Search Results (77)

Background: The prevalence of inflammatory bowel disease (IBD) is increasing worldwide, while the incidence is tending to stabilize. Moreover, the use of biological treatments is increasing; some studies suggest that surgeries and hospitalizations are decreasing instead. Methods: A population-based, retrospective cohort study was conducted using data from the Catalan Health Surveillance System (CHSS). All patients diagnosed with IBD were included between 2017 and 2023. Crude incidence and prevalence rates were calculated for the Catalan population. Data on pharmacological therapy, surgical procedures, hospitalizations, and mortality were analyzed. Trends in age-sex-adjusted rates were also estimated, and logistic regression was used to calculate the adjusted mortality odds ratio (OR). Data for Crohn’s disease (CD) and ulcerative colitis (UC) were analyzed separately. Results: The number of prevalent IBD cases rose from 28,752 in 2017 to 41,423 in 2023. Despite incidence rates remaining stable (30.8 in 2017 and 29.9 per 100,000 inhabitants in 2023), prevalence rates increased (386.9 and 510.9 per 100,000 inhabitants, respectively). The use of biologics significantly increased (from 13.5% in 2017 to 21.0% in 2023), particularly ustekinumab and vedolizumab. In parallel, a decline in the use of immunosuppressants was observed. IBD-related surgeries and hospitalizations decreased during the study period, particularly among CD patients. Mortality remained low but was higher among IBD patients compared to the general population. Conclusions: The incidence of IBD in Catalonia has stabilized, while its prevalence continues rising, suggesting a transition to Stage 3 (compounding prevalence). The use of biological treatments is increasing steadily, whereas rates of surgeries and hospitalizations are consistently decreasing. Full article

Background/Objectives: Although differences seem to exist by age in primary cardiovascular prevention with acetylsalicylic acid (ASA), direct comparisons are lacking, as are studies with real-world data. We sought to examine the effectiveness of ASA in reducing cardiovascular diseases and overall mortality in patients at high risk by age subgroups. Methods: We designed a retrospective cohort study using the database of the Catalan primary care system (SIDIAP), Spain, for the period 2006–2020. Included participants were high-cardiovascular-risk individuals without previous vascular disease. We considered people aged 40 to 59 and ≥60 years of age. We assessed the incidences of atherosclerotic cardiovascular disease (ASCVD), all-cause mortality, and ASA adverse effects using Cox proportional hazards modelling, adjusted by the propensity score of ASA treatment. Results: During the study period, 7576 and 30,282 people were aged 40 to 59 and ≥60 years, respectively. The median follow-up was 11.21 (10.71–11.54) years (40 to 59 year-olds) and 11.09 (10.55–11.54) years (≥60 year-olds). The hazard ratio of ASA use for ASCVD in the group aged 40–59 years was 0.64 (0.41–0.99). The number needed to treat in this group was 40 persons and the number that needed to harm for gastrointestinal bleeding (the only adverse effect with significant hazard ratio) was 75 individuals. Conclusions: This direct comparison of real-world age groups at high cardiovascular risk showed no benefit but increased risk in the older population (≥60 years). In the younger subgroup, our observations would support primary prevention with ASA with a consideration of the individual optimal risk–benefit. Full article

In this study, we define a new family of Gaussian polynomials, called Gaussian Chebyshev polynomials, by extending classical Chebyshev polynomials into the complex domain. These polynomials are characterized by second-order linear recurrence relations, and their connections with the Chebyshev polynomials are established. We also examine properties such as Binet-type formulas and generating functions. Moreover, we characterize some relationships between Gaussian and classical Chebyshev polynomials for the first and second kinds. We obtain some well-known theorems, such as Cassini, Catalan, and d’Ocagne’s theorems, for the first and second kinds. Furthermore, we present important connections among four types of these new polynomials. In the proofs of our results, we utilize the symmetric and antisymmetric properties of the Chebyshev polynomials. Finally, it is shown that Gaussian Chebyshev polynomials are closely related to well-known special sequences such as the Fibonacci, Lucas, Gaussian Fibonacci, and Gaussian Lucas numbers for some specific values of variables. Full article

This paper introduces ACCORD, a support platform designed to digitalize and automate the coordination processes required by the current drone regulatory framework. Drone operators must complete several coordination actions with both aeronautical and non-aeronautical entities. Traditional aeronautical coordination actions relate to the need to access protected airspace volumes around airports. Additional coordination should be established with smaller aeronautical infrastructures, like small aerodromes and heliports, which are not surrounded by any type of pre-defined airspace. Therefore, drone-specific protection volumes have been created. ACCORD enables a single entry point for all the necessary coordination processes for drone operators and infrastructure managers. The objective is to minimize the number of required actions, guarantee full traceability of the process, maximize access to the relevant information, automate the processes as much as possible, and maintain a high level of flexibility to support all coordination processes. After coordination is established, it moves from the strategic/planning phase to the actual execution phase. ACCORD also enables a communication mechanism between the drone operators and the aeronautical infrastructures to extend the coordination to the actual mission execution. ACCORD is currently being tested by some of the most relevant actors in the Catalan drone ecosystem. The current version of the system provides support for all types of aeronautical infrastructures (heliports, aerodromes, and airports) and management duality for situations in which the infrastructure manager and the aeronautical service provider coexist. Full article

Six well-known sequences (Fibonacci and Lucas numbers, Pell and Pell–Lucas polynomials, and Chebyshev polynomials) are characterized by quadratic linear recurrence relations. They are unified and reviewed under a common framework. Several useful properties (such as Binet-form expressions, Cassini identities, and Catalan formulae) and remarkable results concerning power sums, ordinary convolutions, and binomial convolutions are presented by employing the symmetric feature, series rearrangements, and the generating function approach. Most of the classical results concerning these six number/polynomial sequences are recorded as consequences. Full article

This study introduces an innovative approach to Mersenne-type numbers. This paper introduces a new class of numbers, which we call Gersenne numbers. The aim of this paper is to define the Gersenne sequence and to investigate some of their properties, such as the recurrence relation, the summation formula, and the generating function. Moreover, the classical identities are derived, such as the Tagiuri–Vajda, Catalan, Cassini, and d’Ocagne identities for Gersenne numbers. Full article

A method for obtaining integer sequences is presented by defining simple rules for the evolution of a discrete dynamical system. This paper demonstrates that various Catalan-like recurrences of known integer sequences can be obtained from a single stochastic process defined by simple rules. The resulting exact equations that describe the stationary state of the process are derived using combinatorial analysis. A specific reduction of the process is applied, and the solvability of the reduced system of equations is demonstrated. Then, a procedure for providing appropriate parameters for a given sequence is formulated. The general method is illustrated with examples of Catalan, Motzkin, Schröder, and A064641 integer sequences. We also point out that by appropriately changing the parameters of the system, one can smoothly transition between distributions related to Motzkin numbers and shifted Catalan numbers. Full article

The Riordan group of Riordan arrays was first described in 1991, and since then, it has provided useful tools for the study of areas such as combinatorial identities, polynomial sequences (including families of orthogonal polynomials), lattice path enumeration, and linear recurrences. Useful extensions of the idea of a Riordan array have included almost Riordan arrays, double Riordan arrays, and their generalizations. After giving a brief overview of the Riordan group, we define two further extensions of the notion of Riordan arrays, and we give a number of applications for these extensions. The relevance of these applications indicates that these new extensions are worthy of study. The first extension is that of the reverse symmetrization of a Riordan array, for which we give two applications. The first application of this symmetrization is to the study of a family of Riordan arrays whose symmetrizations lead to the famous Robbins numbers as well as to numbers associated with the 20 vertex model of mathematical physics. We provide closed-form expressions for the elements of these arrays, and we also give a canonical Catalan factorization for them. We also describe an alternative family of Riordan arrays whose symmetrizations lead to the same integer sequences. The second application of this symmetrization process is to the area of the enumeration of lattice paths. We remain with the applications to lattice paths for the second extension of Riordan arrays that we introduce, which is the interleaved Riordan array. The methods used include generating functions, linear algebra, weighted compositions, and linear recurrences. In the case of the symmetrization process applied to Riordan arrays, we focus on the principal minor sequences of the resulting square matrices in the context of integrable lattice models. Full article

In this study, we establish some properties of Bronze Fibonacci and Bronze Lucas sequences. Then we find the relationships between the roots of the characteristic equation of these sequences with these sequences. What is interesting here is that even though the roots change, equality is still maintained. Also, we derive the special relations between the terms of these sequences. We give the important relations among these sequences, positive and negative index terms, with the sum of the squares of two consecutive terms being related to these sequences. In addition, we present the application of generalized Bronze Fibonacci sequences to hyperbolic quaternions. For these hyperbolic quaternions, we give the summation formulas, generating functions, etc. Moreover, we obtain the Binet formulas in two different ways. The first is in the known classical way and the second is with the help of the sequence’s generating functions. In addition, we calculate the special identities of these hyperbolic quaternions. Furthermore, we examine the relationships between the hyperbolic Bronze Fibonacci and Bronze Lucas quaternions. Finally, the terms of the generalized Bronze Fibonacci sequences are associated with their hyperbolic quaternion values. Full article

In this study, the $k$-Oresme and $k$-Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the $k$-Oresme and $k$-Oresme-Lucas sequences are presented. In addition, we give these sequences the Binet formulas, generating functions, Cassini identity, Catalan identity etc. Moreover, the $k$-Oresme and $k$-Oresme-Lucas sequences are associated with Fibonacci, Pell numbers and Lucas, and Pell- Lucas numbers, respectively. Finally, the Catalan transforms of these sequences are given and Hankel transforms are applied to these Catalan sequences and associated with the terms of the sequence. Full article

In this paper, we introduce and study balancing hybrinomials, i.e., polynomials being a generalization of balancing hybrid numbers. We provide some properties of the balancing hybrinomials, including Catalan, Cassini, d’Ocagne, and Vajda identities, among others. Moreover, we present a matrix representation of the hybrinomials. Full article

In this article, the regular Schröder–Catalan matrix is constructed and acquired by benefiting Schröder and Catalan numbers. After that, two sequence spaces are introduced, described as the domain of Schröder–Catalan matrix. Additionally, some algebraic and topological properties of the spaces in question, such as completeness, inclusion relations, basis and duals, are examined. In the last two sections, the necessary and sufficient conditions of some matrix classes and compact operators related aforementioned spaces are presented. Full article

In the realm of linguistics, the concept of “semanticity” was recently introduced as a novel measure designed to study linguistic networks. In a given text, semanticity is defined as the ratio of the potential number of meanings associated with a word to the number of different words with which it is linguistically linked. This concept provides a quantitative indicator that reflects a word’s semantic complexity and its role in a language. In this pilot study, we applied the semanticity measure to the Catalan language, aiming to investigate its effectiveness in automatically distinguishing content words from function words. For this purpose, the measure of semanticity has been applied to a large corpus of texts written in Catalan. We show that the semanticity of words allows us to classify the word classes existing in Catalan in a simple way so that both the semantic and syntactic capacity of each word within a language can be integrated under this parameter. By means of this semanticity measure, it has been observed that adverbs behave like function words in Catalan. This approach offers a quantitative and objective tool for researchers and linguists to gain insights into the structure and dynamics of languages, contributing to a deeper understanding of their underlying principles. The application of semanticity to Catalan is a promising pilot study, with potential applications in other languages, which will allow progress to be made in the field of theoretical linguistics and contribute to the development of automated linguistic tools. Full article

In this work, we establish some characteristics for a sequence, ${\mathcal{A}}_{\alpha }(n,k)$, including recurrence relations, generating function and inversion formula, etc. Based on the sequence, we derive, by means of the generating function approach, some transformation formulas concerning certain combinatorial numbers named after Lah, Stirling, harmonic, Cauchy and Catalan, as well as several closed finite sums. In addition, the relationship between ${\mathcal{A}}_{\alpha }(n,k)$ and r-Whitney–Lah numbers is established, and some formulas for the r-Whitney–Lah numbers are obtained. Full article