Delayed switching identities and multi-marginal solutions to the Skorokhod embedding problem

In this article, we consider a generalisation of the Skorokhod embedding problem (SEP) with a delayed starting time. In the delayed SEP, we look for stopping times which embed a given measure in a stochastic process, which occur after a given delay time. Our first contribution is to show that the switching identities introduced in a recent paper of Backhoff, Cox, Grass and Huesmann extend to the case with a delay. We then show that the delayed switching identities can be used to establish an optimal stopping representation of Root and Rost solutions to the multi-marginal Skorokhod embedding problem. We achieve this by rephrasing the multi-period problem into a one-period framework with delay. This not only recovers the known multi-marginal representation of Root, but also establishes a previously unknown optimal stopping representation associated to the multi-marginal Rost solution. The Rost case is more complex than the Root case since it naturally requires randomisation for general initial measures, and we develop the necessary tools to develop these solutions. Our work also provides a comprehensive and complete treatment of discrete Root and Rost solutions, embedding discrete measures into simple symmetric random walks

The mathematics of ageing:

Age is a crucial variable in social sciences and particularly in population dynamics. In this paper, we link methods from formal demography and Operations Research to investigate age-structured models to study the greying of academia. As scientific productivity is usually found to decrease at advanced ages, there was a vivid discussion on the ageing among tenured professors and faculty staff of universities. We investigate population ageing in academia from two perspectives. First, we propose a two-state optimal control model to explain the substantial variations of scientific production over the life cycle of researchers. We identify conditions under which typical hump-shaped age-specific patterns of scientific production turn out to be optimal for individual researchers. The second part of the paper deals with the dynamics of the age structure of scientific institutions. Similar to the university professors, many European learned societies experienced a rapid ageing of their member population, where they face the dilemma that keeping young, i.e. electing young entrants, has the drawback of reducing the replacement rate of members. It turns out that electing a mix of young and old members delivers the optimal solution of the problem, i.e. guaranteeing a young age structure, while ensuring a high recruitment rate

On the Matthew effect on Individual Investments into Skills in Arts, Sports and Science

The paper describes the process of capital accumulation subject to the following characteristics: (i) convex returns to (human) capital; (ii) the need to self _nance the investment. This set up is applicable to explain some peculiarities in arts, sports and science, inter alia, the \Matthew effect" coined in Merton (1968) to explain why prominent researchers get disproportional credit for their work. The potential young artist's (or sportsman's or even scientist's) optimal strategies include quitting, or continuing and even expanding one's human capital in a profession. Both outcomes are separated by a threshold level in human capital. In addition, it can be optimal to stay in business although consumption falls and stays at the subsistence level (we call this outcome a \Sisyphus point")

Current Opinion and Knowledge on Peritoneal Carcinomatosis: A Survey among a Swiss Oncology Network.

The present survey aimed to evaluate current opinion and practice regarding peritoneal metastasis (PM), satisfaction with available treatment options, and need for new therapeutic approaches. This was a qualitative study conducted between October 2016 and October 2017 in the Réseau Suisse Romand d'Oncologie including 101 members of various oncological specialties. Participants' demographics, current practice, knowledge, and satisfaction regarding available treatment options and need for new treatment options were assessed by semantic differential scales through 33 closed questions with automatic reminders at 4-, 8-, 12-, and 16-week intervals. Twenty-seven participants (27%) completed the survey. Participants were gastrointestinal or gynecologic oncologists and surgeons. Most participants (67%) evaluated their knowledge on PM as moderate, while 22% considered themselves as experts. Clinical usefulness of systemic chemotherapy and hyperthermic intraperitoneal chemotherapy was judged to be moderate to high for PM of ovarian and colorectal origin and moderate to poor for gastric origin. Satisfaction with available treatment options was 6/10 (interquartile range [IQR] 4-7) for ovarian, 5/10 (IQR 3-7) for colorectal, and 3/10 (IQR 1-3) for gastric PM. Treatment strategies varied widely for typical case vignettes. The need for new treatment modalities was rated as 8/10 (IQR 6-10). Usefulness of and satisfaction with available treatment options for PM were rated as moderate at best by oncological experts, and treatment strategies differed importantly among participants. There appears to be a clear need for standardization and new treatment modalities

Pressurised intraperitoneal aerosol chemotherapy: rationale, evidence, and potential indications.

Pressurised intraperitoneal aerosol chemotherapy (PIPAC) was introduced as a new treatment for patients with peritoneal metastases in November, 2011. Reports of its feasibility, tolerance, and efficacy have encouraged centres worldwide to adopt PIPAC as a novel drug delivery technique. In this Review, we detail the technique and rationale of PIPAC and critically assess its evidence and potential indications. A systematic search was done to identify all relevant literature on PIPAC published between Jan 1, 2011, and Jan 31, 2019. A total of 106 articles or reports on PIPAC were identified, and 45 clinical studies on 1810 PIPAC procedures in 838 patients were included for analysis. Repeated PIPAC delivery was feasible in 64% of patients with few intraoperative and postoperative surgical complications (3% for each in prospective studies). Adverse events (Common Terminology Criteria for Adverse Events greater than grade 2) occurred after 12-15% of procedures, and commonly included bowel obstruction, bleeding, and abdominal pain. Repeated PIPAC did not have a negative effect on quality of life. Using PIPAC, an objective clinical response of 62-88% was reported for patients with ovarian cancer (median survival of 11-14 months), 50-91% for gastric cancer (median survival of 8-15 months), 71-86% for colorectal cancer (median survival of 16 months), and 67-75% (median survival of 27 months) for peritoneal mesothelioma. From our findings, PIPAC has been shown to be feasible and safe. Data on objective response and quality of life were encouraging. Therefore, PIPAC can be considered as a treatment option for refractory, isolated peritoneal metastasis of various origins. However, its use in further indications needs to be validated by prospective studies

A Dissipative-Particle-Dynamics Model for Simulating Dynamics of Charged Colloid

A mesoscopic colloid model is developed in which a spherical colloid is represented by many interacting sites on its surface. The hydrodynamic interactions with thermal fluctuations are taken accounts in full using Dissipative Particle Dynamics, and the electrostatic interactions are simulated using Particle-Particle-Particle Mesh method. This new model is applied to investigate the electrophoretic mobility of a charged colloid under an external electric field, and the influence of salt concentration and colloid charge are systematically studied. The simulation results show good agreement with predictions from the electrokinetic theory.Comment: 17 pages, 8 figures, submitted to the proceedings of High Performance Computing in Science & Engineering '1

Optimizing end-labeled free-solution electrophoresis by increasing the hydrodynamic friction of the drag-tag

We study the electrophoretic separation of polyelectrolytes of varying lengths by means of end-labeled free-solution electrophoresis (ELFSE). A coarse-grained molecular dynamics simulation model, using full electrostatic interactions and a mesoscopic Lattice Boltzmann fluid to account for hydrodynamic interactions, is used to characterize the drag coefficients of different label types: linear and branched polymeric labels, as well as transiently bound micelles. It is specifically shown that the label's drag coefficient is determined by its hydrodynamic size, and that the drag per label monomer is largest for linear labels. However, the addition of side chains to a linear label offers the possibility to increase the hydrodynamic size, and therefore the label efficiency, without having to increase the linear length of the label, thereby simplifying synthesis. The third class of labels investigated, transiently bound micelles, seems very promising for the usage in ELFSE, as they provide a significant higher hydrodynamic drag than the other label types. The results are compared to theoretical predictions, and we investigate how the efficiency of the ELFSE method can be improved by using smartly designed drag-tags.Comment: 32 pages, 11 figures, submitted to Macromolecule

On the matthew effect on individual investments in skills in arts, sports and science

This paper describes the process of capital accumulation subject to the following characteristics: (i) convex returns to (human) capital and (ii) the need to self-finance investments. Our setup is applicable to some peculiarities in the arts, sports and science, inter alia, coined the Matthew effect in Merton (1968) and explains, e.g., why prominent researchers get disproportional credit for their work. The potential young artist’s (athlete’s or scientist’s) optimal strategies include quitting, or continuing and even expanding one’s human capital in the respective profession. Both outcomes are separated by a threshold level in human capital. In addition, we find that it can be optimal to stay in business although consumption falls and stays at the subsistence level forever (we call this outcome a Sisyphus point). This possibility is also interesting from a theoretical point-of-view, as the optimal control problem may turn abnormal, i.e., the objective does not enter the Hamiltonian

Self-similarity of Mean Flow in Pipe Turbulence

Based on our previous modified log-wake law in turbulent pipe ‡flows, we invent two compound similarity numbers (Y;U), where Y is a combination of the inner variable y+ and outer variable , and U is the pure exect of the wall. The two similarity numbers can well collapse mean velocity profile data with different moderate and large Reynolds numbers into a single universal profile. We then propose an arctangent law for the buffer layer and a general log law for the outer region in terms of (Y;U). From Milikan’s maximum velocity law and the Princeton superpipe data, we derive the von Kármán constant = 0:43 and the additive constant B=6. Using an asymptotic matching method, we obtain a self-similarity law that describes the mean velocity profile from the wall to axis; and embeds the linear law in the viscous sublayer, the quartic law in the bursting sublayer, the classic log law in the overlap, the sine-square wake law in the wake layer, and the parabolic law near the pipe axis. The proposed arctangent law, the general log law and the self-similarity law have been compared with the high-quality data sets, with diffrent Reynolds numbers, including those from the Princeton superpipe, Loulou et al., Durst et al., Perry et al., and den Toonder and Nieuwstadt. Finally, as an application of the proposed laws, we improve the McKeon et al. method for Pitot probe displacement correction, which can be used to correct the widely used Zagarola and Smits data set