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

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

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

CXCR2 deficient mice display macrophage-dependent exaggerated acute inflammatory responses

CXCR2 is an essential regulator of neutrophil recruitment to inflamed and damaged sites and plays prominent roles in inflammatory pathologies and cancer. It has therefore been highlighted as an important therapeutic target. However the success of the therapeutic targeting of CXCR2 is threatened by our relative lack of knowledge of its precise in vivo mode of action. Here we demonstrate that CXCR2-deficient mice display a counterintuitive transient exaggerated inflammatory response to cutaneous and peritoneal inflammatory stimuli. In both situations, this is associated with reduced expression of cytokines associated with the resolution of the inflammatory response and an increase in macrophage accumulation at inflamed sites. Analysis using neutrophil depletion strategies indicates that this is a consequence of impaired recruitment of a non-neutrophilic CXCR2 positive leukocyte population. We suggest that these cells may be myeloid derived suppressor cells. Our data therefore reveal novel and previously unanticipated roles for CXCR2 in the orchestration of the inflammatory response

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

Tree Automata as Algebras: Minimisation and Determinisation

We study a categorical generalisation of tree automata, as algebras for a fixed endofunctor endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these automata. We then build upon and extend an existing generalisation of the Nerode equivalence to a categorical setting and relate it to the existence of minimal automata. Finally, we show that generalised types of side-effects, such as non-determinism, can be captured by this categorical framework, leading to a general determinisation procedure

Concepts of GPCR-controlled navigation in the immune system

G-protein-coupled receptor (GPCR) signaling is essential for the spatiotemporal control of leukocyte dynamics during immune responses. For efficient navigation through mammalian tissues, most leukocyte types express more than one GPCR on their surface and sense a wide range of chemokines and chemoattractants, leading to basic forms of leukocyte movement (chemokinesis, haptokinesis, chemotaxis, haptotaxis, and chemorepulsion). How leukocytes integrate multiple GPCR signals and make directional decisions in lymphoid and inflamed tissues is still subject of intense research. Many of our concepts on GPCR-controlled leukocyte navigation in the presence of multiple GPCR signals derive from in vitro chemotaxis studies and lower vertebrates. In this review, we refer to these concepts and critically contemplate their relevance for the directional movement of several leukocyte subsets (neutrophils, T cells, and dendritic cells) in the complexity of mouse tissues. We discuss how leukocyte navigation can be regulated at the level of only a single GPCR (surface expression, competitive antagonism, oligomerization, homologous desensitization, and receptor internalization) or multiple GPCRs (synergy, hierarchical and non-hierarchical competition, sequential signaling, heterologous desensitization, and agonist scavenging). In particular, we will highlight recent advances in understanding GPCR-controlled leukocyte navigation by intravital microscopy of immune cells in mice

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

Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.

The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition