Regular and Singular Pulse and Front Solutions and Possible Isochronous Behavior in the Short-Pulse Equation: Phase-Plane, Multi-Infinite Series and Variational Approaches

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.Comment: accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

Exploring flexible polynomial regression as a method to align routine clinical outcomes with daily data capture through remote technologies

Data Availability: The data that support the findings of this study are available from Great Ormond Street Hospital, but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Great Ormond Street Hospital.Copyright © The Author(s) 2023. Background: Clinical outcomes are normally captured less frequently than data from remote technologies, leaving a disparity in volumes of data from these different sources. To align these data, flexible polynomial regression was investigated to estimate personalised trends for a continuous outcome over time. Methods: Using electronic health records, flexible polynomial regression models inclusive of a 1st up to a 4th order were calculated to predict forced expiratory volume in 1 s (FEV1) over time in children with cystic fibrosis. The model with the lowest AIC for each individual was selected as the best fit. The optimal parameters for using flexible polynomials were investigated by comparing the measured FEV1 values to the values given by the individualised polynomial. Results: There were 8,549 FEV1 measurements from 267 individuals. For individuals with > 15 measurements (n = 178), the polynomial predictions worked well; however, with < 15 measurements (n = 89), the polynomial models were conditional on the number of measurements and time between measurements. The method was validated using BMI in the same population of children. Conclusion: Flexible polynomials can be used to extrapolate clinical outcome measures at frequent time intervals to align with daily data captured through remote technologies.UCL, GOSH and Toronto SickKids studentship. GD is supported by a Future Leaders Fellowship from UK Research & Innovation (UKRI), Grant reference: MR/T041285. All research at Great Ormond Street Hospital NHS Foundation Trust and UCL Great Ormond Street Institute of Child Health is made possible by the NIHR Great Ormond Street Hospital Biomedical Research Centre

Non-classical symmetries and the singular manifold method: A further two examples

This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the equations to ordinary differential equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics

Real-world effectiveness of airway clearance techniques in children with cystic fibrosis

Data Availability Statement - The study protocol is published open access. De-identified participant data are hosted in a secure DRE through GOSH DRIVE (www.goshdrive.com). Access to the data, data dictionary and informed consent forms through the DRE is available with permission from the corresponding author.Background Cystic fibrosis (CF) is commonly characterised by thick respiratory mucus. From diagnosis, people with CF are prescribed daily physiotherapy, including airway clearance techniques (ACTs). ACTs consume a large proportion of treatment time, yet the efficacy and effectiveness of ACTs are poorly understood. This study aimed to evaluate associations between the quality and quantity of ACTs and lung function in children and young people with CF. Methods Project Fizzyo, a longitudinal observational cohort study in the UK, used remote monitoring with electronic pressure sensors attached to four different commercial ACT devices to record real-time, breath-by-breath pressure data during usual ACTs undertaken at home over 16 months in 145 children. ACTs were categorised either as conformant or not with current ACT recommendations based on breath pressure and length measurements, or as missed treatments if not recorded. Daily, weekly and monthly associations between ACT category and lung function were investigated using linear mixed effects regression models adjusting for clinical confounders. Results After exclusions, 45 224 ACT treatments (135 individuals) and 21 069 days without treatments (141 individuals) were analysed. The mean±SD age of participants was 10.2±2.9 years. Conformant ACTs (21%) had significantly higher forced expiratory volume in 1 s (FEV1) (mean effect size 0.23 (95% CI 0.19–0.27) FEV1 % pred per treatment) than non-conformant (79%) or missed treatments. There was no benefit from non-conformant or missed treatments and no significant difference in FEV1 between them (mean effect size 0.02 (95% CI −0.01–0.05) FEV1 % pred per treatment). Conclusions ACTs are beneficial when performed as recommended, but most people use techniques that do not improve lung function. Work is needed to monitor and improve ACT quality and to increase the proportion of people doing effective airway clearance at home.UK Research and Innovation MR/T041285/1 Rosetrees Trust M712 Cystic Fibrosis Trust CEA010 Great Ormond Street Hospital for Children Higher Education Funding Council for England KEI2017–01–04 Hospital for Sick Children University College London Partners Awar

Regulation of aldosterone secretion by Ca(v)1.3

This work is supported by NIHR Senior Investigator grant NF-SI-0512-10052 awarded to M.J.B.; the Austin Doyle Award (Servier Australia) and the Tunku Abdul Rahman Centenary Fund (St Catharine's College, Cambridge, UK) awarded to E.A.B.A.; Gates Cambridge Scholarship awarded to C.B.X.; L.H.S., S.G. and C.M. are supported by the British Heart Foundation PhD studentship FS/11/35/28871, FS/14/75/31134 and FS/14/12/30540 respectively; J.Z. was supported by the Cambridge Overseas Trust Scholarship and the Sun Hung Kai Properties-Kwoks’ Foundation; A.E.D.T. is funded by the Agency for Science, Technology & Research (A*STAR) Singapore and Wellcome Trust Award 085686/Z/08/A; LHS, JZ and EABA were further supported by the NIHR Cambridge Biomedical Research Centre; the Human Research Tissue Bank is supported by the NIHR Cambridge Biomedical Research Centre. The Cav1.3 constructs were kindly gifted by Dr. Joerg Striessnig and Dr Petronel Tuluc

Quantity and quality of airway clearance in children and young people with cystic fibrosis

Supplementary materials are online at: https://www.sciencedirect.com/science/article/pii/S1569199322006865#sec0016 .Children and young people with CF (CYPwCF) get advice about using positive expiratory pressure (PEP) or oscillating PEP (OPEP) devices to clear sticky mucus from their lungs. However, little is known about the quantity (number of treatments, breaths, or sets) or quality (breath pressures and lengths) of these daily airway clearance techniques (ACTs) undertaken at home. This study used electronic pressure sensors to record real time breath-by-breath data from 145 CYPwCF (6–16y) during routine ACTs over 2 months. ACT quantity and quality were benchmarked against individual prescriptions and accepted recommendations for device use. In total 742,084 breaths from 9,081 treatments were recorded. Individual CYPwCF maintained consistent patterns of ACT quantity and quality over time. Overall, 60% of CYPwCF did at least half their prescribed treatments, while 27% did fewer than a quarter. About 77% of pre-teens did the right number of daily treatments compared with only 56% of teenagers. CYPwCF usually did the right number of breaths. ACT quality (recommended breath length and pressure) varied between participants and depended on device. Breath pressures, lengths and pressure-length relationships were significantly different between ACT devices. PEP devices encouraged longer breaths with lower pressures, while OPEP devices encouraged shorter breaths with higher pressures. More breaths per treatment were within advised ranges for both pressure and length using PEP (30–31%) than OPEP devices (1–3%). Objective measures of quantity and quality may help to optimise ACT device selection and support CYPwCF to do regular effective ACTs.Project Fizzyo was supported by the UCL Rosetrees Stoneygate prize (M712), a Cystic Fibrosis Trust Clinical Excellence and Innovation Award (CEA010), A UCL Partners award and the HEFCE Higher Education Innovation Fund (KEI2017–01–04). HD was funded by the CF Trust Youth Activity Unlimited SRC and an NIHR GOSH BRC internship. All work at UCL GOSICH is supported by the NIHR GOSH BRC

Lagrangian Dynamics And Possible Isochronous Behavior In Several Classes Of Non-Linear Second Order Oscillators Via The Use Of Jacobi Last Multiplier

Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane-Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler-Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical results and attempt to map the potential term to either the simple harmonic oscillator or the isotonic potential for specific values of the coefficient parameters of each non-linear oscillator. We find non-trivial parameter sets corresponding to isochronous dynamics in some of the considered systems, but none in others. Finally, the Lagrangians obtained here are coupled to Noether\u27s theorem, leading to non-trivial conservation laws for several of the oscillators

Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier

In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane\u2013Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler\u2013Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical results and attempt to map the potential term to either the simple harmonic oscillator or the isotonic potential for specific values of the coefficient parameters of each non-linear oscillator. We find non-trivial parameter sets corresponding to isochronous dynamics in some of the considered systems, but none in others. Finally, the Lagrangians obtained here are coupled to Noether\u5f3s theorem, leading to non-trivial conservation laws for several of the oscillators

Two New Inscriptions from İzmir (Smyrna)

[No abstract available

Regular And Singular Pulse And Front Solutions And Possible Isochronous Behavior In The Extended-Reduced Ostrovsky Equation: Phase-Plane, Multi-Infinite Series And Variational Formulations

In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding traveling-wave equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the exROE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized exROE equations considered here, the results obtained are both new and timely