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In recent years, the use of computer aided diagnosis (CAD) has achieved acceptance in mammography and other areas. To facilitate automated detection of brain abnormalities, we propose a novel method for quickly training neural networks to classify brain images. Our method outperforms traditional neural network training methods by achieving a better balance between classification accuracy and training time.
A linear subspace of has the property if every element of its predual has the form with . We prove that if and is a unital operator subalgebra of which has the property , then . We consider whether this is true for arbitrary .
In a finite group, an order subset is a maximal set of elements of the same order. We discuss three questions about finite groups having the property that the cardinalities of all order subsets of divide the order of . We provide a new proof to one of these questions and evidence to support answers to the other two questions.
An algebraic approach to graph theory involves the study of the edge ideal and the cover ideal of a given graph. While a lot is known for the associated primes of powers of the edge ideal, much less is known for the associated primes of the powers of the cover ideal. The associated primes of the cover ideal and its second power are completely determined. A configuration called a wheel is shown to always appear among the associated primes of the third power of the cover ideal.
We examine surfaces of the type proved to be minimizing under a connectivity condition by Dorff et al. We determine which of these surfaces are stable soap films. The connectivity condition is shown to be very restrictive; few of these surfaces are stable (locally minimizing) without it.
The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity. The path cover number of a graph is the minimum size of a path cover. Results for comparing the parameters are presented, with equality of zero forcing number and path cover number shown for all cacti and equality of zero forcing number and maximum nullity for a subset of cacti. (A cactus is a graph where each edge is in at most one cycle.)
We introduce the notion of the rank gradient function of a descending chain of subgroups of finite index and show that the lamplighter group has uncountably many 2-chains (that is, chains in which each subsequent group has index 2 in the previous group) with pairwise different rank gradient functions. In doing so, we obtain some information on subgroups of finite index in the lamplighter group.