Five postdoctoral positions in cosmology

Jason McEwen sent me the following:  www.jasonmcewen.org

Dear Colleagues,

Five postdoctoral positions in cosmology have been advertised at UCL recently (details below). I would be very grateful if you could bring these adverts to the attention of suitable candidates.

In particular, I would like to highlight the two positions in theoretical/numerical cosmology to work closely with Hiranya Peiris and myself as members of the European Research Council project CosmicDawn. Researchers working in signal processing will be considered for these positions, although some knowledge of cosmology would be an advantage.

Best,

Jason

--

www.jasonmcewen.org

Thanks Jason.

=====================================================

UCL Physics and Astronomy: Research Associates - Cosmology x 5

The appointments will be full time on UCL Grade 7. The salary range will be £32,055 - £38,744 per annum, inclusive of London Allowance.

The cosmology group at UCL is very active in observational cosmology, with leading roles in several international projects including: the Dark Energy Survey, Planck, LOFAR, SKA, Euclid and DESpec. The group is looking to appoint 5 research associates who will actively participate in the core research of the cosmology group.

All positions are funded for 3 years in the first instance.

Cosmology with Data from Galaxy Surveys (2 positions)

The successful applicants will be expected to fully participate in the core programme in galaxy surveys carried out at UCL, including the Dark Energy Survey (DES) and spectroscopic followups. The DES has already produced the first science verification of sub-arcsecond images in Sept 2012 and the full survey starts in late 2012. Potential projects are related to large scale structure, weak lensing, photometric redshifts, and spectroscopic target selection from optical surveys. Applicants with strong data analysis background are encouraged to apply.

Theoretical/Numerical Cosmology (2 positions)

The successful applicants will be expected to carry out research in theoretical and/or numerical cosmology, focussing on testing the fundamental physics of the early universe via novel observables, such as non-Gaussianity and statistical anisotropy, and scientific exploitation of next generation CMB data from Planck and large scale structure data, especially DES. Applicants from relevant interdisciplinary backgrounds, such as computer science or signal processing, will be also considered in addition to cosmologists. Experience of developing complex high performance computing algorithms independently (including parallel programming) is desirable.

Photometric redshift and/or WL development for Euclid (1 position)

This position will be funded through the UK-Space Agency for work on Euclid. The successful applicant will be expected to carry out research in algorithm development for photometric redshifts and cosmological measurements with the upcoming Euclid mission. They would be expected to participate in the working group activities and the ground segment efforts within the mission. We encourage people with a strong background on photometric redshifts, large scale structure and weak lensing to apply.

The successful applicants will have a PhD in Cosmology and will be able to analyse and present complex information effectively to a range of audiences.

For further details about the vacancy and how to apply online please go tohttp://www.ucl.ac.uk/hr/jobs/ and search on Reference Number 1286666.

If you have any queries regarding the application process, please contact Mrs Kay Nakum,
email: k.nakum@ucl.ac.uk , tel: +44 (0)20 7679 3458.

Informal enquiries regarding the vacancy can be made to Dr Hiranya Peiris (h.peiris@ucl.ac.uk ), Prof Ofer Lahav ( ucapola@ucl.ac.uk ), or Dr Filipe Abdalla (fba@star.ucl.ac.uk ).

Closing Date: 15/12/2012

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Compressed Sensing with Electron Microscopy and Optical-resolution photoacoustic computed tomography

Today we have two papers on the utilisation of compressive sensing in hardware and sensors. The first one is initially mathematical in nature but does address some of the noise issue of EM and even takes a look at tomography. The second paper is behind paywall so I added two other papers on the same subject that go deeper in the explaining the technique. 

Compressed Sensing and Electron Microscopy by Peter Binev, Wolfgang Dahmen, Ronald DeVore, Philipp Lamby, Daniel Savu, and Robert Sharpley. The abstract reads:

Compressed Sensing (CS) is a relatively new approach to signal acquisition which has as its goal to minimize the number of measurements needed of the signal in order to guarantee that it is captured to a prescribed accuracy. It is natural to inquire whether this new subject has a role to play in Electron Microscopy (EM). In this paper, we shall describe the foundations of Compressed Sensing and then examine which parts of this new theory may be useful in EM.

In vivo optical-resolution photoacoustic computed tomography with compressed sensing by Jing Meng, Lihong V. Wang, Dong Liang, and Liang Song. The abstract reads:

Optical-resolution photoacoustic microscopy is becoming a powerful research tool for studying microcirculation in vivo. Moreover, ultrasonic-array-based optical-resolution photoacoustic computed tomography (OR-PACT), providing comparable resolution at an improved speed, has opened up new opportunities for studying microvascular dynamics. In this Letter, we have developed a compressed sensing with partially known support (CS-PKS) photoacoustic reconstruction strategy for OR-PACT. Compared with conventional backprojection reconstruction, the CS-PKS strategy was shown to produce high-quality in vivo OR-PACT images with threefold less measurement data, which can be leveraged to improve the data acquisition speed and costs of OR-PACT systems.

Multiscale photoacoustic microscopy and computed tomography by Lihong V. Wang. The abstract reads:

Photoacoustic tomography (PAT) is probably the fastest-growing area of biomedical imaging technology, owing to its capacity for high-resolution sensing of rich optical contrast in vivo at depths beyond the optical transport mean free path (~1 mm in human skin). Existing high-resolution optical imaging technologies, such as confocal microscopy and two-photon microscopy, have had a fundamental impact on biomedicine but cannot reach the penetration depths of PAT. By utilizing low ultrasonic scattering, PAT indirectly improves tissue transparency up to 1000-fold and consequently enables deeply penetrating functional and molecular imaging at high spatial resolution. Furthermore, PAT promises in vivo imaging at multiple length-scales; it can image subcellular organelles to organs with the same contrast origin — an important application in multiscale systems biology research.

Compressed sensing in photoacoustic tomography in vivo by Zijian Guo, Changhui Li, Liang Song, Lihong V. Wang. The abstract reads:

The data acquisition speed in photoacoustic computed tomography PACT is limited by the laser repetition rate and the number of parallel ultrasound detecting channels. Reconstructing an image with fewer measurements can effectively accelerate the data acquisition and reduce the system cost. We adapt compressed sensing  CS for the reconstruction in PACT. CS-based PACT is implemented as a nonlinear conjugate gradient descent algorithm and tested with both phantom and in vivo experiments. 

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Learning Manifolds in the Wild

One of Achille's heel of image processing and manifold signal processing in particular, revolves around the difficulty of building manifolds from images thanks to the apparent suboptimal capabilities of the euclidean norm. In short, the Euclidian norm doesn't provide a good means of evaluating similarity information when images are taken in different conditions (pose, illumination etc). Today's approach provides a refreshing look at this central, but often overlooked issue, through the use of the Earth Mover’s Distance on top of keypoint descriptors. Improvement could include the use of FREAK instead of SIFT and a faster Distance computations thanks to  the structure of FREAK or otherwise (see below)

Learning Manifolds in the Wild by Chinmay Hegde, Aswin C. Sankaranarayanan, Richard Baraniuk. The abtstract reads:

Despite the promise of low-dimensional manifold models for image processing, computer vision, and machine learning tasks, their utility has been hamstrung in practice by two fundamental challenges. First, practical image manifolds are non-isometric to their underlying parameter space, while the state-of-the-art manifold modeling and learning frameworks assume isometry. Second, practical image manifolds are strongly perturbed by nuisance parameters such as illumination variations, occlusions, and clutter. In this paper, we develop new theory and practical algorithms for manifold modeling, learning, and processing that directly address these challenges. To address the isometry challenge, we show that the Earth Mover’s Distance (EMD) is a more natural metric for inter-image distances than the standard Euclidean distance and use it to establish the isometry of manifolds generated by translations and rotations of a reference image. To the best of our knowledge, this is the first rigorous result on manifold isometry for generic grayscale image familes. To address the nuisance parameter challenge, we advocate an image representation based on local keypoint features and use it to define a new keypoint articulation manifold (KAM). We employ the KAM framework on a number of real-world image datasets acquired “in the wild” to demonstrate its improved performance over state-of-the-art manifold modeling approaches. A particularly compelling application of our approach is the automatic organization of large, unstructured collections of photographs gathered from the internet.

It turns out it seems possible to compute Earth Mover's Distance faster: Sublinear Time Algorithms for Earth Mover’s Distance by Khanh Do Ba, Huy L. Nguyen, Huy N. Nguyen, Ronitt Rubinfeld. The abstarct reads:

We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions when given access only to samples of the distribution. We give closeness testers and additive-error estimators over domains in [0; 1]d , with sample complexities independent of domain size – permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on the dimension of the domain space and the quality of the result required. We also prove lower bounds showing the dependencies on these parameters to be essentially optimal. Additionally, we consider whether natural classes of distributions exist for which there are algorithms with better dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly, we consider a variant of the EMD, defined over tree metrics instead of the usual `1 metric, and give tight upper and lower bounds.

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Belief Propagation Reconstruction for Discrete Tomography - implementation -

I mentioned their work a while back when they were presenting how a BP algorithm (or AMP) could be leveraged into devising a reconstruction for CT. Here is the paper and the attendant implementation: Belief Propagation Reconstruction for Discrete Tomography by Emmanuelle Gouillart, Florent Krzakala, Marc Mezard, Lenka Zdeborová. The abstract reads:

We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to take the same value, we follow a Bayesian approach and introduce a fast message-passing reconstruction algorithm based on belief propagation. For numerical results, we specialize to the case of binary tomography. We test the algorithm on binary synthetic images with different length scales and compare our results against a more usual convex optimization approach. We investigate the reconstruction error as a function of the number of tomographic measurements, corresponding to the number of projection angles. The belief propagation algorithm turns out to be more efficient than the convex-optimization algorithm, both in terms of recovery bounds for noise-free projections, and in terms of reconstruction quality when Gaussian noise is added to the projections.

I note from the paper: 

Note that this algorithm is of the embarrassingly parallel type, since each line µ can be handled separately when computing line 7 in the above pseudo-code. This could be used to speed up the algorithm by solving each line separately on different cores

An implementation of this algorithm is available on Github here. Three weeks ago, this group advertized for two postdocs.

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Sunday Morning Insight: Quantum Computing and the Steamrollers

I am not an expert in quantum computing and how this will change the world. However, here are some items that might receive a special attention from you the readers considering some of the themes and results witnessed here on Nuit Blanche. 

First item of interest: you might recall this L0 regularization using an adiabatic quantum computing algorithm   as a replacement of current heuristic algorithms ( see here ). While, Random Kitchen Sinks (RKS) seem to already do better than Adaboost, yesterday's posting show another "heuristic" that seems to be on its way to do even better than RKS in terms of speed. Heuristics may be bad because they have no theoretical grounding until you find out there is a good reason they work. The field of compressive sensing took off in 2004 only because some heuristics were finally understood in some specific cases. It led the way to comforting many researchers into thinking it was OK not to have an absolute theoretical grounding to investigate further. Since then, many empirical results do not need the stamp of approval it once needed to go through peer review. People have gotten over some of these fear of rejection issues.

Second item of interest: This arxiv paper that came out last month featuring an O(sqrt(k)log(k)) quantum algorithm for the combinatorial group testing problem that some could see as a subset of compressive sensing. It is indeed an improvement over O(k log(k/N)) but is it worth a change in technology ? The answer is no. While these approaches seem very interesting, I currently fail to see how a combination of concentration of measure/randomization results and silicon can be surpassed within, at least, the next twenty years.

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Fast Functions via Randomized Algorithms: Fastfood versus Random Kitchen Sinks

I just noticed the following while reading Learning at Scale by Alex Smola: a randomized scheme that aims at replacing the Random Kitchen Sinks approximation to Kernel Learning at large scales. Random Kitchen Sinks were featured here a while back, Here is the site to learn more about Random Kitchen Sinks (or Random Features as they were called back then). .

I'll wait for the paper.

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FLAGLET: Exact wavelets on the ball - implementation -

After S2LET, here is a related toolbox FLAGLET producing exact wavelets on the ball. From the paper:

Exact Wavelets on the Ball by B. Leistedt, J. D. McEwen. The abstract reads:

We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre polynomials and develop a corresponding quadrature rule. Combined with the spherical harmonic transform, this approach leads to a sampling theorem on the ball and a novel three-dimensional decomposition which we call the Fourier-Laguerre transform. We relate this new transform to the well-known Fourier-Bessel decomposition and show that band-limitedness in the Fourier-Laguerre basis is a sufficient condition to compute the Fourier-Bessel decomposition exactly. We then construct the flaglet transform on the ball through a harmonic tiling, which is exact thanks to the exactness of the Fourier-Laguerre transform (from which the name flaglets is coined). The corresponding wavelet kernels are well localised in real and Fourier-Laguerre spaces and their angular aperture is invariant under radial translation. We introduce a multiresolution algorithm to perform the flaglet transform rapidly, while capturing all information at each wavelet scale in the minimal number of samples on the ball. Our implementation of these new tools achieves floating-point precision and is made publicly available. We perform numerical experiments demonstrating the speed and accuracy of these libraries and illustrate their capabilities on a simple denoising example.

The code is located at: http://www.flaglets.org/. The introduction reads:

Introduction

The FLAGLET code provides high-performance routines for fast wavelet analysis of signals on the ball using theFlaglet transform (ArXiv | DOI). It exploits S2LET, FLAG and SSHT codes. The flaglet transform is theoretically exact, i.e. the original signal can be synthesises from its wavelet coefficients exactly since the wavelet coefficients capture all the information of band-limited signals.

This page outlines the main features of FLAGLET, installation details as well as the core functionalities and interfaces. References, version, and license information then follows. FLAGLET requires the FLAG, S2LET, SSHT andFFTW libraries.

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S2LET: A code to perform fast wavelet analysis on the sphere - implementation -

Here is an new version of the paper featuring a fast wavelet on the sphere (and expecting a sparse decomposition on the sphere). : S2LET: A code to perform fast wavelet analysis on the sphere by B. Leistedt, J. D. McEwen, P. Vandergheynst, Y. Wiaux. The abstract reads:

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of signals on the sphere. The scale-discretised wavelet transform was developed previously and reduces to the needlet transform in the axisymmetric case. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.

The S2Let package is at: http://www.s2let.org/

From the introduction:

Introduction

The S2LET code (ArXiv paper) provides high performance routines for fast wavelet analysis of signals on the sphere. It uses the SSHT code built on the MW sampling theorem (ArXiv | DOI) to perform exact spherical harmonic transforms on the sphere. The resulting wavelet transform implemented in S2LET is theoretically exact, i.e. a band-limited signal can be recovered from its wavelet coefficients exactly and the wavelet coefficients capture all the information. S2LET also supports the HEALPix sampling scheme, in which case the transforms are not theoretically exact but achieve good numerical accuracy.

This page outlines the main features of S2LET, installation details as well as the core functionalties and interfaces. References, version, and license information then follows. The S2LET code requires the SSHT and FFTW libraries. The IO FITS features require CFITSIO. To support HEALPix, a valid installation of its Fortran implementation must be provided.

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A note from Jelani Nelson on OSNAP

Jelani Nelson responded in the comment section of the post I featured this morning (Low Rank Approximation and Regression in Input Sparsity Time - implementation ) and pointed out to my misunderstanding of a certain issue in a paper I featured yesterday ( OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings ). Here is what  Jelani had to say:

Hi, 

My bad, indeed, David states so in the video, the log factor is gone. 

Sorry to add more confusion to the mix, but I don't think this is what Ken meant (in particular, the video you link to is from before what Ken is talking about). Their work was always, from the first version, able to get nnz(A) + poly(d/eps) time for regression, without the log n. What Huy and I addressed was: how big is the poly? Originally the CW12 poly was d^5*polylog(d), and they were able to make it d^3*polylog(d) (even replacing d with rank(A)) at a sacrifice: by turning nnz(A) into nnz(A)*log n. I think Ken's point is that they no longer have to make that sacrifice with their Oct. 31st version: their sharpened analysis can make it d^3*polylog(d) while still keeping the log n term away from the nnz(A). (See footnote 2 in our manuscript.)

The point of what we did is that (a) it's nnz(A) + d^3*log d, with only one log d multiplying the d^3 term (this difference used to be d^3*log d vs. d^5*polylog(d), and now is d^3*log d vs. d^3*polylog(d) given the Oct. 31 version that Ken referred to; I think this is what Ken's point was in his comment), and (b) if you're willing to make the sacrifice of multiplying nnz(A) by log n then you can make the additive term be d^{omega+gamma} for arbitrarily small gamma>0 (and again, d can be replaced with rank(A) in this bound), where omega < 2.373 is the exponent of matrix multiplication. There are some other differences also, e.g. our analyses don't need as strong hash functions to go through which has some slight advantages in streaming settings (see the paper).

Later he added in a second comment:

I guess I should have mentioned that even for (b) above, you actually don't even have to multiply nnz(A) by log n to get d^{omega+gamma}; rather, you have to multiply nnz(A) by a constant depending on 1/gamma. You do multiply it by log n if you want rank(A)^{omega+gamma} time though.

Thank you Jelani !

Credit photo: NASA, Opportunity :: Navigation Camera :: Sol 3124

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Low Rank Approximation and Regression in Input Sparsity Time - implementation -

Ken Clarkson left a new comment on a previous post "OSNAP: Faster numerical linear algebra algorithms ...": 

Hi. While Huy and Jelani have sharper results, and cleaner proofs, it's worth mentioning that David and I have sharpened our analysis as well, reducing O(nnz(A)log ) to O(nnz(A)) dependence in that second set of results for us in their table, for regression and low-rank approximation. These improvements result from a more careful analysis in the heavy-coordinate, "perfect hashing", part of our proof; they are in the current version of our paper on arXiv.

My bad, indeed, David states so in the video, the log factor is gone. (slides are also listed in the recent Workshop on "Randomized Numerical Linear Algebra (RandNLA): Theory and Practice"). Thanks Ken !

 Again, I hesitate to mention that this is an implementation as the hashing mechanism seems so trivial. The arxiv paper is: Low Rank Approximation and Regression in Input Sparsity Time by Ken Clarkson, David P. Woodruff 

(Submitted on 26 Jul 2012 (v1), last revised 31 Oct 2012 (this version, v3))

We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in \mathbb{R}^d$. Such a matrix $S$ is called a \emph{subspace embedding}. Furthermore, $SA$ can be computed in $\nnz(A) + \poly(d \eps^{-1})$ time, where $\nnz(A)$ is the number of non-zero entries of $A$. This improves over all previous subspace embeddings, which required at least $\Omega(nd \log d)$ time to achieve this property. We call our matrices $S$ \emph{sparse embedding matrices}.

Using our sparse embedding matrices, we obtain the fastest known algorithms for $(1+\eps)$-approximation for overconstrained least-squares regression, low-rank approximation, approximating all leverage scores, and $\ell_p$-regression. The leading order term in the time complexity of our algorithms is $O(\nnz(A))$ or $O(\nnz(A)\log n)$.

We optimize the low-order $\poly(d/\eps)$ terms in our running times (or for rank-$k$ approximation, the $n*\poly(k/eps)$ term), and show various tradeoffs. For instance, we also use our methods to design new preconditioners that improve the dependence on $\eps$ in least squares regression to $\log 1/\eps$. Finally, we provide preliminary experimental results which suggest that our algorithms are competitive in practice.

and here the video:

 
Low Rank Approximation and Regression in Input Sparsity Time, David Woodruff 

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