Mathematical Sciences- Journal Articles
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Item Comparison of a novel methadone rotation method with other commonly used methods(BMJ Publishing Group, 2024) Cunningham, Elaine; DiBiagio, Nicole; O’Connell, Florry; Flannery, Maedhbh; Cronin, Michael; Murphy, Marie; O’Leary, Mary Jane; Kiely, Fiona; Lowney, Aoife C.Objectives To compare a novel method of methadone rotation used in a specialist palliative care inpatient unit (SPCU) in Cork, Ireland, with rapid titration methods using Perth and Brisbane Protocols as well as the Edmonton method of methadone rotation. Methods A retrospective chart review was performed in March–June 2022. All patients who completed rotation to methadone during 2018–2019 in the SPCU were included. 2018–2019 was selected to study a population not affected by the coronavirus pandemic. Oral morphine equivalent (OME) was calculated using the opioid conversion chart. From the OME, the expected daily methadone dose was calculated using the Perth, Brisbane and Edmonton methods. These figures were then compared directly with the actual methadone doses achieved using our dosing schedule. Results A comparison of the expected doses using the Perth and Brisbane rapid titration protocols and stable daily dose achieved revealed that the stable methadone dose was significantly lower than both rapid titration protocols (p=<0.0001) and (p=0.0035, respectively). However, a comparison of the expected dose using the Edmonton method and the dose achieved did not determine any significant difference (p=0.7602). Conclusions This is the first evaluation of a novel Irish method of methadone rotation and demonstrates a lower overall daily methadone dose compared with established protocols.Item Time-resolved eye diagrams to exploit hidden high-energy branches in a nonlinear wideband vibration-energy harvester(American Physical Society, 2023-08-01) Paul, Kankana; Roy, Saibal; Amann, Andreas; Science Foundation Ireland; Horizon 2020A wideband vibration energy harvester with multiple nonlinear forces is investigated. The nonlinearities are due to repulsive magnets and hardening springs, which gives rise to multistabilities between a number of energy branches. Not all branches are accessible by a simple up or down sweep of the driving frequency and in particular the highest energy branch is often hidden, requiring a suitable frequency schedule to be accessed. Detailed theoretical understanding of the energy branch structure along with robust experimental methods are essential for characterizing each of the energy branches to enhance the energy output from such a vibration energy harvesting system. We introduce a graphical representation in the form of eye diagrams based on time-resolved measurements of acceleration and output voltage to study the dynamical features of the different branches. This generic approach allows us to optimize the design, which results in 1.3 mW of power generated at 1 g over the 44-Hz frequency bandwidth while maintaining a small footprint of 1.23 cm3. The energy conversion ratio of the energy harvester at 120-Hz drive frequency is 0.52 for the high-energy branch.Item A restricted 2-plane transform related to Fourier restriction for surfaces of codimension 2(Mathematical Sciences Publishers, 2025) Dendrinos, Spyridon; Mustaţă, Andrei; Vitturi, MarcoWe draw a connection between the affine invariant surface measures constructed by P. Gressman in [30] and the boundedness of a certain geometric averaging operator associated to surfaces of codimension 2 and related to the Fourier Restriction Problem for such surfaces. For a surface given by (ξ, Q1(ξ), Q2(ξ)), with Q1, Q2 quadratic forms on Rd, the particular operator in question is the 2-plane transform restricted to directions normal to the surface, that is T f(x, ξ) := Z Z |s|,|t|≤1 f(x − s∇Q1(ξ) − t∇Q2(ξ), s, t) ds dt, where x, ξ ∈ Rd. We show that when the surface is well-curved in the sense of Gressman (that is, the associated affine invariant surface measure does not vanish) the operator satisfies sharp Lp → Lq inequalities for p, q up to the critical point. We also show that the well-curvedness assumption is necessary to obtain the full range of estimates. The proof relies on two main ingredients: a characterisation of well-curvedness in terms of properties of the polynomial det(s∇2Q1 + t∇2Q2), obtained with Geometric Invariant Theory techniques, and Christ’s Method of Refinements. With the latter, matters are reduced to a sublevel set estimate, which is proven by a linear programming argumentItem Synchronization cluster bursting in adaptive oscillator networks(AIP Publishing, 2024-12-24) Wei, Mengke; Amann, Andreas; Burylko, Oleksandr; Han, Xiujing; Yanchuk, Serhiy; Kurths, Jürgen; Deutsche Forschungsgemeinschaft; China Scholarship Council; Potsdam Institute for Climate Impact Research; National Natural Science Foundation of ChinaAdaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our numerical observations reveal the emergence of synchronization cluster bursting, characterized by periodic transitions between cluster synchronization and global synchronization. By investigating a reduced model, the mechanisms underlying synchronization cluster bursting are clarified. We show that a minimal model exhibiting this phenomenon can be reduced to a phase oscillator with complex-valued adaptation. Furthermore, the adaptivity of the system leads to the appearance of additional symmetries, and thus, to the coexistence of stable bursting solutions with very different Kuramoto order parameters.Item Quantum stochastic cocycles and completely bounded semigroups on operator spaces(Oxford University Press, 2013-03-06) Lindsay, J. Martin; Wills, Stephen J.; UK-India Education and Research InitiativeAn operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analog of stochastic semigroups in the sense of Skorohod. One-to-one correspondences are established between classes of cocycle of interest and corresponding classes of one-parameter semigroups on associated matrix spaces. Each of these “global” semigroups may be viewed as the expectation semigroup of an associated quantum stochastic cocycle on the corresponding matrix space. Proof of the two key characterizations, namely that of completely positive contraction cocycles on a C*-algebra, and contraction cocycles on a Hilbert space, involves all of the analysis undertaken here. As indicated by Accardi and Kozyrev, the Schur-action matrix semigroup viewpoint circumvents technical (domain) limitations inherent in the theory of quantum stochastic differential equations.