On blocks of Deligne's category Rep(S_t)

Recently P. Deligne introduced the tensor category Rep(S_t) (for t not necessarily an integer) which in a certain precise sense interpolates the categories Rep(S_d) of representations of the symmetric groups S_d. In this paper we describe the blocks of Deligne's category Rep(S_t).Comment: 43 pages, final version, includes an added appendix as well as other modifications recommended by the refere

Autonomic Sonar Sensor Fault Manager for Mobile Robots

NASA, ESA, and NSSC space agencies have plans to put planetary rovers on Mars in 2020. For these future planetary rovers to succeed, they will heavily depend on sensors to detect obstacles. This will also become of vital importance in the future, if rovers become less dependent on commands received from earth-based control and more dependent on self-configuration and self-decision making. These planetary rovers will face harsh environments and the possibility of hardware failure is high, as seen in missions from the past. In this paper, we focus on using Autonomic principles where self-healing, self-optimization, and self-adaption are explored using the MAPE-K model and expanding this model to encapsulate the attributes such as Awareness, Analysis, and Adjustment (AAA-3). In the experimentation, a Pioneer P3-DX research robot is used to simulate a planetary rover. The sonar sensors on the P3-DX robot are used to simulate the sensors on a planetary rover (even though in reality, sonar sensors cannot operate in a vacuum). Experiments using the P3-DX robot focus on how our software system can be adapted with the loss of sonar sensor functionality. The autonomic manager system is responsible for the decision making on how to make use of remaining 'enabled' sonars sensors to compensate for those sonar sensors that are 'disabled'. The key to this research is that the robot can still detect objects even with reduced sonar sensor capability

Representation theory of towers of recollement: Theory, notes, and examples

We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley–Lieb algebras. We demonstrate the utility of our formalism by applying it to this class

A seminormal form for partition algebras

Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition algebras the classical formulae given by Young for the symmetric group.Comment: Published version. 51 pages, includes figures and table

7-Hydroxylation of warfarin is strongly inhibited by sesamin, but not by episesamin, caffeic and ferulic acids in human hepatic microsomes

© 2018 Elsevier Ltd Warfarin is a commonly used anticoagulant drug and is a derivate of coumarin. Cytochrome P450 2C9 (CYP2C9) plays the key role in transformation of coumarin and thus, influences determination of warfarin dosage. A number of factors including dietary compounds such as sesamin, caffeic acid and ferulic acids can regulate the activity of CYP2C9. The present study tested the hypothesis that sesamin, episesamin, caffeic acid and ferulic acid decreases the rate of warfarin 7-hydroxylation via inhibition of hepatic CYP2C9. The experiments were conducted on hepatic microsomes from human donors. It was demonstrated that the rate of 7-hydroxylation of warfarin was significantly decreased in the presence of sesamin in the range of concentrations from 5 to 500 nM, and was not affected by episesamin, caffeic acid and ferulic acid in the same range of concentrations. The kinetic analysis indicated non-competitive type of inhibition by sesamin with Ki = 202 ± 18 nM. In conclusion, the results of our in vitro study revealed that sesamin was able to inhibit formation of a major metabolite of warfarin, 7-hydroxywarfarin. The potentially negative consequences of the consumption of high amounts of sesamin-containing food or dietary supplements in warfarin-treated patients need to be further studied