Cancer growth and metastasis as a metaphor of Go gaming: An Ising model approach

© 2018 Barradas-Bautista et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestric ted use, distribution, and reproduction in any medium, provided the original author and source are credited. This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones that play first could correspond to a metaphor of the birth, growth, and metastasis of cancer. Moreover, playing white stones on the second turn could correspond the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may therefore benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. We use the Ising Hamiltonian, that models the energy exchange in interacting particles, for modeling the cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer birth, growth, and metastasis; as well as the biochemical immune system process of defense

Tail universalities in rank distributions as an algebraic problem: the beta-like function

Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions have been proposed to solve the problem, but unfortunately they do not fit at the same time both ending tails. We show that many different data in rank laws, like in granular materials, codons, author impact in scientific journal, etc. are very well fitted by a beta-like function. Then we propose that such universality is due to the fact that a system made from many subsystems or choices, imply stretched exponential frequency-rank functions which qualitatively and quantitatively can be fitted with the proposed beta-like function distribution in the limit of many random variables. We prove this by transforming the problem into an algebraic one: finding the rank of successive products of a given set of numbers

Kuhn’s philosophical revolution

En este artículo postulamos que el trabajo de Kuhn es una revolución filosófica para la filosofía de la ciencia. La búsqueda de revoluciones filosóficas es una extensión de las ideas de Kuhn acerca de las revoluciones científicas. Las revoluciones filosóficas se distinguen de las revoluciones científicas en algunos aspectos que discutimos en este trabajo. Defendemos que la revolución kuhniana consiste en la naturalización de la filosofía de la ciencia que se desprende de sus trabajos y discutimos la analogía biológica que Kuhn empleó como un ejemplo ilustrativo.In this paper we propose that Kuhn's work constitutes a philosophical revolution in the Philosophy of Science. The search for philosophical revolutions is an extension of Kuhn's ideas about scientific revolutions severed from the scientific field. Revolutions in Philosophy are different from those in Science due to some relevant aspects which we briefly discuss in this work. We argue that the Kuhnian philosophical revolution consists in the naturalization of the Philosophy of Science which we find in his writings, finally we discuss Kuhn's biological analogy as an illustrative instance

Modeling the Searching Behavior of Social Monkeys

We discuss various features of the trajectories of spider monkeys looking for food in a tropical forest, as observed recently in an extensive {\it in situ} study. Some of the features observed can be interpreted as the result of social interactions. In addition, a simple model of deterministic walk in a random environment reproduces the observed angular correlations between successive steps, and in some cases, the emergence of L\'evy distributions for the length of the steps.Comment: 7 pages, 3 figure

First passage and arrival time densities for L\'evy flights and the failure of the method of images

We discuss the first passage time problem in the semi-infinite interval, for homogeneous stochastic Markov processes with L{\'e}vy stable jump length distributions $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$), namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method of images leads to a result, which violates a theorem due to Sparre Andersen, according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density (FPTD) governed by the universal long-time decay $\sim t^{-3/2}$. Conversely, we show that for LFs the direct definition known from Gaussian processes in fact defines the probability density of first arrival, which for LFs differs from the FPTD. Our findings are corroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett

Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition

Herewith we discuss a network model of the epithelial–mesenchymal transition (EMT) based on our previous proposed framework. The EMT appears as a “first order” phase transition process, analogous to the transitions observed in the chemical–physical field. Chiefly, EMT should be considered a transition characterized by a supercritical Andronov–Hopf bifurcation, with the emergence of limit cycle and, consequently, a cascade of saddle-foci Shilnikov's bifurcations. We eventually show that the entropy production rate is an EMT-dependent function and, as such, its formalism reminds the van der Waals equation.Fil: Guerra, A.. Universidad de La Habana; CubaFil: Rodriguez, D. J.. Universidad de La Habana; CubaFil: Montero, S.. Medical Sciences University Of Havana; CubaFil: Betancourt Mar, J. A.. Universidad de La Habana; CubaFil: Martín Pardo, Reinaldo Román. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Investigaciones en Tecnología Química. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Instituto de Investigaciones en Tecnología Química; Argentina. Mexican Institute Of Complex Systems. Tamaulipas; MéxicoFil: Silva Lamar, Eduardo. Universidad de La Habana; CubaFil: Bizzarri, María Julia. Universidad de La Habana; CubaFil: Cocho, G.. Universidad Nacional Autónoma de México; MéxicoFil: Mansilla, R.. Universidad Nacional Autónoma de México; MéxicoFil: Nieto Villar, José Manuel. Universidad de La Habana; Cub

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation

We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure