Complexity Estimates for Two Uncoupling Algorithms

Uncoupling algorithms transform a linear differential system of first order into one or several scalar differential equations. We examine two approaches to uncoupling: the cyclic-vector method (CVM) and the Danilevski-Barkatou-Z\"urcher algorithm (DBZ). We give tight size bounds on the scalar equations produced by CVM, and design a fast variant of CVM whose complexity is quasi-optimal with respect to the output size. We exhibit a strong structural link between CVM and DBZ enabling to show that, in the generic case, DBZ has polynomial complexity and that it produces a single equation, strongly related to the output of CVM. We prove that algorithm CVM is faster than DBZ by almost two orders of magnitude, and provide experimental results that validate the theoretical complexity analyses.Comment: To appear in Proceedings of ISSAC'13 (21/01/2013

Synchronous and symmetric migration of Drosophila caudal visceral mesoderm cells requires dual input by two FGF ligands

Caudal visceral mesoderm (CVM) cells migrate synchronously towards the anterior of the Drosophila embryo as two distinct groups located on each side of the body, in order to specify longitudinal muscles that ensheath the gut. Little is known about the molecular cues that guide cells along this path, the longest migration of embryogenesis, except that they closely associate with trunk visceral mesoderm (TVM). The expression of the fibroblast growth factor receptor (FGFR) heartless and its ligands, pyramus (pyr) and thisbe (ths), within CVM and TVM cells, respectively, suggested FGF signaling may influence CVM cell guidance. In FGF mutants, CVM cells die before reaching the anterior region of the TVM. However, an earlier phenotype observed was that the two cell clusters lose direction and converge at the midline. Live in vivo imaging and tracking analyses identified that the movements of CVM cells were slower and no longer synchronous. Moreover, CVM cells were found to cross over from one group to the other, disrupting bilateral symmetry, whereas such mixing was never observed in wild-type embryos. Ectopic expression of either Pyr or Ths was sufficient to redirect CVM cell movement, but only when the endogenous source of these ligands was absent. Collectively, our results show that FGF signaling regulates directional movement of CVM cells and that native presentation of both FGF ligands together is most effective at attracting cells. This study also has general implications, as it suggests that the activity supported by two FGF ligands in concert differs from their activities in isolation

Evaluating and improving the cluster variation method entropy functional for Ising alloys

The success of the "Cluster Variation Method" (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of -TS, so the free energy F=E-TS is more accurate than either of its parts. This insight explains a problem with "hybrid methods" using MC correlation functions in the CVM entropy expression: They give exact energies E and do not give significantly improved -TS relative to CVM, so they do not benefit from the above noted cancellation of errors. Additionally, "hybrid methods" suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the "Entropic Monte Carlo" (EMC), is shown here to provide a means for critically evaluating the CVM entropy. Inspired by EMC results, we find a universal and simple correction to the CVM entropy which produces individual components of the free energy with MC accuracy, but is computationally much less expensive than either MC thermodynamic integration or EMC.Comment: 7 pages, ReVTeX galley format, 4 eps figures embedded using epsf, to be published in J. Chem. Phy

Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising--like) models in equilibrium statistical mechanics, improving on the mean--field approximation and the Bethe--Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models. The foundations of the CVM are briefly reviewed, and the relations with similar techniques are discussed. The main properties of the method are considered, with emphasis on its exactness for particular models and on its asymptotic properties. The problem of the minimization of the variational free energy, which arises in the CVM, is also addressed, and recent results about both provably convergent and message-passing algorithms are discussed.Comment: 36 pages, 17 figure

Nematic phase in the J1_1-J2_2 square lattice Ising model in an external field

The J$_1$-J$_2$ Ising model in the square lattice in the presence of an external field is studied by two approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter $\kappa=J_2/|J_1|$ which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.Comment: 13 pages, 10 figure

Gauge-free cluster variational method by maximal messages and moment matching

We present an implementation of the cluster variational method (CVM) as a message passing algorithm. The kind of message passing algorithm used for CVM, usually named generalized belief propagation (GBP), is a generalization of the belief propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free energy is usually not a one-to-one correspondence because of the existence of a gauge transformation involving the GBP messages. Our contribution is twofold. First, we propose a way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard parent-to-child GBP. We call this approach maximal messages. Second, we focus on the case of binary variables, reinterpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matching method is gauge free, i.e., it guarantees that the resulting GBP is not gauge invariant. We apply our maximal messages and moment matching GBP to obtain an analytical expression for the critical temperature of the Ising model in general dimensions at the level of plaquette CVM. The values obtained outperform Bethe estimates, and are comparable with loop corrected belief propagation equations. The method allows for a straightforward generalization to disordered systems

Efecto de la confianza en la lealtad y el eWOM en las comunidades virtuales de marca.

La confianza en la marca y en la Comunidad Virtual de Marca (CVM) pueden contribuir a la generación de lealtad a la marca y eWOM positivo. Sin embargo, no han sido muchos los estudios empíricos que han incluido ambos tipos de confianza en la evaluación de los resultados de las CVM. Por lo tanto, este trabajo tiene como objetivo explorar cómo la confianza en la marca y la confianza en la comunidad influyen en la lealtad y en el eWOM. Para ello se emplearon datos procedentes de una encuesta realizada a usuarios de CVM que fueron analizados mediante la técnica PLS. Los resultados confirman que la confianza en la marca influye en la lealtad y en el eWOM tanto directamente, como indirectamente a través de la confianza en la CVM. Además, la lealtad favorece la generación de eWOM. Las implicaciones para la práctica de marketing son comentadas.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Evaluation of CBS 600 carburized steel as a gear material

Gear endurance tests were conducted with one lot of consumable-electrode vacuum-melted (CVM) AISI 9310 gears and one lot of air-melt CBS 600 gears. The gears were 8 pitch with a pitch diameter of 8.89 centimeters (3.5 in.). Bench-type rolling-element fatigue tests were also conducted with one lot of CVM AISI 9310, three lots of CVM CBS 600, and one of air-melt CBS 600 material. The rolling-element bars were 0.952 centimeter (0.375 in.) in diameter. The CBS 600 material exhibited pitting fatigue lives in both rolling-element specimens and gears at least equivalent to that of CVM AISI 9310. Tooth fracture failure occurred with the CBS 600 gears after overrunning a fatigue spall, but it did not occur with the CVM AISI 9310 gears. Tooth fracture in the CBS 600 was attributed to excessive carbon content in the case, excessive case depth, and a higher than normal core hardness