Well-Pointed Coalgebras

For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Osius and Taylor. And initial algebras are precisely the final well-founded coalgebras. Finally, the initial iterative algebra consists of all finite well-pointed coalgebras. Numerous examples are discussed e.g. automata, graphs, and labeled transition systems

On Well-Founded and Recursive Coalgebras

This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor's General Recursion Theorem that every well-founded coalgebra is recursive, and we study under which hypothesis the converse holds. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra

Synthesis and reversible hydration behavior of the thiosulfate intercalated layered double hydroxide of Zn and Al

The thiosulfate-intercalated layered double hydroxide of Zn and Al undergoes reversible hydration with a variation in the relative humidity of the ambient. The hydrated and dehydrated phases, which represent the end members of the hydration cycle, both adopt the structure of the 3R1 polytype. In the intermediate range of relative humidity values (40-60), the hydrated and dehydrated phases coexist. The end members of the hydration cycle adopt the structure of the same polytype, and vary only in their basal spacings. This points to the possibility that all the intermediate phases have a kinetic origin. © 2013 Elsevier Inc

How to kill epsilons with a dagger: a coalgebraic take on systems with algebraic label structure

We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or ϵ-transitions. Our approach employs monads with a parametrized fixpoint operator † to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.Funded by the ERDF through the Programme COMPETE and by the Portuguese Foundation for Science and Technology, project ref. FCOMP-01-0124-FEDER-020537 and SFRH/BPD/71956/2010. Acknowledge support by project ANR 12IS0 2001 PACE

Spin dynamics in high-TCT_C superconductors

Key features of antiferromagnetic dynamical correlations in high-$T_C$ superconductors cuprates are discussed. In underdoped regime, the sharp resonance peak, occuring exclusively in the SC state, is accompanied by a broader contribution located around $\sim$ 30 meV which remains above $T_C$. Their interplay may induce incommensurate structure in the superconducting state.Comment: HTS99 Proceedings Miami (January 7-11 1999

Layer by layer - Combining Monads

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e. layers of the language, which then provides a monad structure to the composition of layers, or (ii) identifies precisely the algebraic obstacles to the existence of a distributive law and gives a best approximant language. The running example will involve three layers: a basic imperative language enriched first by adding non-determinism and then probabilistic choice. The first extension works seamlessly, but the second encounters an obstacle, which results in a best approximant language structurally very similar to the probabilistic network specification language ProbNetKAT

Genotype List String: a grammar for describing HLA and KIR genotyping results in a text string

Knowledge of an individual's human leukocyte antigen (HLA) genotype is essential for modern medical genetics, and is crucial for hematopoietic stem cell and solid-organ transplantation. However, the high levels of polymorphism known for the HLA genes make it difficult to generate an HLA genotype that unambiguously identifies the alleles that are present at a given HLA locus in an individual. For the last 20 years, the histocompatibility and immunogenetics community has recorded this HLA genotyping ambiguity using allele codes developed by the National Marrow Donor Program (NMDP). While these allele codes may have been effective for recording an HLA genotyping result when initially developed, their use today results in increased ambiguity in an HLA genotype, and they are no longer suitable in the era of rapid allele discovery and ultra-high allele polymorphism. Here, we present a text string format capable of fully representing HLA genotyping results. This Genotype List (GL) String format is an extension of a proposed standard for reporting killer-cell immunoglobulin-like receptor (KIR) genotype data that can be applied to any genetic data that use a standard nomenclature for identifying variants. The GL String format uses a hierarchical set of operators to describe the relationships between alleles, lists of possible alleles, phased alleles, genotypes, lists of possible genotypes, and multilocus unphased genotypes, without losing typing information or increasing typing ambiguity. When used in concert with appropriate tools to create, exchange, and parse these strings, we anticipate that GL Strings will replace NMDP allele codes for reporting HLA genotypes