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1. Counting the Leaves of Trees
Published: 12/19/2011
Authors: Brian Dale Cloteaux, Luis A. Valentin
Abstract: A number of important combinatorial counting problems can be reformulated into the problem of counting the number of leaf nodes on a tree. Since the basic leaf-counting problem is #P-complete, there is strong evidence that no polynomial time algorith ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908869

2. Extracting Hierarchies With Overlapping Structure From Network Data
Published: 12/11/2011
Author: Brian Dale Cloteaux
Abstract: Relationships between entities in many complex systems, such as the Internet and social networks, have a natural hierarchical organization. Understanding these inherent hierarchies is essential for creating models of these systems. Thus, there is a r ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908870

3. Approximating the Number of Bases for Almost All Matroids
Published: 2/1/2011
Author: Brian Dale Cloteaux
Abstract: We define a class of matroids A for which a fully polynomial randomized approximation scheme (fpras) exists for counting the number of bases of the matroids. We then show that as the number of elements in a matroid increases, the probability that a m ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=900881

4. Modeling Affiliations in Networks
Published: 12/6/2010
Author: Brian Dale Cloteaux
Abstract: One way to help understand the structure of certain networks is to examine what common group memberships the actors in the network share. Linking actors to their common affiliations gives an alternative type of network commonly called an affiliation ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=906038

5. Matching Observed Alpha Helix Lengths to Predicted Secondary Structure
Published: 10/11/2010
Author: Brian Dale Cloteaux
Abstract: Because of the complexity in determining the 3D structure of a protein, the use of partial information determined from experimental techniques can greatly reduce the overall computational expense. We investigate the problem of matching experimentally ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=906041

6. An Approximation Algorithm for the Coefficients of the Reliability Polynomial
Published: 3/15/2010
Authors: Brian Dale Cloteaux, Isabel M Beichl, F Sullivan
Abstract: The reliability polynomial gives the probability that a graph remains connected given that each edge in it can fail independently with a probability p. While in general determining the coefficients of this polynomial is #P-complete, we give a randomi ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=902705

7. A Structural Approach to the Temporal Modeling of Networks
Published: 12/14/2009
Authors: Brian Dale Cloteaux, Isabel M Beichl
Abstract: Simulation of many dynamic real world systems such as the Internet and social networks requires developing dynamic models for the underlying networks in these systems. Currently, there is a large body of work devoted towards determining the underlyin ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=902636

8. Matching Observed Alpha Helix Lengths to Predicted Secondary Structure
Published: 11/1/2009
Authors: Brian Dale Cloteaux, Nadezhda Serova
Abstract: Because of the complexity in determining the 3D structure of a protein, the use of partial information determined from experimental techniques can greatly reduce the overall computational expense. We investigate the problem of matching experimentally ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=903670

9. Lower Bounds for Accessing Information on Pure Pointer Machines
Published: 7/13/2009
Authors: Brian Dale Cloteaux, Desh Ranjan
Abstract: We study the complexity of representing an array on a Pure Pointer Machine (PPM) or a pointer machine without arithmetic capabilities. In particular, we show that lower bounds in access time for information retrieval on a PPM arise from two different ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=51268

10. Measuring the Effectiveness of the s-Metric to Produce Better Network Models
Published: 12/7/2008
Authors: Isabel M Beichl, Brian Dale Cloteaux
Abstract: Recent research has shown that while many complex networks follow a power-law distribution for their vertex degrees, it is not sufficient to model these networks based only on their degree distribution. In order to better distinguish between these ne ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=152128