Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Using Protein Homology Models for Structure-Based Studies: Approaches to Model Refinement

Homology modeling is a computational methodology to assign a 3-D structure to a target protein when experimental data are not available. The methodology uses another protein with a known structure that shares some sequence identity with the target as a template. The crudest approach is to thread the target protein backbone atoms over the backbone atoms of the template protein, but necessary refinement methods are needed to produce realistic models. In this mini-review anchored within the scope of drug design, we show the validity of using homology models of proteins in the discovery of binders for potential therapeutic targets. We also report several different approaches to homology model refinement, going from very simple to the most elaborate. Results show that refinement approaches are system dependent and that more elaborate methodologies do not always correlate with better performances from built homology models

Direct identification of continuous-time LPV models

Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuous time (CT) requiring accurate and low-order CT models of the system. Nonetheless, most of the methods dedicated to the identification of LPV systems are addressed in the discrete-time setting. In practice when discretizing models which are naturally expressed in CT, the dependency on the scheduling variables becomes non-trivial and over-parameterized. Consequently, direct identification of CT-LPV systems in an input-output setting is investigated. To provide consistent model parameter estimates in this setting, a refined instrumental variable approach is proposed. The statistical properties of this approach are demonstrated through a Monte Carlo simulation example

Identification of input-output LPV models

This chapter presents an overview of the available methods for identifying input-output LPV models both in discrete time and continuous time with the main focus on noise modeling issues. First, a least-squares approach and an instrumental variable method are presented for dealing with LPV-ARX models. Then, a refined instrumental variable approach is discussed to address more sophisticated noise models like Box-Jenkins in the LPV context. This latter approach is also introduced in continuous time and efficient solutions are proposed for both the problem of time-derivative approximation and the issue of continuous-time modeling of the noise

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

The menopause transition in women living with HIV: current evidence and future avenues of research

As the life expectancy of people living with HIV improves as a result of antiretroviral therapy, increasing numbers of women living with HIV (WLHIV) are now reaching menopausal age. The menopause transition in WLHIV remains a relatively overlooked area in clinical HIV research. Whilst there is some evidence to suggest that WLHIV experience menopause at an earlier age and that they have more menopausal symptoms, there is no clear consensus in the literature around an impact of HIV infection on either timing or symptomatology of the menopause. Data are also conflicting on whether HIV-related factors such as HIV viral load and CD4 cell count have an impact on the menopause. Furthermore, menopausal symptoms in WLHIV are known to go under-recognised by both healthcare providers and women themselves. There is likely to be a burden of unmet health needs among WLHIV transitioning through the menopause, with significant gaps in the evidence base for their care. With this in mind, we have developed the PRIME study (Positive Transitions Through the Menopause). This mixed-methods observational study will explore, for the first time in the UK, the impact of the menopause on the health and wellbeing of 1500 ethnically diverse WLHIV. In establishing a cohort of women in their midlife and following them up longitudinally, we hope to develop a nuanced understanding of the gendered aspects of ageing and HIV, informing the provision of appropriate services for WLHIV to ensure that they are supported in maintaining optimal health and wellbeing as they get older