A new approach to find project characteristics and multiple possible critical paths in a fuzzy project network

Graphs are widely used to represent data and relationships. Among all graphs, a particularly useful family is the family of trees. In this paper, we utilize a rooted tree to describe a fuzzy project network as it enables simplification in finding earliest starting times and trapezoidal fuzzy numbers to express the operation times for all activities in project network. As there is an increasing demand that the decision maker needs “Multiple possible critical paths” to decrease the decision risk for project management, in this paper, we introduce an effective graphical method to compute project characteristics such as total float, earliest and latest times of activities in fuzzy project network and a new ranking to find possible critical paths. Numerical example is provided to explain the proposed procedure in detail; the results have shown that the procedure is very useful and flexible in finding total floats. By comparing the critical paths obtained by this method with the previous methods, it is shown that the proposed method is effective in finding possible critical paths.     

Network delay inference from additive metrics

We use computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast‐based delay inference, that is, the problem of reconstructing delay characteristics of a network from end‐to‐end delay measurements on network paths. Our inference algorithm is based on additive metric techniques used in phylogenetics. It runs in polynomial time and requires a sample of size only poly(log n). We also show how to recover the topology of the routing tree. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Functional Data Analysis of Tree Data Objects

Data analysis on non-Euclidean spaces, such as tree spaces, can be challenging. The main contribution of this article is establishment of a connection between tree-data spaces and the well-developed area of functional data analysis (FDA), where the data objects are curves. This connection comes through two tree representation approaches, the Dyck path representation and the branch length representation. These representations of trees in the Euclidean spaces enable us to exploit the power of FDA to explore statistical properties of tree data objects. A major challenge in the analysis is the sparsity of tree branches in a sample of trees. We overcome this issue by using a tree-pruning technique that focuses the analysis on important underlying population structures. This method parallels scale-space analysis in the sense that it reveals statistical properties of tree-structured data over a range of scales. The effectiveness of these new approaches is demonstrated by some novel results obtained in the analysis of brain-artery trees. The scale-space analysis reveals a deeper relationship between structure and age. These methods are the first to find a statistically significant gender difference. Supplementary materials for this article are available online.     

Role of the pion mass in triple-Regge physics

This paper is an extension of the investigations of Abarbanel et al., who examined asymptotic total cross sections in a multiperipheral model and obtained the surprising result that the scale for the cross sections is provided not by μ, the mass of the exchanged pion (as anticipated on geometrical grounds) but by m_V, the central mass of the dominant low energy ππ resonance entering the kernel. In this paper the role of the pion mass in triple-Regge physics is clarified by examining the pion pole dominance model for the triple-Regge couplings g_ijk. It is found that m_V provides the scale for the inclusive link and that for this reason the couplings g_ijk depend very little on the intercept α_k of the exchanged reggeon. In the exclusive links if i = j = pomeron, m_V once again is the only active energy scale, whereas if i = j = R, the reggeons of intercept 0.5 or less, the pion mass enters the couplings g_RRk in an essential way. It is shown that the smallness of μ²/m_V² is responsible for the largeness of the ratios g_RRk/g_PPk. These features of the model, which are in qualitative agreement with experiment, are put to a quantitative test.     

Holes in a quantum antiferromagnet: A formalism and some exact results

This is a detailed version of an earlier communication in which a theory of hole motion in a quantum antiferromagnet was developed and some exact results obtained in d=1. In this picture, hole motion is very naturally restricted to sublattice A or B of a bipartite lattice. Holes in A or B behave like oppositely charged particles coupled to a gauge field driven by the antiferromagnetic fluctuations of the medium. The general picture is studied in detail for d=1, for a finite concentration of holes. The continuum theory is that of a massless Dirac fermion coupled to the nonlinear sigma model field via a gauge coupling. It is found that holes can wipe out the topological θ term, reduce the power law antiferromagnetic correlations to exponentials and show a divergent superconducting susceptibility. The style of the paper is rather pedagogical and intended for a broad readership.     

Magnetohydrodynamic unsteady free convection past a hot vertical plate

The free convection flow of an electrically conducting liquid from an infinite plate has been studied in the presence of a uniform magnetic field. General expressions for the velocity field, induced magnetic field, skin-friction and temperature distribution have been obtained when the plate is a perfect conductor and its temperature varies with the law t ⁿ e ^at . The results have been presented through some graphs and tables with the magnetic Prandtl number unity as its value.     

Rhodium ion catalyzed decomposition of aryldiazoalkanes

Aryldiazomethanes are converted by rhodium(II) acetate and iodorhodium(III) tetraphenylporphyrin to $\text{cis}$- rather than $\text{trans}$-1,2-diarylethylenes. Secondary aryldiazoalkanes react with rhodirum(II) acetate to give azines.     

Shape and phase transitions in quantum-Hall skyrmions

The shape deformability of quantum-Hall skyrmions leads to a rich phase diagram in the –g space. We study the long-wavelength physics of a collection of interacting skyrmions using a nonlinear sigma model. At zero temperature the ground state is crystalline with generalized Nèel order. As a function of the filling factor , the skyrmion crystal undergoes a sequence of structural transitions driven by a change of shape of the individual skyrmions. Quantum effects lead to melting and orientational disordering transitions at high and low skyrmion densities, respectively. We show that moment of inertia of skyrmions also arises from the shape deformability of the skyrmions.     

Inlet length by laminar flow of elastico-viscous liquids through straight channel and circular tube

The inlet lengths in a straight channel and a circular tube by the laminar flow of an elastico-viscous liquid have been determined in this paper. Expressions for the inlet lengths have been obtained by the kinetic energy end correction method. For a given pressure drop, the elasticity of the liquid increases the inlet length only if the liquid possesses cross-viscosity. But cross-viscosity which decreases the inlet length has an independent effect on it.