Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Development of a balanced experimental–computational approach to understanding the mechanics of proximal femur fractures

The majority of people who sustain hip fractures after a fall to the side would not have been identified using current screening techniques such as areal bone mineral density. Identifying them, however, is essential so that appropriate pharmacological or lifestyle interventions can be implemented. A protocol, demonstrated on a single specimen, is introduced, comprising the following components; in vitro biofidelic drop tower testing of a proximal femur; high-speed image analysis through digital image correlation; detailed accounting of the energy present during the drop tower test; organ level finite element simulations of the drop tower test; micro level finite element simulations of critical volumes of interest in the trabecular bone. Fracture in the femoral specimen initiated in the superior part of the neck. Measured fracture load was 3760 N, compared to 4871 N predicted based on the finite element analysis. Digital image correlation showed compressive surface strains as high as 7.1% prior to fracture. Voxel level results were consistent with high-speed video data and helped identify hidden local structural weaknesses. We found using a drop tower test protocol that a femoral neck fracture can be created with a fall velocity and energy representative of a sideways fall from standing. Additionally, we found that the nested explicit finite element method used allowed us to identify local structural weaknesses associated with femur fracture initiation.

The Martian Gas-Analytic Package for the Landing Platform Experiments of the ExoMars 2018

The paper describes the architecture of the Martian Gas Analytic Package, which is proposed for the Russian ExoMars Lander 2018.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.

GRAIL gravity field determination using the Celestial Mechanics Approach

The NASA mission GRAIL (Gravity Recovery and Interior Laboratory) inherited its concept from the GRACE (Gravity Recovery and Climate Experiment) mission to determine the gravity field of the Moon. We present lunar gravity fields based on the data of GRAIL’s primary mission phase. Gravity field recovery is realized in the framework of the Celestial Mechanics Approach, using a development version of the Bernese GNSS Software along with Ka-band range-rate data series as observations and the GNI1B positions provided by NASA JPL as pseudo-observations. By comparing our results with the official level-2 GRAIL gravity field models we show that the lunar gravity field can be recovered with a high quality by adapting the Celestial Mechanics Approach, even when using pre-GRAIL gravity field models as a priori fields and when replacing sophisticated models of non-gravitational accelerations by appropriately spaced pseudo-stochastic pulses (i.e., instantaneous velocity changes). We present and evaluate two lunar gravity field solutions up to degree and order 200 – AIUB-GRL200A and AIUB-GRL200B. While the first solution uses no gravity field information beyond degree 200, the second is obtained by using the official GRAIL field GRGM900C up to degree and order 660 as a priori information. This reduces the omission errors and demonstrates the potential quality of our solution if we resolved the gravity field to higher degree.

Analytic validation of a gas chromatography-mass spectrometry method for quantification of six amino acids in canine serum samples.

OBJECTIVE To analytically validate a gas concentration of chromatography-mass spectrometry (GC-MS) method for measurement of 6 amino acids in canine serum samples and to assess the stability of each amino acid after sample storage. SAMPLES Surplus serum from 80 canine samples submitted to the Gastrointestinal Laboratory at Texas A&M University and serum samples from 12 healthy dogs. PROCEDURES GC-MS was validated to determine precision, reproducibility, limit of detection, and percentage recovery of known added concentrations of 6 amino acids in surplus serum samples. Amino acid concentrations in serum samples from healthy dogs were measured before (baseline) and after storage in various conditions. RESULTS Intra- and interassay coefficients of variation (10 replicates involving 12 pooled serum samples) were 13.4% and 16.6% for glycine, 9.3% and 12.4% for glutamic acid, 5.1% and 6.3% for methionine, 14.0% and 15.1% for tryptophan, 6.2% and 11.0% for tyrosine, and 7.4% and 12.4% for lysine, respectively. Observed-to-expected concentration ratios in dilutional parallelism tests (6 replicates involving 6 pooled serum samples) were 79.5% to 111.5% for glycine, 80.9% to 123.0% for glutamic acid, 77.8% to 111.0% for methionine, 85.2% to 98.0% for tryptophan, 79.4% to 115.0% for tyrosine, and 79.4% to 110.0% for lysine. No amino acid concentration changed significantly from baseline after serum sample storage at -80°C for ≤ 7 days. CONCLUSIONS AND CLINICAL RELEVANCE GC-MS measurement of concentration of 6 amino acids in canine serum samples yielded precise, accurate, and reproducible results. Sample storage at -80°C for 1 week had no effect on GC-MS results.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Vitamin D Deficiency and Depressive Symptomatology in Psychiatric Patients Hospitalized with a Current Depressive Episode: A Factor Analytic Study.

BACKGROUND Low vitamin D levels have been associated with depressive symptoms in population-based studies and non-clinical samples as well as with clinical depression. This study aimed to examine the association of vitamin D levels with the severity and dimensions of depressive symptoms in hospitalized patients with a current episode of depression taking into account confounding variables. METHODS We investigated 380 patients (mean age 47 ± 12 years, 70% women) who were consecutively hospitalized with a main diagnosis of an ICD-10 depressive episode. All patients self-rated depressive symptom severity with the Hospital Anxiety and Depression Scale (HADS-D), the Beck Depression Inventory-II (BDI-II), and the Brief Symptom Inventory. A principal component analysis was performed with all 34 items of these questionnaires and serum levels of 25-hydroxyvitamin D3 (25-OH D) were measured. RESULTS Vitamin D deficiency (< 50 nmol/l), insufficiency (50-75 nmol/l), and sufficiency (> 75 nmol/l) were present in 55.5%, 31.8% and 12.6%, respectively, of patients. Patients with vitamin D deficiency scored higher on the HADS-D scale and on an anhedonia symptom factor than those with insufficient (p-values ≤ 0.023) or sufficient (p-values ≤ 0.008) vitamin D. Vitamin D deficient patients also scored higher on the BDI-II scale than those with sufficient vitamin D (p = 0.007); BDI-II cognitive/affective symptoms, but not somatic/affective symptoms, were higher in patients with vitamin D deficiency (p = 0.005) and insufficiency (p = 0.041) relative to those with sufficient vitamin D. Effect sizes suggested clinically relevant findings. CONCLUSIONS Low vitamin D levels are frequent in hospitalized patients with a current episode of depression. Especially 25-OH D levels < 50 nmol/l were associated with cognitive/affective depressive symptoms, and anhedonia symptoms in particular.