Hypercyclic operators on countably dimensional spaces

According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\Sigma(X)$ of countable dense linearly independent subsets of $X$. As a consequence, each $A\in \Sigma(X)$ is an orbit of a hypercyclic operator on $X$. Furthermore, every countably dimensional normed space supports a hypercyclic operator. We show that for a separable infinite dimensional Fr\'echet space $X$, $GL(X)$ acts transitively on $\Sigma(X)$ if and only if $X$ possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator

Mechanisms for MHD Poynting flux generation in simulations of solar photospheric magneto-convection

We investigate the generation mechanisms of MHD Poynting flux in the magnetised solar photosphere. Using radiative MHD modelling of the solar photosphere with initial magnetic configurations that differ in their field strength and geometry, we show the presence of two different mechanisms for MHD Poynting flux generation in simulations of solar photospheric magneto-convection. The weaker mechanism is connected to vertical transport of weak horizontal magnetic fields in the convectively stable layers of the upper photosphere, while the stronger is the production of Poynting flux in strongly magnetised intergranular lanes experiencing horizontal vortex motions. These mechanisms may be responsible for the energy transport from the solar convection zone to the higher layers of the solar atmosphere.Comment: 5 pages, 5 figures, accepted for ApJ

Planning with Pixels in (Almost) Real Time

Recently, width-based planning methods have been shown to yield state-of-the-art results in the Atari 2600 video games. For this, the states were associated with the (RAM) memory states of the simulator. In this work, we consider the same planning problem but using the screen instead. By using the same visual inputs, the planning results can be compared with those of humans and learning methods. We show that the planning approach, out of the box and without training, results in scores that compare well with those obtained by humans and learning methods, and moreover, by developing an episodic, rollout version of the IW(k) algorithm, we show that such scores can be obtained in almost real time.Comment: Published at AAAI-1