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Significance The duration of cerebral ischemia is a key factor in determining the severity of brain damage and the course of action. Thus, an accurate and timely observation of the ischemic process is highly critical. Here we present a molecular neuroimaging approach that enables direct detection and real-time visualization of transient cerebral ischemia. The method relies on high-resolution observation of extracellular calcium alterations associated with the spatiotemporal dynamics of cerebral ischemia, using a selective molecular MRI probe. The rapid detection of calcium fluctuations in healthy and disease states will not only lead to essential insights for successful treatment and recovery of ischemic brain tissue but will also improve our understanding of the underlying neurobiology of neurological and psychiatric disorders., Cerebral ischemia is one of the leading causes of mortality and disability in infants and adults and its timely diagnosis is essential for an efficient treatment. We present a methodology for fast detection and real-time monitoring of fluctuations of calcium ions associated with focal ischemia using a molecular functional MRI approach. We used a dinuclear paramagnetic gadolinium(III) complex chelate that changes MR image contrast through its reversible interaction with extracellular calcium ions, while applying a remote transient middle cerebral artery occlusion as a model for ischemic stroke. Our method sensitively recognizes the onset and follows the dynamics of the ischemic core and penumbra with submillimeter spatial and second-scale temporal resolution, thus paving the way for noninvasive monitoring and development of targeted treatment strategies for cerebral ischemia.

Functional Magnetic Resonance Imaging, fMRI, is a technique used in neuroscience to measurebrain activity based on any signal that can be measured in an MRI scanner. Normally, fMRI isused to detect changes associated with blood flow, but it can also be used to detect changes inconcentrations of molecules with different magnetic properties that might be directly injectedinto the brain of a subject.Regardless of the signal that is measured in fMRI recordings, from a computational pointof view, fMRI recordings will result in a number of time-series. And then those time-seriesshould be analyzed to find the answers to various questions of interest. The length of thetime-series depends on the number of time-steps in which we have measured the signals, andtheir number depends on how-many voxels we have measured (a voxel is a 3-dimensional pixelor the unit of volume in which each fMRI signal is measured). The size of each of these voxelsdepends on the magnetic flux density of the MRI scanner, measured in Tesla (T). The higherthe magnetic flux density, the smaller the voxels can be, and the higher is the spatial resolutionof the measurements. Hence, we end up with one time-series for each of the voxels arrangedin a 3-dimensional structure. One characteristic of the fMRI measurements is that while theycan have a high spatial resolution, and while they allow us to measure brain activity not onlyin the cortex but also in deeper regions of the brain, their temporal resolution is not normallyhigh. And that can provide challenges for researchers who need to analyze the fMRI data.

This paper presents a method to predict the spread of the SARS-CoV-2 in a population with a known age-structure, and then, to quantify the effects of various containment policies, including those policies that affect each age-group differently. The model itself is a compartmental model in which each compartment is divided into a number of age-groups. The parameters of the model are estimated using an optimisation scheme and some known results from the theory of monotone systems such that the model output agrees with some collected data on the spread of SARS-CoV-2.To highlight the strengths of this framework, a few case studies are presented in which different populations are subjected to different containment strategies. They include cases in which the containment policies switch between scenarios with different levels of severity. Then a case study on herd immunity due to vaccination is presented. And then it is shown how we can use this framework to optimally distribute a limited number of vaccine units in a given population to maximise their impact and reduce the total number of infectious individuals.MSC subclass92C60, 92C50

To understand the function of cortical circuits, it is necessary to catalog their cellular diversity. Past attempts to do so using anatomical, physiological or molecular features of cortical cells have not resulted in a unified taxonomy of neuronal or glial cell types, partly due to limited data. Single-cell transcriptomics is enabling, for the first time, systematic high-throughput measurements of cortical cells and generation of datasets that hold the promise of being complete, accurate and permanent. Statistical analyses of these data reveal clusters that often correspond to cell types previously defined by morphological or physiological criteria and that appear conserved across cortical areas and species. To capitalize on these new methods, we propose the adoption of a transcriptome-based taxonomy of cell types for mammalian neocortex. This classification should be hierarchical and use a standardized nomenclature. It should be based on a probabilistic definition of a cell type and incorporate data from different approaches, developmental stages and species. A community-based classification and data aggregation model, such as a knowledge graph, could provide a common foundation for the study of cortical circuits. This community-based classification, nomenclature and data aggregation could serve as an example for cell type atlases in other parts of the body.

This chapter describes the impacts that time delays in feedback have on small signal as well as transient stability of power systems. We present a power system model comprising of delay differential-algebraic equations (DDAEs) and describe general techniques to compute the spectrum of DDAE and to integrate such equations in time domain. The focus is on delays arising in measured signals, e.g., remote frequency measurements for power system stabilizers (PSS) of synchronous machines. Several examples based on a benchmark system, the IEEE 14-bus test system, as well as a real-world system are discussed and analysed.

We study the spread of disease in an SIS model for a structured population. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold parameter for this model in the spirit of the basic reproduction number for time-invariant models. We also present conditions for persistence and the existence of periodic orbits for the switched model and results for a stochastic switched model.

This paper presents a stability analysis of power system stabilizers (PSS) for synchronous generators with inclusion of time delays. The paper shows that a time delay in the PSS feedback loop can improve the small-signal stability of a power system if the regulator gain is properly tuned. The paper provides a proof-of-principle analysis based on the classical model of the synchronous machine as well as a case study based on a detailed transient model of the IEEE 14-bus test system. The paper also provides a discussion on the practical implications that the properties of delayed PSS can have on the control of synchronous machines and of the whole power system.

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems., Comment: 9 pages

Building on recent work on homogeneous cooperative systems, we extend results concerning stability of such systems to subhomogeneous systems. We also consider subhomogeneous cooperative systems with constant input, and relate the global asymptotic stability of the unforced system to the existence and stability of positive equilibria for the system with input.

We correct some errors in the statements and proofs presented in Section V of the above mentioned manuscript.

We introduce a nonlinear definition of D-stability, extending the usual concept for positive linear time-invariant systems. We show that globally asymptotically stable, cooperative systems, homogeneous of any order with respect to arbitrary dilation maps are D-stable. We also prove a strong stability result for delayed cooperative homogeneous systems. Fi- nally, we show that both of these results also hold for planar cooperative systems without the restriction of homogeneity.

We consider a number of questions pertaining to the stability of positive switched linear systems. Recent results on common quadratic, diagonal, and copositive Lyapunov function existence are reviewed and their connection to the stability properties of switched positive linear systems is highlighted. We also generalise the concept of D-stability to positive switched linear systems and present some preliminary results on this topic.