Extinction probability refers to the likelihood that a species or population will become extinct over a given time period. It is a critical concept in conservation biology, ecology, and population dynamics, as it helps researchers and conservationists understand the risks facing a species and the factors that contribute to its survival or decline.
Family-based QTL (Quantitative Trait Locus) mapping is a genetic approach used to identify and locate the genes that contribute to quantitative traits—phenotypic characteristics that vary in degree and can be influenced by multiple genes and environmental factors. QTL mapping aims to establish a statistical relationship between observed traits and genetic markers. In family-based QTL mapping, the focus is typically on utilizing family structures such as pedigrees or related individuals (e.g.
The Fleming-Viot process is a type of stochastic process that is used to model the evolution of genetic diversity in a population over time. It is particularly relevant in the fields of population genetics and mathematical biology. The process incorporates ideas from both diffusion processes and the theory of random measures, making it a powerful tool to study how genetic traits spread and how populations evolve.
Alinaghi Khamoushi is an Iranian political figure known for his involvement in the political landscape of Iran, particularly during the post-revolutionary period. He has been associated with various reformist movements and has held positions in the Iranian government and political institutions.
Landau theory, often referred to as Landau's theory of phase transitions, is a framework developed by the Soviet physicist Lev Landau in the early 20th century to describe phase transitions in physical systems. It provides a mathematical formalism for understanding how a system changes from one phase to another, typically as a function of temperature or other external parameters.
The Langevin equation is a stochastic differential equation that describes the evolution of a system influenced by both deterministic and random forces. It is commonly used in statistical mechanics, classical mechanics, and various fields like physics and chemistry to model systems that exhibit Brownian motion and other forms of stochastic behavior.
The Laplace principle, also known in the context of large deviations theory, provides a way to understand the asymptotic behavior of probability measures for large samples. It typically focuses on the probability of deviations of random variables from their expected values.
The Lieb–Liniger model is a theoretical framework used in condensed matter physics and quantum mechanics to describe a one-dimensional system of interacting particles. Specifically, it focuses on a system of bosons or fermions that interact via a delta-function potential.
The Lifson–Roig model is a theoretical framework used to describe the dynamics of polymer chains, particularly in the context of statistical mechanics and polymer physics. Developed by the physicists I. Lifson and M. Roig in the 1960s, the model provides insights into the behavior of flexible polymers or polypeptides in solution, focusing on aspects such as chain conformation and interactions.
Here is a list of notable textbooks in thermodynamics and statistical mechanics that are widely used in academia: ### Classical Thermodynamics 1. **"Thermodynamics: An Engineering Approach" by Yunus Çengel and Michael Boles** - This book focuses on thermodynamics principles with an engineering application perspective. 2. **"Fundamentals of Thermodynamics" by Richard E. Sonntag, Claus Borgnakke, and Gordon J.
In mathematics, particularly in the field of topology and analysis, "local time" refers to a concept that describes the time evolution of a stochastic process, especially in the context of Brownian motion and other random processes. Local time helps to quantify how often a process visits a particular state or value over time. For instance, in the context of Brownian motion, local time can be viewed as a way to record the "amount of time" the Brownian motion spends at a particular level.
In mathematical physics, particularly in the context of quantum field theory and string theory, a "loop integral" refers to an integral over a loop in momentum space, which arises when calculating certain types of Feynman diagrams during the process of evaluating quantum amplitudes. ### Key Points about Loop Integrals: 1. **Feynman Diagrams**: Loop integrals occur in Feynman diagrams that contain loops, indicating virtual particles that propagate between interactions.
Quantum finance is an emerging interdisciplinary field that applies principles and methods from quantum mechanics to financial modeling and analysis. It seeks to address complex problems in finance, such as pricing derivatives, risk management, portfolio optimization, and algorithmic trading, by taking advantage of quantum computing's capabilities.
Quantum phase transition refers to a fundamental change in the state of matter that occurs at absolute zero temperature (0 K) due to quantum mechanical effects rather than thermal fluctuations, which are more common in classical phase transitions. Unlike classical phase transitions, which occur as a system is heated or cooled and are often driven by changes in temperature and pressure (like the melting of ice to water), quantum phase transitions are induced by changes in external parameters such as magnetic fields, pressure, or chemical composition.
A Trigram tagger is a type of statistical part-of-speech (POS) tagging model that uses the context of words to determine the most probable grammatical tag for a given word based on the tags of the surrounding words. In this model, the term "trigram" refers to the use of sequences of three items—in this case, tags.
Genome-wide significance refers to a statistical threshold used in genome-wide association studies (GWAS) to determine whether a particular association between a genetic variant and a trait (such as a disease) is strong enough to be considered reliable and not due to chance. Given the vast number of genetic variants tested in GWAS—often millions—there's a high risk of false positives due to random chance. To address this, researchers apply a stringent significance threshold.
Frequentist inference is a framework for statistical analysis that relies on the concept of long-run frequencies of events to draw conclusions about populations based on sample data. In this approach, probability is interpreted as the limit of the relative frequency of an event occurring in a large number of trials. Here are some key characteristics and concepts associated with frequentist inference: 1. **Parameter Estimation**: Frequentist methods often involve estimating parameters (such as means or proportions) of a population from sample data.
Informal inferential reasoning refers to the process of drawing conclusions or making inferences based on observations and experiences without employing formal statistical methods or rigorous logical arguments. This type of reasoning relies on informal logic, personal judgments, and anecdotal evidence rather than structured data analysis or established scientific principles. Key characteristics of informal inferential reasoning include: 1. **Contextual Understanding**: It takes into account the context in which observations are made.
A randomised decision rule (also known as a randomized algorithm) is a decision-making framework or mathematical approach that incorporates randomness into its process. It involves making decisions based on probabilistic methods rather than deterministic ones. This can add flexibility, enhance performance, or help manage uncertainty in various contexts. **Key Characteristics of Randomised Decision Rules:** 1. **Randomness:** The decision rule involves an element of randomness where the outcome is not solely determined by the input data.
Resampling in statistics refers to a collection of methods for repeatedly drawing samples from observed data or a statistical model. The main purpose of resampling techniques is to estimate the distribution of a statistic and to validate models or hypotheses when traditional parametric assumptions may not hold. Resampling is particularly useful in situations where the sample size is small or the underlying distribution is unknown.