An implementation of the reduced gradient algorithm is proposed to solve the linear L1 estimation problem (least absolute deviations regression) with linear equality or inequality constraints, including rank deficient and degenerate cases. Degenerate points are treated by solving a derived L1 problem to give a descent direction. The algorithm is a direct descent, active set method that is shown...

Inequality constraints are often needed in optimization problems in order to deal with uncertainty. This paper introduces a simple technique that allows enforcement of inequality constraints in `1 norm problems without any modi cations to existing programs. The solution of `1 norm problems is required, for example, in implementing LAV (Least Absolute Value) state estimators in electric power sy...

1. Sociocultural Behavior Understanding From the intelligence analyst in the command center identifying deviations from typical patterns of life to the small unit leader on the ground negotiating with a village elder, the ability to understand sociocultural behavior is vital for achieving mission success. According to Schmorrow (2011), accurate analysis of sociocultural behavior requires a “tho...

In this paper we start with analysing conservative stable standard of behaviour (CSSB), (Greenberg (1990)) and find that it has very little predictive power in social environments with farsighted players (modelled in Xue (1998)) although intuitively it is quite nice. Therefore, we go into two directions: modify this solution notion a bit and also restrict the class of feasible deviations. We st...

Compliance with social norms requires neural signals related both to the norm and to deviations from it. Recent work using economic games between two interacting subjects has uncovered brain responses related to norm compliance and to an individual's strategic outlook during the exchange. These brain responses possess a provocative relationship to those associated with negative emotional outcom...

We explore the ability to distinguish random from non-random events. Randomness is defined in terms of radioactive decay whereas non-randomness is quantified by excess repetitions (“repeat”) or alternations (“switch”) between successive bits. In the first four experiments no mention was made of randomness, probability, or related concepts in task instructions. We found superior performance in d...

Given n sets on n elements it is shown that there exists a two-coloring such that all sets have discrepancy at most Kn>/2, K an absolute constant. This improves the basic probabilistic method with which K = c(ln«)1/2. The result is extended to 11 finite sets of arbitrary size. Probabilistic techniques are melded with the pigeonhole principle. An alternate proof of the existence of Rudin-Shapiro...

In this paper I offer necessary and sufficient conditions for implementability in a quasi-linear principal-agent model with arbitrary type spaces. I extend Rochet’s Theorem by allowing the principal to observe information that may be correlated with the agent’s type. By viewing the agent’s gains from misreporting as payments in a hypothetical zero-sum game, I show that an allocation is implemen...