Models and observations from real savanna ecosystems and drylands have suggested that they may exhibit both tipping behavior as well as spatial pattern formations. Moreover, spatial ecosystem structures, such as vegetation patterns, are important to predict ecosystem response in the face of environmental change. As ecosystems are inherently spatial, it is important to understand the effects of incorporating spatial processes in models, and how those insights translate to the real world. However, typically ecosystem models that predict tipping do not resolve space explicitly. It predicts potential critical transition from one ecosystem state to a completely different state under increasing environmental stress. ![]() The theory of alternative stable states and tipping points has garnered a lot of attention in the last decades. Rethinking tipping points in spatial ecosystems | 11am, 4th May 2023 This is the first time that such a model is validated on a fully independent cohort without the need for iEEG recordings. Individualised computational models may inform surgical planning by suggesting optimal resection strategies and informing on the likelihood of a good outcome after a proposed resection. The actual resection also overlapped more with the optimal one (AUC=0.64) and had a larger effect decreasing modelled seizure propagation (AUC=0.78) for patients with good outcome. Using the model to find optimal resection strategies, we found smaller resections (AUC=0.65) for patients with good outcome, indicating intrinsic differences in the presurgical data of patients with good and bad outcome. As a consequence iEEG data (highly invasive and not always part of the presurgical evaluation) was not required. We validated the use of the model in the clinic with a blind, independent pseudo-prospective study (N=34) using the parameters as in the retrospective study to avoid over-fitting. Remarkably, the SIR model parameters that best describe the iEEG seizure patterns correspond to the critical transition between the percolating and absorbing phases of the SIR model, and the similarity between the iEEG and modelled seizure predicted surgical outcome (area under the curve AUC = 0.73). We show in a retrospective study (N=15) that this simple dynamic -namely the Susceptible-Infected-Recover (SIR) model- is enough to reproduce the main aspects of seizure propagation as recorded via invasive electroencephalography (iEEG). The propagation of seizures over the brain can be regarded as an epidemic spreading process taking place on the patient's connectome. Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but up to 50% of the patients continue to have seizures one year after the resection. The role of epidemic spreading in seizure propagation and epilepsy surgery | 11am, 11th May 2023 Ĭomputational models of brain dynamics can provide new insights into the prognosis of neurological disorders such as epilepsy. As an application, we derive an accurate multiscale model of the International Trade Network applicable across hierarchically nested geographic partitions. If they are quenched, they can guide the renormalization of real-world networks with node attributes and distance-dependence or communities. ![]() If the hidden variables are annealed, they lead to realistic scale-free networks with density-dependent cut-off, assortatitivy and finite local clustering, even in the sparse regime and in absence of geometry. ![]() ![]() These results highlight a deep conceptual distinction between scale-free and scale-invariant networks, and provide a geometry-free route to renormalization. Renormalizable networks turn out to be consistent with a unique specification of the fitness model, while they are incompatible with preferential attachment, the configuration model or the stochastic blockmodel. This approach reveals a necessary and specific dependence of network topology on additive hidden variables attached to nodes, plus optional dyadic factors. Here we introduce a graph renormalization scheme valid for any hierarchy of coarse-grainings, thereby allowing for the definition of `block-nodes' across multiple scales. community structure, hyperbolicity, scale-free topology), thus remaining incompatible with generic graphs and ordinary lattices. Current network renormalization approaches require strong assumptions (e.g. By contrast, complex networks defy the usual techniques, due to their small-world character and lack of explicit geometric embedding. Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. Multiscale network renormalization: scale-invariance without geometry | 11am, 1st June 2023
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