Translation surfaces can be viewed as polygons with parallel and equal sides identified. An affine homeomorphism φ from a translation surface to itself is called pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger than 2 in absolute value. In this setting, the eigendirections of...
We give explicit pseudo-Anosov homeomorphisms with vanishing
Sah–Arnoux–Fathi invariant. Any translation surface whose Veech group
is commensurable to any of a large class of triangle groups is shown to have
an affine pseudo-Anosov homeomorphism of this type. We also apply a reduction
to finite triangle groups and thereby show the...
We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are...
We give continued fraction algorithms for each conjugacy class of triangle Fuchsian group of signature
(3, n, ∞), with n ≥ 4. In particular, we give an explicit form of the group that is a subgroup of the Hilbert
modular group of its trace field and provide an interval map...
As one of the most popular data types, the point cloud is widely used in various appli- cations, including computer vision, computer graphics and robotics. The capability to directly measure 3D point clouds is invaluable in those applications as depth information could remove a lot of the segmentation ambiguities in...
Abstract: We prove that for all ergodic extensions S-1 of a transformation by a locally compact second countable group G, and for all G-extensions S₂ of an aperiodic transformation, there is a relative speedup of S₁ that is relatively isomorphic to S₂. We apply this result to give necessary and...
Many species have complex life cycles in which a dispersive larval stage is
followed by a relatively sedentary adult stage. For such species, reproductive output
is often high and large variation in survivorship throughout early life-history phases
(eggs and larvae) can lead to dramatic fluctuations in recruitment which may in...
Learning to recognize objects is a fundamental and essential step in human perception and understanding of the world. Accordingly, research of object discovery across diverse modalities plays a pivotal role in the context of computer vision. This field not only contributes significantly to enhancing our understanding of visual information but...
Although differences between selective pressures in hatcheries
and streams have been theorized to cause genetic divergence between
hatchery and wild salmonids, evidence of this is lacking. This study
was initiated to document the presence or absence of genetic change
in hatchery and wild stocks by characterizing genetic traits in fish...