of the art control library (case study: SLICOT) with respect to use of rank revealing subroutines in computing various canonical decompositions of linear time invariant systems. This issue seems to be critical, with potential for causing numerical catastrophes, because the deployed rank revealing code

perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered

-existing concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to solving the norm minimization relaxations, and illustrate our results with numerical examples.

processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decompo- sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum

atmospheric greenhouse-gas concentrations and Antarctic temperature, as well as the strong imprint of obliquity and precession in most of the climate time series. Our records reveal both similarities and differences between the successive interglacial periods. They suggest the lead of Antarctic air

Numerous studies show that happy individuals are successful across multiple life domains, including marriage, friendship, income, work performance, and health. The authors suggest a conceptual model to account for these findings, arguing that the happiness–success link exists not only because

given ranked position. We then demonstrate the use of these evaluation methods in a case study on the effectiveness of query types, based on combinations of query structures and expansion, in retrieving documents of various degrees of relevance. The test was run with a best match retrieval system (In

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F

the framework of competitive learning. This new perspective reveals a number of different possibilities for performance improvements. This paper explores population-based incremental learning (PBIL), a method of combining the mechanisms of a generational genetic algorithm with simple competitive learning

For over 50 years immunologists have based their thoughts, experiments, and clinical treatments on the idea that the immune system functions by making a distinction between self and nonself. Although this paradigm has often served us well, years of detailed examination have revealed a number