Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.

The quadriceps tendon has the anatomic characteristics to produce a graft whose length and volume are both reproducible and predictable, while yielding a graft with a significantly greater intra-articular volume than a patellar tendon graft with a similar width.

Computational vision-based flame detection has drawn significant attention in the past decade with camera surveillance systems becoming ubiquitous. Whereas many discriminating features, such as color, shape, texture, etc., have been employed in the literature, this paper proposes a set of motion features based on motion estimators. The key idea consists of exploiting the difference between the turbulent, fast, fire motion, and the structured, rigid motion of other objects. Since classical optical flow methods do not model the characteristics of fire motion (e.g., non-smoothness of motion, non-constancy of intensity), two optical flow methods are specifically designed for the fire detection task: optimal mass transport models fire with dynamic texture, while a data-driven optical flow scheme models saturated flames. Then, characteristic features related to the flow magnitudes and directions are computed from the flow fields to discriminate between fire and non-fire motion. The proposed features are tested on a large video database to demonstrate their practical usefulness. Moreover, a novel evaluation method is proposed by fire simulations that allow for a controlled environment to analyze parameter influences, such as flame saturation, spatial resolution, frame rate, and random noise.

Detection of fire and smoke in video is of practical and theoretical interest. In this paper, we propose the use of optimal mass transport (OMT) optical flow as a low-dimensional descriptor of these complex processes. The detection process is posed as a supervised Bayesian classification problem with spatio-temporal neighborhoods of pixels;feature vectors are composed of OMT velocities and R,G,B color channels. The classifier is implemented as a single-hidden-layer neural network. Sample results show probability of pixels belonging to fire or smoke. In particular, the classifier successfully distinguishes between smoke and similarly colored white wall, as well as fire from a similarly colored background.