Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Aromatic L-Amino Acid Decarboxylase Deficiency Is a Cause of Long-Fasting Hypoglycemia

Objective/Context: Long-fasting hypoglycemia in children may be induced by neurotransmitter disorders. Case Report: A 5-year-old girl with a medical history of chronic diarrhea presented three episodes of severe hypoglycemia (20 mg/dL) between ages 3 and 5 years. She became pale and sweaty with hypothermia (33.5°C), bradycardia (45 bpm), and acidosis and presented a generalized seizure. During the 17-hour fast test performed to determine the etiology of her hypoglycemia, insulin and C-peptide were appropriately low, and human GH, IGF-I, cortisol, amino acids, and acylcarnitines were in the usual range for fasting duration. However, the presence of vanillactic and vanilpyruvic acids in urine led us to investigate the metabolism of dopamine and serotonin in the cerebrospinal fluid. Indeed, these results indicated an aromatic L-amino acid decarboxylase deficiency that impairs the synthesis of serotonin, dopamine, and catecholamines. The diagnosis was confirmed by the low aromatic L-amino acid decarboxylase (AADC) enzyme activity in plasma (5 pmol/min/mL; reference value, 20–130) and the presence of two heterozygous mutations, c.97G>C (p.V33L, inherited from her father) and c.1385G>C (p.R462P, inherited from her mother) in the DCC gene. She was supplemented with pyridoxine and raw cornstarch (1 g/kg) at evening dinner to reduce the night fast. The episodes of hypoglycemia and the chronic diarrhea were suppressed. Conclusion: Here is the first case report of long-fasting hypoglycemia due to a nontypical AADC deficiency. Hypoglycemia was severe, but the other neurological clinical hallmarks present in AADC-deficient patients were mild to moderate. Thus, neurotransmitter disorders should be considered in any patients presenting hypoglycemia with urine excretion of vanillactic acid

The effect of ECRH on the electron velocity distribution function

Electron cyclotron resonance heating (ECRH) is a mature technology that has progressed constantly over a period of forty years, particularly as a tool in magnetic confinement fusion. As with other heating methods, this technique has seen a steady increase in the sophistication of its applications, from bulk heating through profile tailoring and finally to distribution function engineering. By comparison with other techniques, ECRH presents the significant advantages of good coupling, localized power deposition, easy launching and precise directionality. This paper reviews some recent applications related to third harmonic ECRH and highlights the role of the relaxation dynamics of suprathermal electrons, both in real space and in velocity space, in regulating the overall effect of ECRH on fusion plasmas. A technique for direct visualization of these relaxation phenomena, using modulated ECRH, is described and demonstrated

Observation of confined current ribbon in JET plasmas

we report the identification of a localised current structure inside the JET plasma. It is a field aligned closed helical ribbon, carrying current in the same direction as the background current profile (co-current), rotating toroidally with the ion velocity (co-rotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first ELM.Comment: 10 pages, 6 figure