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...

Background Many studies underline the great benefits of yeast extracts (YE), used as supplements in animal free culture media, on cell growth and recombinant protein production [1,2]. Nevertheless, their unknown composition and batch-to-batch variability of commercial YE remain constraints for industrial processes [3,4]. Consequently, the identification of bioactive YE molecules is challenging ...

Yielding elements (YE) are among those devices that not only help control structural damages, but make better seismic behavior by concentrating the frames in some removable part of the structures. YE are located at the intersection of Concentric Braced Frame (CBF) in a rectangular shape. In this paper, Seismic behavior of the frames with YE will be investigated. For this reason, 5 braced steel ...

This paper reports a wandering weekday effect: the pattern of day seasonality in stock market returns is not fixed, as assumed in the Monday or weekend effects, but changes over time. Analysing daily closing prices in eleven major stock markets during 1993–2007, our results show that the wandering weekday is not conditional on average returns in the previous week (the ‘‘twist” in the Monday eff...

Let K be a number field, let φ(x) ∈ K(x) be a rational function of degree d > 1, and let α ∈ K be a wandering point such that φ(α) = 0 for all n > 0. We prove that if the abc-conjecture holds for K, then for all but finitely many positive integers n, there is a prime p of K such that vp(φ (α)) > 0 and vp(φ (α)) 0 for all positive integers m < n. Under appropriate ramification hypotheses, we can...