Some Weyl modules of the algebraic groups of type E6E_6

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$ is the fundamental weight of the standard $27$-dimensional module. In the process, the structures of other Weyl modules with highest weights linked to $r\omega_1$ are also found. %We also give some computations for the Weyl modules with highest weights %of the form $r(\omega_1+\omega_6)$, which arise in the study of %the graph automorphism and associated twisted finite groups.Comment: 25 page

Joint strategy fictitious play with inertia for potential games

We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion

Cooperative Control and Potential Games

We present a view of cooperative control using the language of learning in games. We review the game-theoretic concepts of potential and weakly acyclic games, and demonstrate how several cooperative control problems, such as consensus and dynamic sensor coverage, can be formulated in these settings. Motivated by this connection, we build upon game-theoretic concepts to better accommodate a broader class of cooperative control problems. In particular, we extend existing learning algorithms to accommodate restricted action sets caused by the limitations of agent capabilities and group based decision making. Furthermore, we also introduce a new class of games called sometimes weakly acyclic games for time-varying objective functions and action sets, and provide distributed algorithms for convergence to an equilibrium

Emission characteristics of a diesel engine using waste cooking oil as biodiesel fuel

In this study, the use of waste cooking oil (WCO) methyl ester as an alternative fuel in a four-stroke turbo diesel engine with four cylinders, direct injection and 85 HP was analyzed. A test was applied in which an engine was fueled with diesel and three different blends of diesel/biodiesel (B25, B50 and B75) made from WCO. The test engine was run at 18 different speeds with a full load, and the results were analyzed. The biodiesel fuels produced slightly less smoke than the conventional diesel fuel, which could be attributed to better combustion efficiency. The use of biodiesel resulted in lower emissions of total hydrocarbon (THC) and CO, and increased emissions of NOx. This study showed that the exhaust emissions of diesel/biodiesel blends were lower than those of the diesel fuels, which indicates that biodiesel has more favorable effects on air quality.Key words: Alternative fuels, biodiesel

Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games

We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are “payoff-based” processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network

Relative Odds of Neck Pain to Helmet Use Among Motorcyclists: a Case-Control Study

Background: Neck pain is a widespread problem among motorcyclists, which is often neglected. There is limited research on the motorcycle's ergonomics, particularly in the context of the interaction between the riders and motorcycle. Motorcycle helmets have proven to increase the weight on the neck, thus causing more burdens which can lead to neck pain. Methodology: Case-Control study design was opted to measure the relative odds of neck pain in relation to the helmet use as an exposure. A total of 260 (mean age of 22.58 ± S.D. 1.95 years) undergraduate students were selected using purposive sampling. The case to control ratio was 1:4 (54 Cases and 206 Controls) where cases were defined as the motorcyclists having neck pain with a riding experience of more than one year. The neck pain and disability scale were obtained using a self-administered questionnaire. Chi-square and binary logistic regression were used to calculate the significant relationship and odds of neck pain amongst motorcyclists with and without helmet use. Results: The study results showed that out of 260 motorcyclists, 190 (73.1%) were helmet users, and 54 (20.8%) had neck pain, 70 (27.9%) helmet users had a neck pain prevalence of 11 (4.2%). The relative odd to have neck pain was 2.13 times more amongst the motorcyclists using the helmet as compared to that of non-helmet users. The logistic regression results showed significant results (P < 0.05) with regards to the BMI, helmet weight and duration of helmet use but did not show a significant relation with average motorcycle use per day unless it exceeded 70 kilometres. Conclusion: Use of helmet can be a potential cause of neck pain amongst motorcyclist users but the odds to have neck pain enhance with the increase in motorcycle use per day. The protective benefits are multi-fold for helmet use which outreaches the negative impact, including neck pain amongst motorcyclists