A class of almost C_0(K)-C*-algebras

We consider in this paper the family of exponential Lie groups Gn,µ, whose Lie algebra is an extension of the Heisenberg Lie algebra by the reals and whose quotient group by the centre of the Heisenberg group is an ax + b-like group. The C*-algebras of the groups Gn,µ give new examples of almost C0(K)-C*-algebras.

Updating Credal Networks is Approximable in Polynomial Time

Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing posterior inferences in extensively specified credal networks, which is empirically shown to outperform a state-of-the-art algorithm. The algorithm is then turned into a provably good approximation scheme, that is, a procedure that for any input is guaranteed to return a solution not worse than the optimum by a given factor. Remarkably, we show that when the networks have bounded treewidth and bounded number of states per variable the approximation algorithm runs in time polynomial in the input size and in the inverse of the error factor, thus being the first known fully polynomial-time approximation scheme for inference in credal networks.

Efficiently Scheduling Task Dataflow Parallelism: A Comparison Between Swan and QUARK

Increased system variability and irregularity of parallelism in applications put increasing demands on the ef- ficiency of dynamic task schedulers. This paper presents a new design for a work-stealing scheduler supporting both Cilk- style recursively parallel code and parallelism deduced from dataflow dependences. Initial evaluation on a set of linear algebra kernels demonstrates that our scheduler outperforms PLASMA’s QUARK scheduler by up to 12% on a 16-thread Intel Xeon and by up to 50% on a 32-thread AMD Bulldozer.

Capturing Goodwillie's Derivative

Recent work of Biedermann and Roendigs has translated Goodwillie's calculus of functors into the language of model categories. Their work focuses on symmetric multilinear functors and the derivative appears only briefly. In this paper we focus on understanding the derivative as a right Quillen functor to a new model category. This is directly analogous to the behaviour of Weiss's derivative in orthogonal calculus. The immediate advantage of this new category is that we obtain a streamlined and more informative proof that the n-homogeneous functors are classified by spectra with an action of the symmetric group on n objects. In a later paper we will use this new model category to give a formal comparison between the orthogonal calculus and Goodwillie's calculus of functors.

Two dimensional unital Riesz algebras, their representations and norms

We describe all two dimensional unital Riesz algebras and study representations of them in Riesz algebras of regular operators. Although our results are not complete, we do demonstrate that very varied behaviour can occur even though all these algebras can be given a Banach lattice algebra norm.

Schur multipliers of Cartan pairs

We define the Schur multipliers of a separable von Neumann algebra M with Cartan masa A, generalising the classical Schur multipliers of B(` 2 ). We characterise these as the normal A-bimodule maps on M. If M contains a direct summand isomorphic to the hyper- finite II1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product A ⊗eh A are strictly contained in the algebra of all Schur multipliers.

Schur idempotents and hyperreflexivity

We show that the set of Schur idempotents with hyperreflexive range is a Boolean lattice which contains all contractions. We establish a preservation result for sums which implies that the weak* closed span of a hyperreflexive and a ternary masa-bimodule is hyperreflexive, and prove that the weak* closed span of finitely many tensor products of a hyperreflexive space and a hyperreflexive range of a Schur idempotent (respectively, a ternary masa-bimodule) is hyperreflexive.

Information Gathering and Processing with Fluorescent Molecules

Molecular information gathering and processing – a young field of applied chemistry - is undergoing good growth. The progress is occurring both in terms of conceptual development and in terms of the strengthening of older concepts with new examples. This review critically surveys these two broad avenues. We consider some cases where molecules emulate one of the building blocks of electronic logic gates. We then examine molecular emulation of various Boolean logic gates carrying one, two or three inputs. Some single-input gates are popular information gathering devices. Special systems, such as ‘lab-on-a-molecule’ and molecular keypad locks, also receive attention. A situation deviating from the Boolean blueprint is also discussed. Some pointers are offered for maintaining the upward curve of the field.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

SOPS: A System for Efficient Processing of Spatial-Keyword Publish/Subscribe

Massive amount of data that are geo-tagged and associated with text information are being generated at an unprecedented scale. These geo-textual data cover a wide range of topics. Users are interested in receiving up-to-date geo-textual objects (e.g., geo-tagged Tweets) such that their locations meet users’ need and their texts are interesting to users. For example, a user may want to be updated with tweets near her home on the topic “dengue fever headache.” In this demonstration, we present SOPS, the Spatial-Keyword Publish/Subscribe System, that is capable of efficiently processing spatial keyword continuous queries. SOPS supports two types of queries: (1) Boolean Range Continuous (BRC) query that can be used to subscribe the geo-textual objects satisfying a boolean keyword expression and falling in a specified spatial region; (2) Temporal Spatial-Keyword Top-k Continuous (TaSK) query that continuously maintains up-to-date top-k most relevant results over a stream of geo-textual objects. SOPS enables users to formulate their queries and view the real-time results over a stream of geotextual objects by browser-based user interfaces. On the server side, we propose solutions to efficiently processing a large number of BRC queries (tens of millions) and TaSK queries over a stream of geo-textual objects.

The basic principles of uncertain information fusion. An organised review of merging rules in different representation frameworks.

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings.

Triangular Objects and Systematic K-Theory

We investigate modules over “systematic” rings. Such rings are “almost graded” and have appeared under various names in the literature; they are special cases of the G-systems of Grzeszczuk. We analyse their K-theory in the presence of conditions on the support, and explain how this generalises and unifies calculations of graded and filtered K-theory scattered in the literature. Our treatment makes systematic use of the formalism of idempotent completion and a theory of triangular objects in additive categories, leading to elementary and transparent proofs throughout.