Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies

Nonlinear Blend Scheduling via Inventory Pinch-based Algorithm using Discrete- and Continuous-time Models

This work uses multi-period, inventory pinch-based algorithm with continuous-time model (MPIP-C algorithm1) for scheduling linear or nonlinear blending processes. MPIP-C decomposes the scheduling problem into (i) approximate scheduling and (ii) detailed scheduling. Approximate scheduling model is further decomposed into two parts: a 1st level model which optimizes nonlinear blend models (with time periods delineated by inventory pinch points), and a 2nd level multi-period mixed-integer linear programming model (which uses fixed blend recipes from the 1st level solution) to determine optimal production plan and swing storage allocation, while minimizing the number of blend instances and product changeovers in the swing tanks. The 3rd level computes schedules using a continuous-time model including constraints based on the short-term plan solution. Nonlinear constraints are used for the Reid vapor pressure in our case studies. Excellent computational performance is illustrated by comparisons with previous approach with discrete-time scheduling model

They Have Names, Too: A Case Study on the First Five Victims of the Green River Killer: Examining the Construction of Society and Its Creation of Victim Availability

This case study follows the example of Rubenhold (2019) to examine the lives of the first five women killed by the Green River Killer, to give the victims a voice to tell their stories that Ridgway robbed from them, and to identify the social constructs that influence victim availability. To explore this issue, the study analyzed multiple sources of information: archival sources, monographs, articles, websites, and newspapers. In analyzing the effects of their upbringing—family history, educational backgrounds, and personal lives—this research will clarify the role that these factors played regarding where they spent their last day alive. Using an intersectional lens helps interpret how these young women’s race, class, and gender were affected by the social system and their vulnerability in society. The qualitative data was beneficial as an explanatory means of the theoretical social constructs and to understand the themes that emerged from this data. This interpretation of these sources helped recognize the constructs that make up for the vulnerability of marginalized populations and why they are high-risk victims.Analyzing individual bodies, experiences, and lives will answer many questions regarding how identity is crucial for how one experiences life

Directed Random Walk on the Lattices of Genus Two

The object of the present investigation is an ensemble of self-avoiding and directed graphs belonging to eight-branching Cayley tree (Bethe lattice) generated by the Fucsian group of a Riemann surface of genus two and embedded in the Pincar\'e unit disk. We consider two-parametric lattices and calculate the multifractal scaling exponents for the moments of the graph lengths distribution as functions of these parameters. We show the results of numerical and statistical computations, where the latter are based on a random walk model.Comment: 17 pages, 8 figure

Non-diffusive transport in plasma turbulence: a fractional diffusion approach

Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time, that incorporate in a unified way space-time non-locality (non-Fickian transport), non-Gaussianity, and non-diffusive scaling. The fractional diffusion model reproduces the shape, and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed super-diffusive scaling