7,296 research outputs found
Characteristics of the Eliashberg formalism on the example of high-pressure superconducting state in phosphor
The work describes the properties of the high-pressure superconducting state
in phosphor: GPa. The calculations were performed in
the framework of the Eliashberg formalism, which is the natural generalization
of the BCS theory. The exceptional attention was paid to the accurate
presentation of the used analysis scheme. With respect to the superconducting
state in phosphor it was shown that: (i) the observed not-high values of the
critical temperature ( K)
result not only from the low values of the electron - phonon coupling constant,
but also from the very strong depairing Coulomb interactions, (ii) the
inconsiderable strong - coupling and retardation effects force the
dimensionless ratios , , and - related to the
critical temperature, the order parameter, the specific heat and the
thermodynamic critical field - to take the values close to the BCS predictions.Comment: 6 pages, 6 figure
Clustering as an example of optimizing arbitrarily chosen objective functions
This paper is a reflection upon a common practice of solving various types of learning problems by optimizing arbitrarily chosen criteria in the hope that they are well correlated with the criterion actually used for assessment of the results. This issue has been investigated using clustering as an example, hence a unified view of clustering as an optimization problem is first proposed, stemming from the belief that typical design choices in clustering, like the number of clusters or similarity measure can be, and often are suboptimal, also from the point of view of clustering quality measures later used for algorithm comparison and ranking. In order to illustrate our point we propose a generalized clustering framework and provide a proof-of-concept using standard benchmark datasets and two popular clustering methods for comparison
Dynamic quantum clustering: a method for visual exploration of structures in data
A given set of data-points in some feature space may be associated with a
Schrodinger equation whose potential is determined by the data. This is known
to lead to good clustering solutions. Here we extend this approach into a
full-fledged dynamical scheme using a time-dependent Schrodinger equation.
Moreover, we approximate this Hamiltonian formalism by a truncated calculation
within a set of Gaussian wave functions (coherent states) centered around the
original points. This allows for analytic evaluation of the time evolution of
all such states, opening up the possibility of exploration of relationships
among data-points through observation of varying dynamical-distances among
points and convergence of points into clusters. This formalism may be further
supplemented by preprocessing, such as dimensional reduction through singular
value decomposition or feature filtering.Comment: 15 pages, 9 figure
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