Uncertainty quantification
Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certa
Discrete modelling
Discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, formulae are fit to discrete data—data that could potentially take on only a countable set of values, such a
System equivalence
In the systems sciences system equivalence is the behavior of a parameter or component of a system in a way similar to a parameter or component of a different system. Similarity means that mathematica
Computational science
Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems.
Manley–Rowe relations
The Manley–Rowe relations are mathematical expressions developed originally for electrical engineers to predict the amount of energy in a wave that has multiple frequencies. They have since been found
Abstract family of acceptors
An abstract family of acceptors (AFA) is a grouping of generalized acceptors. Informally, an acceptor is a device with a finite state control, a finite number of input symbols, and an internal store w
Fictitious domain method
In mathematics, the Fictitious domain method is a method to find the solution of a partial differential equations on a complicated domain , by substituting a given problemposed on a domain , with a ne
Lambda-connectedness
In applied mathematics, lambda-connectedness (or λ-connectedness) deals with partial connectivity for a discrete space. Assume that a function on a discrete space (usually a graph) is given. A degree
Structural complexity (applied mathematics)
Structural complexity is a science of applied mathematics, that aims at relating fundamental physical or biological aspects of a complex system with the mathematical description of the morphological c
Stiffness matrix
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the system of linear equations that must be solved
PottersWheel
PottersWheel is a MATLAB toolbox for mathematical modeling of time-dependent dynamical systems that can be expressed as chemical reaction networks or ordinary differential equations (ODEs). It allows
Cartesian tensor
In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis
Flail space model
The flail space model (FSM) is a model of how a car passenger moves in a vehicle that collides with a roadside feature such as a guardrail or a crash cushion. Its principal purpose is to assess the po
Numerical weather prediction
Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not unt
Cryptography
Cryptography, or cryptology (from Ancient Greek: κρυπτός, romanized: kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively), is the practice and study of
Engineering mathematics
Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. Along with fields like engineering physic
Actuarial present value
The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typ
Mathematical sociology
Mathematical sociology or the sociology of mathematics is an interdisciplinary field of research concerned both with the use of mathematics within sociological research as well as research into the re
Andrews plot
In data visualization, an Andrews plot or Andrews curve is a way to visualize structure in high-dimensional data. It is basically a rolled-down, non-integer version of the Kent–Kiviat radar m chart, o
Discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first
Overfitting
In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict
European Study Groups with Industry
A European Study Group with Industry (ESGI) is usually a week-long meeting where applied mathematicians work on problems presented by industry and research centres. The aim of the meeting is to solve
OLGA (technology)
OLGA is a modelling tool for transportation of oil, natural gas and water in the same pipeline, so-called multiphase transportation. The name is short for "oil and gas simulator". The main challenge w
Reciprocity (engineering)
Reciprocity in linear systems is the principle that a response Rab, measured at a location (and direction if applicable) a, when the system has an excitation signal applied at a location (and directio
Multiparty communication complexity
In theoretical computer science, multiparty communication complexity is the study of communication complexity in the setting where there are more than 2 players. In the traditional two–party communica
Postage stamp problem
The postage stamp problem is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these
Vflo
Vflo is a commercially available, physics-based distributed hydrologic model generated by Vieux & Associates, Inc. Vflo uses radar rainfall data for hydrologic input to simulate distributed runoff. Vf
Simulation governance
Simulation governance is a managerial function concerned with assurance of reliability of information generated by numerical simulation. The term was introduced in 2011 and specific technical requirem
Scarborough criterion
The Scarborough criterion is used for satisfying convergence of a solution while solving linear equations using an iterative method.
Computational topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A
Actuarial notation
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a where symbols are placed as super
Phase boundary
In thermal equilibrium, each phase (i.e. liquid, solid etc.) of physical matter comes to an end at a transitional point, or spatial interface, called a phase boundary, due to the immiscibility of the
Mohr–Coulomb theory
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the cl
Menu dependence
Roughly speaking, in decision theory, game theory, and rational choice, menu dependence arises when the evaluation of alternatives for choice or the mode of selection guiding choice varies parametrica
Weighted planar stochastic lattice
Physicists often use various lattices to apply their favorite models in them. For instance, the most favorite lattice is perhaps the square lattice. There are 14 Bravais space lattice where every cell
Dichromatic reflectance model
In Shafer’s dichromatic reflection model, scene radiance has two components: λ is the wavelength,cb is the body (diffuse) reflected component,cs is the surface (interface) (specular) reflected compone
Single-particle trajectory
Single-particle trajectories (SPTs) consist of a collection of successive discrete points causal in time. These trajectories are acquired from images in experimental data. In the context of cell biolo
Patterns in nature
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmet
Seminar for Applied Mathematics
The Seminar for Applied Mathematics (SAM; from 1948 to 1969 Institute for Applied Mathematics) was founded in 1948 by Prof. Eduard Stiefel. It is part of the Department of Mathematics (D-MATH) of the
Rata Die
Rata Die (R.D.) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. It was named (after the Lat
K-mer
In bioinformatics, k-mers are substrings of length contained within a biological sequence. Primarily used within the context of computational genomics and sequence analysis, in which k-mers are compos
Vector spherical harmonics
In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH are complex-valued functions expressed in the
Signed distance function
In mathematics and its applications, the signed distance function (or oriented distance function) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space, with the s
Gilbert–Johnson–Keerthi distance algorithm
The Gilbert–Johnson–Keerthi distance algorithm is a method of determining the minimum distance between two convex sets. Unlike many other distance algorithms, it does not require that the geometry dat
Fractal derivative
In applied mathematics and mathematical analysis, the fractal derivative or Hausdorff derivative is a non-Newtonian generalization of the derivative dealing with the measurement of fractals, defined i
Journal of Computational and Applied Mathematics
The Journal of Computational and Applied Mathematics is a peer-reviewed scientific journal covering computational and applied mathematics. It was established in 1975 and is published biweekly by Elsev
Two-dimensional window design
Windowing is a process where an index-limited sequence has its maximum energy concentrated in a finite frequency interval. This can be extended to an N-dimension where the N-D window has the limited s
Mathematical Magick
Mathematical Magick (complete title: Mathematical Magick, or, The wonders that may by performed by mechanical geometry.) is a treatise by the English clergyman, natural philosopher, polymath and autho
Topological data analysis
In applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimension
Probabilistic numerics
Probabilistic numerics is a scientific field at the intersection of statistics, machine learning and applied mathematics, where tasks in numerical analysis including finding numerical solutions for in
Total least squares
In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variable
Spectral signal-to-noise ratio
In scientific imaging, the two-dimensional spectral signal-to-noise ratio (SSNR) is a signal-to-noise ratio measure which measures the normalised cross-correlation coefficient between several two-dime
Multivalued treatment
In statistics, in particular in the design of experiments, a multi-valued treatment is a treatment that can take on more than two values. It is related to the dose-response model in the medical litera
Fourier shell correlation
In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3
Explicit algebraic stress model
The algebraic stress model arises in computational fluid dynamics. Two main approaches can be undertaken. In the first, the transport of the turbulent stresses is assumed proportional to the turbulent
Map algebra
Map algebra is an algebra for manipulating geographic data, primarily fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of primitive operations in a geographic information
Mathematics and art
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architec
Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mat
Geometric calculus
In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories includi
NeuroMat
The Research, Innovation, and Dissemination Center for Neuromathematics (RIDC NeuroMat, or simply NeuroMat) is a Brazilian research center established in 2013 at the University of São Paulo that is de
Vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem ("shaking, brandishing"). The oscillations may be periodic, such as th
Uniform field theory
Uniform field theory is a formula for determining the effective electrical resistance of a parallel wire system. By calculating the mean square field acting throughout a section of coil, formulae are
Mathematical psychology
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rule
Bass diffusion model
The Bass model or Bass diffusion model was developed by Frank Bass. It consists of a simple differential equation that describes the process of how new products get adopted in a population. The model
Basque Center for Applied Mathematics
The Basque Center of Applied Mathematics (BCAM) is a research center on applied mathematics, created with the support of the Basque Government and the University of the Basque Country. The BCAM headqu
System size expansion
The system size expansion, also known as van Kampen's expansion or the Ω-expansion, is a technique pioneered by Nico van Kampen used in the analysis of stochastic processes. Specifically, it allows on
Analytical regularization
In physics and applied mathematics, analytical regularization is a technique used to convert boundary value problems which can be written as Fredholm integral equations of the first kind involving sin
Least-squares spectral analysis
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the mos
Cryptanalysis
Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis
How Round Is Your Circle?
How Round Is Your Circle? Where Engineering and Mathematics Meet is a book on the mathematics of physical objects, for a popular audience. It was written by chemical engineer John Bryant and mathemati
Spirangle
In geometry, a spirangle is a figure related to a spiral. Spirangles are similar to spirals in that they expand from a center point as they grow larger, but they are made out of straight line segments
Nonlinear complementarity problem
In applied mathematics, a nonlinear complementarity problem (NCP) with respect to a mapping ƒ : Rn → Rn, denoted by NCPƒ, is to find a vector x ∈ Rn such that where ƒ(x) is a smooth mapping. The case
Discrete calculus
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalization
NK model
The NK model is a mathematical model described by its primary inventor Stuart Kauffman as a "tunably rugged" fitness landscape. "Tunable ruggedness" captures the intuition that both the overall size o
Multi-time-step integration
In numerical analysis, multi-time-step integration, also referred to as multiple-step or asynchronous time integration, is a numerical time-integration method that uses different time-steps or time-in
Doubly linked face list
In applied mathematics, a doubly linked face list (DLFL) is an efficient data structure for storing 2-manifold mesh data. The structure stores linked lists for a 3D mesh's faces, edges, vertices, and
Wahba's problem
In applied mathematics, Wahba's problem, first posed by Grace Wahba in 1965, seeks to find a rotation matrix (special orthogonal matrix) between two coordinate systems from a set of (weighted) vector
Field equation
In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distr
Self-consistent mean field (biology)
The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino acid side chain packing given a fixed protein bac
Computational mathematics
Computational mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation. A large part of computational mathematics consists roughly of using mathema
Tensor network
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend one-dimensional matrix product states to highe
Discrete tomography
Discrete tomography focuses on the problem of reconstruction of binary images (or finite subsets of the integer lattice) from a small number of their projections. In general, tomography deals with the
Weber problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation c
Common cause and special cause (statistics)
Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, "common cause
Asymptotology
Asymptotology has been defined as “the art of dealing with applied mathematical systems in limiting cases” as well as “the science about the synthesis of simplicity and exactness by means of localizat
Statistical field theory
In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions. It does not denote a single theory but encompasses many models, including for magnet
Mathematical sciences
The mathematical sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally consi
Integrable algorithm
Integrable algorithms are numerical algorithms that rely on basic ideas from the mathematical theory of integrable systems.
Routhian mechanics
In classical mechanics, Routh's procedure or Routhian mechanics is a hybrid formulation of Lagrangian mechanics and Hamiltonian mechanics developed by Edward John Routh. Correspondingly, the Routhian
Viral dynamics
Viral dynamics is a field of applied mathematics concerned with describing the progression of viral infections within a host organism. It employs a family of mathematical models that describe changes
Scale analysis (mathematics)
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual
Abstract family of languages
In computer science, in particular in the field of formal language theory,an abstract family of languages is an abstract mathematical notion generalizing characteristics common to the regular language
Social choice theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in
German tank problem
In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without replacement. In simple terms, suppose there
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used
Continuous modelling
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential eq
Trapping region
In applied mathematics, a trapping region of a dynamical system is a region such that every trajectory that starts within the trapping region will move to the region's interior and remain there as the
Geometric phase analysis
Geometric phase analysis is a method of digital signal processing used to determine crystallographic quantities such as d-spacing or strain from high-resolution transmission electron microscope images
Geomathematics
Geomathematics (also: mathematical geosciences, mathematical geology, mathematical geophysics) is the application of mathematical methods to solve problems in geosciences, including geology and geophy