We consider a class of mean field games in which the agents interact through both their states and controls, we focus on situations generic agent tries to adjust her speed (control) an average (the is made neighborhood state space). In such cases, monotonicity assumptions that are frequently theory do not hold, uniqueness cannot be expected general. Such model lead systems forward-backward nonl...

BACKGROUND The federal menu labeling law will require chain restaurants to post caloric information on menus, but the impact of labeling is uncertain. PURPOSE The goal of the current study was to examine the effect of menu labeling on calories purchased, and secondarily, to assess self-reported awareness and use of labels. DESIGN Single-community pre-post-post cross-sectional study. Data we...

The abstract model-theoretic concepts of compactness and Löwenheim–Skolem properties are investigated in the “softer” framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institutio...

A conflict-avoiding code of length n and weight k is defined as a set C ⊆ {0, 1}n of binary vectors, called codewords, all of Hamming weight k such that the distance of arbitrary cyclic shifts of two distinct codewords in C is at least 2k − 2. In this paper, we obtain direct constructions for optimal conflict-avoiding codes of length n = 16m and weight 3 for any m by utilizing Skolem type seque...