Search Results (34)

Background and Objectives: Cardiovascular diseases (CVD) are the primary causes of death throughout the world. Engaging in physical activity (PA) is crucial for the prevention of CVD, as a lack of exercise significantly impacts global health. For health promotion purposes, it is important to optimize PA and develop the main physical components. Multimodal exercise program (MEP) interventions cause unique cardiac changes that can be systematically analyzed using advanced ECG techniques. Using algebraic co-integration methods, this study examined the physiological cardiac adaptations of a 6-week MEP compared to sedentary control subjects. Materials and Methods: A total of 50 physically inactive males, aged 20–35 years, were recruited for a 6-week MEP. The intervention group (IG) consisted of 28 participants, while the control group (CG) included 22 participants. The MEP included balance, endurance, muscle strength, and flexibility exercises in one session. The cardiovascular system (CVS) was assessed using electrocardiography (ECG) and arterial blood pressure during an incremental cycle ergometer test, both before and after the 6-week period. Results: After the post-MEP, the IG’s resting HR showed a slight but insignificant decrease, from 84.5 to 82 bpm, with improved recovery rates at minute 1 (113.1–104.7 bpm). The CG showed a similar trend. pBP in IG significantly increased post-MEP during recovery at minute 1 (73–81) and minute 2 (65–72), where the CG showed a slight but significant difference. DskJT-QRS in IG post-MEP increased significantly during recovery in minutes 1–4, with all values showing p < 0.05. CG showed significance only at minute 3. Conclusions: Both the 6-week MEP and control had a positive impact on the CVS. The statement refers to changes in dynamic interactions between ECG parameters registered during the incremental exercise test and especially during the recovery after workload. Algebraic data co-integration analysis of ECG parameters demonstrated a sensitive assessment of the influence of exercising on the cardiovascular system. Full article

This study aimed to examine changes in the number of live and dying trees in central Lithuanian forests over time. Results were obtained using stochastic differential equations combined with the normal copula function. The examination of each tree’s individual size variables (height and diameter) showed that the mean values of dead or dying trees’ size variables had significantly lower trajectories that were particularly pronounced in mature stands. According to the data set under examination, the tree mortality rate gradually declined with age, reaching approximately 7% after 10 years. Birch trees 60–70 years old were the first species to reach the 1% mortality rate, followed by spruce trees 70–80 years old and pine trees 80–90 years old. The Maple symbolic algebra system was used to implement all results. Full article

In this paper, an ancient Babylonian algorithm for calculating the square root of 2 is unveiled, and the potential link between this primitive technique and an ancient Chinese method is explored. The iteration process is a symmetrical property, whereby the approximate root converges to the exact one through harmonious interactions between two approximate roots. Subsequently, the algorithm is extended in an ingenious manner to solve algebraic equations. To demonstrate the effectiveness of the modified algorithm, a transcendental equation that arises in MEMS systems is considered. Furthermore, the established algorithm is adeptly adapted to handle differential equations and fractal-fractional differential equations. Two illustrative examples are presented for consideration: the first is a nonlinear first-order differential equation, and the second is the renowned Duffing equation. The results demonstrate that this age-old Babylonian approach offers a novel and highly effective method for addressing contemporary problems with remarkable ease, presenting a promising solution to a diverse range of modern challenges. Full article

Changes of mind can become less likely the longer an agent has adopted a given opinion state. This resilience or inertia to change has been called “aging”. We perform a comparative study of the effects of aging on the critical behavior of two standard opinion models with pairwise interactions. One of them is the voter model, which is a two-state model with a dynamic that proceeds via social contagion; another is the so-called kinetic exchange model, which allows a third (neutral) state, and its formed opinion depends on the previous opinions of both interacting agents. Furthermore, in the noisy version of both models, random opinion changes are also allowed, regardless of the interactions. Due to aging, the probability of changing diminishes with the age, and to take this into account, we consider algebraic and exponential kernels. We investigate the situation where aging acts only on pairwise interactions. Analytical predictions for the critical curves of the order parameters are obtained for the opinion dynamics on a complete graph, in good agreement with agent-based simulations. For both models considered, the consensus is optimized via an intermediate value of the parameter that rules the rate of decrease of the aging factor. Full article

Purpose. To study a male Italian cohort (initially aged 40–59, n = 1712) during 61 years and the natural history of major CVD mortality categories including coronary heart disease (CHD), stroke and other heart diseases of uncertain etiology (HDUE), including congestive heart failure) along with their risk factor relationships. Methods and Results. Cox models were run with 12 covariates as possible predictors measured at entry to the study. About 93% of all CVD deaths were covered by the three major groups selected here (N = 751): 37.4% of them were diagnosed as CHD, 30.6% as stroke and 28.5% as HDUE. CHD declined in the last 20 years of follow-up, while a sharp increase in HDUE mortality was seen. Baseline mean levels of serum cholesterol were 209.6, 204.2 and 198.0 mg/dL, respectively, for CHD, stroke and HDUE deaths: the multivariable coefficients of serum cholesterol were positive and significant for CHD (p < 0.0001), and stroke (p = 0.0203) and not significant for HDUE (p = 0.3467). In Fine–Gray models, the algebraic signs of cholesterol coefficients were opposite for CHD versus the other mortality categories (t = 3.13). The predictive performances of remaining risk factors were varied whereas that of Cox models was not very good, probably due to the attrition phenomenon and possible competing risks. Conclusion. Large differences in natural history and risk factors were found comparing the three CVD conditions, potentially indicating different etiologies and pointing to the need of not mixing them up in a grouped CVD category. Full article

In the Eastern Baltics, climatic changes are expected to alter forest composition favouring broadleaved species. The height growth of trees influences the productivity of stands and the competitiveness of species, particularly in mixed sites, thus emphasising the necessity for accurate projections. Accordingly, height models are paramount for projecting productivity and yields of stands. As tree height growth dynamics vary regionally, regional or even local models are needed. Based upon 214 National Forest Inventory plots and 510 individual canopy trees, dominant height growth for small-leaved lime (Tilia cordata Mill.) and Norway maple (Acer platanoides L.) in Latvia were analysed. Height growth was modelled using a generalised algebraic difference approach, testing several non-linear equations. The Sloboda (for lime) and Hossfeld I (for maple) models showed the best fit and were the most realistic, predicting slower initial and middle-age (maturing period) growth, yet also displayed higher asymptotes compared to Western Europe. The predicted height at the age of 80 years was 14–33 m and 13–34 m for lime and maple, accordingly. A longer establishment period and later growth culmination suggest longer rotation, highlighting the assessment of long-term risks. In this case, supplementation of the models with climatic effects appears advantageous. Full article

Objectives: To assess whether competing risks help explain why regions with initially high serum cholesterol have higher mortality from coronary heart disease (CHD) and lower mortality from stroke and other major heart diseases, while the reverse is found for those with initially lower serum cholesterol. Material and Methods. Ten cohorts of men (N = 9063) initially aged 40–59 in six countries were examined and followed for fatal outcomes for 60 years. Major cardiovascular disease (CVD) groups were CHD, stroke, and other Heart Diseases of Uncertain Etiology (HDUE), or the combination of stroke and HDUE (STHD), along with all other causes of death. Fine-Gray competing risk analysis was applied with CHD versus all other causes of death or STHD (direct mode) and all other causes of death or STHD versus CHD (inverse mode), and the effects of 19 covariates (of which 3 references) on the cause-specific hazard of the outcomes were assessed, thus investigating potential etiologic roles. A systematic comparison with results obtained by running the Cox model in direct and inverse modes with the same end-point results was also performed and illustrated graphically. Results. CHD mortality is bound to different risk factor relationships when compared with all other causes of death and with STHD. The role of serum cholesterol is crucial since, in both comparisons, by Fine-Gray, its coefficients are positive and significant for CHD and negative and significant for all other causes of death and STHD. Risk factor capabilities in specific outcome types of the CVD domain (CHD versus STHD) are different depending on the outcome types considered. Risk factor coefficients are smaller in Fine-Gray modelling and larger in the Cox model. Fine-Gray detects different risk factors whose coefficients may have opposite algebraic signs. Conclusions. This is the first report whereby a large group of risk factors are investigated in connection with life-long CVD outcomes by Fine-Gray competing risk analysis, and a systematic comparison is performed with results obtained by Cox models in both direct and inverse modes. Subtypes of CVD mortality should be summed with full awareness that some risk factors vary by pathology, and they should at least be disentangled into CHD and STHD. Full article

In an age where artificial intelligence is reshaping the landscape of education and problem solving, our study unveils the secrets behind three digital wizards, ChatGPT-3.5, ChatGPT-4, and Google Bard, as they engage in a thrilling showdown of mathematical and logical prowess. We assess the ability of the chatbots to understand the given problem, employ appropriate algorithms or methods to solve it, and generate coherent responses with correct answers. We conducted our study using a set of 30 questions. These questions were carefully crafted to be clear, unambiguous, and fully described using plain text only. Each question has a unique and well-defined correct answer. The questions were divided into two sets of 15: Set A consists of “Original” problems that cannot be found online, while Set B includes “Published” problems that are readily available online, often with their solutions. Each question was presented to each chatbot three times in May 2023. We recorded and analyzed their responses, highlighting their strengths and weaknesses. Our findings indicate that chatbots can provide accurate solutions for straightforward arithmetic, algebraic expressions, and basic logic puzzles, although they may not be consistently accurate in every attempt. However, for more complex mathematical problems or advanced logic tasks, the chatbots’ answers, although they appear convincing, may not be reliable. Furthermore, consistency is a concern as chatbots often provide conflicting answers when presented with the same question multiple times. To evaluate and compare the performance of the three chatbots, we conducted a quantitative analysis by scoring their final answers based on correctness. Our results show that ChatGPT-4 performs better than ChatGPT-3.5 in both sets of questions. Bard ranks third in the original questions of Set A, trailing behind the other two chatbots. However, Bard achieves the best performance, taking first place in the published questions of Set B. This is likely due to Bard’s direct access to the internet, unlike the ChatGPT chatbots, which, due to their designs, do not have external communication capabilities. Full article

Laurel (Cordia alliodora Ruiz & Pav. Oken) is a Neotropical native tree that is easily regenerated in the secondary forest within the Amazon region. Amazonian smallholders use this tree regeneration to obtain a homogeneous forest cover when developing local agroforestry systems, which do not depend on nursery seedling production for tree planting. The objective of the present investigation was to develop growth and yield models for Laurel within the local agroforestry systems. A total of 226 sampling plots were measured between 2010–2011 and 2014–2015. Chapman- Richard, Hosslfeld II, and the generalized algebraic difference approach (GADA) form of the Chapman-Richard’s function was used for modeling height-age and diameter-age relationships. Eight volume models were tested to describe total stem volume. The GADA method was suited to describe the Laurel height and diameter-age growth. The cutting cycle for agroforestry systems with a density of 300 trees ha⁻¹ at the best site index (SI) (22 m) produced 13.9 m³ ha⁻¹ year⁻¹ and a total wood yield of 195.1 m³ ha⁻¹ at age 14. In the worst SI (14 m), the average annual yield was 3.5 m³ ha⁻¹, with a total yield of 83.3 m³ ha⁻¹ at age 24 years. The Spurr potential model was the best fit to describe the volume of the Laurel according to the Akaike information criteria. The Laurel biological (optimal) rotation age suggests that the minimum cutting diameter should be lowered from 30 cm of DBH in the research zone. Management of the natural regeneration of secondary forests by smallholders is a local agroforestry practice that should be given greater attention, especially within protected forest areas. Full article

Cervus elaphus populations are spreading and growing in many parts of Europe. This growth can have detrimental effects on biodiversity and ecosystem function. Successful strategies to manage large herbivores require reliable information on density and population trends. This paper presents a methodology to achieve a sustainable distribution of red deer by age and sex classes over time. Instead of traditional algebraic methods, the method consists of a simple iterative process that uses convergence to obtain the dominant eigenvalue and eigenvector of the biological matrix from an initial population. This eigenvalue represents the annual growth rate of the population, and the eigenvector represents the ideal age and sex class distribution of the population. The method has been applied to a fenced preserve in the province of Toledo, Spain. An annual population growth rate of 1.63 (dominant eigenvalue of the biological matrix) was obtained from an initial population and the biological matrix of the deer on the preserve. The convergence of this rate occurred in year 14, but the carrying capacity allows for a population close to the population in year 17 according to the prediction, which is therefore considered to be the year when the ideal population distribution is achieved. This methodology allows managers to numerically justify how to control population growth to preserve biodiversity and sustainability. Full article

We are developing a Virtual Eye for in silico therapies to accelerate research and drug development. In this paper, we present a model for drug distribution in the vitreous body that enables personalized therapy in ophthalmology. The standard treatment for age-related macular degeneration is anti-vascular endothelial growth factor (VEGF) drugs administered by repeated injections. The treatment is risky, unpopular with patients, and some of them are unresponsive with no alternative treatment. Much attention is paid to the efficacy of these drugs, and many efforts are being made to improve them. We are designing a mathematical model and performing long-term three-dimensional Finite Element simulations for drug distribution in the human eye to gain new insights in the underlying processes using computational experiments. The underlying model consists of a time-dependent convection-diffusion equation for the drug coupled with a steady-state Darcy equation describing the flow of aqueous humor through the vitreous medium. The influence of collagen fibers in the vitreous on drug distribution is included by anisotropic diffusion and the gravity via an additional transport term. The resulting coupled model was solved in a decoupled way: first the Darcy equation with mixed finite elements, then the convection-diffusion equation with trilinear Lagrange elements. Krylov subspace methods are used to solve the resulting algebraic system. To cope with the large time steps resulting from the simulations over 30 days (operation time of 1 anti-VEGF injection), we apply the strong A-stable fractional step theta scheme. Using this strategy, we compute a good approximation to the solution that converges quadratically in both time and space. The developed simulations were used for the therapy optimization, for which specific output functionals are evaluated. We show that the effect of gravity on drug distribution is negligible, that the optimal pair of injection angles is $(50{}^{\circ },50{}^{\circ })$, that larger angles can result in 38% less drug at the macula, and that in the best case only 40% of the drug reaches the macula while the rest escapes, e.g., through the retina, that by using heavier drug molecules, more of the drug concentration reaches the macula in an average of 30 days. As a refined therapy, we have found that for longer-acting drugs, the injection should be made in the center of the vitreous, and for more intensive initial treatment, the drug should be injected even closer to the macula. In this way, we can perform accurate and efficient treatment testing, calculate the optimal injection position, perform drug comparison, and quantify the effectiveness of the therapy using the developed functionals. We describe the first steps towards virtual exploration and improvement of therapy for retinal diseases such as age-related macular degeneration. Full article

Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and q-rung orthopair fuzzy sets (q-ROFS) are among those concepts which are widely used in real-world applications. However, these theories have their own limitations in terms of membership and non-membership functions, as they cannot be obtained from the whole unit plane. To overcome these restrictions, we developed the concept of a complex linear Diophantine fuzzy set (CLDFS) by generalizing the notion of a linear Diophantine fuzzy set (LDFS). This concept can be applied to real-world decision-making problems involving complex uncertain information. The main motivation behind this paper is to study the applications of CLDFS in a non-associative algebraic structure (AG-groupoid), which has received less attention as compared to associative structures. We characterize a strongly regular AG-groupoid in terms of newly developed CLDF-score left (right) ideals and CLDF-score $(0,2)$-ideals. Finally, we construct a novel approach to decision-making problems based on the proposed CLDF-score ideals, and some practical examples from civil engineering are considered to demonstrate the flexibility and clarity of the initiated CLDF-score ideals. Full article

In this study, the notion of perfect matrices of Lagrange differences is employed to detect atrial fibrillation episodes based on three ECG parameters (JT interval, QRS interval, RR interval). The case study comprised 8 healthy individuals and 7 unhealthy individuals, and the mean and standard deviation of age was 65.84 ± 1.4 years, height was 1.75 ± 0.12 m, and weight was 79.4 ± 0.9 kg. Initially, it was demonstrated that the sensitivity of algebraic relationships between cardiac intervals increases when the dimension of the perfect matrices of Lagrange differences is extended from two to three. The baseline dataset was established using statistical algorithms for classification by means of the developed decision support system. The classification helps to determine whether the new incoming candidate has indications of atrial fibrillation or not. The application of probability distribution graphs and semi-gauge indicator techniques aided in visualizing the categorization of the new candidates. Though the study’s data are limited, this work provides a strong foundation for (1) validating the sensitivity of the perfect matrices of Lagrange differences, (2) establishing a robust baseline dataset for supervised classification, and (3) classifying new incoming candidates within the classification framework. From a clinical standpoint, the developed approach assists in the early detection of atrial fibrillation in an individual. Full article

Tree growth models describe the growth and development of forest ecosystems by considering how the dimensions of each simulated tree change within a certain time. These models have commonly used three growth parameters that describe various biological processes and behaviours, considering a sigmoid growth function: (i) the upper asymptote (θ₁), which is the maximal yield indicated by a final dimension (such as the maximal stem diameter); (ii) the maximum specific growth rate (θ₂), defined as the slope of the tangent at the inflexion point; and (iii) the time elapsed (θ₃), defined by the intercept of this tangent with the abscissas. To the best of our knowledge, however, associations between the three parameters have not been documented for tree species. Using diameter growth data from pine trees located in typical mixed and uneven-aged pine-oak forests in the Sierra Madre Occidental, Mexico, our study aims were: (i) to quantify the putative associations between the three growth parameters and (ii) to test the accuracy of a proposed Hybrid Chapman-Richards growth model based on associations between the three growth parameters, but including only one single parameter, relative to the widely used Generalized Algebraic Difference Approach (GADA) based on the Chapman-Richards, Lundqvist and Hossfeld models and the Hybrid Weibull Model. For statistical comparison of the quality of the models, we used the mean relative percentage error, root mean square error, coefficient of determination and Akaike information criterion to assess the quality of the fit. Although the quality of the five growth models studied was similar, from a practical point of view, the proposed Hybrid Chapman-Richards Model (CR-H) is easier to apply than the other models and has a lower data collection and computational cost. The parameter of CR-H can be easily obtained, by measuring just the dominant trees, especially in coniferous forests with irregular ages. Moreover, in contrast to the Chapman-Richards-GADA factor χ₀, when θ₂ is assumed to be site-specific, the CR-H has always a closed-form solution. Full article

By nature, growth regulatory networks in biology are dynamic and stochastic, and feedback regulates their growth function at different ages. In this study, we carried out a stochastic modeling of growth networks and demonstrated this method using three mixed effect four-parameter Gompertz-type diffusion processes and a combination thereof using the conditional normal copula function. Using the conditional normal copula, newly derived univariate distributions can be combined into trivariate and bivariate distributions, and their corresponding conditional bivariate and univariate distributions. The link between the predictor variable and the remaining one or two explanatory variables can be formalized using copula-type densities and a numerical integration procedure. In this study, for parameter estimation, we used a semiparametric maximum pseudo-likelihood estimator procedure, which was characterized by a two-step technique, namely, separately estimating the parameters of the marginal distributions and the parameters of the copula. The results were illustrated using two observed longitudinal datasets, the first of which included the age, diameter, and potentially available area of 39,437 trees (48 stands), while the second included the age, diameter, potentially available area, and height of 8604 trees (47 stands) covering uneven mixed-species (pine, spruce, and birch) stands. All results were implemented using the MAPLE symbolic algebra system. Full article