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Migration and proliferation dichotomy in tumor cell invasion
Get PDFWe propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting-time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate
Invariance principles for iterated maps that contract on average
No full textWe consider iterated function schemes that contract on average. Using a transfer operator approach, we prove a version of the almost sure invariance principle. This allows the system to be modelled by a Brownian motion, up to some error term. It follows that many classical statistical properties hold for such systems, such as the weak invariance principle and the law of the iterated logarithm
Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy
Get PDFBy using a combination of 32-bit and 64-bit floating point arithmetic the performance
of many sparse linear algebra algorithms can be significantly enhanced
while maintaining the 64-bit accuracy of the resulting solution. These ideas can
be applied to sparse multifrontal and supernodal direct techniques, and sparse iterative
techniques such as Krylov subspace methods. The approach presented here
can apply not only to conventional processors but also to exotic technologies such
as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU),
and the Cell BE processor
Quantum mushroom billiards
Get PDFWe report the first large-scale statistical study of very high-lying eigenmodes (quantum states) of the mushroom billiard proposed by L. Bunimovich in this journal, 11, 802 (2001). The phase space of this mixed system is unusual in that it has a single regular region and a single chaotic region, and no KAM hierarchy. We verify Percival's conjecture to high accuracy (1.7%). We propose a model for dynamical tunneling and show that it predicts well the chaotic components of predominantly regular modes. Our model explains our observed density of such superpositions dying as E^{-1/3} (E is the eigenvalue). We compare eigenvalue spacing distributions against Random Matrix Theory expectations, using 16000 odd modes (an order of magnitude more than any existing study). We outline new variants of mesh-free boundary collocation methods which enable us to achieve high accuracy and high mode numbers (~ 10^5) orders of magnitude faster than with competing methods
Increased Sequence Diversity Coverage Improves Detection of HIV-Specific T Cell Responses
No full textThe accurate identification of HIV-specific T cell responses is important for determining the relationship between immune response, viral control, and disease progression. HIV-specific immune responses are usually measured using peptide sets based on consensus sequences, which frequently miss responses to regions where test set and infecting virus differ. In this study, we report the design of a peptide test set with significantly increased coverage of HIV sequence diversity by including alternative amino acids at variable positions during the peptide synthesis step. In an IFN-γ ELISpot assay, these "toggled" peptides detected HIV-specific CD4+ and CD8+ T cell responses of significantly higher breadth and magnitude than matched consensus peptides. The observed increases were explained by a closer match of the toggled peptides to the autologous viral sequence. Toggled peptides therefore afford a cost-effective and significantly more complete view of the host immune response to HIV and are directly applicable to other variable pathogens
Reconstruction of a grounded object in an electrostatic halfspace with an indicator function
No full textThis article explores the use of capacitance measurements made between electrodes embedded in or around a display surface, to detect the position, orientation and shape of hands and fingers. This is of interest for unobtrusive 3D gesture input for interactive displays, so called touch-less interaction. The hand is assumed to be grounded and formally the problem is a Cauchy problem for the Laplace equation in which Cauchy data on the boundary (the display surface) is used to reconstruct the zero potential contour of the unknown object (the hand). The problem is solved with the so-called factorisation method developed for acoustic scattering and electrostatic problems. In the factorisation method, a test function is used to characterise points , in which is the Dirichlet to Neumann map on the display surface. We demonstrate a suitable test function appropriate to the boundary conditions present here. In the application, is obtained from measurements at finite precision as a finite matrix and the calculation of is implicitly regularised. The resulting level set is finite and differentiable everywhere. The level representing the object is found through minimising the cost function. Numerical simulations demonstrate that for realistic electrode layouts and noise levels the method provides good reconstruction. The application of explicit regularisation filters can be beneficial and allows a trade-off between resolution and stability
Planar line processes for void and density statistics in thin stochastic fibre networks
No full textUsing results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001
Tailor-made split-plot designs for mixture and process variables
No full textThe design of efficient small experiments involving mixture variables and process variables is a difficult
problem. An additional complication is that such experiments are often conducted using split-plot designs
and therefore lead to correlated observations. The present article demonstrates how algorithmic search can
be used for constructing efficient tailor-made split-plot mixture-process variable designs, when there may
be constraints on the mixture components. The D-optimality criterion is used as the main design criterion.
The article also shows how to construct efficient split-plot mixture-process variable designs when replication
is required for independently estimating the variance components in the split-plot model. It is argued that
it is better to spread the replications over different points of the design than to concentrate them in the
center
Super real closed rings
No full textA super real closed ring is a commutative ring equipped with the operation of all continuous functions . Examples are rings of continuous functions and super real fields attached to -prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed rings, by showing that many constructions of lattice ordered rings can be performed inside super real closed rings; the most important are: residue rings, complete and classical quotients, convex hulls, valuations, Prüfer hulls and real closures over proconstructible subsets. We also give a counterexample to the conjecture that the first order theory of (pure) rings of continuous functions is the theory of real closed rings, which says in addition that a semi-local model is a product of fields
The effect of surface tension on trapped modes in water-wave problems
Get PDFIn this paper the effect of surface tension is considered on two two-dimensional water-wave problems involving pairs of immersed bodies. Both models, having fluid of infinite depth, support localized oscillations, or trapped modes, when capillary effects are excluded. The first pair of bodies is surface-piercing whereas the second pair is fully submerged. In the former case it is shown that the qualitative nature of the streamline shape is unaffected by the addition of surface tension in the free surface condition, no matter how large this parameter becomes. The main objective of this paper, however, is to study the submerged body problem. For this case it is found, by contrast, that there exists a critical value of the surface tension above which it is no longer possible to produce a completely submerged pair of bodies which support trapped modes. This critical value varies as a function of the separation of the two bodies. It can be inferred from this that surface tension does not always play a qualitatively irrelevant role in the linear water-wave problem