An explanatory variable is the "input" variable and the response variable is the "output" variable.
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In other cases, while the historic data describing outcomes exists for you to train an algorithm, it may not capture the input variable under consideration.
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The Casorati matrix is useful in the study of linear difference equations, just as the Wronskian is useful with linear differential equations. It is calculated based on n functions of the single input variable.
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Consider a dataset where each input variable corresponds to a specific gene. Sparse PCA can produce a principal component that involves only a few genes, so researchers can focus on these specific genes for further analysis.
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The key reason for studentizing is that, in regression analysis of a multivariate distribution, the variances of the residuals at different input variable values may differ, even if the variances of the errors at these different input variable values are equal. The issue is the difference between errors and residuals in statistics, particularly the behavior of residuals in regressions. Consider the simple linear regression model : Y = \alpha_0 + \alpha_1 X + \varepsilon. \, Given a random sample (Xi, Yi), i = 1, ..., n, each pair (Xi, Yi) satisfies : Y_i = \alpha_0 + \alpha_1 X_i + \varepsilon_i,\, where the errors \varepsilon_i, are independent and all have the same variance \sigma^2.
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They are configured through standardized programming languages such as IEC-1131. # SLC (single loop controller) - Single loop controllers are appliances that monitor an input variable and effect change on a control output (manipulated variable) to hold the input variable to a setpoint. # PAC (programmable automation controller) - Programmable automation controllers are appliances that embody properties of both PLCs and SLCs enabling the integration of both analog and discrete control. # Universal gateway - A universal gateway appliance has the ability to communicate with a variety of devices through their respective communication protocols, and will affect data transactions between them.
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A numerical (analog) input variable has control properties such as: LOW, HIGH, OK, BAD, UNKNOWN according to its range of desired values. A timer can have its OVER state (time-out occurred) as its most significant control value; other values could be STOPPED, RUNNING etc...
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A program could be considered as a function, P:S → R, where is the set of all possible inputs and the set of all possible outputs. An input variable of function P is mapped to an input parameter of P. P(x) denotes execution of program for certain input x.
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The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.
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The output variable value that is fed backward is used to initiate that corrective action on a regulator. Most control loops in the industry are of the feedback type. In a feed-forward closed loop system, the measured process variable is an input variable. The measured signal is then used in the same fashion as in a feedback system.
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Input variable (u) is a specified variable that commonly include flow rates. It is important to note that the entering and exiting flows are both considered control inputs. The control input can be classified as a manipulated, disturbance, or unmonitored variable. Parameters (p) are usually a physical limitation and something that is fixed for the system, such as the vessel volume or the viscosity of the material.
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Resulting from its geometry, the optical switch is sensitive to the angle of the incident beam. Depending on the shape of the prisms, the transmittance of the switch in its reflective state during a typical day shows characteristic angular dependence. This dependence can be used to find specific transmission curves for different applications, where the geometry of the prisms serves as the input variable.
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Note that because PPR attempts to fit projections of the data, it can be difficult to interpret the fitted model as a whole, because each input variable has been accounted for in a complex and multifaceted way. This can make the model more useful for prediction than for understanding the data, though visualizing individual ridge functions and considering which projections the model is discovering can yield some insight.
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A variable in the VFSM environment may have one or more values which are relevant for the control - in such a case it is an input variable. Those values are the control properties of this variable. Control properties are not necessarily specific data values but are rather certain states of the variable. For instance, a digital variable could provide three control properties: TRUE, FALSE and UNKNOWN according to its possible boolean values.
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Suppose ordinary PCA is applied to a dataset where each input variable represents a different asset, it may generate principal components that are weighted combination of all the assets. In contrast, sparse PCA would produce principal components that are weighted combination of only a few input assets, so one can easily interpret its meaning. Furthermore, if one uses a trading strategy based on these principal components, fewer assets imply less transaction costs.
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There are ways of using probabilities that are definitely not Monte Carlo simulations – for example, deterministic modeling using single-point estimates. Each uncertain variable within a model is assigned a "best guess" estimate. Scenarios (such as best, worst, or most likely case) for each input variable are chosen and the results recorded. By contrast, Monte Carlo simulations sample from a probability distribution for each variable to produce hundreds or thousands of possible outcomes.
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Depending on the context, an independent variable is sometimes called a "predictor variable", regressor, covariate, "manipulated variable", "explanatory variable", exposure variable (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning and pattern recognition) or "input variable".Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. (entry for "independent variable")Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. (entry for "regression") In econometrics, the term "control variable" is usually used instead of "covariate".
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The lambda calculus consists of a language of lambda terms, which is defined by a certain formal syntax, and a set of transformation rules, which allow manipulation of the lambda terms. These transformation rules can be viewed as an equational theory or as an operational definition. As described above, all functions in the lambda calculus are anonymous functions, having no names. They only accept one input variable, with currying used to implement functions with several variables.
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The term event is being used more and more widely in programming; recently it has become one of the most commonly used terms in software development. As opposed to it, the offered approach is based on the term state (State-Driven Architecture). After introduction of the term input action, which could denote an input variable or an event, the term automaton without outputs might be brought in. After adding the term output action, the term “automaton” might be used.
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In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits of polynomial size. Comparator circuits are sorting networks in which each comparator gate is directed, each wire is initialized with an input variable, its negation, or a constant, and one of the wires is distinguished as the output wire. The most important problem which is complete for CC is a decision variant of the stable marriage problem.
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Graph of the linear function: y(x) = -x + 2 In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a line in the plane.Stewart 2012, p. 23 The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input. Linear functions are related to linear equations.
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A shift invariant system is the discrete equivalent of a time-invariant system, defined such that if y(n) is the response of the system to x(n), then y(n-k) is the response of the system to x(n-k).Oppenheim, Schafer, 12 That is, in a shift-invariant system the contemporaneous response of the output variable to a given value of the input variable does not depend on when the input occurs; time shifts are irrelevant in this regard.
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In some contexts, especially in computing, it is useful to consider signed versions of zero, with signed zeros referring to different, discrete number representations (see signed number representations for more). The symbols and rarely appear as substitutes for and used in calculus and mathematical analysis for one-sided limits (right-sided limit and left-sided limit, respectively). This notation refers to the behaviour of a function as its real input variable approaches along positive (resp., negative) values; the two limits need not exist or agree.
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However, the interest is sometimes in finding the optimal value for input variables in terms of the system outcomes. One way could be running simulation experiments for all possible input variables. However, this approach is not always practical due to several possible situations and it just makes it intractable to run experiments for each scenario. For example, there might be too many possible values for input variables, or the simulation model might be too complicated and expensive to run for suboptimal input variable values.
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It is clear that variation of the groundwater levels have significant power at the ocean tidal frequencies. To estimate the extent at which the groundwater levels are influenced by the ocean surface levels, we compute the coherence between them. Let us assume that there is a linear relationship between the ocean surface height and the groundwater levels. We further assume that the ocean surface height controls the groundwater levels so that we take the ocean surface height as the input variable, and the groundwater well height as the output variable.
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In physics, linearity is a property of the differential equations governing many systems; for instance, the Maxwell equations or the diffusion equation. Linearity of a homogenous differential equation means that if two functions f and g are solutions of the equation, then any linear combination is, too. In instrumentation, linearity means that a given change in an input variable gives the same change in the output of the measurement apparatus: this is highly desirable in scientific work. In general, instruments are close to linear over a certain range, and most useful within that range.
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The regulator is able to alter the input variable in response to the signal from the controller. An open-loop system has no feedback or feed forward mechanism, so the input and output signals are not directly related and there is increased traffic variability. There is also a lower arrival rate in such system and a higher loss rate. In an open control system, the controllers can operate the regulators at regular intervals, but there is no assurance that the output variable can be maintained at the desired level.
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For example, it is clear that the atmospheric barometric pressure induces a variation in both the ocean water levels and the groundwater levels, but the barometric pressure is not included in the system model as an input variable. We have also assumed that the ocean water levels drive or control the groundwater levels. In reality it is a combination of hydrological forcing from the ocean water levels and the tidal potential that are driving both the observed input and output signals. Additionally, noise introduced in the measurement process, or by the spectral signal processing can contribute to or corrupt the coherence.
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The distance between that point and the adjacent side is some fraction that is the product of 1 the distance from the vertex, and 2 the magnitude of the opposite side. The second input variable in this type of multiplier positions a slotted plate perpendicular to the adjacent side. That slot contains a block, and that block's position in its slot is determined by another block right next to it. The latter slides along the hypotenuse, so the two blocks are positioned at a distance from the (trig.) adjacent side by an amount proportional to the product.
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In control engineering and control theory the transfer function is derived using the Laplace transform. The transfer function was the primary tool used in classical control engineering. However, it has proven to be unwieldy for the analysis of multiple-input multiple-output (MIMO) systems, and has been largely supplanted by state space representations for such systems. In spite of this, a transfer matrix can always be obtained for any linear system, in order to analyze its dynamics and other properties: each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.
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SELDM is a stochastic model because it uses Monte Carlo methods to produce the random combinations of input variable values needed to generate the stochastic population of values for each component variable. SELDM calculates the dilution of runoff in the receiving waters and the resulting downstream event mean concentrations and annual average lake concentrations. Results are ranked, and plotting positions are calculated, to indicate the level of risk of adverse effects caused by runoff concentrations, flows, and loads on receiving waters by storm and by year. Unlike deterministic hydrologic models, SELDM is not calibrated by changing values of input variables to match a historical record of values.
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This simple control table directs program flow according to the value of the single input variable. Each table entry holds a possible input value to be tested for equality (implied) and a relevant subroutine to perform in the action column. The name of the subroutine could be replaced by a relative subroutine number if pointers are not supported Control tables are tables that control the control flow or play a major part in program control. There are no rigid rules about the structure or content of a control table--its qualifying attribute is its ability to direct control flow in some way through "execution" by a processor or interpreter.
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A further generalization is given by the Veronese variety, when there is more than one input variable. In the theory of quadratic forms, the parabola is the graph of the quadratic form (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form . Generalizations to more variables yield further such objects. The curves for other values of are traditionally referred to as the higher parabolas and were originally treated implicitly, in the form for and both positive integers, in which form they are seen to be algebraic curves.
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If the ordered pairs representing the original input function are equally spaced in their input variable (for example, equal time steps), then the Fourier transform is known as a discrete Fourier transform (DFT), which can be computed either by explicit numerical integration, by explicit evaluation of the DFT definition, or by fast Fourier transform (FFT) methods. In contrast to explicit integration of input data, use of the DFT and FFT methods produces Fourier transforms described by ordered pairs of step size equal to the reciprocal of the original sampling interval. For example, if the input data is sampled every 10 seconds, the output of DFT and FFT methods will have a 0.1 Hz frequency spacing.
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Consider the graph below of a relationship between an input variable x and the output Y, for which it is desired that a value of 7 is taken, of a system of interest. It can be seen that there are two possible values that x can take, 5 and 30. If the tolerance for x is independent of the nominal value, then it can also be seen that when x is set equal to 30, the expected variation of Y is less than if x were set equal to 5. The reason is that the gradient at x = 30 is less than at x = 5, and the random variability in x is suppressed as it flows to Y. File:Robustification.
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The amount of energy input into the system (E) depends on the resistance of the heating elements (R), the current applied to the heating elements (I), and the amount of time the current is applied (t). Alternating current (AC) and direct current (DC) both work in this process. The energy produced is calculated using the following equation: E=I^2Rt Research has shown the input variable with the most impact on the performance of the resulting joint is the current. The same amount of energy can by input into the part by applying a low current for a long period of time or if a high current is applied for a short amount of time.
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Metamodel of Optimal Prognosis (MOP): The prediction quality of an approximation model may be improved if unimportant variables are removed from the model. This idea is adopted in the Metamodel of Optimal Prognosis (MOP) which is based on the search for the optimal input variable set and the most appropriate approximation model (polynomial or Moving Least Squares with linear or quadratic basis). Due to the model independence and objectivity of the CoP measure, it is well suited to compare the different models in the different subspaces. Multi-disciplinary optimization: The optimal variable subspace and approximation model found by a CoP/MOP procedure can also be used for a pre-optimization before global optimizers (evolutionary algorithms, Adaptive Response Surface Methods, Gradient-based methods, biological-based methods) are used for a direct single-objective optimization.
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The control rules for estimating module values are based on logic relationships between inputs and outputs, expressed in linguistic terms by 'if-then' statements. For example, when two input variables (validation metrics) are aggregated four rules are required, formalized as: ____PREMISE____CONCLUSION if x1 is F and x2 is F then yi is B1 if x1 is F and x2 is U then y2 is B2 if x1 is U and x2 is F then y3 is B3 if x1 is U and x2 is U then y4 is B4 where xi is an input variable, yi is an output variable and Bi is a conclusion (or expert weight). The value of each conjunction (… and …) is the minimum of the quantified fuzzy groups, which are obtained from complementary S-shaped distribution curves.
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A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.Enderton, 2001 In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. See the examples below for further clarification.
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The concept of the index of a DVI is important and determines many questions of existence and uniqueness of solutions to a DVI. This concept is closely related to the concept of index for differential algebraic equations (DAE's), which is the number of times the algebraic equations of a DAE must be differentiated in order to obtain a complete system of differential equations for all variables. It is also a notion close to the relative degree of Control Theory, which is, roughly speaking, the number of times an "output" variable has to be differentiated so that an "input" variable appears explicitly in Control Theory this is used to derive a canonical state space form which involves the so-called "zero-dynamics", a fundamental concept for control). For a DVI, the index is the number of differentiations of F(t, x, u) = 0 needed in order to locally uniquely identify u as a function of t and x.
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An XForms document can be as simple as a web form (by only specifying the submission element in the model section, and placing the controls in the body), but XForms includes many advanced features. For example, new data can be requested and used to update the form while it is running, much like using XMLHttpRequest/AJAX except without scripting. The form author can validate user data against XML Schema data types, require certain data, disable input controls or change sections of the form depending on circumstances, enforce particular relationships between data, input variable length arrays of data, output calculated values derived from form data, prefill entries using an XML document, respond to actions in real time (versus at submission time), and modify the style of each control depending on the device they are displayed on (desktop browser versus mobile versus text only, etc.). There is often no need for any scripting with languages such as JavaScript.
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Testing whether the Grundy number of a given graph is at least , for a fixed constant , can be performed in polynomial time, by searching for all possible -atoms that might be subgraphs of the given graph. However, this algorithm is not fixed-parameter tractable, because the exponent in its running time depends on . When is an input variable rather than a parameter, the problem is NP-complete.. The Grundy number is at most one plus the maximum degree of the graph, and it remains NP-complete to test whether it equals one plus the maximum degree.. There exists a constant such that it is NP-hard under randomized reductions to approximate the Grundy number to within an approximation ratio better than .. There is an exact exponential time algorithm for the Grundy number that runs in time . For trees, and graphs of bounded treewidth, the Grundy number may be unboundedly large.. Nevertheless, the Grundy number can be computed in polynomial time for trees, and is fixed-parameter tractable when parameterized by both the treewidth and the Grundy number,.
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Another method to calculate the mean square of error when analyzing the variance of linear regression using a technique like that used in ANOVA (they are the same because ANOVA is a type of regression), the sum of squares of the residuals (aka sum of squares of the error) is divided by the degrees of freedom (where the degrees of freedom equal n − p − 1, where p is the number of parameters estimated in the model (one for each variable in the regression equation, not including the intercept)). One can then also calculate the mean square of the model by dividing the sum of squares of the model minus the degrees of freedom, which is just the number of parameters. Then the F value can be calculated by dividing the mean square of the model by the mean square of the error, and we can then determine significance (which is why you want the mean squares to begin with.). However, because of the behavior of the process of regression, the distributions of residuals at different data points (of the input variable) may vary even if the errors themselves are identically distributed.
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