Search Results (45)

We introduce a family of pseudorandom binary sequences defined by the truncated sum-of-digits function of squares in base-q with $q\ge 2$. Using the Erdős–Turán inequality and Weyl-type bounds for quadratic exponential sums, we estimate the well-distribution measure and the correlation measure of order l for these sequences. For $k=2$ (i.e., using the first two base-q digits), we prove that $W\left(E_{q^2}\right)\ll q{\left(\log q\right)}^2$ and $C_l\left(E_{q^2}\right)\ll 2^{l}q{\left(\log q\right)}^{l+1}$, provided that q is sufficiently large. These bounds show that the sequences exhibit strong pseudorandom properties. Full article

In this paper, we introduce and study Hermite–Kampé de Fériet Hahn–Appell polynomial sequences (HKdF Hahn–Appell sequences) within the unified framework of the Hahn difference operator. We establish three equivalent characterisations of these sequences: an operational definition via the Hahn difference condition, an explicit summation formula involving $\alpha$-binomial coefficients and the falling Hahn basis, and a generating-function criterion. A three-term recurrence relation, a second-order difference equation, and the determinantal representation are also derived for these polynomials. The d-orthogonality of the family is characterised via truncation conditions on the recurrence coefficients $\left\{{\sigma }_k\right\}$; the generating functions of d-orthogonal members are identified as products of $\alpha$-Pochhammer symbols, and the d-dimensional functional vector is expressed in closed form. As principal examples, the HKdF Hahn–Bernoulli, HKdF Hahn–Euler, and HKdF Hahn–Genocchi polynomial sequences are introduced, and for each family, four limiting cases are established. A unifying summary table is provided. Graphical and numerical analysis of the zero distribution for all three families confirms the analytical results and illustrates the convergence of zeros to the classical Hermite–Kampé de Fériet setting as the parameters approach their limiting values. Full article

Background: Mutations in the FBXO7 gene (PARK15) cause an autosomal recessive, early-onset neurodegenerative disorder typically presenting as Parkinsonian-Pyramidal Syndrome (PPS). Despite its recognition, the high phenotypic variability often delays diagnosis. Here, we report a novel Italian family and synthesize data from all published cases to date, offering an updated clinical and molecular overview of the disease. Methods: We performed clinical and molecular characterization of a newly identified family. Furthermore, we conducted a systematic literature review (from 2008 to 2026) to aggregate clinical, genetic, and geographic data of all reported PARK15 cases. Results: Two siblings presented with a complex phenotype including early-onset parkinsonism, cognitive decline, psychiatric symptoms, and aphasia-type speech disorders. Genetic analyses identified two novel likely pathogenic variants: a missense substitution in the UBL domain (p.Ile74Met) and a frameshift indel (p.Val233GlufsTer8). The literature review (incorporating clinical data from Europe, Asia, and South America) confirms a high prevalence of postural instability (87.5%), bradykinesia (83.3%), and pyramidal signs (~60%). We observed a distinct distribution of variants: missense mutations cluster in the N-terminal UBL and F-box domains, while truncating variants are more common in the C-terminal region. Discussion: Our findings expand the FBXO7 mutational landscape and underscore the “atypical” clinical markers, such as pyramidal signs and cognitive decline, that distinguish PARK15 from other recessive forms of parkinsonism like PARK2 and PARK6. The dual role of FBXO7 in mitochondrial quality control and proteasomal assembly suggests a broad disruption of cellular homeostasis. These observations refine genotype–phenotype correlations and may guide variant interpretation in routine diagnostic settings. Full article

Accurate airfoil reconstruction is crucial for aerodynamic analysis, geometric modeling, and computational design applications. This study proposes an optimized M-Hermite interpolation framework for high-accuracy airfoil reconstruction and geometric preservation. Unlike classical Hermite interpolation, the proposed framework integrates a truncated M-derivative formulation through M-inspired parameter-dependent scaling into the interpolation structure, enabling adaptive local geometric control via fractional parameters $\alpha$ and $\beta$. Additionally, a tangential scaling coefficient is incorporated to improve curvature adaptation and reconstruction stability in critical geometric regions. The proposed framework is evaluated using 11 reference airfoil geometries and compared with widely used interpolation methods, including Cubic Spline, B-Spline, Bézier, Catmull-Rom, Classical Hermite, and unoptimized M-Hermite interpolation. Reconstruction performance was assessed using both global and local geometric validation metrics, including RMSE, MAE, maximum error, Hausdorff distance, leading-edge RMSE, trailing-edge RMSE, thickness retention error, and curvature retention error. Experimental results demonstrated that the optimized M-Hermite framework achieved the best overall reconstruction performance and geometric consistency across the evaluated airfoil families. The proposed framework improved reconstruction accuracy, particularly in high-curvature leading-edge regions, while preserving geometrically relevant shape descriptors known to influence aerodynamic behavior, including thickness distribution, camber-line consistency, and curvature structure. Optimization analyses further revealed that reconstruction performance is strongly dependent on geometry-adaptive parameter configurations, particularly the $\beta$ parameter, which governs local geometric behavior. These findings demonstrate that the proposed optimized M-Hermite framework provides an adaptive and computationally efficient interpolation strategy for accurate airfoil reconstruction and geometric shape preservation applications. Full article

Background/Objectives: Recessive titinopathies caused by biallelic TTN truncating variants (TTNtvs) present a clinically heterogeneous spectrum from fetal demise to late-onset slowly progressive distal muscular dystrophy. Prognostic counseling is challenging due to the vast size of the TTN gene, complex splicing patterns, and differential expression throughout developmental stages and tissues. This paper aims to delineate the regional genotype patterns and clinical characteristics of recessive titinopathies described from the prenatal period onwards to inform genotype–phenotype associations and genetic counseling. Methods: We analyzed clinical and genetic data from a prenatal-onset cohort with biallelic TTNtvs from both previously reported cases and novel cases from our center. To characterize the regional distribution of biallelic variants within this specific cohort, a two-dimensional scatter plot was utilized to map variants onto 10 biological regions (R1–R10) and 55 analytical units (U1–U55). We also performed Fisher’s exact tests on the subset of 50 cases with confirmed survival records to evaluate statistically significant associations between biallelic regional or percent spliced-in (PSI) thresholds combinations and severe clinical endpoints (intrauterine demise or death before 5 years). Results: A total of 96 prenatal cases from 76 unrelated families were analyzed. Decreased fetal movement was the most commonly reported symptom, observed in 81.3% (78/96) of cases, which was followed by arthrogryposis in 45.8% (44/96) and amniotic fluid volume abnormalities in 35.4% (34/96). Additionally, of the 95 cases with known pregnancy outcomes, 25.3% (24/95) resulted in termination and 11.6% (11/95) resulted in intrauterine demise (IUD), while 63.2% (60/95) reached birth with over 16.7% (10/60) being preterm. Among 60 live-born infants, severe postnatal morbidity was high: 45.0% (27/60) experienced respiratory failure, and 33.3% (20/60) died before the age of five. In this cohort, 84.4% (81/96) of cases possessed at least one TTNtv in either the metatranscript-only or A-band regions. The most common biallelic changes involved TTNtvs in both the A-band and metatranscript-only regions, accounting for 35.4% (34/96) of cases, followed by metatranscript-only combined with I-band variants at 16.7% (16/96), regardless of the PSI score of exons. Overall, 83.3% (80/96) had ≥1 variant on low-PSI (<50%) exons, and 19.8% (19/96) had both alleles on these low-PSI exons. In the 50 patients with confirmed survival records, biallelic changes (excluding splice-site variants) affecting both high-PSI (>90%) exons were significantly associated with severe outcomes (intrauterine demise or death before 5 years; exact p = 0.015), whereas the metatranscript-only plus I-band combination conferred a significantly lower risk of lethality before 5 years of age (exact p = 0.001). Conclusions: Our findings add to the accumulating evidence that TTNtvs on low PSl exons or metatranscript-only regions are frequently observed among reported prenatal-onset recessive titinopathy. Health surveillance for heterozygous carriers among family members is warranted due to the substantial risk for adult-onset dilated cardiomyopathy and peripartum cardiomyopathy. Full article

We develop a semi-parametric framework for representing discrete probability mass functions through orthogonal polynomial representations. Classical count models, such as the Poisson and negative binomial distributions, impose restrictive structural assumptions that often fail to accommodate empirical features including heavy overdispersion, multimodality, and nonstandard tail behavior. To address these limitations, we introduce a linear-tilt model constructed from orthonormal polynomial systems associated with Poisson and negative binomial baselines, namely the Charlier and Meixner families. The proposed representation improves the baseline distribution using additional information from empirical moments. This allows the distribution to flexibly adjust its shape, capturing differences in skewness and kurtosis. We establish theoretical properties of the expansion within a weighted Hilbert space formulation, where the coefficients arise as orthogonal projections that can be expressed as expectations of the corresponding polynomial basis functions. In addition, we analyze approximation behavior and provide numerical bounds on the resulting numerical error and convergence properties of truncated approximations. The practical relevance of the proposed methodology is illustrated through applications to several empirical datasets, demonstrating its ability to capture complex distributional structures while preserving a tractable semi-parametric form. Full article

We consider the problem of Bayesian parameter inference in the Merton structural credit risk model, where the posterior is induced by a jump-diffusion likelihood and the marginal evidence is not available in closed form. To approximate this posterior, we construct a variational family based on triangular sum-of-squares (SOS) polynomial flows, in which each component map is monotone by construction: its diagonal derivative is a positive definite quadratic form on a monomial basis, yielding a closed-form log-Jacobian and explicit gradients with respect to all flow parameters. The symmetric positive definite matrices parametrizing the flow are optimized by intrinsic Riemannian gradient ascent on the positive definite cone equipped with the affine-invariant metric, which preserves feasibility at every iterate without projection. We show that the rank-one Jacobian gradients produced by the SOS structure have unit norm in the affine-invariant metric, establishing a direct algebraic coupling between the transport family and the optimization geometry and implying a universal 1-Lipschitz bound for the log-Jacobian along geodesics. On the likelihood side, we derive exact score identities for all five structural parameters of the Merton model—drift, volatility, jump intensity, jump mean, and jump volatility—through both the Poisson log-normal mixture and the Fourier inversion representations. Strictly positive parameters are handled via exponential reparametrization, and the resulting gradients propagate end-to-end through the flow. We establish uniform truncation bounds on compact parameter sets for the infinite mixture and its associated score series, providing rigorous control over the finite approximations used in practice. The base distribution is chosen to be uniform on ${[0,1]}^5$, whose bounded support ensures uniform control of the monomial basis and stabilizes the polynomial calculus. These ingredients are assembled into a fully explicit modified ELBO with implementable gradients, combining Euclidean updates for vector parameters and intrinsic manifold updates for matrix parameters. Full article

Rhabdophis lateralis is a snake species within the family Natricidae, which is widely distributed across mainland China, Russia, and Korea. Although this species was once thought to be non-venomous, there are quite a few cases demonstrating its bite could be fatal. In this study, we performed de novo assembly and analysis of the transcriptome data from the Duvernoy’s gland of R. lateralis, aiming to characterize its venom transcriptome and reveal the molecular basis of its toxicity. Among 6196 annotated transcripts, 77 were identified as potential toxin transcripts belonging to 26 toxin families. The most highly expressed toxin family was the SVMP family, accounting for 51.10% of the total toxin expression. The other notable toxins included cysteine-rich secretory proteins (CRISPs, 22.36%), c-type lectins (CTLs and snaclecs, 12.13%), and three-finger toxins (3Ftxs, 6.36%). Phylogenetic analyses indicated that SVMPs, CRISPs, and three-finger toxins (3FTxs) are evolutionarily conserved within Colubridae, whereas CTLs likely arose through convergent evolution. All identified SVMPs were classified as P-III type, with one sequence displaying a unique deletion distinct from conventional truncation patterns. The predominantly expressed CTLs are more likely to combine into dimers, exerting coagulation activity. This study provides an insight into the toxin gene expression in the Duvernoy’s gland of R. lateralis, which will benefit future research into the ecological and pharmacological significance of toxins in the genus Rhabdophis. Full article

Smart energy networks, including electricity distribution and district heating, are increasingly operated as sensor-enabled infrastructures where maintenance decisions must be made under heterogeneous and time-varying operating conditions. In these settings, time-to-event data are rarely complete; preventive actions and limited observation horizons routinely introduce censoring and truncation, so models and validation procedures must account for partially observed lifetimes to avoid biased inference and misleading performance estimates. This review surveys survival models for predictive maintenance (PdM) and remaining useful life (RUL) estimation, spanning non-parametric, semi-parametric, parametric, and learning-based approaches, with emphasis on censoring-aware formulations and the use of static and time-varying covariates derived from sensor, inspection, and contextual information. A structured taxonomy and a systematic mapping of model families to data types, core assumptions (proportional hazards versus parametric distributional structure), and decision-oriented outputs such as risk ranking, horizon failure probabilities, and RUL distributions are presented. Evaluation practice is also synthesized by covering discrimination metrics, censoring-aware RUL accuracy measures, and probabilistic assessment via proper scoring rules, including the time-dependent Brier score and Integrated Brier Score (IBS). The review provides researchers and practitioners with a practical guide to selecting, fitting, and evaluating survival models for risk-informed maintenance planning in smart energy networks. Full article

Afrotropical inland waters remain poorly studied for rotifer diversity. Here, we provide new distribution data from Botswana and connect these local patterns to continental-scale biogeography using an Africa–Europe occurrence dataset. In Botswana, we analyzed rotifer species richness, functional traits, and environmental drivers using 37 samples from 15 water bodies spanning natural and anthropogenic habitats. We recorded 107 rotifer taxa: 92 identified to species or subspecies level, 14 to genus, and one group of unidentified bdelloids. Seventy taxa (~65%) are new records for Botswana, and one species, Donneria sudzukii, is reported for the first time in Africa. Physicochemical gradients explained community structure, with the first two constrained RDA axes accounting for 40.7% and 23.7% of variation. Axis 1 captured a mineralization gradient linked to total dissolved solids and temperature, whereas Axis 2 reflected oxygen concentration and pH. Traits tracked these gradients: warmer, more mineralized waters were associated with specific trophi types, compact body shapes, and intermediate body sizes, whereas less mineralized, better oxygenated sites were related to smaller taxa and alternative feeding morphologies. To place these trait–environment relationships in a broader geographic context, we then analyzed an Africa–Europe dataset (67,170 records) to quantify latitudinal patterns in thermal classes and morphological traits (geometric body shape and trophi type). Diversity showed clear latitudinal structuring: warm-water genera clustered at low latitudes, only Kellicottia and Didymodactylos had mean distributions above 50° N, and bdelloid families were associated with higher latitudes. Morphological traits also varied with latitude, with trilateral truncated pyramid body shapes and malleoramate trophi occurring closest to the equator. Overall, by combining new species-level data from Botswana with continent-scale occurrence patterns, we link local community assembly to macroecological structure in rotifer functional and biogeographical organization. Full article

This study revisits a recently proposed member of the truncated positive family of distributions, referred to as the positively truncated Student’s-t distribution. The distribution retains the structure of the classical Student’s-t distribution while explicitly incorporating a kurtosis parameter, yielding a flexible three-parameter formulation that governs location, scale, and tail behavior. A closed-form quantile function is derived, allowing a novel reparameterization based on the pth quantile and thereby facilitating integration into quantile regression models. The analytical tractability of the quantile function also enables efficient random number generation via the inverse transform method, which supports a comprehensive simulation study demonstrating the strong performance of the proposed estimators, particularly for the degrees-of-freedom parameter. The entire methodology is implemented in the tpn package for the R software. Finally, two real-data applications involving PM2.5 measurements—one without covariates and another with covariates—highlight the model’s robustness and its ability to capture heavy-tailed behavior. Full article

Background/Objectives: Wilson’s disease (WD) is an autosomal recessive disorder characterized by pathological copper accumulation, primarily in the liver and brain. Severe hepatic involvement can be effectively treated with liver transplantation (LT). Geographic variation in ATP7B mutations suggests the presence of regional patterns that may impact disease presentation and management. This study aims to investigate the genetic basis of WD in patients from a major LT center in Iran. Methods: A retrospective analysis was conducted on clinical, biochemical, and pathological data from patients suspected of WD who underwent evaluation for LT between May 2020 and June 2025 at Shiraz University of Medical Sciences. Genetic testing was carried out on 20 patients at the Shiraz Transplant Research Center (STRC). Direct mutation analysis of ATP7B was performed for all patients, and the results correlated with clinical and demographic information. Results: In total, 20 WD patients who underwent liver transplantation (15 males, 5 females) carried 25 pathogenic or likely pathogenic ATP7B variants, 21 of which were previously unreported. Fifteen patients were homozygous, and five were compound-heterozygous; all heterozygous combinations occurred in the offspring of second-degree consanguineous unions. Recurrent changes included p.L549V, p.V872E, and p.P992S/L, while two nonsense variants (p.E1293X, p.R1319X) predicted truncated proteins. Variants were distributed across copper-binding, transmembrane, phosphorylation, and ATP-binding domains, and in silico AlphaMissense scores indicate damaging effects for most novel substitutions. Post-LT follow-up showed biochemical normalization in the majority of recipients, with five deaths recorded during the study period. Conclusions: This single-center Iranian study reveals a highly heterogeneous ATP7B mutational landscape with a large proportion of novel population-specific variants and underscores the benefit of comprehensive gene sequencing for timely WD diagnosis and family counseling, particularly in regions with prevalent consanguinity. Full article

Saussurea involucrata, a rare and endangered medicinal plant of the Asteraceae family, is primarily distributed in high-altitude rocky slopes and meadows at elevations of 2400–4100 m. In nature, this herb endures various abiotic stresses, including intense cold and ultraviolet radiation. In our study, transcriptomic profiles revealed that most of the differentially expressed genes (DEGs) enriched in stress response pathways, such as “response to water”, “response to abscisic acid”, “cold acclimation”, and “response to water deprivation”, were significantly upregulated after low-temperature treatment. In contrast, the majority of genes with lower expression were related to “photosynthesis”, “protein–chromophore linkage”, and “chloroplast thylakoid membrane”. Among them, Kyoto Encyclopedia of Genes and Genomes (KEGG) and Gene Ontology (GO) database analysis revealed that approximately 20 DEGs were identified and annotated as dehydrin genes (DHNs). Quantitative PCR (qPCR) validation also confirmed that these DHNs were upregulated under cold stress. Moreover, SiDHN3, a new dehydrin gene, was cloned by Rapid Amplification of cDNA Ends (RACE). SiDHN3’s heterologous expression in E. coli showed enhanced salt, osmotic, freeze–thaw, and cold stress tolerance. A functional analysis of SiDHN3’s truncated derivatives revealed that the K-segment was critical for its protective function under freeze–thaw and cold stresses. Collectively, our study demonstrated the potential role of various DHNs as a functional protein, enhancing tolerance to cold stress in the high-altitude adaptation of plants. Full article

Phylogenetic studies of the pyruvate kinase family reveal two clusters: the K⁺-dependent and -independent enzymes. Thermoplasma acidophilum pyruvate kinase belongs to the latter but possesses the conserved signature of those K⁺-dependent. Recently, we found two distinct ways for these groups to catalyze. It is interesting to elucidate how the T. acidophilum enzyme achieves its active conformation. A structural model of this enzyme revealed the presence of an extra C-terminal sequence (ECTS). To understand its role, an enzyme lacking this sequence from T. acidophilum was constructed. We then compared the kinetic parameters, far-UV CD spectra, thermal stability, molecular dynamics simulations, and oligomeric states of both the wild-type and truncated enzymes. We found that the truncated enzyme is aggregated and almost inactive, with residual 20% of the total interactions, and it exhibits a soluble fraction of smaller oligomeric states than the wild-type enzyme. These findings suggest that ECTS plays a crucial role in maintaining its active tetrameric state. This sequence is the first reported in an archaeal pyruvate kinase and is also found in other archaea and bacteria. Phylogenetic analysis of ECTS in pyruvate kinases exhibits a sparse distribution that might be explained if ECTS represents an ancient domain prone to loss. Full article

This paper introduces a new family of q-special polynomials, termed q-general Bell polynomials, and systematically explores their structural and analytical properties. We establish their generating functions, derive explicit series representations, and develop recurrence relations to characterize their combinatorial behavior. Additionally, we characterize their quasi-monomial properties and construct associated differential equations governing these polynomials. To demonstrate the versatility and applicability of this family, we investigate certain examples, including the q-Gould–Hopper–Bell and q-truncated exponential-Bell polynomials, deriving analogous results for each. Further, we employ computational tools in Mathematica to examine zero distributions and produce visualizations, offering numerical and graphical insights into polynomial behavior. Full article