Continuum percolation for Gibbs point processes

We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation occurs a.s. above criticality. For locally stable Gibbs point processes we show a converse result, i.e. they do not percolate a.s. at low activity.

The free escape continuum of diffuse ions upstream of the Earth's quasi-parallel bow shock

The Earth's bow shock is very efficient in accelerating ions out of the incident solar wind distribution to high energies (≈ 200 keV/e). Fluxes of energetic ions accelerated at the quasi-parallel bow shock, also known as diffuse ions, are best represented by exponential spectra in energy/charge, which require additional assumptions to be incorporated into these model spectra. One of these assumptions is a so-called "free escape boundary" along the interplanetary magnetic field into the upstream direction. Locations along the IBEX orbit are ideally suited for in situ measurements to investigate the existence of an upstream free escape boundary for bow shock accelerated ions. In this study we use 2 years of ion measurements from the background monitor on the IBEX spacecraft, supported by ACE solar wind observations. The IBEX Background Monitor is sensitive to protons > 14 keV, which includes the energy of the maximum flux for diffuse ions. With increasing distance from the bow shock along the interplanetary magnetic field, the count rates for diffuse ions stay constant for ions streaming away from the bow shock, while count rates for diffuse ions streaming toward the shock gradually decrease from a maximum value to ~1/e at distances of about 10 RE to 14 RE. These observations of a gradual decrease support the transition to a free escape continuum for ions of energy >14 keV at distances from 10 RE to 14 RE from the bow shock.

Continuum of depressive and manic mixed states in patients with bipolar disorder: quantitative measurement and clinical features.

Bipolar mixed states combine depressive and manic features, presenting diagnostic and treatment challenges and reflecting a severe form of the illness. DSM-IV criteria for a mixed state require combined depressive and manic syndromes, but a range of mixed states has been described clinically. A unified definition of mixed states would be valuable in understanding their diagnosis, mechanism and treatment implications. We investigated the manner in which depressive and manic features combine to produce a continuum of mixed states. In 88 subjects with bipolar disorder (DSM-IV), we evaluated symptoms and clinical characteristics, and compared depression-based, mania-based, and other published definitions of mixed states. We developed an index of the extent to which symptoms were mixed (Mixed State Index, MSI) and characterized its relationship to clinical state. Predominately manic and depressive mixed states using criteria from recent literature, as well as Kraepelinian mixed states, had similar symptoms and MSI scores. Anxiety correlated significantly with depression scores in manic subjects and with mania scores in depressed subjects. Discriminant function analysis associated mixed states with symptoms of hyperactivity and negative cognitions, but not subjective depressive or elevated mood. High MSI scores were associated with severe course of illness. For depressive or manic episodes, characteristics of mixed states emerged with two symptoms of the opposite polarity. This was a cross-sectional study. Mixed states appear to be a continuum. An index of the degree to which depressive and manic symptoms combine appears useful in identifying and characterizing mixed states. We propose a depressive or manic episode with three or more symptoms of the opposite polarity as a parsimonious definition of a mixed state.

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.

Finite element analyses of human vertebral bodies embedded in polymethylmethalcrylate or loaded via the hyperelastic intervertebral disc models provide equivalent predictions of experimental strength

Quantitative computer tomography (QCT)-based finite element (FE) models of vertebral body provide better prediction of vertebral strength than dual energy X-ray absorptiometry. However, most models were validated against compression of vertebral bodies with endplates embedded in polymethylmethalcrylate (PMMA). Yet, loading being as important as bone density, the absence of intervertebral disc (IVD) affects the strength. Accordingly, the aim was to assess the strength predictions of the classic FE models (vertebral body embedded) against the in vitro and in silico strengths of vertebral bodies loaded via IVDs. High resolution peripheral QCT (HR-pQCT) were performed on 13 segments (T11/T12/L1). T11 and L1 were augmented with PMMA and the samples were tested under a 4° wedge compression until failure of T12. Specimen-specific model was generated for each T12 from the HR-pQCT data. Two FE sets were created: FE-PMMA refers to the classical vertebral body embedded model under axial compression; FE-IVD to their loading via hyperelastic IVD model under the wedge compression as conducted experimentally. Results showed that FE-PMMA models overestimated the experimental strength and their strength prediction was satisfactory considering the different experimental set-up. On the other hand, the FE-IVD models did not prove significantly better (Exp/FE-PMMA: R²=0.68; Exp/FE-IVD: R²=0.71, p=0.84). In conclusion, FE-PMMA correlates well with in vitro strength of human vertebral bodies loaded via real IVDs and FE-IVD with hyperelastic IVDs do not significantly improve this correlation. Therefore, it seems not worth adding the IVDs to vertebral body models until fully validated patient-specific IVD models become available.

Towards the continuum limit in transport coefficient computations

The analytic continuation needed for the extraction of transport coefficients necessitates in principle a continuous function of the Euclidean time variable. We report on progress towards achieving the continuum limit for 2-point correlator measurements in thermal SU(3) gauge theory, with specific attention paid to scale setting. In particular, we improve upon the determination of the critical lattice coupling and the critical temperature of pure SU(3) gauge theory, estimating r0Tc ≃ 0.7470(7) after a continuum extrapolation. As an application the determination of the heavy quark momentum diffusion coefficient from a correlator of colour-electric fields attached to a Polyakov loop is discussed.

Full and hat inductive definitions are equivalent in NBG

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA 0, those in second order set theory extending NBG (as well as those in n + 3-th order number theory extending the so-called Bernays−Gödel expansion of full n + 2-order number theory etc.) are. In this article, we establish the equivalence between Δ10\bf-LFP and Δ10\bf-FP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bf-LFP and Δn+20\bf-FP). Our proof also shows the equivalence between ID 1 and ^ID1, both of which are defined in the standard way but with the starting theory PA replaced by ZFC (or full n + 2-th order number theory with global well-ordering).

A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP

We introduce a version of operational set theory, OST−, without a choice operation, which has a machinery for Δ0Δ0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke–Platek set theory KPKP with infinity are pairwise Π1Π1 equivalent. We also show analogous assertions for subtheories with ∈-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KPKP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model.

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.

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.

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.

The Three Body Problem and the Runge-Lenz Equivalent Constant of the Motion

The Runge-Lenz equivalent for the Hydrogen Molecular Cation (and the Earth, Moon and Sun) problem is obtained