Novel Computational Approach to Obtain Contact Angles: Application to Carbon Capture and Storage

Imperial Users onl

Nonlinear system identification and prediction

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Separation dimension of bounded degree graphs

The 'separation dimension' of a graph $G$ is the smallest natural number $k$ for which the vertices of $G$ can be embedded in $\mathbb{R}^k$ such that any pair of disjoint edges in $G$ can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family $\mathcal{F}$ of total orders of the vertices of $G$ such that for any two disjoint edges of $G$, there exists at least one total order in $\mathcal{F}$ in which all the vertices in one edge precede those in the other. In general, the maximum separation dimension of a graph on $n$ vertices is $\Theta(\log n)$. In this article, we focus on bounded degree graphs and show that the separation dimension of a graph with maximum degree $d$ is at most $2^{9log^{\star} d} d$. We also demonstrate that the above bound is nearly tight by showing that, for every $d$, almost all $d$-regular graphs have separation dimension at least $\lceil d/2\rceil$.Comment: One result proved in this paper is also present in arXiv:1212.675

TempoCave: Visualizing Dynamic Connectome Datasets to Support Cognitive Behavioral Therapy

We introduce TempoCave, a novel visualization application for analyzing dynamic brain networks, or connectomes. TempoCave provides a range of functionality to explore metrics related to the activity patterns and modular affiliations of different regions in the brain. These patterns are calculated by processing raw data retrieved functional magnetic resonance imaging (fMRI) scans, which creates a network of weighted edges between each brain region, where the weight indicates how likely these regions are to activate synchronously. In particular, we support the analysis needs of clinical psychologists, who examine these modular affiliations and weighted edges and their temporal dynamics, utilizing them to understand relationships between neurological disorders and brain activity, which could have a significant impact on the way in which patients are diagnosed and treated. We summarize the core functionality of TempoCave, which supports a range of comparative tasks, and runs both in a desktop mode and in an immersive mode. Furthermore, we present a real-world use case that analyzes pre- and post-treatment connectome datasets from 27 subjects in a clinical study investigating the use of cognitive behavior therapy to treat major depression disorder, indicating that TempoCave can provide new insight into the dynamic behavior of the human brain