Theory and Algorithms Commons^™

Improving Structure Mcmc For Bayesian Networks Through Markov Blanket Resampling, Chengwei Su, Mark E. Borsuk

Dartmouth Scholarship

Algorithms for inferring the structure of Bayesian networks from data have become an increasingly popular method for uncovering the direct and indirect influences among variables in complex systems. A Bayesian approach to structure learning uses posterior probabilities to quantify the strength with which the data and prior knowledge jointly support each possible graph feature. Existing Markov Chain Monte Carlo (MCMC) algorithms for estimating these posterior probabilities are slow in mixing and convergence, especially for large networks. We present a novel Markov blanket resampling (MBR) scheme that intermittently reconstructs the Markov blanket of nodes, thus allowing the sampler to more effectively …

Trip: Tracking Rhythms In Plants, An Automated Leaf Movement Analysis Program For Circadian Period Estimation, Kathleen Greenham, Ping Lou, Sara E. Remsen, Hany Farid, C Robertson Mcclung

Dartmouth Scholarship

Background: A well characterized output of the circadian clock in plants is the daily rhythmic movement of leaves. This process has been used extensively in Arabidopsis to estimate circadian period in natural accessions as well as mutants with known defects in circadian clock function. Current methods for estimating circadian period by leaf movement involve manual steps throughout the analysis and are often limited to analyzing one leaf or cotyledon at a time.

Methods: In this study, we describe the development of TRiP (Tracking Rhythms in Plants), a new method for estimating circadian period using a motion estimation algorithm that can …

Derivation Of A Novel Efficient Supervised Learning Algorithm From Cortical-Subcortical Loops, Ashok Chandrashekar, Richard Granger

Dartmouth Scholarship

Although brain circuits presumably carry out powerful perceptual algorithms, few instances of derived biological methods have been found to compete favorably against algorithms that have been engineered for specific applications. We forward a novel analysis of a subset of functions of cortical-subcortical loops, which constitute more than 80% of the human brain, thus likely underlying a broad range of cognitive functions. We describe a family of operations performed by the derived method, including a non-standard method for supervised classification, which may underlie some forms of cortically dependent associative learning. The novel supervised classifier is compared against widely used algorithms for …

A Subgroup Algorithm To Identify Cross-Rotation Peaks Consistent With Non-Crystallographic Symmetry, Ryan H. Lilien, Chris Bailey-Kellogg, Amy C. Anderson, Bruce R. Donald

Dartmouth Scholarship

Molecular replacement (MR) often plays a prominent role in determining initial phase angles for structure determination by X-ray crystallography. In this paper, an efficient quaternion-based algorithm is presented for analyzing peaks from a cross-rotation function in order to identify model orientations consistent with proper non-crystallographic symmetry (NCS) and to generate proper NCS-consistent orientations missing from the list of cross-rotation peaks. The algorithm, CRANS, analyzes the rotation differences between each pair of cross-rotation peaks to identify finite subgroups. Sets of rotation differences satisfying the subgroup axioms correspond to orientations compatible with the correct proper NCS. The CRANS algorithm was first …

The Online Median Problem, Ramgopal R. Mettu, C. Greg Plaxton

Dartmouth Scholarship

We introduce a natural variant of the (metric uncapacitated) k-median problem that we call the online median problem. Whereas the k-median problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities are placed one at a time, a facility cannot be moved once it is placed, and the total number of facilities to be placed, k, is not known in advance. The objective of an online median algorithm is to minimize the competitive ratio, that is, the worst-case ratio of the cost of an online placement to …

Approximation Techniques For Average Completion Time Scheduling, Chandra Chekuri, Rajeev Motwani, Balas Natarajan, Clifford Stein

Dartmouth Scholarship

We consider the problem of nonpreemptive scheduling to minimize average ( weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constant-factor approximations for this problem based on solving a preemptive or linear programming relaxation and then using the solution to get an ordering on the jobs. We introduce several new techniques which generalize this basic paradigm. We use these ideas to obtain

improved approximation algorithms for one-machine scheduling to minimize average completion time with release dates. In the process, we obtain an optimal randomized on-line algorithm for the same problem that beats …

Asymptotically Tight Bounds For Performing Bmmc Permutations On Parallel Disk Systems, Thomas H. Cormen, Thomas Sundquist, Leonard F. Wisniewski

Dartmouth Scholarship

This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bit-matrix-multiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an affine transformation over GF(2), where the source and target indices are treated as bit vectors. The class of BMMC permutations includes many common permutations, such as matrix transposition (when dimensions are powers of 2), bit-reversal permutations, vector-reversal permutations, hypercube permutations, matrix reblocking, Gray-code permutations, and inverse Gray-code permutations. The upper bound improves upon the asymptotic …

Fast Discrete Polynomial Transforms With Applications To Data Analysis For Distance Transitive Graphs, J. R. Driscoll, D. M. Healy, D. N. Rockmore

Dartmouth Scholarship

Let $\poly = \{P_0,\dots,P_{n-1}\}$ denote a set of polynomials with complex coefficients. Let $\pts = \{z_0,\dots,z_{n-1}\}\subset \cplx$ denote any set of {\it sample points}. For any $f = (f_0,\dots,f_{n-1}) \in \cplx^n$, the {\it discrete polynomial transform} of f (with respect to $\poly$ and $\pts$) is defined as the collection of sums, $\{\fhat(P_0),\dots,\fhat(P_{n-1})\}$, where $\fhat(P_j) = \langle f,P_j \rangle = \sum_{i=0}^{n-1} f_iP_j(z_i)w(i)$ for some associated weight function w. These sorts of transforms find important applications in areas such as medical imaging and signal processing.

In this paper, we present fast algorithms for computing discrete orthogonal polynomial transforms. For a system …

Low-Degree Spanning Trees Of Small Weight, Samir Khuller, Balaji Raghavachari, Neal Young

Dartmouth Scholarship

Given n points in the plane, the degree-K spanning-tree problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most K. This paper addresses the problem of computing low-weight degree-K spanning trees for $K > 2$. It is shown that for an arbitrary collection of n points in the plane, there exists a spanning tree of degree 3 whose weight is at most 1.5 times the weight of a minimum spanning tree. It is shown that there exists a spanning tree of degree 4 whose weight is at most 1.25 times …

Improved Algorithms For Bipartite Network Flow, Ravindra K. Ahuja, James B. B. Orlin, Clifford Stein, Robert E. Tarjan

Dartmouth Scholarship

In this paper, network flow algorithms for bipartite networks are studied. A network G = (V,E) is called bipartite if its vertex set V can be partitioned into two subsets V_1 and V_2 such that all edges have one endpoint in V_1 and the other in $V_2 $. Let $n = |V|, n_1 = |V_1 | , n_2 = |V_2 |, m = |E| and assume without loss of generality that n_1 \leqslant n_2. A bipartite network is called unbalanced if n_1 \ll n_2 $ and balanced otherwise. (This notion is necessarily imprecise.) It is shown that several maximum flow …