Fuchsian convex bodies: basics of Brunn--Minkowski theory

The hyperbolic space \H^d can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that \H^d/\Gamma is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, globally invariant for the action of a Fuchsian group. A volume can be associated to each Fuchsian convex body, and, if the group is fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be studied in the same manner as convex bodies of Euclidean space in the classical Brunn--Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov--Fenchel and Brunn--Minkowski inequalities. Here the inequalities are reversed

Spatially variable fault friction derived from dynamic modeling of aseismic afterslip due to the 2004 Parkfield earthquake

We investigate fault friction from dynamic modeling of fault slip prior to and following the Mw 6.0 earthquake which ruptured the Parkfield segment of the San Andreas Fault in 2004. The dynamic modeling assumes a purely rate-strengthening friction law, with a logarithmic dependency on sliding rate: μ=μ *+a-blnvv*. The initial state of stress is explicitly taken into account, and afterslip is triggered by the stress change induced by the earthquake source model given a priori. We consider different initial stress states and two coseismic models, and invert for the other model parameters using a nonlinear inversion scheme. The model parameters include the reference friction μ*, the friction rate dependency characterized by the quantity a-b, assumed to be either uniform or depth dependent. The model parameters are determined from fitting the transient postseismic geodetic signal measured at continuous GPS stations. Our study provides a view of frictional properties at the kilometers scale over the 0-15 km depth illuminated by the coseismic stress change induced by the Parkfield earthquake. The reference friction is estimated to be between 0.1 and 0.5. With independent a priori constraints on the amplitude of differential stress, the range of possible values narrows down to 0.1-0.17. The friction rate coefficient a-b is estimated to be � 10- 3 - 10- 2 with a hint that it increases upward from about 1-3 � 10-3 at 3-7 km depth to about 4-7 � 10-3 at 0-1 km depth. It is remarkable that our results are consistent with frictional properties measured on rock samples recovered from the fault zone thanks to the San Andreas Fault Observatory at Depth experiment. ©2013. American Geophysical Union. All Rights Reserved

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page

Particle Physics Explanations for Ultra High Energy Cosmic Ray Events

The origin of cosmic ray events with E \gsim 10^{11} GeV remains mysterious. In this talk I briefly summarize several proposed particle physics explanations: a breakdown of Lorentz invariance, the ``$Z-$burst'' scenario, new hadrons with masses of several GeV as primaries, and magnetic monopoles with mass below $10^{10}$ GeV as primaries. I then describe in a little more detail the idea that these events are due to the decays of very massive, long--lived exotic particles.Comment: Invited plenary talk at PASCOS03, Mumbai, India, January 2003; 13 pages, 1 figur

Ataxia with oculomotor apraxia type 2: clinical, biological and genotype/phenotype correlation study of a cohort of 90 patients

Ataxia with oculomotor apraxia type 2 (AOA2) is an autosomal recessive disease due to mutations in the senataxin gene, causing progressive cerebellar ataxia with peripheral neuropathy, cerebellar atrophy, occasional oculomotor apraxia and elevated alpha-feto-protein (AFP) serum level. We compiled a series of 67 previously reported and 58 novel ataxic patients who underwent senataxin gene sequencing because of suspected AOA2. An AOA2 diagnosis was established for 90 patients, originating from 15 countries worldwide, and 25 new senataxin gene mutations were found. In patients with AOA2, median AFP serum level was 31.0 mu g/l at diagnosis, which was higher than the median AFP level of AOA2 negative patients: 13.8 mu g/l, P = 0.0004; itself higher than the normal level (3.4 mu g/l, range from 0.5 to 17.2 mu g/l) because elevated AFP was one of the possible selection criteria. Polyneuropathy was found in 97.5% of AOA2 patients, cerebellar atrophy in 96%, occasional oculomotor apraxia in 51%, pyramidal signs in 20.5%, head tremor in 14%, dystonia in 13.5%, strabismus in 12.3% and chorea in 9.5%. No patient was lacking both peripheral neuropathy and cerebellar atrophy. The age at onset and presence of occasional oculomotor apraxia were negatively correlated to the progression rate of the disease (P = 0.03 and P = 0.009, respectively), whereas strabismus was positively correlated to the progression rate (P = 0.03). An increased AFP level as well as cerebellar atrophy seem to be stable in the course of the disease and to occur mostly at or before the onset of the disease. One of the two patients with a normal AFP level at diagnosis had high AFP levels 4 years later, while the other had borderline levels. The probability of missing AOA2 diagnosis, in case of sequencing senataxin gene only in non-Friedreich ataxia non-ataxia-telangiectasia ataxic patients with AFP level >= 7 mu g/l, is 0.23% and the probability for a non-Friedreich ataxia non-ataxia-telangiectasia ataxic patient to be affected with AOA2 with AFP levels >= 7 mu g/l is 46%. Therefore, selection of patients with an AFP level above 7 mu g/l for senataxin gene sequencing is a good strategy for AOA2 diagnosis. Pyramidal signs and dystonia were more frequent and disease was less severe with missense mutations in the helicase domain of senataxin gene than with missense mutations out of helicase domain and deletion and nonsense mutations (P = 0.001, P = 0.008 and P = 0.01, respectively). The lack of pyramidal signs in most patients may be explained by masking due to severe motor neuropathy

Polygon model from first order gravity

The gauge fixed polygon model of 2+1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the first order formalism of the theory in terms of the triad and the spin connection. The induced symplectic structure is calculated and shown to agree with the canonical one in terms of the variables.Comment: 20 pages, presentation improved, typos correcte

Usefulness of analysis of cerebrospinal fluid for the diagnosis of neurotransmitters and pterin defects and glucose and folate transport deficiencies across blood brain barrier

Med Clin (Barc). 2006 Jun 17;127(3):81-5. [Usefulness of analysis of cerebrospinal fluid for the diagnosis of neurotransmitters and pterin defects and glucose and folate transport deficiencies across blood brain barrier] [Article in Spanish] Ormazabal A, García Cazorla A, Pérez Dueñas B, Pineda M, Ruiz A, López Laso E, García Silva M, Carilho I, Barbot C, Cormand B, Ribases M, Moller L, Fernández Alvarez E, Campistol J, Artuch R. Hospital Sant Joan de Déu, Esplugues, Barcelona, España. Abstract BACKGROUND AND OBJECTIVE: In the last few years, it has been described inborn errors of neurotransmitter and pterin metabolism and defects in folate and glucose transport across blood brain barrier. All these defects are classified as rare diseases and needs cerebrospinal fluid (CSF) sample analysis for diagnosis. Our aim was to evaluate the results of the application of a CSF analysis protocol in a pediatric population from Spain and Portugal presenting with neurological disorders of unknown origin. PATIENTS AND METHOD: We studied CSF samples from and 283 patients with neurological disorders of unknown origin and 127 controls. Neurotransmitters were analysed by HPLC with electrochemical detection, and pterins and 5-methyltetrahydrofolate were determined by HPLC with fluorescence detection. RESULTS: We diagnosed 3 patients with tyrosine hidroxylase deficiency, 2 with dopa responsive dystonia, 14 with GTP-ciclohydrolase deficiency, 2 with glucose transport deficiency and 43 with cerebral folate deficiency. CONCLUSIONS: This study allowed us to diagnose new patients, and more importantly, the establishment in all of them of a pharmacological or nutritional treatment. The most frequent defect found was CSF 5-methyltetrahydrofolate deficiency, which was present in different groups of patients. PMID: 16827996 [PubMed - indexed for MEDLINE

Sudakov Electroweak effects in transversely polarized beams

We study Standard Model electroweak radiative corrections for fully inclusive observables with polarized fermionic beams. Our calculations are relevant in view of the possibility for Next Generation Linear colliders of having transversely and/or longitudinally polarized beams. The case of initial transverse polarization is particularly interesting because of the interplay of infrared/collinear logarithms of different origins, related both to the nonabelian SU(2) and abelian U(1) sectors. The Standard model effects turn out to be in the 10% range at the TeV scale, therefore particularly relevant in order to disentangle possible New Physics effects.Comment: 5 pages,4 figure

D-Matter

We study the properties and phenomenology of particle-like states originating from D-branes whose spatial dimensions are all compactified. They are non-perturbative states in string theory and we refer to them as D-matter. In contrast to other non-perturbative objects such as 't Hooft-Polyakov monopoles, D-matter states could have perturbative couplings among themselves and with ordinary matter. The lightest D-particle (LDP) could be stable because it is the lightest state carrying certain (integer or discrete) quantum numbers. Depending on the string scale, they could be cold dark matter candidates with properties similar to that of wimps or wimpzillas. The spectrum of excited states of D-matter exhibits an interesting pattern which could be distinguished from that of Kaluza-Klein modes, winding states, and string resonances. We speculate about possible signatures of D-matter from ultra-high energy cosmic rays and colliders.Comment: 25 pages, 5 figures, references adde