Morse-Conley-Floer Homology

For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue of the Conley index and the Morse-Conley relations. The approach will be referred to as Morse-Conley-Floer homology

Functoriality and duality in Morse-Conley-Floer homology

In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known~\cite{abbondandoloschwarz, aizenbudzapolski,audindamian, kronheimermrowka, schwarz}, but the proofs use isomorphisms to other homology theories. We give direct proofs by analyzing appropriate moduli spaces. The notions of isolating map and flow map allows the results to generalize to local Morse homology and Morse-Conley-Floer homology. We prove Poincar\'e type duality statements for local Morse homology and Morse-Conley-Floer homology.Comment: To appear in the Journal of Fixed Point theory and its Application

Physical Therapy Management of a Patient with Hypermobile type Ehlers-Danlos Syndrome for Treatment of Cervicogenic Headaches: A Case Report

The purpose of this case report was to demonstrate the management of a patient diagnosed with hEDS for treatment of Cervicogenic headaches with the use of the CCFT protocol.https://soar.usa.edu/flsaspring2018/1008/thumbnail.jp

On Star Expressions and Completeness Theorems

An open problem posed by Milner asks for a proof that a certain axiomatisation, which Milner showed is sound with respect to bisimilarity for regular expressions, is also complete. One of the main difficulties of the problem is the lack of a full Kleene theorem, since there are automata that can not be specified, up to bisimilarity, by an expression. Grabmayer and Fokkink (2020) characterise those automata that can be expressed by regular expressions without the constant 1, and use this characterisation to give a positive answer to Milner's question for this subset of expressions. In this paper, we analyse Grabmayer and Fokkink's proof of completeness from the perspective of universal coalgebra, and thereby give an abstract account of their proof method. We then compare this proof method to another approach to completeness proofs from coalgebraic language theory. This culminates in two abstract proof methods for completeness, what we call the local and global approaches, and a description of when one method can be used in place of the other

Learning Pomset Automata.

We extend the L⋆ algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata

Microarray analyses demonstrate the involvement of type i interferons in psoriasiform pathology development in D6-deficient mice

The inflammatory response is normally limited by mechanisms regulating its resolution. In the absence of resolution, inflammatory pathologies can emerge, resulting in substantial morbidity and mortality. We have been studying the D6 chemokine scavenging receptor, which played an indispensable role in the resolution phase of inflammatory responses and does so by facilitating removal of inflammatory CC chemokines. In D6-deficient mice, otherwise innocuous cutaneous inflammatory stimuli induce a grossly exaggerated inflammatory response that bears many similarities to human psoriasis. In the present study, we have used transcriptomic approaches to define the molecular make up of this response. The data presented highlight potential roles for a number of cytokines in initiating and maintaining the psoriasis-like pathology. Most compellingly, we provide data indicating a key role for the type I interferon pathway in the emergence of this pathology. Neutralizing antibodies to type I interferons are able to ameliorate the psoriasis-like pathology, confirming a role in its development. Comparison of transcriptional data generated from this mouse model with equivalent data obtained from human psoriasis further demonstrates the strong similarities between the experimental and clinical systems. As such, the transcriptional data obtained in this preclinical model provide insights into the cytokine network active in exaggerated inflammatory responses and offer an excellent tool to evaluate the efficacy of compounds designed to therapeutically interfere with inflammatory processes

CCR7 is required for the in vivo function of CD4+ CD25+ regulatory T cells

CCR7-mediated migration of naive T cells into the secondary lymphoid organs is a prerequisite for their encounter with mature dendritic cells, the productive presentation of cognate antigen, and consequent T cell proliferation and effector differentiation. Therefore, CCR7 was suggested to play an important role in the initiation of adaptive immune responses. In this study, we show that primary immunity can also develop in the absence of CCR7. Moreover, CCR7-deficient knockout (KO) mice display augmented immune responses. Our data cumulatively suggest that enhanced immunity in CCR7 KO mice is caused by the defective lymph node (LN) positioning of FoxP3(+) CD4(+) CD25(+) regulatory T cells (T reg cells) and the consequent impediment of their function. The FoxP3(+) T reg cells express CCR7 and, after their adoptive transfer, migrate into the LNs of wild-type mice. Here, they proliferate in situ upon antigen stimulation and inhibit the generation of antigen-specific T cells. Conversely, transferred CCR7-deficient T reg cells fail to migrate into the LNs and suppress antigen-induced T cell responses. The transfer of combinations of naive and T reg cells from wild-type and CCR7 KO mice into syngeneic severe combined immunodeficient mice directly demonstrates that CCR7-deficient T reg cells are less effective than their wild-type counterparts in preventing the development of inflammatory bowel diseas

Preservation of Equations by Monoidal Monads

If a monad T is monoidal, then operations on a set X can be lifted canonically to operations on TX. In this paper we study structural properties under which T preserves equations between those operations. It has already been shown that any monoidal monad preserves linear equations; affine monads preserve drop equations (where some variable appears only on one side, such as x? y = y) and relevant monads preserve dup equations (where some variable is duplicated, such as x ? x = x). We start the paper by showing a converse: if the monad at hand preserves a drop equation, then it must be affine. From this, we show that the problem whether a given (drop) equation is preserved is undecidable. A converse for relevance turns out to be more subtle: preservation of certain dup equations implies a weaker notion which we call n-relevance. Finally, we identify a subclass of equations such that their preservation is equivalent to relevance

Concurrent Kleene Algebra: Free Model and Completeness

Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the axioms for CKA with bounded parallelism are complete for the semantics proposed in the original paper; consequently, these semantics are the free model for this fragment. This result settles a conjecture of Hoare and collaborators. Moreover, the techniques developed along the way are reusable; in particular, they allow us to establish pomset automata as an operational model for CKA.Comment: Version 2 includes an overview section that outlines the completeness proof, as well as some extra discussion of the interpolation lemma. It also includes better typography and a number of minor fixes. Version 3 incorporates the changes by comments from the anonymous referees at ESOP. Among other things, these include a worked example of computing the syntactic closure by han

Kleene algebra with observations

Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory