This paper presents a general computational treatment of how mammals are able to deal with visual objects and environments. The model tries to cover the entire range from behavior and phenomenological experience to detailed neural encodings in crude but computationally plausible reductive steps. The problems addressed include perceptual constancies, eye movements and the stable visual world, object descriptions, perceptual generalizations, and the representation of extrapersonal space.The entire development is based on an action-oriented notion of perception. The observer is assumed to (...) be continuously sampling the ambient light for information of current value. The central problem of vision is taken to be categorizing and locating objects in the environment. The critical step in this process is the linking of visual information to symbolic object descriptions; this is calledindexing, from the analogy of identifying a book from index terms. The system must also identifysituationsand use this knowledge to guide movement and other actions in the environment. The treatment focuses on the different representations of information used in the visual system.The four representational frames capture information in the following forms: retinotopic, head-based, symbolic, and allocentric. The functional roles of the four frames, the communication among them, and their suggested neurophysiological realization constitute the core of the paper. The model is perforce crude, but appears to be consistent with all relevant findings. (shrink)

This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker showed that a simple game is non-weighted if and only if there exists a trading transform of finite size. They also provided an upper bound on the size of such a trading transform, if it exists. Gvozdeva and Slinko improved that upper bound; their proof employed a property of (...) linear inequalities demonstrated by Muroga. In this study, we provide a new proof of the existence of a trading transform when a given simple game is non-weighted. Our proof employs Farkas’ lemma, and yields an improved upper bound on the size of a trading transform. We also discuss an integer-weight representation of a weighted simple game, improving the bounds obtained by Muroga. We show that our bound on the quota is tight when the number of players is less than or equal to five, based on the computational results obtained by Kurz. Furthermore, we discuss the problem of finding an integer-weight representation under the assumption that we have minimal winning coalitions and maximal losing coalitions. In particular, we show a performance of a rounding method. Finally, we address roughly weighted simple games. Gvozdeva and Slinko showed that a given simple game is not roughly weighted if and only if there exists a potent certificate of non-weightedness. We give an upper bound on the length of a potent certificate of non-weightedness. We also discuss an integer-weight representation of a roughly weighted simple game. (shrink)

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for (...) this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions. (shrink)