A divisive scheme for constructing minimal spanning trees in coordinate space

An algorithm to generate a minimal spanning tree is presented when the nodes with their coordinates in some m-dimensional Euclidean space and the corresponding metric are given. This algorithm is tested on manually generated data sets. The worst case time complexity of this algorithm is O(n log2n) for a collection of n data samples.

OTCYMIST: Otsu-Canny minimal spanning tree for born-digital images

Text segmentation and localization algorithms are proposed for the born-digital image dataset. Binarization and edge detection are separately carried out on the three colour planes of the image. Connected components (CC's) obtained from the binarized image are thresholded based on their area and aspect ratio. CC's which contain sufficient edge pixels are retained. A novel approach is presented, where the text components are represented as nodes of a graph. Nodes correspond to the centroids of the individual CC's. Long edges are broken from the minimum spanning tree of the graph. Pair wise height ratio is also used to remove likely non-text components. A new minimum spanning tree is created from the remaining nodes. Horizontal grouping is performed on the CC's to generate bounding boxes of text strings. Overlapping bounding boxes are removed using an overlap area threshold. Non-overlapping and minimally overlapping bounding boxes are used for text segmentation. Vertical splitting is applied to generate bounding boxes at the word level. The proposed method is applied on all the images of the test dataset and values of precision, recall and H-mean are obtained using different approaches.

Structure-potential relationship and nature of disorder in liquids and glassy solids

A method based on the minimal-spanning tree is extended to a collection of points in three dimensions. Two parameters, the average edge length and its standard deviation characterize the disorder. The structural phase diagram for a monatomic system of particles and the characteristic values for the uniform random distribution of points have been obtained. The method is applied to hard spheres and Lennard-Jones systems. These systems occupy distinct regions in the structural phase diagram. The structure of the Lennard-Jones system approaches that of the defective close-packed arrangements at low temperatures whereas in the liquid regime, it deviates from the close-packed configuration.

Dependence of diffusivity on density and solute diameter in liquid phase: A molecular dynamics study of Lennard-Jones system

Investigations into the variation of self-diffusivity with solute radius, density, and degree of disorder of the host medium is explored. The system consists of a binary mixture of a relatively smaller sized solute, whose size is varied and a larger sized solvent interacting via Lennard-Jones potential. Calculations have been performed at three different reduced densities of 0.7, 0.8, and 0.933. These simulations show that diffusivity exhibits a maximum for some intermediate size of the solute when the solute diameter is varied. The maximum is found at the same size of the solute at all densities which is at variance with the prediction of the levitation effect. In order to understand this anomaly, additional simulations were carried out in which the degree of disorder has been varied while keeping the density constant. The results show that the diffusivity maximum gradually disappears with increase in disorder. Disorder has been characterized by means of the minimal spanning tree. Simulations have also been carried out in which the degree of disorder is constant and only the density is altered. The results from these simulations show that the maximum in diffusivity now shifts to larger distances with decrease in density. This is in agreement with the changes in void and neck distribution with density of the host medium. These results are in excellent agreement with the predictions of the levitation effect. They suggest that the effect of disorder is to shift the maximum in diffusivity towards smaller solute radius while that of the decrease in density is to shift it towards larger solute radius. Thus, in real systems where the degree of disorder is lower at higher density and vice versa, the effect due to density and disorder have opposing influences. These are confirmed by the changes seen in the velocity autocorrelation function, self part of the intermediate scattering function and activation energy. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.3701619]

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Species-area and species-individual relationships for tropical trees: A comparison of three 50-ha plots

1 Species-accumulation curves for woody plants were calculated in three tropical forests, based on fully mapped 50-ha plots in wet, old-growth forest in Peninsular Malaysia, in moist, old-growth forest in central Panama, and in dry, previously logged forest in southern India. A total of 610 000 stems were identified to species and mapped to < Im accuracy. Mean species number and stem number were calculated in quadrats as small as 5 m x 5 m to as large as 1000 m x 500 m, for a variety of stem sizes above 10 mm in diameter. Species-area curves were generated by plotting species number as a function of quadrat size; species-individual curves were generated from the same data, but using stem number as the independent variable rather than area. 2 Species-area curves had different forms for stems of different diameters, but species-individual curves were nearly independent of diameter class. With < 10(4) stems, species-individual curves were concave downward on log-log plots, with curves from different forests diverging, but beyond about 104 stems, the log-log curves became nearly linear, with all three sites having a similar slope. This indicates an asymptotic difference in richness between forests: the Malaysian site had 2.7 times as many species as Panama, which in turn was 3.3 times as rich as India. 3 Other details of the species-accumulation relationship were remarkably similar between the three sites. Rectangular quadrats had 5-27% more species than square quadrats of the same area, with longer and narrower quadrats increasingly diverse. Random samples of stems drawn from the entire 50 ha had 10-30% more species than square quadrats with the same number of stems. At both Pasoh and BCI, but not Mudumalai. species richness was slightly higher among intermediate-sized stems (50-100mm in diameter) than in either smaller or larger sizes, These patterns reflect aggregated distributions of individual species, plus weak density-dependent forces that tend to smooth the species abundance distribution and 'loosen' aggregations as stems grow. 4 The results provide support for the view that within each tree community, many species have their abundance and distribution guided more by random drift than deterministic interactions. The drift model predicts that the species-accumulation curve will have a declining slope on a log-log plot, reaching a slope of O.1 in about 50 ha. No other model of community structure can make such a precise prediction. 5 The results demonstrate that diversity studies based on different stem diameters can be compared by sampling identical numbers of stems. Moreover, they indicate that stem counts < 1000 in tropical forests will underestimate the percentage difference in species richness between two diverse sites. Fortunately, standard diversity indices (Fisher's sc, Shannon-Wiener) captured diversity differences in small stem samples more effectively than raw species richness, but both were sample size dependent. Two nonparametric richness estimators (Chao. jackknife) performed poorly, greatly underestimating true species richness.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Tissue culture of forest trees: Clonal multiplication of Eucalyptus grandis L

Axillary shoot proliferation was obtained using explants of Eucalyptus grandis L. juvenile and mature stages on a defined medium. Murashige and Skoog medium (MS) supplemented with benzyladenine (BA), naphthalene acetic acid (NAA) and additional thiamine. Excised shoots were induced to root on a sequence of three media: (1) White's medium containing indoleacetic acid (IAA), NAA and indole butyric acid; (IBA), (2) half-strength MS medium with charcoal and (3) half-strength MS liquid medium. The two types of explants differed in rooting response, with juvenile-derived shoots giving 60% rooting and adult-derived ones only 35%. Thus, the factors limiting cloning of selected trees in vitro are determined to be those controlling rooting of shoots in E. grandis.

Using tau polarization to probe the stau co-annihilation region of the minimal supergravity model at the LHC

The minimal supergravity model predicts the polarization of the tau coming from the stau to bino decay in the co-annihilation region to +1. This can be exploited to extract this soft tau signal at LHC and also to measure the tiny mass differences between the stau and the bi lightest superparticle. Moreover, this strategy will be applicable for a wider class of bino lightest superparticle models, where the lighter stau has a right component at least of similar size as the left.

Tree-ring based hydroclimate reconstruction over northern Vietnam from Fokienia hodginsii: eighteenth century mega-drought and tropical Pacific influence

We present here the first statistically calibrated and verified tree-ring reconstruction of climate from continental Southeast Asia.The reconstructed variable is March-May (MAM) Palmer Drought Severity Index (PDSI) based on ring widths from 22 trees (42 radial cores) of rare and long-lived conifer, Fokienia hodginsii (Po Mu as locally called) from northern Vietnam. This is the first published tree ring chronology from Vietnam as well as the first for this species. Spanning 535 years, this is the longest cross-dated tree-ring series yet produced from continental Southeast Asia. Response analysis revealed that the annual growth of Fokienia at this site was mostly governed by soil moisture in the pre-monsoon season. The reconstruction passed the calibration-verification tests commonly used in dendroclimatology, and revealed two prominent periods of drought in the mid-eighteenth and late-nineteenth enturies. The former lasted nearly 30 years and was concurrent with a similar drought over northwestern Thailand inferred from teak rings, suggesting a ``mega-drought'' extending across Indochina in the eighteenth century. Both of our reconstructed droughts are consistent with the periods of warm sea surface temperature (SST)anomalies in the tropical Pacific. Spatial correlation analyses with global SST indicated that ENSO-like anomalies might play a role in modulating droughts over the region, with El Nio (warm) phases resulting in reduced rainfall. However, significant correlation was also seen with SST over the Indian Ocean and the north Pacific,suggesting that ENSO is not the only factor affecting the climate of the area. Spectral analyses revealed significant peaks in the range of 53.9-78.8 years as well as in the ENSO-variability range of 2.0 to 3.2 years.

Growth of Mycobacterium smegmatis in minimal and complete media

The growth patterns of Mycobacterium smegmatis SN2 in a minimal medium and in nutrient broth have been compared. The growth was monitored by absorbancy (Klett readings), colony forming units, wet weight and content of DNA, RNA and protein. During the early part of the growth cycle, the bacteria had higher wet weight and macromolecular content in nutrient broth than in minimal media. During the latter half of the growth cycle however, biosynthesis stopped much earlier in nutrient broth and the bacteria had a much lower content of macromolecules than in the minimal medium. In both the media, a general pattern of completing biosynthesis rapidly in the initial phase and a certain amount of cell division at a later time involving the distribution of preformed macromolecules was seen. The possible adaptive significance of this observation has been discussed.

State Minimization of Incompletely Specified Sequential Machines

A simple procedure for the state minimization of an incompletely specified sequential machine whose number of internal states is not very large is presented. It introduces the concept of a compatibility graph from which the set of maximal compatibles of the machine can be very conveniently derived. Primary and secondary implication trees associated with each maximal compatible are then constructed. The minimal state machine covering the incompletely specified machine is then obtained from these implication trees.

A Note on Minimal Reed-Muller Canonical Forms of Switching Functions

A nonexhaustive procedure for obtaining minimal Reed-Muller canonical (RMC) forms of switching functions is presented. This procedure is a modification of a procedure presented earlier in the literature and enables derivation of an upper bound on the number of RMC forms to be derived to choose a minimal one. It is shown that the task of obtaining minimal RMC forms is simplified in the case of symmetric functions and self-dual functions.

On the Structure of Contractible Edges in k-connected Partial k-trees

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k-connected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called non-contractible. In this paper, we present results on the structure of contractible edges in k-trees and k-connected partial k-trees. Firstly, we show that an edge e in a k-tree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2-connected graph. We also show that there are at least |V(G)| + k - 2 contractible edges in a k-tree. Secondly, we show that if an edge e in a partial k-tree is contractible then e is contractible in any k-tree which contains the partial k-tree as an edge subgraph. We also construct a class of contraction critical 2k-connected partial 2k-trees.

Mapping of fuelwood trees using geoinformatics

Rural population of India constitutes about 70% of the total population and traditional fuels account for 75% of the rural energy needs. Depletion of woodlands coupled with the persistent dependency on fuel wood has posed a serious problem for household energy provision in many parts. This study highlights that the traditional fuels still meet 85-95% of fuel needs in rural areas of Kolar district: people prefer fuel wood for cooking and agriculture residues for water heating and other purposes. However, rapid changes in land cover and land use in recent times have affected these traditional fuels availability necessitating inventorying, mapping and monitoring of bioresources for sustainable management of bioresources. Remote sensing data (Multispectal and Panchromatic), Geographic Information System (GIS), field surveys and non-destructive sampling were used to assess spatially the availability and demand of energy. Field surveys indicate that rural household depends on species such as Prosopis juliflora, Acacia nilotica, Acacia auriculiformis to meet fuel wood requirement for domestic activities. Hence, to take stock of fuel wood availability, mapping was done at species level (with 88% accuracy) considering villages as sampling units using fused multispectral and panchromatic data. (C) 2009 Elsevier Ltd. All rights reserved.