The arithmetic of hyperelliptic curves

We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve

Counterterms in semiclassical Horava-Lifshitz gravity

We analyze the semiclassical Ho\v{r}ava-Lifshitz gravity for quantum scalar fields in 3+1 dimensions. The renormalizability of the theory requires that the action of the scalar field contains terms with six spatial derivatives of the field, i.e. in the UV, the classical action of the scalar field should preserve the anisotropic scaling symmetry ($t \to L^{2z}t,$ $\vec{x} \to L^2 \vec{x}$, with $z=3$) of the gravitational action. We discuss the renormalization procedure based on adiabatic subtraction and dimensional regularization in the weak field approximation. We verify that the divergent terms in the adiabatic expansion of the expectation value of the energy-momentum tensor of the scalar field contain up to six spatial derivatives, but do not contain more than two time derivatives. We compute explicitly the counterterms needed for the renormalization of the theory up to second adiabatic order and evaluate the associated $\beta$ functions in the minimal subtraction scheme.Comment: 8 page

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Even Between-Lap Pacing Despite High Within-Lap Variation During Mountain Biking

Purpose: Given the paucity of research on pacing strategies during competitive events, this study examined changes in dynamic high-resolution performance parameters to analyze pacing profiles during a multiple-lap mountain-bike race over variable terrain. Methods: A global-positioning-system (GPS) unit (Garmin, Edge 305, USA) recorded velocity (m/s), distance (m), elevation (m), and heart rate at 1 Hz from 6 mountain-bike riders (mean ± SD age = 27.2 ± 5.0 y, stature = 176.8 ± 8.1 cm, mass = 76.3 ± 11.7 kg, VO2max = 55.1 ± 6.0 mL · kg–1 . min–1) competing in a multilap race. Lap-by-lap (interlap) pacing was analyzed using a 1-way ANOVA for mean time and mean velocity. Velocity data were averaged every 100 m and plotted against race distance and elevation to observe the presence of intralap variation. Results: There was no significant difference in lap times (P = .99) or lap velocity (P = .65) across the 5 laps. Within each lap, a high degree of oscillation in velocity was observed, which broadly reflected changes in terrain, but high-resolution data demonstrated additional nonmonotonic variation not related to terrain. Conclusion: Participants adopted an even pace strategy across the 5 laps despite rapid adjustments in velocity during each lap. While topographical and technical variations of the course accounted for some of the variability in velocity, the additional rapid adjustments in velocity may be associated with dynamic regulation of self-paced exercise

Targeted colonic release formulations of mesalazine - A clinical pharmaco-scintigraphic proof-of-concept study in healthy subjects and patients with mildly active ulcerative colitis.

Colonic targeting of orally applied therapeutic drugs remains a challenge. Tablet coatings relying on gastrointestinal pH and colonic bacterial enzymes as triggers in association with an inner alkaline layer are expected to improve targeting efficiency. Mesalazine release from three differently coated tablets labelled with 1 MBq 153Sm was characterised in a single centre, open-label, parallel group study in nineteen healthy subjects and seven patients with mildly active ulcerative colitis. Two semi-organic and one aqueous-based outer coating with different ratios of enteric polymer and resistant starch were tested. All coatings showed comparable release lagtimes in biorelevant dissolution media and were not affected by neutron-activation of the samarium tracer. Mesalazine pharmacokinetics and gamma scintigraphy were used to characterise drug release, anatomical site of tablet disintegration and gastrointestinal transit. Initial tablet disintegration occurred at the ileo-caecal junction or beyond in 92% of the subjects Time to initial tablet disintegration was inversely correlated with maximal plasma concentrations and systemic mesalazine exposure. Although high inter-subject variability precluded detection of differences between solvent types and different enteric polymer to polysaccharide ratios, the dual pH and enzymatic triggered release system in combination with an inner alkaline layer promoted mesalazine release at the target site with high accuracy

Spearhead Nanometric Field-Effect Transistor Sensors for Single-Cell Analysis.

Nanometric field-effect-transistor (FET) sensors are made on the tip of spear-shaped dual carbon nanoelectrodes derived from carbon deposition inside double-barrel nanopipettes. The easy fabrication route allows deposition of semiconductors or conducting polymers to comprise the transistor channel. A channel from electrodeposited poly pyrrole (PPy) exhibits high sensitivity toward pH changes. This property is exploited by immobilizing hexokinase on PPy nano-FETs to give rise to a selective ATP biosensor. Extracellular pH and ATP gradients are key biochemical constituents in the microenvironment of living cells; we monitor their real-time changes in relation to cancer cells and cardiomyocytes. The highly localized detection is possible because of the high aspect ratio and the spear-like design of the nano-FET probes. The accurately positioned nano-FET sensors can detect concentration gradients in three-dimensional space, identify biochemical properties of a single living cell, and after cell membrane penetration perform intracellular measurements

Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene

The flat bands in bilayer graphene(BLG) are sensitive to electric fields E\bot directed between the layers, and magnify the electron-electron interaction effects, thus making BLG an attractive platform for new two-dimensional (2D) electron physics[1-5]. Theories[6-16] have suggested the possibility of a variety of interesting broken symmetry states, some characterized by spontaneous mass gaps, when the electron-density is at the carrier neutrality point (CNP). The theoretically proposed gaps[6,7,10] in bilayer graphene are analogous[17,18] to the masses generated by broken symmetries in particle physics and give rise to large momentum-space Berry curvatures[8,19] accompanied by spontaneous quantum Hall effects[7-9]. Though recent experiments[20-23] have provided convincing evidence of strong electronic correlations near the CNP in BLG, the presence of gaps is difficult to establish because of the lack of direct spectroscopic measurements. Here we present transport measurements in ultra-clean double-gated BLG, using source-drain bias as a spectroscopic tool to resolve a gap of ~2 meV at the CNP. The gap can be closed by an electric field E\bot \sim13 mV/nm but increases monotonically with a magnetic field B, with an apparent particle-hole asymmetry above the gap, thus providing the first mapping of the ground states in BLG.Comment: 4 figure

Phase diagram of two-component bosons on an optical lattice

We present a theoretical analysis of the phase diagram of two--component bosons on an optical lattice. A new formalism is developed which treats the effective spin interactions in the Mott and superfluid phases on the same footing. Using the new approach we chart the phase boundaries of the broken spin symmetry states up to the Mott to superfluid transition and beyond. Near the transition point, the magnitude of spin exchange can be very large, which facilitates the experimental realization of spin-ordered states. We find that spin and quantum fluctuations have a dramatic effect on the transition making it first order in extended regions of the phase diagram. For Mott states with even occupation we find that the competition between effective Heisenberg exchange and spin-dependent on--site interaction leads to an additional phase transition from a Mott insulator with no broken symmetries into a spin-ordered insulator

The enhancement of phase separation aspect in electron doped manganite Ca0.8Sm0.16Nd0.04MnO3

The complex lanthanide doping of electron manganites results in enhancement of various phase separation effects in physical properties of these compounds. Selecting Ca0.8Sm0.16Nd0.04MnO3 as a model case we show that the first order structural phase transition from paramagnetic semi-metallic phase into anti-ferromagnetic semi-metallic phase at TS ~ 158 +- 4 K is marked by an abrupt decrease in magnetization, a step like anomaly DL/L = 10-4 in thermal expansion and large latent heat DQ = 610 J/mol. In a certain temperature range below TS, the high field magnetization exhibits hysteretic metamagnetic behavior due to field-induced first order transformation. ac-susceptibility, magnetization and resistivity data suggest rather a non-uniform state in Ca0.8Sm0.16Nd0.04MnO3 at low temperatures. The metal - insulator transition occurs at TMI ~112 +- 3 K, accompanied by a step-like increase in magnetization. These features could be ascribed to "sponging" of electrons from neighboring anti-ferromagnetic matrix by clusters undergoing the ferromagnetic ordering.Comment: submitted to J.Phys. Cond. Matte