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

The Neural Representation of Concepts at the Sensor Level

This report presents a mathematical model of the semantics, or meaning, of the connec-tionist structure and stimulus activity of a neural network, whether artificial or biologi-cal. The mathematical model associates concepts about sensed objects with the neuron-like nodes in a neural network and composable concept relationships with the connec-tion pathways in the network. Category-theoretic constructs, specifically colimits, limits, and functors, organize the concept structure and map it to a formal neural network in a structure-preserving manner. Starting with a simple example of a neural vision system, we show that this mathematical model of neural network structure and activity can be used to derive connectionist architectures that work as intended. We also claim an additional advantage of this approach: A properly-functioning connectionist architecture has an ac-companying concept representation and this representation is both local and distributed. These properties are derived from the category-theoretic formalism described here

Neuroengineering of Clustering Algorithms

Cluster analysis can be broadly divided into multivariate data visualization, clustering algorithms, and cluster validation. This dissertation contributes neural network-based techniques to perform all three unsupervised learning tasks. Particularly, the first paper provides a comprehensive review on adaptive resonance theory (ART) models for engineering applications and provides context for the four subsequent papers. These papers are devoted to enhancements of ART-based clustering algorithms from (a) a practical perspective by exploiting the visual assessment of cluster tendency (VAT) sorting algorithm as a preprocessor for ART offline training, thus mitigating ordering effects; and (b) an engineering perspective by designing a family of multi-criteria ART models: dual vigilance fuzzy ART and distributed dual vigilance fuzzy ART (both of which are capable of detecting complex cluster structures), merge ART (aggregates partitions and lessens ordering effects in online learning), and cluster validity index vigilance in fuzzy ART (features a robust vigilance parameter selection and alleviates ordering effects in offline learning). The sixth paper consists of enhancements to data visualization using self-organizing maps (SOMs) by depicting in the reduced dimension and topology-preserving SOM grid information-theoretic similarity measures between neighboring neurons. This visualization\u27s parameters are estimated using samples selected via a single-linkage procedure, thereby generating heatmaps that portray more homogeneous within-cluster similarities and crisper between-cluster boundaries. The seventh paper presents incremental cluster validity indices (iCVIs) realized by (a) incorporating existing formulations of online computations for clusters\u27 descriptors, or (b) modifying an existing ART-based model and incrementally updating local density counts between prototypes. Moreover, this last paper provides the first comprehensive comparison of iCVIs in the computational intelligence literature --Abstract, page iv

A framework for analyzing changes in health care lexicons and nomenclatures

Ontologies play a crucial role in current web-based biomedical applications for capturing contextual knowledge in the domain of life sciences. Many of the so-called bio-ontologies and controlled vocabularies are known to be seriously defective from both terminological and ontological perspectives, and do not sufficiently comply with the standards to be considered formai ontologies. Therefore, they are continuously evolving in order to fix the problems and provide valid knowledge. Moreover, many problems in ontology evolution often originate from incomplete knowledge about the given domain. As our knowledge improves, the related definitions in the ontologies will be altered. This problem is inadequately addressed by available tools and algorithms, mostly due to the lack of suitable knowledge representation formalisms to deal with temporal abstract notations, and the overreliance on human factors. Also most of the current approaches have been focused on changes within the internal structure of ontologies, and interactions with other existing ontologies have been widely neglected. In this research, alter revealing and classifying some of the common alterations in a number of popular biomedical ontologies, we present a novel agent-based framework, RLR (Represent, Legitimate, and Reproduce), to semi-automatically manage the evolution of bio-ontologies, with emphasis on the FungalWeb Ontology, with minimal human intervention. RLR assists and guides ontology engineers through the change management process in general, and aids in tracking and representing the changes, particularly through the use of category theory. Category theory has been used as a mathematical vehicle for modeling changes in ontologies and representing agents' interactions, independent of any specific choice of ontology language or particular implementation. We have also employed rule-based hierarchical graph transformation techniques to propose a more specific semantics for analyzing ontological changes and transformations between different versions of an ontology, as well as tracking the effects of a change in different levels of abstractions. Thus, the RLR framework enables one to manage changes in ontologies, not as standalone artifacts in isolation, but in contact with other ontologies in an openly distributed semantic web environment. The emphasis upon the generality and abstractness makes RLR more feasible in the multi-disciplinary domain of biomedical Ontology change management