Our recent work on linear and affine dynamical systems has laid out a general framework for inferring the parameters of a differential equation model from a discrete set of data points collected from a system being modeled. It introduced a new class of inverse problems where qualitative information about the parameters and the associated dynamics of the system is determined for regions of the data space, rather than just for isolated experiments. Rigorous mathematical results have justified this approach and have identified common features that arise for certain classes of integrable models. In this work we present a thorough numerical investigation that shows that several of these core features extend to a paradigmatic linear-in-parameters model, the Lotka–Volterra (LV) system, which we consider in the conservative case as well as under the addition of terms that perturb the system away from this regime. A central construct for this analysis is a concise representation of parameter and dynamical features in the data space that we call the
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Abstract P n -diagram, which is particularly useful for visualization of the qualitative dependence of the system dynamics on data for low-dimensional (smalln ) systems. Our work also exposes some new properties related to non-uniqueness that arise for these LV systems, with non-uniqueness manifesting as a multi-layered structure in the associatedP 2-diagrams. -
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Abstract The Kölliker–Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnoea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apnoeas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupnoeic as well as RTT‐like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT‐like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late‐expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing.
image Key points The Kölliker–Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation.
Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modelling to explore different dynamical regimes of KF activity and their compatibility with experimental observations.
By analysing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT‐like respiratory patterns and proposes potential KF local circuit organizations.
Two models are presented that simulate both normal breathing and RTT‐like breathing patterns.
These models provide testable hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.
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Free, publicly-accessible full text available September 1, 2024
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null (Ed.)A bstract A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining four single-spin and four double-spin asymmetries allowed in the one-photon-exchange approximation of the semi-inclusive deep-inelastic scattering process for target-polarization orientation perpendicular to the direction of the incoming lepton beam. Among those results, significant non-vanishing cos ( ϕ−ϕ S ) modulations provide evidence for a sizable worm-gear (II) distribution, $$ {g}_{1\mathrm{T}}^q\left(x,{\mathrm{p}}_T^2\right) $$ g 1 T q x p T 2 . Most of the other modulations are found to be consistent with zero with the notable exception of large sin ( ϕ S ) modulations for charged pions and K + .more » « less
