On the Minimum Ropelength of Knots and Links

The ropelength of a knot is the quotient of its length and its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are $C^{1,1}$ curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.Comment: 29 pages, 14 figures; New version has minor additions and corrections; new section on asymptotic growth of ropelength; several new reference

#Portichiusi: the human costs of migrant deterrence in the Mediterranean

Using daily data on forced migration from the IOM, I compare trends in flows and mortality across three major migration routes in the Mediterranean, analysing the effects of the introduction of rescue-deterrence policies in Italy. Controlling for exogenous shocks which affect push and pull factors in mobility, along with sea state conditions and route-day fixed effects, I find that the reduction in refugee migration flows in the Central Mediterranean has been modest, at best. At the same time, these policies have generated a permanent increase in daily mortality rates in the Central Mediterranean, having grown by more than 4 deaths per day. Finally, I investigate whether variations in mortality are sufficient to offset migration flows. Increases in mortality rates, however, are only accompanied by a short-term negative displacement effect, as migration attempts are delayed by increases in absolute mortality, rather than being prevented

The Second Hull of a Knotted Curve

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.Comment: 7 pages, 6 figures; final version (only minor changes) to appear in Amer.J.Mat

Labour market effects of crowdwork in the US and EU: an empirical investigation

Is it possible to estimate the real impact of micro-task crowdwork on wages and working conditions of platform workers? Do workers involved in micro-task outsourcing differ in their characteristics from traditional salaried workers of similar ability? Are micro-task crowdworkers similar or different in the United States and in Europe? In this paper, we address these questions by comparing wages and working conditions across onlineplatform workers and traditional workers in a quasi-experimental approach which exploits caregiving as an instrument for participation in crowdwork. We find evidence that, when controlling for workers’ observed and unobserved ability, traditional workers retain a significant premium in their earnings with respect to platform workers, though this effect is not as large as descriptive statistics may hint. Moreover, labour force in crowdworking arrangements appears to suffer from high levels of under-utilisation, relegating crowdworkers into a new category of idle workers whose human capital is neither fully utilised nor adequately compensated

Cortical pain responses in human infants

Despite the recent increase in our understanding of the development of pain processing, it is still not known whether premature infants are capable of processing pain at a cortical level. In this study, changes in cerebral oxygenation over the somatosensory cortex were measured in response to noxious stimulation using real-time near-infrared spectroscopy in 18 infants aged between 25 and 45 weeks postmenstrual age. The noxious stimuli were heel lances performed for routine blood sampling; no blood tests were performed solely for the purpose of the study. Noxious stimulation produced a clear cortical response, measured as an increase in total hemoglobin concentration [HbT] in the contralateral somatosensory cortex, from 25 weeks (mean Delta[HbT] = 7.74 mu mol/L; SE, 1.10). Cortical responses were significantly greater in awake compared with sleeping infants, with a mean difference of 6.63 mu mol/L [95% confidence interval (CI) limits: 2.35, 10.91 mu mol/L; mean age, 35.2 weeks]. In awake infants, the response in the contralateral somatosensory cortex increased with age ( regression coefficient, 0.698 mu mol/L/week; 95% CI limits: 0.132, 1.265 mu mol/L/week) and the latency decreased with age (regression coefficient, -0.9861 mu mol/L/week; 95% CI limits: -1.5361, -0.4361 mu mol/L/week; age range, 25-38 weeks). The response was modality specific because no response was detected after non-noxious stimulation of the heel, even when accompanied by reflex withdrawal of the foot. We conclude that noxious information is transmitted to the preterm infant cortex from 25 weeks, highlighting the potential for both higher-level pain processing and pain-induced plasticity in the human brain from a very early age

Quadrisecants give new lower bounds for the ropelength of a knot

Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.Comment: v3 is the version published by Geometry & Topology on 25 February 200

Changes in the midpalatal and pterygopalatine sutures induced by micro-implant-supported skeletal expander, analyzed with a novel 3D method based on CBCT imaging.

BackgroundMini-implant-assisted rapid palatal expansion (MARPE) appliances have been developed with the aim to enhance the orthopedic effect induced by rapid maxillary expansion (RME). Maxillary Skeletal Expander (MSE) is a particular type of MARPE appliance characterized by the presence of four mini-implants positioned in the posterior part of the palate with bi-cortical engagement. The aim of the present study is to evaluate the MSE effects on the midpalatal and pterygopalatine sutures in late adolescents, using high-resolution CBCT. Specific aims are to define the magnitude and sagittal parallelism of midpalatal suture opening, to measure the extent of transverse asymmetry of split, and to illustrate the possibility of splitting the pterygopalatine suture.MethodsFifteen subjects (mean age of 17.2 years; range, 13.9-26.2 years) were treated with MSE. Pre- and post-treatment CBCT exams were taken and superimposed. A novel methodology based on three new reference planes was utilized to analyze the sutural changes. Parameters were compared from pre- to post-treatment and between genders non-parametrically using the Wilcoxon sign rank test. For the frequency of openings in the lower part of the pterygopalatine suture, the Fisher's exact test was used.ResultsRegarding the magnitude of midpalatal suture opening, the split at anterior nasal spine (ANS) and at posterior nasal spine (PNS) was 4.8 and 4.3 mm, respectively. The amount of split at PNS was 90% of that at ANS, showing that the opening of the midpalatal suture was almost perfectly parallel antero-posteriorly. On average, one half of the anterior nasal spine (ANS) moved more than the contralateral one by 1.1 mm. Openings between the lateral and medial plates of the pterygoid process were detectable in 53% of the sutures (P < 0.05). No significant differences were found in the magnitude and frequency of suture opening between males and females. Correlation between age and suture opening was negligible (R 2 range, 0.3-4.2%).ConclusionsMidpalatal suture was successfully split by MSE in late adolescents, and the opening was almost perfectly parallel in a sagittal direction. Regarding the extent of transverse asymmetry of the split, on average one half of ANS moved more than the contralateral one by 1.1 mm. Pterygopalatine suture was split in its lower region by MSE, as the pyramidal process was pulled out from the pterygoid process. Patient gender and age had a negligible influence on suture opening for the age group considered in the study

Criticality for the Gehring link problem

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality. Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with finite total curvature. The balance criterion also allows us to explicitly describe critical configurations (and presumed minimizers) for many links including the Borromean rings. We also exhibit a surprising critical configuration for two clasped ropes: near their tips the curvature is unbounded and a small gap appears between the two components. These examples reveal the depth and richness hidden in Gehring's problem and our natural extension.Comment: This is the version published by Geometry & Topology on 14 November 200

Feasibility of chest ultrasound up to 42 m underwater

After recent advancements, ultrasound has extended its applications from bedside clinical practice to wilderness medicine. Performing ultrasound scans in extreme environments can allow direct visualization of unique pathophysiological adaptations but can be technically challenging. This paper summarizes how a portable ultrasound apparatus was marinized to let scientific divers and sonographers perform ultrasound scans of the lungs underwater up to − 42 m. A metallic case protected the ultrasound apparatus inside; a frontal transparent panel with a glove allowed visualization and operation of the ultrasound by the diving sonographer. The inner pressure was equalized with environmental pressure through a compressed air tank connected with circuits similar to those used in SCUBA diving. Finally, the ultrasound probe exited the metallic case through a sealed aperture. No technical issues were reported after the first testing step and the real experiments

Comparing Signal Setting Design Methods through emissions and fuel consumption performance indicators

In order to address the Signal Setting Design at urban level two main approaches may be pursued: the coordination and the synchronisation approaches depending on the steps considered for the optimisation of decision variables (two steps vs. one step). Furthermore, in terms of objective functions mono-criterion or multi-criteria may be adopted. In this paper the coordination approach is implemented considering the multi-criteria optimisation at single junctions and mono-criterion optimisation at network level whereas the synchronisation is implemented considering the mono-criterion optimisation. The main purpose of the paper is the evaluation of the performances of two strategies not only considering indicators such as the total delay, the queue length etc. but also considering other indicators such as the emissions and the fuel consumption. The methodological framework is composed by three stages: (i) the decision variables (green timings and offsets) computation through optimisation methods; (ii) the implementation of optimal signal settings in a microscopic traffic flow simulator (“Simulation of Urban MObility”-SUMO); (iii) the estimation of emissions and fuel consumption indicators