On two variations of identifying codes

Identifying codes have been introduced in 1998 to model fault-detection in multiprocessor systems. In this paper, we introduce two variations of identifying codes: weak codes and light codes. They correspond to fault-detection by successive rounds. We give exact bounds for those two definitions for the family of cycles

Mode identification from monochromatic amplitude and phase variations for the rapidly pulsating subdwarf B star EC 20338-1925

We obtain time-series spectrophotometry observations at the VLT with the aim of partially identifying the dominant oscillation modes in the rapidly pulsating subdwarf B star EC 20338-1925 on the basis of monochromatic amplitude and phase variations. From the data gathered, we detect four previously known pulsations with periods near 147, 168, 126 and 140 s and amplitudes between 0.2 and 2.3 % of the star's mean brightness. We also determine the atmospheric parameters of EC 20338-1925 by fitting our non-LTE model atmospheres to an averaged combined spectrum. The inferred parameters are Teff = 34,153+-94 K, log g =5.966+-0.017 and log[N(He)/N(H)] = - 1.642+-0.022, where the uncertainty estimates quoted refer to the formal fitting errors. Finally, we calculate the observed monochromatic amplitudes and phases for the periodicities extracted using least-squares fitting to the light curves obtained for each wavelength bin. These observed quantities are then compared to the corresponding theoretical values computed on the basis of dedicated model atmosphere codes and also taking into account non-adiabatic effects. We find that the quality of the data is sufficient to identify the dominant pulsation at 146.9 s as a radial mode, while two of the lower amplitude periodicities must be low-degree modes with l=0-2. This is the first time that monochromatic amplitudes and phases have been used for mode identification in a subdwarf B star, and the results are highly encouraging.Comment: 11 pages. Accepted for publication in Astronomy & Astrophysic

Automated Discharging Arguments for Density Problems in Grids

Discharging arguments demonstrate a connection between local structure and global averages. This makes it an effective tool for proving lower bounds on the density of special sets in infinite grids. However, the minimum density of an identifying code in the hexagonal grid remains open, with an upper bound of $\frac{3}{7} \approx 0.428571$ and a lower bound of $\frac{5}{12}\approx 0.416666$. We present a new, experimental framework for producing discharging arguments using an algorithm. This algorithm replaces the lengthy case analysis of human-written discharging arguments with a linear program that produces the best possible lower bound using the specified set of discharging rules. We use this framework to present a lower bound of $\frac{23}{55} \approx 0.418181$ on the density of an identifying code in the hexagonal grid, and also find several sharp lower bounds for variations on identifying codes in the hexagonal, square, and triangular grids.Comment: This is an extended abstract, with 10 pages, 2 appendices, 5 tables, and 2 figure

A robust braille recognition system

Braille is the most effective means of written communication between visually-impaired and sighted people. This paper describes a new system that recognizes Braille characters in scanned Braille document pages. Unlike most other approaches, an inexpensive flatbed scanner is used and the system requires minimal interaction with the user. A unique feature of this system is the use of context at different levels (from the pre-processing of the image through to the post-processing of the recognition results) to enhance robustness and, consequently, recognition results. Braille dots composing characters are identified on both single and double-sided documents of average quality with over 99% accuracy, while Braille characters are also correctly recognised in over 99% of documents of average quality (in both single and double-sided documents)

Mapping the Shadow Economy: Spatial Variations in the use of High Denomination Bank Notes in Brussels

The aim of this paper is to map the spatial variations in the size of the shadow economy within Brussels. Reporting data provided by the National Bank of Belgium on the deposit of high denomination banknotes across bank branches in the 19 municipalities of the Brussels-Capital Region, the finding is that the shadow economy is concentrated in wealthier populations and not in deprived or immigrant communities. The outcome is a call to transcend the association of the shadow economy with marginalized groups and the wider adoption of this indirect method when measuring spatial variations in the shadow economy

Identifying codes of corona product graphs

For a vertex $x$ of a graph $G$, let $N_G[x]$ be the set of $x$ with all of its neighbors in $G$. A set $C$ of vertices is an {\em identifying code} of $G$ if the sets $N_G[x]\cap C$ are nonempty and distinct for all vertices $x$. If $G$ admits an identifying code, we say that $G$ is identifiable and denote by $\gamma^{ID}(G)$ the minimum cardinality of an identifying code of $G$. In this paper, we study the identifying code of the corona product $H\odot G$ of graphs $H$ and $G$. We first give a necessary and sufficient condition for the identifiable corona product $H\odot G$, and then express $\gamma^{ID}(H\odot G)$ in terms of $\gamma^{ID}(G)$ and the (total) domination number of $H$. Finally, we compute $\gamma^{ID}(H\odot G)$ for some special graphs $G$

Solar Magnetic Tracking. I. Software Comparison and Recommended Practices

Feature tracking and recognition are increasingly common tools for data analysis, but are typically implemented on an ad-hoc basis by individual research groups, limiting the usefulness of derived results when selection effects and algorithmic differences are not controlled. Specific results that are affected include the solar magnetic turnover time, the distributions of sizes, strengths, and lifetimes of magnetic features, and the physics of both small scale flux emergence and the small-scale dynamo. In this paper, we present the results of a detailed comparison between four tracking codes applied to a single set of data from SOHO/MDI, describe the interplay between desired tracking behavior and parameterization of tracking algorithms, and make recommendations for feature selection and tracking practice in future work.Comment: In press for Astrophys. J. 200

Supporting Cancer Prevention Strategies Using Geospatial Analysis on HRSA data

This paper uses develops a methodology to geospatially analyze factors associated with disparities in cancer rates