We use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call ‘prime graphs category’; this has as objects labeled undirected bipartite graphs (which we call prime graphs), and as morphisms undirected graph morphisms that preserve the labeling (which we call prime graph morphisms). This theoretical bridge allows us to extend undirected graph techniques to directed graphs by converting the directed graphs into prime graphs. To give a proof of concept, we show that our construction preserves topological features when applied to the problems of network alignment and spectral graph clustering.

Laser induced shockwave (LIS) can be utilized to subject neuronal cells to conditions similar to those occurring during a blast induced traumatic brain injury. We utilized a 532nm Coherent Flare laser to induce a shockwave near cells which had been transfected with a FRET calcium biosensor (D3CPV) so that we could monitor the immediate cellular responses. Our shockwave system was characterized with a high-speed camera to monitor cavitation bubble dynamics and calculate the shear forces cells were subjected to. We found that we could induce forces which have been previously shown to induce injury. Using both phase and fluorescence microscopy we monitored the effects of shear on our cells. We found that at distances up to 120 microns from the laser focal point cells experienced shears greater than 10kPa. At those distances cell fragmentation was observed. Cells that survived and expressed the FRET biosensor demonstrated an immediate calcium elevation irrespective of extracellular or cytoplasmic calcium concentration. Cells recovered to pre-shockwave calcium levels within ~30s. In conclusion, LIS can be utilized to simultaneously monitor the neuronal response to shear stress and nearby cell death or injury.