Related papers: A basic model of mutations
Metabolism and evolution are closely connected: if a mutation incurs extra energetic costs for an organism, there is a baseline selective disadvantage that may or may not be compensated for by other adaptive effects. A long-standing, but to…
Imagine a freely rotating rigid body. The body has three principal axes of rotation. It follows from mathematical analysis of the evolution equations that pure rotations around the major and minor axes are stable while rotation around the…
We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely we use a…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
We propose a probabilistic modeling framework for learning the dynamic patterns in the collective behaviors of social agents and developing profiles for different behavioral groups, using data collected from multiple information sources.…
With the increasing impact of algorithmic decision-making on human lives, the interpretability of models has become a critical issue in machine learning. Counterfactual explanation is an important method in the field of interpretable…
When the process underlying DNA substitutions varies across evolutionary history, the standard Markov models underlying standard phylogenetic methods are mathematically inconsistent. The most prominent example is the general time reversible…
In this paper we demonstrate that any Markovian master equation defining a completely positive evolution for a quantum-classical hybrid state can always be written in terms of four basic coupling mechanisms. Each of them is characterized by…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
Hidden Markov models (HMMs) offer a robust and efficient framework for analyzing time series data, modelling both the underlying latent state progression over time and the observation process, conditional on the latent state. However, a…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…
We propose a new form for the quantum master equation in the theory of open quantum systems. This new formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
The initial transient phase of an emerging epidemic is of critical importance for data-driven model building, model-based prediction of the epidemic trend, and articulation of control/prevention strategies. In principle, quantitative models…
In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained…
In a recent work we presented a recursive algorithm to compute the matrix elements of a generic Gaussian transformation in the photon-number basis. Its purpose was to evolve a quantum state by building the transformation matrix and…