Fisher Models Research Articles

A numerical procedure for approximating time fractional nonlinear Burgers–Fisher models and its error analysis

Burger and Fisher diffusion transfer properties and reactions from the characteristics are studied using a non-linear equation. The nonlinear fractional Burgers–Fisher equation (NFB-FE) appears in realistic physical situations such as ultra-slow kinetics, Brownian motion of particles, anomalous diffusion, polymerases of ribonucleic acid and deoxyribonucleic acid, continuous random movement, and formation of wave patterns. The present study focuses on the collocation scheme based on the shifted Chebyshev basis (SCB) and the compact finite difference method to obtain the numerical scheme of the NFB-FE. The simulation model is created in the two steps: Initially, a semi-discrete is formed in a temporal sense, applying a linear approximation with an accuracy order of two. Next, we examine the unconditional stability and the convergence order. In the second stage, the collocation approach based on the SCB of the fourth type is used to discretize the spatial derivative parts and generate the full-discrete scheme.

New Solutions of Fuzzy-Fractional Fisher Models via Optimal He–Laplace Algorithm

Fuzzy differential equations have gained significant attention in recent years due to their ability to model complex systems in the presence of uncertainty or imprecise information. These equations find applications in various fields, such as biomathematics, horological processes, production inventory models, epidemic models, fluid models, and economic investments. The Fisher model is one such example, which studies the dynamics of a population with uncertain growth rates. This study proposes a dual parametric extension of the He–Laplace algorithm for solving time-fractional fuzzy Fisher models. The proposed methodology uses triangular fuzzy numbers to introduce uncertainty in highly nonlinear fractional differential equations under the generalized Hukuhara differentiability concept. The obtained solutions are validated against existing results in crisp form and are found to be more accurate. The results are analyzed by finding solutions with different values of spatial coordinate ξ , time η , and ς -cut for both upper and lower bounds, and they are presented graphically. The analysis reveals that the uncertain probability density function gradually decreases at left and right boundaries when the fractional order is increased. The study provides valuable insights into the behavior of population growth under uncertain conditions and demonstrates the effectiveness of the proposed methodology in solving fuzzy-fractional models.

Temporomandibular disorders, bite force and osseous changes of the temporomandibular joints in patients with hypermobile Ehlers-Danlos syndrome compared to a healthy control group.

BackgroundEhlers‐Danlos syndrome (EDS) is a hereditary disorder that affects the connective tissue and collagen structures in the body characterised by joint hypermobility, skin hyperextensibility and tissue fragility.ObjectiveThe aim was to investigate temporomandibular disorders (TMD), bite force, teeth in occlusal contact and osseous changes of the temporomandibular joints (TMJs) in 26 patients with hypermobile EDS (hEDS), differentiated by a genetic test, compared to 39 healthy controls.MethodsClinical examination according to Diagnostic Criteria for Temporomandibular Disorders (DC/TMD), radiological examinations of the TMJs by cone‐beam‐computed tomographic (CBCT) scans, registration of bite force and teeth in occlusal contact was performed. Statistical analyses included Fisher's Exact Test, multiple logistic and linear regression models adjusted for age, gender and Body Mass Index (BMI).ResultsSingle symptoms and signs of TMD occurred significantly more often in hEDS (p = .002; p = .001; p = .003; p = <.0001; p = .012) and maximum mouth opening was significantly smaller in hEDS compared to controls (p = <.0001). The DC/TMD diagnosis myalgia, myofascial pain with referral, arthralgia, headache attributed to TMD, disc displacement disorders and degenerative joint disease occurred significantly more often in hEDS compared to controls (p = .000; p = .008; p = .003; p = .000; p = <.0001; p = .010, respectively). No significant differences were found in bite force and in teeth in occlusal contact between the groups (p > .05). On CBCT of the TMJs, subcortical sclerosis occurred significantly more often in hEDS compared to controls (p = .005).ConclusionSymptoms and signs of TMD and osseous changes of the TMJs occurred significantly more often in hEDS. Bite force and teeth in occlusal contact were comparable to controls.

Gestational SARS-CoV-2 infection is associated with placental expression of immune and trophoblast genes

IntroductionMaternal SARS-CoV-2 infection during pregnancy is associated with adverse pregnancy outcomes and can have effects on the placenta, even in the absence of severe disease or vertical transmission to the fetus. This study aimed to evaluate histopathologic and molecular effects in the placenta after SARS-CoV-2 infection during pregnancy. MethodsWe performed a study of 45 pregnant participants from the Generation C prospective cohort study at the Mount Sinai Health System in New York City. We compared histologic features and the expression of 48 immune and trophoblast genes in placentas delivered from 15 SARS-CoV-2 IgG antibody positive and 30 IgG SARS-CoV-2 antibody negative mothers. Statistical analyses were performed using Fisher's exact tests, Spearman correlations and linear regression models. ResultsThe median gestational age at the time of SARS-CoV-2 IgG serology test was 35 weeks. Two of the IgG positive participants also had a positive RT-PCR nasal swab at delivery. 82.2% of the infants were delivered at term (≥37 weeks), and gestational age at delivery did not differ between the SARS-CoV-2 antibody positive and negative groups. No significant differences were detected between the groups in placental histopathology features. Differential expression analyses revealed decreased expression of two trophoblast genes (PSG3 and CGB3) and increased expression of three immune genes (CXCL10, TLR3 and DDX58) in placentas delivered from SARS-CoV-2 IgG positive participants. DiscussionSARS-CoV-2 infection during pregnancy is associated with gene expression changes of immune and trophoblast genes in the placenta at birth which could potentially contribute to long-term health effects in the offspring.

Heat-flow parameters affecting microstructure and mechanical properties of Al–Cu and Al–Ni alloys in directional solidification: an experimental comparative study

Abstract A comparative analysis was carried out of the alloys examined, using the results found for thermal variables, macrostructure, dendrite arm spacing, modulus of elasticity and microhardness. Comparing all the results for variables, a predominance was found of higher values for the Al-5.0 wt.% Cu alloy in relation to those for the Al-5.0 wt.% Ni alloy. Although structural transition has occurred in both alloys, the columnar–equiaxed transition position in castings was not altered during the solidification experiments. Addition of Ni solute into pure aluminum favors a significant decrease in tertiary dendrite spacing, while Cu addition leads to a coarser microstructure. Primary dendrite arm spacing, also, was measured along the castings of both alloys. Theoretical approaches such as the well-known Hunt–Lu, Bouchard–Kirkaldy, and Kurz–Fisher models were used to determine quantitatively this particular microstructural parameter. Good agreement was observed between experimental data and predictions by Hunt–Lu and Bouchard–Kirkaldy models, which assume solidification under a transient heat-flow condition. Finally, empirical equations relating tertiary dendritic arm spacing and mechanical properties to the scale of the dendritic microstructure have been proposed. While no relationship was observed between modulus of elasticity and tertiary dendritic arm spacing, addition of Cu into pure aluminum as an alloying element favored a reduction in the average value of modulus of elasticity when compared with those observed for the Al–Ni alloy. It was found that the microhardness decreases with increasing tertiary dendritic arm spacings. On the other hand, solute addition of Cu into commercially pure aluminum favors a microhardness higher than that verified during upward unidirectional solidification of the Al-5.0 wt.% Ni alloy.

The symmetric coalescent and Wright–Fisher models with bottlenecks

We define a new class of Ξ-coalescents characterized by a possibly infinite measure over the nonnegative integers. We call them symmetric coalescents since they are the unique family of exchangeable coalescents satisfying a symmetry property on their coagulation rates: they are invariant under any transformation that consists of moving one element from one block to another without changing the total number of blocks. We illustrate the diversity of behaviors of this family of processes by introducing and studying a one parameter subclass, the (β,S)-coalescents. We also embed this family in a larger class of Ξ-coalescents arising as the limit genealogies of Wright–Fisher models with bottlenecks. Some convergence results rely on a new Skorokhod type metric, that induces the Meyer–Zheng topology, which allows us to study the scaling limit of non-Markovian processes using standard techniques.

Asymptotic genealogies for a class of generalized Wright–Fisher models

A class of Cannings models is studied, with population size N having a mixed multinomial offspring distribution with random success probabilities ${W_{1}},\dots ,{W_{N}}$ induced by independent and identically distributed positive random variables ${X_{1}},{X_{2}},\dots $ via ${W_{i}}:={X_{i}}/{S_{N}}$, $i\in \{1,\dots ,N\}$, where ${S_{N}}:={X_{1}}+\cdots +{X_{N}}$. The ancestral lineages are hence based on a sampling with replacement strategy from a random partition of the unit interval into N subintervals of lengths ${W_{1}},\dots ,{W_{N}}$. Convergence results for the genealogy of these Cannings models are provided under assumptions that the tail distribution of ${X_{1}}$ is regularly varying. In the limit several coalescent processes with multiple and simultaneous multiple collisions occur. The results extend those obtained by Huillet [J. Math. Biol. 68 (2014), 727–761] for the case when ${X_{1}}$ is Pareto distributed and complement those obtained by Schweinsberg [Stoch. Process. Appl. 106 (2003), 107–139] for models where sampling is performed without replacement from a supercritical branching process.

Stein’s method for the Poisson–Dirichlet distribution and the Ewens sampling formula, with applications to Wright–Fisher models

We provide a general theorem bounding the error in the approximation of a random measure of interest—for example, the empirical population measure of types in a Wright–Fisher model—and a Dirichlet process, which is a measure having Poisson–Dirichlet distributed atoms with i.i.d. labels from a diffuse distribution. The implicit metric of the approximation theorem captures the sizes and locations of the masses, and so also yields bounds on the approximation between the masses of the measure of interest and the Poisson–Dirichlet distribution. We apply the result to bound the error in the approximation of the stationary distribution of types in the finite Wright–Fisher model with infinite-alleles mutation structure (not necessarily parent independent) by the Poisson–Dirichlet distribution. An important consequence of our result is an explicit upper bound on the total variation distance between the random partition generated by sampling from a finite Wright–Fisher stationary distribution, and the Ewens sampling formula. The bound is small if the sample size n is much smaller than N1/6log(N)−1/2, where N is the total population size. Our analysis requires a result of separate interest, giving an explicit bound on the second moment of the number of types of a finite Wright–Fisher stationary distribution. The general approximation result follows from a new development of Stein’s method for the Dirichlet process, which follows by viewing the Dirichlet process as the stationary distribution of a Fleming–Viot process, and then applying Barbour’s generator approach.

Assessing the State of Coupled Social-Ecological Modeling in Support of Ecosystem Based Fisheries Management in the United States

There has been a proliferation of coupled social-ecological systems (SES) models created and published in recent years. However, the degree of coupling between natural and social systems varies widely across the different coupled models and is often a function of the disciplinary background of the team conducting the research. This manuscript examines models developed for and used by NOAA Fisheries in support of Ecosystem Based Fisheries Management (EBFM) in the United States. It provides resource managers and interdisciplinary scientists insights on the strengths and weaknesses of the most commonly used SES models: end-to-end models, conceptual models, bioeconomic models, management strategy evaluations (MSEs), fisher behavior models, integrated social vulnerability models, and regional economic impact models. These model types are not unique to the literature, but allow us to differentiate between one-way coupled models – where outputs from one model are inputs into a second model of another discipline with no feedback to the first model, and two-way coupled models – where there are linkages between the natural and social system models. For a model to provide useful strategic or tactical advice, it should only be coupled to the degree necessary to understand the important dynamics/responses of the system and to create management-relevant performance metrics or potential risks from an (in)action. However, one key finding is to not wait to integrate! This paper highlights the importance of “when” the coupling happens, as timing affects the ability to fully address management questions and multi-sectoral usage conflicts that consider the full SES for EBFM or ecosystem based management (EBM) more generally.

ASSESSMENT OF INVESTMENT ATTRACTIVENESS OF HIGH-TECH COMPANIES

The article considers and systematize different approaches to assessment of investment attractiveness of companies, including high-tech ones, by criteria of the number of used indicators and assessment approach. The paper proposes and tests the authors’ methodology for evaluating the investment attractiveness of high-tech companies, including the assessment of company current situation and development potential, the integral indicator of investment attractiveness and its recommended value. The study forms portfolios of stocks of high-tech companies traded on the Moscow Stock Exchange, using Markowitz and Fisher models to identify the correlation between the level of investment attractiveness of a company and the type of stock portfolio. The paper reveals the correlation between the level of investment attractiveness and shares in the portfolio, as well as the type of portfolio (minimum risk, maximum return, optimal).

Prediction of Outcome Using Quantified Blood Volume in Aneurysmal SAH.

In patients with SAH, the amount of blood is strongly associated with clinical outcome. However, it is commonly estimated with a coarse grading scale, potentially limiting its predictive value. Therefore, we aimed to develop and externally validate prediction models for clinical outcome, including quantified blood volumes, as candidate predictors. Clinical and radiologic candidate predictors were included in a logistic regression model. Unfavorable outcome was defined as a modified Rankin Scale score of 4-6. An automatic hemorrhage-quantification algorithm calculated the total blood volume. Blood was manually classified as cisternal, intraventricular, or intraparenchymal. The model was selected with bootstrapped backward selection and validated with the R 2, C-statistic, and calibration plots. If total blood volume remained in the final model, its performance was compared with models including location-specific blood volumes or the modified Fisher scale. The total blood volume, neurologic condition, age, aneurysm size, and history of cardiovascular disease remained in the final models after selection. The externally validated predictive accuracy and discriminative power were high (R 2 = 56% ± 1.8%; mean C-statistic = 0.89 ± 0.01). The location-specific volume models showed a similar performance (R 2 = 56% ± 1%, P = .8; mean C-statistic = 0.89 ± 0.00, P = .4). The modified Fisher models were significantly less accurate (R 2 = 45% ± 3%, P < .001; mean C-statistic = 0.85 ± 0.01, P = .03). The total blood volume-based prediction model for clinical outcome in patients with SAH showed a high predictive accuracy, higher than a prediction model including the commonly used modified Fisher scale.

Population Pharmacokinetics/Pharmacodynamics of Dabrafenib Plus Trametinib in Patients with BRAF-Mutated Metastatic Melanoma.

Patients treated with dabrafenib/trametinib (DAB/TRA) exhibit a large interindividual variability in clinical outcomes. The aims of this study were to characterize the pharmacokinetics of DAB, hydroxy-dabrafenib (OHD), and TRA in BRAF-mutated patients and to investigate the exposure–response relationship for toxicity and efficacy in metastatic melanoma (MM) patients. Univariate Fisher and Wilcoxon models including drug systemic exposure (area under the plasma concentration curve, AUC) were used to identify prognostic factors for the onset of dose-limiting toxicities (DLT), and Cox models for overall (OS) and progression-free survival (PFS). Seventy-three BRAF-mutated patients were included in pharmacokinetic (n = 424, NONMEM) and 52 in pharmacokinetic/pharmacodynamic analyses. Age and sex were identified as determinants of DAB and OHD clearances (p < 0.01). MM patients experiencing DLT were overexposed to DAB compared to patients without DLT (AUC: 9624 vs. 7485 ng∙h/mL, respectively, p < 0.01). Eastern Cooperative Oncology Group Performance Status (ECOG PS) ≥ 2 and plasma ratio AUCOHD/AUCDAB ≥ 1 were independently associated with shorter OS (HR: 6.58 (1.29–33.56); p = 0.023 and 10.61 (2.34–48.15), p = 0.022, respectively). A number of metastatic sites ≥3 and cerebral metastases were associated with shorter PFS (HR = 3.25 (1.11–9.50); p = 0.032 and HR = 1.23 (1.35–10.39), p = 0.011; respectively). TRA plasma exposure was neither associated with toxicity nor efficacy. Our results suggest that early drug monitoring could be helpful to prevent the onset of DLT in MM patients, especially in fragile patients such as the elderly. Regarding efficacy, the clinical benefit to monitor plasma ratio AUCOHD/AUCDAB deserves more investigation in a larger cohort of MM patients.

Rural Trauma Team Development Course Instills Confidence in Critical Access Hospitals.

The American College of Surgeons' Rural Trauma Team Development Course (RTTDC) was designed to help rural hospitals optimize a team approach to trauma management recognizing the need for early transfer. Little literature exists on the success of RTTDC achieving its objectives. The purpose of this study was to determine the impact of RTTDC on rural trauma team members. RTTDC was hosted at seven rural hospitals. A pre-course 30-question Likert survey gauging confidence managing trauma patients was administered to participants. Four weeks following, participants received a post-course survey with corresponding Likert questions and 11 trauma knowledge-based questions. Chi-square, Fisher's exact tests and general linear models were utilized. Statistical significance is set as p < 0.05. 111 participants completed the pre-course survey; 53 (48%) completed the post-course survey. Results presented on a 5-point Likert scale with 1 = "not at all comfortable" to 5 = "extremely comfortable." Participants knowing their role in the trauma team improved by 16% (p = 0.02). Familiarity with the roles of other trauma team members was significantly improved (3.4 vs. 4.15; p < 0.01). Participants comfort with resuscitating trauma patients and managing traumatic brain injury significantly improved (3.29 vs. 3.69; p = 0.01 and 2.62 vs. 3.14; p = 0.004, respectively). Comfortability communicating with the regional trauma center improved significantly (3.64 vs. 4.19; p = 0.004). Participant decision to transfer trauma patients within 15min of arrival improved by 3.2%. Participants answered 82% of the knowledge-based questions correctly. RTTDC instills confidence in providers at rural hospitals. The information taught is well retained, allowing for quality care and timely patient transfer to the nearest trauma center.

Predicted property investment returns: risk and growth models

Purpose The purpose of this paper is to discuss the principal measures of performance used in property and other investment types. In particular, the briefing will explore the relationship of the expected IRR with the initial return, highlighting the role of growth in the investment dynamic. Design/methodology/approach This education briefing is an overview of investment growth models with worked examples. Findings The analysis of property growth models is akin to the Fisher and Gordon growth models used in other finance markets. Practical implications This comparison of the models can work for all forms of investment. Similarly, instead of looking at the overall return as the measure of comparison (expected vs required), it is possible to work backwards and deduce market expectations and compare these with the investors view on those variables. Originality/value This is a review of existing models.

The geometry of recombination

With the tools of information geometry, we can express relations between marginals of a joint distribution in geometric terms. We develop this framework in the context of population genetics and use this to interpret the famous Ohta–Kimura formula (cf. Ohta and Kimura in Genet Res 13(01):47–55, 1969) and discuss its generalizations for linkage equilibria in Wright–Fisher models with recombination with several loci. The state space associated with the Ohta–Kimura model is simply a Riemannian manifold of constant positive curvature. Furthermore, the equilibria states for recombination can be interpreted geometrically as a product of spheres. In the case of only 2 loci, we also derive the behavior of the mutual information between these two loci.

Equilibrium in Wright–Fisher Models of Population Genetics

For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the current value of the random process and its equilibrium value. Then the drift component of the dynamic process of gene frequencies, primarily expressed as a ratio of two quadratic forms, is transformed into a cubic parabola with a certain normalization factor.

On the number of siblings and p-th cousins in a large population sample.

The number of individuals in a random sample with close relatives in the sample is a quantity of interest when designing Genome Wide Association Studies and other cohort based genetic, and non-genetic, studies. In this paper, we develop expressions for the distribution and expectation of the number of p-th cousins in a sample from a population of size N under two diploid Wright-Fisher models. We also develop simple asymptotic expressions for large values of N. For example, the expected proportion of individuals with at least one p-th cousin in a sample of K individuals, for a diploid dioecious Wright-Fisher model, is approximately [Formula: see text]. Our results show that a substantial fraction of individuals in the sample will have at least a second cousin if the sampling fraction (K/N) is on the order of [Formula: see text]. This confirms that, for large cohort samples, relatedness among individuals cannot easily be ignored.

Inference from the stationary distribution of allele frequencies in a family of Wright–Fisher models with two levels of genetic variability

The distribution of allele frequencies obtained from diffusion approximations to Wright–Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright–Fisher models in which there are two hierarchical levels of genetic variability. The genotypes composed of alleles differing from each other at the selected level have fitness differences with respect to each other and evolve under selection. The genotypes composed of alleles differing from each other only at the neutral level have the same fitness and evolve under neutrality. We show that with an appropriate scaling of the mutation parameter with respect to the number of alleles at each level, the frequencies of alleles at the selected and the neutral level are conditionally independent of each other, conditional on knowing the number of alleles at all levels. This conditional independence allows us to simulate from the joint stationary distribution of the allele frequencies. We use these simulated frequencies to perform inference on parameters of the model with two levels of genetic variability using Approximate Bayesian Computation.

Sleepiness, occlusion, dental arch and palatal dimensions in children attention deficit hyperactivity disorder (ADHD).

This was to compare sleepiness, occlusion, dental arch and palatal dimensions between children with attention deficit hyperactivity disorders (ADHD) and healthy children (control group). 15 children with ADHD (10 boys, 5 girls, mean age 10.98years) and 36 healthy age matched children (21 boys, 15 girls, mean age 10.60years) were included. Intra-oral three-dimensional scans of the teeth and palate were performed to evaluate the occlusion, dental arch and palatal dimensions. Sleepiness was evaluated from the questionnaires. The differences between the two groups were analysed by Fisher's exact test and general linear models adjusted for age and gender. The ADHD children had a significantly narrower dental arch at the gingival level of the canines (p<0.05) and a tendency to increased prevalence of posterior cross-bite compared to the controls (13.3 vs. 0.0%, p=0.086). The ADHD children snored significantly more (p<0.05) and slept restlessly significantly more often (p<0.0005) compared to the controls. The ADHD children had a tendency to sleep fewer hours during the night (p=0.066) and felt inadequately rested in the morning (p=0.051) compared to the controls. The results indicate that sleepiness and palatal width, especially the more anterior skeletal part of the palate, may be affected in children with ADHD. The results may prove valuable in the diagnosis and treatment planning of children with ADHD. Further studies are needed to investigate sleep and dental relations in children with ADHD.

Dental students’ attitudes towards management of pain and anxiety during a dental emergency: educational issues

High levels of patients' pain and anxiety characterise dental emergencies. The main objective of this study was to examine the self-reported attitudes of dental students towards these parameters in emergency conditions. A secondary objective was to determine if individual parameters (gender, personal experience of dental pain, personal dental anxiety and year of study) might affect their attitudes. One-hundred and eighty-seven undergraduate dental students with clinical practice completed a multiple-choice self-administered questionnaire online. The aforesaid individual parameters were collected and the students were asked to rate the frequency of their behaviour towards items representing good management of patients' pain and anxiety. The chi-square test of independence, Fisher's exact test and multiple logistic regression models were used for statistical analysis. Oral assessment of anxiety before treatment was scarce and was significantly associated with the students having personally experienced dental pain (P = 0.007). Pre-, intra- and postoperative pain appeared to be managed unequally by the students. Male students were significantly less likely to inform patients about postoperative pain (P = 0.014). More clinical experience was associated with less systematic consideration for intra-operative pain (P < 0.05). Being dentally anxious showed no significant association with higher frequencies of behaviours towards patients' pain and anxiety. These findings highlight the need for educational improvement regarding pain and anxiety in emergency conditions, especially concerning the assessment methods and continuity in the control of pain. Emergency dental care appears to be a very suitable field for contextual learning.