Diagonal Neighbors Research Articles

Image retrieval using adapted Fourier Descriptors

We present a novel method of representing a shape. It is an adaptation of Fourier-theory-based descriptors. To obtain a good boundary description, we choose to define it in an 8-connectivity. Fourier Descriptors (FDs) have a disadvantage of giving equal weights to all its 8-neighbours. So, the Fourier coefficient formula must be completely recomputed so that horizontal and vertical neighbours are given more weight when compared with the diagonal neighbours. Under Java retrieval framework, we compare our proposed results with the existing FDs and validate the proposed method.

Determinants of 131I radiation dose to thyroid follicular cells

We argued that modeling the thyroid as composed of identical follicles, packed as inside the cubes that are aligned side to side is unrealistic since this leaves too much space between diagonal neighbors and in reality these spaces are occupied by relatively small follicles. This assumption leads to underestimation of self-absorption of 131I radiation in coloidal lumens of the thyroid follicles. We conclude that the degree of intrathyroidal inhomogeneity of 131I beta radiation dose may be larger than estimated by Hindie et al. due to close packing of follicles, which is especially important in cases of relatively large follicles.

Early Prediction of Acute Gvhd Based on Molecular Profiling at the Time of Engraftment after Hematopoietic Stem Cell Transplantation.

Allogeneic hematopoietic stem cell transplantation is an important last resort therapy for hematological diseases. Unfortunately, the success of a large proportion of these transplants is limited by graft-versus-host disease (GVHD). Currently known risk factors for acute GVHD (histoincompatibility, sex mismatch, older patients, previous pregnancies) do not provide a precise estimate of individual patient risk and do not help for individualization of the therapy. Although GVHD may have beneficial graft-versus-tumor effects, observational studies have identified GVHD as the main cause of non-relapse mortality. Thus, early identification of those patients who will develop aGVHD may allow for individualized treatment, and also for the reduction of unnecessary treatment for those patients not at risk. Nowadays, however, there is no diagnostic method that allows prediction of aGVHD. Thus, the goal of our study was to reveal a gene expression profile that would predict the occurrence of aGVHD.Material and methods: Between May 2004 and August 2007, we collected blood samples from 89 recipients of myeloablative (N=71) and non-myeloablative (N=17) HLA-identical sibling allogeneic hematopoietic stem cell transplants at the time of successful engraftment (2–3 weeks after transplantation). Acute GVHD prophylaxis was cyclosporine plus short course of methotrexate and cyclosporine plus mycophenolate mofetil in myeloablative and non myeloablative transplants, respectively. Forty patients (45%) experienced acute GVHD (Glucksberg criteria). All the patients had acute GVHD before the first three months after transplantation (median 31 days; range 21–88 days). We isolated total RNA from the peripheral blood mononuclear cells, amplified it, labeled, and co-hybridized to the microarray slides containing probes for 22,000 genes. We used BRB ArrayTools for data analysis. The patients were divided into training and test groups, the former used to build a model discriminating patients with and without aGVHD and the latter - to test the model on independent samples. We selected the informative genes using “recursive feature elimination” method followed by six different multivariate classification algorithms (compound covariate predictor, diagonal linear discriminant analysis, 1- and 3-nearest neighbor predictor, nearest centroid predictor, support vector machine, Bayesian predictor) in order to establish a molecular classifier in the training set. Then we validated this new classifier in the test set of patients. Because multiple classification algorithms may give different results, we considered a result being robust and a patient being “classifiable” when at least five out of seven algorithms were concordant. The other patients were considered as “unclassifiable” because no reliable prediction regarding development of aGVHD could be made.Results: We found a molecular classifier comprised by 244 gene probes in the training set of samples which were selected based on the most accurate classification. In the test group of samples, we found that 80% of patients could be classified based on the concordance between classification methods as described above. For these patients, the classifier showed 78% of a predictive accuracy (75% of sensitivity and 80% of specificity).Conclusion: Our results show that molecular profiling is able to identify patients under high risk of acute GVHD at the time of engraftment. Establishing of a predictive diagnostic method for aGVHD is the first step of individualization of therapeutic strategy after hematopoetic stem cell transplantation.

Isothermic surfaces in sphere geometries as Moutard nets

We give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to be a novel characterization of discrete isothermic nets as Moutard nets. The latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete Moutard equation. Moutard nets admit also a projective geometric characterization as nets with planar faces with a five-point property: a vertex and its four diagonal neighbours span a three-dimensional space.Restricting the projective theory to quadrics, we obtain Moutard nets in sphere geometries. In particular, Moutard nets in Möbius geometry are shown to coincide with discrete isothermic nets. The five-point property, in this particular case, states that a vertex and its four diagonal neighbours lie on a common sphere, which is a novel characterization of discrete isothermic surfaces. Discrete Laguerre isothermic surfaces are defined through the corresponding five-plane property, which requires that a plane and its four diagonal neighbours share a common touching sphere. Equivalently, Laguerre isothermic surfaces are characterized by having an isothermic Gauss map. S-isothermic surfaces as an instance of Moutard nets in Lie geometry are also discussed.

Quadratic Contact Process: Phase Separation with Interface-Orientation-Dependent Equistability

The quadratic contact process is implemented on a square lattice as a model with random adsorption and correlated desorption requiring empty pairs of diagonal neighbors. The model exhibits a discontinuous phase transition between an active state and an absorbing state, but equistability between these states depends on the orientation of the separating interface. Correspondingly, for a generalized class of models, we find phase coexistence over a finite region of their two-dimensional parameter space. This is in stark contrast to behavior in equilibrium systems.

Simulation of forest fire fronts using cellular automata

In this work a new model for fire front spreading based on two-dimensional cellular automata is proposed. It is a more realistic modification of the model introduced by Karafyllidis and Thanailakis (see [Karafyllidis I, Thanailakis A. A model for predicting forest fire spreading using cellular automata. Ecol Model 1997;99:87–97]), which is based on the transfer of fractional burned area. Specifically, the model proposed in this work introduces a more accurate factor of propagation from a diagonal neighbor cell and includes, in a detailed form, the rate of fire spread. Moreover, the model is useful for both homogeneous and inhomogeneous environments. Some tests have been passed in order to determine the goodness of the method.

An alternative for Wang tiles

In this article we revisit the concept of Wang tiles and introduce corner tiles, square tiles with colored corners. During past years, Wang tiles have become a valuable tool in computer graphics. Important applications of Wang tiles include texture synthesis, tile-based texture mapping, and generating Poisson disk distributions. Through their colored edges, Wang tiles enforce continuity with their direct neighbors. However, Wang tiles do not directly constrain their diagonal neighbors. This leads to continuity problems near tile corners, a problem commonly known as the corner problem. Corner tiles, on the other hand, do impose restrictions on their diagonal neighbors, and thus are not subject to the corner problem. In this article we show that previous applications of Wang tiles can also be done using corner tiles, but that corner tiles have distinct advantages for each of these applications. Compared to Wang tiles, corner tiles are easier to tile, textures synthesized with corner tiles contain more samples from the original texture, corner tiles reduce the required texture memory by a factor of two for tile-based texture mapping, and Poisson disk distributions generated with corner tiles have better spectral properties. Corner tiles result in cleaner, simpler, and more efficient applications.

Diagonal and orthogonal neighbours in grid-based simulations: Buffon's stick after 200 years

Rectangular grids are frequently used in spatial simulations, often with nearest neighbour interactions, but each cell has diagonal as well as orthogonal nearest neighbours. Here, a simple, abstract model of weed spread demonstrates that the relative strength of diagonal and orthogonal interactions affects simulation outcomes, by determining the threshold conditions required for spread from isolated and aggregated colonized cells. The relative strength of diagonal and orthogonal interactions implicitly represents the range of interaction processes. The von Neumann neighbourhood, which has no diagonal interactions, represents processes with zero or negligible range, such as contact processes; increasing the relative strength of diagonal interactions represents processes with increasing range, such as seed dispersal. Diagonal interactions are only likely to equal orthogonal interactions for processes with ranges that allow significant interactions beyond the nearest neighbours of a cell. Thus, the Moore neighbourhood of diagonal and orthogonal nearest neighbours with equal weight may be considered an inaccurate approximation to a larger neighbourhood. Accurate diagonal and orthogonal nearest neighbour interactions can be calculated by a method proposed by Buffon in the 18th century. This method is also useful for calculating the impacts of rescaling a grid on intercellular interactions. If the area represented by each cell in the grid is increased, diagonal interactions should be reduced more than orthogonal interactions. In a rectangular grid, setting diagonal interactions to half the strength of orthogonal interactions can achieve a good match to an equivalent simulation in a hexagonal grid in some cases, but not always.

Ordering in two-dimensional Ising models with competing interactions

We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular region of interactions, corresponding to the Ising sector’s super-antiferromagnetic (SAF) ground state. The spin-SAF transition in the coupled Ising-XY model into a phase with co-existent SAF Ising (pseudospin) long-range order and a spin gap is considered. Along with destruction of the quantum critical point of the Ising sector, the phase diagram of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase. A detailed study of the latter is presented. The mechanism of the re-entrance, due to interplay of interactions in the coupled model, and the conditions of its appearance are established. Applications of the spin-SAF theory for the transition in the quarter-filled ladder compound NaV2O5 are discussed.

Zr4O5N2 — Intergrowth of Fluorite and Bixbyite Anion Layers Formed by Coupled Site‐Selective Anion and Vacancy Ordering.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Zr4O5N2 − Intergrowth of Fluorite and Bixbyite Anion Layers Formed by Coupled Site-Selective Anion and Vacancy Ordering

The defect fluorite Zr4O5N2 is presented. A simple layered intergrowth of the important bixbyite and fluorite structure types, it displays an A4X7 vacancy ordering alternative to that in the pyrochlore and other structures. This ordering is stabilized by proximity of the highly charged N3- anions to the bixbyite-type face diagonal vacancy neighbors in the initially cubic cation coordination environment of fluorite. The existence of this simple structure demonstrates the potential of substitution on the anion sublattice to control the structures of ionic defect systems.

Validity and Failure of the Cauchy-Born Hypothesis in a Two-Dimensional Mass-Spring Lattice

The Cauchy-Born rule postulates that when a monatomic crystal is subjected to a small linear displacement of its boundary, then all atoms will follow this displacement. In the absence of previous mathematical results, we study the validity of this rule in the model case of a 2D cubic lattice interacting via harmonic springs between nearest and diagonal neighbours. Our main result is that for favourable values of the spring constants and spring equilibrium lengths, the CB rule is actually a theorem.

Fast operations on binary images using interpolation-based bintrees

The Interpolation-Based Bintree (IBB) is a new encoding scheme for representing binary images. This encoding scheme combines the features of linear quadtrees, binary trees, and interpolation-based codes. The implementation of the IBB is shown to be very simple and storage-saving. Based on the IBB structure, this paper presents some fast sequential algorithms for set operations (intersection, union, and complement), 4-neighbors finding, and diagonal neighbors finding, respectively. Given two sets of bincodes, B 1, and B 2, with respect to two images, the set operations can be performed in O( n + m) time, where n is the size of B 1 and m is the size of B 2; the complement operation for B 1( B 2) can be performed in O( n)( O( m)) time; and the 4-neighbors finding and the diagonal neighbors finding for B 1( B 2) can be accomplished in O( n log n)( O( m log m)) time.

Optimal and near optimal sets of Latin squares for correlated errors

Abstract Optimality conditions are derived, and designs consisting of sets of Latin squares are connected, for correlated errors which follow a second order autonormal process. The designs balance row/column and diagonal neighbors and have no like neighbors, and are shown to be highly efficient.

The contralateral coordination of walking legs in the crayfish Astacus leptodactylus

In an earlier investigation of those mechanisms which synchronize the leg movements of a multilegged animal during walking (Muller and Cruse 1991) several questions remained open. The movement of an individual leg can be described in analogy to the behaviour of a relaxation oscillator. Following this analogy the interactions between the legs can be compared with the interactions between coupled relaxation oscillators. To understand the behaviour of a system of such coupled oscillators, model calculations were performed by systematically varying the relation of the intrinsic frequencies and the character as well as the strength of the coupling influences to which each oscillator was exposed. The behaviour of several three- and four-oscillator systems was investigated. We found that prediction of the behaviour is often difficult and in some cases even counter-intuitive. It could be shown that in a four-oscillator system (which corresponds to two legs on the left and two legs on the right side of the body) diagonal neighbours can sometimes be more strongly coordinated than direct segmental neighbours, although no coupling was implemented between the diagonally neighbouring oscillators. Necessary conditions for the occurrence of this effect are described. These conditions were fulfilled in the biological experiments described in Part I. A four-oscillator model whose properties are adapted to those found in the above experiments can sufficiently describe the animal's behaviour.

Effect of lateral interactions beyond nearest-neighbors on size and shape of non-equilibrium island on surfaces

Monte Carlo simulations were performed to investigate the island formation of adsorbates on surfaces. The surface is modeled by a N × N square lattice. The adsorbates are initially random distributed over the lattice. The movement of each adsorbate is then monitored by a random walk algorithm. Lateral interactions containing contributions from up to the fourth coordination shell are considered. Inclusion of interactions among diagonal neighbors is found to play a key role for the formation of non-equilibrium island. The effect of the interactions contributed from the third and fourth coordination shell on the island shape is discussed.

Some series constructions for two-dimensional neighbor designs

Terraces and sequencing are used to construct bordered, two-dimensional neighbor designs in which row, column, and diagonal neighbors are accounted for. Columns are generated from terraces, then juxtaposed (with appropriate borders) in such a way that row and diagonal neighbors are balanced or nearly balanced. For v treatments, v × 2 v side-bordered designs are constructed with row, column, and near diagonal balance, where v ≢ 0 (mod 3). Full bordering completes the balance, which for even v is directional. Other series include v × v non-directional designs for v ≡ 2 or 4 (mod 6), and several series of (v + 1) 2 × 2v designs for v odd.

Balanced Polycross Designs

SUMMARY Methods for constructing non-directional balanced polycross designs are presented, the balance being over row, column, and diagonal neighbours. The idea of a terrace is generalised and used to construct a set of arrays which enjoys complete balance. The arrays are then combined to obtain smaller, balanced designs; explicit constructions are given for ν < 20 varieties. Many of the designs are in v or v + 1 replicates and have treatments balanced in rows and columns. As an additional benefit, some of the EBIBD designs of Kiefer and Wynn (1981) are produced.

‘Continuous’ functions on digital pictures

The epsilon-delta definition of continuity has a natural analog for functions that take lattice points into lattice points. It turns out that a function f is ‘continuous’ if and only if it takes neighbors into neighbors, i.e., if Q is a neighbor of P, then f( Q) = f( P) or is a neighbor of f( P) (diagonal neighbors not allowed). Some basic properties of such ‘continuous’ functions are established. In particular, we show that a ‘continuous’ function from a finite block of lattice points into itself has an ‘almost-fixed’ point P such that f( P) is a neighbor of P (diagonal neighbors allowed). We also show that a function is one-to-one and continuous if and only if it is a combination of translations, rotations by multiples of 90°, or reflections in a horizontal, vertical, or diagonal line.

Grid-Orientation Effects and the Use of Orthogonal Curvilinear Coordinates in Reservoir Simulation

Robertson, G.E., Woo, P.T., Members SPE-AIME, Chevron Oil Field P.T., Members SPE-AIME, Chevron Oil Field Research Co., La Habra, Calif. Abstract Grid orientation effects in reservoir simulation recently have received considerable attention. Several authors have proposed methods to reduce or to eliminate these effects. However, the proposed methods require reprogramming of simulators based on standard techniques. The reprogramming effort can be considerable if the numerical model is highly complex, such as in steamflood simulation. An orthogonal curvilinear coordinate system that essentially eliminates the problem of grid orientation was investigated. With no reprogramming, this computing grid can be used readily in existing simulators. Such grids were used to study pattern steamfloods and pattern waterfloods. The results are compared in detail with those obtained by using conventional Cargesian grids. Grid orientation is shown to have a more pronounced effect on the saturation fronts than oil recovery, whether in a steamflood or a waterflood. It is concluded that orthogonal curvilinear grids can be used easily to estimate pattern flood performance without modification of the solution method. Introduction In a simulation study of unfavorable mobility displacement, the areal orientation of the grid system, with respect to the location of the injectors and producers, can affect the calculated results. This is referred to as the "grid-orientation" effect. Fig. 1 illustrates two Cartesian grid orientations for one-eighth of a repeated five-spot pattern. The "parallel" orientation has a direct-flow pattern. The "parallel" orientation has a direct-flow path along the grid lines between the injector and path along the grid lines between the injector and producer, whereas the path is indirect in the producer, whereas the path is indirect in the "diagonal" system. Using a repeated five-spot pattern, Todd et al., Holloway et al., and Yanosik and McCracken investigated grid-orientation effects in gas or waterfloods. Coats et al. reported grid-orientation effects in steamfloods. In all cases, the investigators found that grid orientation significantly affected the movement of saturation fronts and the breakthrough time. Oil recovery was affected to a lesser extent. The effect appears to increase as the mobility ratio becomes more unfavorable and as the transition zone across the saturation front shortens. Todd et al. presented the two-point mobility approximation to alleviate the grid-orientation effect. Holloway et al. introduced a transmissibility modification scheme to reduce this effect further. While these two schemes can be introduced readily into simulators using explicit relative permeability, it is difficult to implement the schemes in simulators using implicit or semi-implicit relative permeability. Yanosik and McCracken observed that the grid-orientation effect probably was caused by the lack of flow from a grid block to its diagonal neighbors and introduced a nine-point finite-difference formula to account for this flow. SPEJ p. 13