We present a strategy for a geometric construction of cross sections for the geodesic flow on locally symmetric orbifolds of rank one. We work it out in detail for Γ\H, where H is the upper half plane and Γ = PΓ0(p), p prime. Its associated discrete dynamical system naturally induces a symbolic dynamics on R. The transfer operator produced from this symbolic dynamics has a particularly simple s...

Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable algebraic systems for being the base for such code generator. This work presents an attempt at realizing such idea in practice. A novel GA-based geometric code gene...

To navigate during their long-distance migration, monarch butterflies (Danaus plexippus) use a time-compensated sun compass. The sun compass timing elements reside in light-entrained circadian clocks in the antennae. Here we show that either antenna is sufficient for proper time compensation. However, migrants with either antenna painted black (to block light entrainment) and the other painted ...

to include the new fact. The goal of error correction is, given a spatial knowledge representation which is not quite accurate and a new fact which is more precise, to improve the representation. Both these problems can be treated by operators, similar to the composition operator, that take two symbolic spatial indexes as arguments (i.e., one representing the initial state and one representing ...

We know little about the neurologic bases of art production. The idea that the right brain hemisphere is the “artistic brain” is widely held, despite the lack of evidence for this claim. Artists with brain damage can offer insight into these laterality questions. The authors used an instrument called the Assessment of Art Attributes to examine the work of two individuals with left-brain damage ...

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transforma...