Angèle M. Hamel

K-ary clustering with optimal leaf ordering for gene expression data

MOTIVATION A major challenge in gene expression analysis is effective data organization and visualization. One of the most popular tools for this task is hierarchical clustering. Hierarchical clustering allows a user to view relationships in scales ranging from single genes to large sets of genes, while at the same time providing a global view of the expression data. However, hierarchical clustering is very sensitive to noise, it usually lacks of a method to actually identify distinct clusters, and produces a large number of possible leaf orderings of the hierarchical clustering tree. In this paper we propose a new hierarchical clustering algorithm which reduces susceptibility to noise, permits up to k siblings to be directly related, and provides a single optimal order for the resulting tree. RESULTS We present an algorithm that efficiently constructs a k-ary tree, where each node can have up to k children, and then optimally orders the leaves of that tree. By combining k clusters at each step our algorithm becomes more robust against noise and missing values. By optimally ordering the leaves of the resulting tree we maintain the pairwise relationships that appear in the original method, without sacrificing the robustness. Our k-ary construction algorithm runs in O(n(3)) regardless of k and our ordering algorithm runs in O(4(k)n(3)). We present several examples that show that our k-ary clustering algorithm achieves results that are superior to the binary tree results in both global presentation and cluster identification. AVAILABILITY We have implemented the above algorithms in C++ on the Linux operating system.

Combinatorial and Algorithmic Aspects of Networking

Workshop Proceedings.- Aggregating Correlated Data in Sensor Networks.- The Efficiency of Optimal Taxes.- Congestion Games, Load Balancing, and Price of Anarchy.- Bandwidth Allocation in Networks: A Single Dual Update Subroutine for Multiple Objectives.- Limits and Power Laws of Models for the Web Graph and Other Networked Information Spaces.- Cuts and Disjoint Paths in the Valley-Free Path Model of Internet BGP Routing.- A Distributed Algorithm to Find Hamiltonian Cycles in Random Graphs.- String Matching on the Internet.- k-Robust Single-Message Transmission.- Stable Local Scheduling Algorithms With Low Complexity and Without Speedup for a Network of Input-Buffered Switches.- The External Network Problem with Edge- or Arc-Connectivity Requirements.- Bipartite Graphs as Models of Complex Networks.- Traceroute-Like Exploration of Unknown Networks: A Statistical Analysis.- Invited Talk: The Many Wonders of the Web Graph.- Survey Articles.- Algorithmic Foundations of the Internet:Foreword.- A Survey of Models of the Web Graph.- You Can Get There from Here: Routing in the Internet.- Search Engines and Web Information Retrieval.- Algorithmic Foundations of the Internet: Roundup.

Symplectic Shifted Tableaux and Deformations of Weyl's Denominator Formula for sp (2 n )

A determinantal expansion due to Okada is used to derive both a deformation of Weyls denominator formula for the Lie algebra sp(2n) of the symplectic group and a further generalisation involving a product of the deformed denominator with a deformation of flagged characters of sp(2n). In each case the relevant expansion is expressed in terms of certain shifted sp(2n)-standard tableaux. It is then re-expressed, first in terms of monotone patterns and then in terms of alternating sign matrices.

Longest increasing subsequences in sliding windows

We consider the problem of finding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the naive generalization of the longest increasing subsequence algorithm and in fact produces an output-sensitive optimal solution.

Optimal scheduling of contract algorithms with soft deadlines

A contract algorithm is an algorithm which is given, as part of its input, a specified amount of allowable computation time, and may not return useful results if interrupted prior to that time. In contrast, an interruptible algorithm will always output some meaningful (albeit suboptimal) solution, even if interrupted during its execution. Simulating interruptible algorithms by means of schedules of executions of contract algorithms in parallel processors is a well-studied problem with significant applications in AI. In the standard model, the interruptions are hard deadlines in which a solution must be reported immediately at the time the interruption occurs. In this paper, we study the more general setting of scheduling contract algorithms in the presence of soft deadlines. In particular, we address the setting in which if an interruption occurs at time t, then the system is given an additional window of time

Half-turn symmetric alternating sign matrices and Tokuyama type factorisation for orthogonal group characters

w(t)\le c \cdot t

K-ary Clustering with Optimal Leaf Ordering for Gene Expression Data

w(t)≤c·t, for constant c, within which the simulation must be completed. We formulate extensions to performance measures of schedules under this setting and derive schedules of optimal performance for all concave functions w.

On color-critical ( P 5 ,co- P 5 )-free graphs

Following Knuth, we approach pfaffians from a combinatorial point of view and produce a number of vector-based identities. Identities of Hirota, Ohta, and Srinivasan are obtained as specializations. We also demonstrate an application to Schur Q-functions.