Primary visual cortex as a saliency map: parameter-free prediction of behavior from V1 physiology

It has been hypothesized that neural activities in the primary visual cortex (V1) represent a saliency map of the visual field to exogenously guide attention. This hypothesis has so far provided only qualitative predictions and their confirmations. We report this hypothesis' first quantitative prediction, derived without free parameters, and its confirmation by human behavioral data. The hypothesis provides a direct link between V1 neural responses to a visual location and the saliency of that location to guide attention exogenously. In a visual input containing many bars, one of them saliently different from all the other bars which are identical to each other, saliency at the singleton's location can be measured by the shortness of the reaction time in a visual search task to find the singleton. The hypothesis predicts quantitatively the whole distribution of the reaction times to find a singleton unique in color, orientation, and motion direction from the reaction times to find other types of singletons. The predicted distribution matches the experimentally observed distribution in all six human observers. A requirement for this successful prediction is a data-motivated assumption that V1 lacks neurons tuned simultaneously to color, orientation, and motion direction of visual inputs. Since evidence suggests that extrastriate cortices do have such neurons, we discuss the possibility that the extrastriate cortices play no role in guiding exogenous attention so that they can be devoted to other functional roles like visual decoding or endogenous attention.Comment: 11 figures, 66 page

Unified pictures of Q-balls and Q-tubes

While Q-balls have been investigated intensively for many years, another type of nontopological solutions, Q-tubes, have not been understood very well. In this paper we make a comparative study of Q-balls and Q-tubes. First, we investigate their equilibrium solutions for four types of potentials. We find, for example, that in some models the charge-energy relation is similar between Q-balls and Q-tubes while in other models the relation is quite different between them. To understand what determines the charge-energy relation, which is a key of stability of the equilibrium solutions, we establish an analytical method to obtain the two limit values of the energy and the charge. Our prescription indicates how the existent domain of solutions and their stability depends on their shape as well as potentials, which would also be useful for a future study of Q-objects in higher-dimensional spacetime.Comment: 11 pages, 14 figure

Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution

Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between B\"acklund transformations for discrete and ultradiscrete KdV equations.Comment: 11 page

Multiconditional Approximate Reasoning with Continuous Piecewise Linear Membership Functions

It is shown that, for some intersection and implication functions, an exact and efficient algorithm exists for the computation of inference results in multiconditional approximate reasoning on domains which are finite intervals of the real numbers, when membership functions are restricted to functions which are continuous and piecewise linear. An implementation of the algorithm is given in the functional programming language Miranda

A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation

The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slow-to-start (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as well as the time continuous limit, which lead the s2s-OVCA to an integral-differential equation, are presented. Several traffic phases such as a free flow as well as slow flows corresponding to multiple metastable states are observed in the flow-density relations of the s2s-OVCA. Based on the properties of the stationary flow of the s2s-OVCA, the formulas for the flow-density relations are derived