arXiv subjects

Veit Elser

Publications and source records attributed to Veit Elser.

At least 37 records · Page 2Linked to original sources

arXiv2018

Deep sub-Ångstrom imaging of 2D materials with a high dynamic range detector

Aberration-corrected optics have made electron microscopy at atomic-resolution a widespread and often essential tool for nanocharacterization. Image resolution is dominated by beam energy and the numerical aperture of the lens (α), with state-of-the-art reaching ~0.47 Å at 300 keV. Two-dimensional materials are imaged at lower beam energies to avoid knock-on damage, limiting spatial resolution to ~1 Å. Here, by combining a new electron microscope pixel array detector with the dynamic range to record the complete distribution of transmitted electrons and full-field ptychography to recover phase information from the full phase space, we increased the spatial resolution well beyond the traditional lens limitations. At 80 keV beam energy, our ptychographic reconstructions significantly improved image contrast of single-atom defects in MoS2, reaching an information limit close to 5α, corresponding to a 0.39 Å Abbe resolution, at the same dose and imaging conditions where conventional imaging modes reach only 0.98 Å.

cond-mat.mtrl-sci↗

arXiv2016

Three lectures on statistical mechanics

These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere packings and tilings.

cond-mat.stat-mech↗

arXiv2016

A network that learns Strassen multiplication

We study neural networks whose only non-linear components are multipliers, to test a new training rule in a context where the precise representation of data is paramount. These networks are challenged to discover the rules of matrix multiplication, given many examples. By limiting the number of multipliers, the network is forced to discover the Strassen multiplication rules. This is the mathematical equivalent of finding low rank decompositions of the $n\times n$ matrix multiplication tensor, $M_n$. We train these networks with the conservative learning rule, which makes minimal changes to the weights so as to give the correct output for each input at the time the input-output pair is received. Conservative learning needs a few thousand examples to find the rank 7 decomposition of $M_2$, and $10^5$ for the rank 23 decomposition of $M_3$ (the lowest known). High precision is critical, especially for $M_3$, to discriminate between true decompositions and "border approximations".

math.NA↗

arXiv2016

The complexity of bit retrieval

Bit retrieval is the problem of reconstructing a binary sequence from its periodic autocorrelation, with applications in cryptography and x-ray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxed-reflect-reflect, is currently the best algorithm for noisy bit retrieval.

cs.DS↗

arXiv2016

Matrix product constraints by projection methods

The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are required to minimize their distance from an arbitrary pair $X_0$ and $Y_0$. This type of decomposition, a projection to a matrix product constraint, in combination with projections that impose structural properties on $X$ and $Y$, forms the basis of a general method of decomposing a matrix into factors with specified properties. Results are presented for the application of these methods to a number of hard problems in exact factorization.

math.OC↗

arXiv2015

Exotic self-trapped states of an electron in superfluid helium

We explore the possibility that the fast and exotic negative ions in superfluid helium are electrons bound to quantized vortex structures, the simplest being a ring. In the states we consider, the electron energy is only slightly below the conduction band minimum of bulk helium. To support our proposal we present two calculations. In the first, we show that the electron pressure on the vortex core is insufficient to cavitate the helium and form an electron bubble. In the second, we estimate the equilibrium radius of the vortex ring that would bind an electron and find it is much smaller than the electron bubble, about 0.7 nm. The many exotic ions reported in experiments might be bound states of an electron with more complex vortex structures.

cond-mat.other↗

arXiv2014

Phonon contribution to the entropy of hard sphere crystals

Comparing the entropies of hard spheres in the limit of close packing, for different stacking sequences of the hexagonal layers, has been a challenge because the differences are so small. Here we present a new method based on a "sticky-sphere" model by which the system interpolates between hard spheres in one limit and a harmonic crystal in the other. For the fcc and hcp stackings we have calculated the entropy difference in the harmonic (sticky) limit, as well as the differences in the free energy change upon removing the stickiness in the model. The former, or phonon entropy, accounts for most of the entropy difference. Our value for the net entropy difference, 0.001164(8) k_B per sphere, is in excellent agreement with the best previous estimate by Mau and Huse [Phys. Rev. E 59, 4396 (1999)].

cond-mat.stat-mech↗

arXiv2014

Breaking the Crowther Limit: Combining Depth-Sectioning and Tilt Tomography for High-Resolution, Wide-Field 3D Reconstructions

To date, high-resolution (< 1 nm) imaging of extended objects in three-dimensions (3D) has not been possible. A restriction known as the Crowther criterion forces a tradeoff between object size and resolution for 3D reconstructions by tomography. Further, the sub-Angstrom resolution of aberration-corrected electron microscopes is accompanied by a greatly diminished depth of field, causing regions of larger specimens (> 6 nm) to appear blurred or missing. Here we demonstrate a three-dimensional imaging method that overcomes both these limits by combining through-focal depth sectioning and traditional tilt-series tomography to reconstruct extended objects, with high-resolution, in all three dimensions. The large convergence angle in aberration corrected instruments now becomes a benefit and not a hindrance to higher quality reconstructions. A through-focal reconstruction over a 390 nm 3D carbon support containing over one hundred dealloyed and nanoporous PtCu catalyst particles revealed with sub-nanometer detail the extensive and connected interior pore structure that is created by the dealloying instability.

cond-mat.mtrl-sci↗

arXiv2013

Real-Space x-ray tomographic reconstruction of randomly oriented objects with sparse data frames

Schemes for X-ray imaging single protein molecules using new x-ray sources, like x-ray free electron lasers (XFELs), require processing many frames of data that are obtained by taking temporally short snapshots of identical molecules, each with a random and unknown orientation. Due to the small size of the molecules and short exposure times, average signal levels of much less than 1 photon/pixel/frame are expected, much too low to be processed using standard methods. One approach to process the data is to use statistical methods developed in the EMC algorithm (Loh & Elser, Phys. Rev. E, 2009) which processes the data set as a whole. In this paper we apply this method to a real-space tomographic reconstruction using sparse frames of data (below $10^{-2}$ photons/pixel/frame) obtained by performing x-ray transmission measurements of a low-contrast, randomly-oriented object. This extends the work by Philipp et al. (Optics Express, 2012) to three dimensions and is one step closer to the single molecule reconstruction problem.

physics.data-an↗

arXiv2013

Direct Phasing of Nanocrystal Diffraction

Recent experiments at free-electron laser x-ray sources have been able to resolve the intensity distributions about Bragg peaks in nanocrystals of large biomolecules. Information derived from small shifts in the peak positions augment the Bragg samples of the particle intensity with samples of its gradients. Working on the assumption that the nanocrystal is entirely generated by lattice translations of a particle, we develop an algorithm that reconstructs the particle from intensities and intensity gradients. Unlike traditional direct phasing methods that require very high resolution data in order to exploit sparsity of the electron density, our method imposes no constraints on the contrast other than positivity and works well at low resolution. We demonstrate successful reconstructions with simulated P1 lysozyme nanocrystal data down to a signal-to-noise ratio of 2 in the intensity gradients.

physics.data-an↗

arXiv2013

An Improved Three-Weight Message-Passing Algorithm

We describe how the powerful "Divide and Concur" algorithm for constraint satisfaction can be derived as a special case of a message-passing version of the Alternating Direction Method of Multipliers (ADMM) algorithm for convex optimization, and introduce an improved message-passing algorithm based on ADMM/DC by introducing three distinct weights for messages, with "certain" and "no opinion" weights, as well as the standard weight used in ADMM/DC. The "certain" messages allow our improved algorithm to implement constraint propagation as a special case, while the "no opinion" messages speed convergence for some problems by making the algorithm focus only on active constraints. We describe how our three-weight version of ADMM/DC can give greatly improved performance for non-convex problems such as circle packing and solving large Sudoku puzzles, while retaining the exact performance of ADMM for convex problems. We also describe the advantages of our algorithm compared to other message-passing algorithms based upon belief propagation.

cs.AI↗

arXiv2013

Magnetic polarons in two-component hard core bosons

We use a high-temperature expansion to explore spin correlations around a single hole in a two- dimensional lattice filled with a hard-core two component bose gas. We find that the spins around the hole develop ferromagnetic order and quantify the degree of polarization at temperatures of order the hopping energy, finding a measurably nonzero polarization. We also discuss the effect of fixing the overall magnetization of the system for finite-sized systems.

cond-mat.quant-gas↗

arXiv2012

Solving Structure with Sparse, Randomly-Oriented X-ray Data

Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing of hundreds of thousands (or more) of images that contain very few x-rays. Each low-flux image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of collecting data at these extremes, averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-flux data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal in the high-noise regime.

physics.ins-det↗

arXiv2011

Three dimensional structure from intensity correlations

We develop the analysis of x-ray intensity correlations from dilute ensembles of identical particles in a number of ways. First, we show that the 3D particle structure can be determined if the particles can be aligned with respect to a single axis having a known angle with respect to the incident beam. Second, we clarify the phase problem in this setting and introduce a data reduction scheme that assesses the integrity of the data even before the particle reconstruction is attempted. Finally, we describe an algorithm that reconstructs intensity and particle density simultaneously, thereby making maximal use of the available constraints.

physics.data-an↗

arXiv2011

Packing-constrained point coverings

In the packing-constrained point covering problem, PC^2, one seeks configurations of points in the plane that cannot all be covered by a packing arrangement of unit disks. We consider in particular the problem of finding the minimum number of points N for which such a configuration exists and obtain the bounds 11 <= N <= 55. The disparity of these bounds is symptomatic, we believe, of the fact that PC^2 belongs in a higher complexity class than the standard packing and covering problems.

math.MG↗

arXiv2010

Dense packing crystal structures of physical tetrahedra

We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all the way to the sphere. Thus, we also connect the two well studied problems of sphere packing and tetrahedron packing on a single axis. Our numerical results uncover a rich optimal-packing behavior, compared to that of other continuous families of particles previously studied. We present four structures as candidates for the optimal packing at different values of the parameter, providing an atlas of crystal structures which might be observed in systems of nano-particles with tetrahedral symmetry.

cond-mat.soft↗

arXiv2010

Uniqueness transition in noisy phase retrieval

Previous criteria for the feasibility of reconstructing phase information from intensity measurements, both in x-ray crystallography and more recently in coherent x-ray imaging, have been based on the Maxwell constraint counting principle. We propose a new criterion, based on Shannon's mutual information, that is better suited for noisy data or contrast that has strong priors not well modeled by continuous variables. A natural application is magnetic domain imaging, where the criterion for uniqueness in the reconstruction takes the form that the number of photons, per pixel of contrast in the image, exceeds a certain minimum. Detailed studies of a simple model show that the uniqueness transition is of the type exhibited by spin glasses.

physics.data-an↗

arXiv2010

Upper bound on the packing density of regular tetrahedra and octahedra

We obtain an upper bound to the packing density of regular tetrahedra. The bound is obtained by showing the existence, in any packing of regular tetrahedra, of a set of disjoint spheres centered on tetrahedron edges, so that each sphere is not fully covered by the packing. The bound on the amount of space that is not covered in each sphere is obtained in a recursive way by building on the observation that non-overlapping regular tetrahedra cannot subtend a solid angle of $4π$ around a point if this point lies on a tetrahedron edge. The proof can be readily modified to apply to other polyhedra with the same property. The resulting lower bound on the fraction of empty space in a packing of regular tetrahedra is $2.6\ldots\times 10^{-25}$ and reaches $1.4\ldots\times 10^{-12}$ for regular octahedra.

math.MG↗