The Heston model is a mathematical model used to describe the evolution of financial asset prices, particularly in the context of options pricing. Developed by Steven Heston in 1993, this model is notable for its incorporation of stochastic volatility, which allows for the volatility of the asset price to change over time in a random manner, as opposed to assuming it is constant, which is a limitation of the classic Black-Scholes model.

Implied volatility (IV) is a measure used in the financial markets to indicate the market's expectation of the future volatility of an asset, usually associated with options pricing. Unlike historical volatility, which measures past price fluctuations, implied volatility reflects the market's forecast of how much an asset's price is likely to move in the future.

The mortgage constant, also known as the mortgage capitalization rate or the mortgage factor, is a financial metric used to calculate the annual debt service (the total amount of principal and interest payments) on a mortgage loan as a percentage of the total loan amount. It provides a way to express the cost of borrowing in relation to the loan amount and is useful in determining the impact of mortgage payments on cash flow for real estate investments.

The Simple Dietz method is a formula used in finance to calculate the time-weighted rate of return for an investment portfolio. It is particularly useful for measuring performance over a period when there are cash flows (deposits and withdrawals) into or out of the portfolio. The method attributes returns to the average capital invested over a specific period by accounting for the timing and size of these cash flows. Its main advantage is that it does not require detailed tracking of each individual cash flow.

Stochastic drift refers to a phenomenon in stochastic processes where a variable exhibits a tendency to change or "drift" over time due to random influences. In mathematical terms, it often describes the behavior of a stochastic process, particularly in the context of diffusion processes or time series analysis. The concept of stochastic drift is commonly associated with models like the Geometric Brownian Motion (GBM), which is frequently used in finance to model asset prices.

Complex systems scientists study complex systems, which are systems composed of many interconnected parts that interact in non-linear ways. These systems can be found in various fields such as biology, ecology, economics, sociology, neuroscience, and engineering, among others. The primary focus of complex systems science is to understand how these interactions lead to emergent behaviors and properties that cannot be understood simply by looking at the individual components in isolation.

Hesperus is a name from classical mythology that refers to the evening star, which is identified with the planet Venus when it is visible in the evening sky. The term is derived from the Greek word "Hesperos." In Greek mythology, Hesperus was often depicted as a personification of the evening star and was sometimes associated with the beautiful sunset. The name has also been used in various literary and philosophical contexts, including references by poets and philosophers such as Plato and Hesiod.

An agent-based model (ABM) is a computational model used to simulate the interactions of individual entities, known as agents, which can represent various real-world entities such as people, animals, organizations, or even groups. Each agent operates based on a set of defined rules and behaviors, allowing for the emergence of complex phenomena through local interactions. ### Key Features of Agent-Based Models: 1. **Agents**: The fundamental components of ABMs.

DYNAMO is a programming language designed for energy and building performance simulations, primarily used within the context of architectural design and analysis. It is a visual programming tool that allows users to create algorithms and workflows without needing extensive coding knowledge. DYNAMO is often associated with the software Autodesk Revit, where it is utilized to enhance parametric design, automate repetitive tasks, and facilitate data manipulation within the building information modeling (BIM) process.

Dynamical systems theory is a mathematical framework used to describe the behavior of complex systems that evolve over time according to specific rules or laws. It provides tools and concepts for analyzing how systems change, often characterized by equations that describe their dynamics. This field encompasses a wide variety of systems in different areas, including physics, biology, economics, engineering, and more.

Programming complexity, also known as computational complexity, refers to the resources required for a program to execute, particularly in terms of time and space. Understanding programming complexity is essential in evaluating the efficiency and feasibility of algorithms and software solutions. Here are some key concepts associated with programming complexity: 1. **Time Complexity**: - **Definition**: This measures the amount of time an algorithm takes to complete as a function of the size of the input data.

A sociocultural system refers to the complex interplay between social and cultural factors that influence the behavior, beliefs, and practices of a group or society. It encompasses the ways in which social structures, institutions, values, norms, and cultural traditions shape human interactions and societal organization. Key elements of a sociocultural system include: 1. **Society**: The collective of individuals who form a community, sharing common social structures such as family, education, and governance.

System dynamics is a methodological framework for understanding and analyzing complex systems over time. It was developed in the 1950s by Jay W. Forrester at the Massachusetts Institute of Technology (MIT). The approach combines elements of feedback loops, stocks and flows, and time delays to model the behavior of systems in various contexts, such as economics, ecology, social systems, and organizational management.

Systems theory is an interdisciplinary framework that studies complex systems in a holistic manner. It emerged in the mid-20th century and is rooted in both science and philosophy, aiming to understand how parts interact within a whole to produce collective behaviors and properties. ### Key Concepts of Systems Theory: 1. **Holism**: Systems are viewed as wholes rather than just collections of parts. The behavior and properties of a system cannot be fully understood by only analyzing its components in isolation.

The UCL Faculty of Mathematical and Physical Sciences (MAPS) is one of the academic faculties at University College London (UCL), a prestigious university located in London, UK. The MAPS faculty encompasses a range of disciplines, including mathematics, physics, astronomy, and various interdisciplinary fields that combine elements of these subjects. The faculty is known for its rigorous academic programs, cutting-edge research, and strong emphasis on both theoretical and practical applications of the sciences.

The term "vortex" can refer to several different concepts depending on the context: 1. **Physics and Fluid Dynamics**: In these fields, a vortex is a region within a fluid where the flow revolves around an axis line, which can be straight or curved. This motion often creates a whirling pattern, with the fluid moving in circular paths around a central point or axis.

Semiconductor analysis refers to the evaluation and examination of semiconductor materials and devices to understand their properties, performance, and applicability in various electronic applications. This type of analysis can encompass a range of techniques and methodologies, depending on the specific goals, such as material characterization, device performance assessment, or failure analysis.

Analysis of Western European colonialism and colonization involves examining the historical processes, motivations, impacts, and legacies of the European powers' expansion into Africa, Asia, and the Americas from the late 15th to the 20th century. This analysis can be approached from various perspectives, including political, economic, cultural, and social dimensions. ### Key Aspects of Western European Colonialism and Colonization 1.

Dialogical analysis is a qualitative research methodology that focuses on understanding the dynamics of conversation and interaction between individuals or groups. It is rooted in the principles of dialogical theory, which emphasizes the importance of dialogue as a means of constructing meaning and understanding reality. Key aspects of dialogical analysis include: 1. **Focus on Interaction**: It studies the process of communication, exploring how people express their thoughts, negotiate meanings, and co-create understandings through dialogue.