CA : A Cancer Journal for Clinicians

In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.

Evolution and the Theory of Games

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is described by the geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy. Investigation of the geometry and structure of such groups turns out to be useful for describing the global behavior of fluids for large time intervals.

Topological methods in hydrodynamics

The N-Vortex Problem

Introduction * N-Vortices in the Plane * Domains with Boundaries * Vortex Motion on a Sphere * Geometric Phases * Statistical Point Vortex Theories * Vortex Patch Models * Vortex Filament Models * References * Index

The N-Vortex Problem: Analytical Techniques

A new ecologically inspired paradigm in cancer treatment known as "adaptive therapy" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent "cycles" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary "absorbing region" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. SIGNIFICANCE: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.

/pdf/towards-multidrug-adaptive-therapy-3wpg9qdmla.pdf

Towards Multidrug Adaptive Therapy.

Motion of three point vortices on a sphere

The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, though not perfectly understood, fashion. A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as 9spreaders9 or 9sponges9 and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multi-directional aspects of cancer progression. We quantify three types of multi-directional mechanisms of progression: (i) self-seeding of the primary tumor; (ii) re-seeding of the primary tumor from a metastatic site (primary re-seeding); and (iii) re-seeding of metastatic tumors (metastasis re-seeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease.
For lung cancer, the main `spreaders9 of systemic disease are the adrenal gland and kidney, whereas the main `sponges9 are regional lymph nodes, liver, and bone. Lung is a significant self-seeder, although it is a `sponge9 site with respect to progression characteristics.

/pdf/spreaders-and-sponges-define-metastasis-in-lung-cancer-a-2e61cva4zw.pdf

Paul K. Newton

Papers

The N-Vortex Problem

The N-Vortex Problem: Analytical Techniques

Towards Multidrug Adaptive Therapy.

Motion of three point vortices on a sphere

Spreaders and Sponges define metastasis in lung cancer: A Markov chain Monte Carlo Mathematical Model