Physical topology classification

A sensor is a device capable of converting a physical or chemical quantity into readable information. In addition to a topological classification (local or distributed, intrinsic or extrinsic), a more basic classification can be made according to the optical parameter affected by the external factor intensity, phase, wavelength, and polarization. 

Topological quantum field theory has become a fascinating and fashionable subject in mathematical physics. At present, the main applications of topological field theory are in mathematics (topology of low-dimensional manifolds) rather than in physics. Its application to the issue of classification of knots and links is one of the most interesting. To approach this problem, one usually tries to somehow encode the topology of a knot or link. As was first noted by Witten... 

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Thus, it should be stressed that the mathematical topological theory investigates, as a rule, the problems of classification of knots and links, the construction of topological invariants, definitions of topological classes, etc. whereas the fundamental physical problem in the theory of topological properties of polymer chains is the determination of the entropy, S = In Z with the fixed topological state of chains. Both these problems are very difficult, but important. 

Therefore, the principal difficulty connected with the application of Eq. (12) is due to the incompleteness of the Gauss invariant. So, the use of the Gauss invariant for adequate classification of topologically different states in many-chain systems is very problematic. Nevertheless, that approach was used repeatedly for consideration of such physically important question as the high-elasticity of polymer networks with topological constraints [15]. Unfortunately,... 

The atomic forms defined by the topology of the charge density are open systems and their boundaries, as defined in real space, satisfy the quantum condition for an open system. Thus all of the properties of an atom in a molecule or a crystal employed in the atomic classification of the properties of matter are predicted by quantum mechanics. The same topological properties of the charge density which define the atom also lead to the definition of bonds, structure and structural stability and the whole of the molecular structure hypothesis is given a basis in physics. ... 

Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 683-683 Slater JC (1939) Introduction to chemical physics. McGraw-Hill, New York, NY Slater JC (1964) Atomic radii in crystals. J Chem Phys 41 3199-3204 Smith JV (1953) Re-examination of the crystal stractrrre of melihte. Amer Mineral 38 643-661 Smith JV (1977) Enumeration of 4-cormected 3-dimertsional nets and classification of framework silicates. 

As mentioned above, the topology, architecture or taxonomy of an ANN (they are synonymous) defines its physical structure, i.e. how many neurons have been set by the user, their cormections (in most applications all neurons in a layer are connected to all the neurons of the following layers, see Figure 6.3), the number of layers, and the number of neurons in each layer. The topology summarises all these characteristics in a simple notation. For instance, an ANN defined as 22/6/1 is a three-layer ANN with 22 neurons in the input layer (they correspond to 22 absorbances measured at 22 time-variables of the atomic peak), 6 neurons in an unique hidden layer and, finally, 1 neuron in the output layer. This would be the typical structure of an ANN used for regression, although we could use it for another sort of classification (if you have only two classes of object, one neuron in the output layer would be sufficient). Therefore it is important to explain clearly what the ANN is being used for. 

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