Partially Ordered Sets in the Analysis of Alkanes Fate in Rivers

Dominance degree is introduced as a mathematical procedure to quantify the order relations between a pair of subsets contained in a partially ordered set obtained from the features of its elements. Dominance degree summarizes the partial order relations of the members of two subsets. If a member of one subset follows an order relation to a member of another subset, then the dominance degree informs how far this relation can be transferred to all elements of the two subsets. Dominance degree was applied to the study of 35 acyclic alkanes (from C5H12 to C8H18) in two river-scenarios: hilly regions and lowland rivers. Each chemical was defined by three fate descriptors estimated by applying the module EXWAT from the E4CHEM package. It was found that CnH2n+2 dominates CmH2m+2 if n > m, which means that when considering the fate descriptors simultaneously, those of CnH2n+2 are higher than those of CmH2m+2. Finally, some particular results were found for the linear isomer of each subset

Genes optimized by evolution for accurate and fast translation encode in Archaea and Bacteria a broad and characteristic spectrum of protein functions

BACKGROUND: In many microbial genomes, a strong preference for a small number of codons can be observed in genes whose products are needed by the cell in large quantities. This codon usage bias (CUB) improves translational accuracy and speed and is one of several factors optimizing cell growth. Whereas CUB and the overrepresentation of individual proteins have been studied in detail, it is still unclear which high-level metabolic categories are subject to translational optimization in different habitats. RESULTS: In a systematic study of 388 microbial species, we have identified for each genome a specific subset of genes characterized by a marked CUB, which we named the effectome. As expected, gene products related to protein synthesis are abundant in both archaeal and bacterial effectomes. In addition, enzymes contributing to energy production and gene products involved in protein folding and stabilization are overrepresented. The comparison of genomes from eleven habitats shows that the environment has only a minor effect on the composition of the effectomes. As a paradigmatic example, we detailed the effectome content of 37 bacterial genomes that are most likely exposed to strongest selective pressure towards translational optimization. These effectomes accommodate a broad range of protein functions like enzymes related to glycolysis/gluconeogenesis and the TCA cycle, ATP synthases, aminoacyl-tRNA synthetases, chaperones, proteases that degrade misfolded proteins, protectants against oxidative damage, as well as cold shock and outer membrane proteins. CONCLUSIONS: We made clear that effectomes consist of specific subsets of the proteome being involved in several cellular functions. As expected, some functions are related to cell growth and affect speed and quality of protein synthesis. Additionally, the effectomes contain enzymes of central metabolic pathways and cellular functions sustaining microbial life under stress situations. These findings indicate that cell growth is an important but not the only factor modulating translational accuracy and speed by means of CUB

Ranking and Prioritization for Multi-indicator Systems

This book provides axioms of partial order and some basic material, for example consequences of "criss-crossing" of data profiles, the role of aggregations of the indicators and the powerful method of formal concept analysis. The interested reader will learn how to apply fuzzy methods in partial order analysis and what 'antagonistic indicator' means

Exploring partial order of European countries

Partial Order Theory has been recently more and more employed in applied science to overcome the intrinsic disadvantage hidden in linear ranking, if a multiple indicator system is available. Despite its numerous positive features, there are many practical cases where the interpretation of the partial order can be rather troublesome. In these cases the analysis of underlying dimensions could be useful to uncover particular data structures. The paper shows a way of addressing the problem with the help of an actual case study, which deals with European opinions on services of general interest. In particular, an overall ranking of countries is firstly provided and then a method to detect dimensions is discussed and applied. The analysis stems directly from the Partially Order Set (poset) and Lattice theory with particular references to dimension theory and Formal Concept Analysis. The study is eventually able to pinpoint role and relevance of both different services and different criteria in defining the partial order.Hasse Diagrams, Dimension Theory in Posets, Planar Lattices, Formal Concept Analysis,

Random and quasi-random designs in variance-based sensitivity analysis for partially ordered sets

A special application of global sensitivity analysis is that on partially ordered sets – posets – that are sets of objects endowed by a binary order relation. In a partial order two objects can be in relation with each other, and are said to be comparable, or not, then they are said to be incomparable. Comparability and incomparability relations between objects can be visualized in a so called Hasse diagram, which is instructive in ranking the objects by multi-criteria/non-compensatory approaches. The interpretation of a Hasse diagram may be difficult even when the number of objects in the set is relatively small. Completely different configurations of the diagram can arise even for small perturbations of the starting data. Global sensitivity indices can shed light on the robustness of the partial order to data value uncertainty. Global measures particularly fit the case since posets are characterized by high number of dimensions and high-order interactions. These distinctive features of sensitivity analysis for posets make quasi-random designs perform almost the same as the random one as it is discussed here with a real test case for comparing the level of competitiveness of EU countries.JRC.G.3-Econometrics and applied statistic