Minimum Average Distance Research Articles

New Bounds on the Minimum Average Distance of Binary Codes

The minimum average Hamming distance of binary codes of length n and cardinality M is denoted by b(n,M). All the known lower bounds b(n,M) are useful when M is at least of size about 2n-1/n . In this paper, for large n, we improve upper and lower bounds for b(n,M). Keywords: Binary code; Hamming distance; Minimum average Hamming distance. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i3.2708 J. Sci. Res. 2 (3), 489-493 (2010)

Dynamic multiple thresholding breast boundary detection algorithm for mammograms

Automated detection of breast boundary is one of the fundamental steps for computer-aided analysis of mammograms. In this study, the authors developed a new dynamic multiple thresholding based breast boundary (MTBB) detection method for digitized mammograms. A large data set of 716 screen-film mammograms (442 CC view and 274 MLO view) obtained from consecutive cases of an Institutional Review Board approved project were used. An experienced breast radiologist manually traced the breast boundary on each digitized image using a graphical interface to provide a reference standard. The initial breast boundary (MTBB-Initial) was obtained by dynamically adapting the threshold to the gray level range in local regions of the breast periphery. The initial breast boundary was then refined by using gradient information from horizontal and vertical Sobel filtering to obtain the final breast boundary (MTBB-Final). The accuracy of the breast boundary detection algorithm was evaluated by comparison with the reference standard using three performance metrics: The Hausdorff distance (HDist), the average minimum Euclidean distance (AMinDist), and the area overlap measure (AOM). In comparison with the authors' previously developed gradient-based breast boundary (GBB) algorithm, it was found that 68%, 85%, and 94% of images had HDist errors less than 6 pixels (4.8 mm) for GBB, MTBB-Initial, and MTBB-Final, respectively. 89%, 90%, and 96% of images had AMinDist errors less than 1.5 pixels (1.2 mm) for GBB, MTBB-Initial, and MTBB-Final, respectively. 96%, 98%, and 99% of images had AOM values larger than 0.9 for GBB, MTBB-Initial, and MTBB-Final, respectively. The improvement by the MTBB-Final method was statistically significant for all the evaluation measures by the Wilcoxon signed rank test (p < 0.0001). The MTBB approach that combined dynamic multiple thresholding and gradient information provided better performance than the breast boundary detection algorithm that mainly used gradient information.

Dinâmica da cobertura vegetal (1980-2004) em um projeto de produção florestal, nos municípios de Bugre e Ibapa, MG

O objetivo principal do trabalho foi analisar a dinâmica da estrutura da paisagem em um projeto de produção florestal, entre os anos de 1980 e 2004, enfatizando-se as alterações ocorridas na paisagem após a implantação de talhões de eucalipto. A área de estudo compreendeu os limites do projeto de produção florestal Macedônia, localizado nos Municípios de Bugre e Ipaba, região leste do Estado de Minas Gerais. O mapeamento do uso da terra referente ao ano de 1980 foi realizado por meio da interpretação visual de um mosaico de fotografias aéreas. Para o mapeamento do uso da terra referente ao ano de 2004, foi empregada uma imagem multiespectral do satélite Quickbird. A caracterização quantitativa da estrutura da paisagem foi descrita utilizando-se índices de ecologia da paisagem. Constatou-se que os plantios de eucalipto foram implantados em áreas de pastagem arborizada (45,2 %) e pastagem limpa (46,9%). Essas duas classes foram as que mais tiveram seu uso alterado; elas deram lugar principalmente a florestas nativas (15,6%). Constatou-se que, dos 938,6 ha das florestas nativas em 1980, 846,42 ha mantiveram inalteradas as respectivas áreas. A conectividade entre as reservas florestais nativas também diminuiu, de 165,04 m de distância mínima média entre elas em 1980 para 15,86 m no ano de 2004. O manejo integrado da propriedade alterou positivamente a estrutura da paisagem, alterando também o uso predominante destinado à produção de madeira e à preservação e conservação da biodiversidade.

클러스터링 알고리즘의 후처리 방안과 분할된 영역들의 분류에 대한 연구

Some clustering algorithms have a problem that an image is over-segmented since both the spatial information between the segmented regions is not considered and the number of the clusters is defined in advance. Therefore, they are difficult to be applied to the applicable fields. This paper proposes the new post-processing methods, a reclassification of the inhomogeneous clusters and a region merging using Baysian algorithm, that improve the segmentation results of the clustering algorithms. The inhomogeneous cluster is firstly selected based on variance and between-class distance and it is then reclassified into the other clusters in the reclassification step. This reclassification is repeated until the optimal number determined by the minimum average within-class distance. And the similar regions are merged using Baysian algorithm based on Kullbeck-Leibler distance between the adjacent regions. So we can effectively solve the over-segmentation problem and the result can be applied to the applicable fields. Finally, we design a classification system for the segmented regions to validate the proposed method. The segmented regions are classified by SVM(Support Vector Machine) using the principal colors and the texture information of the segmented regions. In experiment, the proposed method showed the validity for various real-images and was effectively applied to the designed classification system.

Average Spectra and Minimum Distances of Low-Density Parity-Check Codes over Abelian Groups

Ensembles of regular low-density parity-check codes over any finite Abelian group G are studied. The nonzero entries of the parity matrix are randomly chosen, independently and uniformly, from an arbitrary label group of automorphisms of G. Precise combinatorial results are established for the exponential growth rate of their average type-enumerating functions with respect to the code-length N. Minimum Bhattacharyya-distance properties are analyzed when such codes are employed over a memoryless G-symmetric transmission channel. In particular, minimum distances are shown to grow linearly in N with probability one, and lower bounds are provided for the typical asymptotic normalized minimum distance. Finally, some numerical results are presented, indicating that the choice of the label group strongly affects the value of the typical minimum distance.

Breeding Habitat Use by the Red-legged Cormorant (Phalacrocorax gaimardi) in Patagonia, Argentina

Abstract Twelve colonies where the Red-legged Cormorant (Phalacrocorax gaimardi) breeds in Argentina were visited. Physical and biological characteristics were recorded at 29 nesting cliffs and at different sectors within cliffs. Forty-five percent of the cliffs were located on continental shores, the rest were on islands. Cliff height and length varied (mean height = 14 ± 5 m, length range = 12 to 3,000 m) but their slope was commonly 80 to 90°. Most cliffs had more than 50% of the total available area with apparent suitable breeding sites. Cliff length and available area was positively correlated with the number of nests. Forty-nine different sectors used by Red-legged Cormorant on the cliffs were identified. In those sectors, number of active nests was positively correlated and nest density negatively correlated with area. Highest median density of nests was NE in orientation, protected from predominant winds. Minimum average distance from the tide line to the closest nest group was positively correlat...

Immobilization device for in vivo and in vitro multimodality image registration of rodent tumors

Biological image-guided radiotherapy requires that PET accurately identifies biologically relevant sub-volumes within a tumor. In this framework, an immobilization device was developed to study multi-imaging (CT, micro-MRI, micro-PET, and autoradiography) registration of mouse tumors. The registration accuracy assessed by calculating the average minimal distance between two skew lines was in the order of 0.2–0.3 mm.

On the Minimum Average Distance Spanning Tree of the Hypercube

Given an undirected and connected graph G, with a non-negative weight on each edge, the Minimum Average Distance (MAD) spanning tree problem is to find a spanning tree of G which minimizes the average distance between pairs of vertices. This network design problem is known to be NP-hard even when the edge-weights are equal. In this paper we make a step towards the proof of a conjecture stated by A.A. Dobrynin, R. Entringer and I. Gutman in 2001, and which says that the binomial tree B n is a MAD spanning tree of the hypercube H n . More precisely, we show that the binomial tree B n is a local optimum with respect to the 1-move heuristic which, starting from a spanning tree T of the hypercube H n , attempts to improve the average distance between pairs of vertices, by adding an edge e of H n -T and removing an edge e′ from the unique cycle created by e. We also present a greedy algorithm which produces good solutions for the MAD spanning tree problem on regular graphs such as the hypercube and the torus.

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R e e and the number of distinct visited nodes N v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈 R e e 〉 shows the dynamical scaling behavior 〈 R e e ( ℓ ¯ , t ) 〉 = ℓ ¯ α ( γ , N ) g ( t / ℓ ¯ z ) , where ℓ ¯ is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, 〈 R e e ( ℓ ¯ , t ) 〉 in the limit t → ∞ satisfies the relation 〈 R e e 〉 ∼ ℓ ¯ α ∼ d α , where d is the diameter of network with d ( ℓ ¯ ) ≃ ln N for γ ≥ 3 or d ( ℓ ¯ ) ≃ ln ln N for γ < 3 . Based on the scaling relation 〈 R e e 〉 , we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.

Lower bounds on the minimum average distance of binary codes

Let β ( n , M ) denote the minimum average Hamming distance of a binary code of length n and cardinality M . In this paper we consider lower bounds on β ( n , M ) . All the known lower bounds on β ( n , M ) are useful when M is at least of size about 2 n − 1 / n . We derive new lower bounds which give good estimations when size of M is about n . These bounds are obtained using a linear programming approach. In particular, it is proved that lim n → ∞ β ( n , 2 n ) = 5 / 2 . We also give a new recursive inequality for β ( n , M ) .

A generalization of Sperner’s theorem and an application to graph orientations

A generalization of Sperner’s theorem is established: For a multifamily M = { Y 1 , … , Y p } of subsets of { 1 , … , n } in which the repetition of subsets is allowed, a sharp lower bound for the number φ ( M ) of ordered pairs ( i , j ) satisfying i ≠ j and Y i ⊆ Y j is determined. As an application, the minimum average distance of orientations of complete bipartite graphs is determined.

Extensive Long-Distance Pollen Dispersal in a Fragmented Landscape Maintains Genetic Diversity in White Spruce

Conifers are among the most genetically diverse plants but show the lowest levels of genetic differentiation, even among geographically distant populations. High gene flow among populations may be one of the most important factors in maintaining these genetic patterns. Here, we provide empirical evidence for extensive pollen-mediated gene dispersal between natural stands of a widespread northern temperate/boreal conifer, Picea glauca. We used 6 polymorphic allozyme loci to quantify the proportion of seeds sired by pollen originating from different sources in a landscape fragmented by agriculture in North Central Ontario, Canada. In 7 stands, a small proportion of seeds were sired by self-pollen or neighboring trees but 87.1% (+/-1.7% standard error [SE]) of seeds were sired by pollen from at least 250 to 3000 m away. In 4 single isolated trees, self-fertilization rates were low and more than 96% (+/-1.3% SE) of seeds were sired by immigrant pollen. The average minimum pollen dispersal distance in outcrossed matings was 619 m. These results provide strong evidence that extensive long-distance pollen dispersal plays a primary role in maintaining low genetic differentiation among natural populations of P. glauca and helps maintain genetic diversity and minimize inbreeding in small stands in a fragmented landscape.

On the minimum average distance of binary constant weight codes

Let β ( n , M , w ) denote the minimum average Hamming distance of a binary constant weight code with length n, size M and weight w . In this paper, we study the problem of determining β ( n , M , w ) . Using the methods from coding theory and linear programming, we derive several lower bounds on the average Hamming distance of a binary constant weight code. These lower bounds enable us to determine the exact value for β ( n , M , w ) in several cases.

Cayley Digraphs of Finite Abelian Groups and Monomial Ideals

In the study of double-loop computer networks, the diagrams known as L-shapes arise as a graphical representation of an optimal routing for every graph's node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece of information, we can compute the graph's diameter and average minimum distance. That monomial ideal is the initial ideal of a certain lattice with respect to a graded monomial ordering. This result permits the use of Gröbner bases for computing the ideal and finding an optimal routing. Finally, we present a family of Cayley digraphs parametrized by their diameter d, all of them associated to irreducible monomial ideals.

On the intercluster distance of a tree metric

For two vertex clusters of a tree metric, we show that the sum of the average intracluster distances is always less than or equal to twice of the average intercluster distance. We show the feature in a more general form of weighted distance. This feature provides a 2-approximation algorithm for the minimum average intercluster distance spanning tree problem, which is a generalization of the minimum routing cost spanning tree or minimum average distance spanning tree problem. The results in this paper can be further generalized to more than two clusters.

Geometric parameter analysis to predetermine optimal radiosurgery technique for the treatment of arteriovenous malformation

To develop a method of predicting the values of dose distribution parameters of different radiosurgery techniques for treatment of arteriovenous malformation (AVM) based on internal geometric parameters. For each of 18 previously treated AVM patients, four treatment plans were created: circular collimator arcs, dynamic conformal arcs, fixed conformal fields, and intensity-modulated radiosurgery. An algorithm was developed to characterize the target and critical structure shape complexity and the position of the critical structures with respect to the target. Multiple regression was employed to establish the correlation between the internal geometric parameters and the dose distribution for different treatment techniques. The results from the model were applied to predict the dosimetric outcomes of different radiosurgery techniques and select the optimal radiosurgery technique for a number of AVM patients. Several internal geometric parameters showing statistically significant correlation (p < 0.05) with the treatment planning results for each technique were identified. The target volume and the average minimum distance between the target and the critical structures were the most effective predictors for normal tissue dose distribution. The structure overlap volume with the target and the mean distance between the target and the critical structure were the most effective predictors for critical structure dose distribution. The predicted values of dose distribution parameters of different radiosurgery techniques were in close agreement with the original data. A statistical model has been described that successfully predicts the values of dose distribution parameters of different radiosurgery techniques and may be used to predetermine the optimal technique on a patient-to-patient basis.

TU-FF-A2-04: Geometric Parameter Analysis to Predetermine Optimal Radiosurgery Technique for the Treatment of Arteriovenous Malformation

Purpose: To develop a method of predicting the values of dose distribution parameters of different radiosurgery techniques for treatment of arteriovenous malformations (AVM) based on internal geometric parameters. Method and Materials: For each of eighteen previously treated AVM patients, four treatment plans were created: circular collimator arcs, dynamic conformal arcs, fixed conformal fields and intensity modulated radiosurgery (IMRS). An algorithm was developed to characterize the target and critical structure shape complexity and the position of the critical structures with respect to the target. Multiple regression was employed to establish the correlation between the internal geometric parameters and the dose distributions for different treatment techniques. The results were used develop a statistical model which predicts the values of dose distribution parameters based on internal geometric parameters. The model was applied to predict the dosimetric outcomes of different radiosurgery techniques and select the optimal radiosurgery technique for a random AVM patient. Results: Several internal geometric parameters showing statistically significant correlation (p < 0.05) with the treatment planning results for each technique were identified. The target volume and the average minimum distance between the target and the critical structures were the most effective predictors for normal tissue dose distribution. The structure overlap volume with the target and the mean distance between the target and the critical structure were the most effective predictors for critical structure dose distribution. When the model was applied to a random patient, the predicted treatment results were in close agreement with the original data. Conclusion: A statistical model has been described which successfully predicts the values of dose distribution parameters of different radiosurgery techniques and may be used to determine the optimal technique on patient‐to‐patient basis.

Male Acadian flycatchers, Empidonax virescens, obtain extrapair fertilizations with distant females

We used genetic parentage analysis and radiotracking to determine how far male Acadian flycatchers travel from their territory in search of extrapair matings. Acadian flycatchers on our study site have a linear spatial distribution of territories associated with watercourses. With this type of spatial arrangement, males have only one or two immediate neighbouring females within 100 m and therefore have limited opportunities for extrapair (EP) fertilizations unless they travel far from their territory. In our sample of 53 nests collected over 4 years, 58% of nests contained EP young and 40% of nestlings were EP young. We identified the EP sire and the location of his territory at 13 nests with EP young, and over half (7/13) were not immediate neighbours. The mean distance between the territory of the EP sire and the territory where he attained EP fertilizations was 526 m. We were also able to exclude all immediate neighbours as EP sires for 12 additional nests containing EP young. The minimum average distance between an EP sire's territory and the territory containing an EP young that he sired was estimated to be 910 m. Overall, the EP sire was a neighbour in only 24% of nests with EP young. Radiotelemetry observations showed that six of seven mated males made off-territory forays and averaged 0.4 forays/h. Males travelled an average of 202 m off-territory (range 50–1500 m) and were away from their territories an average of 10.2 min/foray. Because our findings contrast sharply with those of other studies examining extrapair fertilization in passerines, in which most extrapair sires are neighbours, we suggest that when males have few adjacent neighbouring females, the benefits of searching widely to increase the number of potential extrapair mates can outweigh the costs of EP forays.

Calculation of the ground‐state energy and studies of other properties of exotic helium atoms with the use of boundary conditions of wave function

AbstractThe minimum energy and average distance between particles of doubly muonic helium atoms Heμμ (He2+ + 2μ), are calculated with the use of a wave function that satisfies boundary conditions such as the behavior of the wave function when two particles are close to each other or far away from each other. In this wave function, the muon–muon correlation in doubly muonic helium atoms is described to arrive at the correct behavior for r12 tending to zero and infinity. It is shown that the obtained results are very close to the values calculated by others. Finally, to confirm the method and results, calculated values are compared with a similar electronic system, and it is shown that the small differences in the energies of Heμμ and He are due to the reduced masses, as expected. In addition to being very simple, the proposed wave function provides relatively accurate values for the energy and expectation values of r2n, emphasizing the importance of the local properties of the wave functions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Minimum average distance of strong orientations of graphs

The average distance of a graph (strong digraph) G, denoted by μ( G) is the average, among the distances between all pairs (ordered pairs) of vertices of G. If G is a 2-edge-connected graph, then μ → min (G) is the minimum average distance taken over all strong orientations of G. A lower bound for μ → min (G) in terms of the order, size, girth and average distance of G is established and shown to be sharp for several complete multipartite graphs. It is shown that there is no upper bound for μ → min (G) in terms of μ( G). However, if every edge of G lies on 3-cycle, then it is shown that μ → min (G)⩽ 7 4 μ(G) . This bound is improved for maximal planar graphs to 5 3 μ(G) and even further to 3 2 μ(G) for eulerian maximal planar graphs and for outerplanar graphs with the property that every edge lies on 3-cycle. In the last case the bound is shown to be sharp.