Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise

We present new numerical schemes to integrate stochastic partial differential equations which describe the spatio-temporal dynamics of reaction-diffusion (RD) problems under the effect of internal fluctuations. The schemes conserve the nonnegativity of the solutions and incorporate the Poissonian nature of internal fluctuations at small densities, their performance being limited by the level of approximation of density fluctuations at small scales. We apply the new schemes to two different aspects of the Reggeon model namely, the study of its non-equilibrium phase transition and the dynamics of fluctuating pulled fronts. In the latter case, our approach allows to reproduce quantitatively for the first time microscopic properties within the continuum model.Comment: 5 pages, 3 figures, Accepted for publication in Physical Review E as a Rapid Communicatio

Stable transfection of protein kinase C alpha cDNA in hormone-dependent breast cancer cell lines

An inverse relationship between protein kinase C (PKC) activity and oestrogen receptor (ER) expression in human breast cell lines and tumours has been firmly established over the past 10 years. To determine whether specific alterations in PKC expression accompany hormone-independence, we examined the expression of PKC isozymes in the hormone-independent human breast cancer cell clones MCF-7 5C and T47D:C42 compared with their hormone-dependent counterparts, MCF-7 A4, MCF-7 WS8 and T47D:A18 respectively. Both hormone-independent cell clones exhibit elevated PKCα expression and increased basal AP-1 activity compared with the hormone-dependent cell clones. To determine whether PKCα overexpression is sufficient to mediate the hormone-independent phenotype, we stably transfected an expression plasmid containing PKCα cDNA to the T47D:A18 and MCF-7 A4 cell lines. This is the first report of PKCα transfection in T47D cells. In contrast to MCF-7 cells, T47D has the propensity to lose the ER and more readily forms tamoxifen-stimulated tumours in athymic mice. We find that in T47D:A18/PKCα clones, there is concomitant up-regulation of PKC βI and δ, whereas in the MCF-7 A4/PKCα transfectants PKC ɛ is up-regulated. In T47D:A18, but not in MCF-7 A4, PKCα stable transfection is accompanied by down-regulation of ER function whilst basal AP-1 activity is elevated. Our results suggest PKCα overexpression may play a role in growth signalling during the shift from hormone dependent to hormone-independent breast cancers. © 2000 Cancer Research Campaig

Ad Hoc Hypotheses and the Monsters within

Science is increasingly becoming automated. Tasks yet to be fully automated include the conjecturing, modifying, extending and testing of hypotheses. At present scientists have an array of methods to help them carry out those tasks. These range from the well-articulated, formal and unexceptional rules to the semi-articulated and variously understood rules-of-thumb and intuitive hunches. If we are to hand over at least some of the aforementioned tasks to machines, we need to clarify, refine and make formal, not to mention computable, even the more obscure of the methods scientists successfully employ in their inquiries. The focus of this essay is one such less-than-transparent methodological rule. I am here referring to the rule that ad hoc hypotheses ought to be spurned. This essay begins with a brief examination of some notable conceptions of ad hoc-ness in the philosophical literature. It is pointed out that there is a general problem afflicting most such conceptions, namely the intuitive judgments that are supposed to motivate them are not universally shared. Instead of getting bogged down in what ad hoc-ness exactly means, I shift the focus of the analysis to one undesirable feature often present in alleged cases of ad hoc-ness. I call this feature the ‘monstrousness’ of a hypothesis. A fully articulated formal account of this feature is presented by specifying what it is about the internal constitution of a hypothesis that makes it monstrous. Using this account, a monstrousness measure is then proposed and somewhat sketchily compared with the minimum description length approach

What’s so bad about scientism?

In their attempt to defend philosophy from accusations of uselessness made by prominent scientists, such as Stephen Hawking, some philosophers respond with the charge of ‘scientism.’ This charge makes endorsing a scientistic stance, a mistake by definition. For this reason, it begs the question against these critics of philosophy, or anyone who is inclined to endorse a scientistic stance, and turns the scientism debate into a verbal dispute. In this paper, I propose a different definition of scientism, and thus a new way of looking at the scientism debate. Those philosophers who seek to defend philosophy against accusations of uselessness would do philosophy a much better service, I submit, if they were to engage with the definition of scientism put forth in this paper, rather than simply make it analytic that scientism is a mistake

Extensional flow of hyaluronic acid solutions in an optimized micofluidic cross-slot device

We utilize a recently developed microfluidic device, the Optimized Shape Cross-slot Extensional Rheometer (OSCER), to study the elongational flow behavior and rheological properties of hyaluronic acid (HA) solutions representative of the synovial fluid (SF) found in the knee joint. The OSCER geometry is a stagnation point device that imposes a planar extensional flow with a homogenous extension rate over a significant length of the inlet and outlet channel axes. Due to the compressive nature of the flow generated along the inlet channels, and the planar elongational flow along the outlet channels, the flow field in the OSCER device can also be considered as representative of the flow field that arises between compressing articular cartilage layers of the knee joints during running or jumping movements. Full-field birefringence microscopy measurements demonstrate a high degree of localized macromolecular orientation along streamlines passing close to the stagnation point of the OSCER device, while micro-particle image velocimetry is used to quantify the flow kinematics. The stress-optical rule is used to assess the local extensional viscosity in the elongating fluid elements as a function of the measured deformation rate. The large limiting values of the dimensionless Trouton ratio, Tr ∼ O(50), demonstrate that these fluids are highly extensional-thickening, providing a clear mechanism for the load-dampening properties of SF. The results also indicate the potential for utilizing the OSCER in screening of physiological SF samples, which will lead to improved understanding of, and therapies for, disease progression in arthritis sufferers

Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations

In this paper, the Euler–Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE

Obesity: A Biobehavioral Point of View

Excerpt: If you ask an overweight person, “Why are you fat?’, you will, almost invariably, get the answer, “Because 1 eat too much.” You will get this answer in spite of the fact that of thirteen studies, six find no significant differences in the caloric intake of obese versus nonobese subjects, five report that the obese eat significantly less than the nonobese, and only two report that they eat significantly more

On Abduction in Design

The mechanism of design reasoning from function to form is addressed by examining the possibility of explaining it as abduction. We propose a new interpretation to some definitions of innovative abduction, to show first that the concept, idea, as the basis for solution must be present in the inference, and second, that the reasoning from function to form is best modeled as a two-step inference, both of the innovative abduction pattern. This double-abductive reasoning is shown also to be the main form of reasoning in the empirically-derived “parameter analysis” method of conceptual design. Finally, the introduction of abduction into design theory is critically assessed, and in so doing, topics for future research are suggested