## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

MBE

The major goal of evolutionary oncology is to explain how malignant traits evolve to become cancer "hallmarks." One such hallmark---the angiogenic switch---is difficult to explain for the same reason altruism is difficult to explain. An angiogenic clone is vulnerable to "cheater" lineages that shunt energy from angiogenesis to proliferation, allowing the cheater to outcompete cooperative phenotypes in the environment built by the cooperators. Here we show that cell- or clone-level selection is sufficient to explain the angiogenic switch, but not because of direct selection on angiogenesis factor secretion---angiogenic potential evolves only as a pleiotropic afterthought. We study a multiscale mathematical model that includes an energy management system in an evolving angiogenic tumor. The energy management model makes the counterintuitive prediction that ATP concentration in resting cells increases with increasing ATP hydrolysis, as seen in other theoretical and empirical studies. As a result, increasing ATP hydrolysis for angiogenesis can increase proliferative potential, which is the trait directly under selection. Intriguingly, this energy dynamic allows an evolutionary stable angiogenesis strategy, but this strategy is an evolutionary repeller, leading to runaway selection for extreme vascular hypo- or hyperplasia. The former case yields a tumor-on-a-tumor, or hypertumor, as predicted in other studies, and the latter case may explain vascular hyperplasia evident in certain tumor types.

keywords:
evolutionary suicide
,
adaptive dynamics
,
energy charge
,
multiscale models
,
perturbation expansion.
,
Cancer
,
ATP

NHM

Aggregate production planning for highly re--entrant production processes is typically
generated by finding optimal release rates based on clearing function models. For production processes with very long
cycle times, like in semiconductor production, dispatch policies are used to cover short term fluctuations.
We extend the concept of a clearing function to allow control over both, the release rates and priority allocations in re-entrant production.
This approach is used to improve the production planning problem using combined release and the allocation dispatch policy.
The control parameter for priority allocation, called the push-pull point (PPP), separates the beginning of the factory which employs a
push policy from the end of the factory, which uses a pull policy.
The extended clearing function model describes the output of the factory as a function of the work in progress (wip) and the position of the PPP.
The model's qualitative behavior is analyzed. Numerical optimization results are compared to production planning based only on releases. It is found that controlling the PPP significantly reduces the average wip in the system and hence leads to much shorter cycle times.

NHM

A kinetic model for a specific agent based simulation to generate the sales curves of successive generations of high-end computer chips is developed.
The resulting continuum market model consists of transport equations in two variables, representing the availability of money and the desire to buy a new chip.
In lieu of typical collision terms in the kinetic equations that discontinuously change the attributes of an agent, discontinuous changes are initiated
via boundary conditions between sets of partial differential equations. A scaling analysis of the transport equations determines the different time scales that constitute
the market forces, characterizing different sales scenarios. It is argued that the resulting model can be adjusted to generic markets of multi-generational technology products
where the innovation time scale is an important driver of the market.

PROC

This paper presents a continuum - traffic flow like - model for the flow
of products through complex production networks, based on statistical
information obtained from extensive observations of the system.
The resulting model consists of a system of hyperbolic conservation laws,
which, in a relaxation limit, exhibit the correct diffusive properties
given by the variance of the observed data.

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