Fragmented Spatial Maps: State Abstraction and Efficient Planning from Surprisal

When animals explore spatial environments, their representations often fragment into multiple maps. What determines these map fragmentations, and can we predict where they will occur with simple principles? We pose the problem of fragmentation of an environment as one of (online) spatial clustering. Taking inspiration from the notion of a "contiguous region" in robotics, we develop a theory in which fragmentation decisions are driven by surprisal. When this criterion is implemented with boundary, grid, and place cells in various environments, it produces map fragmentations from the first exploration of each space. Augmented with a long-term spatial memory and a rule similar to the distance-dependent Chinese Restaurant Process for selecting among relevant memories, the theory predicts the reuse of map fragments in environments with repeating substructures. Our model provides a simple rule for generating spatial state abstractions and predicts map fragmentations observed in electrophysiological recordings. It further predicts that there should be "fragmentation decision" or "fracture" cells, which in multicompartment environments could be called "doorway" cells. Finally, we show that the resulting abstractions can lead to large (orders of magnitude) improvements in the ability to plan and navigate through complex environments.

A Computer Model of the Spread of the Pandemic and its Analysis

The paper describes and analyzes a mathematical model of the variable state of the incidence of epidemic diseases, which is of great importance for determining the quantity of vaccines and antiviral drugs to be produced. The information model according to the system of differential equations of the spread of the pandemic is illustrated in a structural diagram. The model is presented in a vector-matrix form and the state of equilibrium of the model in the spatial state is proved.The model of the spread of the pandemic was developed, whose implementation with a Matlab software package resulted in obtaining the curves of variation of the state. The developed computer model of the incidence of epidemic diseases can be used to make a projection of the number of infected people, as well as intensity of the process of disseminating information and ideas in the community.

A Graph-Theoretic Approach to Understanding Emergent Behavior in Physical Systems

The exact dynamics of emergence remains one of the most prominent outstanding questions for the field of complexity science. I first discuss various perspectives on emergence in various contexts, then offer a different perspective on understanding emergence in a graph-theoretic representation. From the discussion, an observer’s choice in state space seems to have an effect for that observer to detect emergent behavior. To test these ideas, I analyze the dynamics of all possible spatial state spaces near the critical temperature in an Ising model. As a result, state space topologies that appear more deterministic flip more bits than topologies that appear more random, which is contrary to our intuitions about randomness. In addition, the size of different state spaces constrain a system’s ability to explore various states within the same time frame. These results are important to understanding emergent phenomena in biological systems, which are layered with various state spaces and observational perspectives.

Symmetric cascade distribution of electrons in atoms

Through the spatial state analysis, the symmetrical cascade distribution of electrons in the atom is obtained. This kind of electron distribution can naturally describe the periodicity of elements and the characteristics of each element. The reason for the formation of the common valence of each element can be explained according to the number and state of valence electron orbitals. The rule that the number of electrons in the orbit tends to reach an even number is applicable not only within atoms, but also between atoms, and can uniformly explain the general process of binding between atoms.

A GIS-based three-dimensional landslide generated waves height calculation method

Combined with the spatial data processing capability of geographic information systems (GIS), a three-dimensional (3D) landslide surge height calculation method is proposed based on grid column units. First, the data related to the landslide are rasterized to form grid columns, and a force analysis model of 3D landslides is established. Combining the vertical strip method with Newton's laws of motion, dynamic equilibrium equations are established to solve for the surge height. Moreover, a 3D landslide surge height calculation expansion module is developed in the GIS environment, and the results are compared with those of the two-dimensional Pan Jiazheng method. Comparisons show that the maximum surge height obtained by the proposed method is 24.6 % larger than that based on the Pan Jiazheng method. Compared with the traditional two-dimensional method, the 3D method proposed in this paper better represents the actual spatial state of the landslide and is more suitable for risk assessment.

Expanded Jones complex space model to describe arbitrary higher-order spatial states in fiber

As a new multiplexing dimension, spatial modes are catching increasing attentions nowadays. It is a fundamental task to establish an appropriate theoretical model to describe these spatial modes, especially higher-order spatial modes. However, existing theoretical models are only able to explain some special higher-order spatial states in fiber. The basic problem in these models is that their discussed dimensions are not enough. Indeed, to describe a higher-order spatial state, at least four dimensions are needed. In this paper, we present an expanded Jones complex space model, which is four-dimensional when a single higher-order state is discussed. The expanded Jones model is based on the discussion of an arbitrary combination of four degenerated higher-order modes. As a result, arbitrary spatial states are described. Because the number of used dimensions matches that of the problem, the descriptions of higher-order modes are more complete than other models. Also, we have verified the reliability of the expanded Jones model in our experiment. This model has the potential to simplify many analyses related to spatial modes in fiber.