Random Version Research Articles

Investigating the impact of stochasticity on HIV infection dynamics in CD4+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+}$$\\end{document} T cells using a reaction-diffusion model

The disease dynamics affect the human life. When one person is affected with a disease and if it is not treated well, it can weaken the immune system of the body. Human Immunodeficiency Virus (HIV) is a virus that attacks the immune system, of the body which is the defense line against diseases. If it is not treated well then HIV progresses to its advanced stages and it is known as Acquired Immunodeficiency Syndrome (AIDS). HIV is typically a disease that can transferred from one person to another in several ways such as through blood, breastfeeding, sharing needles or syringes, and many others. So, the need of the hour is to consider such important disease dynamics and that will help mankind to save them from such severe disease. For the said purpose the reaction-diffusion HIV CD4+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+}$$\\end{document} T cell model with drug therapy under the stochastic environment is considered. The underlying model is numerically investigated with two time-efficient schemes and the effects of various parameters used in the model are analyzed and explained in a real-life scenario. Additionally, the obtained results will help the decision-makers to avoid such diseases. The random version of the HIV model is numerically investigated under the influence of time noise in Ito^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\hat{o}}$$\\end{document} sense. The proposed stochastic backward Euler (SBE) scheme and proposed stochastic Implicit finite difference (SIFD) scheme are developed for the computational study of the underlying model. The consistency of the schemes is proven in the mean square sense and the given system of equations is compatible with both schemes. The stability analysis proves that both schemes and schemes are unconditionally stable. The given system of equations has two equilibria, one is disease-free equilibrium (DFE) and the other is endemic equilibrium. The simulations are drawn for the different values of the parameters. The proposed SBE scheme showed the convergent behavior towards the equilibria for the given values of the parameters but also showed negative behavior that is not biological. The proposed SIFD scheme showed better results as compared with the stochastic SBE scheme. This scheme has convergent and positive behavior towards the equilibria points for the given values of the parameters. The effect of various parameters is also analyzed. Simulations are drawn to evaluate the efficacy of the schemes.

Environmental toxicants modulate disease severity in pediatric metabolic dysfunction-associated steatohepatitis.

Metabolic dysfunction-associated steatotic liver disease (MASLD) is common in children. We hypothesized environmental toxins could drive progression to metabolic dysfunction-associated steatohepatitis (MASH), and assayed serum toxins and metabolites in children with histologically characterized MASLD/MASH. Environmental chemicals, common in household items, perfluoroalkyl substances (PFAS), brominated flame retardants (PBDEs), and metabolic profiles were assayed in children enrolled in the multicenter NASH Clinical Research Network Pediatric Database 2. Mixture models, using repeated holdout weighted quantile sum regression (WQSrh) were run in addition to single chemical/metabolite logistic regression. For metabolomic analyses, random subset version of WQSrh was used for the large number of predictors versus participants. Nominal and false discovery rate (FDR) p-values (two-sided) were computed. Four hundred and thirty-five children distributed across MASH (n = 293) and MASLD (n = 142), with 304 (69.9%) males. Mean (standard deviation) for Nonalcoholic Steatohepatitis Score (NAS) and alanine aminotransferase (ALT) for MASLD were 3.1 (1.0), 67.9 (43.4), and for MASH 4.2 (1.4), 144 (121). There was an inverse association between PFAS/PBDE mixture and MASH versus MASLD, lobular inflammation (p = 0.026), NAS (p = 0.009, FDR p = 0.04), and log-transformed ALT (p = 0.005, FDR p = 0.025) driven by perfluorohexane sulfonate (PFHxS). Metabolites from positive hydrophilic interaction liquid chromatography mode, biliverdin (p = 0.002) and 1-methylhistidine (associated with meat ingestion, p = 0.02) and reverse phase negative mode, hippuric acid (solvent exposure, p = 0.022) significantly associated with MASH. Significant negative PFAS/PBDE mixture effect and odds of MASH were dominated by PHFXS. Several metabolites are significantly associated with MASH which inform mechanistic pathways and could drive key therapeutic and diagnostic strategies in children.

A Sharp Threshold for a Random Version of Sperner's Theorem

ABSTRACTThe Boolean lattice consists of all subsets of partially ordered under the containment relation. Sperner's Theorem states that the largest antichain of the Boolean lattice is given by a middle layer: the collection of all sets of size , or also, if is odd, the collection of all sets of size . Given , choose each subset of with probability independently. We show that for every constant , the largest antichain among these subsets is also given by a middle layer, with probability tending to 1 as tends to infinity. This is best possible, and we also characterize the largest antichains for every constant . Our proof is based on some new variations of Sapozhenko's graph container method.

Analyzing market basket data through sparse multivariate logit models

AbstractUsing multivariate logit models, we analyze purchases of product categories made by individual households. We introduce a sparse multivariate logit model that considers only a subset of all two-way interactions. A combined forward and backward selection procedure based on a cross-validated performance measure excludes about 74 % of the possible two-way interactions. We also specify random coefficient versions of both the non-sparse and the sparse model. The fact that the random coefficient models lead to better values of the Bayesian information criterion demonstrates the importance of latent heterogeneity. The random coefficients sparse model attains the best statistical performance if we consider model complexity and offers a better interpretability. We investigate the cross-purchase effects of household segments derived from this random coefficient model. As additional interpretation aid we cluster categories and category pairs by integer programming. We demonstrate what the best performing sparse model implies for cross-selling by product recommendations and store layout. The sparse model leads to managerial implications with respect to the effects of advertising in local newspapers and flyers that are as a rule close to those implied by its non-sparse counterpart.

Effect of Basic Amenities Provision and Residents Satisfaction on Willingness to live in Public Housing Estate Lafia, Nasarawa State

It has been testified that international concerns have been growing over the weakening housing conditions in urban areas of developing nations and the issues of poor housing excellence is therefore a global phenomenon. The study aimed to evaluate the effect of basic amenities provision on willingness to live in public housing estate Lafia, with a view to suggest ways to improve on the level of satisfaction with basic amenities provided in the study area. The study adopted descriptive design and quantitative approach and the study used questionnaire survey from 500 household heads, the study adopted stratified random sampling technique and SPSS software version 22centrs was used for data analysis and the results were presented in tables. The study concludes by demonstrating 13.6% of the willingness to live is influenced by the basic amenities provision and resident’s satisfaction which means that basic amenities provision and residents’ satisfaction have medium effect size on willingness to live in the study and amenity provision and satisfaction have a statistically insignificant effect on the willingness to live with P-value 0.191 and 0.232 > 0.05. The study recommended that the government should increase healthcare centres by building a new clinics or hospitals, or expand existing ones, to bring medical care closer to residents living in 500 housing estate. The study recommended that the government should upgrade or improve infrastructure in existing markets, including proper sanitation, waste management to ease the situation of market facilities in the study area.

Studying the accessibility of healthcare services for cancer patients in Khartoum state amid the COVID-19 pandemic

ObjectivesThis study aims to assess cancer patients' accessibility to healthcare services and perceived barriers during the COVID-19 pandemic in Khartoum state, aiming to explore the consequent impact on cancer patients. It also aims to determine the coping strategies used by patients to overcome these barriers. Study designThis is a retrospective analytical cross-sectional study. MethodsData were collected from August 2020 to March 2021, with a sample size of 316 cancer patients. Systemic random sampling and SPSS version 25 were utilized for data collection and analysis. ResultsThe study found that 55.7 % of the surveyed cancer patients had experienced disruptions in accessing essential cancer healthcare services during the lockdown. The study identified the most common cancers as breast (19.7 %), gastrointestinal (19 %), and ovarian (11 %). Notable barriers included governmental travel restrictions (51.6 %), outpatient service closures (41.8 %), and high costs (27.8 %). Additionally, delayed treatment was directly associated with a 33.3 % fatality rate among the participants. ConclusionsThis study highlights the considerable negative impact of the COVID-19 lockdown on cancer care in Sudan. Recommendations include a focus on telemedicine as an alternative form of patient consultation, the expansion of health insurance schemes to encompass cancer treatments, and strengthening healthcare infrastructure to facilitate cancer care during crises.

Attitude of undergraduate medical students towards euthanasia and physician-assisted suicide: A cross-sectional study.

Euthanasia is categorically prohibited in Pakistan by Islamic law, but a clash of opinions among doctors and human rights advocates still prevails. As a result, medical students are becoming concerned about its practice and this problem needs to be addressed. A cross-sectional study was conducted at Faisalabad Medical University (FMU), Pakistan, from April 2023 to May 2023, using random sampling and statistical programme SPSS version 25, to assess the attitudes of medical students regarding euthanasia and physician-assisted suicide (PAS). Despite the conditions and scenarios presented to the students, most of them expressed opposition to euthanasia and physician-assisted suicide because of their religious beliefs and optimistic approach to life. Most of them favoured palliative care and passive euthanasia. Some students showed compliance with euthanasia even though it is equivalent to murder in Islam. Such contrasting results can baffle a physician to make wise decisions. Hence, it must be covered in medical curriculum in depth in order to help the future physicians clearly understand its practice under all circumstances.

Trend of Macroeconomic Factors Influencing Commercial Property in Abuja, Nigeria

In recent time changes in rent invariably affect every type of real estate although in varying degrees. The aimed of this paper is to investigate the trend of macroeconomic factors influencing commercial property in Abuja. The study adopted quantitative design and questionnaire survey was used for data collection. The study adopted simple random sampling technique and SPSS software version 22 was used for data analysis and the results were presented in tables. Commercial properties under the management of Estate Surveyors and Valuation in Abuja metropolis was served as target population. The study indicates that the macroeconomic indicators considered in the study, namely gross domestic product (GDP), inflation rate, interest rate and exchange rate are all increasing, but at different rates. This suggests that the economy is growing, but that there are also some inflationary pressures and that the central bank is tightening monetary policy in an attempt to bring inflation under control. The rising exchange rate suggests that the domestic currency is becoming more valuable relative to other currencies, which can make exports more expensive and imports cheaper. However, the fact that the indicators are rising at different rates suggests that the growth is not uniform and that there are some challenges that need to be addressed. For example, the rising inflation rate suggests that there is some pressure on prices. This could be due to a number of factors, such as increased demand for goods and services, supply chain disruptions, or rising energy costs. The central bank may need to take steps to address inflation, such as raising interest rates. Macroeconomic indicators significantly influence rental value of commercial properties causing about 73.7% change in rental value of commercial properties. Central banks should monitor inflation closely and take steps to bring it under control if necessary. This could involve raising interest rates or other monetary policy tools. Policymakers should work to address the underlying causes of inflation and unemployment. This could involve measures such as increasing competition in the economy, improving education and training programs, or investing in research and development.

On Some Extremal and Probabilistic Questions for Tree Posets

Given two posets $P,Q$ we say that $Q$ is $P$-free if $Q$ does not contain a copy of $P$. The size of the largest $P$-free family in $2^{[n]}$, denoted by $La(n,P)$, has been extensively studied since the 1980s. We consider several related problems. For posets $P$ whose Hasse diagrams are trees and have radius at most $2$, we prove that there are $2^{(1+o(1))La(n,P)}$ $P$-free families in $2^{[n]}$, thereby confirming a conjecture of Gerbner, Nagy, Patkós and Vizer [Electronic Journal of Combinatorics, 2021] in this case. For such $P$ we also resolve the random version of the $P$-free problem, thus generalising the random version of Sperner's theorem due to Balogh, Mycroft and Treglown [Journal of Combinatorial Theory Series A, 2014], andCollares Neto and Morris [Random Structures and Algorithms, 2016]. Additionally, we make a general conjecture that, roughly speaking, asserts that subfamilies of $2^{[n]}$ of size sufficiently above $La(n,P)$ robustly contain $P$, for any poset $P$ whose Hasse diagram is a tree.

Formation of students' skills and abilities using Formulas-type test tasks in Moodle

The means of countering academic fraud in computer testing are discussed in the article. Special attention is paid to the fight against students compiling a table of correct answers to a test assignment question. It is proposed to use the technology available in Moodle to automate the generation of test task variants. Tasks of the type "Calculated" and "Formulas" are considered. The method of creating a question in a form that allows its repeated use in various random versions of the formulation both at the learning stage in order to form skills and abilities, and in the process of intermediate control is described. Using an example related to programming training, the possibilities of creating program fragments with a random set of identifiers are demonstrated, which forces the student to understand the meaning of the analyzed fragment. An example of solving a physics problem is given, which allows us to show the possibility of controlling knowledge of standard formulas and the ability to perform calculations using them.

An Exploration of Parameter Duality in Statistical Inference

Abstract Well-known debates among statistical inferential paradigms emerge from conflicting views on the notion of probability. One dominant view understands probability as a representation of sampling variability; another prominent view understands probability as a measure of belief. The former generally describes model parameters as fixed values, in contrast to the latter. We propose that there are actually two versions of a parameter within both paradigms: a fixed unknown value that generated the data and a random version to describe the uncertainty in estimating the unknown value. An inferential approach based on CDs deciphers seemingly conflicting perspectives on parameters and probabilities.

Endogeneity of marketing variables in multicategory choice models

A regressor is endogenous if it is correlated with the unobserved residual of a model. Ignoring endogeneity may lead to biased coefficients. We deal with the omitted variable bias that arises if firms set marketing variables considering factors (demand shocks) that researchers do not observe. Whereas publications on sales response or brand choice models frequently take the potential endogeneity of marketing variables into account, multicategory choice models provide a different picture. To consider endogeneity in multicategory choice models, we follow a two-step Gaussian copula approach. The first step corresponds to an individual-level random coefficient version of the multivariate logit model. We analyze yearly shopping data for one specific grocery store, referring to 29 product categories. If the assumption of a Gaussian correlation structure is met, the copula approach indicates the endogeneity of a category-specific marketing variable in about 31% of the categories. The majority of marketing variables rated as endogenous are positively correlated with the omitted variable, implying that ignoring endogeneity leads to an overestimation of the coefficients of the respective marketing variable. Finally, we investigate whether taking endogeneity into account by the copula approach leads to different managerial implications. In this regard, we demonstrate that for our data ignoring endogeneity often suggests a level of marketing activity that is too high.

Predicting the spatial distribution of stable isotopes in precipitation using a machine learning approach: a comparative assessment of random forest variants

Stable isotopes of hydrogen and oxygen are important natural tracers with a wide variety of environmental applications (e.g., the exploration of the water cycle, ecology and food authenticity). The spatially explicit predictions of their variations are obtained through various interpolation techniques. In the present work, a classical random forest (RF) and two of its variants were applied. RF and a random forest version employing buffer distance (RFsp) were applied to each month separately, while a random forest model was trained using all data employing month and year as categorical variables (RFtg). Their performance in predicting the spatial variability of precipitation stable oxygen isotope values for 2008–2017 across Europe was compared. In addition, a comparison was made with a publicly available alternative machine learning model which employs extreme gradient boosting. Input data was retrieved from the Global Network of Isotopes in Precipitation (GNIP; no. of stations: 144) and other national datasets (no. of stations: 127). Comparisons were made on the basis of absolute differences, median, mean absolute error and Lin’s concordance correlation coefficient. All variants were capable of reproducing the overall trends and seasonal patterns over time of precipitation stable isotope variability measured at each chosen validation site across Europe. The most important predictors were latitude in the case of the RF, and meteorological variables (vapor pressure, saturation vapor pressure, and temperature) in the case of the RFsp and RFtg models. Diurnal temperature range had the weakest predictive power in every case. In conclusion, it may be stated that with the merged dataset, combining GNIP and other national datasets, RFsp yielded the smallest mean absolute error 1.345‰) and highest Lin’s concordance correlation coefficient (0.987), while with extreme gradient boosting (based on only the GNIP data) the mean absolute error was 1.354‰, and Lin’s concordance correlation coefficient was 0.984, although it produced the lowers overall median value (1.113‰), while RFsp produced 1.124‰. The most striking systematic bias was observed in the summer season in the northern validation stations; this, however, diminished from 2014 onward, the point after which stations beyond 55° N are available in the training set.

Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as stochastic processes together with some random Gibbs measure. More precisely, we prove a central limit theorem (CLT), an almost sure invariance principle, a moderate deviations principle, Berry-Esseen type estimates and a moderate local central limit theorem for random Birkhoff sums generated by a non-uniformly partially expanding dynamical systems Tω and a random Gibbs measure μω, corresponding to a random potential ϕω with a sufficiently regular variation. In the partially expanding case the maps we consider are similar to the ones in [44], with the exception that the amount of expansion dominates the amount of contraction fiberwise and not only on the average, and with an additional regularity condition on a certain type of local variation of ϕω along inverse branches of Tω. A notable example when the maps are truly partially-expanding is the case when ϕω≡0 which corresponds to random measures of maximal entropy μω, but any potential with a sufficiently small (fiberwise) variation can be considered. Our results in the partially expanding case are new even in the uniformly random case, where all the random variables describing the maps are uniformly controlled. For properly expanding maps (as in [42,33]), the above local regularity condition allows applications also in the smooth case where the Gibbs measure is absolutely continuous with respect to the underlying volume measure and ϕω=−ln⁡JTω. For instance, we can consider certain fiberwise piecewise C2-perturbations of piecewise linear or affine maps. All of the above is achieved by first proving random, real and complex, Ruelle-Perron-Frobenius (RPF) theorems with rates that can be expressed analytically by means of certain random parameters that describe the maps (such rates will be referred to as “effective”). Using these effective rates, our conditions for the limit theorems involve some weak type of upper mixing conditions on the driving system (base map) and some integrability conditions on the norm of the random function generating the Birkhoff sums. A big part of the proof of the moderate deviations, the Berry-Esseen type estimates and the local CLT is to show how Rugh's theory [43] of complex cones contractions applies to the cones considered in [16] (and their random versions in [44]), which is new even for deterministic dynamical systems T, and in that case it yields explicit estimates on the spectral gap of appropriate deterministic complex perturbations of the transfer operator of T, as well as explicit constants in the corresponding Berry-Esseen theorem for deterministic partially expanding dynamical systems.

Crossing edge minimization in radial outerplanar layered graphs using segment paths

Crossing minimization is a natural problem in graph drawing, which consists of drawing it in the plane with a minimum number of crossings on the edges. We present an algorithm to minimize the crossing edges in radial layered graphs. The algorithm determines the optimal location of nodes in their corresponding circle layer and consists of two phases. In the first phase, a counterclockwise rotation of concentric circles is performed; in the next phase, edges are converted into segment paths. Unlike other algorithms with circular drawings, our algorithm does not require the insertion or removal of nodes and edges; only rotation and path construction operations are utilized. Two versions of the algorithm were created; the exhaustive version tests all the possible paths, while the random version tests a few number of paths. The goal is to minimize the crossing edges to obtain a clear visualization using three criteria: rotation, crossing edge detection and segment path construction. The algorithm has been successfully implemented in 30 instances of graphs with 20, 35 and 50 layers, where crossings are minimized in 86–93%, 93–96% and 95–97%, respectively.

Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations. In addition, by finding the solutions of the obtained random complex differential equations, the probability characteristics of the solutions are examined. The random version of the differential transformation method (DTM) is used to obtain an analytical solution close to the solution of the random differential equation. Approximate expected values and variances are calculated using the approximate solution method. The solutions of some random complex differential equations obtained by using random probability characteristics with gamma, normal, and beta distributions were obtained by the DTM method. The probability characteristics obtained are shown graphically with the help of the MAPLE program.

Turán‐type problems for long cycles in random and pseudo‐random graphs

AbstractWe study the Turán number of long cycles in random and pseudo‐random graphs. Denote by the random variable counting the number of edges in a largest subgraph of without a copy of . We determine the asymptotic value of , where is a cycle of length , for and . The typical behaviour of depends substantially on the parity of . In particular, our results match the classical result of Woodall on the Turán number of long cycles, and can be seen as its random version, showing that the transference principle holds here as well. In fact, our techniques apply in a more general sparse pseudo‐random setting. We also prove a robustness‐type result, showing the likely existence of cycles of prescribed lengths in a random subgraph of a graph with a nearly optimal density. Finally, we also present further applications of our main tool (the Key Lemma) for proving results on Ramsey‐type problems about cycles in sparse random graphs.

New random version of stability via fixed point method

We studied the stability of the cubic functional equation: 
 3 ß( +3 ƴ)-ß(3 + ƴ)=12 [ß( + ƴ)+ß( - ƴ)]+80 ß(ƴ)-48 ß( ). (1.1)
 via fixed point method in random normed space (ȐṄ −space).

Deterministic and Random Generalized Complex Numbers Related to a Class of Positively Homogeneous Functionals

Based upon a new general vector-valued vector product, generalized complex numbers with respect to certain positively homogeneous functionals including norms and antinorms are introduced and a vector-valued Euler type formula for them is derived using a vector valued exponential function. Furthermore, generalized Cauchy–Riemann differential equations for generalized complex differentiable functions are derived. For random versions of the considered new type of generalized complex numbers, moments are introduced and uniform distributions on discs with respect to functionals of the considered type are analyzed. Moreover, generalized uniform distributions on corresponding circles are studied and a connection with generalized circle numbers, which are natural relatives of π, is established. Finally, random generalized complex numbers are considered which are star-shaped distributed.

A Random Adaptation Perspective on Distributed Averaging

We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed learning. Namely, we show that the ergodicity of a stochastic chain is equivalent to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">almost sure</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a.s.)</i> finite-time agreement attainment in the proposed random adaptation dynamics. Using this result, we provide a new interpretation for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">absolute probability sequence</i> of an ergodic chain. We then modify the base-case dynamics into a time-reversed inhomogeneous Markov chain, and we show that in this case ergodicity is equivalent to the uniqueness of the limiting distributions of the Markov chain. Finally, we introduce and study a time-varying random adaptation version of the Friedkin-Johnsen model and a rank-one perturbation of the base-case dynamics.