Universal asymptotic clone size distribution for general population growth
Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria-Delbr\"uck or Lea-Coulson model, is often assumed but seldom realistic. In this article we generalise this model to different types of wild-type population growth, with mutants evolving as a birth-death branching process. Our focus is on the size distribution of clones - that is the number of progeny of a founder mutant - which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. Additionally for a large class of population growth we prove that the long time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. Considering metastases in cancer as the mutant clones, upon analysing a data-set of their size distribution, we indeed find that a power-law tail is more likely than an exponential one.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Model-Free Universal AI
In general reinforcement learning, all established optimal agents, including AIXI, are model-based, explicitly maintaining and using environment models. This paper introduces Universal AI with Q-Induction (AIQI), the fir…
General Reinforcement LearningCloneShield: A Framework for Universal Perturbation Against Zero-Shot Voice Cloning
Recent breakthroughs in text-to-speech (TTS) voice cloning have raised serious privacy concerns, allowing highly accurate vocal identity replication from just a few seconds of reference audio, while retaining the speaker…
text-to-speechText to SpeechVoice CloningDynamics of T Cell Receptor Distributions Following Acute Thymic Atrophy and Resumption
Naive human T cells are produced in the thymus, which atrophies abruptly and severely in response to physical or psychological stress. To understand how an instance of stress affects the size and "diversity" of the perip…
Universal Asymptotic Optimality of Polyak Momentum
We consider the average-case runtime analysis of algorithms for minimizing quadratic objectives. In this setting, and contrary to the more classical worst-case analysis, non-asymptotic convergence rates and optimal algor…
Cloning Outfits from Real-World Images to 3D Characters for Generalizable Person Re-Identification
Recently, large-scale synthetic datasets are shown to be very useful for generalizable person re-identification. However, synthesized persons in existing datasets are mostly cartoon-like and in random dress collocation, …
Generalizable Person Re-identificationPerson Re-IdentificationUnsupervised Domain AdaptationUnsupervised Person Re-Identification