Preservation of choice principles under realizability

Especially nice models of intuitionistic set theories are realizability models V(A)V(A)⁠, where AA is an applicative structure or partial combinatory algebra. This paper is concerned with the preservation of various choice principles in V(A)V(A) if assumed in the underlying universe VV⁠, adopting Constructive Zermelo–Fraenkel as background theory for all of these investigations. Examples of choice principles are the axiom schemes of countable choice, dependent choice, relativized dependent choice and the presentation axiom. It is shown that any of these axioms holds in V(A)V(A) for every applicative structure AA if it holds in the background universe.1 It is also shown that a weak form of the countable axiom of choice, ACω,ωACω,ω⁠, is rendered true in any V(A)V(A) regardless of whether it holds in the background universe. The paper extends work by McCarty (1984, Realizability and Recursive Mathematics, PhD Thesis) and Rathjen (2006, Realizability for constructive Zermelo–Fraenkel set theory

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

Mechanical Behaviour of the Short Models of LHC Main Dipole Magnets

A series of single and twin aperture 1 metre magnet models has been built and tested in the framework of the R&D program of main superconducting dipole magnets for the Large Hadron Collider project. The se models, designed for a nominal field of 8.3 T at 1.8 K, have been constructed to test the performance of SC coils and to optimise various design options for the full length 15 metre long dipoles. T he models have been extensively equipped with a specially developed mechanical instrumentation, enabling both the control of main assembly parameters - like coil azimuthal and axial pre-load, stress i n the outer shrinking cylinder - and also the monitoring of magnet behaviour during cooling and energising, under the action of electromagnetic forces. The instrumentation used, mainly based on strain gauge transducers, is described and the results of mechanical measurements obtained during power tests of the models are discussed and compared with the design predictions based on Finite Element calc ulations

Water movement into dormant and non-dormant wheat (Triticum aestivum L.) grains

The movement of water into harvest-ripe grains of dormant and non-dormant genotypes of wheat (Triticum aestivum L.) was investigated using Magnetic Resonance Micro-Imaging (MRMI). Images of virtual sections, both longitudinal and transverse, throughout the grain were collected at intervals after the start of imbibition and used to reconstruct a picture of water location within the different grain tissues and changes over time. The observations were supplemented by the weighing measurements of water content and imbibition of grains in water containing I2/KI which stains starch and lipid, thereby acting as a marker for water. In closely related genotypes, with either a dormant or a non-dormant phenotype, neither the rate of increase in water content nor the pattern of water distribution within the grain was significantly different until 18 h, when germination became apparent in the non-dormant genotype. Water entered the embryo and scutellum during the very early stages of imbibition through the micropyle and by 2 h water was clearly evident in the micropyle channel. After 12 h of imbibition, embryo structures such as the coleoptile and radicle were clearly distinguished. Although water accumulated between the inner (seed coat) and outer (pericarp) layers of the coat surrounding the grain, there was no evidence for movement of water directly across the coat and into the underlying starchy endosperm

The tomato Prf complex is a molecular trap for bacterial effectors based on Pto transphosphorylation

The bacteria Pseudomonas syringae is a pathogen of many crop species and one of the model pathogens for studying plant and bacterial arms race coevolution. In the current model, plants perceive bacteria pathogens via plasma membrane receptors, and recognition leads to the activation of general defenses. In turn, bacteria inject proteins called effectors into the plant cell to prevent the activation of immune responses. AvrPto and AvrPtoB are two such proteins that inhibit multiple plant kinases. The tomato plant has reacted to these effectors by the evolution of a cytoplasmic resistance complex. This complex is compromised of two proteins, Prf and Pto kinase, and is capable of recognizing the effector proteins. How the Pto kinase is able to avoid inhibition by the effector proteins is currently unknown. Our data shows how the tomato plant utilizes dimerization of resistance proteins to gain advantage over the faster evolving bacterial pathogen. Here we illustrate that oligomerisation of Prf brings into proximity two Pto kinases allowing them to avoid inhibition by the effectors by transphosphorylation and to activate immune responses

The cell adhesion molecule L1 regulates the expression of choline acetyltransferase and the development of septal cholinergic neurons

Mutations in the L1 gene cause severe brain malformations and mental retardation. We investigated the potential roles of L1 in the regulation of choline acetyltransferase (ChAT) and in the development of septal cholinergic neurons, which are known to project to the hippocampus and play key roles in cognitive functions. Using stereological approaches, we detected significantly fewer ChAT-positive cholinergic neurons in the medial septum and vertical limb of the diagonal band of Broca (MS/VDB) of 2-week-old L1-deficient mice compared to wild-type littermates (1644 ± 137 vs. 2051 ± 165, P = 0.038). ChAT protein levels in the septum were 53% lower in 2-week-old L1-deficient mice compared to wild-type littermates. ChAT activity in the septum was significantly reduced in L1-deficient mice compared to wild-type littermates at 1 (34%) and 2 (40%) weeks of age. In vitro, increasing doses of L1-Fc induced ChAT activity in septal neurons with a significant linear trend (*P = 0.0065). At 4 weeks of age in the septum and at all time points investigated in the caudate-putamen (CPu), the number of ChAT-positive neurons and the levels of ChAT activity were not statistically different between L1-deficient mice and wild-type littermates. The total number of cells positive for the neuronal nuclear antigen (NeuN) in the MS/VDB and CPu was not statistically different in L1-deficient mice compared to wild-type littermates, and comparable expression of the cell cycle marker Ki67 was observed. Our results indicate that L1 is required for the timely maturation of septal cholinergic neurons and that L1 promotes the expression and activity of ChAT in septal neurons

Cholinergic modulation of disorder-relevant human defensive behaviour in generalised anxiety disorder

Drugs that are clinically effective against anxiety disorders modulate the innate defensive behaviour of rodents, suggesting these illnesses reflect altered functioning in brain systems that process threat. This hypothesis is supported in humans by the discovery that the intensity of threat-avoidance behaviour is altered by the benzodiazepine anxiolytic lorazepam. However, these studies used healthy human participants, raising questions as to their validity in anxiety disorder patients, as well as their generalisability beyond GABAergic benzodiazepine drugs. BNC210 is a novel negative allosteric modulator of the alpha 7 nicotinic acetylcholine receptor and we recently used functional Magnetic Resonance Imaging to show it reduced amygdala responses to fearful faces in generalised anxiety disorder patients. Here we report the effect of BNC210 on the intensity of threat-avoidance behaviour in 21 female GAD patients from the same cohort. We used the Joystick Operated Runway Task as our behavioural measure, which is a computerised human translation of the Mouse Defense Test Battery, and the Spielberger state anxiety inventory as our measure of state affect. Using a repeated-measures, within-subjects design we assessed the effect of BNC210 at two dose levels versus placebo (300 mg and 2000 mg) upon two types of threat-avoidance behaviour (Flight Intensity and Risk Assessment Intensity). We also tested the effects of 1.5 mg of the benzodiazepine lorazepam as an active control. BNC210 significantly reduced Flight Intensity relative to placebo and the low dose of BNC210 also significantly reduced self-reported state anxiety. Risk Assessment Intensity was not significantly affected. Results show both human defensive behaviour and state anxiety are influenced by cholinergic neurotransmission and there provide converging evidence that this system has potential as a novel target for anxiolytic pharmacotherapy