Modelling the structure of star clusters with fractional Brownian motion

The degree of fractal substructure in molecular clouds can be quantified by comparing them with Fractional Brownian Motion (FBM) surfaces or volumes. These fields are self-similar over all length scales and characterised by a drift exponent $H$, which describes the structural roughness. Given that the structure of molecular clouds and the initial structure of star clusters are almost certainly linked, it would be advantageous to also apply this analysis to clusters. Currently, the structure of star clusters is often quantified by applying $\mathcal{Q}$ analysis. $\mathcal{Q}$ values from observed targets are interpreted by comparing them with those from artificial clusters. These are typically generated using a Box-Fractal (BF) or Radial Density Profile (RDP) model. We present a single cluster model, based on FBM, as an alternative to these models. Here, the structure is parameterised by $H$, and the standard deviation of the log-surface/volume density $\sigma$. The FBM model is able to reproduce both centrally concentrated and substructured clusters, and is able to provide a much better match to observations than the BF model. We show that $\mathcal{Q}$ analysis is unable to estimate FBM parameters. Therefore, we develop and train a machine learning algorithm which can estimate values of $H$ and $\sigma$, with uncertainties. This provides us with a powerful method for quantifying the structure of star clusters in terms which relate to the structure of molecular clouds. We use the algorithm to estimate the $H$ and $\sigma$ for several young star clusters, some of which have no measurable BF or RDP analogue.Comment: 11 Pages, accepted by MNRA

Mechanical Systems: Symmetry and Reduction

Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are \factored out" and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems

Characterising lognormal fractional-Brownian-motion density fields with a Convolutional Neural Network

In attempting to quantify statistically the density structure of the interstellar medium, astronomers have considered a variety of fractal models. Here we argue that, to properly characterise a fractal model, one needs to define precisely the algorithm used to generate the density field, and to specify -- at least -- three parameters: one parameter constrains the spatial structure of the field; one parameter constrains the density contrast between structures on different scales; and one parameter constrains the dynamic range of spatial scales over which self-similarity is expected (either due to physical considerations, or due to the limitations of the observational or numerical technique generating the input data). A realistic fractal field must also be noisy and non-periodic. We illustrate this with the exponentiated fractional Brownian motion (xfBm) algorithm, which is popular because it delivers an approximately lognormal density field, and for which the three parameters are, respectively, the power spectrum exponent, $\beta$, the exponentiating factor, ${\cal S}$, and the dynamic range, ${\cal R}$. We then explore and compare two approaches that might be used to estimate these parameters: Machine Learning and the established $\Delta$-Variance procedure. We show that for $2\leq\beta \leq 4$ and $0\leq{\cal S}\leq 3$, a suitably trained Convolutional Neural Network is able to estimate objectively both $\beta$ (with root-mean-square error $\epsilon_{_\beta}\sim 0.12$) and ${\cal S}$ (with $\epsilon_{_{\cal S}}\sim 0.29$). $\;\Delta$-variance is also able to estimate $\beta$, albeit with a somewhat larger error ($\epsilon_{_\beta}\sim 0.17$) and with some human intervention, but is not able to estimate ${\cal S}$

Synergism between cAMP and PPARγ signalling in the initiation of UCP1 gene expression in HIB1B brown adipocytes

Expression of the brown adipocyte-specific gene, uncoupling protein 1 (UCP1), is increased by both PPAR stimulation and cAMP activation through their ability to stimulate the expression of the PPAR coactivator PGC1. In HIB1B brown preadipocytes, combination of the PPAR agonist, rosiglitazone, and the cAMP stimulator forskolin synergistically increased UCP1 mRNA expression, but PGC1 expression was only increased additively by the two drugs. The PPAR antagonist, GW9662, and the PKA inhibitor, H89, both inhibited UCP1 expression stimulated by rosiglitazone and forskolin but PGC1 expression was not altered to the same extent. Reporter studies demonstrated that combined rosiglitazone and forskolin synergistically activated transcription from a full length 3.1 kbp UCP1 luciferase promoter construct, but the response was only additive and much reduced when a minimal 260 bp proximal UCP1 promoter was examined. Rosiglitazone and forskolin in combination were able to synergistically stimulate promoters comprising of tandem repeats of either PPREs or CREs. We conclude that rosiglitazone and forskolin act together to synergistically activate the UCP1 promoter directly rather than by increasing PGC1 expression and by a mechanism involving cross-talk between the signalling systems regulating the CRE and PPRE on the promoters

Gene expression of inflammatory markers in adipose tissue between obese women with polycystic ovary and normal obese women

OBJECTIVE: The pathogenesis of polycystic ovary syndrome (PCOS), a common endocrine disease and metabolic disturbance, is still unknown. The aim of the study was to investigate whether patients with PCOS display increased expression of inflammatory markers in adipose tissue. PATIENTS AND METHODS: Two groups of women were investigated, those diagnosed with PCOS (n = 8) and age and BMI-matched normal women (n = 12). Their age was between 20-45 years and all subjects were apparently healthy and did not take any medications. Adipose tissue levels of mRNA of inflammatory markers were determined by use of real-time PCR. RESULTS: There were no differences between obese patients and obese PCOS in levels of adipocytokines. CONCLUSIONS: There were no effects of PCOS on the expression of any of the adipocytokines genes measured in subcutaneous adipose tissue

Quality assurance in stereotactic radiosurgery/radiotherapy according to DIN 6875-1

The new DIN (' Deutsche Industrie- Norm') 6875- 1, which is currently being finalised, deals with quality assurance ( QA) criteria and tests methods for linear accelerator and Gamma Knife stereotactic radiosurgery/ radiotherapy including treatment planning, stereotactic frame and stereotactic imaging and a system test to check the whole chain of uncertainties. Our existing QA program, based on dedicated phantoms and test procedures, has been refined to fulfill the demands of this new DIN. The radiological and mechanical isocentre corresponded within 0.2 mm and the measured 50% isodose lines were in agreement with the calculated ones within less than 0.5 mm. The measured absorbed dose was within 3%. The resultant output factors measured for the 14-, 8- and 4- mm collimator helmet were 0.9870 +/- 0.0086, 0.9578 +/- 0.0057 and 0.8741 +/- 0.0202, respectively. For 170 consecutive tests, the mean geometrical accuracy was 0.48 +/- 0.23 mm. Besides QA phantoms and analysis software developed in- house, the use of commercially available tools facilitated the QA according to the DIN 6875- 1 with which our results complied. Copyright (C) 2004 S. Karger AG, Basel

The broken 'Ring of Fire'; a new radiological sign as predictor of syndesmosis injury?

Background We noticed that subcircumferential periosteal oedema above the ankle joint was frequently present on MRI with syndesmosis injuries but was not previously reported. Fluid height within the interosseous membrane has also not been shown to be associated with syndesmosis injury severity. Purpose Investigate whether a new sign on MRI and measurement of the length of fluid within the interosseous membrane above the ankle may be used to enable early identification of a syndesmosis injury and allow differentiation from lateral ligament injury. Methods Three groups of patients were identified from a database and the MRI scans retrieved – those with an isolated syndesmosis injury (SI group), isolated lateral ligament injury (LLI group) and or no injury (NI group) who had an ankle MRI for another reason. The scans were anonymized and independently assessed by eight clinicians (surgeons and radiologists) who were blinded to the diagnosis. The maximum length of fluid above the ankle within the intraosseous membrane was measured for each patient. The presence or absence of distal anterior, lateral and posterior tibial periosteal oedema was recorded (‘Ring of Fire’). Results Measurement of the length of fluid above the ankle had excellent intra-observer reliability (ICC=0.97 [0.93-0.99]) but poor interobserver reliability. Fluid extended higher in both the LLI group (p=0.0043) and SI group (p=0.0058) than the NI group but there was no significant difference between the LLI and SI groups (p=0.3735) indicating that this measurement cannot differentiate between the injuries. The presence of the ‘Ring of Fire’ around the distal tibia was significantly more frequent in the SI group when compared to both LLI and NI groups (p<0.00001). The sensitivity of this sign is 49% but when present this sign has a 98% specificity for syndesmosis injury

Characterizing the Rigidly Rotating Magnetosphere Stars HD 345439 and HD 23478

The SDSS III APOGEE survey recently identified two new $\sigma$ Ori E type candidates, HD 345439 and HD 23478, which are a rare subset of rapidly rotating massive stars whose large (kGauss) magnetic fields confine circumstellar material around these systems. Our analysis of multi-epoch photometric observations of HD 345439 from the KELT, SuperWASP, and ASAS surveys reveals the presence of a $\sim$0.7701 day period in each dataset, suggesting the system is amongst the faster known $\sigma$ Ori E analogs. We also see clear evidence that the strength of H-alpha, H I Brackett series lines, and He I lines also vary on a $\sim$0.7701 day period from our analysis of multi-epoch, multi-wavelength spectroscopic monitoring of the system from the APO 3.5m telescope. We trace the evolution of select emission line profiles in the system, and observe coherent line profile variability in both optical and infrared H I lines, as expected for rigidly rotating magnetosphere stars. We also analyze the evolution of the H I Br-11 line strength and line profile in multi-epoch observations of HD 23478 from the SDSS-III APOGEE instrument. The observed periodic behavior is consistent with that recently reported by Sikora and collaborators in optical spectra.Comment: Accepted in ApJ

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic R\"ossler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure