Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably accurate res
ults are obtained by methods that recommend objects based on user or object similarity. In this paper we introduce a new algorithm specifically to address the challenge of diversity and show how it can be used to resolve this apparent dilemma when combined in an elegant hybrid with an accuracy-focused algorithm. By tuning the hybrid appropriately we are able to obtain, without relying on any semantic or context-specific information, simultaneous gains in both accuracy and diversity of recommendations.
One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval). In this r
epresentation, the firm size is directly associated with the size of its selling interval. The recursive synchronous dynamics of economic evolution is discussed where the growth rate is proportional to the firm size incremented by the term including the overlap of the selling area with areas of competing firms. Other words, the overlap of selling areas inherently generate a negative feedback originated from the pattern of demand. Numerical simulations focused on the obtaining of the firm size distributions uncovered that the range of free parameters where the Paretos law holds corresponds to the range for which the pair correlation between the nearest neighbor firms attains its minimum.
