How large dimension guarantees a given angle?

Minimum Rectilinear Polygons for Given Angle Sequences

In this paper, we consider the problem of computing, for a given rectilinear angle sequence, a “small” rectilinear polygon. A rectilinear angle sequence S is a sequence of left (90◦) turns and right (270◦) turns, that is, S = (s1, . . . , sn) ∈ {L, R}, where n is the length of S. As we consider only rectilinear angle sequences, we usually drop the term “rectilinear.” A polygon P realizes an ang...

Quantitative Recurrence Near a Given Point and Dimension

Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point x in a decreasing sequence of neighborhoods of another point y. It is proved that these recurrence indicators are a.e. greater or equal to the local dimension at y, then these recurrence indicators can be used to have a numerical upper bound on the local dimension of an invariant measure.

Grammatical evolution to design fractal curves with a given dimension

Lindenmayer Grammars have been applied frequently to represent fractal curves. In this work, the ideas behind Grammar Evolution are used to automatically generate and evolve Lindenmayer Grammars that represent fractal curves with a fractal dimension that approximates a pre-defined required value. For many dimensions, this is a non trivial task to be performed manually. The procedure we are prop...

Constant-Work-Space Image Scan with a Given Angle

Reduced-dimension multiuser detection: detectors and performance guarantees

We explore several reduced-dimension multiuser detection (RD-MUD) structures that significantly decrease the number of required correlation branches at the receiver frontend, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that the number of active users is typically small relative to the total number of users in the syste...