Evolution of dispersal and the analysis of a resource flourished population model with harvesting

This study explores a spatially distributed harvesting model that signifies the outcome of the competition of two species in a heterogeneous environment. The model is controlled by reaction-diffusion equations with resource-based diffusion strategies. Two different situations are maintained by the harvesting effects: when the harvesting rates are independent in space and do not exceed the intrinsic growth rate; and when they are proportional to the time-independent intrinsic growth rate. In particular, the competition between both species differs only by their corresponding migration strategy and harvesting intensity. We have computed the main results for the global existence of solutions that represent either coexistence or competitive exclusion of two competing species depending on the harvesting levels and different imposed diffusion strategies. We also established some estimates on harvesting efforts for which coexistence is apparent. Also, some numerical results are exhibited in one and two spatial dimensions, which shed some light on the ecological implementation of the model.

USING CONVOLUTIONAL NEURAL NETWORK-BASED SEGMENTATION FOR IMAGE-BASED COMPUTATIONAL FLUID DYNAMICS SIMULATIONS OF BRAIN ANEURYSMS: INITIAL EXPERIENCE IN AUTOMATED MODEL CREATION

"Image-based" computational fluid dynamics (CFD) simulations provide insights into each patient's hemodynamic environment. However, current standard procedures for creating CFD models start with manual segmentation and are time-consuming, hindering the clinical translation of image-based CFD simulations. This feasibility study adopts deep-learning-based image segmentation (hereafter referred to as Artificial Intelligence (AI) segmentation) to replace manual segmentation to accelerate CFD model creation. Two published convolutional neural network-based AI methods (MIScnn and DeepMedic) were selected to perform CFD model extraction from three-dimensional (3D) rotational angiography data containing intracranial aneurysms. In this study, aneurysm morphological and hemodynamic results using models generated by AI segmentation methods were compared with those obtained by two human users for the same data. Interclass coefficients (ICC), Bland-Altman plots, and Pearson's correlation coefficients (PCC) were combined to assess how well AI-generated CFD models were performed. We found that almost perfect agreement was obtained between the human and AI results for all eleven morphological and five out of eight hemodynamic parameters, while a moderate agreement was obtained from the remaining three hemodynamic parameters. Given this level of agreement, using AI segmentation to create CFD models is feasible, given more developments.

The space of homogeneous probability measures on Γ\X¯maxS is compact: With an appendix by Jialun Li

In this paper we prove that the space of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space is compact. As an application, we explain some consequences for the distribution of weakly special subvarieties of Shimura varieties.

Selection, calibration, and validation of models of tumor growth

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as "model agnostic" in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology (in vivo). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction-diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory animals while demonstrating successful implementations of OPAL.