A GRASP algorithm for the multi-criteria minimum spanning tree problem

This paper proposes a GRASP (Greedy Randomized Adaptive Search Procedure) algorithm for the multi-criteria minimum spanning tree problem, which is NP-hard. In this problem a vector of costs is defined for each edge of the graph and the problem is to find all Pareto optimal or efficient spanning trees (solutions). The algorithm is based on the optimization of different weighted utility functions. In each iteration, a weight vector is defined and a solution is built using a greedy randomized constructive procedure. The found solution is submitted to a local search trying to improve the value of the weighted utility function. We use a drop-and-add neighborhood where the spanning trees are represented by Prufer numbers. In order to find a variety of efficient solutions, we use different weight vectors, which are distributed uniformly on the Pareto frontier. The proposed algorithm is tested on problems with r=2 and 3 criteria. For non-complete graphs with n=10, 20 and 30 nodes, the performance of the algorithm is tested against a complete enumeration. For complete graphs with n=20, 30 and 50 nodes the performance of the algorithm is tested using two types of weighted utility functions. The algorithm is also compared with the multi-criteria version of the Kruskal’s algorithm, which generates supported efficient solutions. This work was funded by the Municipal Town Hall of Campos dos Goytacazes city. The used computer was acquired with resource of CNPq.     

An adaptive approach of conic trust-region method for unconstrained optimization problems

In this paper, an adaptive trust region method based on the conic model for unconstrained optimization problems is proposed and analyzed. We establish the global and superlinear convergence results of the method. Numerical tests are reported that confirm the efficiency of the new method.     

Renormalization Conditions and the Sliding Scale in the Implicit Regularization Scheme: A Simple Connection

We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the calculation, the introduction of a mass scale is a direct consequence of a set of renormalization conditions. As an illustration the one-loop -function for QED and ⁴ theories are derived. They are given in terms of derivatives of appropriately systematized functions (related to definite parts of the amplitudes) with respect to a mass scale . Our formal scheme can be easily generalized for higher loop calculations.     

Biospeckle numerical values over spectral image maps of activity

The image analysis presents itself as a powerful instrument applied to all sort of biological phenomena monitoring. The development of many optical approaches to carry out a feasible image assembling and analysis to different demands has been the main effort in this application area. A consequence of that effort is the adoption of the biospeckle laser technique as a potential alternative to pursue the optical metrology. Particularly, the monitoring of the biological activity under the laser illumination presents as a reliable tool to many applications in many areas, such as to identify the changes in the micro-blood flow in animal tissues, or even to monitor the vegetal and the animal tissues and their metabolism. However, one limitation of biospeckle is the access of graphical maps of activity with any numerical information linked to them. This work had the objective to present a protocol to separate different tissues in the same material by means of the frequency signature, and by means of the association of graphical and numerical results from the biospeckle laser images. In order to confirm the efficiency of the proposed protocol we applied it to separate embryo and endosperm in maize seed and as well to separate tumour cells and normal tissues in animals. The results showed the feasibility of the approach proposed offering results with graphical maps associated to numerical information.     

Absolute configuration assignment of caffeic acid ester derivatives from Tithonia diversifolia by vibrational circular dichroism: the pitfalls of deuteration

Recently, it was observed that infrared (IR) and vibrational circular dichroism (VCD) calculations including deuterated hydroxyl groups in phenolic and saccharide moieties improved significantly the agreement with experimental data obtained in methanol-d₄. In the present study, the relative and absolute configurations of three methanol-soluble caffeic acid ester derivatives 1–3, isolated from Tithonia diversifolia, were established by a combined use of experimental and calculated ¹³C NMR chemical shifts, as well as electronic circular dichroism (ECD) and VCD spectroscopies. Interestingly, the attempt to reproduce the deuteration pattern arising from possible isotopic exchange in methanol-d₄ solution led to nearly mirror image calculated VCD spectra for 1 when compared to the non-deuterated molecule with the same absolute configuration. This latter fact can potentially lead to absolute configuration misassignments. A closer inspection of the vibrational chiroptical properties of 1 revealed that the deuteration status of the tertiary hydroxyl group at C-2 is critical for the correct reproduction of experimental VCD data in protic solvents. Therefore, in the case of stereochemical analysis of polar chiral natural product molecules, a combination of VCD and ECD is recommended.     

A second‐order time accurate finite element method for quasi‐incompressible viscous flows

A finite element method for quasi‐incompressible viscous flows is presented. An equation for pressure is derived from a second‐order time accurate Taylor–Galerkin procedure that combines the mass and the momentum conservation laws. At each time step, once the pressure has been determined, the velocity field is computed solving discretized equations obtained from another second‐order time accurate scheme and a least‐squares minimization of spatial momentum residuals. The terms that stabilize the finite element method (controlling wiggles and circumventing the Babuska–Brezzi condition) arise naturally from the process, rather than being introduced a priori in the variational formulation. A comparison between the present second‐order accurate method and our previous first‐order accurate formulation is shown. The method is also demonstrated in the computation of the leaky‐lid driven cavity flow and in the simulation of a crossflow past a circular cylinder. In both cases, good agreement with previously published experimental and computational results has been obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Restricted coloring problems on Graphs with few P 4’s

In this paper, we obtain linear time algorithms to determine the acyclic chromatic number, the star chromatic number, the non repetitive chromatic number and the clique chromatic number of P ₄-tidy graphs and (q, q ? 4)-graphs, for every fixed q, which are the graphs such that every set with at most q vertices induces at most q ? 4 distinct P ₄’s. These classes include cographs and P ₄-sparse graphs. We also obtain a linear time algorithm to compute the harmonious chromatic number of connected P ₄-tidy graphs and connected (q, q ? 4)-graphs. All these coloring problems are known to be NP-hard for general graphs. These algorithms are fixed parameter tractable on the parameter q(G), which is the minimum q such that G is a (q, q ? 4)-graph. We also prove that every connected (q, q ? 4)-graph with at least q vertices is 2-clique-colorable and that every acyclic coloring of a cograph is also nonrepetitive, generalizing the main result of Lyons (2011).     

Three different guises for the dynamics of a rotating beam

The dynamics of a flexible beam forced by a prescribed rotation around an axis perpendicular to its plane is addressed. Three approaches are considered, two of them related with simplified theories, within Strength of Materials, and the third one using Finite Elasticity. In the Strength of Materials approaches, the governing equations of motion are derived by superposing the deformations and the rigid motion in the first model, and in the second by stating the stationarity of the Lagrangian (including first- and second-order effects in order to capture the stiffening due to the centrifugal forces) through Hamilton's principle. Two actions are considered: gravity forces (pendulum) and prescribed rotation. Comparison of the two Strength of Materials models with the model derived from Finite Elasticity is carried out. Predictions for the same problems, interpreted in the context of the specific model, are compared and it was found that sometimes they give rather different results, both in the results and in the computational cost. Energy analyses are performed in order to obtain information about the quality of the numerical solutions. The paper ends with an example of a pendulum with a finite pivot including friction and flexibility. When the structural elements are sufficiently slender and the rotational speeds are low, so that the resulting deformations are small, the Strength of Material model that includes the load stiffening and the Finite Elasticity approach, lead to similar results. It can be concluded that the stiffening phenomenon is appropriately considered in the first model. On the contrary, when the Strength of Material hypothesis are not fulfilled, the problem should be addressed via the Finite Elasticity model. Additionally, cases with complexities such as friction at a finite pivot can only be addressed by Finite Elasticity.