Algorithms For Extracting Timeliness Graphs

We consider asynchronous message-passing systems in which some links are timely and processes may crash. Each run defines a timeliness graph among correct processes: (p; q) is an edge of the timeliness graph if the link from p to q is timely (that is, there is bound on communication delays from p to q). The main goal of this paper is to approximate this timeliness graph by graphs having some properties (such as being trees, rings, ...). Given a family S of graphs, for runs such that the timeliness graph contains at least one graph in S then using an extraction algorithm, each correct process has to converge to the same graph in S that is, in a precise sense, an approximation of the timeliness graph of the run. For example, if the timeliness graph contains a ring, then using an extraction algorithm, all correct processes eventually converge to the same ring and in this ring all nodes will be correct processes and all links will be timely. We first present a general extraction algorithm and then a more specific extraction algorithm that is communication efficient (i.e., eventually all the messages of the extraction algorithm use only links of the extracted graph)

A low optical depth region in the inner disk of the HerbigAe star HR5999

Circumstellar disks surrounding young stars are known to be the birthplaces of planets, and the innermost astronomical unit is of particular interest. We present new long-baseline spectro-interferometric observations of the HerbigAe star, HR5999, obtained in the H and K bands with the AMBER instrument at the VLTI, and aim to produce near-infrared images at the sub-AU spatial scale. We spatially resolve the circumstellar material and reconstruct images using the MiRA algorithm. In addition, we interpret the interferometric observations using models that assume that the near-infrared excess is dominated by the emission of a circumstellar disk. We compare the images reconstructed from the VLTI measurements to images obtained using simulated model data. The K-band image reveals three main elements: a ring-like feature located at ~0.65 AU, a low surface brightness region inside, and a central spot. At the maximum angular resolution of our observations (1.3 mas), the ring is resolved while the central spot is only marginally resolved, preventing us from revealing the exact morphology of the circumstellar environment. We suggest that the ring traces silicate condensation, i.e., an opacity change, in a circumstellar disk around HR 5999. We build a model that includes a ring at the silicate sublimation radius and an inner disk of low surface brightness responsible for a large amount of the near-infrared continuum emission. The model successfully fits the SED, visibilities, and closure phases, and provides evidence of a low surface brightness region inside the silicate sublimation radius. This study provides additional evidence that in HerbigAe stars, there is material in a low surface brightness region, probably a low optical depth region, located inside the silicate sublimation radius and of unknown nature.Comment: 11 pages, 10 figure

The radius of a subcategory of modules

We introduce a new invariant for subcategories X of finitely generated modules over a local ring R which we call the radius of X. We show that if R is a complete intersection and X is resolving, then finiteness of the radius forces X to contain only maximal Cohen-Macaulay modules. We also show that the category of maximal Cohen-Macaulay modules has finite radius when R is a Cohen-Macaulay complete local ring with perfect coefficient field. We link the radius to many well-studied notions such as the dimension of the stable category of maximal Cohen-Macaulay modules, finite/countable Cohen-Macaulay representation type and the uniform Auslander condition.Comment: Final version, to appear in Algebra and Number Theor

Homology of perfect complexes

It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective dimension, obstructions to realizing R as a closed fiber of some flat local homomorphism. Other applications include, as special cases, uniform proofs of known results on free actions of elementary abelian groups and of tori on finite CW complexes. The arguments use numerical invariants of objects in general triangulated categories, introduced here and called levels. They allow one to track, through changes of triangulated categories, homological invariants like projective dimension, as well as structural invariants like Loewy length. An intermediate result sharpens, with a new proof, the New Intersection Theorem for commutative algebras over fields. Under additional hypotheses on the ring $R$ stronger estimates are proved for Loewy lengths of modules of finite projective dimension.Comment: This version corrects an error in the statement (and proof) of Theorem 7.4 in the published version of the paper [Adv. Math. 223 (2010) 1731--1781]. These changes do not affect any other results or proofs in the paper. A corrigendum has been submitted