On C*-algebras generated by pairs of q-commuting isometries

We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treate

Atomic jet from SMM1 (FIRS1) in Serpens uncovers non-coeval binary companion

We report on the detection of an atomic jet associated with the protostellar source SMM1 (FIRS1) in Serpens. The jet is revealed in [FeII] and [NeII] line maps observed with Spitzer/IRS, and further confirmed in HiRes IRAC and MIPS images. It is traced very close to SMM1 and peaks at ~5 arcsec" from the source at a position angle of $\sim 125 degrees. In contrast, molecular hydrogen emission becomes prominent at distances > 5" from the protostar and extends at a position angle of 160 degrees. The morphological differences suggest that the atomic emission arises from a companion source, lying in the foreground of the envelope surrounding the embedded protostar SMM1. In addition the molecular and atomic Spitzer maps disentangle the large scale CO (3-2) emission observed in the region into two distinct bipolar outflows, giving further support to a proto-binary source setup. Analysis at the peaks of the [FeII] jet show that emission arises from warm and dense gas (T ~1000 K, n(electron) 10^5 - 10^6 cm^-3). The mass flux of the jet derived independently for the [FeII] and [NeII] lines is 10^7 M(sun)/yr, pointing to a more evolved Class~I/II protostar as the driving source. All existing evidence converge to the conclusion that SMM1 is a non-coeval proto-binary source.Comment: 10 pages, 7 figures, 1 table. Accepted for publication in Astronomy \& Astrophysic

On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Penicillium verrucosum occurrence and Ochratoxin A contents in organically cultivated grain with special reference to ancient wheat types and drying practice

This study addresses the relationship between the ochratoxigenic strains of Penicillium verrucosum and ochratoxin A (OTA) contents in organically cultivated grain. It included 37 combined, non-dried grain samples from farmers with no drying facilities as well as 19 non-dried and 22 dried samples from six farms with on-farm drying facilities (Case studies 1-6). The study focused on the ancient wheat type spelt but also included samples of wheat, rye, barley, oats, triticale, emmer, and einkorn. All 78 samples were analysed for moisture content (MC) and occurrence of P. verrucosum. The latter was assessed by plating non-disinfected kernels on DYSG agar and counting those contaminated by the fungus. Fiftyfive samples were analysed for OTA. Most of the combine harvested samples (82%) were contaminated with P. verrucosum prior to drying. This was ascribed to difficult harvest conditions and many samples of spelt, which was significantly more contaminated by P. verrucosum than oats, wheat and barley. Though not statistically significant, the results also indicated that spelt was more contaminated than rye, which is usually regarded the most sensitive small grain cereal. No correlation was found between number of kernels contaminated by P. verrucosum and OTA content. Despite many non-dried samples being contaminated by P. verrucosum, only two exceeded the EU maximum limit for grain (5 ng OTA g-1), both being spring spelt with 18 and 92 ng g-1, respectively. The problems were most likely correlated to a late harvest and high MC of the grain. The case studies showed exceedings of the maximum limit in a batch of dried oats and spring wheat, respectively, probably to be explained by insufficient drying of late harvested grain with high MC. Furthermore, our results clearly indicate that OTA is not produced in significant amounts in samples with MCs below 17%. All dried samples with MCs above 18% exceeded the 5 ng OTA g-1 limit in grain. However, no correlation between MC and the amount of OTA produced was found