DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

Geospatial virtual reality for cyberlearning in the field of topographic surveying: Moving towards a cost-effective mobile solution

In spite of the tremendous success in artificial intelligence technology and a high level of automation in geospatial data obtaining processes, there is still a need for topographical field data collection by professional surveyors. Understanding terrain topology and topography is a cognitive skill set that has to be demonstrated by geospatial Subject Matter Experts (SME) for the productive work in the topographic surveying field. For training of the mentioned above skillset, one has to be exposed to the theory and must also practice with surveying instruments in field conditions. The challenge of any surveying/geospatial engineering workforce training is to expose students to field conditions which might be limited due to equipment expenses and meteorological conditions that prevent good data collection. To meet this challenge, the Integrated Geospatial Technology research group is working on a geospatial virtual reality (VR) project which encompasses the following components: (a) immersive visualization of terrain; (b) virtual total station instrument; (c) virtual surveyor with reflector installed on the virtual rod. The application scenario of the technology we are working with has the following stages: (1) student is installing total station on the optimal location; (2) students move virtual surveyor on the sampling points they consider to be important (3) contours are generated and displayed in 3D being superimposed on 3D terrain; (4) accuracy of terrain modeling is observable and measurable by comparing the sampling model with initial one

Accounting for Skill in Trend, Variability, and Autocorrelation Facilitates Better Multi-Model Projections: Application to the AMOC and Temperature Time Series

We present a novel quasi-Bayesian method to weight multiple dynamical models by their skill at capturing both potentially non-linear trends and first-order autocorrelated variability of the underlying process, and to make weighted probabilistic projections. We validate the method using a suite of one-at-a-time cross-validation experiments involving Atlantic meridional overturning circulation (AMOC), its temperature-based index, as well as Korean summer mean maximum temperature. In these experiments the method tends to exhibit superior skill over a trend-only Bayesian model averaging weighting method in terms of weight assignment and probabilistic forecasts. Specifically, mean credible interval width, and mean absolute error of the projections tend to improve. We apply the method to a problem of projecting summer mean maximum temperature change over Korea by the end of the 21st century using a multi-model ensemble. Compared to the trend-only method, the new method appreciably sharpens the probability distribution function (pdf) and increases future most likely, median, and mean warming in Korea. The method is flexible, with a potential to improve forecasts in geosciences and other fields

Preconditions for the Tax Environment of a Alterglobal Development

In this article, we analyzed economic surroundings as a precondition for the development of the tax environment in the context of alterglobal development. We admitted that economic globalization is harmful to the environment because it depends on its own viability: the constant increase in commodity consumption, the increased use of resources and the growing disposition to pollute waste in the ocean, on the ground, and in the air. So, we proposed considering and analyzing alterglobalization as a process oriented towards self-determination for peoples, communities and nations. In this context, we developed the idea about Environmental Fiscal Reform, including increasing green taxation and the phase-out of environmentally harmful subsidies as well as financial incentives, VAT reductions and tax breaks for green initiatives – providing the perfect conditions for the transition to a circular economy. As the new economy is developing at a rapid pace today – 10% per year, more than three times the global economic growth rate – it has a significant impact on competitiveness

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

The Hard X-Ray View of the Young Supernova Remnant G1.9+0.3

NuSTAR observed G1.9+0.3, the youngest known supernova remnant in the Milky Way, for 350 ks and detected emission up to $\sim$30 keV. The remnant's X-ray morphology does not change significantly across the energy range from 3 to 20 keV. A combined fit between NuSTAR and CHANDRA shows that the spectrum steepens with energy. The spectral shape can be well fitted with synchrotron emission from a power-law electron energy distribution with an exponential cutoff with no additional features. It can also be described by a purely phenomenological model such as a broken power-law or a power-law with an exponential cutoff, though these descriptions lack physical motivation. Using a fixed radio flux at 1 GHz of 1.17 Jy for the synchrotron model, we get a column density of N$_{\rm H}$ = $(7.23\pm0.07) \times 10^{22}$ cm$^{-2}$, a spectral index of $\alpha=0.633\pm0.003$, and a roll-off frequency of $\nu_{\rm rolloff}=(3.07\pm0.18) \times 10^{17}$ Hz. This can be explained by particle acceleration, to a maximum energy set by the finite remnant age, in a magnetic field of about 10 $\mu$G, for which our roll-off implies a maximum energy of about 100 TeV for both electrons and ions. Much higher magnetic-field strengths would produce an electron spectrum that was cut off by radiative losses, giving a much higher roll-off frequency that is independent of magnetic-field strength. In this case, ions could be accelerated to much higher energies. A search for $^{44}$Ti emission in the 67.9 keV line results in an upper limit of $1.5 \times 10^{-5}$ $\,\mathrm{ph}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$ assuming a line width of 4.0 keV (1 sigma).Comment: 9 pages, 6 figures, accepted Ap

Heavy Metal Distribution and Groundwater Quality Assessment for a Coastal Area on a Chinese Island

Chongming Island is located in the lower Yangtze Estuary in China. Due to the Leachate from a refuse landfill and the hydrodynamics of the Yangtze Estuary, the groundwater environment is particularly complicated on Chongming Island. Field observations were carried out around the landfill disposal site. The groundwater table, temperature, pH, salinity, and dissolved oxygen were measured in the field by portable equipment, and 192 water samples were collected at eight groundwater sites and one surface water site. Through laboratory analysis we found the highest measured concentration of Cr to be 54.07 μg/L, and the measured concentration of Zn was in the range of 8 1.1 μg/L to more than 200 μg/L, which were both higher than their background values. Strong correlations were found between the heavy metal (Cr, Ni, Cu) concentrations and physico-chemical characteristics (salinity and pH), which indicated that both the landfill and the tides played an important role in the distribution of heavy metal concentrations. Both the BM and PoS Indices were greater than their critical values near the disposal site, indicating groundwater pollution by heavy metals. We show that Cr and Ni are the major heavy metals causing groundwater contamination in the study region

Spectroscopic properties of cool Ursa Major group members

Until now, most members of the Ursa Major (UMa) group of stars have been identified by means of kinematic criteria. However, in many cases kinematic criteria alone are insufficient to ascertain, whether an individual star is really a member of this group. Since photometric criteria are ineffective in the case of cool dwarf members, one must use spectroscopic criteria. Nevertheless, resulting membership criteria are inconclusive. We reanalyse spectroscopic properties of cool UMa group dwarfs. In particular, we study the distribution of iron abundance, the strength of the Li I absorption at 6708 A and the Li abundance, and the infilling of the core of the H alpha line. Twenty-five cool and northern bona-fide members are carefully selected from the literature. Homogeneously measured stellar parameters and iron abundances are given for all Sun-like stars selected, based on spectra of high resolution and high signal-to-noise ratio. In addition, we measure the Li equivalent width and abundance as well as the relative intensity of the H alpha core and the corresponding chromospheric flux. The studied stars infer an average Ursa Major group iron abundance of -0.03+-0.05 dex, which is higher by about 0.06 dex than determined elsewhere. The Li abundance derived of Ursa Major group dwarf stars is higher than in the Hyades at effective temperatures cooler than the Sun, but lower than in the younger Pleiades, a result which is independent of the exact value of the effective temperature adopted. The Sun-like and cooler dwarfs also display chromospheric infilling of the H alpha core. We present spectroscopic criteria that may be used to exclude non-members.Comment: accepted for publication in A&A, 19 pages, 10 figures, 7 table