Note on SLE and logarithmic CFT

It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable highest-weight module of the Virasoro algebra, the representation theory of the logarithmic conformal field theory is related to entities conserved in mean under the stochastic process.Comment: 10 pages, LaTeX, v2: version to be publishe

Transforming fixed-length self-avoiding walks into radial SLE_8/3

We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial SLE with kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and then apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial SLE. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial SLE, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values

Reactivity to human papillomavirus type 16 Ll virus-like particles in sera from patients with genital cancer and patients with carcinomas at five different extragenital sites

A retrospective seroepidemiologic study was performed to examine the association between human papillomaviruses (HPV) 16 infection and carcinomas of the oropharynx, the oesophagus, penis and vagina. Sera were selected from the serum bank from the Antoni van Leeuwenhoek Hospital (Netherlands Cancer Institute) and the Slotervaart Hospital in Amsterdam, the Netherlands. Presence of HPV 16 specific antibody was assessed using HPV 16 L1 capsids. Sera positive for HPV 16 capsid antibody were further tested for antibody against HPV 16 E7 peptides. Prevalence of antibody against H PV 16 L1 capsids among both the negative control group without cancer and the negative control group with gastric cancer was 18%, while seroprevalence among the control group of patients with HPV-associated cervical squamous cell carcinoma was 47% (P < 0.001). Among the patients with penile squamous cell carcinoma seroprevalence was 38% (P < 0.001), among patients with oropharyngeal carcinoma 33% (P = 0.04) and among patients with oesophageal squamous cell carcinoma 14% (P = 0.7). The serological evidence for association between HPV 16 infection and both oropharyngeal carcinoma and penile carcinoma was established. The conclusion that no association was found between the presence of antibody against HPV 16 L1 capsids and oesophageal squamous cell carcinoma was in accordance with results of other studies carried out in the Netherlands using HPV DNA technology. In the subjects with HPV 16 L1 capsid antibody, no association was found between the antibody against HPV 16 E7 and clinical outcome

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

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

LERW as an example of off-critical SLEs

Two dimensional loop erased random walk (LERW) is a random curve, whose continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter kappa=2. In this article we study ``off-critical loop erased random walks'', loop erasures of random walks penalized by their number of steps. On one hand we are able to identify counterparts for some LERW observables in terms of symplectic fermions (c=-2), thus making further steps towards a field theoretic description of LERWs. On the other hand, we show that it is possible to understand the Loewner driving function of the continuum limit of off-critical LERWs, thus providing an example of application of SLE-like techniques to models near their critical point. Such a description is bound to be quite complicated because outside the critical point one has a finite correlation length and therefore no conformal invariance. However, the example here shows the question need not be intractable. We will present the results with emphasis on general features that can be expected to be true in other off-critical models.Comment: 45 pages, 2 figure

A mathematical model of the metabolic and perfusion effects on cortical spreading depression

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarization, CSD also involves significant changes in perfusion and metabolism -- aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium--ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD -- vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization -- found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.Comment: 17 pages including 9 figures, accepted by PLoS On

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