A penalized Fischer-Burmeister NCP-function

We introduce a new NCP-function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. This new NCP-function turns out to have stronger theoretical properties than the widely used Fischer-Burmeister function and other NCP-functions suggested previously. Moreover, numerical experience indicates that a semismooth Newton method based on this new NCP-function performs considerably better than the corresponding method based on the Fischer-Burmeister function. Received: March 10, 1997 / Accepted: February 15, 2000?Published online May 12, 2000     

Convergent sequences of sparse graphs: A large deviations approach

Models based on sparse graphs are of interest to many communities: they appear as basic models in combinatorics, probability theory, optimization, statistical physics, information theory, and more applied fields of social sciences and economics. Different notions of similarity (and hence convergence) of sparse graphs are of interest in different communities. In probability theory and combinatorics, the notion of Benjamini‐Schramm convergence, also known as left‐convergence, is used quite frequently. Statistical physicists are interested in the the existence of the thermodynamic limit of free energies, which leads naturally to the notion of right‐convergence. Combinatorial optimization problems naturally lead to so‐called partition convergence, which relates to the convergence of optimal values of a variety of constraint satisfaction problems. The relationship between these different notions of similarity and convergence is, however, poorly understood. In this paper we introduce a new notion of convergence of sparse graphs, which we call Large Deviations or LD‐convergence, and which is based on the theory of large deviations. The notion is introduced by “decorating” the nodes of the graph with random uniform i.i.d. weights and constructing corresponding random measures on and . A graph sequence is defined to be converging if the corresponding sequence of random measures satisfies the Large Deviations Principle with respect to the topology of weak convergence on bounded measures on . The corresponding large deviations rate function can be interpreted as the limit object of the sparse graph sequence. In particular, we can express the limiting free energies in terms of this limit object. We then establish that LD‐convergence implies the other three notions of convergence discussed above, and at the same time establish several previously unknown relationships between the other notions of convergence. In particular, we show that partition‐convergence does not imply left‐ or right‐convergence, and that right‐convergence does not imply partition‐convergence. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 52–89, 2017     

Progress and challenge in polymer crazing and fatigue

In this review on polymer crazing and fatigue three aspects have been treated more explicitely: the molecular rearrangements preceding and provoking craze initiation, the competition between disentanglement and chain scission during lateral craze growth, and the distinct fatigue failure mechanism occurring in cyclically loaded PET and PA fibers. An overview on other aspects is given including references to work in progress.     

Reduced field-of-view DTI segmentation of cervical spine tissue

The number of diffusion tensor imaging (DTI) studies regarding the human spine has considerably increased and it is challenging because of the spine’s small size and artifacts associated with the most commonly used clinical imaging method. A novel segmentation method based on the reduced field-of-view (rFOV) DTI dataset is presented in cervical spinal canal cerebrospinal fluid, spinal cord grey matter and white matter classification in both healthy volunteers and patients with neuromyelitis optica (NMO) and multiple sclerosis (MS). Due to each channel based on high resolution rFOV DTI images providing complementary information on spinal tissue segmentation, we want to choose a different contribution map from multiple channel images. Via principal component analysis (PCA) and a hybrid diffusion filter with a continuous switch applied on fourteen channel features, eigen maps can be obtained and used for tissue segmentation based on the Bayesian discrimination method. Relative to segmentation by a pair of expert readers, all of the automated segmentation results in the experiment fall in the good segmentation area and performed well, giving an average segmentation accuracy of about 0.852 for cervical spinal cord grey matter in terms of volume overlap. Furthermore, this has important applications in defining more accurate human spinal cord tissue maps when fusing structural data with diffusion data. rFOV DTI and the proposed automatic segmentation outperform traditional manual segmentation methods in classifying MR cervical spinal images and might be potentially helpful for detecting cervical spine diseases in NMO and MS.     

FOURIER ANALYSIS OF TEMPORAL AND SPATIAL OSCILLATIONS OF TUNNELING CURRENT IN SCANNING TUNNELING MICROSCOPY

Partially oxidized Si(111) surfaces and surfaces of highly oriented pyrolytic graphite (HOPG) were studied by two different ultrahigh vacuum scanning tunneling microscope (UHV-STM) systems and by an STM system working under ambient conditions, respectively. The STM current images of partially oxidized Si(111) surfaces and HOPG surfaces were analyzed by one/two-dimensional fast Fourier transformation (1D-FFT/2D-FFT). The phenomenon of temporal oscillations of tunneling current on the partially oxidized Si(111) surfaces was detected with both UHV-STM systems. Temporal as well as spatial oscillations of tunneling current appeared in highly resolved STM current images of the Si(111) surfaces simultaneously, but both kinds of oscillations could be discriminated according to their different influence on the 2D-FFT spectra of the current images, while varying the scanning range and rate. On clean HOPG surfaces only spatial oscillations of tunneling current induced by the surface structure were observed.     

Ant colony optimization: Introduction and recent trends

Ant colony optimization is a technique for optimization that was introduced in the early 1990's. The inspiring source of ant colony optimization is the foraging behavior of real ant colonies. This behavior is exploited in artificial ant colonies for the search of approximate solutions to discrete optimization problems, to continuous optimization problems, and to important problems in telecommunications, such as routing and load balancing. First, we deal with the biological inspiration of ant colony optimization algorithms. We show how this biological inspiration can be transfered into an algorithm for discrete optimization. Then, we outline ant colony optimization in more general terms in the context of discrete optimization, and present some of the nowadays best-performing ant colony optimization variants. After summarizing some important theoretical results, we demonstrate how ant colony optimization can be applied to continuous optimization problems. Finally, we provide examples of an interesting recent research direction: The hybridization with more classical techniques from artificial intelligence and operations research.     

High order harmonic generation from solid targets: Towards intense attosecond pulses

Experiments and computer simulations on high order harmonic generation (HOHG) from steep plasma gradients using intense femtosecond laser pulses are presented. The importance of the plasma scale length for the efficiency of HOHG is demonstrated. By changing the pump intensity and the target parameters the regime of HOHG can be switched from non-relativistic to relativistic. Simulations show that attosecond pulses should already be present in our experiments in both interaction regimes. Two-color driven harmonic generation is shown to provide a highly efficient way of attosecond pulse production.