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

Concepts for manned lunar habitats

The design philosophy that will guide the design of early lunar habitats will be based on a compromise between the desired capabilities of the base and the economics of its development and implantation. Preferred design will be simple, make use of existing technologies, require the least amount of lunar surface preparation, and minimize crew activity. Three concepts for an initial habitat supporting a crew of four for 28 to 30 days are proposed. Two of these are based on using Space Station Freedom structural elements modified for use in a lunar-gravity environment. A third concept is proposed that is based on an earlier technology based on expandable modules. The expandable modules offer significant advantages in launch mass and packaged volume reductions. It appears feasible to design a transport spacecraft lander that, once landed, can serve as a habitat and a stand-off for supporting a regolith environmental shield. A permanent lunar base habitat supporting a crew of twelve for an indefinite period can be evolved by using multiple initial habitats. There appears to be no compelling need for an entirely different structure of larger volume and increased complexity of implantation

(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor changes added relating to previous wor

(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks

In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \tit{cellular networks} and \tit{random graphs}. One of our main themes is the development of the concept of \tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \tit{two-story-concept} of \tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.Comment: 35 pages, Latex, under consideration by CQ

A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

A Topos Foundation for Theories of Physics: I. Formal Languages for Physics

This paper is the first 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 discuss two different types of language that can be attached to a system, S. The first is a propositional language, PL(S); the second is a higher-order, typed language L(S). Both languages provide deductive systems with an intuitionistic logic. The reason for introducing PL(S) is that, as shown in paper II of the series, it is the easiest way of understanding, and expanding on, the earlier work on topos theory and quantum physics. However, the main thrust of our programme utilises the more powerful language L(S) and its representation in an appropriate topos.Comment: 36 pages, no figure

'The Brick' is not a brick : A comprehensive study of the structure and dynamics of the Central Molecular Zone cloud G0.253+0.016

© 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.In this paper we provide a comprehensive description of the internal dynamics of G0.253+0.016 (a.k.a. 'the Brick'); one of the most massive and dense molecular clouds in the Galaxy to lack signatures of widespread star formation. As a potential host to a future generation of high-mass stars, understanding largely quiescent molecular clouds like G0.253+0.016 is of critical importance. In this paper, we reanalyse Atacama Large Millimeter Array cycle 0 HNCO $J=4(0,4)-3(0,3)$ data at 3 mm, using two new pieces of software which we make available to the community. First, scousepy, a Python implementation of the spectral line fitting algorithm scouse. Secondly, acorns (Agglomerative Clustering for ORganising Nested Structures), a hierarchical n-dimensional clustering algorithm designed for use with discrete spectroscopic data. Together, these tools provide an unbiased measurement of the line of sight velocity dispersion in this cloud, $\sigma_{v_{los}, {\rm 1D}}=4.4\pm2.1$ kms$^{-1}$, which is somewhat larger than predicted by velocity dispersion-size relations for the Central Molecular Zone (CMZ). The dispersion of centroid velocities in the plane of the sky are comparable, yielding $\sigma_{v_{los}, {\rm 1D}}/\sigma_{v_{pos}, {\rm 1D}}\sim1.2\pm0.3$. This isotropy may indicate that the line-of-sight extent of the cloud is approximately equivalent to that in the plane of the sky. Combining our kinematic decomposition with radiative transfer modelling we conclude that G0.253+0.016 is not a single, coherent, and centrally-condensed molecular cloud; 'the Brick' is not a \emph{brick}. Instead, G0.253+0.016 is a dynamically complex and hierarchically-structured molecular cloud whose morphology is consistent with the influence of the orbital dynamics and shear in the CMZ.Peer reviewedFinal Accepted Versio

A lineage-specific protein network at the trypanosome nuclear envelope

The nuclear envelope (NE) separates translation and transcription and is the location of multiple functions, including chromatin organization and nucleocytoplasmic transport. The molecular basis for many of these functions have diverged between eukaryotic lineages. Trypanosoma brucei, a member of the early branching eukaryotic lineage Discoba, highlights many of these, including a distinct lamina and kinetochore composition. Here, we describe a cohort of proteins interacting with both the lamina and NPC, which we term lamina-associated proteins (LAPs). LAPs represent a diverse group of proteins, including two candidate NPC-anchoring pore membrane proteins (POMs) with architecture conserved with S. cerevisiae and H. sapiens, and additional peripheral components of the NPC. While many of the LAPs are Kinetoplastid specific, we also identified broadly conserved proteins, indicating an amalgam of divergence and conservation within the trypanosome NE proteome, highlighting the diversity of nuclear biology across the eukaryotes, increasing our understanding of eukaryotic and NPC evolution.</p

Zinc in innate and adaptive tumor immunity

Zinc is important. It is the second most abundant trace metal with 2-4 grams in humans. It is an essential trace element, critical for cell growth, development and differentiation, DNA synthesis, RNA transcription, cell division, and cell activation. Zinc deficiency has adverse consequences during embryogenesis and early childhood development, particularly on immune functioning. It is essential in members of all enzyme classes, including over 300 signaling molecules and transcription factors. Free zinc in immune and tumor cells is regulated by 14 distinct zinc importers (ZIP) and transporters (ZNT1-8). Zinc depletion induces cell death via apoptosis (or necrosis if apoptotic pathways are blocked) while sufficient zinc levels allows maintenance of autophagy. Cancer cells have upregulated zinc importers, and frequently increased zinc levels, which allow them to survive. Based on this novel synthesis, approaches which locally regulate zinc levels to promote survival of immune cells and/or induce tumor apoptosis are in order