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A primary goal of modern cancer research is to characterize tumour growth and evolution, to improve clinical forecasting and individualized treatment. Agent-based models support this endeavour but existing models either oversimplify spatial…

Quantitative Methods · Quantitative Biology 2023-01-20 Maciej Bak , Blair Colyer , Veselin Manojlović , Robert Noble

In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor…

Analysis of PDEs · Mathematics 2018-02-05 Jian-Guo Liu , Min Tang , Li Wang , Zhennan Zhou

In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…

Other Quantitative Biology · Quantitative Biology 2017-05-03 Yehor Surkov , Ihor Samofalov , Mironenko Anastasia

We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…

Quantum Physics · Physics 2017-06-05 Leonardo Novo , Dominic W. Berry

Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagu\'e…

Tissues and Organs · Quantitative Biology 2019-03-12 Zehor Belkhatir , Michele Pavon , James C. Mathews , Maryam Pouryahya , Joseph O. Deasy , Larry Norton , Allen R. Tannenbaum

Quantum computation is an attractive front for many problems that are intractable for computers today. One such problem is nonadiabatic quantum molecular dynamics, where quantized internal states coupling to parameterized modes result in a…

Quantum Physics · Physics 2026-04-22 Joshua Courtney

We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…

Optimization and Control · Mathematics 2016-08-02 Harald Garcke , Kei-Fong Lam , Elisabetta Rocca

We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…

Adaptation and Self-Organizing Systems · Physics 2025-03-27 Christian Kuehn

We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the…

Analysis of PDEs · Mathematics 2016-05-26 Harald Garcke , Kei Fong Lam

In the end of the second decade of 20th century, Warburg showed how cancer cells present a fermentative respiration process, related to a metabolic injury. Here, we develop an analysis of the cell process based on its heat outflow, in order…

Cell Behavior · Quantitative Biology 2021-07-27 Umberto Lucia , Giulia Grisolia

In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…

Analysis of PDEs · Mathematics 2013-06-11 Martin Kohlmann

To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…

Quantum Physics · Physics 2026-04-02 Peng Guo , Paul LeVan , Frank X. Lee , Yong Zhao

Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either…

Cell Behavior · Quantitative Biology 2014-11-07 Kamran Kaveh , Mohammad Kohandel , Siv Sivaloganathan

We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state. The optimization of…

Quantum Physics · Physics 2023-07-11 Gerald E. Fux , Eoin P. Butler , Paul R. Eastham , Brendon W. Lovett , Jonathan Keeling

A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…

Quantum Physics · Physics 2017-11-23 Oscar Rosas-Ortiz , Kevin Zelaya

Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…

Quantum Physics · Physics 2022-06-08 Thais de Lima Silva , Lucas Borges , Leandro Aolita

Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a…

Physics and Society · Physics 2025-05-13 Hugo Spring-Ragain

Spatial agent-based models are increasingly used to investigate the evolution of solid tumours subject to localised cell-cell interactions and microenvironmental heterogeneity. Here we present a non-technical step by step guide to…

Quantitative Methods · Quantitative Biology 2023-11-08 Blair Colyer , Maciej Bak , David Basanta , Robert Noble

Despite acute interest in the dynamics of non-Hermitian systems, there is a lack of consensus in the mathematical formulation of non-Hermitian quantum mechanics in the community. Different methodologies are used in the literature to study…

Quantum Physics · Physics 2025-03-31 Karin Sim , Nicolò Defenu , Paolo Molignini , R. Chitra

We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…

Quantum Physics · Physics 2018-08-02 Andrew M. Childs , Nathan Wiebe