Regularization parameter determination for discrete ill-posed problems

Straightforward solution of discrete ill-posed linear systems of equations or least-squares problems with error contaminated data does not, in general, give meaningful results, because the propagated error destroys the computed solution. The problems have to be modified to reduce their sensitivity to the error in the data. The amount of modification is determined by a regularization parameter. It can be difficult to determine a suitable value of the regularization parameter when no knowledge of the norm of error in the data is available. This paper proposes a new simple technique for determining a value of the regularization parameter that can be applied in this situation. It is based on comparing computed solutions determined by Tikhonov regularization and truncated singular value decomposition. Analogous comparisons are proposed for large-scale problems. The technique for determining the regularization parameter implicity provides an estimate for the norm of the error in the data. Keywords: Ill-posed problem; Regularization; Noise level estimation; TSVD; Tikhonov regularization; Heuristic parameter choice rul

Search for Tau Flavour Violation at the LHC

We explore the prospects for searches at the LHC for sparticle decays that violate $\tau$ lepton number, in the light of neutrino oscillation data and the seesaw model for neutrino masses and mixing. We analyse the theoretical and phenomenological conditions required for tau flavour violation to be observable in \chi_2 \to \chi + \tau^\pm \mu^\mp decays, for cosmologically interesting values of the relic neutralino LSP density. We study the relevant supersymmetric parameter space in the context of the Constrained Minimal Supersymmetric Extension of the Standard Model (CMSSM) and in SU(5) extensions of the theory. We pay particular attention to the possible signals from hadronic tau decays, that we analyse using PYTHIA event simulation. We find that a signal for \tau flavour-violating \chi_2 decays may be observable if the branching ratio exceeds about 10%. This may be compatible with the existing upper limit on \tau \to \mu \gamma decays if there is mixing between right-handed sleptons, as could be induced in non-minimal SU(5) GUTs.Comment: 24 pages, 10 fig

Estudio sobre las propiedades mecánicas de cementos óseos preparados con metacrilatos funcionalizados

Los cementos óseos son materiales poliméricos que se utilizan con el objeto de fijar prótesis metálicas. Han estado en el mercado por casi 40 años desde que Sir John Charnley propuso su uso en ortopedia. Los cementos óseos convencionales exhiben altos calores de reacción, alta contracción y un elevado contenido de monómero residual; estas propiedades se traducen en un comportamiento mecánico inadecuado y finalmente en el aflojamiento de la prótesis. Nuevas formulaciones hacen uso de activadores de baja toxicidad, monómeros de bajo calor de reacción y cerámicos bioactivos para mejorar la biocompatibilidad. En este trabajo reportamos el uso de mezclas de metacrilato de metilo con ácido metacrílico (MAA) o dietil amino etil metacrilato (DEAEMA) en la síntesis de cementos óseos. Tiempos de curado y propiedades en tensión, compresión y flexión son reportadas en muestras sin y con acondicionamiento en fluido corporal simulado. Tiempos de curado cortos fueron observados en cementos preparados con MAA mientras que tiempos largos fueron obtenidos en muestras que contenían DEAEMA. Los ensayos mecánicos mostraron un aumento en la resistencia a la compresión y flexión en aquellos cementos que contenían ácido metacrílico comparada con la exhibida por los cementos preparados sin comonómero. Elevadas temperaturas de transición vítrea fueron asociadas a este comportamiento. Los cementos óseos preparados con DEAEMA en altas concentraciones presentaron una resistencia a la tensión, flexión y compresión menor a la obtenida con el cemento preparado sin comonómero. En general, las propiedades mecánicas exhibidas por estos cementos experimentales fueron comparables a las propiedades de cementos óseos comerciales disponibles en México. Sin embargo, las muestras acondicionadas en fluido corporal simulado presentaron una reducción en sus propiedades después de 3 meses de acondicionamiento. Pese a esto, el valor mínimo de resistencia a la compresión sugerido para su uso como cemento óseos (70 MPa) fue cumplido en todas las formulaciones excepto en aquellas preparadas con DEAEMA en altas concentraciones.Peer Reviewe

Fermi Surface Measurements on the Low Carrier Density Ferromagnet Ca1-xLaxB6 and SrB6

Recently it has been discovered that weak ferromagnetism of a dilute 3D electron gas develops on the energy scale of the Fermi temperature in some of the hexaborides; that is, the Curie temperature approximately equals the Fermi temperature. We report the results of de Haas-van Alphen experiments on two concentrations of La-doped CaB6 as well as Ca-deficient Ca1-dB6 and Sr-deficient Sr1-dB6. The results show that a Fermi surface exists in each case and that there are significant electron-electron interactions in the low density electron gas.Comment: 4 pages, 5 figures, submitted to PR

Theory of High \tc Ferromagnetism in SrB6SrB_6 family: A case of Doped Spin-1 Mott insulator in a Valence Bond Solid Phase

Doped divalent hexaborides such as $Sr_{1-x}La_xB_6$ exhibit high \tc ferromagnetism. We isolate a degenerate pair of $2p$-orbitals of boron with two valence electrons, invoke electron correlation and Hund coupling, to suggest that the undoped state is better viewed as a spin-1 Mott insulator; it is predicted to be a type of 3d Haldane gap phase with a spin gap $\sim 0.1 eV$, much smaller than the charge gap of $> 1.0 eV$ seen in ARPES. The experimentally seen high \tc `ferromagnetism' is argued to be a complex magnetic order in disguise - either a canted 6-sublattice AFM ($\approx 120^0$) order or its quantum melted version, a chiral spin liquid state, arising from a type of double exchange mechanism.Comment: 4 pages, 2 figures; minor corrections, references adde

Anomalous NMR Spin-Lattice Relaxation in SrB_{6} and Ca_{1-x}La_{x}B_{6}

We report the results of {11}B nuclear magnetic resonance (NMR) measurements of SrB_{6} and Ca_{0.995}La_{0.05}B_{6} below room temperature. Although the electrical resistivities of these two materials differ substantially, their {11}B-NMR responses exhibit some strikingly common features. Both materials exhibit ferromagnetic order, but their {11}B-NMR spectra reveal very small hyperfine fields at the Boron sites. The spin lattice relaxation T_{1}^{-1} varies considerably with external field but changes with temperature only below a few K. We discuss these unusual results by considering various different scenarios for the electronic structure of these materials.Comment: Accepted for publication in Phys. Rev. B Rapid communication, 4 pages, 3 figures. This manuscript replaces an earlier version and includes some minor changes in the text and in Fig.

Charge dynamics and "ferromagnetism" of A1-xLaxB6 (A=Ca and Sr)

Ferromagnetism has been reported recently in La-doped alkaline-earth hexaborides, A1-xLaxB6 (A=Ca, Sr, and Ba). We have performed the reflectivity, Hall resistivity, and magnetization measurements of A1-xLaxB6. The results indicate that A1-xLaxB6 can be regarded as a simple doped semimetal, with no signature of an excitonic state as suggested by several theories. It is also found that the surface of as-grown samples (10 micrometer in thickness) has a different electronic structure from a bulk one, and a fairly large number of paramagnetic moments are confined in this region. After eliminating these paramagnetic moments at the surface, we could not find any evidence of an intrinsic ferromagnetic moment in our samples, implying the possibility that the ferromagnetism of A1-xLaxB6 reported so far is neither intrinsic.Comment: 7 pages, 8 figure

Time series modeling of cell cycle exit identifies Brd4 dependent regulation of cerebellar neurogenesis

Cerebellar neuronal progenitors undergo a series of divisions before irreversibly exiting the cell cycle and differentiating into neurons. Dysfunction of this process underlies many neurological diseases including ataxia and the most common pediatric brain tumor, medulloblastoma. To better define the pathways controlling the most abundant neuronal cells in the mammalian cerebellum, cerebellar granule cell progenitors (GCPs), we performed RNA-sequencing of GCPs exiting the cell cycle. Time-series modeling of GCP cell cycle exit identified downregulation of activity of the epigenetic reader protein Brd4. Brd4 binding to the Gli1 locus is controlled by Casein Kinase 1δ (CK1 δ)-dependent phosphorylation during GCP proliferation, and decreases during GCP cell cycle exit. Importantly, conditional deletion of Brd4 in vivo in the developing cerebellum induces cerebellar morphological deficits and ataxia. These studies define an essential role for Brd4 in cerebellar granule cell neurogenesis and are critical for designing clinical trials utilizing Brd4 inhibitors in neurological indications