The development and applications of ultrafast electron nanocrystallography

We review the development of ultrafast electron nanocrystallography as a method for investigating structural dynamics for nanoscale materials and interfaces. Its sensitivity and resolution are demonstrated in the studies of surface melting of gold nanocrystals, nonequilibrium transformation of graphite into reversible diamond-like intermediates, and molecular scale charge dynamics, showing a versatility for not only determining the structures, but also the charge and energy redistribution at interfaces. A quantitative scheme for three-dimensional retrieval of atomic structures is demonstrated with few-particle (< 1000) sensitivity, establishing this nanocrystallographic method as a tool for directly visualizing dynamics within isolated nanomaterials with atomic scale spatio-temporal resolution.Comment: 33 pages, 17 figures (Review article, 2008 conference of ultrafast electron microscopy conference and ultrafast sciences

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

3D Reconstruction of Proteins and Viruses from Angular Correlations of the Scattered Intensities

There is a remarkable shortage of the detailed knowledge of membrane proteins at atomic resolution despite the fact that they are the targets of many of today\u27s drugs. The reason is that membrane proteins tend to have large hydrophobic surfaces which ensure their correct positioning in a membrane. However, this seems to make crystallization difficult, and this makes traditional methods of structure determination by X-ray crystallography difficult. In this thesis, we take advantage of this very fact to suggest an alternative method for structure determination by X-ray scattering of the projected structures of membrane proteins in their natural environments. Although in such environments the proteins are not perfectly aligned as in a crystal, we find that the algorithm suggested by Kurta and Pedrini appears to promise structure determination, perhaps down to atomic resolution. We also suggest and develop how the method may be extended to obtain general (non-symmetric) 3D structures by exploiting the curved nature of Ewald spheres at lower energy. The extension of the 2D idea into 3D is straightforward, since a curved Ewald sphere also consists of a set of rings (one expects the different rings have different q_z components). We can get the intensities in 3D reciprocal space as that is exactly what we need for 3D structure recovery via a phasing program. Of course, the construction of intensity data on a uniform grid in 3D reciprocal space (required by a typical phasing program) requires a girdding program. The registry between the I_m(q)\u27s on different q\u27s can be found as before if one knows B_m(q_1,q_2) from the experiment, as can be found from a set of diffraction patterns of the same energy. Of course, varying the energy then gives us the 3D reciprocal space for a range of q_z\u27s, just what we need for getting info about the 3D structure. In the second part of this thesis, we have reconstructed icosahedral images of the Coliphage PR772 and Rice Dwarf (RDV) viruses from the angular correlations of experimental data. We calculate the correlations using the standard method that Hanbury, Brown and Twiss developed in astronomy. The pattern of dominant icosahedral angular momentum quantum numbers that results is a strong indication of the icosahedral nature of the capsid. Having first determined by objective means that the structure of the capsid has icosahedral symmetry, we then recover a dodecahedral diffraction volume from which we correctly reconstruct an icosahedral structure using our phasing algorithm. We quantify the quality of the reconstructed image using the Fourier shell correlation curve of two independent datasets. For PR772, the FSC curve stays above 0.5 throughout the range of experimental data, which suggests that the resolution is still determined by the limitations of the experimental data rather than by the reconstruction method. For RDV, the resolution is around 200A. We also calculated an R_spllit quantity that compares two randomly split diffraction patterns for PR772 and RDV data and, as expected, they remained low. In a nutshell, three most important things to come out of this work are: 1-We recover the 2D structure of an individual membrane proteins up to atomic resolution using our suggested 2D phasing algorithm. 2-We develop an idea for producing 3D images using 2D diffraction patterns by combining multi-wavelength data from a soft X-ray fluctuation scattering experiment on membrane proteins partially oriented in a membrane, for the first time. 3- We also determine the the three-dimensional structure of PR772 and RDV viruses from experimental data, using our new 3D method

Computational Imaging Systems for High-speed, Adaptive Sensing Applications

Driven by the advances in signal processing and ubiquitous availability of high-speed low-cost computing resources over the past decade, computational imaging has seen the growing interest. Improvements on spatial, temporal, and spectral resolutions have been made with novel designs of imaging systems and optimization methods. However, there are two limitations in computational imaging. 1), Computational imaging requires full knowledge and representation of the imaging system called the forward model to reconstruct the object of interest. This limits the applications in the systems with a parameterized unknown forward model such as range imaging systems. 2), the regularization in the optimization process incorporates strong assumptions which may not accurately reflect the a priori distribution of the object. To overcome these limitations, we propose 1) novel optimization frameworks for applying computational imaging on active and passive range imaging systems and achieve 5-10 folds improvement on temporal resolution in various range imaging systems; 2) a data-driven method for estimating the distribution of high dimensional objects and a framework of adaptive sensing for maximum information gain. The adaptive strategy with our proposed method outperforms Gaussian process-based method consistently. The work would potentially benefit high-speed 3D imaging applications such as autonomous driving and adaptive sensing applications such as low-dose adaptive computed tomography(CT)

Generalized frustration in the multidimensional Kuramoto model

The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit vector. For $D=2$ the particles move on the unit circle and the vectors can be described by a single phase, recovering the original Kuramoto model. This multidimensional description can be further extended by promoting the coupling constant between the particles to a matrix that acts on the unit vectors, representing a type of generalized frustration. In a recent paper we have analyzed in detail the role of the coupling matrix for $D=2$. Here we extend this analysis to arbitrary dimensions, presenting a study of synchronous states and their stability. We show that when the natural frequencies of the particles are set to zero, the system converges either to a stationary synchronized state with well defined phase, or to an effective two-dimensional dynamics, where the synchronized particles rotate on the sphere. The stability of these states depend on the eigenvalues and eigenvectors of the coupling matrix. When the natural frequencies are not zero, synchronization depends on whether $D$ is even or odd. In even dimensions the transition to synchronization is continuous and rotating states are replaced by active states, where the order parameter rotates while its module oscillates. If $D$ is odd the phase transition is discontinuous and active states are suppressed, occurring only for a restricted class of coupling matrices.Comment: 23 pages, 3 figure

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.Comment: Review article. v2: published version, 135 pages, 34 figure