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\"An award-winning mathematician shows how we prove what's true, and what to do when we can't. How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods-logical, empirical, intuitive, and more-to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth. As mathematician Adam Kucharski shows, however, there is far more to proof than axioms, theories, and laws: when demonstrating that a new medical treatment works, persuading a jury of someone's guilt, or deciding whether you trust a self-driving car, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty-and never more so than when existing methods fail. Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof-and, just as importantly, of how to go forward when supposed facts falter\"-- Provided by publisher.

In order to continuously improve the construction capacity of power grid projects, improve the level of construction technology, and promote the transformation and upgrading of construction enterprises, power companies actively promote the mechanized construction of transmission lines. On the basis of summarizing the existing calculation rules of mechanized construction area, through on-site investigation and extensive collection of funds, research and excavate indicators that adapt to the new situation and new regulations. According to the actual area composition of the mechanized construction site, scientific calculation rules are formulated by modeling analysis and other methods. Compare and verify the calculated area of the new rule with the actual compensation area and the calculated area of the original rule, and propose a complete set of calculation rules for mechanized construction area, which has the conditions and value for popularization and application.

Background The objective was to explore the current advances and extent of DES (Discrete Event Simulation) applied to assisting with health decision making, as well as to categorize the wide spectrum of health-related topics where DES was applied. Methods A systematic review was conducted of the literature published over the last two decades. Original research articles were included and reviewed if they concentrated on the topic of DES technique applied to health care management with model frameworks explicitly demonstrated. No restriction regarding the settings of DES application was applied. Results A total of 211 papers met the predefined inclusion criteria. The number of publications included increased significantly especially after 2010.101 papers (48%) stated explicitly disease areas targeted, the most frequently modeled of which are related to circulatory system, nervous system and Neoplasm. The DES applications were distributed unevenly into 4 major classes: health and care systems operation (HCSO) (65%), disease progression modeling (DPM) (28%), screening modeling (SM) (5%) and health behavior modeling (HBM) (2%). More than 68% of HCSO by DES were focused on specific problems in individual units. However, more attempts at modeling highly integrated health service systems as well as some new trends were identified. Conclusions DES technique has been an effective tool to approach a wide variety of health care issues. Among all DES applications in health care, health system operations research occupied the most considerable proportion and increased most significantly. Health Economic Evaluation (HEE) was the second most common topic for DES in health care, but with stable rather than increasing numbers of publications.

The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.

I argue that we cannot adequately characterize idealization and abstraction and the distinction between the two on the grounds that they have distinct semantic properties. By doing so, on the one hand, we focus on the conceptual products of the two processes in making the distinction and we overlook the importance of the nature of the thought processes that underlie model-simplifying assumptions. On the other hand, we implicitly rely on a sense of abstraction as subtraction, which is unsuitable for explicating scientific model construction. Instead, I argue that a sense of abstraction as extraction is more suitable. Finally, I suggest a different way to distinguish the two processes that avoids these problems. Namely, that both idealization and abstraction could be understood as particular modes of application of the same cognitive process: selective attention.

Teachers’ understanding of scientific models is essential for supporting meaningful learning of chemical reaction rates. Yet little is known about how teachers coordinate different dimensions of model understanding in this context. This study examined chemistry teachers’ epistemic understanding of models related to reaction rates, focusing on model selection, prerequisite conditions, and model use. A mixed-methods explanatory sequential design was employed. Open-ended questionnaire items were administered to 52 in-service chemistry teachers, followed by interviews with 10 teachers to elaborate on quantitative trends. The results showed limited understanding across all three dimensions. Many teachers treated the collision model as a literal depiction rather than one representational choice among alternatives. Teachers frequently applied the half-life concept as a universal rule without recognizing assumptions such as constant volume. When interpreting concentration dependence, most relied on simplified textbook patterns rather than using rate laws as representational models grounded in reaction mechanisms. These findings indicate the need for teacher education that explicitly addresses model selection, underlying assumptions, and the functional use of models in reaction-rate instruction. This study contributes a three-dimensional analytical framework for examining teachers’ model-based reasoning and provides a foundation for future research and professional development. Keywords: scientific models, reaction rates, selection of models, prerequisite conditions, use of models

Ascertaining which patients are at highest risk of poor postoperative outcomes could improve care and enhance safety. This study aimed to construct and validate a propensity index for 30-day postoperative mortality. A retrospective cohort study was conducted at Hospital de Clínicas de Porto Alegre, Brazil, over a period of 3 years. A dataset of 13524 patients was used to develop the model and another dataset of 7254 was used to validate it. The primary outcome was 30-day in-hospital mortality. Overall mortality in the development dataset was 2.31% [n = 311; 95% confidence interval: 2.06-2.56%]. Four variables were significantly associated with outcome: age, ASA class, nature of surgery (urgent/emergency vs elective), and surgical severity (major/intermediate/minor). The index with this set of variables to predict mortality in the validation sample (n = 7253) gave an AUROC = 0.9137, 85.2% sensitivity, and 81.7% specificity. This sensitivity cut-off yielded four classes of death probability: class I, 10%. Model application showed that, amongst patients in risk class IV, the odds of death were approximately fivefold higher (odds ratio 5.43, 95% confidence interval: 2.82-10.46) in those admitted to intensive care after a period on the regular ward than in those sent to the intensive care unit directly after surgery. The SAMPE (Anaesthesia and Perioperative Medicine Service) model accurately predicted 30-day postoperative mortality. This model allows identification of high-risk patients and could be used as a practical tool for care stratification and rational postoperative allocation of critical care resources.

Alzheimer’s disease (AD) research is plagued by a proliferation of competing etiological theories, often coexisting without undergoing systematic critical comparison. This article examines the epistemological limitations of the traditional falsifiability criterion, formulated by Karl Popper, and demonstrates how this principle fails to function effectively in the context of AD research. Biological complexity, the absence of unequivocal biomarkers, institutional resistance to paradigm shifts, and academic incentives to preserve dominant hypotheses all contribute to the erosion of falsifiability as an operational standard. In response, we propose an alternative framework based on Bayesian inference, understood as eliminative induction—a process in which scientific theories are modeled as probabilistic hypotheses with gradable plausibility, continuously updated considering new evidence. Within this framework, models are not regarded as literally “true,” but as pragmatic tools whose predictive performance determines their scientific value. We advocate for a more comparative, predictive, and transparent scientific practice, wherein progress does not hinge on identifying a unique cause or on proving (or disproving) a hypothesis, but rather on enhancing our ability to rationally distinguish among competing models using quantitative criteria.

Novels and scientific models have in common being functional kinds, being products of make-believe, essentially involving narration, being schematic/sketchy, having cognitive functions, concretising abstract ideas, having representative functions without necessarily having truth values, essentially involving scenarios, and being instruments for the filtering of experience. Suspension of disbelief is required for the understanding of both novels and models. Novels refer to real world instantiations of some, or all of, the concepts of actions, subjectivity, situations, and things. Novels involve implicitly two kinds of models: Internal models of the Storyworld and External models of the slices of reality that pertain to the Storyworld. They filter experiences and emotions. Keywords: Scientific models, literary models, make-believe, literary emotions, believability

While Bhutanese biology teachers are expected to possess a rich understanding of scientific models, little is known about their perceptions of scientific models. This study, thus, examined Bhutanese biology teachers’ perceptions of scientific models. The study recruited one hundred and eleven (N = 111) biology teachers using a total population sampling strategy. Quantitative data were collected using an online survey questionnaire, whereas, qualitative data were collected through semi-structured interviews. Quantitative and qualitative data were analysed using statistical methods and content analysis respectively. Findings indicated that Bhutanese biology teachers' views surrounding multiplicity and tentativeness of scientific models were almost entirely correct. However, they held a range of incorrect views in that they openly considered photographs as scientific models, scientific models as exact copies of realities, and physical objects as only real scientific models. Furthermore, their views regarding the potential application of scientific models appeared increasingly limited with models being a mere communication devices. The independent sample t -test revealed a lack of significant difference in Bhutanese biology teachers’ perceptions of scientific models based on gender ( p  > .05). Similarly, the three-factor ANOVA revealed no significant effects of an individual or the combination of academic qualifications, school type, and teaching experiences on Bhutanese biology teachers’ perceptions of scientific models ( p  > .05). Further, the multiple linear regression model indicated no significant influence of gender, academic qualifications, school type, and teaching experiences on Bhutanese biology teachers’ perceptions of scientific models ( p  > .05). Research implications related to the Ministry of Education, science curriculum developers, and teacher training modules are discussed.