The Angiopoietin ligands and Tie receptors: potential diagnostic biomarkers of vascular disease

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The Angiopoietin-1 (Angpt1)/Tie2 signaling pathway is important in regulating vascular function. Angpt1-induced Tie2 activation promotes vascular endothelial cell survival and reduces vascular leakage. Angiopoietin-2 (Angpt2), a weak agonist/antagonist of Tie2, opposes and regulates Angpt1 action. The Tie family of receptor tyrosine kinases, Tie2 and Tie1, exist as either homo-or heterodimers. The molecular complex between the receptors is also crucial in controlling Angpt1 signaling; hence, the molecular balance between Angpt1:Angpt2 and Tie2:Tie1 is important in determining endothelial integrity and vascular stability. This review presents evidence of the change observed in the Angiopoietin/Tie molecules in various pathophysiological conditions and discusses the potential clinical applications of these molecules in vascular complications

Singular SPDEs on Homogeneous Lie Groups

The aim of this article is to extend the scope of the theory of regularity structures in order to deal with a large class of singular SPDEs of the form $$\partial_t u = \mathfrak{L} u+ F(u, \xi)\ ,$$ where the differential operator $\mathfrak{L}$ fails to be elliptic. This is achieved by interpreting the base space $\mathbb{R}^{d}$ as a non-trivial homogeneous Lie group $\mathbb{G}$ such that the differential operator $\partial_t -\mathfrak{L}$ becomes a translation invariant hypoelliptic operator on $\mathbb{G}$. Prime examples are the kinetic Fokker-Planck operator $\partial_t -\Delta_v - v\cdot \nabla_x$ and heat-type operators associated to sub-Laplacians. As an application of the developed framework, we solve a class of parabolic Anderson type equations $$\partial_t u = \sum_{i} X^2_i u + u (\xi-c)$$ on the compact quotient of an arbitrary Carnot group

Singular SPDEs on Homogeneous Lie Groups

The aim of this article is to extend the scope of the theory of regularity structures in order to deal with a large class of singular SPDEs of the form $$\partial_t u = \mathfrak{L} u+ F(u, \xi)\ ,$$ where the differential operator $\mathfrak{L}$ fails to be elliptic. This is achieved by interpreting the base space $\mathbb{R}^{d}$ as a non-trivial homogeneous Lie group $\mathbb{G}$ such that the differential operator $\partial_t -\mathfrak{L}$ becomes a translation invariant hypoelliptic operator on $\mathbb{G}$. Prime examples are the kinetic Fokker-Planck operator $\partial_t -\Delta_v - v\cdot \nabla_x$ and heat-type operators associated to sub-Laplacians. As an application of the developed framework, we solve a class of parabolic Anderson type equations $$\partial_t u = \sum_{i} X^2_i u + u (\xi-c)$$ on the compact quotient of an arbitrary Carnot group

Periodic space-time homogenisation of the ϕ24\phi^4_2 equation

We consider the homogenisation problem for the $\phi^4_2$ equation on the torus $\mathbb{T}^2$, namely the behaviour as $\varepsilon \to 0$ of the solutions to the equation \textit{suggestively} written as $$\partial_t u_\varepsilon - \nabla\cdot {A}(x/\varepsilon,t/\varepsilon^2) \nabla u_\varepsilon = -u^3_\varepsilon +\xi$$ where $\xi$ denotes space-time white noise and $A: \mathbb{T}^2\times \mathbb{R}$ is uniformly elliptic, periodic and H\"older continuous. When the noise is regularised at scale $\delta \ll 1$ we show that any joint limit $\varepsilon,\delta \to 0$ recovers the classical dynamical $\phi^4_2$ model. In certain regimes or if the regularisation is chosen in a specific way adapted to the problem, we show that the counterterms can be chosen as explicit local functions of $A$.Comment: 43 page

The effect of interleukin 1 on vascular angiopoietin 1 signalling

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Open access

Strong convergence of parabolic rate 11 of discretisations of stochastic Allen-Cahn-type equations

Consider the approximation of stochastic Allen-Cahn-type equations (i.e. $1+1$-dimensional space-time white noise-driven stochastic PDEs with polynomial nonlinearities $F$ such that $F(\pm \infty)=\mp \infty$) by a fully discrete space-time explicit finite difference scheme. The consensus in literature, supported by rigorous lower bounds, is that strong convergence rate $1/2$ with respect to the parabolic grid meshsize is expected to be optimal. We show that one can reach almost sure convergence rate $1$ (and no better) when measuring the error in appropriate negative Besov norms, by temporarily `pretending' that the SPDE is singular.Comment: 28 page

The use of near-peer tutors to improve level of learning & confidence in areas of human physiology

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This study investigates the impact near-peer tutors (NPTs) have on the learning experience of students enrolled on the biomedical and medical science programmes at De Montfort University, UK. Using a questionnaire, tutees were able to comment on their confidence level on certain academic taught topics in human physiology before and after attending near-peer tutored sessions. Statistical analysis showed a significant increase in the level of confidence observed by the tutees after attending the sessions (before vs after, p < 0.05). Tutees enjoyed the level of interaction and active learning with huge praise towards the NPTs. Qualitative data were also captured on the experience and skills gained by NTPs. The near-peer tutors highlighted the importance of these sessions in enhancing their knowledge and gaining valuable employability skills for the workplace. In conclusion, supporting lecturers with additional student-led sessions improved confidence levels and understanding of topics in human physiology among tutees. Having similar NPTs sessions across programmes can prove to be beneficial to student engagement & learning in higher educatio