Dynamical Networks in Function Dynamics

As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given as a dynamical system of a 1-dimensional map. Through the time evolution of this system, a dynamical graph (a network) emerges. This graph has three interesting properties: i) vertices appear as stable elements, ii) the terminals of directed edges change in time, and iii) some vertices determine the dynamics of edges, and edges determine the stability of the vertices, complementarily. Two aspects of FD are studied, the generation of a graph (network) structure and the dynamics of this graph (network) in the system.Comment: 29 pages, 10 figure

Geometric Suppression of Single-Particle Energy Spacings in Quantum Antidots

Quantum Antidot (AD) structures have remarkable properties in the integer quantum Hall regime, exhibiting Coulomb-blockade charging and the Kondo effect despite their open geometry. In some regimes a simple single-particle (SP) model suffices to describe experimental observations while in others interaction effects are clearly important, although exactly how and why interactions emerge is unclear. We present a combination of experimental data and the results of new calculations concerning SP orbital states which show how the observed suppression of the energy spacing between states can be explained through a full consideration of the AD potential, without requiring any effects due to electron interactions such as the formation of compressible regions composed of multiple states, which may occur at higher magnetic fields. A full understanding of the regimes in which these effects occur is important for the design of devices to coherently manipulate electrons in edge states using AD resonances.Comment: 4 pages, 2 figure

Towards concept analysis in categories: limit inferior as algebra, limit superior as coalgebra

While computer programs and logical theories begin by declaring the concepts of interest, be it as data types or as predicates, network computation does not allow such global declarations, and requires *concept mining* and *concept analysis* to extract shared semantics for different network nodes. Powerful semantic analysis systems have been the drivers of nearly all paradigm shifts on the web. In categorical terms, most of them can be described as bicompletions of enriched matrices, generalizing the Dedekind-MacNeille-style completions from posets to suitably enriched categories. Yet it has been well known for more than 40 years that ordinary categories themselves in general do not permit such completions. Armed with this new semantical view of Dedekind-MacNeille completions, and of matrix bicompletions, we take another look at this ancient mystery. It turns out that simple categorical versions of the *limit superior* and *limit inferior* operations characterize a general notion of Dedekind-MacNeille completion, that seems to be appropriate for ordinary categories, and boils down to the more familiar enriched versions when the limits inferior and superior coincide. This explains away the apparent gap among the completions of ordinary categories, and broadens the path towards categorical concept mining and analysis, opened in previous work.Comment: 22 pages, 5 figures and 9 diagram

Inverse Compton X-ray Emissions from TeV blazar Mrk421 during a Historical Low-Flux State Observed with NuSTAR

We report on the detection of excess hard X-ray emission from the TeV BL Lac object Mrk421 during the historical low-flux state of the source in January 2013. NuSTAR observations were conducted four times between MJD56294 and MJD56312 with a total exposure of 80.9 ksec. The source flux in the 3-40 keV range was nearly constant except for MJD56307, when the average flux level increased by a factor of three. Throughout the exposure, the X-ray spectra of Mrk421 were well represented by a steep power-law model with a photon index of 3.1, although a significant excess was noted above 20 keV in the MJD56302 data when the source was in its faintest state. Moreover, Mrk421 was detected at more than the 4-sigma level in the 40-79 keV count maps for both MJD56307 and MJD56302 but not during the remaining two observations. The detected excess hard X-ray emissions connect smoothly with the extrapolation of the high-energy gamma-ray continuum of the blazar constrained by Fermi-LAT during the source quiescence. These findings indicate that, while the overall X-ray spectrum of Mrk421 is dominated by the highest-energy tail of the synchrotron continuum, the variable excess hard X-ray emission above 20 keV (on the timescale of a week) is related to the inverse Compton emission component. We discuss the resulting constraints on the variability and spectral properties of the low-energy segment of the electron energy distribution in the source.Comment: 6 pages, 4 figures, accepted for publication in Ap