Algorithms for detecting dependencies and rigid subsystems for CAD

Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then, we focus on identifying the "special positions" of a design in which generically independent constraints become dependent. We present combinatorial algorithms for identifying subgraphs associated to factors of a particular polynomial, whose vanishing indicates a special position and resulting dependency. Further factoring in the Grassmann- Cayley algebra may allow a geometric interpretation giving conditions (e.g., "these two lines being parallel cause a dependency") determining the special position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract based on v1

A Reduction in Delay Discounting by Using Episodic Future Imagination and the Association with Episodic Memory Capacity

Delay discounting (DD) refers to the phenomenon that individuals discount future consequences. Previous studies showed that future imagination reduces DD, which was mediated by functional connectivity between medial prefrontal valuation areas and a key region for episodic memory (hippocampus). Future imagination involves an initial period of construction and a later period of elaboration, with the more elaborative latter period recruiting more cortical regions. This study examined whether elaborative future imagination modulated DD, and if so, what are the underlying neural substrates. It was assumed that cortical areas contribute to the modulation effect during the later period of imagination. Since future imagination is supported by episodic memory capacity, we additionally hypothesize that the neural network underlying the modulation effect is related to individual episodic memory capacity. Twenty-two subjects received an extensive interview on personal future events, followed by an fMRI DD experiment with and without the need to perform elaborative future imagination simultaneously. Subjects' episodic memory capacity was also assessed. Behavioral results replicate previous findings of a reduced discount rate in the DD plus imagination condition compared to the DD only condition. The behavioral effect positively correlated with: (i) subjective value signal changes in midline brain structures during the initial imagination period; and (ii) signal changes in left prefrontoparietal areas during the later imagination period. Generalized psychophysiological interaction (gPPI) analyses reveal positive correlations between the behavioral effect and functional connectivity among the following areas: right anterior cingulate cortex (ACC) and left hippocampus; left inferior parietal cortex (IPC) and left hippocampus; and left IPC and bilateral occipital cortices. These changes in functional connectivity are also associated with episodic memory capacity. A hierarchical multiple regression indicates that the model with both the valuation related signal changes in the right ACC and the imagination related signal changes in the left IPC best predicts the reduction in DD. This study illustrates interactions between the left hippocampus and multiple cortical regions underlying the modulation effect of elaborative episodic future imagination, demonstrating, for the first time, empirical support for a relation to individual episodic memory capacity

The Principles of Menu Making (Second Edition)

Determining the distribution of disease prevalence among heterogeneous populations at the national scale is fundamental for epidemiology and public health. Here, we use a combination of methods (spatial scan statistic, topological data analysis, epidemic profile) to study measurable differences in malaria intensity by regions and populations of Colombia. This study explores three main questions: What are the regions of Colombia where malaria is epidemic? What are the regions and populations in Colombia where malaria is endemic? What associations exist between epidemic outbreaks between regions in Colombia? \textit{Plasmodium falciparum} is most prevalent in the Pacific Coast, some regions of the Amazon Basin, and some regions of the Magdalena Basin. \textit{Plasmodium vivax} is the most prevalent parasite in Colombia, particularly in the Northern Amazon Basin, the Caribbean, and municipalities of Sucre, Antioquia and Cordoba. Malaria has been reported to be most common among 15-45 year old men. We find that the age-class suffering high risk of malaria infection ranges from 20 to 30 with an acute peak at 25 years of age. Second, this pattern was not found to be generalizable across Colombian populations, Indigenous and Afrocolombian populations experience endemic malaria (with household transmission). Third, clusters of epidemic malaria for \textit{Plasmodium vivax} were detected across Southern Colombia including the Amazon Basin and the Southern Pacific region. \textit{Plasmodium falciparum}, was is epidemic in 13 of the 1,123 municipalities (1.2\%). Some key locations act as bridges between epidemic and endemic regions. Finally, we generate a regional classification based on intensity and synchrony, dividing the country into epidemic areas and bridge areas