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

A proposal for regularly updated review/survey articles: "Perpetual Reviews"

We advocate the publication of review/survey articles that will be updated regularly, both in traditional journals and novel venues. We call these "perpetual reviews." This idea naturally builds on the dissemination and archival capabilities present in the modern internet, and indeed perpetual reviews exist already in some forms. Perpetual review articles allow authors to maintain over time the relevance of non-research scholarship that requires a significant investment of effort. Further, such reviews published in a purely electronic format without space constraints can also permit more pedagogical scholarship and clearer treatment of technical issues that remain obscure in a brief treatment.Comment: This is a draft white paper and we seek comments from the communit

Cross-language Wikipedia Editing of Okinawa, Japan

This article analyzes users who edit Wikipedia articles about Okinawa, Japan, in English and Japanese. It finds these users are among the most active and dedicated users in their primary languages, where they make many large, high-quality edits. However, when these users edit in their non-primary languages, they tend to make edits of a different type that are overall smaller in size and more often restricted to the narrow set of articles that exist in both languages. Design changes to motivate wider contributions from users in their non-primary languages and to encourage multilingual users to transfer more information across language divides are presented.Comment: In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI 2015. AC

When the Conditions are the Confinement: Eighth Amendment Habeas Claims During COVID-19

The COVID-19 pandemic cast into harsher relief much that was already true about mass incarceration in the United States. It also cast into harsher relief much that was already true about the legal barriers confronting people seeking to make its conditions more humane. This Article offers a brief overview of the legal landscape as the COVID-19 crisis arose and then surveys eight prominent federal cases involving Eighth Amendment claims related to COVID-19 outbreaks at carceral facilities, most of which included significant litigation over whether they could secure release through habeas corpus. The Article then distills six key tensions from these cases—each a potential stumbling block for courts and litigants—and discusses their implications for future litigation and doctrine. Specifically, the Article addresses the following: (A) the relationship between habeas corpus and classic “conditions of confinement” cases; (B) the nature of Eighth Amendment “deliberate indifference” in this context; (C) the efficacy and availability of class-wide procedures for adjudicating these kinds of claims; (D) issues involving federalism and comity and how such concerns may motivate stricter enforcement of exhaustion requirements; (E) whether temporary release in the Eighth Amendment habeas context is better conceived of as preliminary or final relief; and (F) the fraught interplay between rights and remedies. The Article concludes by suggesting potential solutions for courts and legislatures

Hardness of approximation for quantum problems

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact hard to approximate. Using these techniques, we also obtain hardness of approximation for the class QCMA. Our approach is based on the use of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomial hierarchy [Umans, FOCS 1999]. The problems for which we prove hardness of approximation for include, among others, a quantum version of the Succinct Set Cover problem, and a variant of the local Hamiltonian problem with hybrid classical-quantum ground states.Comment: 21 pages, 1 figure, extended abstract appeared in Proceedings of the 39th International Colloquium on Automata, Languages and Programming (ICALP), pages 387-398, Springer, 201

The Chemical Composition of an Extrasolar Minor Planet

We report the relative abundances of 17 elements in the atmosphere of the white dwarf star GD 362, material that, very probably, was contained previously in a large asteroid or asteroids with composition similar to the Earth/Moon system. The asteroid may have once been part of a larger parent body not unlike one of the terrestrial planets of our solar system.Comment: ApJ, in pres

Echoes of a decaying planetary system: the gaseous and dusty disks surrounding three white dwarfs

We have performed a comprehensive ground-based observational program aimed at characterizing the circumstellar material orbiting three single white dwarf stars previously known to possess gaseous disks. Near-infrared imaging unambiguously detects excess infrared emission towards Ton 345 and allows us to refine models for the circumstellar dust around all three white dwarf stars. We find that each white dwarf hosts gaseous and dusty disks that are roughly spatially coincident, a result that is consistent with a scenario in which dusty and gaseous material has its origin in remnant parent bodies of the white dwarfs' planetary systems. We briefly describe a new model for the gas disk heating mechanism in which the gaseous material behaves like a "Z II" region. In this Z II region, gas primarily composed of metals is photoionized by ultraviolet light and cools through optically thick allowed Ca II-line emission.Comment: 43 pages, 9 tables, 9 figures. Accepted to Ap

The International Affiliation Network of YouTube Trends

Online video, a ubiquitous, visual, and highly shareable medium, is well-suited to crossing geographic, cultural, and linguistic barriers. Trending videos in particular, by virtue of reaching a large number of viewers in a short span of time, are powerful as both influencers and indicators of international communication flows. In this work, we study a large set of videos trending across 57 nations, collected from YouTube over a 7-month period. We consider the set as a network of content flowing between nations, then develop conditional co-affiliation, a nation-nation co-affiliation index that enables a meaningful interpretation of network path length and the application of betweenness centrality. We observe a highly-interlinked network with remarkably similar co-affiliation levels between very different nations. However, Arabic-speaking nations appear more isolated, with the U.A.E. emerging as a key bridge. By analyzing video trend lifespans, we show that nations having many globally-popular video trends are reliably not the nation where those trends are strongest: we see no evidence to support the widely discussed idea of cultural exporter or trendsetter nations. We model correlations between co-affiliation and a selection of contextual factors. We note a surprisingly complex interaction between migration and shared video trends. Consistent with existing work on video popularity, we find that long trending times within one nation do not necessarily translate to reaching a wide global audience. This work expands on previous studies of the geographic popularity of videos by incorporating trending data and extending our analysis from video-nation affiliations to nation-nation co-affiliations. Characterizing these relationships is key to understanding the international cultural impact and potential of online video

Lithium Depletion Boundary in a Pre-Main Sequence Binary System

A lithium depletion boundary is detected in HIP 112312 (GJ 871.1 A and B), a \~12 Myr old pre-main sequence binary system. A strong (EW 300 mA) Li 6708 A absorption feature is seen at the secondary (~M4.5) while no Li 6708 A feature is detected from the primary (~M4). The physical companionship of the two stars is confirmed from common proper motions. Current theoretical pre-main sequence evolutionary models cannot simultaneously match the observed colors, brightnesses, and Li depletion patterns of this binary system. At the age upper limit of 20 Myr, contemporary theoretical evolutionary models predict too slow Li depletion. If true Li depletion is a faster process than predicted by theoretical models, ages of open clusters (Pleiades, alpha Persei, and IC 2391) estimated from the Li depletion boundary method are all overestimated. Because of the importance of the open cluster age scale, development of self-consistent theoretical models to match the HIP 112312 data is desirable.Comment: Accepted in ApJL. 5 pages total (3 tables, 3 figures