The Power of Low Frequencies: Faraday Tomography in the sub-GHz regime

Faraday tomography, the study of the distribution of extended polarized emission by strength of Faraday rotation, is a powerful tool for studying magnetic fields in the interstellar medium of our Galaxy and nearby galaxies. The strong frequency dependence of Faraday rotation results in very different observational strengths and limitations for different frequency regimes. I discuss the role these effects take in Faraday tomography below 1 GHz, emphasizing the 100-200 MHz band observed by the Low Frequency Array and the Murchison Widefield Array. With that theoretical context, I review recent Faraday tomography results in this frequency regime, and discuss expectations for future observations.Comment: 12 pages, 4 figures. Accepted for publication in Galaxies as part of the special issue "The Power of Faraday Tomography

Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

The propagation of solar waves through the sunspot of AR 9787 is observed using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magneto-hydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere, less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.Comment: 21 pages, Accepted in Solar Physic

Physical conditions in the primitive solar nebula

Physical conditions for model of primitive solar nebul

On the distribution of multiplicatively dependent vectors

In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\R^n$ and \C^n. We also study this property in a more detailed manner by considering the covering radius of such vectors.Comment: 19 page

Do Attitudes Towards Corruption Differ Across Cultures? Experimental Evidence from Australia, India, Indonesia andSingapore

This paper examines cultural differences in attitudes towards corruption by analysing individual-decision making in a corrupt experimental environment. Attitudes towards corruption play a critical role in the persistence of corruption. Our experiments differentiate between the incentives to engage in corrupt behaviour and the incentives to punish corrupt behaviour and allow us to explore whether, in environments characterized by lower levels of corruption, there is both a lower propensity to engage in corrupt behaviour and a higher propensity to punish corrupt behaviour. Based on experiments run in Australia (Melbourne), India (Delhi), Indonesia (Jakarta) and Singapore, we find that there is more variation in the propensities to punish corrupt behaviour than in the propensities to engage in corrupt behaviour across cultures. The results reveal that the subjects in India exhibit a higher tolerance towards corruption than the subjects in Australia while the subjects in Indonesia behave similarly to those in Australia. The subjects in Singapore have a higher propensity to engage in corruption than the subjects in Australia. We also vary our experimental design to examine the impact of a more effective punishment system and the effect of the perceived cost of bribery.Corruption, Experiments, Punishment, Cultural Analysis

Feedback computability on Cantor space

We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show that the feedback computable functions are precisely the effectively Borel functions. With this as motivation we define the notion of a feedback computable function on a structure, independent of any coding of the structure as a real. We show that this notion is absolute, and as an example characterize those functions that are computable from a Gandy ordinal with some finite subset distinguished

Fourier and Beyond: Invariance Properties of a Family of Integral Transforms

The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized by an intertwining relation with dilations and by having a Gaussian as an eigenfunction. This broadens the perspective to an entire family of Fourier-like transforms that are uniquely identified by the same dilation property and having Gaussian-like functions as eigenfunctions. We show that these transforms share many properties with the Fourier transform, particularly unitarity, periodicity and eigenvalues. We also establish short-time analogues of these transforms and show a reconstruction property and an orthogonality relation for the short-time transforms.Comment: 14 page