Self-Organizing Map Neural Architectures Based on Limit Cycle Attractors

Recent efforts to develop large-scale neural architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason is that most conventional SOMs use a static encoding representation: Each input is typically represented by the fixed activation of a single node in the map layer. This not only carries information in an inefficient and unreliable way that impedes building robust multi-SOM neural architectures, but it is also inconsistent with rhythmic oscillations in biological neural networks. Here I develop and study an alternative encoding scheme that instead uses limit cycle attractors of multi-focal activity patterns to represent input patterns/sequences. Such a fundamental change in representation raises several questions: Can this be done effectively and reliably? If so, will map formation still occur? What properties would limit cycle SOMs exhibit? Could multiple such SOMs interact effectively? Could robust architectures based on such SOMs be built for practical applications? The principal results of examining these questions are as follows. First, conditions are established for limit cycle attractors to emerge in a SOM through self-organization when encoding both static and temporal sequence inputs. It is found that under appropriate conditions a set of learned limit cycles are stable, unique, and preserve input relationships. In spite of the continually changing activity in a limit cycle SOM, map formation continues to occur reliably. Next, associations between limit cycles in different SOMs are learned. It is shown that limit cycles in one SOM can be successfully retrieved by another SOM’s limit cycle activity. Control timings can be set quite arbitrarily during both training and activation. Importantly, the learned associations generalize to new inputs that have never been seen during training. Finally, a complete neural architecture based on multiple limit cycle SOMs is presented for robotic arm control. This architecture combines open-loop and closed-loop methods to achieve high accuracy and fast movements through smooth trajectories. The architecture is robust in that disrupting or damaging the system in a variety of ways does not completely destroy the system. I conclude that limit cycle SOMs have great potentials for use in constructing robust neural architectures.

DISSIMILAR CONTEMPORARIES: SELECTED PIANO MUSIC OF SERGEI RACHMANINOFF AND SERGEI PROKOFIEV

Virtual contemporaries, Sergei Rachmaninoff and Sergei Prokofiev were pianists, steeped in the traditions of Russian pianism; recordings of both pianists-composers playing their own works are available. Although the composers can be perceived as having little in common, in fact both composed in classical forms, both had a strong lyrical sense and both had an unbreakable connection with their Russian heritage. Rachmaninoff was the last great representative of Russian late Romanticism as well as one of the finest pianists of his generation. He cultivated a sweepingly passionate and melodious idiom, with pronounced lyrical quality, expressive breath and structural ingenuity. Prokofiev, on the other hand, tried to push the Russian Romantic traditions to a point of exacerbation and caricature before experimenting with various kinds of modernism. Stressing simplicity, he helped invent Neo-Classicism. His melodies are essentially tonal with wide skips and sweeping long lines. Harmonically, he used triadic harmony full of dissonances, strange inversions, unusual spacings, and jarring juxtapositions. Writing in classical forms, he incorporated rhythmic vitality and lyrical elements into his music. I have chosen to perform five works by each composer, written in a variety of genres, including the sonata, the toccata, variations, the concerto. I also have divided the pieces into three recital programs to show the idiosyncratic characteristics of the composers. I have endeavored to select pieces based on the technical and artistic challenges that they offer, thereby allowing me to grow as a pianist and an artist. My goal is to gain a thorough understanding of not only the pieces but also the musical styles of both composers.

Scrapbook

The poems in Scrapbook are rooted in memory and the act of remembering. While the poems explore different personas and landscapes, they continually return to the poet’s childhood home: a falling apart 50s rancher, where the domestic and mundane are always accompanied by the bizarre. While the mother tries to make order out of these experiences, the poet becomes the quiet observer, journaling and collecting memories her mother would prefer to silence. Influenced by Elizabeth Bishop, Patricia Smith and Shuntaro Tanikawa, these poems tell stories through colloquial language that understates the strange details of everyday life.

The New Jersey Meadowlands: Inhabiting an Urban Wilderness

The New Jersey Meadowlands is a thirty square mile industrial wetland between New York City and the commercial district of East Rutherford, NJ. The place is both strange and fascinating; many mysteries are hidden between the reed grasses and scattered garbage. Often exposed to subjectivity, the Meadowlands is commonly perceived as a weird, polluted, industrial, and even an other-worldly space; few know its beauty. These differing perceptions create a challenge when thinking of a cohesive identity and sense of place in the marsh. Over time, the once pure landscape has suffered from infrastructural slices, illegal dumping, and environmental abuse, resulting in fragmented land areas along the Hackensack River’s edge. This thesis explores how to inhabit an ecologically devalued and residual landscape through ideas of place-making and re-connecting communities. Investigating the paradox of this massive urban landscape and capitalizing on the ecological and educational potential of the site, lends also to a challenge of converging modern and forgotten life. Designing a place-based ecological research community within this currently placeless environment, will engage the public, re-connect lost communities, and bring a sense of renewal to the marsh.