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In some global optimization problems the analytical definition of the objective function is unknown and it is only possible to get values at fixed points. There are objective functions in which the cost of an evaluation is very high, for example when the evaluation is the result of an experiment or a particularly onerous measurement.
In both the global and local cases, the concept of a strict extremum can be defined. For example, x ∗ is a strict global maximum point if for all x in X with x ≠ x ∗, we have f(x ∗) > f(x), and x ∗ is a strict local maximum point if there exists some ε > 0 such that, for all x in X within distance ε of x ∗ with x ≠ x ∗, we ...
Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.
Quantitative psychological research findings result from mathematical modeling and statistical estimation or statistical inference. The two types of research differ in the methods employed, rather than the topics they focus on. There are three main types of psychological research: Correlational research; Descriptive research; Experimental research
After establishing the critical points of a function, the second-derivative test uses the value of the second derivative at those points to determine whether such points are a local maximum or a local minimum. [1] If the function f is twice-differentiable at a critical point x (i.e. a point where f ′ (x) = 0), then:
Experimental psychology refers to work done by those who apply experimental methods to psychological study and the underlying processes. Experimental psychologists employ human participants and animal subjects to study a great many topics, including (among others) sensation, perception, memory, cognition, learning, motivation, emotion; developmental processes, social psychology, and the neural ...
The oddball method was first used in event-related potential (ERP) research by Nancy Squires, Kenneth Squires and Steven Hillyard at the UC San Diego. [2] The P300 response of different healthy subjects in a two-tone auditory oddball paradigm. The plots show the average response to oddball (red) and standard (blue) trials and their difference ...
For the purpose of detecting grey-level blobs (local extrema with extent) from a watershed analogy, Lindeberg developed an algorithm based on pre-sorting the pixels, alternatively connected regions having the same intensity, in decreasing order of the intensity values. Then, comparisons were made between nearest neighbours of either pixels or ...