Particle Creation at a Point Source by Means of Interior-Boundary Conditions

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.Comment: 41 page

Effects of acetyl-DL-leucine on cerebellar ataxia (ALCAT trial): study protocol for a multicenter, multinational, randomized, double-blind, placebo-controlled, crossover phase III trial

BACKGROUND: Cerebellar ataxia (CA) is a frequent and often disabling condition that impairs motor functioning and impacts on quality of life (QoL). No medication has yet been proven effective for the symptomatic or even causative treatment of hereditary or non-hereditary, non-acquired CA. So far, the only treatment recommendation is physiotherapy. Therefore, new therapeutic options are needed. Based on three observational studies, the primary objective of the acetyl-DL-leucine on ataxia (ALCAT) trial is to examine the efficacy and tolerability of a symptomatic therapy with acetyl-DL-leucine compared to placebo on motor function measured by the Scale for the Assessment and Rating of Ataxia (SARA) in patients with CA. METHODS/DESIGN: An investigator-initiated, multicenter, European, randomized, double-blind, placebo-controlled, 2-treatment 2-period crossover phase III trial will be carried out. In total, 108 adult patients who meet the clinical criteria of CA of different etiologies (hereditary or non-hereditary, non-acquired) presenting with a SARA total score of at least 3 points will be randomly assigned in a 1:1 ratio to one of two different treatment sequences, either acetyl-DL-leucine (up to 5 g per day) followed by placebo or vice versa. Each sequence consists of two 6-week treatment periods, separated by a 4-week wash-out period. A follow-up examination is scheduled 4 weeks after the end of treatment. The primary efficacy outcome is the absolute change in the SARA total score. Secondary objectives are to demonstrate that acetyl-DL-leucine is effective in improving (1) motor function measured by the Spinocerebellar Ataxia Functional Index (SCAFI) and SARA subscore items and (2) QoL (EuroQoL 5 dimensions and 5 level version, EQ-5D-5 L), depression (Beck Depression Inventory, BDI-II) and fatigue (Fatigue Severity Score, FSS). Furthermore, the incidence of adverse events will be investigated. DISCUSSION: The results of this trial will inform whether symptomatic treatment with the modified amino-acid acetyl-DL-leucine is a worthy candidate for a new drug therapy to relieve ataxia symptoms and to improve patient care. If superiority of the experimental drug to placebo can be established it will also be re-purposing of an agent that has been previously used for the symptomatic treatment of dizziness. TRIAL REGISTRATION: The trial was prospectively registered at www.clinicaltrialsregister.eu (EudraCT no. 2015-000460-34) and at https://www.germanctr.de (DRKS-ID: DRKS00009733 )

Interior-boundary conditions for many-body Dirac operators and codimension-1 boundaries

We are dealing with boundary conditions for Dirac-type operators, i.e., first order differential operators with matrix-valued coefficients, including in particular physical many-body Dirac operators. We characterize (what we conjecture is) the general form of reflecting boundary conditions (which includes known boundary conditions such as the one of the MIT bag model) and, as our main goal, of interior-boundary conditions (IBCs). IBCs are a new approach to defining UV-regular Hamiltonians for quantum field theories without smearing particles out or discretizing space. For obtaining such Hamiltonians, the method of IBCs provides an alternative to renormalization and has been successfully used so far in non-relativistic models, where it could be applied also in cases in which no renormalization method was known. A natural next question about IBCs is how to set them up for the Dirac equation, and here we take first steps towards the answer. For quantum field theories, the relevant boundary consists of the surfaces in $n$-particle configuration space $\mathbb{R}^{3n}$ on which two particles have the same location in $\mathbb{R}^3$. While this boundary has codimension 3, we focus here on the more basic situation in which the boundary has codimension 1 in configuration space. We describe specific examples of IBCs for the Dirac equation, we prove for some of these examples that they rigorously define self-adjoint Hamiltonians, and we develop the general form of IBCs for Dirac-type operators.Comment: 33 pages LaTeX, no figures; v2: Section 2.4 and Appendix A adde

Update on the pharmacotherapy of cerebellar and central vestibular disorders.

An overview of the current pharmacotherapy of central vestibular syndromes and the most common forms of central nystagmus as well as cerebellar disorders is given. 4-aminopyridine (4-AP) is recommended for the treatment of downbeat nystagmus, a frequent form of acquired persisting fixation nystagmus, and upbeat nystagmus. Animal studies showed that this non-selective blocker of voltage-gated potassium channels increases Purkinje cell excitability and normalizes the irregular firing rate, so that the inhibitory influence of the cerebellar cortex on vestibular and deep cerebellar nuclei is restored. The efficacy of 4-AP in episodic ataxia type 2, which is most often caused by mutations of the PQ-calcium channel, was demonstrated in a randomized controlled trial. It was also shown in an animal model (the tottering mouse) of episodic ataxia type 2. In a case series, chlorzoxazone, a non-selective activator of small-conductance calcium-activated potassium channels, was shown to reduce the DBN. The efficacy of acetyl-DL-leucine as a potential new symptomatic treatment for cerebellar diseases has been demonstrated in three case series. The ongoing randomized controlled trials on episodic ataxia type 2 (sustained-release form of 4-aminopyridine vs. acetazolamide vs. placebo; EAT2TREAT), vestibular migraine with metoprolol (PROVEMIG-trial), cerebellar gait disorders (sustained-release form of 4-aminopyridine vs. placebo; FACEG) and cerebellar ataxia (acetyl-DL-leucine vs. placebo; ALCAT) will provide new insights into the pharmacotherapy of cerebellar and central vestibular disorders

Conjugate Eye Deviation in Unilateral Lateral Medullary Infarction.

BACKGROUND AND PURPOSE The initial diagnosis of medullary infarction can be challenging since CT and even MRI results in the very acute phase are often negative. METHODS A retrospective, observer-blinded study of horizontal conjugate eye deviation was performed in 1) 50 consecutive patients [age 58±15 years (mean±SD), 74% male, National Institutes of Health Stroke Scale 2±1] with acute unilateral lateral medullary infarction as seen in MRI (infarction group), 2) 54 patients with transient brainstem symptoms [transient ischemic attack of brainstem (TIA) group; age 69±16 years, 59% male], and 3) 53 patients (age 59±20 years, 49% male) with diagnoses other than stroke (control group). RESULTS Conjugate eye deviation was found in all patients in the infarction group [n=47 (94%) with ipsilesional deviation and n=3 (6%) with contralesional deviation] compared to 41% (n=22) in the brainstem TIA group and 15% (n=8) in the control group (p<0.0001). Within all groups mean deviation and range were similar for both sides (to the right vs. to the left side 26.6°±12.3 vs. 26.1°±12.3 in the infarction group, 10.5°±5.8 vs. 8.4°±6.3 in the brainstem TIA group and 4.5°±3.2 vs. 7.5°±3.2 in the control group). The extent of eye deviation was significantly greater in the infarction group (p<0.05). CONCLUSIONS All patients with MRI-demonstrated unilateral medullary infarction showed conjugate eye deviation. Therefore, conjugate eye deviation in patients with suspected acute lateral medullary infarction is a helpful sensitive sign for supporting the diagnosis, particularly if the deviation is >20°

Real-time computer-based visual feedback improves visual acuity in downbeat nystagmus - a pilot study.

BACKGROUND Patients with downbeat nystagmus syndrome suffer from oscillopsia, which leads to an unstable visual perception and therefore impaired visual acuity. The aim of this study was to use real-time computer-based visual feedback to compensate for the destabilizing slow phase eye movements. METHODS The patients were sitting in front of a computer screen with the head fixed on a chin rest. The eye movements were recorded by an eye tracking system (EyeSeeCam®). We tested the visual acuity with a fixed Landolt C (static) and during real-time feedback driven condition (dynamic) in gaze straight ahead and (20°) sideward gaze. In the dynamic condition, the Landolt C moved according to the slow phase eye velocity of the downbeat nystagmus. The Shapiro-Wilk test was used to test for normal distribution and one-way ANOVA for comparison. RESULTS Ten patients with downbeat nystagmus were included in the study. Median age was 76 years and the median duration of symptoms was 6.3 years (SD +/- 3.1y). The mean slow phase velocity was moderate during gaze straight ahead (1.44°/s, SD +/- 1.18°/s) and increased significantly in sideward gaze (mean left 3.36°/s; right 3.58°/s). In gaze straight ahead, we found no difference between the static and feedback driven condition. In sideward gaze, visual acuity improved in five out of ten subjects during the feedback-driven condition (p = 0.043). CONCLUSIONS This study provides proof of concept that non-invasive real-time computer-based visual feedback compensates for the SPV in DBN. Therefore, real-time visual feedback may be a promising aid for patients suffering from oscillopsia and impaired text reading on screen. Recent technological advances in the area of virtual reality displays might soon render this approach feasible in fully mobile settings

Dalfampridine in patients with downbeat nystagmus—an observational study

We investigated the effects of dalfampridine, the sustained-release form of 4-aminopyridine, on slow phase velocity (SPV) and visual acuity (VA) in patients with downbeat nystagmus (DBN) and the side effects of the drug. In this proof-of-principle observational study, ten patients received dalfampridine 10 mg bid for 2 weeks. Recordings were conducted at baseline, 180 min after first administration, after 2 weeks of treatment and after 4 weeks of wash-out. Mean SPV decreased from a baseline of 2.12 deg/s ± 1.72 (mean ± SD) to 0.51 deg/s ± 1.00 180 min after first administration of dalfampridine 10 mg and to 0.89 deg/s ± 0.75 after 2 weeks of treatment with dalfampridine (p < 0.05; post hoc both: p < 0.05). After a wash-out period of 1 week, mean SPV increased to 2.30 deg/s ± 1.6 (p < 0.05; post hoc both: p < 0.05). The VA significantly improved during treatment with dalfampridine. Also, 50 % of patients did not report any side effects. The most common reported side effects were abdominal discomfort and dizziness. Dalfampridine is an effective treatment for DBN in terms of SPV. It was well-tolerated in all patients