A simple and accurate approximation for the Q stability parameter in multi-component and realistically thick discs

In this paper, we propose a Q stability parameter that is more realistic than those commonly used, and is easy to evaluate [see Eq. (19)]. Using our Q_N parameter, you can take into account several stellar and/or gaseous components as well as the stabilizing effect of disc thickness, you can predict which component dominates the local stability level, and you can do all that simply and accurately. To illustrate the strength of Q_N, we analyse the stability of a large sample of spirals from The HI Nearby Galaxy Survey (THINGS), treating stars, HI and H_2 as three distinct components. Our analysis shows that H_2 plays a significant role in disc (in)stability even at distances as large as half the optical radius. This is an important aspect of the problem, which was missed by previous (two-component) analyses of THINGS spirals. We also show that HI plays a negligible role up to the edge of the optical disc; and that the stability level of THINGS spirals is, on average, remarkably flat and well above unity.Comment: MNRAS, in pres

Learning deep dynamical models from image pixels

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement mapping and the transition mapping (system dynamics) in latent space can be challenging. For linear system dynamics and measurement mappings efficient solutions for system identification are available. However, in practical applications, the linearity assumptions does not hold, requiring non-linear system identification techniques. If additionally the observations are high-dimensional (e.g., images), non-linear system identification is inherently hard. To address the problem of non-linear system identification from high-dimensional observations, we combine recent advances in deep learning and system identification. In particular, we jointly learn a low-dimensional embedding of the observation by means of deep auto-encoders and a predictive transition model in this low-dimensional space. We demonstrate that our model enables learning good predictive models of dynamical systems from pixel information only.Comment: 10 pages, 11 figure

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Modeling and interpolation of the ambient magnetic field by Gaussian processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic

Charge fluctuations in nonlinear heat transport

We show that charge fluctuation processes are crucial for the nonlinear heat conductance through an interacting nanostructure, even far from a resonance. We illustrate this for an Anderson quantum dot accounting for the first two leading orders of the tunneling in a master equation. The often made assumption that off-resonant transport proceeds entirely by virtual occupation of charge states, underlying exchange-scattering models, can fail dramatically for heat transport. The identified energy-transport resonances in the Coulomb blockade regime provide new qualitative information about relaxation processes, for instance by strong negative differential heat conductance relative to the heat current. These can go unnoticed in the charge current, making nonlinear heat-transport spectroscopy with energy-level control a promising experimental tool

We can believe the Error Theory

Bart Streumer argues that it is not possible for us to believe the error theory, where by ‘error theory’ he means the claim that our normative beliefs are committed to the existence of normative properties even though such properties do not exist. In this paper, we argue that it is indeed possible to believe the error theory. First, we suggest a critical improvement to Streumer’s argument. As it stands, one crucial premise of that argument—that we cannot have a belief while believing that there is no reason to have it—is implausibly strong. We argue that for his purposes, Streumer’s argument only requires a weaker premise, namely that we cannot rationally have a belief while believing that there is no reason to have it. Secondly, we go on to refute the improved argument. Even in its weaker form, Streumer’s argument is either invalid or the crucial premise should be rejected