Interaction effects in a microscopic quantum wire model with strong spin-orbit interaction

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with spin-orbit interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at $k = 0$ and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger Liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton-antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments

Minimal error momentum Bregman-Kaczmarz

The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for large-scale systems. To speed up convergence, we investigate acceleration by heavy ball momentum in the so-called dual update. Heavy ball acceleration of the Kaczmarz method with constant parameters has turned out to be difficult to analyze, in particular no accelerated convergence for the L2-error of the iterates has been proven to the best of our knowledge. Here we propose a way to adaptively choose the momentum parameter by a minimal-error principle similar to a recently proposed method for the standard randomized Kaczmarz method. The momentum parameter can be chosen to exactly minimize the error in the next iterate or to minimize a relaxed version of the minimal error principle. The former choice leads to a theoretically optimal step while the latter is cheaper to compute. We prove improved convergence results compared to the non-accelerated method. Numerical experiments show that the proposed methods can accelerate convergence in practice, also for matrices which arise from applications such as computational tomography

A Bregman-Kaczmarz method for nonlinear systems of equations

We propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes gradients of component functions and uses Bregman projections onto the solution space of a Newton equation. In the special case of euclidean projections, the method is known as nonlinear Kaczmarz method. Furthermore, if the component functions are nonnegative, we are in the setting of optimization under the interpolation assumption and the method reduces to SGD with the recently proposed stochastic Polyak step size. For general Bregman projections, our method is a stochastic mirror descent with a novel adaptive step size. We prove that in the convex setting each iteration of our method results in a smaller Bregman distance to exact solutions as compared to the standard Polyak step. Our generalization to Bregman projections comes with the price that a convex one-dimensional optimization problem needs to be solved in each iteration. This can typically be done with globalized Newton iterations. Convergence is proved in two classical settings of nonlinearity: for convex nonnegative functions and locally for functions which fulfill the tangential cone condition. Finally, we show examples in which the proposed method outperforms similar methods with the same memory requirements

Aharonov-Bohm oscillations in the presence of strong spin-orbit interactions

We have measured highly visible Aharonov-Bohm (AB) oscillations in a ring structure defined by local anodic oxidation on a p-type GaAs heterostructure with strong spin-orbit interactions. Clear beating patterns observed in the raw data can be interpreted in terms of a spin geometric phase. Besides h/e oscillations, we resolve the contributions from the second harmonic of AB oscillations and also find a beating in these h/2e oscillations. A resistance minimum at B=0T, present in all gate configurations, is the signature of destructive interference of the spins propagating along time-reversed paths.Comment: 4 pages, 3 figures, published versio

Accuracy of a magnetic resonance imaging‐based 3D printed stereotactic brain biopsy device in dogs

Background: Brain biopsy of intracranial lesions is often necessary to determine specific therapy. The cost of the currently used stereotactic rigid frame and optical tracking systems for brain biopsy in dogs is often prohibitive or accuracy is not sufficient for all types of lesion. Objectives: To evaluate the application accuracy of an inexpensive magnetic resonance imaging‐based personalized, 3D printed brain biopsy device. Animals: Twenty‐two dog heads from cadavers were separated into 2 groups according to body weight (20 kg). Methods: Experimental study. Two target points in each cadaver head were used (target point 1: caudate nucleus, target point 2: piriform lobe). Comparison between groups was performed using the independent Student's t test or the nonparametric Mann‐Whitney U Test. Results: The total median target point deviation was 0.83 mm (range 0.09‐2.76 mm). The separate median target point deviations for target points 1 and 2 in all dogs were 0.57 mm (range: 0.09‐1.25 mm) and 0.85 mm (range: 0.14‐2.76 mm), respectively. Conclusion and Clinical Importance: This magnetic resonance imaging‐based 3D printed stereotactic brain biopsy device achieved an application accuracy that was better than the accuracy of most brain biopsy systems that are currently used in veterinary medicine. The device can be applied to every size and shape of skull and allows precise positioning of brain biopsy needles in dogs

Takotsubo cardiomyopathy – an unexpected complication in spine surgery

Introduction: Takotsubo cardiomyopathy is an apical ballooning syndrome, which can be triggeredby stress. Only few case reports describe the onset of Takotsubo as a complication of neurosurgery procedures. Clinical presentation: A case of a 53 year-old female with a spinal neurinoma and surgery-associated Takotsubo cardiomyopathy is demonstrated. The patient developed typical signs of a myocardial infarction with circulation depression and ST elevation, but normal cardiac enzymes at the end of surgery. Cardiac catheterization and levocardiography confirmed the absence of any critical coronary disease but the presence of a typical apical ballooning and midventricular hypokinesis. The patient recovered completely under supportive conservative and cardiological therapy, showing regular left ventricular pumpfunction. Conclusion: Interventions in neurosurgery and perioperative care should be kept as stress free as possible. Due to the possibility of neurogenic mechanisms related to cardiomyopathy, Takotsubo cardiomyopathy as an entity of stress-induced complications should be taken into consideration

A Comparative Study of Automatic Localization Algorithms for Spherical Markers within 3D MRI Data

Localization of features and structures in images is an important task in medical image-processing. Characteristic structures and features are used in diagnostics and surgery planning for spatial adjustments of the volumetric data, including image registration or localization of bone-anchors and fiducials. Since this task is highly recurrent, a fast, reliable and automated approach without human interaction and parameter adjustment is of high interest. In this paper we propose and compare four image processing pipelines, including algorithms for automatic detection and localization of spherical features within 3D MRI data. We developed a convolution based method as well as algorithms based on connected-components labeling and analysis and the circular Hough-transform. A blob detection related approach, analyzing the Hessian determinant, was examined. Furthermore, we introduce a novel spherical MRI-marker design. In combination with the proposed algorithms and pipelines, this allows the detection and spatial localization, including the direction, of fiducials and bone-anchors

Case Report: Clinical Use of a Patient-Individual Magnetic Resonance Imaging-Based Stereotactic Navigation Device for Brain Biopsies in Three Dogs

Three-dimensional (3D) printing techniques for patient-individual medicine has found its way into veterinary neurosurgery. Because of the high accuracy of 3D printed specific neurosurgical navigation devices, it seems to be a safe and reliable option to use patient- individual constructions for sampling brain tissue. Due to the complexity and vulnerability of the brain a particularly precise and safe procedure is required. In a recent cadaver study a better accuracy for the 3D printed MRI-based patient individual stereotactic brain biopsy device for dogs is determined compared to the accuracies of other biopsy systems which are currently used in veterinary medicine. This case report describes the clinical use of this 3D printed MRI-based patient individual brain biopsy device for brain sampling in three dogs. The system was characterized by a simple handling. Furthermore, it was an effective and reliable tool to gain diagnostic brain biopsy samples in dogs with no significant side effects