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

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 epigenetic regulator ATF7ip inhibits Il2 expression, regulating Th17 responses.

T helper 17 cells (Th17) are critical for fighting infections at mucosal surfaces; however, they have also been found to contribute to the pathogenesis of multiple autoimmune diseases and have been targeted therapeutically. Due to the role of Th17 cells in autoimmune pathogenesis, it is important to understand the factors that control Th17 development. Here we identify the activating transcription factor 7 interacting protein (ATF7ip) as a critical regulator of Th17 differentiation. Mice with T cell-specific deletion of Atf7ip have impaired Th17 differentiation secondary to the aberrant overproduction of IL-2 with T cell receptor (TCR) stimulation and are resistant to colitis in vivo. ChIP-seq studies identified ATF7ip as an inhibitor of Il2 gene expression through the deposition of the repressive histone mark H3K9me3 in the Il2-Il21 intergenic region. These results demonstrate a new epigenetic pathway by which IL-2 production is constrained, and this may open up new avenues for modulating its production

Playing well with others: a case study of collective impact in the early care and education policy arena

The quality and quantity of early childhood care and education services have risen as a key reform area for influencing educational and economic outcomes. However, changes in this policy arena are stymied by the fragmentation of this policy arena. Collaborative approaches have been proposed to create systems-level change. Collective impact is one such approach; however, few examples exist in the early childhood care and education literature, especially at the state level. This ethnographic case study conceptualizes collective impact as a policy network capable of change in a fractured policy arena and reports the results from the first year of a statewide collective impact effort examines stakeholder perceptions of mobilization and development of a common agenda, or shared understandings. The results illustrate the importance of relationship building, ongoing attention to common understandings through multiple processes and mechanisms, the importance of the backbone organization, and the need to attend to mindset shifts that accompany early collective impact work

The Carina-Near Moving Group

We identify a group of ~20 co-moving, mostly southern hemisphere, ~200 Myr old stars near Earth. Of the stars likely to be members of this Carina-Near Moving Group, in either its nucleus (~30 pc from Earth) or surrounding stream, all but 3 are plausible members of a multiple star system. The nucleus is (coincidentally) located quite close to the nucleus of the AB Doradus moving group notwithstanding that the two groups have substantially different ages and Galactic space motions, UVW.Comment: 9 pages, 1 table, 2 figures. Accepted in ApJ

Discovery of seven T Tauri stars and a brown dwarf candidate in the nearby TW Hydrae Association

We report the discovery of five T Tauri star systems, two of which are resolved binaries, in the vicinity of the nearest known region of recent star formation, the TW Hydrae Association. The newly discovered systems display the same signatures of youth (namely high X-ray flux, large Li abundance and strong chromospheric activity) and the same proper motion as the original five members. These similarities firmly establish the group as a bona fide T Tauri association, unique in its proximity to Earth and its complete isolation from any known molecular clouds. At an age of ~10 Myr and a distance of ~50 pc, the association members are excellent candidates for future studies of circumstellar disk dissipation and the formation of brown dwarfs and planets. Indeed, as an example, our speckle imaging revealed a faint, very likely companion 2" north of CoD-33 7795 (TWA 5). Its color and brightness suggest a spectral type ~M8.5 which, at an age of ~10^7 years, implies a mass ~20 M(Jupiter).Comment: 6 pages, 4 figures and 1 table. AAS LaTeX aas2pp4.sty. To be published in Ap

Topological Orthoalgebras

We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show that a compact TOA in which 0 is an isolated point is atomic and of finite height. We identify and study a particularly tractable class of TOAs, which we call {\em stably ordered}: those in which the upper-set generated by an open set is open. This includes all topological OMLs, and also the projection lattices of Hilbert spaces. Finally, we obtain a topological version of the Foulis-Randall representation theory for stably ordered TOAsComment: 16 pp, LaTex. Minor changes and corrections in sections 1; more substantial corrections in section

Deep imaging survey of young, nearby austral stars: VLT/NACO near-infrared Lyot-coronographic observations

Context. High contrast and high angular resolution imaging is the optimal search technique for substellar companions to nearby stars at physical separations larger than typically 10 AU. Two distinct populations of substellar companions, brown dwarfs and planets, can be probed and characterized. As a result, fossile traces of processes of formation and evolution can be revealed by physical and orbital properties, both for individual systems and as an ensemble. Aims. Since November 2002, we have conducted a large, deep imaging, survey of young, nearby associations of the southern hemisphere. Our goal is detection and characterization of substellar companions with projected separations in the range 10–500 AU. We have observed a sample of 88 stars, primarily G to M dwarfs, younger than 100 Myr, and within 100 pc of Earth. Methods. The VLT/NACO adaptive optics instrument of the ESO Paranal Observatory was used to explore the faint circumstellar environment between typically 0.1 and 10". Diffraction-limited observations in H and K_s-band combined with Lyot-coronagraphy enabled us to reach primary star-companion brightness ratios as small as 10^(-6). The existence of planetary mass companions could therefore be probed. We used a standardized observing sequence to precisely measure the position and flux of all detected sources relative to their visual primary star. Repeated observations at several epochs enabled us to discriminate comoving companions from background objects. Results. We report the discovery of 17 new close (0.1–5.0") multiple systems. HIP 108195 AB and C (F1 III-M6), HIP 84642 AB (a~14 AU, K0-M5) and TWA22 AB (a~1.8 AU; M6-M6) are confirmed comoving systems. TWA22 AB is likely to be a rare astrometric calibrator that can be used to test evolutionary model predictions. Among our complete sample, a total of 65 targets were observed with deep coronagraphic imaging. About 240 faint companion candidates were detected around 36 stars. Follow-up observations with VLT or HST for 83% of these stars enabled us to identify a large fraction of background contaminants. Our latest results that pertain to the substellar companions to GSC 08047-00232, AB Pic and 2M1207 (confirmed during this survey and published earlier), are reviewed. Finally, a statistical analysis of our complete set of coronagraphic detection limits enables us to place constraints on the physical and orbital properties of giant planets between typically 20 and 150 AU

Presymplectic current and the inverse problem of the calculus of variations

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon and Lawson and generalizes an older result of Henneaux from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to published versio

A cool, magnetic white dwarf accreting planetary debris

We present an analysis of spectroscopic data of the cool, highly magnetic and polluted white dwarf 2MASS J0916-4215. The atmosphere of the white dwarf is dominated by hydrogen, but numerous spectral lines of magnesium, calcium, titanium, chromium, iron, strontium, along with Li I, Na I, Al I, and K I lines, are found in the incomplete Paschen-Back regime, most visibly, in the case of Ca II lines. Extensive new calculations of the Paschen-Back effect in several spectral lines are presented and results of the calculations are tabulated for the Ca II H&K doublet. The abundance pattern shows a large lithium and strontium excess, which may be viewed as a signature of planetary debris akin to Earth's continental crust accreted onto the star, although the scarcity of silicon indicates possible dilution in bulk Earth material. Accurate abundance measurements proved sensitive to the value of the broadening parameter due to collisions with neutral hydrogen (Gamma_HI), particularly in saturated lines such as the resonance lines of Ca I and Ca II. We found that Gamma_HI if formulated with values from the literature could be overestimated by a factor of 10 in most resonance lines.Comment: Accepted for publication in MNRA