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Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scientific computing, but their mathematical reliability is often difficult to quantify, especially when one is interested in the output of a given simulation, rather than in the asymptotic regime where the discretization parameter tends to zero. In this paper we present a computer-assisted proof methodology to perform rigorous time integration for scalar semilinear parabolic PDEs with periodic boundary conditions. We formulate an equivalent zero-finding problem based on a variation of constants formula in Fourier space. Using Chebyshev interpolation and domain decomposition, we then finish the proof with a Newton–Kantorovich type argument. The final output of this procedure is a proof of existence of an orbit, together with guaranteed error bounds between this orbit and a numerically computed approximation. We illustrate the versatility of the approach with results for the Fisher equation, the Swift–Hohenberg equation, the Ohta–Kawasaki equation and the Kuramoto–Sivashinsky equation. We expect that this rigorous integrator can form the basis for studying boundary value problems for connecting orbits in partial differential equations. [ABSTRACT FROM AUTHOR]

Background: This study assesses the incidence of gastrointestinal symptoms in the first year after resection of esophageal or gastric cancer and its association with health-related quality of life (HRQoL), functioning, work productivity, and daily activities. Patients and Methods: Patients diagnosed with esophageal or gastric cancer between 2015 and 2021, who underwent a resection, and completed ≥ 2 questionnaires from the time intervals prior to resection and 0–3, 3–6, 6–9, and 9–12 months after resection were included. Multivariable generalized linear mixed models were used to assess changes in gastrointestinal symptoms over time and the impact of the number of gastrointestinal symptoms on HRQoL, functioning, work productivity, and daily activities for patients who underwent an esophagectomy or gastrectomy separately. Results: The study population consisted of 961 (78.8%) and 259 (21.2%) patients who underwent an esophagectomy and gastrectomy, respectively. For both groups, the majority of gastrointestinal symptoms changed significantly over time. Most clinically relevant differences were observed 0–3 after resection compared with prior to resection and included increased diarrhea, appetite loss, and eating restrictions, and specifically after esophagectomy dry mouth, trouble with coughing, and trouble talking. At 9–12 after resection one or more severe gastrointestinal symptoms were reported by 38.9% after esophagectomy and 33.7% after gastrectomy. A higher number of gastrointestinal symptoms was associated with poorer functioning, lower HRQoL, higher impairment in daily activities, and lower work productivity. Conclusions: This study shows that gastrointestinal symptoms are frequently observed and burdensome after esophagectomy or gastrectomy, highlighting the importance to address these sequelae for high quality survivorship. [ABSTRACT FROM AUTHOR]

In this paper, we study travelling front solutions for nonlocal equations of the type ∂ t u = N ∗ S (u) + ∇ F (u) , u (t , x) ∈ R d. Here, N ∗ denotes a convolution-type operator in the spatial variable x ∈ R , either continuous or discrete. We develop a Morse-type theory, the Conley–Floer homology, which captures travelling front solutions in a topologically robust manner, by encoding fronts in the boundary operator of a chain complex. The equations describing the travelling fronts involve both forward and backward delay terms, possibly of infinite range. Consequently, these equations lack a natural phase space, so that classic dynamical systems tools are not at our disposal. We therefore develop, from scratch, a general transversality theory, and a classification of bounded solutions, in the absence of a phase space. In various cases the resulting Conley–Floer homology can be interpreted as a homological Conley index for multivalued vector fields. Using the Conley–Floer homology, we derive existence and multiplicity results on travelling front solutions. [ABSTRACT FROM AUTHOR]

In this paper we develop a general computer-assisted proof method for periodic solutions to delay differential equations. The class of problems considered includes systems of delay differential equations with an arbitrary number of (forward and backward) delays. When the nonlinearities include nonpolynomial terms we introduce auxiliary variables to first rewrite the problem into an equivalent polynomial one. We then apply a flexible fixed point technique in a space of geometrically decaying Fourier coefficients. We showcase the efficacy of this method by proving periodic solutions in the well-known Mackey–Glass delay differential equation for the classical parameter values. [ABSTRACT FROM AUTHOR]

In this paper, a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier–Stokes equations on the three-torus is proposed. After introducing a zero finding problem posed on a Banach space of geometrically decaying Fourier coefficients, a Newton–Kantorovich theorem is applied to obtain the (computer-assisted) proofs of existence. The required analytic estimates to verify the contractibility of the operator are presented in full generality and symmetries from the model are used to reduce the size of the problem to be solved. As applications, we present proofs of existence of spontaneous periodic orbits in the Navier–Stokes equations with Taylor–Green forcing. [ABSTRACT FROM AUTHOR]

To make progress toward better computability of Morse–Floer homology and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative index of equilibria. Since even the existence of nontrivial stationary points is often difficult to accomplish, extracting their index information is usually out of reach. In this paper, we establish a computer-assisted proof approach to determining relative indices of stationary states. We introduce the general framework and then focus on three example problems described by partial differential equations to show how these ideas work in practice. Based on a rigorous implementation, with accompanying code made available, we determine the relative indices of many stationary points. Moreover, we show how forcing results can be then used to prove theorems about connecting orbits and traveling waves in partial differential equations. [ABSTRACT FROM AUTHOR]

BACKGROUND: Improvement in health-related quality of life (HRQoL) is one of the main goals in treating chronic obstructive pulmonary disease (COPD). Impaired HRQoL in COPD is associated with increased morbidity and mortality, hospitalisations and burden on our health-care system. The Clinical COPD Questionnaire (CCQ) is a validated, reliable, short questionnaire for the evaluation of disease-specific HRQoL in patients with COPD in primary care. AIMS: To investigate factors that might be associated with CCQ outcome in COPD in a primary care setting. METHODS: In a population of COPD patients in primary care, multiple regression analyses were used to assess associations between CCQ outcome and depression, heart failure, FEV1% predicted, FEV1/FVC, age, sex, body mass index and current smoking. RESULTS: Data from 341 patients (mean age 68.1 ± 10.3, COPD GOLD class I-III) were used for analyses. Together, heart failure and depression explained 23% of the variance in CCQ total score (Po0.001, N = 93). Heart failure was most strongly associated with CCQ functional score (27% explained variance, Po0.001, N = 100), whereas depression was most strongly associated with CCQ mental score (22% explained variance, Po0.001, N = 93). CONCLUSIONS: CCQ outcomes are higher in COPD patients with heart failure and depression. These findings might imply that heart failure and depression affect HRQoL of patients with COPD, and thus emphasise the importance of a holistic approach of this complex disease, leading to a correct diagnosis of COPD and its comorbidities, to achieve better tailored treatment of chronic patients. [ABSTRACT FROM AUTHOR]

This paper presents the first bibliometric mapping analysis of the field of computer and information ethics (C&IE). It provides a map of the relations between 400 key terms in the field. This term map can be used to get an overview of concepts and topics in the field and to identify relations between information and communication technology concepts on the one hand and ethical concepts on the other hand. To produce the term map, a data set of over thousand articles published in leading journals and conference proceedings in the C&IE field was constructed. With the help of various computer algorithms, key terms were identified in the titles and abstracts of the articles and co-occurrence frequencies of these key terms were calculated. Based on the co-occurrence frequencies, the term map was constructed. This was done using a computer program called VOSviewer. The term map provides a visual representation of the C&IE field and, more specifically, of the organization of the field around three main concepts, namely privacy, ethics, and the Internet. [ABSTRACT FROM AUTHOR]

To reveal farmers' motives for on-farm diversification and integration of farming components in the Mekong Delta, Vietnam, we developed a fuzzy logic model (FLM) using a 10-step approach. Farmers' decision-making was mimicked in a three-layer hierarchical architecture of fuzzy inference systems, using data of 72 farms. The model includes three variables for family motives of diversification, six variables related to component integration, next to variables for the production factors and for farmers' appreciation of market prices and know-how on 10 components. To obtain a good classification rate of the less frequent activities, additional individual fine-tuning was necessary after general model calibration. To obtain the desired degree of sensitivity to each variable, it was necessary to use up to five linguistic values for some of the input and output variables in the intermediate hierarchical layers. Model's sensitivity to motivational variables determining diversification and integration was of the same magnitude as its sensitivity to market prices and farmers' know-how of the activities, but less than its sensitivity to labour, capital and land endowment. Modelling to support strategic decision-making seems too elaborate for individual farms, but FLM will be useful to integrate farmers' opinions in strategic decision-making at higher hierarchical levels. [ABSTRACT FROM AUTHOR]

About 30% of the potato plants from a ( Solanum tuberosum × S. berthaultii) × S. tuberosum backcross population had chlorotic, malformed leaves; but a gradation in symptom severity suggested regulation by more than one gene. The study was undertaken to determine whether this was the case, whether any genes previously reported to control chlorosis in potato were involved, and to see how symptoms were related to effects on chlorophyll content. Testing for quantitative trait loci indicated major control by a single recessive gene on chromosome 1, close to one or more loci that have been reported to produce chlorosis in tomato, but distinct from similar genes previously identified in potato. The proposed symbol for the potato gene that confers phenotype with chlorotic and malformed leaves is cml (chlorotic and malformed leaves). The effects of this gene appeared to be accentuated by a second gene, located on chromosome 12. Chlorotic plants showed a 50% decrease in chlorophyll b level in the affected parts of leaves. It is concluded that cml is different from previously reported genes for chlorosis in potato, that at least one other gene modifies the intensity of symptom expression, and that the observed chlorosis is produced through effects on chlorophyll b level. [ABSTRACT FROM AUTHOR]