The problem of finding a longest increasing subsequence (LIS) is a well known task in sequence processing. There are many variants of the basic task. We discuss a recently introduced variant of LIS, a minimal height longest increasing subsequence problem and propose a new algorithm for it, which improves its time complexity. Moreover, we define a family of similar problems and introduce algorit...

Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , n, for the uniform distribution on the set of permutations. We discuss the “hydrodynamical approach” to the analysis of the limit behavior, which probably started with Hammersley (1972), and was subsequently further developed by several authors. We also give two proofs of an exact (non-a...

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

nowadays, air pollution is one of the major problems in developed and developing countries. in recent years, effects of air pollution on neuroinflammatory diseases such as alzheimer disease and parkinson disease have been studied. researches on polluted cities citizens indicate increasing in central nervous system (cns) inflammatory factors in comparison with clean cities; also air pollution ex...

Increasing attention is being paid to spatial distribution characteristics of haze pollution and its relation with socioeconomic factors. This study investigates the spatial autocorrelation of haze pollution in China and the effect of foreign direct investment (FDI) on haze pollution in China using a panel data of 31 provinces over the period 2000-12. Using a widely used spatial autocorrelation...

the study was aimed to investigate the change of some fatty acids to ambient air pollution in four legumes species Pisum sativum L. and (Vicia faba L.m and during summer season were Glycine max and Vigna sinensis grown in five sites mostly affected by high traffic intensity and or industrial activities in Riyadh city capital of Saudi Arabia. The results showed increasing of air pollution (O3, N...

Losses of corals worldwide emphasize the need to understand what drives reef decline. Stressors such as overfishing and nutrient pollution may reduce resilience of coral reefs by increasing coral-algal competition and reducing coral recruitment, growth and survivorship. Such effects may themselves develop via several mechanisms, including disruption of coral microbiomes. Here we report the resu...

The objective of the study was to determine whether long-term metal pollution affects communities of epigeal spiders (Aranea), studied at three taxonomic levels: species, genera, and families. Biodiversity was defined by three indices: the Hierarchical Richness Index (HRI), Margalef index (D(M)) and Pielou evenness index (J). In different ways the indices describe taxa richness and the distribu...