Abstract Many results about mass partitions are proved by lifting $\mathds {R}^d$ to a higher-dimensional space and dividing the into pieces. We extend such methods use arguments polyhedral surfaces. Among other results, we prove existence of equipartitions $d+1$ measures in parallel hyperplanes $d+2$ concentric spheres. For whose supports sufficiently well separated, where one can cut fixed (p...

This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic speedup possible calculation problem finding girth or number circuits (bases, flats, hyperplanes) a matroid, and decision deciding whether uniform Eulerian, by giving lower bound $\Omega(\sqrt{\binom{n}{\lfloor n/2\rfloor}})$ on query complexity all these On other hand, problem, an asy...

Reduction of this type may help to solve one of the greatest problems in pattern recognition, i.e. the compromise between the time of making a decision and its correctness. In the analysis of biomedical data, classification time is less important than certainty that classification is correct, i.e. that reliability of classification is accepted by the algorithm’s operator. It is usually possible...

Most popular deep learning based models for action recognition are designed to generate separate predictions within their short temporal windows, which are often aggregated by heuristic means to assign an action label to the full video segment. Given that not all frames from a video characterize the underlying action, pooling schemes that impose equal importance to all frames might be unfavorab...

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which interval scale data can appe...

State-of-the-art methods for clustering data drawn from a union of subspaces are based on sparse and low-rank representation theory. Existing results guaranteeing the correctness of such methods require the dimension of the subspaces to be small relative to the dimension of the ambient space. When this assumption is violated, as is, for example, in the case of hyperplanes, existing methods are ...