Positive Transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps

In this paper we will develop a general approach which shows that generalized "critical relations" of families of locally defined holomorphic maps on the complex plane unfold transversally. The main idea is to define a transfer operator, which is a local analogue of the Thurston pullback operator, using holomorphic motions. Assuming a so-called lifting property is satisfied, we obtain information about the spectrum of this transfer operator and thus about transversality. An important new feature of our method is that it is not global: the maps we consider are only required to be defined and holomorphic on a neighbourhood of some finite set. We will illustrate this method by obtaining transversality for a wide class of one-parameter families of interval and circle maps, for example for maps with flat critical points, but also for maps with complex analytic extensions such as certain polynomial-like maps. As in Tsujii's approach \cite{Tsu0,Tsu1}, for real maps we obtain {\em positive} transversality (where $>0$ holds instead of just $\ne 0$), and thus monotonicity of entropy for these families, and also (as an easy application) for the real quadratic family. This method additionally gives results for unimodal families of the form $x\mapsto |x|^\ell+c$ for $\ell>1$ not necessarily an even integer and $c$ real

The dynamics of complex box mappings

In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out to be extremely useful in tackling diverse problems. The purpose of this paper is: -To illustrate some pathologies that can occur when a complex box mapping is not induced by a globally defined map and when its domain has infinitely many components, and to give conditions to avoid these issues. -To show that once one has a box mapping for a rational map, these conditions can be assumed to hold in a very natural setting. Thus we call such complex box mappings dynamically natural. -Many results in holomorphic dynamics rely on an interplay between combinatorial and analytic techniques: (*)the Enhanced Nest by Kozlovski-Shen-van Strien; (*)the Covering Lemma by Kahn-Lyubich; (*)the QC-Criterion, the Spreading Principle. The purpose of this paper is to make these tools more accessible so that they can be used as a 'black box', so one does not have to redo the proofs in new settings. -To give an intuitive, but also rather detailed, outline of the proof of the following results by Kozlovski-van Strien for non-renormalizable dynamically natural box mappings: (*)puzzle pieces shrink to points; (*)topologically conjugate non-renormalizable polynomials and box mappings are quasiconformally conjugate. -We prove the fundamental ergodic properties for dynamically natural box mappings. This leads to some necessary conditions for when such a box mapping supports a measurable invariant line field on its filled Julia set. These mappings are the analogues of Lattes maps in this setting. -We prove a version of Mane's Theorem for complex box mappings concerning expansion along orbits of points that avoid a neighborhood of the set of critical points

Effects of Insulin Detemir and NPH Insulin on Body Weight and Appetite-Regulating Brain Regions in Human Type 1 Diabetes: A Randomized Controlled Trial

Studies in rodents have demonstrated that insulin in the central nervous system induces satiety. In humans, these effects are less well established. Insulin detemir is a basal insulin analog that causes less weight gain than other basal insulin formulations, including the current standard intermediate-long acting Neutral Protamine Hagedorn (NPH) insulin. Due to its structural modifications, which render the molecule more lipophilic, it was proposed that insulin detemir enters the brain more readily than other insulins. The aim of this study was to investigate whether insulin detemir treatment differentially modifies brain activation in response to food stimuli as compared to NPH insulin. In addition, cerebral spinal fluid (CSF) insulin levels were measured after both treatments. Brain responses to viewing food and non-food pictures were measured using functional Magnetic Resonance Imaging in 32 type 1 diabetic patients, after each of two 12-week treatment periods with insulin detemir and NPH insulin, respectively, both combined with prandial insulin aspart. CSF insulin levels were determined in a subgroup. Insulin detemir decreased body weight by 0.8 kg and NPH insulin increased weight by 0.5 kg (p = 0.02 for difference), while both treatments resulted in similar glycemic control. After treatment with insulin detemir, as compared to NPH insulin, brain activation was significantly lower in bilateral insula in response to visual food stimuli, compared to NPH (p = 0.02 for right and p = 0.05 for left insula). Also, CSF insulin levels were higher compared to those with NPH insulin treatment (p = 0.003). Our findings support the hypothesis that in type 1 diabetic patients, the weight sparing effect of insulin detemir may be mediated by its enhanced action on the central nervous system, resulting in blunted activation in bilateral insula, an appetite-regulating brain region, in response to food stimuli.ClinicalTrials.gov NCT00626080

Mapping Proprioception across a 2D Horizontal Workspace

Relatively few studies have been reported that document how proprioception varies across the workspace of the human arm. Here we examined proprioceptive function across a horizontal planar workspace, using a new method that avoids active movement and interactions with other sensory modalities. We systematically mapped both proprioceptive acuity (sensitivity to hand position change) and bias (perceived location of the hand), across a horizontal-plane 2D workspace. Proprioception of both the left and right arms was tested at nine workspace locations and in 2 orthogonal directions (left-right and forwards-backwards). Subjects made repeated judgments about the position of their hand with respect to a remembered proprioceptive reference position, while grasping the handle of a robotic linkage that passively moved their hand to each judgement location. To rule out the possibility that the memory component of the proprioceptive testing procedure may have influenced our results, we repeated the procedure in a second experiment using a persistent visual reference position. Both methods resulted in qualitatively similar findings. Proprioception is not uniform across the workspace. Acuity was greater for limb configurations in which the hand was closer to the body, and was greater in a forward-backward direction than in a left-right direction. A robust difference in proprioceptive bias was observed across both experiments. At all workspace locations, the left hand was perceived to be to the left of its actual position, and the right hand was perceived to be to the right of its actual position. Finally, bias was smaller for hand positions closer to the body. The results of this study provide a systematic map of proprioceptive acuity and bias across the workspace of the limb that may be used to augment computational models of sensory-motor control, and to inform clinical assessment of sensory function in patients with sensory-motor deficits

Application of biomedical informatics to chronic pediatric diseases: a systematic review

<p>Abstract</p> <p>Background</p> <p>Chronic diseases affect millions of children worldwide leading to substantial disease burden to the children and their families as well as escalating health care costs. The increasing trend in the prevalence of complex pediatric chronic diseases requires innovative and optimal delivery of care. Biomedical informatics applications play an important role in improving health outcomes while being cost-effective. However, their utility in pediatric chronic diseases has not been studied in a comprehensive and systematic way. The objective of this study was to conduct a systematic review of the effects of biomedical informatics applications in pediatric chronic diseases.</p> <p>Methods</p> <p>A comprehensive literature search was conducted using MEDLINE, the Cochrane Library and EMBASE databases from inception of each database to September 2008. We included studies of any methodological type and any language that applied biomedical informatics to chronic conditions in children and adolescents 18 years of age or younger. Two independent reviewers carried out study selection and data extraction. Quality assessment was performed using a study design evaluation instrument to appraise the strength of the studies and their methodological adequacy. Because of heterogeneity in the conditions and outcomes we studied, a formal meta-analysis was not performed.</p> <p>Results</p> <p>Based on our search strategy, 655 titles and abstracts were reviewed. From this set we identified 27 relevant articles that met our inclusion criteria. The results from these studies indicated that biomedical informatics applications have favourable clinical and patient outcomes including, but not limited to, reduced number of emergency room visits, improved knowledge on disease management, and enhanced satisfaction. Seventy percent of reviewed papers were published after year 2000, 89% of users were patients and 11% were either providers or caregivers. The majority (96%) of the selected studies reported improved outcomes.</p> <p>Conclusion</p> <p>Published studies suggested positive impacts of informatics predominantly in pediatric asthma. As electronic tools become more widely adopted, there will be opportunities to improve patient care in a wide range of chronic illnesses through informatics solutions.</p

Local connectivity of the Julia set of real polynomials

One of the main questions in the field of complex dynamics is the question whether the Mandelbrot set is locally connected, and related to this, for which maps the Julia set is locally connected. In this paper we shall prove the following Main Theorem: Let f be a polynomial of the form f(z)=zd+c with d an even integer and c real. Then the Julia set of f is either totally disconnected or locally connected. In particular, the Julia set of z2+c is locally connected if c∈[−2,1/4] and totally disconnected otherwise

Data from: The structural and functional connectivity of the grassland plant Lychnis flos-cuculi

Understanding the relationship between structural and functional connectivity is essential for successful restoration and conservation management, particularly in intensely managed agricultural landscapes. We evaluated the relationship between structural and functional connectivity of the wetland plant Lychnis flos-cuculi in a fragmented agricultural landscape using landscape genetic and network approaches. First, we studied the effect of structural connectivity, such as geographic distance and various landscape elements (forest, agricultural land, settlements and ditch verges), on gene flow among populations as a measurement of functional connectivity. Second, we examined the effect of structural graph-theoretic connectivity measures on gene flow among populations and on genetic diversity within populations of L. flos-cuculi. Among landscape elements, forests hindered gene flow in L. flos-cuculi, whereas gene flow was independent of geographic distance. Among the structural graph-theoretic connectivity variables, only intrapopulation connectivity, which was based on population size, had a significant positive effect on gene flow, that is, more gene flow took place among larger populations. Unexpectedly, interpopulation connectivity of populations, which takes into account the spatial location and distance among populations, did not influence gene flow in L. flos-cuculi. However, higher observed heterozygosity and lower inbreeding was observed in populations characterised by higher structural interpopulation connectivity. This finding shows that a spatially coherent network of populations is significant for maintaining the genetic diversity of populations. Nevertheless, lack of significant relationships between gene flow and most of the structural connectivity measures suggests that structural connectivity does not necessarily correspond to functional connectivity