Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: A visualization system comprising a persistent memory, storing a dataset, and a non-persistent memory implements a pattern visualizing method. The dataset contains discrete attribute values for each first entity of a first type in a plurality of first entities of the first type and discrete attribute values for each first entity of a second type in a plurality of first entities of the second type for each second entity in a plurality of second entities. The dataset is compressed by blocked compression and represents discrete attribute values in both compressed sparse row and column formats. The discrete attribute values are clustered to assign each second entity to a cluster in a plurality of clusters.

Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: A visualization system comprising processing cores, memory, and a display performs a visualization method by obtaining a block of data. The data represents a single-cell characteristic of cells in a plurality of cells across each bin in a plurality of bins. Each bin maps to a different portion of a reference genome. The cells are clustered based upon the single-cell characteristic across the plurality of bins, thereby forming a tree structure that includes a current root node, a plurality of intermediate nodes, and the plurality of cells. Th plurality of cells constitute terminal nodes in the tree structure and each respective intermediate node has a corresponding plurality of daughter nodes, each daughter node being an intermediate node or a cell. The single-cell characteristic is plotted for the current root node of the tree on the screen using the dataset, across all or the portion of the plurality of bins.

Abstract: A dataset is obtained comprising data blocks, each representing a different characteristic, for a plurality of cells across a plurality of bins, each bin representing a different portion of a reference sequence. Cells are clustered on one such characteristic across the bins thereby forming a tree that includes root, intermediate, and terminal nodes, where the cells are terminal nodes and intermediate nodes have daughter nodes, themselves being intermediate nodes or a cell. A subset of the tree is displayed that includes the root and leaves, each leaf representing an intermediate node or a cell. A heat map of the characteristic is also displayed, the map including a segment for each leaf, across the bins. When a segment represents an intermediate node, it is an average of the characteristic across daughters of the node. Graphs of characteristics for the root across the bins are also displayed.

Abstract: A visualization system comprising a persistent memory, storing a dataset, and a non-persistent memory implements a pattern visualizing method. The dataset contains discrete attribute values for each first entity of a first type in a plurality of first entities of the first type and discrete attribute values for each first entity of a second type in a plurality of first entities of the second type for each second entity in a plurality of second entities. The dataset is compressed by blocked compression and represents discrete attribute values in both compressed sparse row and column formats. The discrete attribute values are clustered to assign each second entity to a cluster in a plurality of clusters.

Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: A dataset is obtained comprising data blocks, each representing a different characteristic, for a plurality of cells across a plurality of bins, each bin representing a different portion of a reference sequence. Cells are clustered on one such characteristic across the bins thereby forming a tree that includes root, intermediate, and terminal nodes, where the cells are terminal nodes and intermediate nodes have daughter nodes, themselves being intermediate nodes or a cell. A subset of the tree is displayed that includes the root and leaves, each leaf representing an intermediate node or a cell. A heat map of the characteristic is also displayed, the map including a segment for each leaf, across the bins. When a segment represents an intermediate node, it is an average of the characteristic across daughters of the node. Graphs of characteristics for the root across the bins are also displayed.

Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: A dataset is obtained comprising data blocks, each representing a different characteristic, for a plurality of cells across a plurality of bins, each bin representing a different portion of a reference sequence. Cells are clustered on one such characteristic across the bins thereby forming a tree that includes root, intermediate, and terminal nodes, where the cells are terminal nodes and intermediate nodes have daughter nodes, themselves being intermediate nodes or a cell. A subset of the tree is displayed that includes the root and leaves, each leaf representing an intermediate node or a cell. A heat map of the characteristic is also displayed, the map including a segment for each leaf, across the bins. When a segment represents an intermediate node, it is an average of the characteristic across daughters of the node. Graphs of characteristics for the root across the bins are also displayed.

Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: Systems and methods for spatial analysis of analytes include placing a sample on a substrate having fiducial markers and capture spots. Then, an image of the sample is acquired and sequence reads are obtained from the capture spots. Each capture probe plurality in a set of capture probe pluralities is (i) at a different capture spot, (ii) directly or indirectly associates with analytes from the sample and (iii) has a unique spatial barcode. The sequencing reads serve to detect the analytes. Sequencing reads include a spatial barcode of the corresponding capture probe plurality. Spatial barcodes localize reads to corresponding capture spots, thereby dividing them into subsets, each subset for a respective capture spot. Fiducial markers facilitate a composite representation comprising (i) the image aligned to the capture spots and (ii) a representation of each subset of sequence reads at respective positions within the image mapping to the corresponding capture spots.

Abstract: A discrete attribute value dataset is obtained that is associated with a plurality of probe spots each assigned a different probe spot barcode. The dataset comprises spatial projections, each comprising images of a biological sample. Each image includes a corresponding plurality of discrete attribute values for the probe spots. Each such value is associated with a probe spot in the plurality of probes spots based on the probe spot barcodes. The dataset is clustered using the discrete attribute values, or dimension reduction components thereof, for a plurality of loci at each respective probe spot across the images of the projections thereby assigning each probe spot to a cluster in a plurality of clusters. Morphological patterns are identified from the spatial arrangement of the probe spots in the various clusters.

Abstract: A dataset is obtained comprising data blocks, each representing a different characteristic, for a plurality of cells across a plurality of bins, each bin representing a different portion of a reference sequence. Cells are clustered on one such characteristic across the bins thereby forming a tree that includes root, intermediate, and terminal nodes, where the cells are terminal nodes and intermediate nodes have daughter nodes, themselves being intermediate nodes or a cell. A subset of the tree is displayed that includes the root and leaves, each leaf representing an intermediate node or a cell. A heat map of the characteristic is also displayed, the map including a segment for each leaf, across the bins. When a segment represents an intermediate node, it is an average of the characteristic across daughters of the node. Graphs of characteristics for the root across the bins are also displayed.

Abstract: A visualization system comprising a persistent memory, storing a dataset, and a non-persistent memory implements a pattern visualizing method. The dataset contains discrete attribute values for each first entity of a first type in a plurality of first entities of the first type and discrete attribute values for each first entity of a second type in a plurality of first entities of the second type for each second entity in a plurality of second entities. The dataset is compressed by blocked compression and represents discrete attribute values in both compressed sparse row and column formats. The discrete attribute values are clustered to assign each second entity to a cluster in a plurality of clusters.

Abstract: Performance of an integrated circuit design, whether embodied as a design encoding or as a fabricated integrated circuit, can be improved by selectively substituting low Vt transistors in a way that prioritizes substitution opportunities based on multi-path timing analysis and evaluates such opportunities based on one or more substitution constraints. By valuing, in a prioritization of substitution opportunities, contributions for all or substantially all timing paths through the substitution opportunity that violate a max-time constraint, repeated passes through a timing analysis phase can be advantageously avoided or limited. In addition, by recognizing one or more constraints on actual low Vt substitutions, particular noise-oriented constraints, the scope of post substitution design analysis can be greatly reduced. In some realizations, substitutions are performed so long as a leakage current budget is not expended.

Abstract: Performance of an integrated circuit design, whether embodied as a design encoding or as a fabricated integrated circuit, can be improved by selectively substituting low Vt transistors in a way that prioritizes substitution opportunities based on multi-path timing analysis and evaluates such opportunities based on one or more substitution constraints. By valuing, in a prioritization of substitution opportunities, contributions for all or substantially all timing paths through the substitution opportunity that violate a max-time constraint, repeated passes through a timing analysis phase can be advantageously avoided or limited. In addition, by recognizing one or more constraints on actual low Vt substitutions, particular noise-oriented. constraints, the scope of post substitution design analysis can be greatly reduced. In some realizations, substitutions are performed so long as a leakage current budget is not expended.