Related papers: Large Deviations of Cancer Recurrence Timing
An early phase clinical trial is the first step in evaluating the effects in humans of a potential new anti-disease agent or combination of agents. Usually called "phase I" or "phase I/II" trials, these experiments typically have the…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant…
The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. Although treatment may initially achieve short-term disease control, resistant…
In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or "driver," mutations from "passenger" mutations that have no selective effect. Toward this end, we prove results concerning the…
Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated stochastic model, whose law of large numbers…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
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…
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…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
Drug resistance and metastasis - the major complications in cancer - both entail adaptation of cancer cells to stress, whether a drug or a lethal new environment. Intriguingly, these adaptive processes share similar features that cannot be…
We propose a method for determining the most likely cause, in terms of conventional generator outages and renewable fluctuations, of power system frequency reaching a predetermined level that is deemed unacceptable to the system operator.…
We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing…
Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and…
Phenotypic heterogeneity in cancer cells is widely observed and is often linked to drug resistance. In several cases, such heterogeneity in drug sensitivity of tumors is driven by stochastic and reversible acquisition of a drug tolerant…
The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
We investigate large deviations for the empirical measure of the forward and backward recurrence time processes associated with a classical renewal process with arbitrary waiting-time distribution. The Donsker-Varadhan theory cannot be…
Cancer progression is an example of a rapid adaptive process where evolving new traits is essential for survival and requires a high mutation rate. Precancerous cells acquire a few key mutations that drive rapid population growth and…