Search Results (41)

The goal of this research is to analyze the mean squared error (MSE) of the kernel estimator for the conditional hazard rate, assuming that the sequence of real random vector variables ${\left(U_n\right)}_{n\in \mathbb{N}}$ satisfies the quasi-association condition. By employing kernel smoothing techniques and asymptotic analysis, we derive the exact asymptotic expression for the leading terms of the quadratic error, providing a precise characterization of the estimator’s convergence behavior. In addition to the theoretical derivations and a controlled simulation study that validates the asymptotic properties, this work includes a real-data application involving monthly unemployment rates in the United States from 1948 to 2025. The comparison between the estimated and observed values confirms the relevance and robustness of the proposed method in a practical economic context. This study thus extends existing results on hazard rate estimation by addressing more complex dependence structures and by demonstrating the applicability of the methodology to real functional data, thereby contributing to both the theoretical development and empirical deployment of kernel-based methods in survival and labor market analysis. Full article

Value-at-Risk (VaR) estimation using the GARCH model is an important topic in financial data analysis. It allows for an increase in the accuracy of risk assessment by controlling time-varying volatility. In this paper, we enhance this feature by exploring the functional path of the financial data. More precisely, we study the nonparametric estimation of the multi-functional VaR function using the local linear method, construct an estimator, and establish its stochastic consistency. The derived asymptotic result provides a rigorous mathematical foundation that permits boosting the use of the VaR function in financial data analysis. Furthermore, an empirical analysis is performed in order to examine the efficiency of the proposed algorithm. Additionally, a real data application is created to highlight the multi-functionality of the VaR estimation for multi-asset risk management. Full article

The investigation of free additive convolution is a key concept in free probability theory, offering a framework for studying the sum of freely independent random variables. This paper uses free additive convolution and measure dilations to investigate various aspects of Marchenko–Pastur and free Gamma laws in the setting of Cauchy-Stieltjes Kernel (CSK) families. Our investigation reveals the essential links between analytic function theory and free probability, highlighting the usefulness of CSK families in developing the theoretical and computational aspects of free additive convolution. Full article

Background: The Hall Technique (HT) in pediatric dentistry is a minimally invasive method for treating carious primary molars by sealing cavities with preformed stainless-steel crowns, eliminating the need for local anesthesia, caries removal or tooth preparation. Objectives: To assess the knowledge, attitude, and teaching of HT among pediatric dentistry faculty in Riyadh, Saudi Arabia. Methods: A cross-sectional descriptive study involved 36 pediatric dentistry faculty members from six dental colleges in Riyadh. Data were collected using a validated questionnaire covering demographics and professional information, HT knowledge, attitude, and teaching strategies. Results: Thirty-one pediatric dentistry faculty responded to the questionnaire, and 67.74% of participants use HT clinically, primarily for asymptomatic carious primary molars. Most participants learned about HT during postgraduate residency (61.29%), while only 6.45% were introduced to it in undergraduate training. Teaching practices varied, with 51.61% teaching HT to undergraduate and/or postgraduate students, and 16.13% omitting it from their curriculum. Key barriers to HT adoption included limited undergraduate exposure, misconceptions, and a lack of standardized guidelines. Fisher’s Exact Test showed that gender, academic position, and years of experience were significantly associated with HT use. Only years of experience were significantly associated with recommending HT use by undergraduate students. No factors were significantly associated with teaching HT. Conclusions: While awareness of HT is high among pediatric dentistry faculty, inconsistent teaching and limited clinical use hinder its full integration. Addressing these barriers through curriculum updates and professional development could enhance the acceptance and quality of HT use in pediatric dentistry in Saudi Arabia. Full article

Background: Shigella flexneri is a major cause of shigellosis in developing regions and is known to cause outbreaks in institutional settings. Transmission occurs via the fecal–oral route. It invades intestinal epithelial cells, causing diarrhea, systemic symptoms, and complications such as hemolytic uremic syndrome. This study aimed to characterize the clinical presentation, administered treatment, infection outcomes, and infection control measures during a local S. flexneri outbreak at a rehabilitation center. Methods: This case series at King Saud University Medical City (Oct–Dec 2024) investigated S. flexneri infections from a rehabilitation center. Stool and blood samples were cultured and analyzed using microbiological methods. Molecular studies were used to verify the genetic linkage between the isolates and to study their virulence genes. Results: Four cases of S. flexneri were included, involving patients with various comorbidities, residing in a rehabilitation center, and presenting with symptoms like fever and diarrhea. Laboratory investigations revealed leukocytosis, electrolyte imbalances, and elevated inflammatory markers. Imaging studies showed findings consistent with colitis in two cases. Patients were managed with IV fluids and targeted antibiotics, leading to symptom resolution. Molecular studies confirmed the genetic relatedness between the S. flexneri isolates, with virulence genes indicating cellular invasion and inflammation as primary drivers of disease severity. Outbreak management comprised contact isolation, environmental disinfection, and education. Conclusions: S. flexneri outbreaks in long-term care facilities pose challenges among bedbound patients. Diapers may facilitate transmission, and infections may cause severe complications. Robust infection control, identifying outbreak sources, and strengthening prevention strategies are essential to protect vulnerable populations. Full article

This article delves into some properties of free and Boolean multiplicative convolutions, in connection with the theory of Cauchy–Stieltjes kernel (CSK) families and their respective variance functions (VFs). Consider ${\mathcal{K}}_{-}\left(\mu \right)=\{Q_m^{\mu }\left(ds\right):m\in (m_{-}^{\mu },m_0^{\mu })\}$, a CSK family induced by a non-degenerate probability measure $\mu$ on the positive real line with a finite first-moment $m_0^{\mu }$. For $\gamma >1$, we introduce a new family of measures: ${\left({\mathcal{K}}_{-}\left(\mu \right)\right)}^{⊠\gamma }=\left\{{\left(Q_m^{\mu }\right)}^{⊠\gamma }\left(ds\right):m\in (m_{-}^{\mu },m_0^{\mu })\right\}.$ We show that if ${\left({\mathcal{K}}_{-}\left(\mu \right)\right)}^{⊠\gamma }$ represents a re-parametrization of the CSK family ${\mathcal{K}}_{-}\left(\mu \right)$, then $\mu$ is characterized by its corresponding VF ${\mathcal{V}}_{\mu }\left(m\right)=c{m}^{2}ln\left(m\right)$, with $c>0$. We also prove that if ${\left({\mathcal{K}}_{-}\left(\mu \right)\right)}^{⊠\gamma }$ is a re-parametrization of ${\mathcal{K}}_{-}\left(D_{1/\gamma }\left({\mu }^{⊞\gamma }\right)\right)$ (where ⊞ is the additive free convolution and $D_a\left(\mu \right)$ denotes the dilation $\mu$ by a number $a\ne 0$), then $\mu$ is characterized by its corresponding VF ${\mathcal{V}}_{\mu }\left(m\right)=c_1{(mln\left(m\right))}^2$, with $c_1>0$. Similar results are obtained if we substitute the free multiplicative convolution ⊠ with the Boolean multiplicative convolution ⨃. Full article

The free Meixner family ($\mathbb{FMF}$) is the family of measures that produces quadratic Cauchy–Stieltjes Kernel (CSK) families (i.e., meaning that the associated variance function (VF) is a polynomial with degree $\le 2$ in the mean). Furthermore, a cubic class is introduced in the context of CSK families and is connected to the quadratic class via a reciprocity relation. The associated probability measures are the so-called free analog of the Letac–Mora class (with VF of degree 3). In free probability theory, these two classes of probabilities are crucial. However, a novel transformation of measures is introduced in the setting of free probability, known as the $T_a$-transformation of probability measures. Denote by $\mathcal{P}$ the set of (non-degenerate) real probabilities. For $\nu \in \mathcal{P}$ and $a\in \mathbb{R}$, consider the transformation of measure $\nu$, denoted $T_a\left(\nu \right)$, defined by ${\mathcal{F}}_{T_a\left(\nu \right)}\left(w\right)={\mathcal{F}}_{\nu }(w-a)+a,$ where ${\mathcal{F}}_{\nu }(·)$ is the inverse of the Cauchy–Stieltjes transformation of $\nu$. In this study, we provide important insights into the notion of the $T_a$-transformation of probabilities. We demonstrate that the $\mathbb{FMF}$ (respectively, the free counterpart of the Letac–Mora class of measures) is invariant under the $T_a$-transformation. Furthermore, we develop additional characteristics of the $T_a$-transformation, which yield intriguing findings for significant free probability distributions such as the free Poisson and free Gamma distributions. Full article

We aim to analyze the dynamics of multiple financial assets with variable volatility. Instead of a standard analysis based on the Black–Scholes model, we proceed with the multidimensional Volterra model, which allows us to treat volatility as a stochastic process. Taking advantage of the long memory function of this type of model, we analyze the reproduced movements using recent algorithms in the field of functional data analysis (FDA). In fact, we develop, in particular, new risk tools based on the asymmetric least squares loss function. We build an estimator using the multifunctional kernel (MK) method and then establish its asymptotic properties. The multidimensionality of the Volterra process is explored through the dispersion component of the convergence rate, while the nonparametric path of the risk tool affects the bias component. An empirical analysis is conducted to demonstrate the ease of implementation of our proposed approach. Additionally, an application on real data is presented to compare the effectiveness of expectile-based measures with Value at Risk (VaR) in financial risk management for multiple assets. Full article

The concept of r-free convolution (which is represented by $\begin{array}{|c|}\hline r\\ \hline\end{array}$) was introduced for $0\le r\le 1$. It is equal to the Boolean additive convolution ⊎ if $r=0$ and reduced to the free additive convolution ⊞ when $r=1$. This paper presents certain features of the r-free convolution in relation to the CSK families and their associated variance functions. We provide the variance function formula under $\begin{array}{|c|}\hline r\\ \hline\end{array}$-convolution power. We then estimate members of the r-free Gaussian and r-free Poisson CSK families using the variance function and the $\begin{array}{|c|}\hline r\\ \hline\end{array}$-convolution, respectively. Additionally, a novel limit theorem for the $\begin{array}{|c|}\hline r\\ \hline\end{array}$-convolution is provided utilizing the variance functions and the free multiplicative convolution. Full article

Mixture models are widely used in mathematical statistics and theoretical probability. However, the mixture probability distribution is rarely explicit in its formula. One must then decide whether to keep the parent probability distribution or to obtain an approximation of the mixture probability distribution. In such cases, it is essential to estimate or evaluate the distance between a mixture probability distribution and its parent probability distribution. On the other hand, orthogonal polynomials offer a versatile mathematical tool for approximating, fitting, and analyzing mixture models, facilitating more accurate and efficient modeling in statistics and data science. This article considers mixture models in Cauchy–Stieltjes Kernel (CSK) families. Using a suitable basis of polynomials, we obtain an expression for the distance in the $L^2$-norm between the mixed probability distribution and its parent probability distribution which belongs to a given CSK family. For the distance between the corresponding distribution functions, bounds are derived in $L^1$-norm. The results are illustrated by some examples from quadratic CSK families. Full article

Background: The COVID-19 pandemic triggered a global transition to distance learning, which significantly impacted children’s mental health. In Saudi Arabia, remote education began on 8 March 2020, lasting between 1.5 to 2.5 years. This study aims to explore the psychological effects of distance learning on children and adolescents, with a focus on mental health challenges and coping mechanisms. Methods: A cross-sectional study was conducted using an online survey distributed to parents of children aged 6 to 18 in the major metropolitan areas of Jeddah and Riyadh. The survey included demographic questions and the Arabic version of the Vanderbilt ADHD Diagnostic Rating Scale, a tool for assessing behavioral challenges, anxiety, and symptoms of attention deficit hyperactivity disorder (ADHD). Results: A total of 71.6% of families reported a positive experience with distance learning. A significant correlation was found between parents’ marital status and children’s ability to cope with remote education. Interestingly, children without ADHD symptoms experienced three times more negative outcomes than those with ADHD symptoms. However, despite reporting fewer negative experiences, children with ADHD exhibited increased symptom severity and academic difficulties. Of the students, 5.4% were diagnosed with predominantly inattentive ADHD, 1.8% with predominantly hyperactive/impulsive ADHD, and 3.9% with combined ADHD. Additionally, 7.2% of students screened positive for oppositional defiant disorder, 1.5% for conduct disorder, and 6.6% for anxiety or depression. Children from separated or divorced families were more likely to exhibit ADHD symptoms (p = 0.002). Children with ADHD symptoms reported a more positive experience with distance learning (p < 0.05). Conclusion: This study represents the first comprehensive, multi-city investigation in Saudi Arabia examining the relationship between distance learning, sociodemographic factors, and mental health symptoms in children. The findings highlight the psychological challenges faced by children during the pandemic and emphasize the need for targeted interventions to support both mental health and academic outcomes. These results offer valuable insights for future research and inform strategies to address children’s well-being in scenarios involving distance learning. Full article

Background: Sickle cell disease (SCD) is a genetic hematological disorder associated with significant mortality and a range of complex complications that manifest differently across various age groups. Methods: This study aimed to evaluate the demographic, clinical, and laboratory characteristics of SCD patients in Taif City, Saudi Arabia, with a focus on variations among children, adolescents, adults, and middle-aged individuals. A multicenter retrospective cohort study included 129 patients with confirmed diagnosis of SCD between January 2018 to October 2023 and divided into 4 cohorts. The analysis compared hospital stay durations, admission rates, SCD complications, and medication usage. Results: Among the participants, 35 were children (27%), 18 adolescents (14%), 63 adults (49%), and 13 middle-aged individuals (10%). Clinical complications as splenic disease in children (34.3%) were more frequent compared to adolescents (5.6%) and adults (4.8%). Additionally, chronic kidney disease was more prevalent in middle-aged patients (15.4%). Pain was reported in 65.1% of patients, with vascular occlusive crises occurring in 41.1%. Treatment adherence varied, with children showing higher penicillin use (74.3%), while opioid usage was greater in middle-aged patients (76.9%). Conclusions: The findings underscore the necessity for age-specific management strategies in SCD. Further research with larger populations is suggested to enhance the understanding of disease progression and treatment efficacy across different age groups. Full article

Candida albicans (C. albicans) adhering to denture-based resins (DBRs) is a known cause of denture stomatitis. A new approach to prevent denture stomatitis is to include antimicrobial substances within DBRs. Here, we examined the mechanical performance and antifungal properties of DBRs containing benzyldimethyldodecyl ammonium chloride (C₁₂BDMA-Cl) as an antimicrobial compound. C₁₂BDMA-Cl is a quaternary ammonium compound, and its antifungal properties have never been investigated when combined with dental acrylic resin. Therefore, we modified a commercially available heat-polymerized acrylic DBR to contain 3 and 5 wt.% of C₁₂BDMA-Cl. Unmodified DBR was used as a control group. Specimens were prepared using the conventional heat processing method. The specimen’s flexural strength, elastic modulus, microhardness, and surface roughness were evaluated. C. albicans biofilm was grown on the specimens and assessed via colony-forming units (CFUs) and scanning electron microscopy (SEM). In silico molecular docking was applied to predict the potential C₁₂BDMA-Cl inhibition activity as an antifungal drug. The 3% C₁₂BDMA-Cl DBR demonstrated antifungal activities without a deterioration effect on the mechanical performance. SEM images indicated fewer colonies in DBR containing C₁₂BDMA-Cl, which can be a potential approach to managing denture stomatitis. In conclusion, C₁₂BDMA-Cl is a promising antifungal agent for preventing and treating denture stomatitis. Full article

Symmetrical fractional differential equations have been explored through a variety of methods in recent years. In this paper, we analyze the existence and uniqueness of a class of pantograph integro-fractional stochastic differential equations (PIFSDEs) using the Banach fixed-point theorem (BFPT). Also, Gronwall inequality is used to demonstrate the Ulam–Hyers stability (UHS) of PIFSDEs. The results are illustrated by two examples. Full article

This paper introduces an innovative concentration inequality for Extended Negative Dependence (END) random variables, providing new insights into their almost complete convergence. We apply this inequality to analyze END variable sequences, particularly focusing on the first-order auto-regressive (AR(1)) model. This application highlights the dynamics and convergence properties of END variables, expanding the analytical tools available for their study. Our findings contribute to both the theoretical understanding and practical applications of END variables in fields such as finance and machine learning, where understanding variable dependencies is crucial. Full article