In this thesis, we consider hom-associative algebras, which is an algebra with multiplication that is not necessarily commutative nor associative, but obeys a twisted version of associativity by a linear homomorphism. We will give some conditions for associativity, which helps us determine commuting elements. Under other conditions, such as different types of unitality conditions, we can also state some results regarding commuting elements in the general, non-associative case.

Neuropsychiatric disorders severely impact quality of life in millions of patients, contributing more Disease Affected Life Years (DALYs) than cancer or cardiovascular disease. The human brain is a complex system of 100 billion neurons connected by 100 trillion synapses, and human studies of neural disease focus on network-level circuit activity changes, rather than on cellular mechanisms. To probe for neural dynamics on the cellular level, animal models such as the nematode C. elegans have been used to investigate the biochemical and genetic factors contributing to neurological disease. C. elegans are ideal for neurophysiological studies due to their small nervous system, neurochemical homology to humans, and compatibility with non-invasive neural imaging. To better study the cellular mechanisms contributing to neurological disease, we developed automated analysis methods for characterizing the behaviors and associated neural activity during sleep and learning in C. elegans: two neural functions that involve a high degree of behavioral and neural plasticity. We developed two methods to study previously uncharacterized spontaneous adult sleep in C. elegans. A large microfluidic device facilitates population-wide assessment of long-term sleep behavior over 12 hours including effects of fluid flow, oxygen, feeding, odors, and genetic perturbations. Smaller devices allow simultaneous recording of sleep behavior and neuronal activity. Since the onset of adult sleep is stochastically timed, we developed a closed-loop sleep detection system that delivers chemical stimuli to individual animals during sleep and awake states to assess state-dependent changes to neural responses. Sleep increased the arousal threshold to aversive chemical stimulation, yet sensory neuron (ASH) and first-layer interneuron (AIB) responses were unchanged. This localizes adult sleep-dependent neuromodulation within interneurons presynaptic to the AVA premotor interneurons, rather than afferent sensory circuits. Traditionally, the study of learning in C. elegans observes taxis on agar plates which present variable environmental conditions that can lead to a reduction in test-to-test reproducibility. We also translated the butanone enhancement learning assay such that animals can be trained and tested all within the controlled environment of a microfluidic device. Using this system, we demonstrated that C. elegans are capable of associative learning by observing stimulus evoked behavioral responses, rather than taxis. This system allows for more reproducible results and can be used to seamlessly study stimulus-evoked neural plasticity associated with learning. Together, these systems provide platforms for studying the connections between behavioral plasticity and neural circuit modulation in sleep and learning. We can use these systems to further our understanding of the mechanisms underlying neural regulation, function, and disorder using human disease models in C. elegans.

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<p>One of the most central and current debates among those studying human contingency learning (HCL) concerns whether it is best understood as the result of associative learning, a product of higher-order cognitive processes, or some combination thereof. Though the field appears to be moving toward the latter accounts, much of the evidence being generated to evaluate and select among them comes from tasks that typically present only information about the few variables involved in the contingency(s), in the exact same manner on every trial. While effective for examining how the statistical properties of experience affect learning, these procedures do not capture some of the conditions of everyday cognition and are apt to be less effective for engaging non-associative and top-down influences on performance.</p> <p>The current work introduces a task that involves learning contingencies in others' behavior from descriptions that require the learner to determine the focus of learning, and to deal with both variability in manifestation of the objects of learning and extraneous information. Across several experiments, performance reflects phenomena, including ΔP, outcome density and blocking effects, which have been well established in HCL and are consistent with associative accounts. At the same time, the findings also suggest that (a) domain-specific theories affect the weighting of evidence in contingency perception and the discoverability of contingencies, and (b) outcome predictions, a typical measure in HCL, are influenced by specific instance memory in addition to abstract contingency knowledge. These findings are difficult to reconcile with the data-driven nature of associative views, and join a growing number of demonstrations suggesting that a viable account of HCL must involve higher-order cognitive processes or top-down influences on performance.</p> / Thesis / Doctor of Philosophy (PhD)

Children with ADHD exhibit impairments in memory retrieval processes that are required for successful performance in a wide range of activities including social/interpersonal interactions, as well as academic success. There have been few attempts of explaining the relationship between these memory retrieval deficits in children with ADHD and specific executive functions such as working memory. The current study addresses the possible mediating effects of the subsystems of working memory (phonological short-term memory, visual-spatial short-term memory, and the central executive) on memory retrieval. Children ages 8-12 with ADHD and typically developing children completed a counterbalanced series of working memory tasks that were specific to the subsystems (phonological and visual-spatial). The Central Executive portion of working memory was obtained using a regression approach of these measures. The children also completed the Kaufman Test of Educational Achievement (KTEA-II), as the associational fluency task was used as the memory retrieval measure for this investigation.

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O objetivo deste trabalho é estudar a estrutura dos módulos sobre uma álgebra trivial de dimensão dois na variedade M das álgebras comutativas de potências associativas. Em particular classificamos os módulos irredutíveis. Estes resultados nos permitem compreender melhor a estrutura das nilálgebras comutativas de dimensão finita e nilíndice 4. Finalmente classificamos, sob isomorfismos, as nilálgebras comutativas de potências associativas de dimensão n e nilíndice n. / The aim of this work is to study the structure of the modules over a trivial algebra of dimension two in the variety M of commutative and power-associative algebras. In particular we classify the irreducible modules. These results enables us to understand better the structure of finite-dimensional power-associative nilalgebras of nilindex 4. Finally, we classify, up to isomorphism, commutative power associative nilalgebras of nilindex n and dimension n.

Associative Memories (AMs) are essential building blocks for brain-like intelligent computing with applications in artificial vision, speech recognition, artificial intelligence, and robotics. Computations for such applications typically rely on spatial and temporal associations in the input patterns and need to be robust against noise and incomplete patterns. The conventional method for implementing AMs is through Artificial Neural Networks (ANNs). Improving the density of ANN based on conventional circuit elements poses a challenge as devices reach their physical scalability limits. Furthermore, stored information in AMs is vulnerable to destructive input signals. Novel nano-scale components, such as memristors, represent one solution to the density problem. Memristors are non-linear time-dependent circuit elements with an inherently small form factor. However, novel neuromorphic circuits typically use memristors to replace synapses in conventional ANN circuits. This sub-optimal use is primarily because there is no established design methodology to exploit the memristor's non-linear properties in a more encompassing way. The objective of this thesis is to explore denser and more robust AM designs using memristor networks. We hypothesize that such network AMs will be more area-efficient than the traditional ANN designs if we can use the memristor's non-linear property for spatial and time-dependent temporal association. We have built a comprehensive simulation framework that employs Genetic Programming (GP) to evolve AM circuits with memristors. The framework is based on the ParadisEO metaheuristics API and uses ngspice for the circuit evaluation. Our results show that we can evolve efficient memristor-based networks that have the potential to replace conventional ANNs used for AMs. We obtained AMs that a) can learn spatial and temporal correlation in the input patterns; b) optimize the trade-off between the size and the accuracy of the circuits; and c) are robust against destructive noise in the inputs. This robustness was achieved at the expense of additional components in the network. We have shown that automated circuit discovery is a promising tool for memristor-based circuits. Future work will focus on evolving circuits that can be used as a building block for more complicated intelligent computing architectures.