Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

First principles simulations of direct coexistence of solid and liquid aluminium

First principles calculations based on density functional theory, with generalised gradient corrections and ultrasoft pseudopotentials, have been used to simulate solid and liquid aluminium in direct coexistence at zero pressure. Simulations have been carried out on systems containing up to 1000 atoms for 15 ps. The points on the melting curve extracted from these simulations are in very good agreement with previous calculations, which employed the same electronic structure method but used an approach based on the explicit calculation of free energies [L. Vo\v{c}adlo and D. Alf\`e, Phys. Rev. B, {\bf 65}, 214105 (2002).]Comment: To appear in Phys. Rev.

Elliptic curves of large rank and small conductor

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page break

Regulator constants and the parity conjecture

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K^\infty/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their "regulator constants", and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat

Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve

{\em Ab initio} techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earth's core. The {\em ab initio} free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the {\em ab initio} system, with thermal averages computed by {\em ab initio} molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical {\em ab initio} techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent {\em ab initio} predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Gr\"{u}neisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure/high-temperature Fe based on experimental data.Comment: 16 pages including 6 figures and 5 table

An exploratory study on the potential of social enterprise to act as the institutional glue of network governance

This study combines two topics of contemporary salience for public administration: social enterprise and governance networks. While operating at different levels, both are institutions which attempt to draw together the three pillars of state, market, and civil society. Nevertheless, the respective literatures focus on particular aspects of the three pillars. We connect the two concepts and suggest that some social enterprises can act as the institutional glue of networks due to their ability to benefit organizations in each of the three sectors. This requires social enterprises to have the managerial capacity to diffuse social know-how, and is facilitated by the trust of other organizations and a supportive policy framework. The links are explicated at the conceptual level before providing evidence from South Korea and the UK. Finally, research propositions are offered, which suggest new avenues for future research

Portion Size: What We Know and What We Need to Know

There is increasing evidence that the portion sizes of many foods have increased and in a laboratory at least this increases the amount eaten. The conclusions are, however, limited by the complexity of the phenomenon. There is a need to consider meals freely chosen over a prolonged period when a range of foods of different energy densities are available. A range of factors will influence the size of the portion size chosen: amongst others packaging, labeling, advertising, and the unit size rather than portion size of the food item. The way portion size interacts with the multitude of factors that determine food intake needs to be established. In particular, the role of portion size on energy intake should be examined as many confounding variables exist and we must be clear that it is portion size that is the major problem. If the approach is to make a practical contribution, then methods of changing portion sizes will need to be developed. This may prove to be a problem in a free market, as it is to be expected that customers will resist the introduction of smaller portion sizes, given that value for money is an important motivator

Assessment of systemic AAV-microdystrophin gene therapy in the GRMD model of Duchenne muscular dystrophy

Duchenne muscular dystrophy (DMD) is a progressive muscle wasting disease caused by the absence of dystrophin, a membrane-stabilizing protein encoded by the DMD gene. Although mouse models of DMD provide insight into the potential of a corrective therapy, data from genetically homologous large animals, such as the dystrophin-deficient golden retriever muscular dystrophy (GRMD) model, may more readily translate to humans. To evaluate the clinical translatability of an adeno-associated virus serotype 9 vector (AAV9)–microdystrophin (μDys5) construct, we performed a blinded, placebo-controlled study in which 12 GRMD dogs were divided among four dose groups [control, 1 × 1013 vector genomes per kilogram (vg/kg), 1 × 1014 vg/kg, and 2 × 1014 vg/kg; n = 3 each], treated intravenously at 3 months of age with a canine codon-optimized microdystrophin construct, rAAV9-CK8e-c-μDys5, and followed for 90 days after dosing. All dogs received prednisone (1 milligram/kilogram) for a total of 5 weeks from day-7 through day 28. We observed dose-dependent increases in tissue vector genome copy numbers; μDys5 protein in multiple appendicular muscles, the diaphragm, and heart; limb and respiratory muscle functional improvement; and reduction of histopathologic lesions. As expected, given that a truncated dystrophin protein was generated, phenotypic test results and histopathologic lesions did not fully normalize. All administrations were well tolerated, and adverse events were not seen. These data suggest that systemically administered AAV-microdystrophin may be dosed safely and could provide therapeutic benefit for patients with DMD

Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study

A41 Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study In: Addiction Science & Clinical Practice 2017, 12(Suppl 1): A4

Description of Atmospheric Conditions at the Pierre Auger Observatory using the Global Data Assimilation System (GDAS)

Atmospheric conditions at the site of a cosmic ray observatory must be known for reconstructing observed extensive air showers. The Global Data Assimilation System (GDAS) is a global atmospheric model predicated on meteorological measurements and numerical weather predictions. GDAS provides altitude-dependent profiles of the main state variables of the atmosphere like temperature, pressure, and humidity. The original data and their application to the air shower reconstruction of the Pierre Auger Observatory are described. By comparisons with radiosonde and weather station measurements obtained on-site in Malarg\"ue and averaged monthly models, the utility of the GDAS data is shown