Hypergroupoids and C*-algebras

Let $G$ be a locally compact groupoid. If $X$ is a free and proper $G$-space, then $(X*X)/G$ is a groupoid equivalent to $G$. We consider the situation where $X$ is proper but no longer free. The formalism of groupoid C*-algebras and their representations is suitable to attach C*-algebras to this new object.Comment: This is the authors' English version of a work that was published in Comptes rendus-Math\'ematique [Ser. I 351 (2013) 911-914]. References [5,6,10,12] have been added since publicatio

C∗^*-algebras of Fell bundles over \'etale groupoids

We describe a construction for the full C$^*$-algebra of a possibly unsaturated Fell bundle over a possibly non-Hausdorff locally compact \'etale groupoid without appealing to Renault's disintegration theorem. This construction generalises the standard construction given by Muhly and Williams.Comment: 15 pages. Initial version, comments are welcom

Improving circuit miniaturization and its efficiency using Rough Set Theory

High-speed, accuracy, meticulousness and quick response are notion of the vital necessities for modern digital world. An efficient electronic circuit unswervingly affects the maneuver of the whole system. Different tools are required to unravel different types of engineering tribulations. Improving the efficiency, accuracy and low power consumption in an electronic circuit is always been a bottle neck problem. So the need of circuit miniaturization is always there. It saves a lot of time and power that is wasted in switching of gates, the wiring-crises is reduced, cross-sectional area of chip is reduced, the number of transistors that can implemented in chip is multiplied many folds. Therefore to trounce with this problem we have proposed an Artificial intelligence (AI) based approach that make use of Rough Set Theory for its implementation. Theory of rough set has been proposed by Z Pawlak in the year 1982. Rough set theory is a new mathematical tool which deals with uncertainty and vagueness. Decisions can be generated using rough set theory by reducing the unwanted and superfluous data. We have condensed the number of gates without upsetting the productivity of the given circuit. This paper proposes an approach with the help of rough set theory which basically lessens the number of gates in the circuit, based on decision rules.Comment: The International Conference on Machine Intelligence Research and Advancement,ICMIRA-201

Auxiliary Network: Scalable and agile online learning for dynamic system with inconsistently available inputs

Streaming classification methods assume the number of input features is fixed and always received. But in many real-world scenarios, some features are reliable while others are unreliable or inconsistent. We propose a novel online deep learning-based model called Auxiliary Network (Aux-Net), which is scalable and agile and can handle any number of inputs at each time instance. The Aux-Net model is based on the hedging algorithm and online gradient descent. It employs a model of varying depth in an online setting using single pass learning. Aux-Net is a foundational work towards scalable neural network for a dynamic complex environment dealing ad hoc or inconsistent inputs. The efficacy of Aux-Net is shown on the Italy Power Demand dataset