Soft x ray tomoholography

We demonstrate an x ray imaging method that combines Fourier transform holography with tomography tomoholography for threedimensional 3D microscopic imaging. A 3D image of a diatom shell with a spatial resolution of 140 nm is presented. The experiment is realized by using a small gold sphere as the reference wave source for holographic imaging. This setup allows us to rotate the sample and to collect a number of 2D projections for tomograph

Are clinical measures of foot posture and mobility associated with foot kinematics when walking?

Background: There is uncertainty as to which foot posture measures are the most valid in terms of predicting kinematics of the foot. The aim of this study was to investigate the associations of clinical measures of static foot posture and mobility with foot kinematics during barefoot walking. Method: Foot posture and mobility were measured in 97 healthy adults (46 males, 51 females; mean age 24.4 ± 6.2 years). Foot posture was assessed using the 6-item Foot Posture Index (FPI), Arch Index (AI), Normalised Navicular Height (NNHt) and Normalised Dorsal Arch Height (DAH). Foot mobility was evaluated using the Foot Mobility Magnitude (FMM) measure. Following this, a five-segment foot model was used to measure tri-planar motion of the rearfoot, midfoot, medial forefoot, lateral forefoot and hallux. Peak and range of motion variables during load acceptance and midstance/propulsion phases of gait were extracted for all relative segment to segment motion calculations. Hierarchical regression analyses were conducted, adjusting for potential confounding variables. Results: The degree of variance in peak and range of motion kinematic variables that was independently explained by foot posture measures was as follows: FPI 5 to 22 %, NNHt 6 to 20 %, AI 7 to 13 %, DAH 6 to 8 %, and FMM 8 %. The FPI was retained as a significant predictor across the most number of kinematic variables. However, the amount of variance explained by the FPI for individual kinematic variables did not exceed other measures. Overall, static foot posture measures were more strongly associated with kinematic variables than foot mobility measures and explained more variation in peak variables compared to range of motion variables. Conclusions: Foot posture measures can explain only a small amount of variation in foot kinematics. Static foot posture measures, and in particular the FPI, were more strongly associated with foot kinematics compared with foot mobility measures. These findings suggest that foot kinematics cannot be accurately inferred from clinical observations of foot posture alone

How to think about informal proofs

This document is the Accepted Manuscript version of the following article: Brendan Larvor, ‘How to think about informal proofs’, Synthese, Vol. 187(2): 715-730, first published online 9 September 2011. The final publication is available at Springer via doi:10.1007/s11229-011-0007-5It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the fieldPeer reviewedFinal Accepted Versio

A formally verified abstract account of Gödel's incompleteness theorems

We present an abstract development of Gödel’s incompleteness theorems, performed with the help of the Isabelle/HOL theorem prover. We analyze sufficient conditions for the theorems’ applicability to a partially specified logic. In addition to the usual benefits of generality, our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser’s variation of the first theorem, Jeroslow’s variation of the second theorem, and the S ́wierczkowski–Paulson semantics-based approach. As part of our framework’s validation, we upgrade Paulson’s Isabelle proof to produce a mech- anization of the second theorem that does not assume soundness in the standard model, and in fact does not rely on any notion of model or semantic interpretation

Conformation of phosphatidylethanolamine in the gel phase as seen by neutron diffraction

For confirmation of some general aspects of phospholipid conformation in membranes and extension of previous neutron diffraction studies on dipalmitoyllecithin, measurements have now been made on 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) in the gel phase by the same method. Three selectively deuterated samples were investigated; in one of the specimens the first methylene segment close to the glycerol backbone in both chains was deuterated, and in the other two samples one of the methylene segments in the phosphoethanolamine group was replaced by CD2. Together with the undeuterated DPPE, these probes were investigated at very low water content (about 1.5--2 molecules of water per lipid) as oriented samples at 25 degrees C. The intensities of the first 12 reflections were collected and phased, and the mean positions of the segments were determined. The results confirm the idea that the conformation of a DPPE molecule in the gel state is very similar to the crystal structure of rac-1,2-dilauroyl-sn-glycero-3-phosphoethanolamine. The two main features are (1) the chains remain in all all-trans conformation having an axial displacement of about 3--4 A, (2) the zwitterionic dipoles in the head groups of both compounds are found to be aligned almost parallel to the bilayer surface. The main advantage of the method results in the fact that the combination of neutron scattering with selectively deuterated probes allows the determination of the mean label position to an accuracy of up to +/- 1 A

Force-induced conformational change of bacteriorhodopsin

The cytoplasmic surface topography of purple membranes imaged by the atomic force microscope depends mainly on the force applied to the stylus. Imaged at forces of 300 pN, individual bacteriorhodopsin molecules reveal two domains. The resulting donut-shaped trimers reversibly transform into structures exhibiting three prominent protrusions when scanned at 100 pN. In parallel, the height of the protein moiety above the lipid layer increases from 4 A to 6 A. From the known structure of bacteriorhodopsin it appears that this change may be related to a bending of the most prominent cytoplasmic loop

A neutron diffraction study of the headgroup conformation of phosphatidylglycerol from Escherichia coli membranes

By using neutron diffraction, the headgroup conformation of purified phosphatidylglycerol from Escherichia coli membranes has been investigated. Measurements at 25 degrees C and 15% relative humidity on oriented multilayers of lipid selectively deuterated at the sn-3-position of the glycerol backbone and of the gamma-position of the glycerol headgroup show that the labels are at a mean distance of 23.0 A and 27.6 A from the centre of the hydrocarbon chain region. This suggests that the negatively charged headgroup is oriented at about 30 degrees to the membrane surface. The orientation of the phosphatidylglycerol headgroup makes the negatively charged phosphate group easily accessible to cations present in the adjacent water layer