On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions

Symbolic ultrametrics define edge-colored complete graphs K_n and yield a simple tree representation of K_n. We discuss, under which conditions this idea can be generalized to find a symbolic ultrametric that, in addition, distinguishes between edges and non-edges of arbitrary graphs G=(V,E) and thus, yielding a simple tree representation of G. We prove that such a symbolic ultrametric can only be defined for G if and only if G is a so-called cograph. A cograph is uniquely determined by a so-called cotree. As not all graphs are cographs, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of G. The latter problem is equivalent to find an optimal cograph edge k-decomposition {E_1,...,E_k} of E so that each subgraph (V,E_i) of G is a cograph. An upper bound for the integer k is derived and it is shown that determining whether a graph has a cograph 2-decomposition, resp., 2-partition is NP-complete

Enhanced bioavailability and reduced pharmacokinetic variability of Oral PTH (1-34) in man

An orally administered PTH may have prodigious advantages in the treatment of hypoparathyroidism and osteoporosis. Unfortunately, the oral delivery of biologic macromolecules is characterized by a negligible bioavailability and a high dose-to-dose variability in absorption, resulting in difficulty in accurately titrating the drug effect. We present clinical study data of a novel oral peptide delivery technology demonstrating an enhanced bioavailability with reduced Cmax variability. Methods: A Phase I, open label crossover pharmacokinetic (PK) study to assess the safety and PK of oral PTH (1-34) in ten healthy male adult volunteers was conducted. The PK profile of a fixed dose - 1.5mg PTH (1-34) of three different oral formulations was compared. PTH (1-34) levels in the plasma of subjects was analyzed at a number of time points post administration, utilizing a PTH (1-34) immunoassay (IDS; Bolden, UK). In parallel, to assess the pharmacodynamic (PD) effect, serum calcium of subjects receiving the different formulations of oral PTH (1-34) was analyzed. Results: PK profiles of all oral PTH (1-34) formulations were characterized by a rapid absorption and elimination. The systemic exposure (AUC) of the basic oral formulation and two modified formulation versions were 3481 ±1843 pg*min/mL, 7976 ±2556 pg*min/mL and 11369 ±3719 pg*min/mL (mean ± SE). The maximal plasma concentration (Cmax) of these formulations were 145 ±56pg/mL, 375 ±108pg/mL, and 481 ±101pg/mL, respectively. Cmax coefficients of variation (CV%) of the same formulations were 123%, 91% and 67%, respectively. Similarly to the drug absorption, PD response of the modified formulations, presented as the maximal relative increase in albumin adjusted calcium, was improved from 0.07 ±0.29mg/dL to 0.32 ±0.24mg/dL. Discussion: Inherent to oral drug delivery of biopharmaceuticals is the extremely low bioavailability and high absorption variability. The current results indicate that Entera’s delivery technology can overcome these two principal obstacles by achieving repeatable, clinically relevant systemic drug exposure. Entera’s proprietary delivery platform was optimized and achieved anenhancement in drug bioavailability in parallel with the significant decrease in its absorption variability. Similarly, its effect on blood calcium was enhanced by the novel oral formulation of PTH (1-34) pointing out the potential of the drug to be a first line treatment of hypoparathyroidism and osteoporosis

Dark Energy and Extending the Geodesic Equations of Motion: Connecting the Galactic and Cosmological Length Scales

Recently, an extension of the geodesic equations of motion using the Dark Energy length scale was proposed. Here, we apply this extension to the analyzing the motion of test particles at the galactic scale and longer. A cosmological check of the extension is made using the observed rotational velocity curves and core sizes of 1393 spiral galaxies. We derive the density profile of a model galaxy using this extension, and with it, we calculate $\sigma_8$ to be $0.73_{\pm 0.12}$; this is within experimental error of the WMAP value of $0.761_{-0.048}^{+0.049}$. We then calculate $R_{200}$ to be $206_{\pm 53}$ kpc, which is in reasonable agreement with observations.Comment: 25 pages. Accepted for publication in General Relativity and Gravitation. Paper contains the published version of the second half of arXiv:0711.3124v2 with corrections include

Toy models of crossed Andreev reflection

We propose toy models of crossed Andreev reflection in multiterminal hybrid structures containing out-of-equilibrium conductors. We apply the description to two possible experiments: (i) to a device containing a large quantum dot inserted in a crossed Andreev reflection circuit. (ii) To a device containing an Aharonov-Bohm loop inserted in a crossed Andreev reflection circuit.Comment: 5 pages, 9 figures, minor modification

Age Estimations of M31 Globular Clusters from Their Spectral Energy Distributions

This paper presents accurate spectral energy distributions (SEDs) of 16 M31 globular clusters (GCs) confirmed by spectroscopy and/or high spatial-resolution imaging, as well as 30 M31 globular cluster candidates detected by Mochejska et al. Most of these candidates have m_V > 18, deeper than previous searches, and these candidates have not yet been confirmed to be globular clusters. The SEDs of these clusters and candidates are obtained as part of the BATC Multicolor Survey of the Sky, in which the spectrophotometrically-calibrated CCD images of M31 in 13 intermediate-band filters from 4000 to 10000 A were observed. These filters are specifically designed to exclude most of the bright and variable night-sky emission lines including the OH forest. In comparison to the SEDs of true GCs, we find that some of the candidate objects are not GCs in M31. SED fits show that theoretical simple stellar population (SSP) models can fit the true GCs very well. We estimate the ages of these GCs by comparing with SSP models. We find that, the M31 clusters range in age from a few ten Myr to a few Gyr old, as well as old GCs, confirming the conclusion that has been found by Barmby et a, Williams & Hodge, Beasley et al., Burstein et al. and Puzia et al. in their investigations of the SEDs of M31 globular clusters.Comment: Accepted for Publication in A&Ap, 13 pages, 6 figure

The Sagittarius dwarf irregular galaxy: metallicity and stellar populations

We present deep $BVI$ observations of the dwarf irregular galaxy UKS1927-177 in Sagittarius. Statistically cleaned $V$, $(B-I)$ CMDs clearly display the key evolutionary features in this galaxy. Previously detected C stars are located in the CMDs and shown to be variable, thus confirming the presence of a significant upper-AGB intermediate age population. A group of likely red supergiants is also identified, whose magnitude and color is consistent with a 30 Myr old burst of star formation. The observed colors of both blue and red stars in SagDIG are best explained by introducing a differential reddening scenario in which internal dust extinction affects the star forming regions. Adopting a low reddening for the red giants, $E(B-V) = 0.07 \pm 0.02$, gives [Fe/H]=$-2.1 \pm 0.2$ for the mean stellar metallicity, a value consistent with the [O/H] abundance measured in the HII regions. This revised metallicity, which is in accord with the trend of metallicity against luminosity for dwarf irregular galaxies, is indicative of a ``normal'', although metal-poor, dIrr galaxy. A quantitative description is given of the spatial distribution of stars in different age intervals, in comparison with the distribution of the neutral hydrogen. We find that the youngest stars are located near the major peaks of emission on the HI shell, whereas the red giants and intermediate-age C stars define an extended halo or disk with scale length comparable to the size of the hydrogen cloud. The relationship between the distribution of ISM and star formation is briefly discussed.Comment: 10 pages, 7 figures, accepted A&