The categorical limit of a sequence of dynamical systems

Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns out to be subject to ambiguity. Depending on the interpretation of the sequence, i.e. depending on how the behaviors of the systems in the sequence are related, it may vary what the limit should be. Topologies, and in particular metrics, define limits uniquely, if they exist. Thus they select one interpretation implicitly and leave no room for other interpretations. In this paper, we define limits using category theory, and use the mentioned relations between system behaviors explicitly. This resolves the problem of ambiguity in a more controlled way. We introduce a category of prefix orders on executions and partial history preserving maps between them to describe both discrete and continuous branching time dynamics. We prove that in this category all projective limits exist, and illustrate how ambiguity in the definition of limits is resolved using an example. Moreover, we show how various problems with known topological approaches are now resolved, and how the construction of projective limits enables us to approximate continuous time dynamics as a sequence of discrete time systems.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods

Measurements of optical turbulence time series data using unattended instruments over long time intervals inevitably lead to data drop-outs or degraded signals. We present a comparison of methods using both Principal Component Analysis, which is also known as the Karhunen--Loeve decomposition, and ARIMA that seek to correct for these event-induced and mechanically-induced signal drop-outs and degradations. We report on the quality of the correction by examining the Intrinsic Mode Functions generated by Empirical Mode Decomposition. The data studied are optical turbulence parameter time series from a commercial long path length optical anemometer/scintillometer, measured over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University, London, U

Humidity contribution to C_n^2 over a 600m pathlength in a tropical marine environment

We present new optical turbulence structure parameter measurements, C_n^2, over sea water between La Parguera and Magueyes Island (17.6N 67W) on the southwest coast of Puerto Rico. The 600 meter horizontal paths were located approximately 1.5 m and 10 m above sea level. No data of this type has ever been made available in the literature. Based on the data, we show that the C_n^2 measurements are about 7 times less compared to equivalent land data. This strong evidence reinforces our previous argument that humidity must be accounted for to better ascertain the near surface atmospheric turbulence effects, which current visible / near infrared C_n^2 bulk models fail to do. We also explore the generalised fractal dimension of this littoral data and compare it to our reference land data. We find cases that exhibit monofractal characteristics, that is to say, the effect of rising temperatures during the daylight hours upon turbulence are counterbalanced by humidity, leading to a single characteristic scale for the measurements. In other words, significant moisture changes in the measurement volume cancels optical turbulence increases due to temperature rises. Figures available as JPG only.Comment: 7 pages, 4 figures, 1 table, SPIE Photonics West 2007, paper 6457B-2

SPEKTRALE IJNTERSUCHUNG DER ABBILDUNG 5)'( 'X-N X -L XNT • - p- I - q

SPECTRAL ANALYSIS OF MAPPING ~l:X .. N-X XNI - Description is given of the spectral analysis of mapping ~(:X .-- NqX XN,q interpreted in the space of p .q- type matrices of complex elements where Np [Gi.j-I]' 1, ] L .... p, is a nilpotent matrix of order p, and Nl is the tramposed of Nq• ?Je is shown to be a nilpotent operator with the ex- ponent p q 1: hence its eigenvectors are solutions of matrix equation NpX + XNJ ~~O For linearly independent eigenvectors Xrl; = [( _1)i Tl Gi+ j'f+ rl. i= L .... p, j = L ... , q a Jordan's chain of principal yectors is produced, demonstrating them to be of maximum length

Applying the Hilbert--Huang Decomposition to Horizontal Light Propagation C_n^2 data

The Hilbert Huang Transform is a new technique for the analysis of non--stationary signals. It comprises two distinct parts: Empirical Mode Decomposition (EMD) and the Hilbert Transform of each of the modes found from the first step to produce a Hilbert Spectrum. The EMD is an adaptive decomposition of the data, which results in the extraction of Intrinsic Mode Functions (IMFs). We discuss the application of the EMD to the calibration of two optical scintillometers that have been used to measure C_n^2 over horizontal paths on a building rooftop, and discuss the advantage of using the Marginal Hilbert Spectrum over the traditional Fourier Power Spectrum.Comment: 9 pages, 11 figures, proc. SPIE 626

Low variability of single-molecule conductance assisted by bulky metal-molecule contacts

A detailed study of the trimethylsilylethynyl moiety, –C[triple bond]CSiMe3 (TMSE) , as an anchoring group in metalmoleculemetal junctions, using a combination of experiment and density functional theory is presented. It is shown that the TMSE anchoring group provides improved control over the molecule-substrate arrangement within metalmoleculemetal junctions, with the steric bulk of the methyl groups limiting the number of highly transmissive binding sites at the electrode surface, resulting in a single sharp peak in the conductance histograms recorded by both the in situ break junction and I(s) STM techniques. As a consequence of the low accessibility of the TMSE group to surface binding configurations of measurable conductance, only about 10% of gold break junction formation cycles result in the clear formation of molecular junctions in the experimental histograms. The DFT-computed transmission characteristics of junctions formed from the TMSE-contacted oligo(phenylene)ethynylene (OPE)-based molecules described here are dominated by tunneling effects through the highest-occupied molecular orbitals (HOMOs). This gives rise to similar conductance characteristics in these TMSE-contacted systems as found in low conductance-type junctions based on comparably structured OPE-derivatives with amine-contacts that also conduct through HOMO-based channels.R. R. F. thanks the Consejería de Educación del Principado de Asturias for a Severo Ochoa grant (BP11-069). V. M. G.-S. thanks the Spanish Ministerio de Economía y Competitividad for a Ramón y Cajal fellowship (RYC-2010-06053). R. R. F., J. F. and V. M. G.-S. wish to acknowledge financial support from the Spanish grant FIS2012-34858 and the Marie Curie Network MOLESCO. P. C. and S. M. are grateful for financial assistance from the Ministerio de Economía y Competitividad of Spain in the framework of the project CTQ2012-33198 as well as the award of the CTQ2013-50187-EXP grant. H. M. O., P. C., and S. M. thank the support from DGA and Fondos FEDER for funding through the Platon research group. H. M. O. is also grateful for financial assistance from the Secretaría Nacional de Educación Superior, Ciencia, Tecnología e Innovaciín from Ministerio de Educación (Ecuador). S. M. thanks the Ministerio de Educación from Spain for financial support through the framework of the Campus de Excelencia Internacional, CEI Iberus. S. J. H., R. J. N., P. J. L. and S. M.-G. thank the EPSRC for funding (EPSRC grants EP/K007785/1, EP/H035184/1, EP/K007548/1, EP/H005595/1). P. J. L. holds an Australian Research Council Future Fellowship (FT120100073) and gratefully acknowledges funding for this work from the ARC (DP140100855).Peer Reviewe

Mashairi ya waadhi `verses of admonition`:

Aliyetunga kasiga hii, Sheikh Abgallah al-Husni, alikuwa ni mtu maarufu sana Mombasa .. Kwa muda wa myaka arobaini takriban alikuwa akisomesha elimu za gini, msikiti wa Anisa, Mjuwakale; piya alikuwa akitoa waadhi msikiti huu na mahali pengine .. Antunga kasiga mbili za waadhi, moja katika hizo ndiyo hii tuliyoishereheya katika makala haya .. W akati wa kutungwa waadhi huu - 1368 (mwaka 1948 wa milagi) - Mombasa ilikuwa ikali mji wa kiSawahili, yaani mji wa kilsilamu; lakini kulikuwa kuna mabadiliko makubwa yaanza, mabadiliko ambayo mwisho yanaondowa sura za uSawahili katika Mombasa na pwani nzima ya Afrika ya mashariki