Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

The role of diet in the aetiopathogenesis of inflammatory bowel disease

Crohn’s disease and ulcerative colitis, collectively known as IBD, are chronic inflammatory disorders of the gastrointestinal tract. Although the aetiopathogenesis of IBD is largely unknown, it is widely thought that diet has a crucial role in the development and progression of IBD. Indeed, epidemiological and genetic association studies have identified a number of promising dietary and genetic risk factors for IBD. These preliminary studies have led to major interest in investigating the complex interaction between diet, host genetics, the gut microbiota and immune function in the pathogenesis of IBD. In this Review, we discuss the recent epidemiological, gene–environment interaction, microbiome and animal studies that have explored the relationship between diet and the risk of IBD. In addition, we highlight the limitations of these prior studies, in part by explaining their contradictory findings, and review future directions

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

Oral Serum-Derived Bovine Immunoglobulin/Protein Isolate Has Immunomodulatory Effects on the Colon of Mice that Spontaneously Develop Colitis

Dietary immunoglobulin concentrates prepared from animal plasma can modulate the immune response of gut-associated lymphoid tissue (GALT). Previous studies have revealed that supplementation with serum-derived bovine immunoglobulin/protein isolate (SBI) ameliorates colonic barrier alterations in the mdr1a-/- genetic mouse model of IBD. Here, we examine the effects of SBI on mucosal inflammation in mdr1a-/- mice that spontaneously develop colitis. Wild type (WT) mice and mice lacking the mdr1a gene (KO) were fed diets supplemented with either SBI (2% w/w) or milk proteins (Control diet), from day 21 (weaning) until day 56. Leucocytes in mesenteric lymph nodes (MLN) and in lamina propria were determined, as was mucosal cytokine production. Neutrophil recruitment and activation in MLN and lamina propria of KO mice were increased, but were significantly reduced in both by SBI supplementation (p < 0.05). The increased neutrophil recruitment and activation observed in KO mice correlated with increased colon oxidative stress (p < 0.05) and SBI supplementation reduced this variable (p < 0.05). The Tact/Treg lymphocyte ratios in MLN and lamina propria were also increased in KO animals, but SBI prevented these changes (both p < 0.05). In the colon of KO mice, there was an increased production of mucosal proinflammatory cytokines such as IL-2 (2-fold), IL-6 (26-fold) and IL-17 (19-fold), and of chemokines MIP-1β (4.5-fold) and MCP-1 (7.2-fold). These effects were significantly prevented by SBI (p < 0.05). SBI also significantly increased TGF-β secretion in the colon mucosa, suggesting a role of this anti-inflammatory cytokine in the modulation of GALT and the reduction of the severity of the inflammatory response during the onset of colitis

The development of a decision aid for patients with operable oropharyngeal carcinoma in the Netherlands - A mixed methods study

OBJECTIVE: The aim of this project is to create an interactive online patient decision aid (PDA) for oropharyngeal cancer (OPSCC) patients, eligible for transoral (robotic) surgery with an ultimate goal to assist both physicians and patients in making treatment choices.MATERIALS AND METHODS: Following the International Patient Decision Aid Standards, a mixed-methods approach was employed. The study involved semi-structured in-depth interviews with patients and physicians, thinking-out-loud sessions, and study-specific questionnaires. Thematic coding and analysis were conducted on verbatim transcriptions of audio-recorded interviews.RESULTS: The PDA drafts were evaluated by twenty OPSCC survivors and twenty multidisciplinary specialists. Significant revisions were made after phase 1 to enhance readability and reduce text, whilst incorporating videos and graphics. Following all phases, both patients and specialists rated the PDA as comprehensible, feasible, and a valuable addition to regular counseling.CONCLUSION: This study showcases the development of a PDA for early stage oropharyngeal cancer patients considering surgery and radiotherapy options. The decision aid emphasizes the disparities in short- and long-term side effects between the two treatments. Patients and physicians found the decision aid to be understandable, user-friendly, and helpful for future patients. The PDA is available on https://beslissamen.nl/.</p