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Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.
In this paper, we introduce new types of variational segmentation cost functions and associated active contour methods that are based on pairwise similarities or dissimilarities of the pixels. As a solution to a minimization problem, we introduce a new curve evolution framework, the graph partitioning active contours (GPAC). Using global features, our curve evolution is able to produce results close to the ideal minimization of such cost functions. New and efficient implementation techniques are also introduced in this paper. Our experiments show that GPAC solution is effective on natural images and computationally efficient. Experiments on gray-scale, color, and texture images show promising segmentation results.
We present an approach to visualizing correlations in 3D multifield scalar data. The core of our approach is the computation of correlation fields, which are scalar fields containing the local correlations of subsets of the multiple fields. While the visualization of the correlation fields can be done using standard 3D volume visualization techniques, their huge number makes selection and handling a challenge. We introduce the Multifield-Graph to give an overview of which multiple fields correlate and to show the strength of their correlation. This information guides the selection of informative correlation fields for visualization. We use our approach to visually analyze a number of real and synthetic multifield datasets.
The formation of alpha(2) dimer in Escherichia coli core RNA polymerase (RNAP) is thought to be the first step toward the assembly of the functional enzyme. A large number of evidences indicate that the alpha-subunit dimerizes through its N-terminal domain (NTD). The crystal structures of the alpha-subunit NTD and that of a homologous Thermus aquaticus core RNAP are known. To identify the stabilizing interactions in the dimer interface of the alpha-NTD of E. coli RNAP, we identified side-chain clusters by using the crystal structure coordinates of E. coli alpha-NTD. A graph spectral algorithm was used to identify side-chain clusters. This algorithm considers the global nonbonded side-chain interactions of the residues for the clustering procedure and is unique in identifying residues that make the largest number of interactions among the residues that form clusters in a very quantitative way. By using this algorithm, a nine-residue cluster consisting of polar and hydrophobic residues was identified in the subunit interface adjacent to the hydrophobic core. The residues forming the cluster are relatively rigid regions of the interface, as measured by the thermal factors of the residues. Most of the cluster residues in the E. coli enzyme were topologically and sequentially conserved in the T. aquaticus RNAP crystal structure. Residues 35F and 46I were predicted to be important in the stability of the alpha-dimer interface, with 35F forming the center of the cluster. The predictions were tested by isolating single-point mutants alpha-F35A and alpha-I46S on the dimer interface, which were found to disrupt dimerization. Thus, the identified cluster at the edge of the dimer interface seems to be a vital component in stabilizing the alpha-NTD.
In this investigation, using previously derived equations by Vedernikov and Morel-Seytoux, closed-form solutions have been obtained to compute the seepage from a slit and a strip. Also, a graphical solution as an extension of Vedernikov's graph has been presented for computing quantity of seepage from triangular, rectangular, and trapezoidal canals. The solution replaces approximately the cumbersome evaluation of improper integrals with unknown implicit transformation variables.
Because of the ubiquitous nature of anthropogenic nitrate (NO3(-)) in many parts of the world, determining background concentrations of NO3(-) in shallow ground water from natural sources is probably impossible in most environments. Present-day background must now include diffuse sources of NO3(-) such as disruption of soils and oxidation of organic matter, and atmospheric inputs from products of combustion and evaporation of ammonia from fertilizer and livestock waste. Anomalies can be defined as NO3(-) derived from nitrogen (N) inputs to the environment from anthropogenic activities, including synthetic fertilizers, livestock waste, and septic effluent. Cumulative probability graphs were used to identify threshold concentrations separating background and anomalous NO(3)-N concentrations and to assist in the determination of sources of N contamination for 232 spring water samples and 200 well water samples from karst aquifers. Thresholds were 0.4, 2.5, and 6.7 mg/L for spring water samples, and 0.1, 2.1, and 17 mg/L for well water samples. The 0.4 and 0.1 mg/L values are assumed to represent thresholds for present-day precipitation. Thresholds at 2.5 and 2.1 mg/L are interpreted to represent present-day background concentrations of NO(3)-N. The population of spring water samples with concentrations between 2.5 and 6.7 mg/L represents an amalgam of all sources of NO3(-) in the ground water basins that feed each spring; concentrations > 6.7 mg/L were typically samples collected soon after springtime application of synthetic fertilizer. The 17 mg/L threshold (adjusted to 15 mg/L) for well water samples is interpreted as the level above which livestock wastes dominate the N sources.
Although many numerical clustering algorithms have been applied to gene expression data analysis, the essential step is still biological interpretation by manual inspection. The correlation between genetic co-regulation and affiliation to a common biological process is what biologists expect. Here, we introduce some clustering algorithms that are based on graph structure constituted by biological knowledge. After applying a widely used dataset, we compared the result clusters of two of these algorithms in terms of the homogeneity of clusters and coherence of annotation and matching ratio. The results show that the clusters of knowledge-guided analysis are the kernel parts of the clusters of Gene Ontology (GO)-Cluster software, which contains the genes that are most expression correlative and most consistent with biological functions. Moreover, knowledge-guided analysis seems much more applicable than GO-Cluster in a larger dataset.
Bond graphs are used to model the acoustic behavior of the respiratory system. The model includes the distributed dynamics of the upper airways while the lower passage generations are represented by "lumping" of resistance and compliance effects. The lower airway representation is terminated with ten lung segments. The model is accurate for frequencies as high as 8500 Hz. The model is currently capable of predicting system eigenvalues as a function of system parameters and geometry for a "nonbreathing" lung. Future plans include modifying the model to include lung segment expansion and contraction as well as turbulence generation at airway bifurcations.
A new leaf-sequencing algorithm for step-and-shoot IMRT that is based on a graph-searching technique is described. An iterative process guided by a quantitative measure for the complexity of the initial or residual intensity pattern is used to identify the field segments shaped by a multileaf collimator (MLC). Given a user selected number of intensity levels, the algorithm searches deliverable segment candidates considering all intensity levels and two collimator positions separated by 90 degrees. The candidates for each intensity level are obtained as the least number of segments to cover the areas with equal or higher intensity. The shape of a deliverable segment is adjusted by leaving out certain beam elements for later delivery if this results in a simpler residual intensity pattern and the segment is still deliverable. For a MLC design that does not allow leaf interdigitation, it is initially assumed that a single segment cannot cover two disjoined areas. Among all candidates the segment with the greatest reduction of the complexity of the residual intensity distribution is chosen for the current step of iteration. The iterative process generates a set of deliverable segments of simply connected areas. These segments are combined later under specific MLC constraints. Different orders of segment combination are considered for minimizing the beam-on time. The final segments are sequenced to minimize the leaf travel. This algorithm has been tested using randomly generated intensity distributions and clinical cases for the Varian, Siemens, and Elekta MLC systems. The results show that as the number of intensity levels is increased, the numbers of segments and MUs increase only modestly. Using two collimator angles results in decreases in the required number of segments and the number of monitor units that can be as much as 20%.
Graphs of labeled mitoses, derived from autoradiographs of cell populations with (3)H-thymidine, show depressions in the curves at their midpoints. These depressions reflect interruption of DNA synthesis midway through S phase. Such interruptions revealed by the method of labeled mitoses should be considered when determining cell-cycle times.
Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically.
Instance Based Query Generation is defined and applied to the problem of recognising amino acid residues in medium resolution critical point graphs. The technique is an amalgamation of Relational Instance Based Learning and Frequent Query Discovery in First Order Logic. Instances are automatically constructed from a deductive database and first order association rules are derived from the instances. The initial investigations presented here indicate that the technique is able to discriminate some of the larger amino acid types as well as discriminating the protein from background solvent. Identification of the smaller amino acids remains difficult and requires further work.
A graph method was employed to analyse spatial neuronal patterns of pontine nuclei with ascending aminergic projections to the forebrain (nucleus centralis superior (NCS), raphes dorsalis (NRD) and locus coeruleus (LC)), in Alzheimer disease (AD), Huntington disease (HD), and vascular (VD) as well as "mixed-type" (VA) dementia, compared with non-demented controls (CO) and a small sample of brains from schizophrenics ("dementia praecox" (DP)). The quantitative evaluations by the "minimal spanning tree (MST)" were complemented by rough neurofibrillary tangle (NFT) counts and by semiquantitative immunohistochemical assessment of amyloid deposition, neuritic plaque formation, and cellular gliosis. The AD cases showed a significant decline of neuronal density in all nuclei examined, as compared with controls and DP. Neuronal loss was not significant in VD, while the mixed cases with both vascular and Alzheimer-type pathology exhibited pronounced changes of neuronal density. Amyloid deposition occurred almost exclusively in AD and VA, as a rule, being of moderate degree, except for two presenile AD cases where it was marked. NFT were significantly increased in all nuclei in AD and in the VA cases, while they only occasionally appeared beyond age 55 in HD, DP and CO. The four HD cases showed in the NCS and NRD neuronal loss as severe as in AD. This neuronal loss implicates impairment of serotoninergic and noradrenergic neuromodulation as one basic mechanism promoting dementia in AD, VA and perhaps in HD.
This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an m-dimensional manifold initially residing in an n-dimensional Euclidean space where n >> m. Motivated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of the original data may be achieved for some d < or = 2m + 1. To implement this network, we propose the idea of a good-projection, which enhances the generalization capabilities of the network, and an adaptive secant basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.
We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations--a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.
In a previous article, we considered game trees as graphical models. Adopting an evaluation function that returned a probability distribution over values likely to be taken at a given position, we described how to build a model of uncertainty and use it for utility-directed growth of the search tree and for deciding on a move after search was completed. In some games, such as chess and Othello, the same position can occur more than once, collapsing the game tree to a directed acyclic graph (DAG). This induces correlations among the distributions at sibling nodes. This article discusses some issues that arise in extending our algorithms to a DAG. We give a simply described algorithm for correctly propagating distributions up a game DAG, taking account of dependencies induced by the DAG structure. This algorithm is exponential time in the worst case. We prove that it is #P complete to propagate distributions up a game DAG correctly. We suggest how our exact propagation algorithm can yield a fast but inexact heuristic.
This paper describes the adaptation of evolutionary algorithms (EAs) to the structural optimization of chemical engineering plants, using rigorous process simulation combined with realistic costing procedures to calculate target function values. To represent chemical engineering plants, a network representation with typed vertices and variable structure will be introduced. For this representation, we introduce a technique on how to create problem specific search operators and apply them in stochastic optimization procedures. The applicability of the approach is demonstrated by a reference example. The design of the algorithms will be oriented at the systematic framework of metric-based evolutionary algorithms (MBEAs). MBEAs are a special class of evolutionary algorithms, fulfilling certain guidelines for the design of search operators, whose benefits have been proven in theory and practice. MBEAs rely upon a suitable definition of a metric on the search space. The definition of a metric for the graph representation will be one of the main issues discussed in this paper. Although this article deals with the problem domain of chemical plant optimization, the algorithmic design can be easily transferred to similar network optimization problems. A useful distance measure for variable dimensionality search spaces is suggested.
A neural network is presented that explicitly represents form attributes and relations between them, thus solving the binding problem without temporal coding. Rather, the network create a graph representation by dynamically allocating nodes to code local form attributes and establishing arcs to link them. With this representation, the network selectively groups and segments in depth objects based on line junction information, producing results consistent with those of several recent visual search experiments. In addition to depth-from-occlusion, the network provides a sufficient framework for local line-labeling processes to recover other three-dimensional (3-D) variables, such as edge/surface contiguity, edge slant, and edge convexity.