## Postdoctoral Researchers

** Vacancies for postdoctoral researchers
are available now**, as described below.

Please don't hesitate to contact me with informal enquires regarding current posts.

### Research Associate in Data Science

We are seeking an excellent postdoctoral researcher in signal processing, applied mathematics, physics, statistics, computer science, or a related field, to develop novel signal analysis techniques for extracting scientific information from large observational data-sets. Research aims will include a focus on signal analysis on the sphere but can be extended to incorporate the interests and expertise of the successful applicant.

Signals defined on the sphere are prevalent in a diverse range of fields, including cosmology, geophysics, acoustics, and computer graphics, for example. In cosmology, observations made by the European Space Agency's Planck and Euclid satellites live on the celestial sphere, leading to very large and precise spherical data-sets, the robust analysis of which can reveal a great deal about the nature of our Universe. The successful applicant will focus on the theoretical and methodological foundations of the analysis of signals defined on the sphere and will work closely with another postdoctoral researcher who will fill a complementary post focused on application to observational data.

The successful applicant will be based in the Astrophysics Group at the Mullard Space Science Laboratory (MSSL) of University College London (UCL) and will join the multi-disciplinary astroinformatics team, which comprises researchers with expertise in astrophysics, applied mathematics, signal processing, statistics and software engineering. The goal of the astroinformatics team is to develop and apply novel analysis techniques to extract scientific information from very large data sets, in order to develop a deeper understanding of the fundamental physics underlying the evolution of our Universe. The successful applicant will work closely with Dr Jason McEwen, while also interacting with other members of the astroinformatics team and the Astrophysics Group.

** Further information and details on how to apply is available **here.

## Postdoctoral Fellowships

I very much encourage young researchers to apply for postdoctoral fellowships. I am happy to support and assist strong candidates that would like to apply for fellowships with MSSL as the host institution.

If you are interested in discussing this further then please email me, including '[Fellowship enquiry]' in the subject of your email. I receive many enquires and so will only reply if your expertise are well matched to my research interests and there is a high chance of submitting a successful application.

More information on various fellowships can he found here:

- Royal Society (RS) University Research Fellowship(URF)
- Royal Society (RS) Newton International Fellowships (for researchers coming from abroad)
- Royal Society (RS) Dorothy Hodgkin Fellowships
- STFC Ernest Rutherford Fellowships (ERF)
- Royal Astronomical Society (RAS) Fellowships
- Leverhulme Trust Early Career Fellowships (ECF)
- Royal Commission for the Exhibition of 1851 Fellowships
- Marie Curie Fellowships (for researchers coming from Europe)
- Daphne Jackson Fellowships (for researchers returning from a career break)

## PhD Students

The PhD projects that I offer are typically multi-disciplinary and include a combination of cosmology, statistics, and informatics (e.g. signal processing, harmonic analysis, etc.). A relatively strong mathematical background is usually required for these types of projects. Programming skills are also an advantage. Some example projects are listed below, however the scope of projects can be modified to meet the interests of potential students.

If you are interested in discussing PhD projects further then please email me, including '[PhD enquiry]' in the subject of your email, and attach a CV. I receive many enquires and so will only reply if your expertise are well matched to my research interests and there is a high chance of submitting a successful application. Further information on how to submit an official application can be found here.

Some examples of illustrative projects follow.

### Weak gravitational lensing

We have recently entered an era of precision cosmology. The Big Bang cosmological model that describes our Universe explains many cosmological observations to exquisite accuracy, including the relic radiation of the Big Bang, the so-called cosmic microwave background (CMB). However, we remain ignorant of many of the components of this model. We know very little about dark matter and dark energy, which together constitute approximately 95% of the energy content of the Universe.

Weak lensing is a powerful technique that can be used to uncover the secrets of dark energy. Weak lensing refers to the deflection of light due to the gravitational influence of intervening matter as it travels to us through the Universe. The lensing is weak in the sense that it is small and difficult to detect from a single background source, however its statistical impact can be studied.

The goal of this project is to learn about dark energy through weak lensing. New analysis techniques will be developed to estimate the shear of galaxies due to weak lensing and to use this signal to constrain dark energy models. Novel 3D weak lensing techniques will also be developed. These new analysis techniques will build on recent developments in wavelet methods and compressive sensing, a revolutionary new development in the field of sampling theory. Data from current and forthcoming experiments will be used, such as the CFHTLenS and ESO KiDS surveys. The resulting analysis techniques are also expected to be used in the ESA Euclid mission, in which MSSL is playing a leading role.

#### Recommended reading

- L. Miller, T. D. Kitching, C. Heymans, A. F. Heavens, L. Van Waerbeke, Bayesian galaxy shape measurement for weak lensing surveys - I. Methodology and a fast fitting algorithm. Mon. Not. Roy. Astron. Soc., 2007.
- T. D. Kitching, L. Miller, C. E. Heymans, L. van Waerbeke, A. F. Heavens, Bayesian galaxy shape measurement for weak lensing surveys - II. Application to simulations. Mon. Not. Roy. Astron. Soc., 2008.
- A. F. Heavens, 3D weak lensing. Mon. Not. Roy. Astron. Soc., 2003.
- B. Leistedt and J. D. McEwen. Exact wavelets on the ball. IEEE Trans. Sig. Proc., 2012.

### Cosmoinformatics

Cosmological observations are inherently made on the celestial sphere, yielding data-sets defined on spherical manifolds, such as the sphere (e.g. surface of the Earth) and ball (e.g. interior of the Earth). For example, observations of the cosmic microwave background (CMB), the relic radiation of the Big Bang, are made on the sphere, while observations of the large-scale structure (LSS) of the Universe, such as clusters of galaxies, are made on the ball. However, signal processing techniques are typically restricted to Euclidean spaces.

Signal processing techniques that live natively on spherical manifolds are thus required to analyse cosmological observations accurately. New signal representations, such as wavelets and learnt dictionaries, are required, in addition to new techniques for solving the inverse problems that typically arise in these settings. For example, denoising and deconvolution problems arise in a vast number of applications and, consequently, related algorithms have received considerable attention. However, many of these applications and algorithms have been restricted to Euclidean spaces, such as audio signals on the line and images on the plane, for example. Denoising and deconvolution algorithms for signals defined on the sphere, such as the CMB, have received relatively little attention.

The goal of this project is to develop new signal representations on spherical manifolds and to apply these to solve inverse problems, such as denoising and deconvolution problems. The primary applications to be considered include the analysis of cosmological observations, such as the CMB. However, other domains of application, such as computer graphics, may also be considered.

#### Recommended reading

- B. Leistedt and J. D. McEwen. Exact wavelets on the ball. IEEE Trans. Sig. Proc., 2012.
- B. Leistedt, J. D. McEwen, P. Vandergheynst, and Y. Wiaux. S2LET: A code to perform fast wavelet analysis on the sphere. Astron. & Astrophys., 558(A128):1-9, 2013.
- J. D. McEwen and Y. Wiaux. A novel sampling theorem on the sphere. IEEE Trans. Sig. Proc., 2011.
- Y. Wiaux, J. D. McEwen, P. Vandergheynst, and O. Blanc. Exact reconstruction with directional wavelets on the sphere. Mon. Not. Roy. Astron. Soc., 2008.

### Machine learning and informatics techniques to detect cosmic strings

Symmetry breaking phase transitions in the early Universe may have lead to the creation of topological defects. Cosmic strings are one particular type of defect, where axial or cylindrical symmetry is broken, leading to line-like discontinuities in the fabric of the Universe. Although we have not yet observed cosmic strings, we have observed string-like topological defects in other media, such as liquid crystals (see image). Note that cosmic strings are distinct to the fundamental superstrings of string theory. However recent developments in string theory suggest the existence of macroscopic superstrings, which could play a similar role to cosmic strings.

Spacetime about a cosmic string is conical. Consequently, strings moving transverse to the line of sight induce line-like discontinuities in the cosmic microwave background (CMB), the relic radiation of the Big Bang. The detection of cosmic strings from CMB observations would open a new window into the physics of the early Universe.

The goal of this project is to develop and apply methods to search for evidence of cosmic strings from observations of the CMB. In the absence of a detection, the allowable string tension (energy level) will be constrained. Novel techniques will be developed by combining ideas from Bayesian inference, machine learning and compressive sensing, a revolutionary new development in the field of sampling theory. Both Planck and WMAP observations of the CMB will be analysed.

#### Recommended reading

- Planck Collaboration XXV. Planck 2013 results: Searches for cosmic strings and other topological defects. Astron. & Astrophys., 2013.
- C. Ringeval and F. R. Bouchet. All sky CMB map from cosmic strings integrated Sachs-Wolfe effect. Phys. Rev. D., 2012.
- N. Kaiser and A. Stebbins, Microwave anisotropy due to cosmic strings. Nature, 1984.

### Radio interferometric imaging

Radio interferometric telescopes allow astronomers to make radio observations of the sky at otherwise inaccessible angular resolution and sensitivity. We are about to enter a new era of radio astronomy, with new radio interferometers under construction and design. One notable example is the Square Kilometre Array (SKA), whose science goals range from cosmology and astrobiology, to strong field gravity. However, novel imaging techniques will be required to ensure that new radio telescopes meet their scientific goals.

Radio interferometric observations provide incomplete measurements of the Fourier space of the image on the sky of interest. Recovering interferometric images is therefore an ill-posed inverse problem, which has recently been tackled successfully with compressed sensing techniques, a revolutionary new development in the field of sampling theory. In order to remain as close to the theory of compressed sensing as possible, these techniques have typically considered simulated interferometric observations that are idealised. To realise the enhancement in quality provided by these novel techniques on real radio interferometric observations, their extension to realistic interferometric configuration is now of considerable importance. Next-generation telescopes will also exhibit very wide fields of view, for which novel wide-field modelling wil be required to ensure these telescopes reach their full potential.

The goal of this project is to develop and apply novel compressed sensing techniques to recover images from real observations made by radio interferometric telescopes. Furthermore, these techniques will be extended to wide-field settings, which are essential to model next-generation telescopes accurately. Data observed by current radio interferometric telescopes will be provided through international collaboration with researchers in the UK, Europe and South Africa.

#### Recommended reading

- R. E. Carrillo, J. D. McEwen, and Y. Wiaux, Why CLEAN when you can PURIFY? Mon. Not. Roy. Astron. Soc., 2013.
- L. Wolz, J. D. McEwen, F. B. Abdalla, R. E. Carrillo, and Y. Wiaux, Revisiting the spread spectrum effect in radio interferometric imaging: a sparse variant of the w-projection algorithm. Mon. Not. Roy. Astron. Soc., 2013.
- R. E. Carrillo, J. D. McEwen, and Y. Wiaux, Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging. Mon. Not. Roy. Astron. Soc., 2012.
- A. R. Thompson, J. M. Moran, and G. W. Swenson Jr. Interferometry and synthesis in radio astronomy. Wiley-VCH, Weinheim, 2nd edition, 2001.

## Masters Students

I am not offering any additional Masters projects at present but when I am they will appear here.

## Internship Students

I am not offering any specific internship projects at present. However, if you are interested in discussing internship possibilities further then please email me, including '[Internship enquiry]' in the subject of your email, and attach a CV. I receive many enquires and so will only reply if your expertise are well matched to my research interests and there is a high chance of a placement.