Exact Solutions for Loewner Evolutions

In this note, we solve the Loewner equation in the upper half-plane with forcing function xi(t), for the cases in which xi(t) has a power-law dependence on time with powers 0, 1/2 and 1. In the first case the trace of singularities is a line perpendicular to the real axis. In the second case the trace of singularities can do three things. If xi(t)=2*(kappa*t)^1/2, the trace is a straight line set at an angle to the real axis. If xi(t)=2*(kappa*(1-t))^1/2, the behavior of the trace as t approaches 1 depends on the coefficient kappa. Our calculations give an explicit solution in which for kappa<4 the trace spirals into a point in the upper half-plane, while for kappa>4 it intersects the real axis. We also show that for kappa=9/2 the trace becomes a half-circle. The third case with forcing xi(t)=t gives a trace that moves outward to infinity, but stays within fixed distance from the real axis. We also solve explicitly a more general version of the evolution equation, in which xi(t) is a superposition of the values +1 and -1.Comment: 20 pages, 7 figures, LaTeX, one minor correction, and improved hyperref

Systemic risk approach to mitigate delay cascading in railway networks

In public railway systems, minor disruptions can trigger cascading events that lead to delays in the entire system. Typically, delays originate and propagate because the equipment is blocking ways, operational units are unavailable, or at the wrong place at the needed time. The specific understanding of the origins and processes involved in delay-spreading is still a challenge, even though large-scale simulations of national railway systems are becoming available on a highly detailed scale. Without this understanding, efficient management of delay propagation, a growing concern in some Western countries, will remain impossible. Here, we present a systemic risk-based approach to manage daily delay cascading on national scales. We compute the {\em systemic impact} of every train as the maximum of all delays it could possibly cause due to its interactions with other trains, infrastructure, and operational units. To compute it, we design an effective impact network where nodes are train services and links represent interactions that could cause delays. Our results are not only consistent with highly detailed and computationally intensive agent-based railway simulations but also allow us to pinpoint and identify the causes of delay cascades in detail. The systemic approach reveals structural weaknesses in railway systems whenever shared resources are involved. We use the systemic impact to optimally allocate additional shared resources to the system to reduce delays with minimal costs and effort. The method offers a practical and intuitive solution for delay management by optimizing the effective impact network through the introduction of new cheap local train services.Comment: 27 pages, 14 figure

Pentamidine Dosage: A Base/Salt Confusion

Pentamidine has a long history in the treatment of human African trypanosomiasis (HAT) and leishmaniasis. Early guidelines on the dosage of pentamidine were based on the base-moiety of the two different formulations available. Confusion on the dosage of pentamidine arose from a different labelling of the two available products, either based on the salt or base moiety available in the preparation. We provide an overview of the various guidelines concerning HAT and leishmaniasis over the past decades and show the confusion in the calculation of the dosage of pentamidine in these guidelines and the subsequent published reports on clinical trials and reviews. At present, only pentamidine isethionate is available, but the advised dosage for HAT and leishmaniasis is (historically) based on the amount of pentamidine base. In the treatment of leishmaniasis this is probably resulting in a subtherapeutic treatment. There is thus a need for a new, more transparent and concise guideline concerning the dosage of pentamidine, at least in the treatment of HAT and leishmaniasi

Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic Loewner evolution (SLE_kappa), one can consider observables related to nonlocal degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity beta = -2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models LM(p,p'). These theories describe lattice systems with nonlocal degrees of freedom. We present results for critical dense polymers LM(1,2), critical percolation LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising model LM(4,5) as well as LM(3,5). Our results are compared with rigourous results from SLE_kappa, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLE_kappa, geometric exponents and the conformal dimensions of the underlying CFTs.Comment: Added reference

Osteosarcoma of the mobile spine†

Background The aims of this analysis were to investigate features and outcome of high-grade osteosarcomas of the mobile spine. Patients and methods Since 1977, 20 Cooperative Osteosarcoma Study Group patients had a diagnosis of high-grade osteosarcomas of the mobile spine and were included in this retrospective analysis of patient-, tumor- and treatment-related variables and outcome. Results The median age was 29 years (range 5-58). Most frequent tumor sites were thoracic and lumbar spine. All but three patients had nonmetastatic disease at diagnosis. Treatment included surgery and chemotherapy for all patients, 13 were also irradiated. Eight patients failed to achieve a macroscopically complete surgical remission (five local, one primary metastases, two both), six died, two are alive, both with radiotherapy. Of 12 patients with complete remission at all sites, three had a recurrence (two local, one metastases) and died. The median follow-up of the 11 survivors was 8.7 years (range 3.1-22.3), 5-year overall and event-free survival rates were 60% and 43%. Age <40 years, nonmetastatic disease at diagnosis and complete remission predicted for better overall survival (OS, P < 0.05). Conclusions Osteosarcomas of the mobile spine are rare. With complete resection (and potentially radiotherapy) and chemotherapy, prognosis may be comparable with that of appendicular osteosarcoma

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The velocity of ~3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or non-instantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimisation of this feedback is elaborated for different control schemes and ranges of control parameters

Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow

We review modeling of astrocyte ion dynamics with a specific focus on the implications of so-called spatial potassium buffering, where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. We thus include the key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure

High-Grade Osteosarcoma of the Foot: Presentation, Treatment, Prognostic Factors, and Outcome of 23 Cooperative Osteosarcoma Study Group COSS Patients

Osteosarcoma of the foot is a very rare presentation of a rare tumor entity. In a retrospective analysis, we investigated tumor- and treatment-related variables and outcome of patients registered in the Cooperative Osteosarcoma Study Group (COSS) database between January 1980 and April 2016 who suffered from primary high-grade osteosarcoma of the foot. Among the 23 eligible patients, median age was 32 years (range: 6-58 years), 10 were female, and 13 were male. The tarsus was the most commonly affected site (n=16). Three patients had primary metastases. All patients were operated: 5 underwent primary surgery and 18 received surgery following preoperative chemotherapy. In 21 of the 23 patients, complete surgical remission was achieved. In 4 of 17 patients, a poor response to neoadjuvant chemotherapy was observed in the resected primary tumors. Median follow-up was 4.2 years (range: 0.4-18.5). At the last follow-up, 15 of the 23 patients were alive and 8 had died. Five-year overall and event-free survival estimates were 64% (standard error (SE) 12%) and 54% (SE 13%), which is similar to that observed for osteosarcoma in general. Event-free and overall survival correlated with primary metastatic status and completeness of surgery. Our findings show that high-grade osteosarcoma in the foot has a similar outcome as osteosarcoma of other sites

The influence of tumor- and treatment-related factors on the development of local recurrence in osteosarcoma after adequate surgery. An analysis of 1355 patients treated on neoadjuvant Cooperative Osteosarcoma Study Group protocols

Background: Local recurrence (LR) in osteosarcoma is associated with very poor prognosis. We sought to evaluate which factors correlate with LR in patients who achieved complete surgical remission with adequate margins. Patients and methods: We analyzed 1355 patients with previously untreated high-grade central osteosarcoma of the extremities, the shoulder and the pelvis registered in neoadjuvant Cooperative Osteosarcoma Study Group trials between 1986 and 2005. Seventy-six patients developed LR. Results: Median follow-up was 5.56 years. No participation in a study, pelvic tumor site, limb-sparing surgery, soft tissue infiltration beyond the periosteum, poor response to neoadjuvant chemotherapy, failure to complete the planned chemotherapy protocol and biopsy at a center other than the one performing the tumor resection were significantly associated with a higher LR rate. No differences were found for varying surgical margin widths. Surgical treatment at centers with small patient volume and additional surgery in the primary tumor area, other than biopsy and tumor resection, were significantly associated with a higher rate of ablative surgery. Conclusions: Patient enrollment in clinical trials and performing the biopsy at experienced institutions capable of undertaking the tumor resection without compromising the oncological and functional outcome should be pursued in the futur