Circuit topology refers to the arrangement and interconnection of components in an electrical or electronic circuit. It describes how the various elements of a circuit—such as resistors, capacitors, inductors, and active devices like transistors and operational amplifiers—are connected to each other and to the power supply.

GeneMark is a software tool used for gene prediction in prokaryotic and eukaryotic genomes. Developed by the bioinformatics researcher Mark Borodovsky and his colleagues, GeneMark utilizes statistical models to identify potential genes based on sequences in the genome. The software employs methods such as Hidden Markov Models (HMMs) and language-like models to differentiate coding regions (genes) from non-coding regions based on sequence characteristics.

Gene prediction refers to the process of identifying the locations of genes within a genome. This involves determining the sequences of DNA that correspond to functional genes, as well as predicting their structures, including coding regions (exons), non-coding regions (introns), regulatory sequences, and other features that are essential for gene function and expression.

Haldane's dilemma is a concept in evolutionary biology proposed by the British geneticist J.B.S. Haldane in the early 20th century. It addresses the genetic implications of natural selection, specifically regarding the limits of adaptation in populations. The key idea behind Haldane's dilemma is that for a population to evolve beneficial traits through natural selection, there are finite limits to how quickly these traits can spread through the population based on genetic changes.

The Infinite Sites Model is a concept used in population genetics, particularly in the context of genetic mutation and variation. In this model, it is assumed that there are an infinite number of possible genetic loci (sites) that can mutate. Each locus can mutate independently, and each mutation is considered to create a new, unique genetic variant. This means that over time, as mutations accumulate, the genetic diversity in a population can increase without limit, due to the assumption of infinite sites.

The Journal of Mechanics of Materials and Structures (JMMS) is a peer-reviewed academic journal that focuses on research related to the mechanics of materials and structures. It encompasses a wide range of topics within the fields of mechanics, materials science, and structural engineering. The journal publishes original research articles, reviews, and possibly other types of contributions that explore theoretical, computational, and experimental studies related to the behavior of materials and structures under various loading conditions.

Integrodifference equations are a type of mathematical equation used to model discrete-time processes where dynamics are influenced by both local and non-local (or distant) interactions. These equations are particularly useful in various fields such as population dynamics, ecology, and spatial modeling where the future state of a system depends not only on its current state but also on the states of neighboring systems or regions.

The Journal of Biological Dynamics is a scientific journal that focuses on the mathematical and computational modeling of biological phenomena. It publishes research articles that explore theoretical and applied aspects of dynamics in biological systems, including but not limited to population dynamics, ecological interactions, disease dynamics, and the modeling of biological processes. The journal serves as a platform for researchers to share their findings and methodologies, often emphasizing interdisciplinary approaches that combine biology, mathematics, and computational techniques.

Kinetic proofreading is a molecular mechanism that enhances the fidelity of biological processes, particularly in protein synthesis and DNA replication. It involves a series of kinetic steps that allow the system to discriminate between correct and incorrect substrates or interactions, thus reducing the likelihood of errors. In the context of protein synthesis, for example, kinetic proofreading refers to the way ribosomes ensure that the correct aminoacyl-tRNA is matched with the corresponding codon on the mRNA.

Kolmogorov equations refer primarily to a set of differential equations that describe the evolution of probabilities in stochastic processes, particularly in the contexts of Markov processes and stochastic differential equations. These equations are pivotal in the study of probability theory and were developed by the Russian mathematician Andrey Kolmogorov.

The Mathematical Biosciences Institute (MBI) is an interdisciplinary research institute based at The Ohio State University. It focuses on the application of mathematical techniques and methods to solve problems in the biological sciences. The institute aims to foster collaboration between mathematicians, biologists, and other scientists to advance understanding in areas such as ecology, evolutionary biology, epidemiology, and systems biology.

Theoretical ecology is a subfield of ecology that focuses on the development and application of mathematical models and theoretical frameworks to understand ecological processes and interactions within ecosystems. It aims to provide insights into the dynamics of populations, communities, and ecosystems by using formal models to simulate and predict ecological phenomena. Key aspects of theoretical ecology include: 1. **Modeling Ecological Interactions**: Theoretical ecologists create models to represent relationships between different species, as well as between species and their environment.

Risa Wechsler is an astrophysicist known for her work in cosmology, particularly in the areas of galaxy formation, large-scale structure, and dark energy. She has contributed to our understanding of the universe's evolution and the distribution of galaxies. Wechsler has been involved in various research projects and collaborations, including those focused on cosmic surveys and simulations to study the properties of dark matter and the expansion of the universe.

The Narrow Escape Problem is a concept often encountered in mathematical biology, particularly in the field of diffusion processes and stochastic processes. It refers to the study of how particles (or small organisms) escape from a confined space through a narrow opening or boundary. In more technical terms, it examines the diffusion of particles that are subject to certain conditions, such as being confined within a domain but having a small chance of escaping through a specific narrow region (e.g., an exit or an absorbing boundary).

"On Growth and Form" is a seminal work written by the British biologist D'Arcy Wentworth Thompson and first published in 1917. The book explores the relationship between biology and geometry, examining how the forms of living organisms are influenced by physical and mathematical principles. Thompson emphasizes that the shapes of organisms cannot be understood simply through evolutionary biology; instead, he argues that physical forces, mechanical properties, and mathematical patterns play a crucial role in shaping biological structures.

The Paradox of Enrichment is a concept in ecology that describes a situation in which increasing the productivity or nutrient levels of an ecosystem can lead to a decline in biodiversity and even the stability of certain species populations. This counterintuitive phenomenon was first articulated by ecologist John T. Curtis in the context of predator-prey dynamics. In a simplified model, consider a predator-prey system where an increase in food resources (enriching the environment) allows prey populations to grow.

The Paradox of the Plankton refers to an ecological conundrum identified by G.E. Hutchinson in 1961 regarding the coexistence of a large number of planktonic algal species in aquatic ecosystems, particularly in the face of competition for limited resources. According to the competitive exclusion principle, two species competing for the same resources cannot coexist indefinitely; one species will typically outcompete the other.

The Plateau Principle, often discussed in evolutionary biology and ecology, suggests that there are limits to the benefits that can be gained from continuous improvement or optimization in a certain context. Essentially, after a certain point, further efforts in enhancing performance, efficiency, or adaptation yield diminishing returns. In more specific applications, such as in fitness training or learning, the Plateau Principle can manifest as periods where performance levels off and does not improve despite continued effort.

The Population Balance Equation (PBE) is a mathematical formulation used to describe the dynamics of a population of particles or entities as they undergo various processes such as growth, aggregation, breakage, and interactions. It is widely used in fields like chemical engineering, materials science, pharmacology, and environmental engineering to model systems involving dispersed phases, such as aerosols, emulsions, or biological cells.

The golden ratio, approximately 1.618, has been used in various fields, especially art, architecture, and design, since ancient times. Here’s a list of notable works and structures where the golden ratio is believed to have been employed: ### Art 1. **"The Last Supper" by Leonardo da Vinci** - The proportions of the composition, especially the placement of Christ and the apostles, exhibit the golden ratio.