Mixture of experts is a prediction aggregation method in machine learning that aggregates the predictions of specialized experts. This method often outperforms Bayesian methods despite the Bayesian having stronger inductive guarantees. We argue that this is due to the greater functional capacity of mixture of experts. We prove that in a limiting case of mixture of experts will have greater capacity than equivalent Bayesian methods, which we vouchsafe through experiments on non-limiting cases. Finally, we conclude that mixture of experts is a type of abductive reasoning in the Peircean sense of hypothesis construction.

In this paper, we study the T-periodic solutions of the parameter-dependent ϕ-Laplacian equation

\begin{equation*}(\phi(x'))'=F(\lambda,t,x,x').\end{equation*}

Based on the topological degree theory, we present some atypical bifurcation results in the sense of Prodi–Ambrosetti, i.e., bifurcation of T-periodic solutions from λ = 0. Finally, we propose some applications to Liénard-type equations.

Dedicated to Professor Maria Patrizia Pera on the occasion of her 70th birthday

Introduced over a century ago, Whittaker–Henderson smoothing remains widely used by actuaries in constructing one-dimensional and two-dimensional experience tables for mortality, disability, and other life insurance risks. In this paper, we reinterpret this smoothing technique within a modern statistical framework and address six practically relevant questions about its use. First, we adopt a Bayesian perspective on this method to construct credible intervals. Second, in the context of survival analysis, we clarify how to choose the observation and weight vectors by linking the smoothing technique to a maximum likelihood estimator. Third, we improve accuracy by relaxing the method’s reliance on an implicit normal approximation. Fourth, we select the smoothing parameters by maximizing a marginal likelihood function. Fifth, we improve computational efficiency when dealing with numerous observation points and consequently parameters. Finally, we develop an extrapolation procedure that ensures consistency between estimated and predicted values through constraints.

For cardinals $\mathfrak {a}$ and $\mathfrak {b}$, we write $\mathfrak {a}=^\ast \mathfrak {b}$ if there are sets A and B of cardinalities $\mathfrak {a}$ and $\mathfrak {b}$, respectively, such that there are partial surjections from A onto B and from B onto A. $=^\ast $-equivalence classes are called surjective cardinals. In this article, we show that $\mathsf {ZF}+\mathsf {DC}_\kappa $, where $\kappa $ is a fixed aleph, cannot prove that surjective cardinals form a cardinal algebra, which gives a negative solution to a question proposed by Truss [J. Truss, Ann. Pure Appl. Logic 27, 165–207 (1984)]. Nevertheless, we show that surjective cardinals form a “surjective cardinal algebra”, whose postulates are almost the same as those of a cardinal algebra, except that the refinement postulate is replaced by the finite refinement postulate. This yields a smoother proof of the cancellation law for surjective cardinals, which states that $m\cdot \mathfrak {a}=^\ast m\cdot \mathfrak {b}$ implies $\mathfrak {a}=^\ast \mathfrak {b}$ for all cardinals $\mathfrak {a},\mathfrak {b}$ and all nonzero natural numbers m.

High BMI is an important risk factor for female colon and rectal, ovarian and uterine cancers. Current comprehensive studies on its effects on these cancers are limited. This paper aims to explore regional and age differences in the impact of high BMI on these cancers and the commonalities among the three by using the Global Burden of Disease 2021. Deaths, disability-adjusted life years and their age-standardised rates for these cancers were retrieved from 1990 to 2021, and burden trends were assessed using the estimated annual percentage change and percentage changes. The study also analysed the correlation between age-standardised rate and socio-demographic index across twenty-one regions and projected future disease burden trends using the Bayesian Age-Period-Cohort model. Results showed that the global burden of female colon and rectal cancer declined since 1990 but remained at the highest level among the three cancers in 2021. At the same time, these three cancers had high burdens in high-income areas. Since 1990, ovarian and uterine cancer burdens attributable to high BMI increased, and all three burdens grew fastest in low-middle-income regions and among younger people. The burden of all three is projected to continue increasing through 2050. This study confirms that high BMI’s impact on these cancers is regional and age-specific, with long-term effects. Therefore, subsequent public health interventions should adopt more targeted obesity prevention and control strategies based on national and regional situations to effectively mitigate the adverse effects of high BMI on these cancers.

This article advocates for a pragmatist view on quantum theory, offering a response to David Wallace’s recent criticisms of Richard Healey’s quantum pragmatism. In particular, I challenge Wallace’s general claim that quantum pragmatists—and antirepresentationalists more broadly—lack the resources to make sense of the novel “quantum” language used throughout modern physics in applications of quantum theory. I conclude by posing a challenge to quantum representationalists.

Can we acquire apriori mathematical knowledge from the outputs of computer programs? Although we claim Appel and Haken acquired apriori knowledge of the Four Color Theorem from their computer program insofar as it merely automated human forms of mathematical reasoning, the opacity of modern LLMs and DNNs creates obstacles in obtaining apriori mathematical knowledge in analogous ways. If however a proof-checker automating human forms of proof-checking is attached to such machines, we can indeed obtain apriori mathematical knowledge from them, even though the original machines are entirely opaque to us and the outputted proofs are not human-surveyable.

Age is the main risk factor for many neurodegenerative diseases such as Alzheimer’s disease, Parkinson’s disease and frontotemporal dementia. Despite our limited understanding of cellular mechanisms of ageing-associated neuronal loss, an increasing number of studies demonstrate that oxidative stress and inflammation are key drivers. Epidemiological studies indicate that diet during middle adulthood can influence the risk of developing neurodegenerative diseases later in life, so it is important to investigate dietary interventions to combat oxidative stress and inflammation. In this study, we hypothesised that treatment with fucoxanthin, a marine carotenoid with strong antioxidant properties, prevents ageing-associated oxidative stress that is known to be related to natural brain ageing. Treatment with fucoxanthin protected rat primary hippocampal neurons against oxidative stress and ageing in vitro. In our in vivo study, middle-aged male Sprague-Dawley rats were gavaged with fucoxanthin (1 mg/kg, 5 d/week, n 6) or vehicle (n 6) for 4 weeks. After supplementation was completed, brain samples were harvested and subjected to quantitative and bioinformatic analyses. Fucoxanthin was detected and shown to decrease lipid peroxidation in the brains of the animals supplemented with fucoxanthin. Microarray analysis showed that treatment with fucoxanthin changed 5602 genes. Together, our results suggest that treatment with fucoxanthin prevents ageing-associated oxidative stress and is capable of regulating genes that potentially ameliorate age-related changes to the brain.

Chalcedony forms across a wide area in eastern Iran, particularly in the Sarbisheh district near Birjand city, with notable occurrences in the Qazdez-Bahamarz region. Here, cryptocrystalline quartz is found in hydrothermal veins and veinlets within volcanic rocks hosted by carbonate and intermediate igneous formations. Chalcedony samples of various colours—black, purple, green, blue, lavender, grey, lemon yellow and white—were analysed using diverse techniques. These chalcedony samples display fibrous and granular textures, comprising microcrystalline quartz, cryptocrystalline moganite, and opal-CT and opal-C interlayers. Elements that affect the colouration of chalcedony include iron (producing red and yellow tones), chromium (green), manganese (black, blue and grey patterns), nickel (purple) and copper (also purple). Altered carbonate host rocks are enriched in Fe, Cu, Zn and Cd, with Al and Mn depletion. Stable isotope analyses show δ18O values in agates range from +14.9‰ to +25.5‰, whereas δ18O and δ13C values in carbonate minerals and chalcedony range from +14.1‰ to +24.8‰ and –5.7‰ to +0.7‰, indicating agate formation from mantle-derived hydrothermal fluids mixed with meteoric waters. Raman spectroscopy detected moganite, α-quartz, goethite, aragonite and illite in agate interlayers. Analyses by field-emission scanning electron microscopy (FE-SEM) and energy dispersive X-ray spectroscopy (EDS) revealed minerals of Fe, Cr, Ni, Ti and Sn. X-ray diffraction confirmed chalcedony, moganite and opal-CT, whereas EPR spectroscopy showed strong magnetic backgrounds from goethite and silicon-vacancy centres formed by radioactive decay of U, Th and their byproducts.

Spacetime singularities are expected to disappear in quantum gravity. Singularity resolution prima facie supports the view that spacetime singularities are mathematical pathologies of gen- eral relativity. However, this conclusion might be premature. Spacetime singularities are more accurately understood as global properties of spacetime, rather than things. Therefore, if space- time emerges in quantum gravity – as it is often claimed – then so may its singular structure. Although this proposal is intriguing, the attempt to uphold that spacetime singularities may be emergent fails. I provide three arguments in support of this claim, drawing upon different views on spacetime emergence.

Galaxy clusters are commonly used tracers of cosmology. Gravitational lensing analysis of the Bullet Cluster is claimed to evidentially support dark matter, an important component in the ΛCDM cosmology. I argue that such ΛCDM-based models of individual galaxy clusters should be explanatory to meet such claims, but hardly in an ontic sense, due to galaxy cluster anisotropies, empirically equivalent non-ΛCDM-based models, and currently unaccountable cases. I propose that adopting an alternative epistemic/representational conception of scientific explanation can maintain the explanatory nature of individual galaxy cluster models, cope with the three complications, and be potentially generalizable to other branches of astrophysics.

According to the Developmental Origins of Health and Disease (DOHaD) hypothesis, low-birthweight (LBW) infants are programmed to seek additional resources as compensation for early deprivation. However, no study has yet explored this in the context of delay discounting (DD), which refers to the tendency to prefer smaller, immediate rewards over larger, delayed ones. Both prenatal factors, such as LBW, and postnatal factors, including adverse childhood experiences (ACEs) and exposure to natural disasters, may influence DD. To investigate whether LBW children seek larger future rewards, we analyzed LBW’s effect on DD, accounting for ACEs and natural disaster exposure. This prospective cohort study involved 167 children from areas affected by the Great East Japan Earthquake (GEJE), with a mean age of 8.3 years at the time of the DD experiment. LBW was assessed in the 2012 baseline questionnaire using the Mother-Child Handbook, along with ACEs prior to the GEJE and traumatic earthquake experiences. In 2014, DD was assessed through a token-based experiment where children allocated tokens for either immediate rewards (one candy per token for “now”) or delayed rewards (two candies per token for “one month later”). Our results showed that children with LBW and three or more ACEs exhibited lower DD, while traumatic earthquake experiences were not associated with DD. These findings suggest that children with LBW and multiple ACEs may develop adaptive strategies to seek more resources, indicating a responsive reward system to childhood adversity, even after exposure to a severe natural disaster.

This paper discusses the role of data within scientific reasoning and as evidence for theoretical claims, arguing for the idea that data can yield theoretically grounded models and be inferred, predicted, or explained from/by such models. Contrary to Bogen and Woodward's rejection of data-to-theory and theory-to-data inferences/predictions, we draw upon artificial intelligence as applied to science literature to argue that (a) many models are routinely inferred and predicted from the data and routinely used to infer and predict data, and (b) such models can, at least in some contexts, play the role of theories.