General equilibrium analysis in ordered topological vector spaces

The second welfare theorem and the core-equivalence theorem have been proved to be fundamental tools for obtaining equilibrium existence theorems, especially in an infinite dimensional setting. For well-behaved exchange economies that we call proper economies, this paper gives (minimal) conditions for supporting with prices Pareto optimal allocations and decentralizing Edgeworth equilibrium allocations as non-trivial equilibria. As we assume neither transitivity nor monotonicity on the preferences of consumers, most of the existing equilibrium existence results are a consequence of our results. A natural application is in Finance, where our conditions lead to new equilibrium existence results, and also explain why some financial economies fail to have equilibrium.Equilibrium; Valuation equilibrium; Pareto-optimum; Edgeworth equilibrium; Properness; ordered topological vector spaces; Riesz-Kantorovich formula; sup-convolution

Application of Spatiotemporal Fuzzy C-Means Clustering for Crime Spot Detection

The various sources generate large volume of spatiotemporal data of different types including crime events. In order to detect crime spot and predict future events, their analysis is important. Crime events are spatiotemporal in nature; therefore a distance function is defined for spatiotemporal events and is used in Fuzzy C-Means algorithm for crime analysis. This distance function takes care of both spatial and temporal components of spatiotemporal data. We adopt sum of squared error (SSE) approach and Dunn index to measure the quality of clusters. We also perform the experimentation on real world crime data to identify spatiotemporal crime clusters.

An overview of clustering methods with guidelines for application in mental health research

Cluster analyzes have been widely used in mental health research to decompose inter-individual heterogeneity by identifying more homogeneous subgroups of individuals. However, despite advances in new algorithms and increasing popularity, there is little guidance on model choice, analytical framework and reporting requirements. In this paper, we aimed to address this gap by introducing the philosophy, design, advantages/disadvantages and implementation of major algorithms that are particularly relevant in mental health research. Extensions of basic models, such as kernel methods, deep learning, semi-supervised clustering, and clustering ensembles are subsequently introduced. How to choose algorithms to address common issues as well as methods for pre-clustering data processing, clustering evaluation and validation are then discussed. Importantly, we also provide general guidance on clustering workflow and reporting requirements. To facilitate the implementation of different algorithms, we provide information on R functions and librarie