"Minesweeper" and spectrum of discrete Laplacians

The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.Comment: We add consideration of tables based on the triangle tiling of the plane. Its paper version encounters situations typical for the computer "Minesweeper" gam

Processor Verification Using Efficient Reductions of the Logic of Uninterpreted Functions to Propositional Logic

The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Decision Diagrams (BDDs) and Boolean satisfiability checkers to perform the verification. We can exploit characteristics of the formulas describing the verification conditions to greatly simplify the propositional formulas generated. In particular, we exploit the property that many equations appear only in positive form. We can therefore reduce the set of interpretations of the function symbols that must be considered to prove that a formula is universally valid to those that are ``maximally diverse.'' We present experimental results demonstrating the efficiency of this approach when verifying pipelined processors using the method proposed by Burch and Dill.Comment: 46 page

A feasibility study of wearable activity monitors for pre-adolescent school-age children.

IntroductionUnderstanding physical activity is key in the fight against childhood obesity. The objective of this study was to examine the feasibility of using certain wearable devices to measure physical activity among children.MethodsA qualitative study was conducted with 25 children aged 7 to 10 years to assess acceptability and compliance of wearable activity devices in this age group. During March through August 2012, children participated in a 4-week study of 3 accelerometer models and a heart rate monitor. Children were asked to use a different device each week for 7 consecutive days. Children and their parents completed structured interviews after using each device; they also completed a final exit interview.ResultsThe wrist-worn Polar Active was the device most preferred by children and was associated with the highest level of compliance. Devices that are comfortable to wear, fit properly, have engaging features, and are waterproof increase feasibility and are associated with higher levels of compliance.ConclusionThe wrist-worn device was the most feasible for measuring physical activity among children aged 7 to 10 years. These findings will inform researchers in selecting tools for measuring children's physical activity

The effect of Fe atoms on the adsorption of a W atom on W(100) surface

We report a first-principles calculation that models the effect of iron (Fe) atoms on the adsorption of a tungsten (W) atom on W(100) surfaces. The adsorption of a W atom on a clean W(100) surface is compared with that of a W atom on a W(100) surface covered with a monolayer of Fe atoms. The total energy of the system is computed as the function of the height of the W adatom. Our result shows that the W atom first adsorbs on top of the Fe monolayer. Then the W atom can replace one of the Fe atoms through a path with a moderate energy barrier and reduce its energy further. This intermediate site makes the adsorption (and desorption) of W atoms a two-step process in the presence of Fe atoms and lowers the overall adsorption energy by nearly 2.4 eV. The Fe atoms also provide a surface for W atoms to adsorb facilitating the diffusion of W atoms. The combination of these two effects result in a much more efficient desorption and diffusion of W atoms in the presence of Fe atoms. Our result provides a fundamental mechanism that can explain the activated sintering of tungsten by Fe atoms.Comment: 9 pages, 2 figure