Spatiotemporal Barcodes for Image Sequence Analysis

Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a spatiotemporal 0–barcode encoding lifetime of connected components on the image sequence over time. This information may not coincide with the one provided by the 0–barcode encoding the 0–persistent homology, since the latter does not respect the principle that it is not possible to move backwards in time. A cell complex K is computed from the given sequence, being the cells of K classified as spatial or temporal depending on whether they connect two consecutive frames or not. A spatiotemporal path is defined as a sequence of edges of K forming a path such that two edges of the path cannot connect the same two consecutive frames. In our algorithm, for each vertex v ∈ K, a spatiotemporal path from v to the “oldest” spatiotemporally-connected vertex is computed and the corresponding spatiotemporal 0–bar is added to the spatiotemporal 0–barcode.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-3270

Topological tracking of connected components in image sequences

Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphi- cal representation of such information. A filtration might be determined by time in a set of spatiotemporal data, but classical methods for computing persistent homology do not respect the fact that we can not move back- wards in time. In this paper, taking as input a time-varying sequence of two-dimensional (2D) binary digital images, we develop an algorithm for en- coding, in the so-called spatiotemporal barcode, lifetime of connected compo- nents (of either the foreground or background) that are moving in the image sequence over time (this information may not coincide with the one provided by the persistence barcode). This way, given a connected component at a specific time in the sequence, we can track the component backwards in time until the moment it was born, by what we call a spatiotemporal path. The main contribution of this paper with respect to our previous works lies in a new algorithm that computes spatiotemporal paths directly, valid for both foreground and background and developed in a general context, setting the ground for a future extension for tracking higher dimensional topological features in nD binary digital image sequences.Ministerio de Economía y Competitividad MTM2015-67072-

Marine nematode taxonomy in the DNA age: the present and future of molecular tools to access their biodiversity

Molecular taxonomy is one of the most promising yet challenging fields of biology. Molecular markers such as nuclear and mitochondrial genes are being used in a variety of studies surveying marine nematode taxa. Sequences from more than 600 species have been deposited to date in online databases. These barcode sequences are assigned to 150 nominal species from 104 genera. There are 41 species assigned to Enoplea and 109 species to Chromadorea. Morphology-based surveys are greatly limited by processing speed, while barcoding approaches for nematodes are hampered by difficulties in matching sequence data with morphology-based taxonomy. DNA barcoding is a promising approach because some genes contain variable regions that are useful to discriminate species boundaries, discover cryptic species, quantify biodiversity and analyse phylogeny. We advocate a combination of several approaches in studies of molecular taxonomy, DNA barcoding and conventional taxonomy as a necessary step to enhance the knowledge of biodiversity of marine nematodes

Gating of memory encoding of time-delayed cross-frequency MEG networks revealed by graph filtration based on persistent homology

To explain gating of memory encoding, magnetoencephalography (MEG) was analyzed over multi-regional network of negative correlations between alpha band power during cue (cue-alpha) and gamma band power during item presentation (item-gamma) in Remember (R) and No-remember (NR) condition. Persistent homology with graph filtration on alpha-gamma correlation disclosed topological invariants to explain memory gating. Instruction compliance (R-hits minus NR-hits) was significantly related to negative coupling between the left superior occipital (cue-alpha) and the left dorsolateral superior frontal gyri (item-gamma) on permutation test, where the coupling was stronger in R than NR. In good memory performers (R-hits minus false alarm), the coupling was stronger in R than NR between the right posterior cingulate (cue-alpha) and the left fusiform gyri (item-gamma). Gating of memory encoding was dictated by inter-regional negative alpha-gamma coupling. Our graph filtration over MEG network revealed these inter-regional time-delayed cross-frequency connectivity serve gating of memory encoding

Multiplexed Dynamic Imaging of Genomic Loci by Combined CRISPR Imaging and DNA Sequential FISH

Visualization of chromosome dynamics allows the investigation of spatiotemporal chromatin organization and its role in gene regulation and other cellular processes. However, current approaches to label multiple genomic loci in live cells have a fundamental limitation in the number of loci that can be labeled and uniquely identified. Here we describe an approach we call “track first and identify later” for multiplexed visualization of chromosome dynamics by combining two techniques: CRISPR imaging and DNA sequential fluorescence in situ hybridization. Our approach first labels and tracks chromosomal loci in live cells with the CRISPR-Cas9 system, then barcodes those loci by DNA sequential fluorescence in situ hybridization in fixed cells and resolves their identities. We demonstrate our approach by tracking telomere dynamics, identifying 12 unique subtelomeric regions with variable detection efficiencies, and tracking back the telomere dynamics of respective chromosomes in mouse embryonic stem cells