2D pattern evolution constrained by complex network dynamics

Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, lesser attention has been focused on hybrid systems, \textit{i.e.} involving more than one type of network and/or dynamics. Because several real systems present such an organization (\textit{e.g.} the dynamics of a disease coexisting with the dynamics of the immune system), it becomes important to address such hybrid systems. The current paper investigates a specific system involving a diffusive (linear and non-linear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models, whose nodes can be displaced spatially. More specifically, the complex network is expected to control, and if possible to extinguish, the diffusion of some given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray-Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the spreading. The main findings include the identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome

The prognostic value of tumor mitotic rate in children and adolescents with cutaneous melanoma:A retrospective cohort study

Background: Mitotic rate is a strong predictor of outcome in adult patients with primary cutaneous melanoma, but for children and adolescent patients this is unknown. Objective: We sought to assess the prognostic value of primary tumor mitotic rate in children and adolescents with primary melanoma. Methods: This was a cohort study of 156 patients who were <20 years of age and who had clinically localized cutaneous melanoma. Patients <12 years of age were classified as children and those 12 to 19 years of age as adolescents. Clinicopathologic and outcome data were collected. Recurrence-free and melanoma-specific survival were calculated. Univariable and multivariable analyses were performed using Cox proportional hazard models. Results: Thirteen of 156 patients (8%) were children. The mitotic rate was ≥1/mm2 in 104 patients (67%) and correlated with increasing Breslow thickness. A positive sentinel node was found in 23 of 61 patients (38%) in whom a sentinel lymph node biopsy specimen was obtained. The median follow-up was 61 months. Five-year melanoma-specific and recurrence-free survival rates were 91% and 84%, respectively. Mitotic rate was a stronger predictor of outcome than tumor thickness and was the only factor independently associated with recurrence-free survival. Limitations: This research was conducted at a single institution and the sample size was small. Conclusion: Mitotic rate is an independent predictor of recurrence-free survival in children and adolescents with clinically localized melanoma

Preface

Preface - The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013

Rendering an Account: An Open-State Archive in Postgraduate Supervision

The paper begins with a brief account of the transformation of research degree studies under the pressures of global capitalism and neo-liberal governmentality. A parallel transformation is occurring in the conduct of research through the use of information and communication technologies. Yet the potential of ICTs to shape practices of surveillance or to produce new student-supervisor relations and enhance the processes of developing the dissertation has received almost no critical attention. As doctoral supervisor and student, we then describe the features and uses of a web-based open state archive of the student's work-in-progress, developed by the student and accessible to his supervisor. Our intention was to encourage more open conversations between data and theorising, student and supervisor, and ultimately between the student and professional community. However, we recognise that relations of accountability, as these have developed within a contemporary "audit revolution" (Power, 1994, 1997) in universities, create particular "lines of visibility" (Munro, 1996). Thus while the open-state archive may help to redefine in less managerial terms notions of quality, transparency, flexibility and accountability, it might also make possible greater supervisory surveillance. How should we think about the panoptical potential of this archive? We argue that the diverse kinds of interactional patterns and pedagogical intervention it encourages help to create shifting subjectivities. Moreover, the archive itself is multiple, in bringing together an array of diverse materials that can be read in various ways, by following multiple paths. It therefore constitutes a collage, which we identify as a mode of cognition and of accounting distinct from but related to argument and narrative. As a more "open" text (Iser, 1978) it has an indeterminacy which may render it less open to abuse for the technologies of managerial accountability

Lookback option pricing using the Fourier transform B-spline method

We derive a new, efficient closed-form formula approximating the price of discrete lookback options, whose underlying asset price is driven by an exponential semimartingale process, which includes (jump) diffusions, Lévy models, affine processes and other models. The derivation of our pricing formula is based on inverting the Fourier transform using B-spline approximation theory. We give an error bound for our formula and establish its fast rate of convergence to the true price. Our method provides lookback option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods. We provide an alternative proof to the Spitzer formula for the characteristic function of the maximum of a discretely observed stochastic process, which yields a numerically efficient algorithm based on convolutions. This is an important result which could have a wide range of applications in which the Spitzer formula is utilized. We illustrate the numerical efficiency of our algorithm by applying it in pricing fixed and floating discrete lookback options under Brownian motion, jump diffusion models, and the variance gamma process

Concise Reporting of Benign Endometrial Biopsies is an Acceptable Alternative to Descriptive Reporting

In the United Kingdom, endometrial biopsy reports traditionally consist of a morphologic description followed by a conclusion. Recently published consensus guidelines for reporting benign endometrial biopsies advocate the use of standardized terminology. In this project we aimed to assess the acceptability and benefits of this simplified "diagnosis only" format for reporting non-neoplastic endometrial biopsies. Two consultants reported consecutive endometrial biopsies using 1 of 3 possible formats: (i) diagnosis only, (ii) diagnosis plus an accompanying comment, and (iii) the traditional descriptive format. Service users were asked to provide feedback on this approach via an anonymized online survey. The reproducibility of this system was assessed on a set of 53 endometrial biopsies among consultants and senior histopathology trainees. Of 370 consecutive benign endometrial biopsies, 245 (66%) were reported as diagnosis only, 101 (27%) as diagnosis plus a brief comment, and 24 (7%) as diagnosis following a morphologic description. Of the 43 survey respondents (28 gynecologists, 11 pathologists, and 4 clinical nurse specialists), 40 (93%) preferred a diagnosis only, with 3 (7%) being against/uncertain about a diagnosis only report. Among 3 histopathology consultants and 4 senior trainees there was majority agreement on the reporting format in 53/53 (100%) and 52/53 (98%) biopsies. In summary, we found that reporting benign specimens within standardized, well-understood diagnostic categories is an acceptable alternative to traditional descriptive reporting, with the latter reserved for the minority of cases that do not fit into specific categories. This revised approach has the potential to improve reporting uniformity and reproducibility

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

A finite difference method for pricing European and American options under a geometric Lévy process

In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process