Computational Complexity of Computing a Quasi-Proper Equilibrium

We study the computational complexity of computing or approximating a quasi-proper equilibrium for a given finite extensive form game of perfect recall. We show that the task of computing a symbolic quasi-proper equilibrium is $\mathrm{PPAD}$-complete for two-player games. For the case of zero-sum games we obtain a polynomial time algorithm based on Linear Programming. For general $n$-player games we show that computing an approximation of a quasi-proper equilibrium is $\mathrm{FIXP}_a$-complete.Comment: Full version of paper to appear at the 23rd International Symposium on Fundamentals of Computation Theory (FCT 2021

Approximate Well-supported Nash Equilibria below Two-thirds

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee

Mannan-Binding Lectin in Diabetic Kidney Disease: The Impact of Mouse Genetics in a Type 1 Diabetes Model

Background. Mannan-binding lectin (MBL) is involved in the development of diabetic nephropathy. MBL is a part of the innate immune system where it can activate the complement system. Serum MBL level predicts later renal impairment in diabetes patients. Direct involvement of MBL in the development of diabetic kidney disease is observed in one animal strain. However, this involvement may differ among the animal strains. We thus examined the impact of the genetic background on the role of MBL in diabetic nephropathy. Materials/Methods. C57BL/6JBomTac and 129S6/SvEvTac mice were compared. In both strains, experimental type 1 diabetes was induced in wild-type (WT) and MBL-knockout (MBL-KO) mice by streptozotocin. Nondiabetic WT and MBL-KO mice were used as controls. We tested if MBL modified the diabetes-induced kidney changes by two-way ANOVA allowing for interaction. Results. MBL aggravated diabetes-induced kidney growth and glomerulus enlargement in C57BL/6JBomTac mice. MBL did not modify diabetes effects on glomerular basement membrane thickness or mesangial volume in any strain. Diabetes-induced changes in renal gene transcription of growth factors and matrix components were unaffected by MBL. Conclusions. Strain-specific MBL effects were found on downstream diabetic kidney changes. This emphasizes the importance of genetic background in this model of diabetic complications

Modelling hurricane track memory

It has been observed that hurricanes that are close in time often follow similar paths. If this can be shown to be statistically significant, it could have implications for how insurance premiums are calculated in areas of the US prone to hurricanes. We developed two independent path distance metrics and while one suggested that sequential storms within a given hurricane season are more likely to follow each other than any other pair of storms within that season, this conclusion was not supported by the other metric. Some considerations of how local and large scale air pressure gradients might affect hurricane paths were considered. A point vortex model in the presence of a steering flow field was developed and used to simulate the path of two time displaced vortices. In order for the vortices to follow each other they had to be relatively weak compared to the steering flow field. At realistic vortex strength, the trajectories became chaotic. In summary, our metrics provided conflicting evidence towards the no- tion of hurricane track memory. A large-scale steering flow field did not appear to provide sufficient explanation for hurricanes following each other, though this does not preclude hurricane track memory being due to localised physical changes following a large storm

Verdipapirforetakets lojalitetsplikt ved inngåelse av kommersielle investeringsavtaler - Privatrettslige følger av informasjonspliktene i MiFID artikkel 19 samt verdipapirhandelloven § 10-11

Oppgaven tar for seg forholdet mellom de offentligrettslige reglene for verdipapirforetakets opptreden og det privatrettslige ansvaret ved inngåelse av investeringsparter med næringsdrivende kunder. Fokus er på hvordan dette påvirker verdipapirforetaket lojalitetsplikt og for å sette problemstillingen i et større perspektiv medtas en komparativ komponent som redegjør for i hvilken grad de offentligrettslige reglenes mål om en harmonisert investorbeskyttelse oppnås gjennom den privatrettslige innvirkningen i engelsk privatrett samt hvilken betydning en eventuell utvidelse av lojalitetsplikten får for denne grunnleggende karakteristikken som skiller common law og civil law