126 research outputs found
Holographic single particle imaging for weakly scattering, heterogeneous nanoscale objects
Single particle imaging (SPI) at X-ray free electron lasers (XFELs) is a technique to determine the 3D structure of nanoscale objects like biomolecules from a large number of diffraction patterns of copies of these objects in random orientations. Millions of low signal-to-noise diffraction patterns with unknown orientation are collected during an X-ray SPI experiment. The patterns are then analyzed and merged using a reconstruction algorithm to retrieve the full 3D-structure of particle. The resolution of reconstruction is limited by background noise, signal-to-noise ratio in diffraction patterns and total amount of data collected. We recently introduced a reference-enhanced holographic single particle imaging methodology [Optica 7,593-601(2020)] to collect high enough signal-to-noise and background tolerant patterns and a reconstruction algorithm to recover missing parameters beyond orientation and then directly retrieve the full Fourier model of the sample of interest. Here we describe a phase retrieval algorithm based on maximum likelihood estimation using pattern search dubbed as MaxLP, with better scalability for fine sampling of latent parameters and much better performance in the low signal limit. Furthermore, we show that structural variations within the target particle are averaged in real space, significantly improving robustness to conformational heterogeneity in comparison to conventional SPI. With these computational improvements, we believe reference-enhanced SPI is capable of reaching sub-nm resolution biomolecule imaging
Continuous Diffraction of Molecules and Disordered Molecular Crystals
The diffraction pattern of a single non-periodic compact object, such as a
molecule, is continuous and is proportional to the square modulus of the
Fourier transform of that object. When arrayed in a crystal, the coherent sum
of the continuous diffracted wave-fields from all objects gives rise to strong
Bragg peaks that modulate the single-object transform. Wilson statistics
describe the distribution of continuous diffraction intensities to the same
extent that they apply to Bragg diffraction. The continuous diffraction
obtained from translationally-disordered molecular crystals consists of the
incoherent sum of the wave-fields from the individual rigid units (such as
molecules) in the crystal, which is proportional to the incoherent sum of the
diffraction from the rigid units in each of their crystallographic
orientations. This sum over orientations modifies the statistics in a similar
way that crystal twinning modifies the distribution of Bragg intensities. These
statistics are applied to determine parameters of continuous diffraction such
as its scaling, the beam coherence, and the number of independent wave-fields
or object orientations contributing. Continuous diffraction is generally much
weaker than Bragg diffraction and may be accompanied by a background that far
exceeds the strength of the signal. Instead of just relying upon the smallest
measured intensities to guide the subtraction of the background it is shown how
all measured values can be utilised to estimate the background, noise, and
signal, by employing a modified "noisy Wilson" distribution that explicitly
includes the background. Parameters relating to the background and signal
quantities can be estimated from the moments of the measured intensities. The
analysis method is demonstrated on previously-published continuous diffraction
data measured from imperfect crystals of photosystem II.Comment: 34 pages, 11 figures, 2 appendice
Possible Detection of Causality Violation in a Non-local Scalar Model
We consider the possibility that there may be causality violation detectable
at higher energies. We take a scalar nonlocal theory containing a mass scale
as a model example and make a preliminary study of how the causality
violation can be observed. We show how to formulate an observable whose
detection would signal causality violation. We study the range of energies
(relative to ) and couplings to which the observable can be used.Comment: Latex, 30 page
Matrix product solution to an inhomogeneous multi-species TASEP
We study a multi-species exclusion process with inhomogeneous hopping rates.
This model is equivalent to a Markov chain on the symmetric group that
corresponds to a random walk in the affine braid arrangement. We find a matrix
product representation for the stationary state of this model. We also show
that it is equivalent to a graphical construction proposed by Ayyer and
Linusson, which generalizes Ferrari and Martin's construction
Remarks on the multi-species exclusion process with reflective boundaries
We investigate one of the simplest multi-species generalizations of the one
dimensional exclusion process with reflective boundaries. The Markov matrix
governing the dynamics of the system splits into blocks (sectors) specified by
the number of particles of each kind. We find matrices connecting the blocks in
a matrix product form. The procedure (generalized matrix ansatz) to verify that
a matrix intertwines blocks of the Markov matrix was introduced in the periodic
boundary condition, which starts with a local relation [Arita et al, J. Phys. A
44, 335004 (2011)]. The solution to this relation for the reflective boundary
condition is much simpler than that for the periodic boundary condition
Phase diagram of a generalized ABC model on the interval
We study the equilibrium phase diagram of a generalized ABC model on an
interval of the one-dimensional lattice: each site is occupied by a
particle of type \a=A,B,C, with the average density of each particle species
N_\a/N=r_\a fixed. These particles interact via a mean field
non-reflection-symmetric pair interaction. The interaction need not be
invariant under cyclic permutation of the particle species as in the standard
ABC model studied earlier. We prove in some cases and conjecture in others that
the scaled infinite system N\rw\infty, i/N\rw x\in[0,1] has a unique
density profile \p_\a(x) except for some special values of the r_\a for
which the system undergoes a second order phase transition from a uniform to a
nonuniform periodic profile at a critical temperature .Comment: 25 pages, 6 figure
On the dynamical behavior of the ABC model
We consider the ABC dynamics, with equal density of the three species, on the
discrete ring with sites. In this case, the process is reversible with
respect to a Gibbs measure with a mean field interaction that undergoes a
second order phase transition. We analyze the relaxation time of the dynamics
and show that at high temperature it grows at most as while it grows at
least as at low temperature
A central limit theorem for time-dependent dynamical systems
The work [8] established memory loss in the time-dependent (non-random) case
of uniformly expanding maps of the interval. Here we find conditions under
which we have convergence to the normal distribution of the appropriately
scaled Birkhoff-like partial sums of appropriate test functions. A substantial
part of the problem is to ensure that the variances of the partial sums tend to
infinity (cf. the zero-cohomology condition in the autonomous case). In fact,
the present paper is the first one where non-random, i. e. specific examples
are also found, which are not small perturbations of a given map. Our approach
uses martingale approximation technique in the form of [9]
Transfer matrices for the totally asymmetric exclusion process
We consider the totally asymmetric simple exclusion process (TASEP) on a
finite lattice with open boundaries. We show, using the recursive structure of
the Markov matrix that encodes the dynamics, that there exist two transfer
matrices and that intertwine the Markov
matrices of consecutive system sizes:
. This semi-conjugation property of
the dynamics provides an algebraic counterpart for the matrix-product
representation of the steady state of the process.Comment: 7 page
Combinatorial Markov chains on linear extensions
We consider generalizations of Schuetzenberger's promotion operator on the
set L of linear extensions of a finite poset of size n. This gives rise to a
strongly connected graph on L. By assigning weights to the edges of the graph
in two different ways, we study two Markov chains, both of which are
irreducible. The stationary state of one gives rise to the uniform
distribution, whereas the weights of the stationary state of the other has a
nice product formula. This generalizes results by Hendricks on the Tsetlin
library, which corresponds to the case when the poset is the anti-chain and
hence L=S_n is the full symmetric group. We also provide explicit eigenvalues
of the transition matrix in general when the poset is a rooted forest. This is
shown by proving that the associated monoid is R-trivial and then using
Steinberg's extension of Brown's theory for Markov chains on left regular bands
to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in
terms of discrete time Markov chain
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