Episodic Memory via Spans and Cospans: A Hierarchy of Spatiotemporal Colimits

We introduce a category-theoretic account of episodic memory as an outgrowth of an existing mathematical theory of the semantics of neural networks. We propose that neu- ral systems which can be said to have episodic memory represent sequences of events and their associated information within a hierarchy of concepts, represented in their neu- ral networks. In the categorical model presented here, the hierarchy is based upon col- imits. Colimits “put everything together” mathematically, and appear throughout many categories. The event-sequence colimits can be visualized as assemblies of categorical structures known as spans and cospans. A string of cospans formalizes a hierarchy of overlapping episode segments, with the segments increasing in length by adding a next event as an episode progresses. The concept category can be mapped into a category that expresses the structure and activity of a neural architecture. An episodic sequence is for- malized as a string of cospans of its overlapping episodic segments. This kind of neural structure supports the tracing of its event sequence in either the forward or reverse direc- tion during recall, but it also does much more: It allows a holistic access to an episode or entire segments of the episode, it maintains the continuity of that information which is preserved between successive events, and, finally, the cospan cells serve as explicit repre- sentatives of the temporal order of events, making a sequence available not only for recall but also for direct access to subsequences of greatest interest. We end with a preliminary sketch of the application of this episodic memory model to understanding the interaction of the hippocampus with other structures of the mammalian medial temporal lobe

LONG-PERIOD SOLAR OSCILLATIONS: A SEISMOLOGICAL AND INTERCOMPARATIVE STUDY

This work deals with the subject of global solar oscillations. These oscillations are observed as fluctuations in the diameter of the sun. A diameter is determined by a mathematical solar edge definition at the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA) instrument. The oscillations have periods ranging from a few minutes to several hours and have amplitudes measured in millionths of a solar radius. These small amplitudes are observable only due to the unique properties of the edge definition. The properties of the observed solar oscillations are determined from the data; their statistical significance and repeatability are then tested. The possibility of using the observed oscillations as a seismic tool for understanding the solar interior and its motions is explored

A Low Complexity Recursive Force-Directed Tree Layout Algorithm Based on the Lennard-Jones Potential

In this paper, a low complexity force-directed tree layout algorithm based on the Lennard-Jones potential is described. The recursive method lays out sub-trees as small disks contained in their parent disk. Inside each disk, children disks are dynamically laid out using a new force directed simulation. Unlike most other force directed layout methods which run in quadratic time for each simulation step, this algorithm runs in O   m ¡ 1 n ¢ m time per each step for a tree with n nodes, depth m and all the nodes having uniform number of children. The layout uses space efficiently and reflects both global structure and local detail. The method supports runtime insertion and deletion. Both operations and the evolving process are rendered with smooth animation to preserve visual continuity. The method could be used to monitor in real time, visualize and analyze a wide variety of data which has a rooted tree structure, e.g. internet hosts could be laid out by domain name (DNS) hierarchies. This paper gives a description of the algorithm, a complexity analysis and an example of how the algorithm is implemented to visualize DNS tree