Corecursive Algebras, Corecursive Monads and Bloom Monads

An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the concept of corecursive monad is a generalization of Elgot's iterative monads, analogous to corecursive algebras generalizing completely iterative algebras. We also characterize the Eilenberg-Moore algebras for the free corecursive monad and call them Bloom algebras

Enriched weakness

The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniqueness requirement and asks only for existence. The enriched versions of the usual notions involve certain morphisms between hom-objects being invertible; here we introduce enriched versions of the weak notions by asking that the morphisms between hom-objects belong to a chosen class of "surjections". We study in particular injectivity (weak orthogonality) in the enriched context, and illustrate how it can be used to describe homotopy coherent structures.Comment: 25 pages; v2 minor changes, to appear in JPA

Limits of small functors

For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K*,V]. If K is large, its free completion under colimits is the V-category PK of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on PK.Comment: 17 page

Improved Acceleration of the GPU Fourier Domain Acceleration Search Algorithm

We present an improvement of our implementation of the Correlation Technique for the Fourier Domain Acceleration Search (FDAS) algorithm on Graphics Processor Units (GPUs) (Dimoudi & Armour 2015; Dimoudi et al. 2017). Our new improved convolution code which uses our custom GPU FFT code is between 2.5 and 3.9 times faster the than our cuFFT-based implementation (on an NVIDIA P100) and allows for a wider range of filter sizes then our previous version. By using this new version of our convolution code in FDAS we have achieved 44% performance increase over our previous best implementation. It is also approximately 8 times faster than the existing PRESTO GPU implementation of FDAS (Luo 2013). This work is part of the AstroAccelerate project (Armour et al. 2002), a many-core accelerated time-domain signal processing library for radio astronomy.Comment: proceeding from ADASS XXVII conference, 4 page