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Making Content-Based Medical Image Retrieval Systems Worth for Computer-Aided Diagnosis: From Theory to Application
Published in de Azevedo-Marques Paulo Mazzoncini, Mencattini Arianna, Salmeri Marcello, Rangayyan Rangaraj M., Medical Image Analysis and Informatics: Computer-Aided Diagnosis and Therapy, 2018
Agma Juci Machado Traina, Marcos Vinícius Naves Bedo, Lucio Fernandes Dutra Santos, Luiz Olmes Carvalho, Glauco Vítor Pedrosa, Alceu Ferraz Costa, Caetano Traina Jr.
Definition20.2 (Metric). Given a data domaindouble-struckS, a distance functiond:double-struckS ×double-struckS↦ℝ+ is called a metric ondouble-struckS iff, for alla,b,c∈double-struckS, there holds:d (a,b) > 0 (non-negativity)d (a,b) = 0 ⟺ a = b (identity of indiscernibles)d (a,b) = d (b,a) (symmetry)d (a,b) ≤ d (a,c) + d (b,c) (triangle inequality)
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Published in Carl W. Hall, Laws and Models, 2018
cb = specific vapor capacity p = pressure s = density of porous material Keywords: drying, expansion, molar, porous, vapor LEBEDEV, P. D., twentieth century, Russian engineer;* or LEBVEDEV, Sergei Vassilievich, 1874-1934, Russian chemist (other references) Sources: Gillispie, C. C. 1981; Hall, C. W. 1979; *Lykov, A. V. and Mikhaylov, Y. A. 1961; Parker, S. P. 1992. See also LUIKOV; MINIOVICH LE CHATELIER LAW OF RADIATION The intensity of radiation of red light is represented by: I = 106.7 T–3210/T where I = intensity T = absolute temperature Keywords: intensity, radiation, red light LE CHATELIER, Henry Louis, 1850-1936, French chemist Source: Rothman, M. A. 1963. See also STEFAN-BOLTZMANN LE CHATELIER PRINCIPLE OR LAW (1884); PRINCIPLE OF LEAST ACTION; LE CHATELIER-BRAUN PRINCIPLE; LAW OF MOBILE EQUILIBRIUM In a system initially at equilibrium, if any stress or force is exerted on the system, the equilibrium will shift in a direction that tends to decrease the intensity of the stress or force. The factors of equilibrium are temperature, pressure, electromotive force, corresponding to three forms of energy, heat, electricity, and mechanical energy. Keywords: equilibrium, force, shift, stress LE CHATELIER, Henri Louis, 1850-1936, French chemist Sources: Considine, D. M. 1955; Honig, J. M. 1953: Lotka, A. J. 1956; Mandel, S. 1972; Parker, S. P. 1989; Stedman, T. L. 1976. See also ROBIN; VAN'T HOFF LEDUC LAW OR EFFECT; ALSO RIGHI-LEDUC EFFECT The volume of a gas mixture is equal to the sum of the volumes that would be occupied by each of the components of the mixture if at the temperature and pressure of the mixture. Keywords: components, gas, mixture, pressure, temperature, volume LEDUC, Stephane Armand Nicolas, 1853-1939, French physicist RIGHI, Augusto, 1850-1920, Italian physicist Sources: Ballentyne, D. W. G. and Lovett, D. R. 1972; Freiberger, W. F. 1960; Hunt, V. D. 1979. Also see AMAGAT-LEDUC; LE CHATELIER LEIBNIZ (LEIBNITZ) LAW This law includes two different principles: (1) the principle of the indiscernibility of identicals, and (2) the identity of indiscernibles. The first asserts that if a is identical to b, whatever is true of a is true of b, and vice versa. The second asserts that if whatever is true of a is true of b, and vice versa, then a is identical to b.
Modification of the Maximin and ϕp (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points
Published in Technometrics, 2020
Miroslav Vořechovský, Jan Eliáš
In the periodic space, we now redefine the Euclidean distance between points and , formerly Lij, to be the length of the line segment connecting point with the closest image of point . This is achieved by considering the shortest 1D periodic projections along each individual coordinate, . The new periodic distance metric yields with defined in Equation (5). One can easily show that such a function fulfills the conditions imposed on metrics: it provides a mapping which fulfills the conditions of (i) nonnegativity, (ii) the identity of indiscernibles, (iii) symmetry, and (iv) triangle inequality. Technically, this improvement is very easy to implement in computer programs and the additional amount of computer time necessary to perform the comparison and selection of the minima is negligible.
A mosaic of Chu spaces and Channel Theory I: Category-theoretic concepts and tools
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2019
Chris Fields, James F. Glazebrook
For observational purposes, we may regard the ‘attributes’ as providing information about the structural and dynamical configurations of and between the ‘objects’. Two objects can be distinguished if, but only if, there is at least one attribute that they do not share. Otherwise, objects are said to be equivalent. This sense of equivalence formalises Leibniz’ principle of ‘identity of indiscernibles’. The ‘objects’ and ‘attributes’ can equally well be thought of as ‘states’ and ‘events’, with ‘states’ distinguished by the ‘events’ that can occur in them or, as we will see, in terms of ‘tokens’ and ‘types’ or by other similar pairs of concepts.Definition 2.2. A morphism or Chu transform of a Chu space to a Chu space is a pair of functions with , and , such that for any , and , we have , if and only if .