Topological mappings between graphs, trees and generalized trees

We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. (c) 2006 Elsevier Inc. All rights reserved.

Convex extendable trees

The concept of convex extendability is introduced to answer the problem of finding the smallest distance convex simple graph containing a given tree. A problem of similar type with respect to minimal path convexity is also discussed.

Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications. (C) 2010 Elsevier Inc. All rights reserved.

Examples from trees, related to discrete subsets, pseudo-radiality and omega-boundedness

We construct some examples using trees. Some of them are consistent counterexamples for the discrete reflection of certain topological properties. All the properties dealt with here were already known to be non-discretely reflexive if we assume CH and we show that the same is true assuming the existence of a Suslin tree. In some cases we actually get some ZFC results. We construct also, using a Suslin tree, a compact space that is pseudo-radial but it is not discretely generated. With a similar construction, but using an Aronszajn tree, we present a ZFC space that is first countable, omega-bounded but is not strongly w-bounded, answering a question of Peter Nyikos. (C) 2008 Elsevier B.V. All rights reserved.

The Tripartite Ramsey Number for Trees

We prove that for all epsilon>0 there are alpha>0 and n(0)is an element of N such that for all n >= n(0) the following holds. For any two-coloring of the edges of Kn, n, n one color contains copies of all trees T of order t <=(3 - epsilon)n/2 and with maximum degree Delta(T)<= n(alpha). This confirms a conjecture of Schelp. (c) 2011 Wiley Periodicals, Inc. J Graph Theory 69: 264300, 2012

Cutting Arcs For Torus Links And Trees

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An , Dn , E6 , E7 and E8 ) among all positive tree-like Hopf plumbings.

Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1 trees. For instance, the number of labeled interval orders that can be obtained from n intervals I1,..., In of generic lengths is counted. There is also discussed an arrangement due to N. Linial whose number of regions is the number of alternating (or intransitive) trees, as defined by Gelfand, Graev, and Postnikov [Gelfand, I. M., Graev, M. I., and Postnikov, A. (1995), preprint]. Finally, a refinement is given, related to counting labeled trees by number of inversions, of a result of Shi [Shi, J.-Y. (1986), Lecture Notes in Mathematics, no. 1179, Springer-Verlag] that a certain deformation of the braid arrangement has (n + 1)n-1 regions.

Decomposition of graphs into trees /

"UILU-ENG 77 1715."

Classification Trees as a Technique for Creating Anomaly-Based Intrusion Detection Systems

Intrusion detection is a critical component of security information systems. The intrusion detection process attempts to detect malicious attacks by examining various data collected during processes on the protected system. This paper examines the anomaly-based intrusion detection based on sequences of system calls. The point is to construct a model that describes normal or acceptable system activity using the classification trees approach. The created database is utilized as a basis for distinguishing the intrusive activity from the legal one using string metric algorithms. The major results of the implemented simulation experiments are presented and discussed as well.