Perception of Space by Multiple Intrinsic Frames of Reference

It has been documented that when memorizing a physical space, the person's mental representation of that space is biased with distortion and segmentation. Two experiments reported here suggest that distortion and segmentation arise due to a hierarchical organization of the spatial representation. The spatial relations associated with salient landmarks are more strongly encoded and easier to recall than those associated with non-salient landmarks. In the presence of multiple salient landmarks, multiple intrinsic frames of reference are formed and spatial relations are anchored to each individual frame of reference. Multiple such representations may co-exist and interactively determine a person's spatial performance

On some impulsive fractional differential equations in Banach spaces

This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of $PC$-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration

Asymptotically Efficient Quasi-Newton Type Identification with Quantized Observations Under Bounded Persistent Excitations

This paper is concerned with the optimal identification problem of dynamical systems in which only quantized output observations are available under the assumption of fixed thresholds and bounded persistent excitations. Based on a time-varying projection, a weighted Quasi-Newton type projection (WQNP) algorithm is proposed. With some mild conditions on the weight coefficients, the algorithm is proved to be mean square and almost surely convergent, and the convergence rate can be the reciprocal of the number of observations, which is the same order as the optimal estimate under accurate measurements. Furthermore, inspired by the structure of the Cramer-Rao lower bound, an information-based identification (IBID) algorithm is constructed with adaptive design about weight coefficients of the WQNP algorithm, where the weight coefficients are related to the parameter estimates which leads to the essential difficulty of algorithm analysis. Beyond the convergence properties, this paper demonstrates that the IBID algorithm tends asymptotically to the Cramer-Rao lower bound, and hence is asymptotically efficient. Numerical examples are simulated to show the effectiveness of the information-based identification algorithm.Comment: 16 pages, 3 figures, submitted to Automatic

On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces

In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration

Insight into others’ minds: spatio-temporal representations by intrinsic frame of reference

Recent research has seen a growing interest in connections between domains of spatial and social cognition. Much evidence indicates that processes of representing space in distinct frames of reference (FOR) contribute to basic spatial abilities as well as sophisticated social abilities such as tracking other’s intention and belief. Argument remains, however, that belief reasoning in social domain requires an innately dedicated system and cannot be reduced to low-level encoding of spatial relationships. Here we offer an integrated account advocating the critical roles of spatial representations in intrinsic frame of reference. By re-examining the results from a spatial task (Tamborello etal., 2012) and a false-belief task (Onishi and Baillargeon, 2005), we argue that spatial and social abilities share a common origin at the level of spatio-temporal association and predictive learning, where multiple FOR-based representations provide the basic building blocks for efficient and flexible partitioning of the environmental statistics. We also discuss neuroscience evidence supporting these mechanisms. We conclude that FOR-based representations may bridge the conceptual as well as the implementation gaps between the burgeoning fields of social and spatial cognition