13,329 research outputs found
Linear convergence of accelerated conditional gradient algorithms in spaces of measures
A class of generalized conditional gradient algorithms for the solution of
optimization problem in spaces of Radon measures is presented. The method
iteratively inserts additional Dirac-delta functions and optimizes the
corresponding coefficients. Under general assumptions, a sub-linear
rate in the objective functional is obtained, which is sharp
in most cases. To improve efficiency, one can fully resolve the
finite-dimensional subproblems occurring in each iteration of the method. We
provide an analysis for the resulting procedure: under a structural assumption
on the optimal solution, a linear convergence rate is
obtained locally.Comment: 30 pages, 7 figure
Biogenesis of mitochondrial c-type cytochromes
Cytochromesc andc 1 are essential components of the mitochondrial respiratory chain. In both cytochromes the heme group is covalently linked to the polypeptide chain via thioether bridges. The location of the two cytochromes is in the intermembrane space; cytochromec is loosely attached to the surface of the inner mitochondrial membrane, whereas cytochromec 1 is firmly anchored to the inner membrane. Both cytochromec andc 1 are encoded by nuclear genes, translated on cytoplasmic ribosomes, and are transported into the mitochondria where they become covalently modified and assembled. Despite the many similarities, the import pathways of cytochromec andc 1 are drastically different. Cytochromec 1 is made as a precursor with a complex bipartite presequence. In a first step the precursor is directed across outer and inner membranes to the matrix compartment of the mitochondria where cleavage of the first part of the presequence takes place. In a following step the intermediate-size form is redirected across the inner membrane; heme addition then occurs on the surface of the inner membrane followed by the second processing reaction. The import pathway of cytochromec is exceptional in practically all aspects, in comparison with the general import pathway into mitochondria. Cytochromec is synthesized as apocytochromec without any additional sequence. It is translocated selectively across the outer membrane. Addition of the heme group, catalyzed by cytochromec heme lyase, is a requirement for transport. In summary, cytochromec 1 import appears to follow a conservative pathway reflecting features of cytochromec 1 sorting in prokaryotic cells. In contrast, cytochromec has invented a rather unique pathway which is essentially non-conservative
Foundations for an iteration theory of entire quasiregular maps
The Fatou-Julia iteration theory of rational functions has been extended to
quasiregular mappings in higher dimension by various authors. The purpose of
this paper is an analogous extension of the iteration theory of transcendental
entire functions. Here the Julia set is defined as the set of all points such
that complement of the forward orbit of any neighbourhood has capacity zero. It
is shown that for maps which are not of polynomial type the Julia set is
non-empty and has many properties of the classical Julia set of transcendental
entire functions.Comment: 31 page
Maximal uniform convergence rates in parametric estimation problems
This paper considers parametric estimation problems with i.i.d. data. It focusses on rate-effciency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates.parametric estimators, uniform convergence, Hellinger distance, Locally Asymptotically Quadratic (LAQ) Families
Maximal uniform convergence rates in parametric estimation problems
This paper considers parametric estimation problems with independent, identically,non-regularly distributed data. It focuses on rate-effciency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion,largely unexplored in parametric estimation.Under mild conditions, the Hellinger metric,defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates. These rates are shown to be attainable in general classes of parametric estimation problems.
Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems
In this paper we consider a problem of initial data identification from the
final time observation for homogeneous parabolic problems. It is well-known
that such problems are exponentially ill-posed due to the strong smoothing
property of parabolic equations. We are interested in a situation when the
initial data we intend to recover is known to be sparse, i.e. its support has
Lebesgue measure zero. We formulate the problem as an optimal control problem
and incorporate the information on the sparsity of the unknown initial data
into the structure of the objective functional. In particular, we are looking
for the control variable in the space of regular Borel measures and use the
corresponding norm as a regularization term in the objective functional. This
leads to a convex but non-smooth optimization problem. For the discretization
we use continuous piecewise linear finite elements in space and discontinuous
Galerkin finite elements of arbitrary degree in time. For the general case we
establish error estimates for the state variable. Under a certain structural
assumption, we show that the control variable consists of a finite linear
combination of Dirac measures. For this case we obtain error estimates for the
locations of Dirac measures as well as for the corresponding coefficients. The
key to the numerical analysis are the sharp smoothing type pointwise finite
element error estimates for homogeneous parabolic problems, which are of
independent interest. Moreover, we discuss an efficient algorithmic approach to
the problem and show several numerical experiments illustrating our theoretical
results.Comment: 43 pages, 10 figure
Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices
Since the experimental realization of synthetic gauge fields for neutral
atoms, the simulation of topologically non-trivial phases of matter with
ultracold atoms has become a major focus of cold atom experiments. However,
several obvious differences exist between cold atom and solid state systems,
for instance the finite size of the atomic cloud and the smooth confining
potential. In this article we show that sharp boundaries are not required to
realize quantum Hall or quantum spin Hall physics in optical lattices and, on
the contrary, that edge states which belong to a smooth confinement exhibit
additional interesting properties, such as spatially resolved splitting and
merging of bulk bands and the emergence of robust auxiliary states in bulk gaps
to preserve the topological quantum numbers. In addition, we numerically
validate that these states are robust against disorder. Finally, we analyze
possible detection methods, with a focus on Bragg spectroscopy, to demonstrate
that the edge states can be detected and that Bragg spectroscopy can reveal how
topological edge states are connected to the different bulk bands.Comment: 12 pages, 10 figures, updated figures and minor text correction
Expected neutrino fluence from short Gamma-Ray Burst 170817A and off-axis angle constraints
We compute the expected neutrino fluence from SGRB 170817A, associated with
the gravitational wave event GW 170817, directly based on Fermi observations in
two scenarios: structured jet and off-axis (observed) top-hat jet. While the
expected neutrino fluence for the structured jet case is very small, large
off-axis angles imply high radiation densities in the jet, which can enhance
the neutrino production efficiency. In the most optimistic allowed scenario,
the neutrino fluence can reach only of the sensitivity of the
neutrino telescopes. We furthermore demonstrate that the fact that gamma-rays
can escape limits the baryonic loading (energy in protons versus photons) and
the off-axis angle for the internal shock scenario. In particular, for a
baryonic loading of ten, the off-axis angle is more strongly constrained by the
baryonic loading than by the time delay between the gravitational wave event
and the onset of the gamma-ray emission.Comment: 9 pages, 6 figure
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