βi - βj)/αj as a measure of the SEI thickness evolution from the i to j state in terms of the cycle number. As an intriguing finding, the SEI thickness evolves up to about 3 times that of its initial state, beyond which it does not appear to grow any more.

The formation of invariant optical soliton structures to electric-signal in the telegraph lines on basis of the tunnel diode and chaos visualization, conserved quantities: Lie point symmetry approach

This study critically examines the nonlinear Lonngren wave model, a mathematical representation used to describe waves in shallow water environments such as beaches, lakes, and rivers, as well as electrical signals in semiconductor materials like tunnel diodes. The symmetry generators take into account the Lie invariance criteria. A three-dimensional Lie algebra can be obtained by using the suggested methodology. It links translation symmetries in space and time, respectively, with conservation of mass and energy. The third symmetry pertains to scaling or dilation. Recognizing the constraints of the inverse scattering transform in addressing the Cauchy problem for this equation, the investigation adopts new auxiliary equation approach to ordinary differential equations. This approach yields closed-form analytical solutions for the wave model. The obtained solutions include a plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, smooth soliton, trigonometric solution, mixed singular solution, complex solitary and singular solution. Furthermore, the study develops the Hamiltonian function of the dynamical system to discuss the total energy of the system in terms of its position and momentum. Chaos analysis is performed to describe periodic, quasi-periodic, and chaotic behaviours, and a sensitivity analysis highlights the model’s sensitivity to different wave numbers. Graphical representations of selected solutions are presented in both 3-D and 2-D, illustrating the behaviour under specific physical conditions. The study concludes by identifying a comprehensive set of local conservation laws for the nonlinear Lonngren wave equation, applicable to arbitrary constant coefficients, using conservation laws multipliers.

Blockchain Technology Adoption Through the UTAUT Model

This paper studies the adoption of blockchain technology under the scope of the Unified Theory of Acceptance and Use of Technology (UTAUT). Previous results on Management Information Systems (MIS) research are divergent about the significance of UTAUT variables in explaining the adoption behaviour of blockchain technology. The paper focuses on this specific concern and tries to contribute to existing studies by testing the model in a specific context (Tunisia) and by considering the individual variable “trust in technology” as a mediating one. For this aim, a structural equation approach is adopted among 95 Tunisian professional respondents operating in technology-based sectors. The findings stipulate the importance of facilitating conditions and performance expectancy as drivers of the adoption intention. Additionally, the study reveals that trust in technology is significant in its mediating role in influencing the intention of adoption with the facilitating conditions and the social influence constructs. Moreover, the paper uncovers a direct relationship with the same variable. These findings provide valuable insights for both researchers and practitioners in understanding the factors that influence blockchain technology adoption in the Tunisian context and stress the indirect role of trust in technology with which decision-makers should be concerned.

Gender-age effects in assessing attitudes toward statistics among undergraduate students: structural equation approach

Gender-age effects in assessing attitudes toward statistics among undergraduate students: structural equation approach

Abstract 3410: Financial toxicity among patients with advanced prostate cancer in the United States

Abstract Background: Advanced prostate cancer is defined as metastatic hormone-sensitive prostate cancer (mHSPC) or castration-resistant prostate cancer (CRPC). Newer and aggressive treatments are leading to increasing lifespans in this population. As such, studying quality of life could have a large impact on the survivorship experience. An important component of quality of life is financial toxicity, defined as the financial burden and distress that can arise for patients and their families because of cancer treatment. Objectives: To understand the prevalence and predictors of financial toxicity in advanced prostate cancer. Methods: IRONMAN (International Registry of Men with Advanced Prostate Cancer) is a prospective cohort of patients with newly diagnosed mHSPC or CRPC enrolling in 15 countries. Financial toxicity was collected using the EORTC QLQ-C30 (“has your physical condition or medical treatment caused you financial difficulties?”) at enrollment and every three months thereafter. For this analysis, we studied 997 patients cared for at 37 US sites enrolled from 7/2017 to 7/2023. We examined baseline and longitudinal reports of financial toxicity across clinical and demographic factors: age at enrollment, race and ethnicity, disease state, marital status, education, employment, military status, and type of health center. We conducted adjusted risk difference analysis and multivariable regression modeling to identify predictors of financial toxicity using a generalized estimating equations approach to calculate odds ratios (OR and 95% confidence intervals, CI). Results: At enrollment, 125 (13%) patients reported experiencing “quite a bit” or “very much” financial toxicity. 21% of Black patients experienced toxicity compared to 10% of White patients. Even after incorporating all other predictors, Black patients experienced 5% (95% CI: 0, 11) greater toxicity than White patients. Independently of other predictors, patients >75 experienced 11% (CI: -17, -4) lower toxicity compared to those <65 years (while patients in the 65-74 group experienced 6% less, CI: -12, 1). Toxicity was 6% greater in patients with mHSPC (CI: 2, 10) than in patients with CRPC, and disabled or unemployed patients were at substantially higher risk. In the multivariable longitudinal analyses, older age (> 75) remained associated with significantly lower odds for financial toxicity (OR: 0.30, 0.15-0.61) while mHSPC (OR: 1.91, 1.14-3.20) and being unemployed (OR: 2.69, 1.03-6.99) or disabled (OR: 5.14, 2.29-11.6) were associated with higher odds. Conclusions: Financial toxicity is prevalent in advanced prostate cancer, especially in patients who are Black, younger than 75, diagnosed with mHSPC, or unemployed/disabled. These results may inform identification of patients at high risk for financial toxicity to support delivery of patient-situation-informed care by clinicians and targeted aid for patients at highest risk. Citation Format: Isani Singh, Bailey Vaselkiv, Emily Rencsok, Karen Autio, Deborah Enting, Alicia Morgans, Joel Nowak, Kevin Kensler, David Nanus, Robert Dreicer, Brian Lewis, Oliver Sartor, Elisabeth Heath, Phillip Kantoff, Deborah Kaye, Daniel George, Lorelei Mucci. Financial toxicity among patients with advanced prostate cancer in the United States [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 3410.

Population Size Estimation for Open Population Capture-Recapture Using Generalized Estimating Equations

This study applied a Generalized Estimating Equation (GEE) approach accounting for heterogeneity, behavioural and environmental effects to estimate the population-size for open population capture-recapture experiment. A non-spatial open population capture-recapture data was simulated using three different trapping occasions (m =4, 5, 6) with population size (N=1000). The GEE estimates for behavioral/heterogeneity covariates and heterogeneity/behavioral/environmental covariates models under different working correlation structures were also presented. The simulation results, show that, for the heterogeneity/behavioral model, the root mean square error (RMSE) for (m = 4, 5, 6) recapture occasions when N=1000 are (199.2171, 199.2573, 1193.2222) and for the heterogeneity/behavioral/environmental covariates model, the RMSE for (m= 4, 5, 6) recapture occasions when N=1000 are (199.2071, 199.2252, 1193.2052). The comparison results between behavioral/heterogeneity covariates model and heterogeneity/behavioral/environmental covariates model show that, the heterogeneity/behavioral/environmental covariates model performs better in estimating the population-size in terms of accuracy as indicated by the smallest values of RMSE. The study concludes that; environmental factors play an important role when estimating the population-size for open population capture-recapture experiments. Capture-recapture, Open oopulation, Population-size, GEE, QIC, RMSE

Variance and higher moments in the sigmoidal self-assembly of branched fibrils.

Self-assembly of functional branched filaments, such as actin filaments and microtubules, or dysfunctional ones, such as amyloid fibrils, plays important roles in many biological processes. Here, based on the master equation approach, we study the kinetics of the formation of the branched fibrils. In our model, a branched fibril has one mother branch and several daughter branches. A daughter branch grows from the side of a pre-existing mother branch or daughter branch. In our model, we consider five basic processes for the self-assembly of the branched filaments, namely, the nucleation, the dissociation of the primary nucleus of fibrils, the elongation, the fragmentation, and the branching. The elongation of a mother branch from two ends and the elongation of a daughter branch from two ends can, in principle, occur with four different rate constants associated with the corresponding tips. This leads to a pronounced impact of the directionality of growth on the kinetics of the self-assembly. Here, we have unified and generalized our four previously presented models of branched fibrillogenesis in a single model. We have obtained a system of non-linear ordinary differential equations that give the time evolution of the polymer numbers and the mass concentrations along with the higher moments as observable quantities.

How a general vulnerability for psychopathology during adolescence manifests in young adults' daily lives.

There is widespread interest in the general factor of psychopathology or 'p factor', which has been proposed to reflect vulnerability to psychopathology. We examined to what extent this 'vulnerability' is associated with dysregulations in affect and behavior that occur in daily life. As such we hoped to provide an account of how this vulnerability may be maintained. We used data from the Tracking Adolescents' Individual Lives Survey (TRAILS; N = 2,772) collected at ages 11, 14, 16, 19, and 22 years to fit a bifactor model with a general psychopathology factor, alongside internalizing, externalizing (EXT), attention-deficit/hyperactivity, and autism spectrum problem domains. Following the fifth TRAILS assessment, a subsample of participants (n = 133, age = 22.6, 43% women) with heightened risk for psychopathology completed a 6-month daily diary protocol with one assessment each day. Using a dynamic structural equation approach, we examined to what extent mean intensity, variability, inertia, and within-day co-occurrence of EXT, anxious-tense, and depressed-withdrawn affects and behaviors were associated with general factor scores. Unexpectedly, higher general factor scores were not associated with higher mean intensity of any of the three types of daily negative affects and behaviors, but were associated with higher variability and less carryover (inertia) EXT affects and behaviors. We showed that individual differences in general factor scores do not manifest as differences in average levels of daily affects and behaviors, but instead were related to a type of EXT reactivity to the environment. Future research is necessary to investigate whether reactive irritable moods may be involved in or signal vulnerability sustained psychopathology.

A relaxation approach to modeling properties of hyperbolic–parabolic type models

In this work, we propose a novel relaxation modeling approach for partial differential equations (PDEs) involving convective and diffusive terms. We reformulate the original convection–diffusion problem as a system of hyperbolic equations coupled with relaxation terms. In contrast to existing literature on relaxation modeling, where the solution of the reformulated problem converges to certain types of equations in the diffusive limit, our formalism treats the augmented problem as a system of coupled hyperbolic equations with relaxation acting on both the convective flux and the source term. Furthermore, we demonstrate that the new system of equations satisfies Liu’s sub-characteristic condition. To verify the robustness of our proposed approach, we perform numerical experiments on various important models, including nonlinear convection–diffusion problems with discontinuous coefficients. The results show the promising potential of our relaxation modeling approach for both pure and applied mathematical sciences, with applications in different models and areas.

Development of a Social Risk Score in the Electronic Health Record to Identify Social Needs Among Underserved Populations: Retrospective Study.

Patients with unmet social needs and social determinants of health (SDOH) challenges continue to face a disproportionate risk of increased prevalence of disease, health care use, higher health care costs, and worse outcomes. Some existing predictive models have used the available data on social needs and SDOH challenges to predict health-related social needs or the need for various social service referrals. Despite these one-off efforts, the work to date suggests that many technical and organizational challenges must be surmounted before SDOH-integrated solutions can be implemented on an ongoing, wide-scale basis within most US-based health care organizations. We aimed to retrieve available information in the electronic health record (EHR) relevant to the identification of persons with social needs and to develop a social risk score for use within clinical practice to better identify patients at risk of having future social needs. We conducted a retrospective study using EHR data (2016-2021) and data from the US Census American Community Survey. We developed a prospective model using current year-1 risk factors to predict future year-2 outcomes within four 2-year cohorts. Predictors of interest included demographics, previous health care use, comorbidity, previously identified social needs, and neighborhood characteristics as reflected by the area deprivation index. The outcome variable was a binary indicator reflecting the likelihood of the presence of a patient with social needs. We applied a generalized estimating equation approach, adjusting for patient-level risk factors, the possible effect of geographically clustered data, and the effect of multiple visits for each patient. The study population of 1,852,228 patients included middle-aged (mean age range 53.76-55.95 years), White (range 324,279/510,770, 63.49% to 290,688/488,666, 64.79%), and female (range 314,741/510,770, 61.62% to 278,488/448,666, 62.07%) patients from neighborhoods with high socioeconomic status (mean area deprivation index percentile range 28.76-30.31). Between 8.28% (37,137/448,666) and 11.55% (52,037/450,426) of patients across the study cohorts had at least 1 social need documented in their EHR, with safety issues and economic challenges (ie, financial resource strain, employment, and food insecurity) being the most common documented social needs (87,152/1,852,228, 4.71% and 58,242/1,852,228, 3.14% of overall patients, respectively). The model had an area under the curve of 0.702 (95% CI 0.699-0.705) in predicting prospective social needs in the overall study population. Previous social needs (odds ratio 3.285, 95% CI 3.237-3.335) and emergency department visits (odds ratio 1.659, 95% CI 1.634-1.684) were the strongest predictors of future social needs. Our model provides an opportunity to make use of available EHR data to help identify patients with high social needs. Our proposed social risk score could help identify the subset of patients who would most benefit from further social needs screening and data collection to avoid potentially more burdensome primary data collection on all patients in a target population of interest.

Stability of a Multi-Span Current-Carrying Beam Resting on Periodic Supports and Exposed to an External Magnetic Field

Abstract The stability of a current-carrying beam in an external magnetic field is studied in this paper. The beam rests on periodic supports and is modeled as an Euler–Bernoulli elastic beam. Based on the linearized stability equation and propagator transfer matrix approach for a multi-span finite-length beam, the stability equation and solutions of the several boundary value problems are obtained. While the Floquet–Bloch theory is widely used in the dynamic problem of phononic and photonic structure conditions, its application to the solution of infinite length beam static stability problem is novel. The stability values of the periodic infinite beam model are in very good agreement with one of the finite-length multi-span beams.

A Fresh Perspective on the Concatenation Model in Optical Fibers with Kerr Law of Self-Phase Modulation

The current work revisits the concatenation model having Kerr law of self-phase modulation and takes a fresher look with three different forms of integration technologies. The extended simple equation approach, the tanh-coth method, and the improved modified extended tanh-function approach yielded a spectrum of soliton solutions to the model. These reveal a spectrum of 1-soliton solutions to the model and they are all classified as well. The surface plots are also presented.