Abstract: The Block Sorting problem is to sort a given
permutation moving blocks. A block is defined as a substring
of the given permutation, which is also a substring of the
identity permutation. Block Sorting has been proved to be
NP-Hard. Until now two different 2-Approximation algorithms
have been presented for block sorting. These are the best known
algorithms for Block Sorting till date. In this work we present
a different characterization of Block Sorting in terms of a
transposition cycle graph. Then we suggest a heuristic,
which we show to exhibit a 2-approximation performance
guarantee for most permutations.
Abstract: A complex valued neural network is a neural network
which consists of complex valued input and/or weights and/or thresholds
and/or activation functions. Complex-valued neural networks
have been widening the scope of applications not only in electronics
and informatics, but also in social systems. One of the most important
applications of the complex valued neural network is in signal
processing. In Neural networks, generalized mean neuron model
(GMN) is often discussed and studied. The GMN includes a new
aggregation function based on the concept of generalized mean of all
the inputs to the neuron. This paper aims to present exhaustive results
of using Generalized Mean Neuron model in a complex-valued neural
network model that uses the back-propagation algorithm (called
-Complex-BP-) for learning. Our experiments results demonstrate the
effectiveness of a Generalized Mean Neuron Model in a complex
plane for signal processing over a real valued neural network. We
have studied and stated various observations like effect of learning
rates, ranges of the initial weights randomly selected, error functions
used and number of iterations for the convergence of error required on
a Generalized Mean neural network model. Some inherent properties
of this complex back propagation algorithm are also studied and
discussed.
Abstract: Bioinformatics and computational biology involve
the use of techniques including applied mathematics,
informatics, statistics, computer science, artificial intelligence,
chemistry, and biochemistry to solve biological problems
usually on the molecular level. Research in computational
biology often overlaps with systems biology. Major research
efforts in the field include sequence alignment, gene finding,
genome assembly, protein structure alignment, protein structure
prediction, prediction of gene expression and proteinprotein
interactions, and the modeling of evolution. Various
global rearrangements of permutations, such as reversals and
transpositions,have recently become of interest because of their
applications in computational molecular biology. A reversal is
an operation that reverses the order of a substring of a permutation.
A transposition is an operation that swaps two adjacent
substrings of a permutation. The problem of determining the
smallest number of reversals required to transform a given
permutation into the identity permutation is called sorting by
reversals. Similar problems can be defined for transpositions
and other global rearrangements. In this work we perform a
study about some genome rearrangement primitives. We show
how a genome is modelled by a permutation, introduce some
of the existing primitives and the lower and upper bounds
on them. We then provide a comparison of the introduced
primitives.