Improved approximation of phase-space densities on triangulated domains using Discrete Flow Mapping with p-refinement

We consider the approximation of the phase-space flow of a dynamical system on a triangulated surface using an approach known as Discrete Flow Mapping. Such flows are of interest throughout statistical mechanics, but the focus here is on flows arising from ray tracing approximations of linear wave equations. An orthogonal polynomial basis approximation of the phase-space density is applied in both the position and direction coordinates, in contrast with previous studies where piecewise constant functions have typically been applied for the spatial approximation. In order to improve the tractability of an orthogonal polynomial approximation in both phase-space coordinates, we propose a careful strategy for computing the propagation operator. For the favourable case of a Legendre polynomial basis we show that the integrals in the definition of the propagation operator may be evaluated analytically with respect to position and via a spectrally convergent quadrature rule for the direction coordinate. A generally applicable spectral quadrature scheme for integration with respect to both coordinates is also detailed for completeness. Finally, we provide numerical results that motivate the use of p-refinement in the orthogonal polynomial basis

Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations

textabstractThermal bath coupling mechanisms as utilized in molecular dynamics are applied to partial differential equation models. Working from a semi-discrete (Fourier mode) formulation for the Burgers–Hopf or Korteweg–de Vries equation, we introduce auxiliary variables and stochastic perturbations in order to drive the system to sample a target ensemble which may be a Gibbs state or, more generally, any smooth distribution defined on a constraint manifold. We examine the ergodicity of approaches based on coupling of the heat bath to the high wave numbers, with the goal of controlling the ensemble through the fast modes. We also examine different thermostat methods in the extent to which dynamical properties are corrupted in order to accurately compute the average of a desired observable with respect to the invariant distribution. The principal observation of this paper is that convergence to the invariant distribution can be achieved by thermostatting just the highest wave number, while the evolution of the slowest modes is little affected by such a thermostat

Stochastic-dynamical thermostats for constraints and stiff restraints

A broad array of canonical sampling methods are available for molecular simulation based on stochastic-dynamical perturbation of Newtonian dynamics, including Langevin dynamics, Stochastic Velo- city Rescaling, and methods that combine Nosé-Hoover dynamics with stochastic perturbation. In this article we discuss several stochastic-dynamical thermostats in the setting of simulating systems with holonomic constraints. The approaches described are easily implemented and facilitate the recovery of correct canonical averages with minimal disturbance of the underlying dynamics. For the purpose of illustrating our results, we examine the numerical application of these methods to a simple atomic chain, where a Fixman term is required to correct the thermodynamic ensemble

Discrete breathers in ϕ4\phi^4 and related models

We touch upon the wide topic of discrete breather formation with a special emphasis on the the $\phi^4$ model. We start by introducing the model and discussing some of the application areas/motivational aspects of exploring time periodic, spatially localized structures, such as the discrete breathers. Our main emphasis is on the existence, and especially on the stability features of such solutions. We explore their spectral stability numerically, as well as in special limits (such as the vicinity of the so-called anti-continuum limit of vanishing coupling) analytically. We also provide and explore a simple, yet powerful stability criterion involving the sign of the derivative of the energy vs. frequency dependence of such solutions. We then turn our attention to nonlinear stability, bringing forth the importance of a topological notion, namely the Krein signature. Furthermore, we briefly touch upon linearly and nonlinearly unstable dynamics of such states. Some special aspects/extensions of such structures are only touched upon, including moving breathers and dissipative variations of the model and some possibilities for future work are highlighted

ACCELERATE and European Medicines Agency Paediatric Strategy Forum for medicinal product development of checkpoint inhibitors for use in combination therapy in paediatric patients

The third multistakeholder Paediatric Strategy Forum organised by ACCELERATE and the European Medicines Agency focused on immune checkpoint inhibitors for use in combination therapy in children and adolescents. As immune checkpoint inhibitors, both as monotherapy and in combinations have shown impressive success in some adult malignancies and early phase trials in children of single agent checkpoint inhibitors have now been completed, it seemed an appropriate time to consider opportunities for paediatric studies of checkpoint inhibitors used in combination. Among paediatric patients, early clinical studies of checkpoint inhibitors used as monotherapy have demonstrated a high rate of activity, including complete responses, in Hodgkin lymphoma and hypermutant paediatric tumours. Activity has been very limited, however, in more common malignancies of childhood and adolescence. Furthermore, apart from tumour mutational burden, no other predictive biomarker for monotherapy activity in paediatric tumours has been identified. Based on these observations, there is collective agreement that there is no scientific rationale for children to be enrolled in new monotherapy trials of additional checkpoint inhibitors with the same mechanism of action of agents already studied (e.g. anti-PD1, anti-PDL1 anti-CTLA-4) unless additional scientific knowledge supporting a different approach becomes available. This shared perspective, based on scientific evidence and supported by paediatric oncology cooperative groups, should inform companies on whether a paediatric development plan is justified. This could then be proposed to regulators through the available regulatory tools. Generally, an academic-industry consensus on the scientific merits of a proposal before submission of a paediatric investigational plan would be of great benefit to determine which studies have the highest probability of generating new insights. There is already a rationale for the evaluation of combinations of checkpoint inhibitors with other agents in paediatric Hodgkin lymphoma and hypermutated tumours in view of the activity shown as single agents. In paediatric tumours where no single agent activity has been observed in multiple clinical trials of anti-PD1, anti-PDL1 and anti-CTLA-4 agents as monotherapy, combinations of checkpoint inhibitors with other treatment modalities should be explored when a scientific rationale indicates that they could be efficacious in paediatric cancers and not because these combinations are being evaluated in adults. Immunotherapy in the form of engineered proteins (e.g. monoclonal antibodies and T cell engaging agents) and cellular products (e.g. CAR T cells) has great therapeutic potential for benefit in paediatric cancer. The major challenge for developing checkpoint inhibitors for paediatric cancers is the lack of neoantigens (based on mutations) and corresponding antigen-specific T cells. Progress critically depends on understanding the immune macroenvironment and microenvironment and the ability of the adaptive immune system to recognise paediatric cancers in the absence of high neoantigen burden. Future clinical studies of checkpoint inhibitors in children need to build upon strong biological hypotheses that take into account the distinctive immunobiology of childhood cancers in comparison to that of checkpoint inhibitor responsive adult cancers