Comparison of Shape Derivatives Using CutFEM for Ill-posed Bernoulli Free Boundary Problem

In this paper we study and compare three types of shape derivatives for free boundary identification problems. The problem takes the form of a severely ill-posed Bernoulli problem where only the Dirichlet condition is given on the free (unknown) boundary, whereas both Dirichlet and Neumann conditions are available on the fixed (known) boundary. Our framework resembles the classical shape optimization method in which a shape dependent cost functional is minimized among the set of admissible domains. The position of the domain is defined implicitly by the level set function. The steepest descent method, based on the shape derivative, is applied for the level set evolution. For the numerical computation of the gradient, we apply the Cut Finite Element Method (CutFEM), that circumvents meshing and re-meshing, without loss of accuracy in the approximations of the involving partial differential models. We consider three different shape derivatives. The first one is the classical shape derivative based on the cost functional with pde constraints defined on the continuous level. The second shape derivative is similar but using a discretized cost functional that allows for the embedding of CutFEM formulations directly in the formulation. Different from the first two methods, the third shape derivative is based on a discrete formulation where perturbations of the domain are built into the variational formulation on the unperturbed domain. This is realized by using the so-called boundary value correction method that was originally introduced to allow for high order approximations to be realized using low order approximation of the domain. The theoretical discussion is illustrated with a series of numerical examples showing that all three approaches produce similar result on the proposed Bernoulli problem

Predictors of total morbidity burden on days 3, 5 and 8 after cardiac surgery.

BACKGROUND: Post-operative morbidity affects up to 36% of cardiac surgical patients. However, few countries reliably record morbidity outcome data, despite patients wanting to be informed of all the risks associated with surgery. The Cardiac Post-Operative Morbidity Score (C-POMS) is a new tool for describing and scoring (0-13) total morbidity burden after cardiac surgery, derived by noting the presence/absence of 13 morbidity domains on days 3, 5, 8 and 15. Identifying modifiable C-POMS risk factors may suggest targets for intervention to reduce morbidity and healthcare costs. Thus, we explored the association of C-POMS with previously identified predictors of post-operative morbidity. METHODS: A systematic literature review of pre-operative risk assessment models for post-operative morbidity was conducted to identify variables associated with post-operative morbidity. The association of those variables with C-POMS was explored in patients drawn from the original C-POMS study (n = 444). RESULTS: Seventy risk factors were identified, of which 56 were available in the study and 49 were suitable for analysis. Numbers were too few to analyse associations on D15. Thirty-three (67.3%) and 20 (40.8%) variables were associated with C-POMS on at least 1 or 2 days, respectively. Pre-operative albumin concentration, left ventricular ejection fraction and New York Heart Association functional class were associated with C-POMS on all days. Of the 16 independent risk factors, pre-operative albumin and haemoglobin concentrations and weight are potentially modifiable. CONCLUSIONS: Different risk factors are associated with total morbidity burden on different post-operative days. Pre-operative albumin and haemoglobin concentrations and weight were independently predictive of post-operative total morbidity burden suggesting therapeutic interventions aimed at these might reduce both post-operative morbidity risk and health-care costs in patients undergoing cardiac surgery

Kinship underlies costly cooperation in Mosuo villages

The relative importance of social evolution theories such as kin selection, direct reciprocity and need-based transfers in explaining real-world cooperation is the source of much debate. Previous field studies of cooperation in human communities have revealed variability in the extent to which each of these theories explains human sociality in different contexts. We conducted multivariate social network analyses predicting costly cooperation-labouring on another household's farm-in 128 082 dyads of Mosuo farming households in southwest China. Through information-theoretic model selection, we tested the roles played by genealogical relatedness, affinal relationships (including reproductive partners), reciprocity, relative need, wealth, household size, spatial proximity and gift-giving in an economic game. The best-fitting model included all factors, along with interactions between relatedness and (i) reciprocity, (ii) need, (iii) the presence of own children in another household and (iv) proximity. Our results show how a real-world form of cooperation was driven by kinship. Households tended to help kin in need (but not needy non-kin) and travel further to help spatially distant relatives. Households were more likely to establish reciprocal relationships with distant relatives and non-kin but closer kin cooperated regardless of reciprocity. These patterns of kin-driven cooperation show the importance of inclusive fitness in understanding human social behaviour

Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample Breakdown Point, we propose the Expected Finite Sample Breakdown Point to produce less configuration-dependent values while still preserving the finite sample aspect of the former definition. We apply this notion for joint estimation of scale and shape (with only scale-equivariance available), exemplified for generalized Pareto, generalized extreme value, Weibull, and Gamma distributions. In these settings, we are interested in highly-robust, easy-to-compute initial estimators; to this end we study Pickands-type and Location-Dispersion-type estimators and compute their respective breakdown points.Comment: 21 pages, 4 figure

Herschel Hi-GAL imaging of massive young stellar objects

We used Herschel Hi-GAL (Herschel infrared Galactic Plane survey) data to determine whether massive young stellar objects (MYSOs) are resolved at 70 μm and to study their envelope density distribution. Our analysis of three relatively isolated sources in the l = 30° and 59° Galactic fields show that the objects are partially resolved at 70 μm. The Herschel Hi-GAL survey data have a high scan velocity which makes unresolved and partially resolved sources appear elongated in the 70 μm images. We analysed the two scan directions separately and examine the intensity profile perpendicular to the scan direction. Spherically symmetric radiative transfer models with a power-law density distribution were used to study the circumstellar matter distribution. Single dish submm data were also included to study how different spatial information affects the fitted density distribution. The density distribution which best fits both the 70 μm intensity profile and spectral energy distribution has an average index of ∼0.5. This index is shallower than expected and is probably due to the dust emission from bipolar outflow cavity walls not accounted for in the spherical models. We conclude that 2D axisymmetric models and Herschel images at low scan speeds are needed to better constrain the matter distribution around MYSOs

Water quality impacts and river system recovery following the 2014 Mount Polley mine tailings dam spill, British Columbia, Canada

The Mount Polley mine tailings embankment breach on August 4th 2014, in British Columbia, Canada, is the second largest mine waste spill on record. The mine operator responded swiftly by removing significant quantities of tailings from the primary receiving watercourse, stabilizing the river corridor and beginning construction of a new river channel. This presented a unique opportunity to study spatial patterns of element cycling in a partially-restored and alkaline river system. Overall, water quality impacts are considered low with Cu, and to a lesser extent V, being the only elements of concern. However, the spatial pattern of stream Cu loading suggested chemical (dominant at low flow) and physical (dominant at high flow) mobilization processes operating in different parts of the watershed. Chemical mobilization was hypothesized to be due to Cu sulfide (chalcopyrite) oxidation in riparian tailings and reductive dissolution of Cu-bearing Fe oxides in tailings and streambed sediments whereas physical mobilization was due to erosion and suspension of Cu-rich stream sediments further downstream. Although elevated aqueous Cu was evident in Hazeltine Creek, this is considered a relatively minor perturbation to a watershed with naturally elevated stream Cu concentrations. The alkaline nature of the tailings and the receiving watercourse ensures most aqueous Cu is rapidly complexed with dissolved organic matter or precipitates as secondary mineral phases. Our data highlights how swift removal of spilled tailings and river corridor stabilization can limit chemical impacts in affected watersheds but also how chemical mobilization (of Cu) can still occur when the spilled tailings and the receiving environment are alkaline. We present a conceptual model of Cu cycling in the Hazeltine Creek watershed

Large-Scale Sleep Condition Analysis Using Selfies from Social Media

Sleep condition is closely related to an individual's health. Poor sleep conditions such as sleep disorder and sleep deprivation affect one's daily performance, and may also cause many chronic diseases. Many efforts have been devoted to monitoring people's sleep conditions. However, traditional methodologies require sophisticated equipment and consume a significant amount of time. In this paper, we attempt to develop a novel way to predict individual's sleep condition via scrutinizing facial cues as doctors would. Rather than measuring the sleep condition directly, we measure the sleep-deprived fatigue which indirectly reflects the sleep condition. Our method can predict a sleep-deprived fatigue rate based on a selfie provided by a subject. This rate is used to indicate the sleep condition. To gain deeper insights of human sleep conditions, we collected around 100,000 faces from selfies posted on Twitter and Instagram, and identified their age, gender, and race using automatic algorithms. Next, we investigated the sleep condition distributions with respect to age, gender, and race. Our study suggests among the age groups, fatigue percentage of the 0-20 youth and adolescent group is the highest, implying that poor sleep condition is more prevalent in this age group. For gender, the fatigue percentage of females is higher than that of males, implying that more females are suffering from sleep issues than males. Among ethnic groups, the fatigue percentage in Caucasian is the highest followed by Asian and African American.Comment: 2017 International Conference on Social Computing, Behavioral-Cultural Modeling, & Prediction and Behavior Representation in Modeling and Simulation (SBP-BRiMS'17

A network-based dynamical ranking system for competitive sports

From the viewpoint of networks, a ranking system for players or teams in sports is equivalent to a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based ranking systems are derived from static networks, i.e., aggregation of the results of games over time. However, the score of a player (or team) fluctuates over time. Defeating a renowned player in the peak performance is intuitively more rewarding than defeating the same player in other periods. To account for this factor, we propose a dynamic variant of such a network-based ranking system and apply it to professional men's tennis data. We derive a set of linear online update equations for the score of each player. The proposed ranking system predicts the outcome of the future games with a higher accuracy than the static counterparts.Comment: 6 figure

Bone mineral content after renal transplantation

Forearm bone mineral content (BMC), as evaluated by photonabsorption densitometry, was measured in 28 cadaver kidney donor recipients who entered the study 8 weeks postoperatively and were followed up for 18 months. BMC decreased signifiantly (p<0.05) but marginally in placebo-treated patients (n=14) (initial BMC 1.09±0.25 g/cm; final BMC 1.05±0.24). Fourteen patients were prophylactically given 1,25(OH)2vitamin D3 in a dose which avoided hypercalcemia and hypercalciuria (sim0.25 µg/day); under 1,25(OH)2 vitamin D3 prophylaxis a significant decrease of forearm BMC was observed no longer (initial BMC 0.94±0.21 g/cm; final BMC 0.95±0.21), but the difference between placebo and 1,25(OH)2 vitamin D3 narrowly missed statistical significance (p=0.066). It is concluded that the decrease of forearm BMC is negligible in transplant recipients with low steroid regimens. The data suggest a trend for prophylaxis with 1,25(OH)2 vitamin D3 to slightly ameliorate forearm (cortical) BMC loss