Multifocality and recurrence risk: a quantitative model of field cancerization

Primary tumors often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical observations have suggested that these premalignant fields pose high risks for emergence of secondary recurrent tumors if left behind after surgical removal of the primary tumor. In this work, we develop a spatio-temporal stochastic model of epithelial carcinogenesis, combining cellular reproduction and death dynamics with a general framework for multi-stage genetic progression to cancer. Using this model, we investigate how macroscopic features (e.g. size and geometry of premalignant fields) depend on microscopic cellular properties of the tissue (e.g.\ tissue renewal rate, mutation rate, selection advantages conferred by genetic events leading to cancer, etc). We develop methods to characterize how clinically relevant quantities such as waiting time until emergence of second field tumors and recurrence risk after tumor resection. We also study the clonal relatedness of recurrent tumors to primary tumors, and analyze how these phenomena depend upon specific characteristics of the tissue and cancer type. This study contributes to a growing literature seeking to obtain a quantitative understanding of the spatial dynamics in cancer initiation.Comment: 36 pages, 11 figure

Triviality of the 2D stochastic Allen-Cahn equation

We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term

The cellular dynamics of bone remodeling: a mathematical model

The mechanical properties of vertebrate bone are largely determined by a process which involves the complex interplay of three different cell types. This process is called {\it bone remodeling}, and occurs asynchronously at multiple sites in the mature skeleton. The cells involved are bone resorbing osteoclasts, bone matrix producing osteoblasts and mechanosensing osteocytes. These cells communicate with each other by means of autocrine and paracrine signaling factors and operate in complex entities, the so-called bone multicellular units (BMU). To investigate the BMU dynamics in silico, we develop a novel mathematical model resulting in a system of nonlinear partial differential equations with time delays. The model describes the osteoblast and osteoclast populations together with the dynamics of the key messenger molecule RANKL and its decoy receptor OPG. Scaling theory is used to address parameter sensitivity and predict the emergence of pathological remodeling regimes. The model is studied numerically in one and two space dimensions using finite difference schemes in space and explicit delay equation solvers in time. The computational results are in agreement with in vivo observations and provide new insights into the role of the RANKL/OPG pathway in the spatial regulation of bone remodeling

A model of transport nonuniversality in thick-film resistors

We propose a model of transport in thick-film resistors which naturally explains the observed nonuniversal values of the conductance exponent t extracted in the vicinity of the percolation transition. Essential ingredients of the model are the segregated microstructure typical of thick-film resistors and tunneling between the conducting grains. Nonuniversality sets in as consequence of wide distribution of interparticle tunneling distances.Comment: 3 pages, 1 figur

Expanding Cities – Diminishing Space: Will Cities Remain Liveable, Accessible, Human-Oriented Places: for Whom and How?

The CORP 2018 brief of 'Expanding Cities – Diminishing Space' rests on the unassailable credo in techno-fixes. The argument here is that while technologies have always influenced urban change, cities have evolved with techno-fixes in combination with many other development processes. As evidence shows that with globalisation development has become more unevenly distributed in urban space what matters is whether techno-fixes are contributing or alleviating uneven spatial and social justice and urban quality of life

Changing Cities – Changing Minds

Long established planning practices are hard to overcome. Top down control mechanisms remain in place with little devolution and self-determination. In many countries ministers can overrule elected regions and municipalities and governments continue to hold the purse strings, invoking national interest to legitimise their reserve powers. Although conventional wisdom claims that cities are the drivers of future prosperity, many city dwellers undergo precarious employment, expensive commuting, overpriced housing, congestion, pollution and erosion of the public realm, undermining their quality of life. Disillusioned by party politics, some are turning to alternatives. Out of necessity, a parallel universe is emerging in urban areas, also in the developed world, relying on own resources and contributing creatively to a 'vibrant city'. Yet, activists may become the victims of their own success when the developing industry reaps the benefits of their efforts, not seldom acquiesced by planning. The motivation of this paper is not just a 'vibrant city' but a more equitable and inclusive city. It draws on twelve cities in north-west Europe where dynamic stakeholders are realising their aspirations by reinventing planning in cooperation with bottom-up forces

Panta Rhei? What about When Movements Come to a Halt?

Panta rhei means 'everything in perpetual motion'. This may be true for the cosmos but on planet earth movement of people cohabits with staying put. Even nomads –historic and contemporary – alternative between movement and temporary station. Movement in cities is interdependent with arriving, staying put, or moving from one travel mode or one place to another. Normally, movements of people have a purpose of arriving. There exists therefore interdependence between flows and nodes to use Manuel Castells concepts. All types of movements of people on planet earth require man made infrastructure for the flows as well as for the nodes, regardless of mode of movement. The paper concentrates on urban dynamics related to railway infrastructure and selected railway stations in London. It argues that railway privatisation shifted the emphasis from flows to nodes, as privatised railway land and stations had greater development potential than still quasi publically owned and run railway tracks. This shift could have provided an opportunity for greater integration between transportation and land use planning, long an aspiration but more rarely implemented in practice. The corporate separation between railtracks and other key rail functions like running trains and stations may well have constituted a hindrance to such integration, except at interchanges, where flows meet nodes. Since the revival of rail travel in the UK railway stations and their surroundings became the place for massive regeneration projects. In particular, stations were transformed from mere spaces of connection betweeen people travelling and using the city into places in their own right, parts of urban fabric with urban functions other than sheer interchanges between modes of movements. They were accommoding urban activities such as commerce and entertainment for people to linger, stay and use. They and their surroundings had become a destination in their own right. How do these destinations compare with other urban places? Examples of station development are discussed by comparing their different approaches with special attention to their function as railway stations and their surroundings as public realm. The paper critically examines the impact of privatised railway strategies on station regeneration, the local environment surrounding them including land grab and, in particular, the sustainability or otherwise of the redesigned public realm, the 'relique pacificae' to 'panta rhei' as key to urbanity