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

Is the Food and Drug Administration Safe and Effective?

In the United States, drug safety and efficacy are primarily regulated by the Food and Drug Administration (FDA) and the legal system, which gives manufacturers large incentives to produce safe drugs and provide proper warnings for side effects, since patients can sue manufacturers that provide unsafe drugs and/or insufficient warnings. In this paper, we begin by examining the efficiency implications of this joint regulation of drug safety. We find that joint regulation of drug safety can be inefficient when the regulatory authority mandates a binding and well enforced level of safety investment. In this case, product liability has no effect on a firm's safety investment, but affects welfare by raising a firm's costs and therefore prices. Using these results, we calibrate a model of the pharmaceutical market and find that, depending on the share of liability costs in marginal costs, a product liability exemption for activities that are well regulated by the FDA could increase consumer welfare by $47.8-$754.7 billion annually (4-66 percent of sales) and producer welfare by $11.9-$173.9 billion annually (1-15 percent of sales). In addition, we summarize the welfare effects of recent legislation, the Prescription Drug User Fee Acts (PDUFA), which mandated faster FDA review times in exchange for user fees levied on the pharmaceutical industry. Overall, we find that the faster review times mandated by PDUFA raised social surplus by $18-31 billion, and that at most, the concomitant cost of reduced drug safety was$5.6-$16.6 billion.

Selectivity of Metsulfuron Methyl to Six Common Littoral Species in Florida

Many Central Florida lakes, particularly those in the Kissimmee River watershed, are maintained 0.5 to 1.0 m lower than historic (pre-1960) levels during the summer hurricane season for flood control purposes. These lower water levels have allowed proliferation and formation of dense monotypic populations of pickerelweed ( Pontederia cordata L.) and other broadleaf species that out compete more desirable native grasses (Hulon, pers. comm., 2002). Due to the limited availability of data on the effects of metsulfuron methyl on wetland plants, particularly in Florida, the present study was carried out with the objective of testing its phytotoxicity on six wetland species, to determine the feasibility of its use for primary pickerelweed control

The disjointness of stabilizer codes and limitations on fault-tolerant logical gates

Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code families to find similar bounds on the level of the hierarchy attainable by constant depth circuits, regardless of their geometric locality. For instance, we can show that symmetric 2D surface codes cannot have non-local constant depth circuits for non-Clifford gates.Comment: 8+3 pages, 2 figures. Comments welcom

The micropolar Navier-Stokes equations: A priori error analysis

The unsteady Micropolar Navier-Stokes Equations (MNSE) are a system of parabolic partial differential equations coupling linear velocity and pressure with angular velocity: material particles have both translational and rotational degrees of freedom. We propose and analyze a first order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier-Stokes equations. With the help of our scheme we explore some qualitative properties of the MNSE related to ferrofluid manipulation and pumping. Finally, we propose a second order scheme and show that it is almost unconditionally stable

Merit Motives and Government Intervention: Public Finance in Reverse

A common view in public finance is that there is an efficiency-redistribution tradeoff in which distortions are tolerated in order to redistribute income. However, the fact that so much public- and private redistributive activity involves in-kind transfers rather than cash may be indicative of merit motives on the part of the payers rather than a preference for the well-being of the recipients. Efficiency-enhancing public policy in a merit good economy has the primary purpose of creating distortions and may only redistribute income from rich to poor in order to create those distortions the reverse of the conventional efficiency-redistribution tradeoff. We discuss why the largest programs on the federal and local level in the US including Social Security, Medicare and Medicaid, and Public Schooling seem consistent with the reverse tradeoff rather than the classic one. Transfers are not lump sum in a merit good economy, and explicitly accounting for this when calculating tax incidence reduces the estimated progressivity of government policy. As one example, we calibrate the conventional life-cycle model to show how the amount of over-saving induced on the poor by Social Security hurts them at least as much as the progressive' benefits help them. When the distortions outweigh fiscal transfers in this manner, the classic efficiency-redistribution tradeoff cannot justify the program and the program is far less progressive than conventional analysis suggests.