Abstract: The present disclosure generally relates to spatial detection of a nucleic acid, such as a genomic DNA or a RNA transcript, in a cell comprised in a tissue sample. The present disclosure provides methods for detecting and/or analyzing nucleic acids, such as chromatin or RNA transcripts, so as to obtain spatial information about the localization, distribution or expression of genes in a tissue sample. The present disclosure thus provides a process for performing “spatial transcriptomics” or “spatial genomics,” which enables the user to determine simultaneously the expression pattern, or the location/distribution pattern of the genes expressed or genes or genomic loci present in a single cell while retaining information related to the spatial location of the cell within the tissue architecture.

Abstract: Based on a metric that represents a value of a game of chance, a payout distribution is optimized with respect to the metric.

Abstract: Historical information is stored about demand behavior associated with different sizes of styles of items of commerce. A size assortment recommendation is generated based on the stored historical information and on objectives with respect to purchase or allocation decisions about assortments of the different sizes.

Abstract: From data that includes prices and unit sales of an item of commerce for a succession of time periods during which the item was sold, a relationship is derived that represents variation of unit sales of the item as a function of price and time of sale. A maximum profit is predicted by optimizing the price or inventory or both over time in accordance with the relationship. The optimized price or inventory or both over time are used in connection with making price decisions or inventory decisions or both with respect to marketing the item of commerce. A group of the data is aggregated, the group being chosen so that the aggregated data for the group will have an enhanced signal-to-noise ratio with respect to information about sales trends. The aggregated data for the group is analyzed for use in making price decisions with respect to marketing the items of commerce.

Abstract: A set of data is received containing values associated with respective data points, the values associated with each of the data points being characterized by a distribution. The values for each of the data points are expressed in a form that includes information about a distribution of the values for each of the data points. The distribution information is used in clustering the set of data with at least one other set of data containing values associated with data points.