Coalgebraic Automata Theory: Basic Results

We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves weak pullbacks. We show that the class of recognizable languages of F-coalgebras is closed under taking unions, intersections, and projections. We also prove that if a nondeterministic F-automaton accepts some coalgebra it accepts a finite one of the size of the automaton. Our main technical result concerns an explicit construction which transforms a given alternating F-automaton into an equivalent nondeterministic one, whose size is exponentially bound by the size of the original automaton.Comment: 43 page

Gluon confinement criterion in QCD

We fix exactly and uniquely the infrared structure of the full gluon propagator in QCD, not solving explicitly the corresponding dynamical equation of motion. By construction, this structure is an infinite sum over all possible severe (i.e., more singular than $1/q^2$) infrared singularities. It reflects the zero momentum modes enhancement effect in the true QCD vacuum, which is due to the self-interaction of massless gluons. It existence automatically exhibits a characteristic mass (the so-called mass gap). It is responsible for the scale of nonperturbative dynamics in the true QCD ground state. The theory of distributions, complemented by the dimensional regularization method, allows one to put the severe infrared singularities under the firm mathematical control. By an infrared renormalization of a mass gap only, the infrared structure of the full gluon propagator is exactly reduced to the simplest severe infrared singularity, the famous $(q^2)^{-2}$. Thus we have exactly established the interaction between quarks (concerning its pure gluon (i.e., nonlinear) contribution) up to its unimportant perturbative part. This also makes it possible for the first time to formulate the gluon confinement criterion and intrinsically nonperturbative phase in QCD in a manifestly gauge-invariant ways.Comment: 10 pages, no figures, no tables. Typos corrected and the clarification is intoduced. Shorten version to appear in Phys. Lett.

The Critical Aggregation Concentration of ß-Lactoglobulin-Based Fibril Formation

The critical aggregation concentration (CAC) for fibril formation of ß-lactoglobulin (ß-lg) at pH 2 was determined at 343, 353, 358, 363, and 383 K using a Thioflavin T assay and was approximately 0.16 wt%. The accuracy of the CAC was increased by measuring the conversion into fibrils at different stirring speeds. The corresponding binding energy per mol, as determined from the CAC, was 13 RT (~40 kJ mol¿1) for the measured temperature range. The fact that the CAC was independent of temperature within the experimental error indicates that the fibril formation of ß-lg at pH 2 and the measured temperature range is an entropy-driven process

Characterization of knot complements in the 4-sphere

AbstractKnot complements in S4 are characterized as follows: A connected open set W ⊂ S4 is homeomorphic to the complement of some locally flat 2-sphere in S4 if and only if H1(W) is infinite cyclic, W has one end, and the fundamental group of that end is infinite cyclic. Applications include a characterization of weakly flat 2-spheres in S4 and a complement theorem for 2-spheres in S4

Representing homology classes of simply connected 4-manifolds

AbstractThe main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;Z) can be represented by a locally flat topological embedding of S2

Mid-Infrared Instrumentation for the European Extremely Large Telescope

MIDIR is the proposed thermal/mid-IR imager and spectrograph for the European Extremely Large Telescope (E-ELT). It will cover the wavelength range of 3 to at least 20 microns. Designed for diffraction-limited performance over the entire wavelength range, MIDIR will require an adaptive optics system; a cryogenically cooled system could offer optimal performance in the IR, and this is a critical aspect of the instrument design. We present here an overview of the project, including a discussion of MIDIR's science goals and a comparison with other infrared (IR) facilities planned in the next decade; top level requirements derived from these goals are outlined. We describe the optical and mechanical design work carried out in the context of a conceptual design study, and discuss some important issues to emerge from this work, related to the design, operation and calibration of the instrument. The impact of telescope optical design choices on the requirements for the MIDIR instrument is demonstrated.Comment: for publication in SPIE Proceedings vol. 6692, Cryogenic Optical Systems and Instrumentation XII, eds. J.B. Heaney and L.G. Burriesci, San Diego, Aug 200