On polynomials orthogonal with respect to certain Sobolev inner products

AbstractWe are concerned with polynomials {pn(λ)} that are orthogonal with respect to the Sobolev inner product 〈 f, g 〉λ = ∝ fg dϑ + λ ∝ f′g′ dψ, where λ is a non-negative constant. We show that if the Borel measures dϑ and dψ obey a specific condition then the Pn(λ)'s can be expanded in the polynomials orthogonal with respect to dϑ in such a manner that, subject to correct normalization, the expansion coefficients, except for the last, are independent of n and are themselves orthogonal polynomials in λ. We explore several examples and demonstrate how our theory can be used for efficient evaluation of Sobolev-Fourier Coefficients

A Laser Frequency Comb System for Absolute Calibration of the VTT Echelle Spectrograph

A wavelength calibration system based on a laser frequency comb (LFC) was developed in a co-operation between the Kiepenheuer-Institut f\"ur Sonnenphysik, Freiburg, Germany and the Max-Planck-Institut f\"ur Quantenoptik, Garching, Germany for permanent installation at the German Vacuum Tower Telescope (VTT) on Tenerife, Canary Islands. The system was installed successfully in October 2011. By simultaneously recording the spectra from the Sun and the LFC, for each exposure a calibration curve can be derived from the known frequencies of the comb modes that is suitable for absolute calibration at the meters per second level. We briefly summarize some topics in solar physics that benefit from absolute spectroscopy and point out the advantages of LFC compared to traditional calibration techniques. We also sketch the basic setup of the VTT calibration system and its integration with the existing echelle spectrograph.Comment: 9 pages, 2 figures; Solar Physics 277 (2012

Enhanced fluorine-19 MRI sensitivity using a cryogenic radiofrequency probe: technical developments and ex vivo demonstration in a mouse model of neuroinflammation

Neuroinflammation can be monitored using fluorine-19 ((19)F)-containing nanoparticles and (19)F MRI. Previously we studied neuroinflammation in experimental autoimmune encephalomyelitis (EAE) using room temperature (RT) (19)F radiofrequency (RF) coils and low spatial resolution (19)F MRI to overcome constraints in signal-to-noise ratio (SNR). This yielded an approximate localization of inflammatory lesions. Here we used a new (19)F transceive cryogenic quadrature RF probe ((19) F-CRP) that provides the SNR necessary to acquire superior spatially-resolved (19)F MRI. First we characterized the signal-transmission profile of the (19) F-CRP. The (19) F-CRP was then benchmarked against a RT (19)F/(1)H RF coil. For SNR comparison we used reference compounds including (19)F-nanoparticles and ex vivo brains from EAE mice administered with (19)F-nanoparticles. The transmit/receive profile of the (19) F-CRP diminished with increasing distance from the surface. This was counterbalanced by a substantial SNR gain compared to the RT coil. Intraparenchymal inflammation in the ex vivo EAE brains was more sharply defined when using 150 μm isotropic resolution with the (19) F-CRP, and reflected the known distribution of EAE histopathology. At this spatial resolution, most (19)F signals were undetectable using the RT coil. The (19) F-CRP is a valuable tool that will allow us to study neuroinflammation with greater detail in future in vivo studies

Unusual bound states of quark matter within the NJL model

Properties of dense quark matter in and out of chemical equilibrium are studied within the SU(3) Nambu-Jona-Lasinio model. In addition to the 4-fermion scalar and vector terms the model includes also the 6-fermion flavour mixing interaction. First we study a novel form of deconfined matter, meso-matter, which is composed of equal number of quarks and antiquarks. It can be thought of as a strongly compressed meson gas where mesons are melted into their elementary constituents, quarks and antiquarks. Strongly bound states in this quark-antiquark matter are predicted for all flavour combinations of quark-antiquark pairs. The maximum binding energy reaches up to 180 MeV per pair for mixtures with about 70% of strange quark-antiquark pairs. Equilibrated baryon-rich quark matter with various flavour compositions is also studied. In this case only shallow bound states appear in systems with a significant admixture (about 40%) of strange quarks (strangelets). Their binding energies are quite sensitive to the relative strengths of scalar and vector interactions. The common property of all these bound states is that they appear at high particle densities when the chiral symmetry is nearly restored. Thermal properties of meso-matter as well as chemically equilibrated strange quark matter are also investigated. Possible decay modes of these bound states are discussed.Comment: 26 pages, 16 PostScript figures, RevTe

Indirect Dark Matter Detection from Dwarf Satellites: Joint Expectations from Astrophysics and Supersymmetry

We present a general methodology for determining the gamma-ray flux from annihilation of dark matter particles in Milky Way satellite galaxies, focusing on two promising satellites as examples: Segue 1 and Draco. We use the SuperBayeS code to explore the best-fitting regions of the Constrained Minimal Supersymmetric Standard Model (CMSSM) parameter space, and an independent MCMC analysis of the dark matter halo properties of the satellites using published radial velocities. We present a formalism for determining the boost from halo substructure in these galaxies and show that its value depends strongly on the extrapolation of the concentration-mass (c(M)) relation for CDM subhalos down to the minimum possible mass. We show that the preferred region for this minimum halo mass within the CMSSM with neutralino dark matter is ~10^-9-10^-6 solar masses. For the boost model where the observed power-law c(M) relation is extrapolated down to the minimum halo mass we find average boosts of about 20, while the Bullock et al (2001) c(M) model results in boosts of order unity. We estimate that for the power-law c(M) boost model and photon energies greater than a GeV, the Fermi space-telescope has about 20% chance of detecting a dark matter annihilation signal from Draco with signal-to-noise greater than 3 after about 5 years of observation

Spatial representation of temporal information through spike timing dependent plasticity

We suggest a mechanism based on spike time dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely connected by STDP synapses. All synapses are modified according to the so-called normal STDP rule observed in various real biological synapses. After conditioning through repeated input of a limited number of of temporal sequences the system is able to complete the temporal sequence upon receiving the input of a fraction of them. This is an example of effective unsupervised learning in an biologically realistic system. We investigate the dependence of learning success on entrainment time, system size and presence of noise. Possible applications include learning of motor sequences, recognition and prediction of temporal sensory information in the visual as well as the auditory system and late processing in the olfactory system of insects.Comment: 13 pages, 14 figures, completely revised and augmented versio

Quark Potential in a Quark-Meson Plasma

We investigate quark potential by considering meson exchanges in the two flavor Nambu--Jona-Lasinio model at finite temperature and density. There are two kinds of oscillations in the chiral restoration phase, one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark-meson plasma is strongly coupled in the temperature region $1\le T/T_c \lesssim 3$ with $T_c$ being the critical temperature of chiral phase transition. The maximum coupling in this region is located at the critical point.Comment: 8 pages and 8 figure

Phenotyping placental oxygenation in Lgals1 deficient mice using (19)F MRI

Placental hypoperfusion and hypoxia are key drivers in complications during fetal development such as fetal growth restriction and preeclampsia. In order to study the mechanisms of disease in mouse models, the development of quantitative biomarkers of placental hypoxia is a prerequisite. The goal of this exploratory study was to establish a technique to noninvasively characterize placental partial pressure of oxygen (PO(2)) in vivo in the Lgals1 (lectin, galactoside-binding, soluble, 1) deficient mouse model of preeclampsia using fluorine magnetic resonance imaging. We hypothesized a decrease in placental oxygenation in knockout mice. Wildtype and knockout animals received fluorescently labeled perfluoro-5-crown-15-ether nanoemulsion i.v. on day E14-15 during pregnancy. Placental PO(2) was assessed via calibrated (19)F MRI saturation recovery T(1) mapping. A gas challenge with varying levels of oxygen in breathing air (30%, 60% and 100% O(2)) was used to validate that changes in oxygenation can be detected in freely breathing, anesthetized animals. At the end of the experiment, fluorophore-coupled lectin was injected i.v. to label the vasculature for histology. Differences in PO(2) between breathing conditions and genotype were statistically analyzed with linear mixed-effects modeling. As expected, a significant increase in PO(2) with increasing oxygen in breathing air was found. PO(2) in Lgals1 knockout animals was decreased but this effect was only present at 30% oxygen in breathing air, not at 60% and 100%. Histological examinations showed crossing of the perfluorocarbon nanoemulsion to the fetal blood pool but the dominating contribution of (19)F MR signal is estimated at > 70% from maternal plasma based on volume fraction measurements of previous studies. These results show for the first time that (19)F MRI can characterize oxygenation in mouse models of placental malfunction

N=8 SCFT and M Theory on AdS_4 x RP^7

We study M theory on AdS_4 \times \RP^7 corresponding to 3 dimensional ${\cal N}=8$ superconformal field theory which is the strong coupling limit of 3 dimensional super Yang-Mills theory. For SU(N) theory, a wrapped M5 brane on \RP^5 can be interpreted as baryon vertex. For $SO(N)/Sp(2N)$ theory, by using the property of (co-)homology of \RP^7, we classify various wrapping branes and consider domain walls and the baryon vertex.Comment: 17 pages, Changed baryon like operator as M5 branes in M theory rather than D6 brane in IIA theory. To appear in Phys.Rev.

Elastic Scattering and Transport Coefficients for a Quark Plasma in SUf(3)SU_f(3) at Finite Temperatures

The temperature dependence of the elastic scattering processes $qq'\to qq'$ and $q\bar q'\to q\bar q'$, with $q, q' = u, d, s$ is studied as a function of the scattering angle and the center of mass energy of the collision within the framework of the $SU_f(3)$ Nambu--Jona--Lasinio model. Critical scattering at threshold is observed in the $q\bar q'\to q\bar q'$ process, leading to an enhancement of the cross section as occurs in the phenomenon of critical opalescence. Transport properties such as viscosity, mean free paths and thermal relaxation times are calculated. Strangeness enhancement is investigated via the chemical relaxation times, which are found to be considerably higher than those calculated via perturbative QCD. A comparison with the experimental values for the strangeness enhancement in $S+S$ collisions leads to an upper limit of 4~fm/$c$ for the lifetime of the plasma.Comment: 35 pages ReVTeX, 18 PostScript figures, uufiles format, to appear in Nucl. Phys.