A Topos Foundation for Theories of Physics: IV. Categories of Systems

This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this programme for a single system. In the present paper, we turn to considering a collection of systems: in particular, we are interested in the relation between the topos representation for a composite system, and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category.Comment: 38 pages, no figure

A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf--the topos quantum analogue of a classical state space. In the second part of the paper we change gear with the introduction of the more sophisticated local language L(S). From this point forward, throughout the rest of the series of papers, our attention will be devoted almost entirely to this language. In the present paper, we use L(S) to study `truth objects' in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence there are no microstates in the sense of classical physics. Truth objects therefore play a crucial role in our formalism.Comment: 34 pages, no figure

Faint young Sun paradox remains

The Sun was fainter when the Earth was young, but the climate was generally at least as warm as today; this is known as the `faint young Sun paradox'. Rosing et al. [1] claim that the paradox can be resolved by making the early Earth's clouds and surface less reflective. We show that, even with the strongest plausible assumptions, reducing cloud and surface albedos falls short by a factor of two of resolving the paradox. A temperate Archean climate cannot be reconciled with the low level of CO2 suggested by Rosing et al. [1]; a stronger greenhouse effect is needed.Comment: 3 pages, no figures. In press in Nature. v2 corrects typo in author list in original submissio

Effect of Maternally Derived Anti-protein and Anticapsular IgG Antibodies on the Rate of Acquisition of Nasopharyngeal Carriage of Pneumococcus in Newborns

BACKGROUND: In developing countries, introduction of pneumococcal conjugate vaccine has not eliminated circulation of vaccine serotypes. Vaccinating pregnant mothers to increase antibody concentrations in their newborn infants may reduce the acquisition of pneumococcal carriage and subsequent risk of disease. We explored the efficacy of passive immunity, attributable to anti-protein and anticapsular pneumococcal antibodies, against acquisition of carriage. METHODS: We examined the rate of nasopharyngeal acquisition of pneumococci in the first 90 days of life associated with varying anticapsular and anti-protein antibody concentrations in infant cord/maternal venous blood in Kilifi, Kenya. We used multivariable Cox proportional hazard models to estimate continuous functions relating acquisition of nasopharyngeal carriage to the concentration of maternally derived antibody. RESULTS: Cord blood or maternal venous samples were collected from 976 mother-infant pairs. Pneumococci were acquired 561 times during 33,905 person-days of follow-up. Increasing concentrations of anti-protein antibodies were associated with either a reduction (PhtD1, PspAFam2, Spr0096, StkP) or, paradoxically, an increase (CbpA, LytC, PcpA, PiaA, PspAFam1, RrgBT4) in acquisition rate. We observed a nonsignificant reduction in the incidence of homologous carriage acquisition with high concentrations of maternally derived anticapsular antibodies to 5 serotypes (6A, 6B, 14, 19F, and 23F). CONCLUSION: The protective efficacy of several anti-protein antibodies supports the strategy of maternal vaccination to protect young infants from carriage and invasive disease. We were not able to demonstrate that passive anticapsular antibodies were protective against carriage acquisition at naturally occurring concentrations though it remains possible they may do so at the higher concentrations elicited by vaccination

Pneumococcal conjugate vaccine dose-ranging studies in humans: A systematic review

Background: Streptococcus pneumoniae is one of the most common bacterial pathogens of infants and young children. Antibody responses against the pneumococcal polysaccharide capsule are the basis of vaccine-mediated protection. We examined the relationship between the dose of polysaccharide in pneumococcal conjugate vaccines (PCVs) and immunogenicity. Methods: A systematic search of English publications that evaluated the immunogenicity of varying doses of pneumococcal conjugate vaccines was performed in Medline and Embase (Ovid Sp) databases in August 2019. We included only articles that involved administration of pneumococcal conjugate vaccine in humans and assessed the immunogenicity of more than one serotype-specific saccharide dose. Results were synthesised descriptively due to the heterogeneity of product valency, product content and vaccine schedule. Results: We identified 1691 articles after de-duplication; 9 studies met our inclusion criteria; 2 in adults, 6 in children and 1 in both. Doses of polysaccharide evaluated ranged from 0.44 mcg to 17.6 mcg. In infants, all doses tested elicited IgG geometric mean concentrations (GMCs) above the established correlate of protection (COP; 0.35 mcg/ml). A month after completion of the administered vaccine schedule, 95% confidence intervals of only three out of all the doses evaluated had GMCs that crossed below the COP. In the adult studies, all adults achieved GMCs that would be considered protective in children who have received 3 standard vaccine doses. Conclusion: For some products, the mean antibody concentrations induced against some pneumococcal serotypes increased with increasing doses of the polysaccharide conjugate, but for other serotypes, there were no clear dose–response relationships or the dose response curves were negative. Fractional doses of polysaccharide which contain less than is included in currently distributed formulations may be useful in the development of higher valency vaccines, or dose-sparing delivery for paediatric use

Th2 Cytokine Levels Distort the Association of IL-10 and IFN-γ with Allergic Phenotypes

The expression of allergic phenotypes involves complex inter-relationships among several Th2 and Th1 cytokines as well as the regulator cytokine interleukin (IL)-10. These direct or indirect interrelationships may distort the true associations of cytokine responses with these phenotypes. In this study, we aimed to clarify the effects of the regulatory cytokine IL-10 and Th1 cytokine interferon-gamma (IFN-?) on allergic phenotypes after adjusting for the correlations with Th2 cytokines. After adjusting for Th2 cytokines, IL-10 and IFN-? were protective against atopy. Adjusted levels of IL-10 and IFN-? stimulated with house-dust mite (HDM) were significantly lower in atopics than non-atopics, for IL-10 adjusting for IL-5 (P = 0.002), IL-13 (P = 0.012), IL-9 (P = 0.016), and IL-4 (P = 0.043), and for IFN-? adjusting for IL-5 (P = 0.005), IL-13 (P = 0.005), and IL-9 (P = 0.037). IL-10 and IFN-? levels stimulated with phytohaemagglutinin (PHA) and staphylococcal enterotoxin B (SEB) exhibited a similar pattern. The adjusted levels of IL-10 and IFN-? stimulated with HDM, PHA or SEB were all significantly negatively correlated with total serum IgE, except for IFN-? stimulated with SEB. Levels of Th2 cytokines distort the associations of IL-10 and IFN-? with allergic phenotypes. Removing the covariance with Th2 cytokines, both IL-10 and IFN-? were protective against atopy

Atmospheric Evolution

Earth's atmosphere has evolved as volatile species cycle between the atmosphere, ocean, biomass and the solid Earth. The geochemical, biological and astrophysical processes that control atmospheric evolution are reviewed from an "Earth Systems" perspective, with a view not only to understanding the history of Earth, but also to generalizing to other solar system planets and exoplanets.Comment: 34 pages, 3 figures, 2 tables. Accepted as a chapter in "Encyclopaedia of Geochemistry", Editor Bill White, Springer-Nature, 201

Antibody responses to nasopharyngeal carriage of Streptococcus pneumoniae in adults: A longitudinal household study

Background. Natural immunity to Streptococcus pneumoniae is thought to be induced by exposure to S. pneumoniae or cross-reactive antigens. No longitudinal studies of carriage of and immune responses to S. pneumoniae have been conducted using sophisticated immunological laboratory techniques.Methods. We enrolled 121 families with young children into this study. Nasopharyngeal (NP) swabs were collected monthly for 10 months from all family members and were cultured in a standard fashion. Cultured S. pneumoniae isolates were serotyped. At the beginning (month 0) and end (month 10) of the study, venous blood was collected from family members 118 years old. Serotype-specific antipolysaccharide immunoglobulin G (IgG) and functional antibody and antibodies to pneumolysin, pneumococcal surface protein A (PspA), and pneumococcal surface antigen A (PsaA) were measured in paired serum samples.Results. Levels of anticapsular IgG increased significantly after carriage of serotypes 9V, 14, 18C, 19F, and 23F by an individual or family member. For serotype 14, a higher level of anticapsular IgG at the beginning of the study was associated with reduced odds of carriage (P = .0006). There was a small (similar to 20%) but significant increase in titers of antibodies to PsaA and pneumolysin but no change in titers of antibody to PspA.Conclusions. Adults respond to NP carriage by mounting anticapsular and weak antiprotein antibody responses, and naturally induced anticapsular IgG can prevent carriage

A Topological Study of Contextuality and Modality in Quantum Mechanics

Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence of sections of sheaves, we give an extended version of Kochen-Specker theorem over this new structure. This allows us to prove that contextuality remains a central feature even in the enriched propositional system.Comment: 10 pages, no figures, submitted to I. J. Th. Phy

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all $M$-sets, where $M$ is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a `neo-realist' interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction