We compute the smooth 4-genera of prime knots with 12 crossings whose values, as reported on KnotInfo website, were unknown. This completes calculation 4-genus for all or fewer crossings.

This study investigated differences in simulated driver risk-taking behavior among U.S., Spanish, and West German subjects. The task consisted of performing a simulated intersection crossing on a video display. Subjects were shown an intersection with moving traffic on a horizontal road, and they were asked to attempt (under time pressure) a fixed number of crossings with a car moving verticall...

Trail-based recreation has increased over recent decades, raising the environmental management issue of soil erosion that originates from unsurfaced, recreational trail systems. Trail-based soil erosion that occurs near stream crossings represents a non-point source of pollution to streams. We modeled soil erosion rates along multiple-use (hiking, mountain biking, and horseback riding) recreati...

The fractal index (Y and fractal dimension D of a Gaussian process are characteristics that describe the smoothness of the process. In principle, smoother processes have fewer crossings of a given level, and so level crossings might be employed to estimate (Y or D. However, the number of crossings of a level by a non-differentiable Gaussian process is either zero or infinity, with probability o...

Clustered graphs are an enhanced graph model with a recursive clustering of the vertices according to a given nesting relation. This prime technique for expressing coherence of certain parts of the graph is used in many applications, such as biochemical pathways and UML class diagrams. For directed clustered graphs usually level drawings are used, leading to clustered level graphs. In this thes...

The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...

It is currently necessary to solve several bottlenecks in railway infrastructure. This important because it needed improve infrastructure be faster, safer and of high quality. Rail crossings on lines are also a significant bottleneck. There still many rail number accidents countries the European Union. The issue must addressed reduce flow road traffic. However, about safety transportation, as s...