Abstract We apply deep kernel learning (DKL), which can be viewed as a combination of a Gaussian process (GP) and a deep neural network (DNN), to compression ignition engine emissions and compare its performance to a selection of other surrogate models on the same dataset. Surrogate models are a class of computationally cheaper alternatives to physics-based models. High-dimensional model representation (HDMR) is also briefly discussed and acts as a benchmark model for comparison. We apply the considered methods to a dataset, which was obtained from a compression ignition engine and includes as outputs soot and NOx emissions as functions of 14 engine operating condition variables. We combine a quasi-random global search with a conventional grid-optimization method in order to identify suitable values for several DKL hyperparameters, which include network architecture, kernel, and learning parameters. The performance of DKL, HDMR, plain GPs, and plain DNNs is compared in terms of the root mean squared error (RMSE) of the predictions as well as computational expense of training and evaluation. It is shown that DKL performs best in terms of RMSE in the predictions whilst maintaining the computational cost at a reasonable level, and DKL predictions are in good agreement with the experimental emissions data.

Background: Alzheimer’s disease (AD) trials now focus on preventative rather than reactive administration, meaning the identification and engagement of those at risk for dementia has never been more important. Models of Patient Engagement in AD (MOPEAD) aims to evaluate four patient engagement strategies for identifying individuals at risk of Alzheimer’s disease: online screening, an open house initiative, primary care engagement and tertiary care engagement. We present the interim analysis of patients recruited through the online-screening model. Methods: The online tool was available in five countries (Sweden, Slovenia, Spain, Netherlands and Germany) with localised marketing strategies. Participants completed the Cambridge Neuropsychological Test Automated Battery (CANTAB Recruit): delivering Paired Associates Learning (PAL) and Spatial Working Memory (SWM) tasks to assess episodic and working memory, respectively. An algorithm was then applied to automatically score participants against pre-set criteria for further diagnostic evaluation. Results: As of February 2019, the website had received 15,000 visits and approximately 1500 participants had been screened via the web-based platform on CANTAB tests, with 75% compliance. The number of participants recruited differed by country with Germany recruiting the lowest number (n 1⁄4 32) while Slovenia met the target already (n 1⁄4 400). Demographic data showed the target age range of 65-85 years old was achieved across all five countries (Females mean age 69 years (SD 4.96 years); Males mean age 70 years (SD 5.37 years)). Age-related performance changes on CANTAB tests, across gender and education met expectations. Overall, 38% of participants met the criteria for further diagnostic evaluation. For four countries, a large proportion recruited were healthy adults, thus between 60-65% of participants did not meet criteria. Conversely, in the Netherlands, 53% of participants met the criteria for impairment. These differences could be partially attributed to the localised marketing strategy. Conclusions: This interim analysis has demonstrated that older adults (65-85 years old) are willing and able to engage in web-based assessments. Furthermore, CANTAB Recruit provides an effective strategy to identify those with impairments in episodic and working memory domains. The feasibility and sensitivity of online screening for older adults at risk of Alzheimer’s disease is encouraging.

This paper addresses the issue of modeling meanfield behavior in heterogeneous populations of linear timeinvariant SISO systems. Our analysis is conducted in the frequency domain, where the heterogeneity of input-output mappings (transfer functions) is modeled as a complex-valued Gaussian process. The mean-field model of diffusively coupled agents is obtained as a Gaussian approximation of averaged input-output behavior. It is shown that the strong coupling and the large number of agents reduce the population variance.

The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion paper is to point out some open problems in the theory of PDE and compartmental ODE models of balanced reaction-diffusion networks.

Dit proefschrift behandelt de structuurbehoudende discretisatie van open ver-deelde-parameter systemen met gegeneraliseerde Hamiltonse dynamica. Gebruikmakend van het formalisme van discrete uitwendige differentiaalrekening voer ik simpliciale Diracstructuren in als discrete analogieen van de Stokes-Diracstructuur, en laat ik zien hoe zij een natuurlijk kader bieden om eindigdimensionale poort-Hamiltonse systemen af te leiden die hun oneindigdimensionale tegenhangers nabootsen. Het ruimtelijke domein, in de continue theorie weergegeven door een eindigdimensionale gladde varieteit met rand, wordt vervangen door een homologisch simpliciaal complex en zijn circumcentrische duale. De gladde differentiaalvormen worden in de discrete context vervangen door co-ketens op de primaire en duale complexen, terwijl de discrete uitwendige afgeleide wordt gedefinieerd met behulp van de duale randoperator. Deze benadering door middel van de meetkunde van discrete uitwendige differentiaalrekening maakt het mogelijk om, anders dan het discretiseren van de partiele differentiaalvergelijkingen, eerst de onderliggende Stokes-Diracstruc-tuur te discretiseren en daarna de eindigdimensionale poort-Hamiltonse dynamica hierop te definieren. Op deze manier worden een aantal belangrijke intrinsieke topologische en meetkundige eigenschappen van het systeem behouden. Ik pas deze algemene beschouwingen toe op een aantal fysische voorbeelden, waaronder reactie-diffusie systemen, in welk geval de structuurbehoudende discretisatie het standaard compartimentele model oplevert. Vervolgens laat ik zien hoe op een soortgelijke manier een Poissonsymmetrie reductie van Diracstructuren geassocieerd met oneindig- en eindigdimensionale modellen kan worden uitgevoerd.

Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying manifold leads to the so-called simplicial Dirac structures, discrete analogues of Stokes-Dirac structures, and thus provides a natural framework for deriving finite-dimensional port-Hamiltonian systems that emulate their infinite-dimensional counterparts. The port-Hamiltonian systems defined with respect to Stokes-Dirac and simplicial Dirac structures exhibit gauge and a discrete gauge symmetry, respectively. In this paper, employing Poisson reduction we offer a unified technique for the symmetry reduction of a generalized canonical infinite-dimensional Dirac structure to the Poisson structure associated with Stokes-Dirac structures and of a fine-dimensional Dirac structure to simplicial Dirac structures. We demonstrate this Poisson scheme on a physical example of the vibrating string.

Geometric structures behind a variety of physical systems stemming from mechanics, electromagnetism and chemistry exhibit a remarkable unity enunciated by Dirac structures. The open dynamical systems defined with respect to these structures belong to the class of so-called port-Hamiltonian systems. These systems arise naturally from the energybased modeling. Apart from offering a geometric content of Hamiltonian systems, Dirac structures supply a framework for modeling port-Hamiltonian systems as interconnected and constrained systems. From a network-modeling perspective, this means that port-Hamiltonian systems can be reticulated into a set of energy-storing elements, a set of energy-dissipating elements, and a set of energy port by which the interconnection of these blocks and environment is modeled. It is well-known that such a modeling strategy also utilizes control synthesis for these systems. The port-Hamiltonian formalism transcends the lumpedparameter scenario and has been successfully applied to study of a number of distributed-parameter systems [1]. The centrepiece of the efforts concerning infinite-dimensional case is the Stokes-Dirac structure. The canonical StokesDirac structure is an infinite-dimensional Dirac structure de- fined in terms of differential forms on a smooth manifold with boundary. The Hamiltonian equations associated to this Dirac structure.

Abstract This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by the coboundary operators. This finite-dimensional Dirac structure, as discrete analogue of the canonical Stokes-Dirac structure, allows for the formulation of finite-dimensional port-Hamiltonian systems that emulate the behaviour of the open distributed-parameter systems with Hamiltonian dynamics.