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.

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.

Genomics of Divergence along a Continuum of Parapatric Population Differentiation

The patterns of genomic divergence during ecological speciation are shaped by a combination of evolutionary forces. Processes such as genetic drift, local reduction of gene flow around genes causing reproductive isolation, hitchhiking around selected variants, variation in recombination and mutation rates are all factors that can contribute to the heterogeneity of genomic divergence. On the basis of 60 fully sequenced three-spined stickleback genomes, we explore these different mechanisms explaining the heterogeneity of genomic divergence across five parapatric lake and river population pairs varying in their degree of genetic differentiation. We find that divergent regions of the genome are mostly specific for each population pair, while their size and abundance are not correlated with the extent of genome-wide population differentiation. In each pair-wise comparison, an analysis of allele frequency spectra reveals that 25–55% of the divergent regions are consistent with a local restriction of gene flow. Another large proportion of divergent regions (38–75%) appears to be mainly shaped by hitchhiking effects around positively selected variants. We provide empirical evidence that alternative mechanisms determining the evolution of genomic patterns of divergence are not mutually exclusive, but rather act in concert to shape the genome during population differentiation, a first necessary step towards ecological speciation.

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.

Clitics, affixes, and wordhood in Garifuna (Arawak): A multidimensional continuum of morphosyntactic boundness

Recent research on wordhood and morphosyntactic boundness suggests that the domains word and clitic do not lend themselves to cross-linguistic categorization but must be defined language specifically. In most languages, it is necessary to define word on two separate levels, the phonological word (p-word) and the grammatical word (g-word), and to describe mismatches between the two. This paper defines those domains for Garifuna, an Arawak language spoken in Honduras, Central America. Garifuna has auxiliary and classifier constructions which make up two p-words, and only one g-word. P-words made up of more than one g-word involve second position enclitics, word scope clitics, and proclitic connectives and prepositions. Garifuna clitics are typically unstressed, able to attach to hosts of any word class and able to string together into clusters. Enclitics are used to express tense-aspect, modality, and adverbial meanings, among others. In other languages, clitic clusters tend to display a fixed order; Garifuna clitic order seems quite free, although certain orders are preferred. Also, contrary to cross-linguistic tendencies, proclitic connectives can act as hosts for enclitic clusters, contradicting the commonly used definition of clitics as phonologically weak elements that need to attach to a host to form a p-word; such clitic-only p-words are problematic for traditional definitions of clitics.

Continuum damage interactions between tension and compression in osteonal bone

Skeletal diseases such as osteoporosis impose a severe socio-economic burden to ageing societies. Decreasing mechanical competence causes a rise in bone fracture incidence and mortality especially after the age of 65 y. The mechanisms of how bone damage is accumulated under different loading modes and its impact on bone strength are unclear. We hypothesise that damage accumulated in one loading mode increases the fracture risk in another. This study aimed at identifying continuum damage interactions between tensile and compressive loading modes. We propose and identify the material constants of a novel piecewise 1D constitutive model capable of describing the mechanical response of bone in combined tensile and compressive loading histories. We performed several sets of loading–reloading experiments to compute stiffness, plastic strains, and stress-strain curves. For tensile overloading, a stiffness reduction (damage) of 60% at 0.65% accumulated plastic strain was detectable as stiffness reduction of 20% under compression. For compressive overloading, 60% damage at 0.75% plastic strain was detectable as a stiffness reduction of 50% in tension. Plastic strain at ultimate stress was the same in tension and compression. Compression showed softening and tension exponential hardening in the post-yield regime. The hardening behaviour in compression is unaffected by a previous overload in tension but the hardening behaviour in tension is affected by a previous overload in compression as tensile reloading strength is significantly reduced. This paper demonstrates how damage accumulated under one loading mode affects the mechanical behaviour in another loading mode. To explain this and to illustrate a possible implementation we proposed a theoretical model. Including such loading mode dependent damage and plasticity behaviour in finite element models will help to improve fracture risk analysis of whole bones and bone implant structures.

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.

Evidence for a perception memory continuum: an EEG study in a healthy population

In line with current memory theories of a perception-memory continuum along the ventral visual pathway, there is evidence that the specific profile of enhanced memory in special populations (e.g. synaesthesia) is based on increased perceptual sensitivity. The main goal of this study was to test in a more general population, if increased perceptual sensitivity is indeed associated with enhanced memory performance. We measured ERPs in response to simple perceptual stimuli biasing either the ventral or the dorsal route and established if perceptual sensitivity in response to ventrally (but not dorsally) processed stimuli is associated with visual short term memory performance in a change detection task. Preliminary results confirm the hypothesis and strengthen the assumption of a perceptual-memory-continuum.