Fingerprints of cancer by persistent homology

We have carried out a topological data analysis of gene expressions for different databases based on the Fermat distance between the z scores of different tissue samples. There is a critical value of the filtration parameter at which all clusters collapse in a single one. This critical value for healthy samples is gapless and smaller than that for cancerous ones. After collapse in a single cluster, topological holes persist for larger filtration parameter values in cancerous samples. Barcodes, persistence diagrams and Betti numbers as functions of the filtration parameter are different for different types of cancer and constitute fingerprints thereof.

Influences of Catchment and River Channel Characteristics on the Magnitude and Dynamics of Storage and Re-Suspension of Fine Sediments in River Beds

Fine particles or sediments are one of the important variables that should be considered for the proper management of water quality and aquatic ecosystems. In the present study, the effect of catchment characteristics on the performance of an already developed model for the estimation of fine sediments dynamics between the water column and sediment bed was tested, using 13 catchments distributed worldwide. The model was calibrated to determine two optimal model parameters. The first is the filtration parameter, which represents the filtration of fine sediments through pores of the stream bed during the recession period of a flood event. The second parameter is the bed erosion parameter that represents the active layer, directly related to the re-suspension of fine sediments during a flood event. A dependency of the filtration parameter with the catchment area was observed in catchments smaller than ~100 km2, whereas no particular relationship was observed for larger catchments (>100 km2). In contrast, the bed erosion parameter does not show a noticeable dependency with the area or other environmental characteristics. The model estimated the mass of fine sediments released from the sediment bed to the water column during flood events in the 13 catchments within ~23% bias.