Search Results (375)

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, r-Whitney numbers, and hyperharmonic polynomials, as well as Bernoulli numbers and polynomials. We also provide formulas for the higher-order derivatives of Cauchy polynomials and obtain corresponding formulas and identities for poly-Cauchy polynomials. Furthermore, we introduce a multiparameter framework for poly-Cauchy polynomials, unifying earlier generalizations like shifted poly-Cauchy numbers and polynomials with a q parameter. Full article

Clostridioides difficile is an obligate anaerobe and is primarily transmitted via the fecal–oral route. Data characterizing the microbiome changes accompanying transitions from non-colonized to C. difficile colonized subjects are currently lacking. In this retrospective cohort study, we examined 16S rRNA gene sequencing data in a total of 481 fecal samples belonging to 107 patients. Based on C. difficile status over time, patients were categorized as Negative-to-Positive, Negative Control, and Positive Control. A linear mixed effects model was fitted to investigate the changes in the Shannon α-diversity index over time. Zero-inflated negative binomial/Poisson mixed effects models or generalized linear mixed models with negative binomial/Poisson distribution were used to investigate the changes in taxon counts over time among different groups. A total of 107 patients were eligible for the study. The median number of stool samples per patient was 3 (IQR 2–4). A total of 42 patients transitioned from C. difficile negative to positive (Negative-to-Positive), 47 patients remained negative throughout their tests (Negative Control) and 18 were always C. difficile positive (Positive Control). A significant difference in microbiome composition between the last negative samples and the first positive samples were shown in Negative-to-Positive patients, ANOSIM p = 0.022. In Negative-to-Positive patients, the phylum Pseudomonadota and family Enterobacteriaceae increased significantly in the first positive samples compared to the last negative samples, p = 0.0075 and p = 0.0094, respectively. Within the first 21 days, Actinomycetota decreased significantly over time in the Positive Control group compared to the other two groups (p < 0.001) while Bacillota decreased in both the Negative-to-Positive group and Positive Control. These results demonstrate that the transition from C. difficile negative to C. difficile positive is associated with alterations in gut microbial communities and their compositional patterns over time. Moreover, these changes play an important role in both the emergence and intensification of the gut microbiome dysbiosis in patients who transitioned from C. difficile negative to positive and those who always tested positive. Full article

Background/Objectives: Breastfeeding is essential to maternal and child health, and multiple factors influence its success. This study examined the factors associated with breastfeeding type among infants aged 0 to 12 weeks. Methods: A mixed-methods study, employing a convergent design, was conducted in the rooming in unit of a hospital in Espírito Santo, Brazil. A total of 296 mothers of neonates ≥ 34 weeks participated in both the quantitative and qualitative phases. The qualitative phase involved semi-structured interviews conducted in the hospital setting. In the quantitative phase, data were collected via telephone in three waves (on days 14, 40, and 90 postpartum), critical moments for establishing and maintaining breastfeeding, analyzing sociodemographic factors (age, education, marital status, number of pregnancies), clinical factors (gestational age, mode of delivery, milk production) and support factors (social and hospital). Descriptive statistical analysis and binomial and multinomial logistic regression models were used, conducted in R 4.3.3 software. The qualitative and quantitative findings were integrated through simultaneous incorporation and presented in a joint display. Results: The analysis showed that although most mothers had high adherence to prenatal care, breastfeeding counseling was insufficient. In addition to the type of delivery and immediate skin-to-skin contact, other factors were also found to be relevant to maintaining exclusive breastfeeding. Higher maternal education and a greater number of pregnancies were associated with better breastfeeding practices, albeit with variations in statistical significance. Support received during hospitalization, especially from the healthcare team, also emerged as a central element in the qualitative reports, reinforcing its role as a protective factor for continued breastfeeding. Early formula use within the first 48 h was identified as a barrier to initiating and maintaining breastfeeding. Conclusions: The duration and maintenance of exclusive breastfeeding varied over time, depending on factors such as the number of prenatal appointments, education level, number of pregnancies, mode of delivery, immediate skin-to-skin contact, and, most importantly, the use of formula in the first 48 h. The early introduction of formula in maternity wards represented a significant obstacle to breastfeeding, reinforcing the importance of integrated public policies and multidisciplinary initiatives that promote breastfeeding from birth. Full article

Let $q_1+\cdots +q_n+m$ objects be arranged in n rows with $q_1,\dots ,q_n$ objects and one last row with m objects. The Janjić–Petković counting function denotes the number of $(n+k)$-insets, defined as subsets containing $n+k$ objects such that at least one object is chosen from each of the first n rows, generalizing the binomial coefficient that is recovered for $q_1$ = … = $q_n$ = 1, as then only the last row matters. Here, we discuss two explicit forms, combinatorial interpretations, recursion relations, an integral representation, generating functions, convolutions, special cases, and inverse pairs of summation formulas. Based on one of the generating functions, we show that the Janjić–Petković counting function, like the binomial coefficients that it generalizes, may be regarded as a Riordan array, leading to additional identities. As an application to a physical system, we calculate the heat capacity of a many-body system for which the configurations are constrained as described by the Janjić–Petković counting function, resulting in a modified Schottky anomaly. Full article

The multi-factorial hypothesis of quantitative trait inheritance originated from Nilson’s wheat hybridization experiments. It takes unit traits as the object and is based on the binomial distribution mathematically. Due to the requirement of the same distribution, it cannot include genes of other distributions. This is its limitation. Moreover, it does not incorporate the environmental effects that constitute the phenotype, so it is not comprehensive enough. This article started from the overallness of quantitative traits, was based on the central limit theorem, and was analyzed from both the genotype and the environment and proposed the assumption on the inheritance of dual multi-factors and tri-normal distributions of quantitative traits. This genetic model was tested with practical examples, and three inferences were made. Method and Results: Firstly, the overallness of quantitative traits was discussed, thus the above assumption was proposed. Next, using many examples of normal distribution of quantitative characters in the homogeneous populations, the research on the identification of the environments without GEI was carried out. Then, the examples of normal distribution of the same quantitative characters in the homogeneous populations and in the segregated populations of the same family were used. By means of normal distribution of quantitative characters in the homogeneous populations, it was indicated that the test locations were the environments without GEI. By utilizing the properties of normal distribution and variance, it was proven that normal distribution of phenotypic value for quantitative traits in a segregated population was formed by adding normal distribution of genotypic value and environmental effect, which enables the genetic model to be tested in practice. Three types of normal distribution of quantitative traits were inferred, indicating that the quantitative characters of a considerable number of organisms in nature obey a normal distribution, expressing continuous variation. Full article

This study proposes a hybrid deep learning framework for predicting vehicle crash frequency (F_i) using nationwide traffic accident and traffic volume data from the United States (2019–2022). Crash frequency is defined as the product of exposure frequency ($N_a$) and crash risk rate ($\lambda$), a structure widely adopted for its ability to separate physical exposure from the crash likelihood. $N_a$ was computed using an extended Safety Performance Function (SPF) that incorporates roadway traffic volume, segment length, number of lanes, and traffic density, while $\lambda$ was estimated using a multilayer perceptron-based deep neural network (DNN) with inputs such as impact speed, road surface condition, and vehicle characteristics. The DNN integrates rectified linear unit (ReLU) activation, batch normalization, dropout layers, and the Huber loss function to capture nonlinearity and over-dispersion beyond the capability of traditional statistical models. Model performance, evaluated through five-fold cross-validation, achieved R² = 0.7482, MAE = 0.1242, and MSE = 0.0485, demonstrating a strong capability to identify high-risk areas. Compared to traditional regression approaches such as Poisson and negative binomial models, which are often constrained by equidispersion assumptions and limited flexibility in capturing nonlinear effects, the proposed framework demonstrated substantially improved predictive accuracy and robustness. Unlike prior studies that loosely combined SPF terms with machine learning, this study explicitly decomposes F_i into $N_a$ and $\lambda$, ensuring interpretability while leveraging DNN flexibility for crash risk estimation. This dual-layer integration provides a unique methodological contribution by jointly achieving interpretability and predictive robustness, validated with a nationwide dataset, and highlights its potential for evidence-based traffic safety assessments and policy development. Full article

Coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was first identified in Wuhan, China, in December 2019. Since then, it has evolved into a global pandemic. Forecasting the number of COVID-19 cases is a crucial task that can greatly aid management decisions. Numerous methods have been proposed in the literature to forecast COVID-19 case numbers; however, most do not yield highly accurate results. Rather than focusing solely on predicting exact case numbers, providing robust upper bounds may offer a more practical approach to support effective decision-making and resource preparedness. This study proposes the use of tolerance interval methods to construct upper bounds for daily new COVID-19 case numbers. The tolerance limits derived from the normal, Poisson, and negative binomial distributions are compared. These methods rely either on historical data alone or on a combination of historical data and auxiliary data from other regions. The results demonstrate that the proposed methods can generate informative upper bounds for COVID-19 case counts, offering a valuable alternative to traditional forecasting models that emphasize exact number estimation. This approach can improve pandemic preparedness through better equipment planning, resource allocation, and timely response strategies. Full article

Introduction: Marathon runs conducted in tropical environments can result in high injury rates. This study was conducted to provide information about the burden of injuries in such environments, to aid planning for similar mass events, enhance medical support, and improve participant safety. Methods: This was a retrospective review of casualty data from the Singapore Marathon races from 2013 to 2016. Patient Presentation Rate (PPR) and Transport to Hospital Rate (THR) were calculated and correlated with heat index, derived from weather information. Injury types were also reviewed. The negative binomial regression was performed to investigate impact of heat index on casualty rates. The medical response plan is briefly described. Results: During the four-year period covered, heat index increased from 29° to 35°. There were more casualties amongst the participants from the full marathon than other race categories. The THR was 0.3 to 0.68 per 1000 participants. Two participants had cardiac arrest. Negative binomial regression showed significant impact of heat index on casualty rate. Incidence rate ratio was 1.22 for severe casualties, which indicated that every 1 unit increase in heat index resulted in 22% rise in severe casualty numbers. Compared with 10 km racers, half marathon racers experienced 1.58 times greater likelihood of all injuries and full marathon racers, a 3.87 times greater risk. Conclusions: Adverse weather conditions with high-heat index can increase injury rates during strenuous physical activities such as the marathon. Applying careful measures to minimise the impact of heat and high humidity may help minimise such injuries. Full article

Multidrug-resistant (MDR) Shiga toxin-producing Escherichia coli O157 (STEC O157) is a public health threat. This study analyzed publicly available surveillance data collected by the National Antimicrobial Resistance Monitoring System (NARMS) to assess temporal and regional differences and co-resistance patterns in MDR STEC O157 human clinical isolates across the United States. Co-resistance patterns were assessed by hierarchical clustering and Phi coefficient network analyses. A negative binomial regression model estimated the incidence rate ratios (IRRs) for the number of antimicrobial classes to which an isolate was resistant, across years and geographic regions. Out of 1955 isolates, 151 (7.57%) were MDR. The most important clusters were Cluster 1 (n = 1632), which included susceptible isolates, and Cluster 3 (n = 255), comprising the majority of the MDR isolates, having a high resistance prevalence to tetracyclines (TET) (0.97), folate pathway inhibitors (FPI) (0.77), and phenicols (PHN) (0.49). In the co-resistance network, TET, FPI, and PHN served as central hubs, with large nodes and thick edges, suggesting that they are frequently co-selected. The highest IRRs were observed in Regions 6 (IRR = 2.72) and 9 (IRR = 2.00), compared to Region 4. Compared to 2010, a significant increase in the IRR was observed in each year from 2015 to 2021 (IRRs 2.5–4.38). Antimicrobial stewardship programs and public health interventions targeting MDR E. coli O157 are needed to mitigate the emergence of antimicrobial resistance. Full article

As part of this study, we design a reliability acceptance sampling plan under the assumption that the lifetime of a product follows the Topp–Leone generated Weibull (TLGW) distribution, a model that exhibits structural symmetry in its hazard rate behavior and distributional form. The fundamental procedures for constructing such a plan are described. We compute and tabulate the minimum sample sizes required for given risk criteria using both binomial and Poisson models for the number of failures. We also provide the operating characteristic (OC) values for the proposed sampling plans, and determine the minimum ratios of true mean life to specified mean life needed to satisfy a given producer’s risk. The role of symmetry in the TLGW distribution is highlighted in its balanced tail properties and shape characteristics, which influence the performance of the acceptance sampling plan. Finally, we illustrate the applicability of the proposed plan with real-world data. Full article

Multimorbidity, or the presence of two or more co-occurring chronic medical conditions, is extremely prevalent within the United States (US), with disproportionately high incidence rates in individuals with minoritized identities. Sleep disturbances are an empirically supported risk factor contributing to disease status and maintenance throughout the lifespan. Given this, this study examines the relationship between disturbed sleep and multiple chronic conditions (MCCs) in adults using cross-sectional data from (n = 1013) participants enrolled in the Survey of Midlife Development in the US Study (MIDUS-2). Participants within this study were predominantly female (54.9%), white (93.2%), middle-aged (M_AGE = 58 years old), and experienced multimorbidity (56.6%) by having two or more (M_CHRON = 2.25) chronic health conditions in the past year. A negative binomial regression indicated that sleep disturbances significantly predict the number of chronic health conditions, with sleep-disturbed individuals reporting a 41% increase in reported health conditions (IRR = 1.407, p < 0.001). Findings suggest that disturbed sleep is significantly related to disease presence in aging populations and should be addressed through early intervention to mitigate negative health consequences. Full article

Finite sums involving reciprocals of binomial coefficients have long intrigued mathematicians, owing to their elegant structure and unexpected identities. In this work, we present a comprehensive general formula that unifies and extends several results previously studied in the literature. To demonstrate the breadth and utility of our approach, we also investigate a variety of significant special cases, shedding light on deeper patterns and connections. This unified perspective aims to appeal to researchers interested in combinatorics, number theory, and special functions. Full article

In this study, we explore the paired disjunctive domination number—a recently introduced parameter by Henning et al.—within the broader framework of graph and network sensitivity and vulnerability analysis. Building on this concept, we introduce and investigate the paired disjunctive bondage number (PDBN), which measures the minimum number of edge deletions required to increase the paired disjunctive domination number of a graph or its corresponding network model. We begin by computing this new bondage number for several well-known network classes. The focus then shifts to specific families of trees, where we first determine their paired disjunctive domination numbers in detail. Using these values, we calculate the corresponding bondage numbers for various structurally symmetric, hierarchical, and compound tree structures, including double star, comet, double comet, $E_p^t$, and binomial trees, all of which model different types of infrastructural networks. Finally, we present an algorithm for computing PDBN, accompanied by a complexity analysis, and illustrate the practical relevance of the parameter through a case study applying it to a real-life network problem. Our results offer foundational insights into the behavior of this new domination parameter and its bondage variant, contributing to the growing literature on graph vulnerability and suggesting potential applications in the design of resilient and failure-aware networks. Full article

Background/Objectives: The overuse of short-acting β₂-agonists (SABAs) has been associated with increased asthma morbidity and mortality, prompting changes in treatment guidelines. However, the role of frequent short-acting muscarinic antagonists (SAMAs) use remains poorly defined and unaddressed in current recommendations. This study offers the first real-world analysis of SAMA overuse in asthma, quantifying its association with exacerbation risk and healthcare utilization and comparing its predictive value to that of SABAs. Methods: A retrospective multicenter cohort study analyzed electronic health records (EHRs) from 132 adults with asthma in the Spanish National Health System (SNS). Associations between annual SAMA use and clinical outcomes were assessed using negative binomial regression and 5000-sample bootstrap simulations. Interaction and threshold models were applied to explore how SAMA use affected outcomes and identify clinically actionable cutoffs. Results: SAMA use was independently associated with a 19.2% increase in exacerbation frequency per canister and a nearly sixfold increase in the odds of experiencing ≥1 exacerbation (OR = 5.97; 95% CI: 2.43–14.66). An inflection point at 2.5 canisters/year marked the threshold beyond which annual exacerbations exceeded one. Increased SAMA use was also associated with a higher number of respiratory consultations and with more frequent prescriptions of systemic corticosteroids and antibiotics. The risk increased more sharply with SAMAs than with SABAs, and the lack of correlation between them suggests distinct clinical patterns underlying their use. Conclusions: SAMA use emerges as a digitally traceable and clinically meaningful indicator of asthma instability. While the associations observed are robust and consistent across multiple outcomes, they should be considered provisional due to the study’s retrospective design and limited sample size. Replication in larger and more diverse cohorts is needed to confirm external validity. These findings support the integration of SAMA tracking into asthma management tools—alongside SABAs—to enable the earlier identification of uncontrolled disease and guide therapeutic adjustment. Full article

One of the main motivations of this paper is to construct generating functions for generalization of the Touchard polynomials (or generalization exponential functions) and certain special numbers. Many novel formulas and relations for these polynomials are found by using the Euler derivative operator and functional equations of these functions. Some novel relations among these polynomials, beta polynomials, Bernstein polynomials, related to Binomial distribution from discrete probability distribution classes, are given. Full article