Curvature-direction measures of self-similar sets

We obtain fractal Lipschitz-Killing curvature-direction measures for a large class of self-similar sets F in R^d. Such measures jointly describe the distribution of normal vectors and localize curvature by analogues of the higher order mean curvatures of differentiable submanifolds. They decouple as independent products of the unit Hausdorff measure on F and a self-similar fibre measure on the sphere, which can be computed by an integral formula. The corresponding local density approach uses an ergodic dynamical system formed by extending the code space shift by a subgroup of the orthogonal group. We then give a remarkably simple proof for the resulting measure version under minimal assumptions.Comment: 17 pages, 2 figures. Update for author's name chang

Average distances on self-similar sets and higher order average distances of self-similar measures

The purpose of this paper is twofold: (1) we study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of ℝ

Diffusion magnetic resonance imaging assessment of regional white matter maturation in preterm neonates

PURPOSE: Diffusion magnetic resonance imaging (dMRI) studies report altered white matter (WM) development in preterm infants. Neurite orientation dispersion and density imaging (NODDI) metrics provide more realistic estimations of neurite architecture in vivo compared with standard diffusion tensor imaging (DTI) metrics. This study investigated microstructural maturation of WM in preterm neonates scanned between 25 and 45 weeks postmenstrual age (PMA) with normal neurodevelopmental outcomes at 2 years using DTI and NODDI metrics. METHODS: Thirty-one neonates (n = 17 male) with median (range) gestational age (GA) 32+1 weeks (24+2-36+4) underwent 3 T brain MRI at median (range) post menstrual age (PMA) 35+2 weeks (25+3-43+1). WM tracts (cingulum, fornix, corticospinal tract (CST), inferior longitudinal fasciculus (ILF), optic radiations) were delineated using constrained spherical deconvolution and probabilistic tractography in MRtrix3. DTI and NODDI metrics were extracted for the whole tract and cross-sections along each tract to assess regional development. RESULTS: PMA at scan positively correlated with fractional anisotropy (FA) in the CST, fornix and optic radiations and neurite density index (NDI) in the cingulum, CST and fornix and negatively correlated with mean diffusivity (MD) in all tracts. A multilinear regression model demonstrated PMA at scan influenced all diffusion measures, GA and GAxPMA at scan influenced FA, MD and NDI and gender affected NDI. Cross-sectional analyses revealed asynchronous WM maturation within and between WM tracts.). CONCLUSION: We describe normal WM maturation in preterm neonates with normal neurodevelopmental outcomes. NODDI can enhance our understanding of WM maturation compared with standard DTI metrics alone

Exploring the multiple-hit hypothesis of preterm white matter damage using diffusion MRI.

Background: Preterm infants are at high risk of diffuse white matter injury and adverse neurodevelopmental outcome. The multiple hit hypothesis suggests that the risk of white matter injury increases with cumulative exposure to multiple perinatal risk factors. Our aim was to test this hypothesis in a large cohort of preterm infants using diffusion weighted magnetic resonance imaging (dMRI). Methods: We studied 491 infants (52% male) without focal destructive brain lesions born at < 34 weeks, who underwent structural and dMRI at a specialist Neonatal Imaging Centre. The median (range) gestational age (GA) at birth was 30+ 1 (23+ 2-33+ 5) weeks and median postmenstrual age at scan was 42+ 1 (38-45) weeks. dMRI data were analyzed using tract based spatial statistics and the relationship between dMRI measures in white matter and individual perinatal risk factors was assessed. We tested the hypothesis that increased exposure to perinatal risk factors was associated with lower fractional anisotropy (FA), and higher radial, axial and mean diffusivity (RD, AD, MD) in white matter. Neurodevelopmental performance was investigated using the Bayley Scales of Infant and Toddler Development, Third Edition (BSITD-III) in a subset of 381 infants at 20 months corrected age. We tested the hypothesis that lower FA and higher RD, AD and MD in white matter were associated with poorer neurodevelopmental performance. Results: Identified risk factors for diffuse white matter injury were lower GA at birth, fetal growth restriction, increased number of days requiring ventilation and parenteral nutrition, necrotizing enterocolitis and male sex. Clinical chorioamnionitis and patent ductus arteriosus were not associated with white matter injury. Multivariate analysis demonstrated that fetal growth restriction, increased number of days requiring ventilation and parenteral nutrition were independently associated with lower FA values. Exposure to cumulative risk factors was associated with reduced white matter FA and FA values at term equivalent age were associated with subsequent neurodevelopmental performance. Conclusion: This study suggests multiple perinatal risk factors have an independent association with diffuse white matter injury at term equivalent age and exposure to multiple perinatal risk factors exacerbates dMRI defined, clinically significant white matter injury. Our findings support the multiple hit hypothesis for preterm white matter injury

Multifractal tubes

Tube formulas refer to the study of volumes of $r$ neighbourhoods of sets. For sets satisfying some (possible very weak) convexity conditions, this has a long history. However, within the past 20 years Lapidus has initiated and pioneered a systematic study of tube formulas for fractal sets. Following this, it is natural to ask to what extend it is possible to develop a theory of multifractal tube formulas for multifractal measures. In this paper we propose and develop a framework for such a theory. Firstly, we define multifractal tube formulas and, more generally, multifractal tube measures for general multifractal measures. Secondly, we introduce and develop two approaches for analysing these concepts for self-similar multifractal measures, namely: (1) Multifractal tubes of self-similar measures and renewal theory. Using techniques from renewal theory we give a complete description of the asymptotic behaviour of the multifractal tube formulas and tube measures of self-similar measures satisfying the Open Set Condition. (2) Multifractal tubes of self-similar measures and zeta-functions. Unfortunately, renewal theory techniques do not yield "explicit" expressions for the functions describing the asymptotic behaviour of the multifractal tube formulas and tube measures of self-similar measures. This is clearly undesirable. For this reason, we introduce and develop a second framework for studying multifractal tube formulas of self-similar measures. This approach is based on multifractal zeta-functions and allow us obtain "explicit" expressions for the multifractal tube formulas of self-similar measures, namely, using the Mellin transform and the residue theorem, we are able to express the multifractal tube formulas as sums involving the residues of the zeta-function.Comment: 122 page

Psychological and physiological effects of compassionate mind training: A pilot randomised controlled study

The development of the compassionate self, associated with practices such as slow and deeper breathing, compassionate voice tones and facial expressions and compassionate focusing is central to Compassion Focused Therapy. This study explores the impact of a two-week Compassionate Mind Training (CMT) program on emotional, self-evaluative and psychopathology measures and on heart rate variability (HRV). Participants (general population and college students) were randomly assigned to one of two conditions: CMT (n=56) and Wait-List Control (n=37). Participants in the CMTcondition were instructed to practice CMT exercises during two weeks. Self-report measures of compassion, positive affect, fears of compassion, self-criticism, shame, depression, anxiety and stress, and HRV were collected at pre and post intervention in both conditions. Compared to the control group, the experimental group showed significant increases in positive emotions, associated with feeling relaxed and also safe and content, but not activated; and in self-compassion, compassion for others and compassion from others. There were significant reductions in shame, self-criticism, fears of compassion, and stress. Only the experimental group reported significant improvement in HRV. Developing awareness of the evolved nature and inherent difficulties of our minds allied with practicing CMT exercises has beneficial effects on participants' psychological and physiological well-being.N/

A Genome Wide Association Scan of Bovine Tuberculosis Susceptibility in Holstein-Friesian Dairy Cattle

peer-reviewedBackground: Bovine tuberculosis is a significant veterinary and financial problem in many parts of the world. Although many factors influence infection and progression of the disease, there is a host genetic component and dissection of this may enlighten on the wider biology of host response to tuberculosis. However, a binary phenotype of presence/absence of infection presents a noisy signal for genomewide association study. Methodology/Principal Findings: We calculated a composite phenotype of genetic merit for TB susceptibility based on disease incidence in daughters of elite sires used for artificial insemination in the Irish dairy herd. This robust measure was compared with 44,426 SNP genotypes in the most informative 307 subjects in a genome wide association analysis. Three SNPs in a 65 kb genomic region on BTA 22 were associated (i.e. p,1025, peaking at position 59588069, p = 4.0261026) with tuberculosis susceptibility. Conclusions/Significance: A genomic region on BTA 22 was suggestively associated with tuberculosis susceptibility; it contains the taurine transporter gene SLC6A6, or TauT, which is known to function in the immune system but has not previously been investigated for its role in tuberculosis infection

Sex-specific genetic effects influence variation in body composition

Aims/hypothesis: Despite well-known sex differences in body composition it is not known whether sex-specific genetic or environmental effects contribute to these differences. Methods: We assessed body composition in 2,506 individuals, from a young Dutch genetic isolate participating in the Erasmus Rucphen Family study, by dual-energy X-ray absorptiometry and anthropometry. We used variance decomposition procedures to partition variation of body composition into genetic and environmental components common to both sexes and to men and women separately and calculated the correlation between genetic components in men and women. Results: After accounting for age