199137
Scaling of Accuracy in Extremely Large Phylogenetic Trees
The accuracy of phylogenetic inference was examined in simulated data sets up to nearly 10,000 taxa, the size of the largest set of homologous genes in existing molecular sequence databases. Even with a simple search algorithm (maximum parsimony without branch swapping), the number of characters needed to estimate 80% of a tree correctly can scale remarkably well at optimal substitution rates (on the order of log N, where N is the number of taxa). In other words, the number of taxa in an analysis can be doubled and only an arithmetic increase in the number of characters is required to maintain the same level of accuracy. Even substitution rates that are much higher than normally used in phylogenetic studies did not affect the scaling too adversely. However, scaling is usually worse than log N for more stringent levels of accuracy. Moreover, errors are not distributed randomly throughout the tree. Shallow nodes are remarkably easy to reconstruct and display favourable log-linear scaling. The deepest nodes are extremely difficult to reconstruct accurately, even with branch swapping, and the scaling is poor. Therefore, the strategy of sequencing large numbers of homologous genes may not always provide global solutions to extreme phylogenetic problems and alternative strategies may be required.
32992816
A Combinatorial Toolbox for Protein Sequence Design and Landscape Analysis in the Grand Canonical Model
In modern biology, one of the most important research problems is to understand how protein sequences fold into their native 3D structures. To investigate this problem at a high level, one wishes to analyze the protein landscapes, i.e., the structures of the space of all protein sequences and their native 3D structures. Perhaps the most basic computational problem at this level is to take a target 3D structure as input and design a fittest protein sequence with respect to one or more fitness functions of the target 3D structure. We develop a toolbox of combinatorial techniques for protein landscape analysis in the Grand Canonical model of Sun, Brem, Chan, and Dill. The toolbox is based on linear programming, network flow, and a linear-size representation of all minimum cuts of a network. It not only substantially expands the network flow technique for protein sequence design in Kleinberg's seminal work but also is applicable to a considerably broader collection of computational problems than those considered by Kleinberg. We have used this toolbox to obtain a number of efficient algorithms and hardness results. We have further used the algorithms to analyze 3D structures drawn from the Protein Data Bank and have discovered some novel relationships between such native 3D structures and the Grand Canonical model.
7701199
Gradient LASSO for feature selection
LASSO (Least Absolute Shrinkage and Selection Operator) is a useful tool to achieve the shrinkage and variable selection simultaneously. Since LASSO uses the L1 penalty, the optimization should rely on the quadratic program (QP) or general non-linear program which is known to be computational intensive. In this paper, we propose a gradient descent algorithm for LASSO. Even though the final result is slightly less accurate, the proposed algorithm is computationally simpler than QP or non-linear program, and so can be applied to large size problems. We provide the convergence rate of the algorithm, and illustrate it with simulated models as well as real data sets.
38004947
On-Line Detection of Errors in Homogeneous Multiprocessor Systems
1198499
A new base station receiver for increasing diversity order in a CDMA cellular system
A new base station receiver is proposed and analyzed for a code-division multiple-access (CDMA) cellular system. The proposed receiver can achieve remarkable diversity gain by increasing diversity order with reasonable cost and complexity. From the numerical results, it is confirmed that the proposed receiver structure can be a practical solution for enhancing reverse-link capacity and improving performance in CDMA cellular system operations. The result in the letter can find its applications to legacy IS-95/cdma2000 1x base stations with simple modifications.
14012710
Interference-Minimizing Colorings of Regular Graphs
Communications problems that involve frequency interference, such as the channel assignment problem in the design of cellular telephone networks, can be cast as graph coloring problems in which the frequencies (colors) assigned to an edge's vertices interfere if they are too similar. The paper considers situations modeled by vertex-coloring d-regular graphs with n vertices using a color set 1, 2,..., n, where colors i and j are said to interfere if their circular distance $\min \{ | i-j | , n- | i-j | \}$ does not exceed a given threshold value $\alpha$. Given a d-regular graph G and threshold $\alpha$, an interference-minimizing coloring is a coloring of vertices that minimizes the number of edges that interfere. Let $I_\alpha (G)$ denote the minimum number of interfering edges in such a coloring of $G$. For most triples $(n, \alpha ,d),$ we determine the minimum value of $I_\alpha (G)$ over all d-regular graphs and find graphs that attain it. In determining when this minimum value is 0, we prove that for $r \geq 3$ there exists a d-regular graph G on n vertices that is r-colorable whenever $d \leq (1- \frac{1}{r}) n-1$ and nd is even. We also study the maximum value of $I_\alpha (G)$ over all d-regular graphs and find graphs that attain this maximum in many cases.
2978705
Reconstructing the Temporal Ordering of Biological Samples Using Microarray Data
MOTIVATION
Accurate time series for biological processes are difficult to estimate due to problems of synchronization, temporal sampling and rate heterogeneity. Methods are needed that can utilize multi-dimensional data, such as those resulting from DNA microarray experiments, in order to reconstruct time series from unordered or poorly ordered sets of observations.


RESULTS
We present a set of algorithms for estimating temporal orderings from unordered sets of sample elements. The techniques we describe are based on modifications of a minimum-spanning tree calculated from a weighted, undirected graph. We demonstrate the efficacy of our approach by applying these techniques to an artificial data set as well as several gene expression data sets derived from DNA microarray experiments. In addition to estimating orderings, the techniques we describe also provide useful heuristics for assessing relevant properties of sample datasets such as noise and sampling intensity, and we show how a data structure called a PQ-tree can be used to represent uncertainty in a reconstructed ordering.


AVAILABILITY
Academic implementations of the ordering algorithms are available as source code (in the programming language Python) on our web site, along with documentation on their use. The artificial 'jelly roll' data set upon which the algorithm was tested is also available from this web site. The publicly available gene expression data may be found at http://genome-www.stanford.edu/cellcycle/ and http://caulobacter.stanford.edu/CellCycle/.