339 research outputs found
Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
A maximal minor of the Laplacian of an -vertex Eulerian digraph
gives rise to a finite group
known as the sandpile (or critical) group of . We determine
of the generalized de Bruijn graphs with
vertices and arcs for and , and closely related generalized Kautz graphs, extending and
completing earlier results for the classical de Bruijn and Kautz graphs.
Moreover, for a prime and an -cycle permutation matrix
we show that is isomorphic to the
quotient by of the centralizer of in
. This offers an explanation for the coincidence of
numerical data in sequences A027362 and A003473 of the OEIS, and allows one to
speculate upon a possibility to construct normal bases in the finite field
from spanning trees in .Comment: I+24 page
A REVIEW OF PROBABILISTIC GRAPH MODELS FOR FEATURE SELECTION WITH APPLICATIONS IN ECONOMIC AND FINANCIAL TIME SERIES FORECASTING
In every field of life, people are interested to be able to forecast future.  A number of techniques are available to predict and forecasting upto a certain level of accuracy. Many techniques involve statistical tools and techniques for forecasting, modeling and control. Use of statistical techniques is growing with time and new techniques are being developed very rapidly. Especially in the field of economics and finance, the estimation and forecasting of economic and financial indicators play a vital role in decision making. Many models are developed in the last 2 decades to get better accuracy and efficiency in time series analysis and still there is a scope of learning and getting betterment in this field is available. In this research we have reviewed probability graphs, directed acyclic graphs, Bayesian networks, feature selection algorithms and Markov blankets for time series forecasting on the economic and financial problems (like stock exchange forecasting, multi-objective business risk analysis, consumers’ analysis, portfolio optimization, credit scoring etc). This is a new dimension for adaptive modeling techniques in economics and finance modeling
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