Search

Abstract We present a novel strategy aimed at restoring correct convergence in complex Langevin simulations. The central idea is to incorporate system-specific prior knowledge into the simulations, in order to circumvent the NP-hard sign problem. In order to do so, we modify complex Langevin using kernels and propose the use of modern auto-differentiation methods to learn optimal kernel values. The optimization process is guided by functionals encoding relevant prior information, such as symmetries or Euclidean correlator data. Our approach recovers correct convergence in the non-interacting theory on the Schwinger-Keldysh contour for any real-time extent. For the strongly coupled quantum anharmonic oscillator we achieve correct convergence up to three-times the real-time extent of the previous benchmark study. An appendix sheds light on the fact that for correct convergence not only the absence of boundary terms, but in addition the correct Fokker-Plank spectrum is crucial.

Abstract This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively large Langevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time steps. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.

We present the first lattice QCD study of up to 3S and 2P bottomonia at non-zero temperatures. Correlation functions of bottomonia were computed using novel bottomonium operators and a variational technique, within the lattice non-relativistic QCD framework. We analyzed the bottomonium correlation functions based on simple physically-motivated spectral functions. We found evidence of sequential in-medium modifications, in accordance with the sizes of the bottomonium states. Keywords: Heavy-ion collision, Quark-gluon plasma, Quarkonium, Lattice QCD

Applications in biotechnology such as gene expression analysis and image processing have led to a tremendous development of statistical methods with emphasis on reliable solutions to severely underdetermined systems. Furthermore, interpretations of such solutions are of importance, meaning that the surplus of inputs has been reduced to a concise model. At the core of this development are methods which augment the standard linear models for regression, classification and decomposition such that sparse solutions are obtained. This toolbox aims at making public available carefully implemented and well-tested variants of the most popular of such methods for the MATLAB programming environment. These methods consist of easy-to-read yet efficient implementations of various coefficient-path following algorithms and implementations of sparse principal component analysis and sparse discriminant analysis which are not available in MATLAB. The toolbox builds on code made public in 2005 and which has since been used in several studies.

Multiple sclerosis (MS) damages central white matter pathways which has considerable impact on disease-related disability. To identify disease-related alterations in anatomical connectivity, 34 patients (19 with relapsing remitting MS (RR-MS), 15 with secondary progressive MS (SP-MS) and 20 healthy subjects underwent diffusion magnetic resonance imaging (dMRI) of the brain. Based on the dMRI, anatomical connectivity mapping (ACM) yielded a voxel-based metric reflecting the connectivity shared between each individual voxel and all other brain voxels. To avoid biases caused by inter-individual brain-shape differences, they were estimated in a spatially normalized space. Voxel-based statistical analyses using ACM were compared with analyses based on the localized microstructural indices of fractional anisotropy (FA). In both RR-MS and SP-MS patients, considerable portions of the motor-related white matter revealed decreases in ACM and FA when compared with healthy subjects. Patients with SP-MS exhibited reduced ACM values relative to RR-MS in the motor-related tracts, whereas there were no consistent decreases in FA between SP-MS and RR-MS patients. Regional ACM statistics exhibited moderate correlation with clinical disability as reflected by the expanded disability status scale (EDSS). The correlation between these statistics and EDSS was either similar to or stronger than the correlation between FA statistics and the EDSS. Together, the results reveal an improved relationship between ACM, the clinical phenotype, and impairment. This highlights the potential of the ACM connectivity indices to be used as a marker which can identify disease related-alterations due to MS which may not be seen using localized microstructural indices.

Aims: The aim was to demonstrate a method for automated image analysis of immunohistochemically stained tissue samples for extracting features that correlate with patient disease. We address the problem of quantifying tumor tissue and segmenting and counting cell nuclei. Materials and Methods: Our method utilizes a flexible segmentation method based on sparse coding trained from representative image samples. Nuclei counting is based on a nucleus model that takes size, shape, and nucleus probability into account. Nuclei clustering and overlays are resolved using a gray-weighted distance transform. We obtain a probability measure for pixels belonging to a nucleus from our segmentation procedure. Experiments are carried out on two sets of immunohistochemically stained images - one set based on the estrogen receptor (ER) and the other on antigen KI-67. For the nuclei separation we have selected 207 ER image samples from 58 tissue micro array-cores corresponding to 58 patients and 136 KI-67 image samples also from 58 cores. The images are hand-annotated by marking the center position of each nucleus. For the ER data we have a total of 1006 nuclei and for the KI-67 we have 796 nuclei. Segmentation performance was evaluated in terms of missing nuclei, falsely detected nuclei, and multiple detections. The proposed method is compared to state-of-the-art Bayesian classification. Statistical analysis used: The performance of the proposed method and a state-of-the-art algorithm including variations thereof is compared using the Wilcoxon rank sum test. Results: For both the ER experiment and the KI-67 experiment the proposed method exhibits lower error rates than the state-of-the-art method. Total error rates were 4.8 % and 7.7 % in the two experiments, corresponding to an average of 0.23 and 0.45 errors per image, respectively. The Wilcoxon rank sum tests show statistically significant improvements over the state-of-the-art method. Conclusions: We have demonstrated a method and obtained good performance compared to state-of-the-art nuclei separation. The segmentation procedure is simple, highly flexible, and we demonstrate how it, in addition to the nuclei separation, can perform precise segmentation of cancerous tissue. The complexity of the segmentation procedure is linear in the image size and the nuclei separation is linear in the number of nuclei. Additionally the method can be parallelized to obtain high-speed computations.