On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

ACM Computing Classification System (1998): G.2.2.

Convergence Of A Specialized Root Trait In Plants From Nutrient-impoverished Soils: Phosphorus-acquisition Strategy In A Nonmycorrhizal Cactus.

In old, phosphorus (P)-impoverished habitats, root specializations such as cluster roots efficiently mobilize and acquire P by releasing large amounts of carboxylates in the rhizosphere. These specialized roots are rarely mycorrhizal. We investigated whether Discocactus placentiformis (Cactaceae), a common species in nutrient-poor campos rupestres over white sands, operates in the same way as other root specializations. Discocactus placentiformis showed no mycorrhizal colonization, but exhibited a sand-binding root specialization with rhizosheath formation. We first provide circumstantial evidence for carboxylate exudation in field material, based on its very high shoot manganese (Mn) concentrations, and then firm evidence, based on exudate analysis. We identified predominantly oxalic acid, but also malic, citric, lactic, succinic, fumaric, and malonic acids. When grown in nutrient solution with P concentrations ranging from 0 to 100 μM, we observed an increase in total carboxylate exudation with decreasing P supply, showing that P deficiency stimulated carboxylate release. Additionally, we tested P solubilization by citric, malic and oxalic acids, and found that they solubilized P from the strongly P-sorbing soil in its native habitat, when the acids were added in combination and in relatively low concentrations. We conclude that the sand-binding root specialization in this nonmycorrhizal cactus functions similar to that of cluster roots, which efficiently enhance P acquisition in other habitats with very low P availability.

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

Optimization and Complexity Reduction of Switch-Reconfigured Antennas Using Graph Models

This letter addresses the optimization and complexity reduction of switch-reconfigured antennas. A new optimization technique based on graph models is investigated. This technique is used to minimize the redundancy in a reconfigurable antenna structure and reduce its complexity. A graph modeling rule for switch-reconfigured antennas is proposed, and examples are presented.

Characterization of rat behavior in the elevated plus-maze using a directed graph

The elevated plus-maze is a device widely used to assess rodent anxiety under the effect of several treatments, including pharmacological agents. The animal is placed at the center of the apparatus, which consists of two open arms and two arms enclosed by walls, and the number of entries and duration of stay in each arm are measured for a 5-min exposure period. The effect of an anxiolytic drug is to increase the percentage of time spent and number of entries into the open arms. In this work, we propose a new measure of anxiety levels in the rat submitted to the elevated plus-maze. We represented the spatial structure of the elevated plus-maze in terms of a directed graph and studied the statistics of the rat`s transitions between the nodes of the graph. By counting the number of times each transition is made and ordering them in descending frequency we represented the rat`s behavior in a rank-frequency plot. Our results suggest that the curves obtained under different pharmacological conditions can be well fitted by a power law with an exponent sensitive to both the drug type and the dose used. (C) 2009 Elsevier B.V. All rights reserved.

Effects of feeding high levels of cactus (Opuntia ficus-indica Mill) cladodes on urinary output and electrolyte excretion in goats

A study was conducted to determine the effects of feeding spineless cactus cladodes on diuresis and urinary electrolyte excretion in goats. Five bucks were used in a 5 x 5 Latin square experiment with 17-day periods. Experimental diets contained (g/kg dry matter (DM) basis) 370, 470, 570, 670, and 770 spineless cactus cladodes. Water consumption from feed and urine output increased linearly (P<0.05) as the level of cactus cladodes in the diet increased. However, water intake from drinking was low and unaffected by cactus cladode level. Creatinine clearance and urinary Na excretion were similar for all dietary treatments while K excretion decrease linearly (P<0.05) as the level of cactus cladodes in the diet increased. Feeding cactus cladodes caused diuresis and reduced urinary K excretion in goats. Possible reasons for these effects include water over-consumption from cactus cladodes and high dietary K intake. (C) 2007 Elsevier B.V. All rights reserved.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.