On the interpretation of Andrews’ theorem

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

High sensitivity recording of afferent nerve activity using ultra-compliant microchannel electrodes: an acutein vivovalidation

Neuroprostheses interfaced with transected peripheral nerves are technological routes to control robotic limbs as well as convey sensory feedback to patients suffering from traumatic neural injuries or degenerative diseases. To maximize the wealth of data obtained in recordings, interfacing devices are required to have intrafascicular resolution and provide high signal-to-noise ratio (SNR) recordings. In this paper, we focus on a possible building block of a three-dimensional regenerative implant: a polydimethylsiloxane (PDMS) microchannel electrode capable of highly sensitive recordings in vivo. The PDMS 'micro-cuff' consists of a 3.5 mm long (100 µm × 70 µm cross section) microfluidic channel equipped with five evaporated Ti/Au/Ti electrodes of sub-100 nm thickness. Individual electrodes have average impedance of 640 ± 30 kΩ with a phase angle of −58 ± 1 degrees at 1 kHz and survive demanding mechanical handling such as twisting and bending. In proof-of-principle acute implantation experiments in rats, surgically teased afferent nerve strands from the L5 dorsal root were threaded through the microchannel. Tactile stimulation of the skin was reliably monitored with the three inner electrodes in the device, simultaneously recording signal amplitudes of up to 50 µV under saline immersion. The overall SNR was approximately 4. A small but consistent time lag between the signals arriving at the three electrodes was observed and yields a fibre conduction velocity of 30 m s−1. The fidelity of the recordings was verified by placing the same nerve strand in oil and recording activity with hook electrodes. Our results show that PDMS microchannel electrodes open a promising technological path to 3D regenerative interfaces.

Evaluation of an elastomer based gold microelectrode array for neural recording applications

We are reporting on the fabrication and electrical characterization of a novel elastomer based micro-cuff neural interface. Electrodes are gold (Au) tracks of sub-100nm thickness and are thermally evaporated on a 0.5 mm thick polydimethylsiloxane (PDMS) substrate. We investigate how electrode area and immersion in phosphate buffered saline (PBS) at 37°C influence electrode impedance. A microfluidic channel is bonded to the electrode array to form the cuff. In an acute, in-vivo, proof-of-principle recording, the device is capable of detecting light stroking and pinch of a hind leg of an anaesthetized rat.

'Score it upon my taille': the use (and abuse) of tallies by the medieval Exchequer

The paper traces the evolution of the tally from a receipt for cash payments into the treasury, to proof of payments made by royal officials outside of the treasury and finally to an assignment of revenue to be paid out by royal officials. Each of these processes is illustrated by examples drawn from the Exchequer records and explains their significance for royal finance and for historians working on the Exchequer records.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

Design and baseline characteristics of the Food4Me study: a web-based randomised controlled trial of personalised nutrition in seven European countries

Improving lifestyle behaviours has considerable potential for reducing the global burden of non-communicable diseases, promoting better health across the life-course and increasing well-being. However, realising this potential will require the development, testing and implementation of much more effective behaviour change interventions than are used conventionally. Therefore, the aim of this study was to conduct a multi-centre, web-based, proof-of-principle study of personalised nutrition (PN) to determine whether providing more personalised dietary advice leads to greater improvements in eating patterns and health outcomes compared to conventional population-based advice. A total of 5,562 volunteers were screened across seven European countries; the first 1,607 participants who fulfilled the inclusion criteria were recruited into the trial. Participants were randomly assigned to one of the following intervention groups for a 6-month period: Level 0-control group-receiving conventional, non-PN advice; Level 1-receiving PN advice based on dietary intake data alone; Level 2-receiving PN advice based on dietary intake and phenotypic data; and Level 3-receiving PN advice based on dietary intake, phenotypic and genotypic data. A total of 1,607 participants had a mean age of 39.8 years (ranging from 18 to 79 years). Of these participants, 60.9 % were women and 96.7 % were from white-European background. The mean BMI for all randomised participants was 25.5 kg m(-2), and 44.8 % of the participants had a BMI ≥ 25.0 kg m(-2). Food4Me is the first large multi-centre RCT of web-based PN. The main outcomes from the Food4Me study will be submitted for publication during 2015.

What are the limitations on the wider therapeutic use of phage?

Bacterial resistance to antibiotics poses a serious health threat. Since research into new antibiotics is not progressing at the same rate as the development of bacterial resistance, widespread calls for alternatives to antibiotics have been made. Phage therapy is an ideal alternative candidate to be investigated. However the success of phage therapy may be hampered by a lack of investment support from large pharmaceutical companies, due to their narrow spectrum of activity in antibiotics, very large costs associated with clinical trials of the variety of phages needed, and regulatory requirements remaining unclear. Intellectual property is difficult to secure for therapeutic phage products for a variety of reasons, and patenting procedures vary widely between the US and the EU. Consequently, companies are more likely to invest in phage products for decontamination or veterinary use, rather than clinical use in humans. Some still raise questions as to the safety of phage therapy overall, suggesting the possibility of cytotoxicity and immunogenicity, depending on the phage preparation and route. On the other hand, with patients dying because of infections untreatable with conventional antibiotics, the question arises as to whether it is ethical not to pursue phage therapy more diligently. A paradigm shift about how phage therapy is perceived is required, as well as more rigorous proof of efficacy in the form of clinical trials of existing medicinal phage products. Phage therapy potential may be fulfilled in the meantime by allowing individual preparations to be used on a named-patient basis, with extensive monitoring and multidisciplinary team input. The National Health Service and academia have a role in carrying out clinical phage research, which would be beneficial to public health, but not necessarily financially rewarding.

Pleistovultur nevesi gen. et sp nov (Aves: Vulturidae) and the diversity of condors and vultures in the South American Pleistocene

Pleistovultur nevesi, a new genus and species of a large Vulturidae is described from the Upper Pleistocene or beginning of the Holocene, based on a complete and well preserved right tibiotarsus from the Cuvieri cave deposits, one of the hundreds of caves of the Lagoa Santa region in Minas Gerais state, Brazil. Also described here is a distal half of a left tibiotarsus from Gruta dos Brejoes, a cave in Morro do Chapeu, Bahia state, Brazil, which probably belongs to another not-yet-known genus and species of the Vulturidae. The described material, added to prior literature, is proof of the appreciable diversity of the Vulturidae during the Pleistocene in South America.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their symmetries

For an embedded singly periodic minimal surface (M) over tilde with genus rho >= 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces.