Pre-torsors and Galois comodules over mixed distributive laws

We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions $(N_A,R_A)$ and $(N_B,R_B)$ on one hand, and the category of regular comonad arrows $(R_A,\xi)$ from some equalizer preserving comonad ${\mathbb C}$ to $N_BR_B$ on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of coalgebras.Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad ${\mathbb D}$ and a co-regular comonad arrow from ${\mathbb D}$ to $N_A R_A$, such that the comodule categories of ${\mathbb C}$ and ${\mathbb D}$ are equivalent.Comment: 34 pages LaTeX file. v2: a few typos correcte

Design methodology and simulation of a fleet management system for an advanced helicopter platform

This research is part of a major helicopter acquisition and upgrade program of the Australian Defence Forces (ADF) under a 20+ year strategic plan. The ‘Air 9000’ program aims to rationalise the number of helicopter types operated, simplify operational requirements and reduce through-life-support costs. This research program developed and modelled a Fleet Management System (FMS) for the newly acquired Multi-Role Helicopter-90 (MRH-90 / NHI NH-90) platform. It assessed current practices in aerospace technology management of civil and military aircraft fleets, and established requirements of civil & military rotary-wing platforms for the development of a fleet management methodology for the MRH-90 platform. A novel approach was adopted by applying systems engineering principles to design the FMS. The systems engineering approach enabled identification and implementation of the additional rotary-wing design parameters, required for system adaptability to future network-centric military & civil operational environments from a life-cycle perspective. This approach has resulted in the development and implementation of an adaptable prototype FMS software with integrated fleet management capabilities. Subsequent simulation & validation demonstrated significant enhancements in operational effectiveness over state-of-the art rotary-wing fleet management practices, by holistically and systematically addressing the present and future system needs of helicopter life-cycle management

Weak Projections onto a Braided Hopf Algebra

We show that, under some mild conditions, a bialgebra in an abelian and coabelian braided monoidal category has a weak projection onto a formally smooth (as a coalgebra) sub-bialgebra with antipode; see Theorem 1.12. In the second part of the paper we prove that bialgebras with weak projections are cross product bialgebras; see Theorem 2.12. In the particular case when the bialgebra $A$ is cocommutative and a certain cocycle associated to the weak projection is trivial we prove that $A$ is a double cross product, or biproduct in Madjid's terminology. The last result is based on a universal property of double cross products which, by Theorem 2.15, works in braided monoidal categories. We also investigate the situation when the right action of the associated matched pair is trivial

Molecular mechanisms underlying pMHC-II recognition

The immune system is a complex network of cells and molecules working together with the purpose of fending off potentially harmful pathogens. CD4+ T cells take key roles within this network by orchestrating a multitude of its players. They recognise pathogen or self-derived peptides (p) bound to molecules of the major histocompatibility class II (MHC-II) through their T cell receptor (TCR). Cytokines secreted in response to recognition aid antibody production and cytotoxic T cell activity, both critical for anti-viral immunity. In this thesis, TCR/pMHC-II interactions were investigated using a range of functional and molecular approaches in order to gain valuable insight into the mechanisms underlying successful antigen recognition. To aid these investigations, a versatile, insect cell based expression system for HLA-DR1 was successfully implemented to generate soluble protein for use in multimer stainings and biophysical assays. Two HLA-DR1 restricted peptides encoded within influenza heamagglutinin (HA) were confirmed as being highly conserved making them ideal targets for vaccine development and allowing identification of influenza specific CD4+ T cells. Furthermore, the various roles of peptide flanking residues (PFR) were investigated using two experimental models. In a HA derived peptide, C-terminal PFR proved essential for peptide binding stability to HLA-DR1 and in consequence, CD4+ T cell activation. Clonotyping of CD4+ T cells grown against peptides of varying PFR lengths showed that TCR gene selection was heavily influenced by PFR. A HIV gag24 derived peptide displaying an unusual secondary structure within its N-terminal PFR gave further insight into how seemingly small modifications to PFR can have wide reaching impact on CD4+ T cell activation. Both studies highlighted the need for more in depths investigations into this emerging field and the wide reaching impacts of this inherent feature of MHC-II restricted peptides. Overall, the results in this thesis added novel insight into the mechanisms underlying TCR/pMHC-II interactions

Age-Related Interference between the Selection of Input-Output Modality Mappings and Postural Control—a Pilot Study

Age-related decline in executive functions and postural control due to degenerative processes in the central nervous system have been related to increased fall-risk in old age. Many studies have shown cognitive-postural dual-task interference in old adults, but research on the role of specific executive functions in this context has just begun. In this study, we addressed the question whether postural control is impaired depending on the coordination of concurrent response-selection processes related to the compatibility of input and output modality mappings as compared to impairments related to working-memory load in the comparison of cognitive dual and single tasks. Specifically, we measured total center of pressure (CoP) displacements in healthy female participants aged 19–30 and 66–84 years while they performed different versions of a spatial one-back working memory task during semi- tandem stance on an unstable surface (i.e., balance pad) while standing on a force plate. The specific working-memory tasks comprised: (i) modality compatible single tasks (i.e., visual-manual or auditory-vocal tasks), (ii) modality compatible dual tasks (i.e., visual-manual and auditory-vocal tasks), (iii) modality incompatible single tasks (i.e., visual-vocal or auditory- manual tasks), and (iv) modality incompatible dual tasks (i.e., visual-vocal and auditory-manual tasks). In addition, participants performed the same tasks while sitting. As expected from previous research, old adults showed generally impaired performance under high working-memory load (i.e., dual vs. single one-back task). In addition, modality compatibility affected one-back performance in dual-task but not in single-task conditions with strikingly pronounced impairments in old adults. Notably, the modality incompatible dual task also resulted in a selective increase in total CoP displacements compared to the modality compatible dual task in the old but not in the young participants. These results suggest that in addition to effects of working- memory load, processes related to simultaneously overcoming special linkages between input- and output modalities interfere with postural control in old but not in young female adults. Our preliminary data provide further evidence for the involvement of cognitive control processes in postural tasks

Tannaka-Krein duality for Hopf algebroids

We develop the Tannaka-Krein duality for monoidal functors with target in the categories of bimodules over a ring. The \coend of such a functor turns out to be a Hopf algebroid over this ring. Using the result of a previous paper we characterize a small abelian, locally finite rigid monoidal category as the category of rigid comodules over a transitive Hopf algebroid.Comment: 25 pages, final version, to appear in Israel Journal of Mathematic

On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.Comment: additional references, fixed some typos, minor additions including a questions and some remark

Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications

In this paper we introduce generalizations of diagonal crossed products, two-sided crossed products and two-sided smash products, for a quasi-Hopf algebra H. The results we obtain may be applied to H^*-Hopf bimodules and generalized Yetter-Drinfeld modules. The generality of our situation entails that the "generating matrix" formalism cannot be used, forcing us to use a different approach. This pays off because as an application we obtain an easy conceptual proof of an important but very technical result of Hausser and Nill concerning iterated two-sided crossed products.Comment: 41 pages, no figure

Twisting algebras using non-commutative torsors

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchange

Using X-ray Crystallography, Biophysics, and Functional Assays to Determine the Mechanisms Governing T-cell Receptor Recognition of Cancer Antigens.

Human CD8+ cytotoxic T lymphocytes (CTLs) are known to play an important role in tumor control. In order to carry out this function, the cell surface-expressed T-cell receptor (TCR) must functionally recognize human leukocyte antigen (HLA)-restricted tumor-derived peptides (pHLA). However, we and others have shown that most TCRs bind sub-optimally to tumor antigens. Uncovering the molecular mechanisms that define this poor recognition could aid in the development of new targeted therapies that circumnavigate these shortcomings. Indeed, present therapies that lack this molecular understanding have not been universally effective. Here, we describe methods that we commonly employ in the laboratory to determine how the nature of the interaction between TCRs and pHLA governs T-cell functionality. These methods include the generation of soluble TCRs and pHLA and the use of these reagents for X-ray crystallography, biophysical analysis, and antigen-specific T-cell staining with pHLA multimers. Using these approaches and guided by structural analysis, it is possible to modify the interaction between TCRs and pHLA and to then test how these modifications impact T-cell antigen recognition. These findings have already helped to clarify the mechanism of T-cell recognition of a number of cancer antigens and could direct the development of altered peptides and modified TCRs for new cancer therapies