Let f : C → Ĉ be a transcendental meromorphic function. Suppose that the finite part P(f)∩C of the postsingular set of f is bounded, that f has no recurrent critical points or wandering domains, and that the degree of pre-poles of f is uniformly bounded. Then we show that f supports no invariant line fields on its Julia set. We prove this by generalizing two results about rational functions to ...

Let f be a transcendental entire function and let I(f) be the set of points whose iterates under f tend to infinity. We show that I(f) has at least one unbounded component. In the case that f has a Baker wandering domain, we show that I(f) is a connected unbounded set.

W. P. Thurston introduced closed σd-invariant laminations (where σd = z : S → S, d ≥ 2) as a tool in complex dynamics. He defined wandering triangles as triples T ⊂ S such that σ d (T ) consists of three distinct points for all n ≥ 0 and the convex hulls of all the sets σ d (T ) in the plane are pairwise disjoint, and proved that σ2 admits no wandering triangles. We show that for every d ≥ 3 th...

We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics f is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which f acts bijectively. The statement of this result is both infinitesimal and dynamical. Up to our knowledg...

In this paper, we propose deep architecture to dynamically learn the most discriminative features from data for both single-cell and object tracking in computational biology and computer vision. Firstly, the discriminative features are automatically learned via a convolutional deep belief network (CDBN). Secondly, we design a simple yet effective method to transfer features learned from CDBNs o...

Individual differences across a variety of cognitive processes are functionally associated with individual differences in intrinsic networks such as the default mode network (DMN). The extent to which these networks correlate or anticorrelate has been associated with performance in a variety of circumstances. Despite the established role of the DMN in mind wandering processes, little research h...

Mind wandering has been considered as a mental process that is either independent from the concurrent task or regulated like a secondary task. These accounts predict that the form of mind wandering (i.e., images or words) should be either unaffected by or different from the modality form (i.e., visual or auditory) of the concurrent task. Findings from this study challenge these accounts. We mea...

This study developed and examined the validity of Japanese versions of the Daydream Frequency Scale (DDFS) and the Mind Wandering Questionnaire (MWQ), which measures propensity for spontaneous thoughts and mind wandering, respectively. In Study 1, we translated the items of the DDFS and the MWQ into Japanese and verified their validity. In Study 2, we confirmed the correlation of both scales wi...

Mind-wandering is both pervasive and detrimental to task performance. As such, identifying covert physiological measures that are associated with this off-task state could inform theories of mind-wandering and lead to interventions that improve task focus. Although previous work suggests that pupil dilation (PD) may vary between on- and off-task states, no studies have examined whether PD syste...