Mathematical Foundations of Consciousness

We employ the Zermelo-Fraenkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo-Fraenkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so- called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question

An Infinity of Questions: Dramatizing Science on Stage

My Honors thesis, An Infinity of Questions, explores the performance of science on stage using two plays: The Life of Galileo, challenging the status quo, by Bertolt Brecht and Copenhagen, examining the origins of intention, by Michael Frayn. I focus on these two plays because not only because they impress me personally, but both spring from historical events and are thematically concerned with physics and the atomic bomb. They also make an interesting juxtaposition since Galileo has a decidedly political agenda, while Copenhagen is a philosophic inquiry. I argue that these dramas are exceptional science plays because of how they literally enact the ideas that they examine and bring science to life on stage by means of modeling ideas

An Infinity of Questions: Dramatizing Science on Stage

My Honors thesis, An Infinity of Questions, explores the performance of science on stage using two plays: The Life of Galileo, challenging the status quo, by Bertolt Brecht and Copenhagen, examining the origins of intention, by Michael Frayn. I focus on these two plays because not only because they impress me personally, but both spring from historical events and are thematically concerned with physics and the atomic bomb. They also make an interesting juxtaposition since Galileo has a decidedly political agenda, while Copenhagen is a philosophic inquiry. I argue that these dramas are exceptional science plays because of how they literally enact the ideas that they examine and bring science to life on stage by means of modeling ideas

Predicting Combinatorial Binding of Transcription Factors to Regulatory Elements in the Human Genome by Association Rule Mining

Cis-acting transcriptional regulatory elements in mammalian genomes typically contain specific combinations of binding sites for various transcription factors. Although some cisregulatory elements have been well studied, the combinations of transcription factors that regulate normal expression levels for the vast majority of the 20,000 genes in the human genome are unknown. We hypothesized that it should be possible to discover transcription factor combinations that regulate gene expression in concert by identifying over-represented combinations of sequence motifs that occur together in the genome. In order to detect combinations of transcription factor binding motifs, we developed a data mining approach based on the use of association rules, which are typically used in market basket analysis. We scored each segment of the genome for the presence or absence of each of 83 transcription factor binding motifs, then used association rule mining algorithms to mine this dataset, thus identifying frequently occurring pairs of distinct motifs within a segment. Results: Support for most pairs of transcription factor binding motifs was highly correlated across different chromosomes although pair significance varied. Known true positive motif pairs showed higher association rule support, confidence, and significance than background. Our subsets of high-confidence, high-significance mined pairs of transcription factors showed enrichment for co-citation in PubMed abstracts relative to all pairs, and the predicted associations were often readily verifiable in the literature. Conclusion: Functional elements in the genome where transcription factors bind to regulate expression in a combinatorial manner are more likely to be predicted by identifying statistically and biologically significant combinations of transcription factor binding motifs than by simply scanning the genome for the occurrence of binding sites for a single transcription factor.NIAAA Alcohol Training GrantNational Science FoundationCellular and Molecular Biolog

Constitute: The world’s constitutions to read, search, and compare

Constitutional design and redesign is constant. Over the last 200 years, countries have replaced their constitutions an average of every 19 years and some have amended them almost yearly. A basic problem in the drafting of these documents is the search and analysis of model text deployed in other jurisdictions. Traditionally, this process has been ad hoc and the results suboptimal. As a result, drafters generally lack systematic information about the institutional options and choices available to them. In order to address this informational need, the investigators developed a web application, Constitute [online at http://www.constituteproject.org], with the use of semantic technologies. Constitute provides searchable access to the world’s constitutions using the conceptualization, texts, and data developed by the Comparative Constitutions Project. An OWL ontology represents 330 ‘‘topics’’ – e.g. right to health – with which the investigators have tagged relevant provisions of nearly all constitutions in force as of September of 2013. The tagged texts were then converted to an RDF representation using R2RML mappings and Capsenta’s Ultrawrap. The portal implements semantic search features to allow constitutional drafters to read, search, and compare the world’s constitutions. The goal of the project is to improve the efficiency and systemization of constitutional design and, thus, to support the independence and self-reliance of constitutional drafters.Governmen

DADO: A Parallel Processor for Expert Systems

DADO is a parallel, tree-structured machine designed to provide significant performance improvements in the execution of large expert systems implemented in production system form. A full-scale version of the DADO machine would comprise a large (on the order of a hundred thousand) set of processing elements (PE's), each containing its own processor, a small amount (16K bytes, in the current prototype design) of local random access memory, and a specialized I/O switch. The PE's are introduced to form a complete binary tree. This paper describes the application domain of the DADO machine and the rationale for its design. We then focus on the machine architecture and detail the hardware design of a moderately large prototype comprising 1023 microprocessors currently under development at Columbia University. We conclude with very encouraging performance statistics recently calculated from an analysis of extensive simulations of the system

Bounded-time fault-tolerant rule-based systems

Two systems concepts are introduced: bounded response-time and self-stabilization in the context of rule-based programs. These concepts are essential for the design of rule-based programs which must be highly fault tolerant and perform in a real time environment. The mechanical analysis of programs for these two properties is discussed. The techniques are used to analyze a NASA application