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wiki_700_chunk_0 | Deterministic simulation | In mathematical modeling, deterministic simulations contain no random variables and no degree of randomness, and consist mostly of equations, for example difference equations. These simulations have known inputs and they result in a unique set of outputs. Contrast stochastic (probability) simulation, which includes ran... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_701_chunk_0 | Deterministic simulation | Deterministic simulation models are usually designed to capture some underlying mechanism or natural process. They are different from statistical models (for example linear regression) whose aim is to empirically estimate the relationships between variables. The deterministic model is viewed as a useful approximation o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_702_chunk_0 | Underfitting | 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 future observations reliably". An overfitted model is a mathematical model that contains more parameters than can be ju... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_703_chunk_0 | Underfitting | : 45 Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_704_chunk_0 | Underfitting | Under-fitting would occur, for example, when fitting a linear model to non-linear data. Such a model will tend to have poor predictive performance. The possibility of over-fitting exists because the criterion used for selecting the model is not the same as the criterion used to judge the suitability of a model. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_705_chunk_0 | Underfitting | For example, a model might be selected by maximizing its performance on some set of training data, and yet its suitability might be determined by its ability to perform well on unseen data; then over-fitting occurs when a model begins to "memorize" training data rather than "learning" to generalize from a trend. As an ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_706_chunk_0 | Underfitting | Such a model, though, will typically fail severely when making predictions. The potential for overfitting depends not only on the number of parameters and data but also the conformability of the model structure with the data shape, and the magnitude of model error compared to the expected level of noise or error in the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_707_chunk_0 | Underfitting | In particular, the value of the coefficient of determination will shrink relative to the original data. To lessen the chance or amount of overfitting, several techniques are available (e.g., model comparison, cross-validation, regularization, early stopping, pruning, Bayesian priors, or dropout). The basis of some tech... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_708_chunk_0 | Resilience (mathematics) | In mathematical modeling, resilience refers to the ability of a dynamical system to recover from perturbations and return to its original stable steady state. It is a measure of the stability and robustness of a system in the face of changes or disturbances. If a system is not resilient enough, it is more susceptible t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_709_chunk_0 | Extraneous variables | In mathematical modeling, the dependent variable is studied to see if and how much it varies as the independent variables vary. In the simple stochastic linear model yi = a + bxi + ei the term yi is the ith value of the dependent variable and xi is the ith value of the independent variable. The term ei is known as the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_710_chunk_0 | Extraneous variables | This is also called a bivariate dataset, (x1, y1)(x2, y2) ...(xi, yi). The simple linear regression model takes the form of Yi = a + Bxi + Ui, for i = 1, 2, ... , n. In this case, Ui, ... ,Un are independent random variables. This occurs when the measurements do not influence each other. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_711_chunk_0 | Extraneous variables | Through propagation of independence, the independence of Ui implies independence of Yi, even though each Yi has a different expectation value. Each Ui has an expectation value of 0 and a variance of σ2. Expectation of Yi Proof: E = E = α + β x i + E = α + β x i . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_712_chunk_0 | Extraneous variables | {\displaystyle E=E=\alpha +\beta x_{i}+E=\alpha +\beta x_{i}.} The line of best fit for the bivariate dataset takes the form y = α + βx and is called the regression line. α and β correspond to the intercept and slope, respectively.In an experiment, the variable manipulated by an experimenter is something that is proven... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_713_chunk_0 | Extraneous variables | The dependent variable is the event expected to change when the independent variable is manipulated.In data mining tools (for multivariate statistics and machine learning), the dependent variable is assigned a role as target variable (or in some tools as label attribute), while an independent variable may be assigned a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_714_chunk_0 | Effective reproduction number | In mathematical modelling of infectious disease, the dynamics of spreading is usually described through a set of non-linear ordinary differential equations (ODE). So there is always n {\displaystyle n} coupled equations of form C i ˙ = d C i d t = f ( C 1 , C 2 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_715_chunk_0 | Effective reproduction number | , C n ) {\displaystyle {\dot {C_{i}}}={\operatorname {d} \!C_{i} \over \operatorname {d} \!t}=f(C_{1},C_{2},...,C_{n})} which shows how the number of people in compartment C i {\displaystyle C_{i}} changes over time. For example, in a SIR model, C 1 = S {\displaystyle C_{1}=S} , C 2 = I {\displaystyle C_{2}=I} , and C ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_716_chunk_0 | Effective reproduction number | In other words, as a rule, there is an infection-free steady state. This solution, also usually ensures that the disease-free equilibrium is also an equilibrium of the system. There is another fixed point known as an Endemic Equilibrium (EE) where the disease is not totally eradicated and remains in the population. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_717_chunk_0 | Effective reproduction number | Mathematically, R 0 {\displaystyle R_{0}} is a threshold for stability of a disease-free equilibrium such that: R 0 ≤ 1 ⇒ lim t → ∞ ( C 1 ( t ) , C 2 ( t ) , ⋯ , C n ( t ) ) = DFE {\displaystyle R_{0}\leq 1\Rightarrow \lim _{t\to \infty }(C_{1}(t),C_{2}(t),\cdots ,C_{n}(t))={\textrm {DFE}}} R 0 > 1 , I ( 0 ) > 0 ⇒ lim ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_718_chunk_0 | Effective reproduction number | Epidemiologically, the linearisation reflects that R 0 {\displaystyle R_{0}} characterizes the potential for initial spread of an infectious person in a naive population, assuming the change in the susceptible population is negligible during the initial spread. A linear system of ODEs can always be described by a matri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_719_chunk_0 | Effective reproduction number | Note that this operator (matrix) is responsible for the number of infected people, not all the compartments. Iteration of this operator describes the initial progression of infection within the heterogeneous population. So comparing the spectral radius of this operator to unity determines whether the generations of inf... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_720_chunk_0 | Inverse-square law | In mathematical notation the inverse square law can be expressed as an intensity (I) varying as a function of distance (d) from some centre. The intensity is proportional (see ∝) to the reciprocal of the square of the distance thus: It can also be mathematically expressed as: or as the formulation of a constant quantit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_721_chunk_0 | Place value system | In mathematical numeral systems the radix r is usually the number of unique digits, including zero, that a positional numeral system uses to represent numbers. In some cases, such as with a negative base, the radix is the absolute value r = | b | {\displaystyle r=|b|} of the base b. For example, for the decimal system ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_722_chunk_0 | Place value system | The highest symbol of a positional numeral system usually has the value one less than the value of the radix of that numeral system. The standard positional numeral systems differ from one another only in the base they use. The radix is an integer that is greater than 1, since a radix of zero would not have any digits,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_723_chunk_0 | Place value system | It is important that the radix is finite, from which follows that the number of digits is quite low. Otherwise, the length of a numeral would not necessarily be logarithmic in its size. (In certain non-standard positional numeral systems, including bijective numeration, the definition of the base or the allowed digits ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_724_chunk_0 | Heuristic search | In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution. This is achieved by tradi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_725_chunk_0 | Zero-one loss function | In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_726_chunk_0 | Zero-one loss function | The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_727_chunk_0 | Zero-one loss function | In the context of economics, for example, this is usually economic cost or regret. In classification, it is the penalty for an incorrect classification of an example. In actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of Harald Cramér in the 1920s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_728_chunk_0 | Relaxation (approximation) | In mathematical optimization and related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem that is easier to solve. A solution of the relaxed problem provides information about the original problem. For example, a linear programming relaxation of an i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_729_chunk_0 | Relaxation (approximation) | A Lagrangian relaxation of a complicated problem in combinatorial optimization penalizes violations of some constraints, allowing an easier relaxed problem to be solved. Relaxation techniques complement or supplement branch and bound algorithms of combinatorial optimization; linear programming and Lagrangian relaxation... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_730_chunk_0 | Linear complementarity problem | In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_731_chunk_0 | Bland's rule | In mathematical optimization, Bland's rule (also known as Bland's algorithm, Bland's anti-cycling rule or Bland's pivot rule) is an algorithmic refinement of the simplex method for linear optimization. With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling.The original sim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_732_chunk_0 | Cunningham's rule | In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed 1979 by W. H. Cunningham to defeat the deformed hypercube constructions by Klee and Minty et al. (see, e.g.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_733_chunk_0 | Cunningham's rule | History-based rules defeat the deformed hypercube constructions because they tend to average out how many times a variable pivots. It has recently been shown by David Avis and Oliver Friedmann that there is a family of linear programs on which the simplex algorithm equipped with Cunningham's rule requires exponential t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_734_chunk_0 | Simplex algorithm | In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_735_chunk_0 | Himmelblau's function | In mathematical optimization, Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms. The function is defined by: f ( x , y ) = ( x 2 + y − 11 ) 2 + ( x + y 2 − 7 ) 2 . {\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\quad } It has one local maximum at x = − 0.27... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_736_chunk_0 | Wolfe duality | In mathematical optimization, Wolfe duality, named after Philip Wolfe, is type of dual problem in which the objective function and constraints are all differentiable functions. Using this concept a lower bound for a minimization problem can be found because of the weak duality principle. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_737_chunk_0 | Zermelo's navigation problem | In mathematical optimization, Zermelo's navigation problem, proposed in 1931 by Ernst Zermelo, is a classic optimal control problem that deals with a boat navigating on a body of water, originating from a point A {\displaystyle A} to a destination point B {\displaystyle B} . The boat is capable of a certain maximum spe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_738_chunk_0 | Solution space | In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_739_chunk_0 | Solution space | The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x 2 + y 4 . {\displaystyle x^{2}+y^{4}.} In many problems, the feasible set reflects a constraint that one or more variables must be non-negative. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_740_chunk_0 | Solution space | In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices. Constraint satisfaction is the proc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_741_chunk_0 | Quadratically constrained quadratic program | In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form minimize 1 2 x T P 0 x + q 0 T x subject to 1 2 x T P i x + q i T x + r i ≤ 0 for i = 1 , … , m , A x = b , {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_742_chunk_0 | Affine scaling | In mathematical optimization, affine scaling is an algorithm for solving linear programming problems. Specifically, it is an interior point method, discovered by Soviet mathematician I. I. Dikin in 1967 and reinvented in the U.S. in the mid-1980s. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_743_chunk_0 | Constrained minimisation | In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_744_chunk_0 | Linearization | In mathematical optimization, cost functions and non-linear components within can be linearized in order to apply a linear solving method such as the Simplex algorithm. The optimized result is reached much more efficiently and is deterministic as a global optimum. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_745_chunk_0 | Fractional programming | In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program is a ratio of two functions that are in general nonlinear. The ratio to be optimized often describes some kind of efficiency of a system. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_746_chunk_0 | Linear-fractional programming | In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a speci... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_747_chunk_0 | Very large-scale neighborhood search | In mathematical optimization, neighborhood search is a technique that tries to find good or near-optimal solutions to a combinatorial optimisation problem by repeatedly transforming a current solution into a different solution in the neighborhood of the current solution. The neighborhood of a solution is a set of simil... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_748_chunk_0 | Very large-scale neighborhood search | If neighborhood searched is limited to just one or a very small number of changes from the current solution, then it can be difficult to escape from local minima, even with additional meta-heuristic techniques such as Simulated Annealing or Tabu search. In large neighborhood search techniques, the possible changes from... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_749_chunk_0 | Oracle complexity (optimization) | In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_750_chunk_0 | Ackley function | In mathematical optimization, the Ackley function is a non-convex function used as a performance test problem for optimization algorithms. It was proposed by David Ackley in his 1987 PhD dissertation.On a 2-dimensional domain it is defined by: f ( x , y ) = − 20 exp − exp + e + 20 {\displaystyle {\begin{aligned}f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_751_chunk_0 | KKT conditions | In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied. Allowing inequali... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_752_chunk_0 | Klee–Minty cube | In mathematical optimization, the Klee–Minty cube is an example that shows the worst-case computational complexity of many algorithms of linear optimization. It is a deformed cube with exactly 2D corners in dimension D. Klee and Minty showed that Dantzig's simplex algorithm visits all corners of a (perturbed) cube in d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_753_chunk_0 | Rastrigin function | In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed in 1974 by Rastrigin as a 2-dimensional function and has been generalized by Rudolph. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_754_chunk_0 | Rastrigin function | The generalized version was popularized by Hoffmeister & Bäck and Mühlenbein et al. Finding the minimum of this function is a fairly difficult problem due to its large search space and its large number of local minima. On an n {\displaystyle n} -dimensional domain it is defined by: f ( x ) = A n + ∑ i = 1 n {\displays... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_755_chunk_0 | Rosenbrock function | In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. It is also known as Rosenbrock's valley or Rosenbrock's banana function. The global minimum is inside a long, narrow, parab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_756_chunk_0 | Rosenbrock function | To converge to the global minimum, however, is difficult. The function is defined by f ( x , y ) = ( a − x ) 2 + b ( y − x 2 ) 2 {\displaystyle f(x,y)=(a-x)^{2}+b(y-x^{2})^{2}} It has a global minimum at ( x , y ) = ( a , a 2 ) {\displaystyle (x,y)=(a,a^{2})} , where f ( x , y ) = 0 {\displaystyle f(x,y)=0} . Usually, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_757_chunk_0 | Active set | In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem. An opt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_758_chunk_0 | Active set | The active set at x 0 {\displaystyle x_{0}} is made up of those constraints g i ( x 0 ) {\displaystyle g_{i}(x_{0})} that are active at the current point (Nocedal & Wright 2006, p. 308). The active set is particularly important in optimization theory, as it determines which constraints will influence the final result o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_759_chunk_0 | Criss-cross algorithm | In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_760_chunk_0 | Cutting plane | In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_761_chunk_0 | Cutting plane | The theory of Linear Programming dictates that under mild assumptions (if the linear program has an optimal solution, and if the feasible region does not contain a line), one can always find an extreme point or a corner point that is optimal. The obtained optimum is tested for being an integer solution. If it is not, t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_762_chunk_0 | Cutting plane | Finding such an inequality is the separation problem, and such an inequality is a cut. A cut can be added to the relaxed linear program. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_763_chunk_0 | Cutting plane | Then, the current non-integer solution is no longer feasible to the relaxation. This process is repeated until an optimal integer solution is found. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_764_chunk_0 | Cutting plane | Cutting-plane methods for general convex continuous optimization and variants are known under various names: Kelley's method, Kelley–Cheney–Goldstein method, and bundle methods. They are popularly used for non-differentiable convex minimization, where a convex objective function and its subgradient can be evaluated eff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_765_chunk_0 | Ellipsoidal algorithm | In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions. When specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_766_chunk_0 | Firefly algorithm | In mathematical optimization, the firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_767_chunk_0 | Lagrange multiplier | In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_768_chunk_0 | Lagrange multiplier | This means that all partial derivatives should be zero, including the partial derivative with respect to λ {\displaystyle \lambda ~} . ∂ L ∂ x = 0 {\displaystyle \ {\frac {\ \partial {\mathcal {L}}\ }{\partial x}}=0\qquad } and ∂ L ∂ λ = 0 ; {\displaystyle \qquad {\frac {\ \partial {\mathcal {L}}\ }{\partial \lambda }}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_769_chunk_0 | Lagrange multiplier | The solution corresponding to the original constrained optimization is always a saddle point of the Lagrangian function, which can be identified among the stationary points from the definiteness of the bordered Hessian matrix.The great advantage of this method is that it allows the optimization to be solved without exp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_770_chunk_0 | Network simplex algorithm | In mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. The algorithm is usually formulated in terms of a minimum-cost flow problem. The network simplex method works very well in practice, typically 200 to 300 times faster than the simplex method applied... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_771_chunk_0 | Perturbation function | In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem. In many cases this takes the form of shifting the constraints.In some texts the value function is called t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_772_chunk_0 | Non-negative least squares | In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative. That is, given a matrix A and a (column) vector of response variables y, the goal is to find a r g m i n x ‖ A x − y ‖ 2 2 {\displays... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_773_chunk_0 | Proximal operator | In mathematical optimization, the proximal operator is an operator associated with a proper, lower semi-continuous convex function f {\displaystyle f} from a Hilbert space X {\displaystyle {\mathcal {X}}} to {\displaystyle } , and is defined by: prox f ( v ) = arg min x ∈ X ( f ( x ) + 1 2 ‖ x − v ‖ X 2 ) . {\disp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_774_chunk_0 | Push–relabel maximum flow algorithm | In mathematical optimization, the push–relabel algorithm (alternatively, preflow–push algorithm) is an algorithm for computing maximum flows in a flow network. The name "push–relabel" comes from the two basic operations used in the algorithm. Throughout its execution, the algorithm maintains a "preflow" and gradually c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_775_chunk_0 | Push–relabel maximum flow algorithm | The generic algorithm has a strongly polynomial O(V 2E) time complexity, which is asymptotically more efficient than the O(VE 2) Edmonds–Karp algorithm. Specific variants of the algorithms achieve even lower time complexities. The variant based on the highest label node selection rule has O(V 2√E) time complexity and i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_776_chunk_0 | Revised simplex algorithm | In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the constrai... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_777_chunk_0 | Total dual integrality | In mathematical optimization, total dual integrality is a sufficient condition for the integrality of a polyhedron. Thus, the optimization of a linear objective over the integral points of such a polyhedron can be done using techniques from linear programming. A linear system A x ≤ b {\displaystyle Ax\leq b} , where A ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_778_chunk_0 | Liability threshold model | In mathematical or statistical modeling a threshold model is any model where a threshold value, or set of threshold values, is used to distinguish ranges of values where the behaviour predicted by the model varies in some important way. A particularly important instance arises in toxicology, where the model for the eff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_779_chunk_0 | Prime filter | In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion. Ideals are of great importance for many constructions in order and l... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_780_chunk_0 | Gravitational instantons | In mathematical physics and differential geometry, a gravitational instanton is a four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations. They are so named because they are analogues in quantum theories of gravity of instantons in Yang–Mills theory. In accordance with this analogy with s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_781_chunk_0 | Gravitational instantons | From a physical point of view, a gravitational instanton is a non-singular solution of the vacuum Einstein equations with positive-definite, as opposed to Lorentzian, metric. There are many possible generalizations of the original conception of a gravitational instanton: for example one can allow gravitational instanto... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_782_chunk_0 | ADHM construction | In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper "Construction of Instantons." | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_783_chunk_0 | Quadratic Fourier transform | In mathematical physics and harmonic analysis, the quadratic Fourier transform is an integral transform that generalizes the fractional Fourier transform, which in turn generalizes the Fourier transform.Roughly speaking, the Fourier transform corresponds to a change of variables from time to frequency (in the context o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_784_chunk_0 | Pauli matrices | In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field. They also represent the interaction states of two polarization filters for horizontal / vertical polarization, 45 degree polarization (right/left), and circul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_785_chunk_0 | Pauli matrices | This means that any 2 × 2 Hermitian matrix can be written in a unique way as a linear combination of Pauli matrices, with all coefficients being real numbers. Hermitian operators represent observables in quantum mechanics, so the Pauli matrices span the space of observables of the complex 2 dimensional Hilbert space. I... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_786_chunk_0 | Pauli matrices | {\displaystyle \ \mathbb {R} ^{3}~.} The Pauli matrices (after multiplication by i to make them anti-Hermitian) also generate transformations in the sense of Lie algebras: the matrices iσ1, iσ2, iσ3 form a basis for the real Lie algebra s u ( 2 ) {\displaystyle {\mathfrak {su}}(2)} , which exponentiates to the special ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_787_chunk_0 | Continuum limit | In mathematical physics and mathematics, the continuum limit or scaling limit of a lattice model refers to its behaviour in the limit as the lattice spacing goes to zero. It is often useful to use lattice models to approximate real-world processes, such as Brownian motion. Indeed, according to Donsker's theorem, the di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_788_chunk_0 | Gaussian q-distribution | In mathematical physics and probability and statistics, the Gaussian q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution. It was introduced by Diaz and Teruel. It is a q-analog of the Gaussian or normal distribution. T... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_789_chunk_0 | Orbital stability | In mathematical physics and the theory of partial differential equations, the solitary wave solution of the form u ( x , t ) = e − i ω t ϕ ( x ) {\displaystyle u(x,t)=e^{-i\omega t}\phi (x)} is said to be orbitally stable if any solution with the initial data sufficiently close to ϕ ( x ) {\displaystyle \phi (x)} forev... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_790_chunk_0 | KZ equation | In mathematical physics the Knizhnik–Zamolodchikov equations, or KZ equations, are linear differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level. They form a system of complex partial differ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_791_chunk_0 | Clebsch–Gordan coefficients for SU(3) | In mathematical physics, Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations, where ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_792_chunk_0 | Gleason's theorem | In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from the usual mathematical representation of measurements in quantum physics together with the assumption of non-contextuality. Andrew M. Gleason first proved the theorem... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_793_chunk_0 | Hilbert-Ackermann system | In mathematical physics, Hilbert system is an infrequently used term for a physical system described by a C*-algebra.In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal deduction attribute... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_794_chunk_0 | Kundt spacetime | In mathematical physics, Kundt spacetimes are Lorentzian manifolds admitting a geodesic null congruence with vanishing optical scalars (expansion, twist and shear). A well known member of Kundt class is pp-wave. Ricci-flat Kundt spacetimes in arbitrary dimension are algebraically special. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_795_chunk_0 | Geometry of special relativity | In mathematical physics, Minkowski space (or Minkowski spacetime) () combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field. A four-vector (x,y,z,t) consists of a coordina... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_796_chunk_0 | Geometry of special relativity | The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others, and said it "was grown on experimental physical grounds." Minkowsk... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_797_chunk_0 | Geometry of special relativity | While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events. Minkowski space differs from four-dimensional Euclidean space insofar as it treats time diff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_798_chunk_0 | Geometry of special relativity | It is generated by rotations, reflections and translations. When time is appended as a fourth dimension, the further transformations of translations in time and Lorentz boosts are added, and the group of all these transformations is called the Poincaré group. Minkowski's model follows special relativity where motion ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_799_chunk_0 | Geometry of special relativity | Spacetime is equipped with an indefinite non-degenerate bilinear form, variously called the Minkowski metric, the Minkowski norm squared or Minkowski inner product depending on the context. The Minkowski inner product is defined so as to yield the spacetime interval between two events when given their coordinate differ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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