Dynamics towards the Feigenbaum attractor

We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.Comment: 8 pages, 12 figure

Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review

Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices

Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitken's block diagonalization formula. It yields to a kind of LU (similar to Cholesky's factorization) decomposition (under congruence) of arbitrary skew-symmetric matrices that is well suited both for the numeric and symbolic evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90) implementing both methods are given. We also provide simple implementations in Python and Mathematica for purpose of testing, or for exploratory studies of methods that make use of pfaffians.Comment: 13 pages, Download links: http://gamma.ft.uam.es/robledo/Downloads.html and http://www.phys.washington.edu/users/bertsch/computer.htm

Evaluation of the Operational Performance in Implementing Lean Manufacturing and Six Sigma

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The Key Success Factors for Lean Manufacturing versus Six Sigma

The aim of this study is to investigate and identify the key success factors of implementing lean manufacturing and six sigma in separate ways. The study applies a quantitative approach and statistical analysis to determine the results collected from the French industry. Findings revealed that there exist statistically significant differences in the level of importance between the implementation of lean manufacturing and six sigma across the common success factors such as culture change, communication and involvement of employees, among others. On the other hand, there were similarities in the degrees of importance regarding the common success including top management commitment, skill and expertise and linking method to supplier, etc. The findings can assist an organization to be more careful with the success factors of each method, in addition to helping them in determining the appropriate method that enables exploration between lean manufacturing and six sigma based on the capacity of an organization to apply the success factors. Literature reviews regarding comparison of key success factors of lean manufacturing and six sigma had not been tested earlier, which have been considered in this study.

Evaluation of the CGIAR Research Program on Climate Change, Agriculture and Food Security (CCAFS)

This evaluation has been commissioned by the Independent Evaluation Arrangement (IEA) of CGIAR. Following consultation with the ISP and CCAFS management, the Evaluation addressed four key evaluation questions. 1) How well is strategic collaboration and integration both within and outside the CGIAR being achieved? 2) To what extent is CCAFS generating unique international public goods for agriculture, food security and climate change? 3) How well do the Flagship Projects link together and combine at output and outcome levels in the regions; and, to what extent are successes toward outcomes transferable from region to region? 4) How robust are the monitoring, evaluation and learning processes of the Program? As its main approach, the Evaluation selected nine projects for case studies to address the evaluation criteria and questions at three levels: global Program level, Flagship level and Regional Program level. The methodology also included document review, field visits to all regions, interviews of over 150 stakeholders, survey of CCAFS researchers, identification of exemplary cases of CCAFS work with high impact potential using a triple loop learning analysis, bibliometric analysis and H-index analysis of senior researchers. An independent third-party review team contributed to the evaluation of quality of science by assessing a random sample of journal articles published by CCAFS

Assessment of Lean Manufacturing and Six sigma operation with decesion making based on the Analytic Hierarchy Process

In this paper, an AHP model was used for determining the optimal method and the most efficient methodologies of lean manufacturing and six sigma in various industries based on three criteria. These criteria are financial performance, operational performance, and innovation performance. Study results show the impact of three categories that are based on the implementation of a specific method. Findings show that companies implementing lean and six sigma were more effective than companies that implemented either lean manufacturing only or used limited tools of lean six sigma across operational and financial performance. Meanwhile companies that used limited tools of lean six sigma gained minimal performance improvements. Additionally, the results illustrated that automobile industries followed by service and electronics industries have the most effectiveness in innovation, operational and financial performance. Moreover, this study shows struggle of lean manufacturing and/or six sigma implementation with transportation and health industries. Bibliographic investigation showed there is limited scientific research focusing on lean manufacturing and six sigma implementation within French industries

Intermittency at critical transitions and aging dynamics at edge of chaos

We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the generalized Lyapunov coefficients $\lambda_{q}$ that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the edge of chaos with the appearance of a special value for the entropic index $q$. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.Comment: Proceedings of: STATPHYS 2004 - 22nd IUPAP International Conference on Statistical Physics, National Science Seminar Complex, Indian Institute of Science, Bangalore, 4-9 July 2004. Pramana, in pres

A recent appreciation of the singular dynamics at the edge of chaos

We study the dynamics of iterates at the transition to chaos in the logistic map and find that it is constituted by an infinite family of Mori's $q$-phase transitions. Starting from Feigenbaum's $\sigma$ function for the diameters ratio, we determine the atypical weak sensitivity to initial conditions $\xi _{t}$ associated to each $q$-phase transition and find that it obeys the form suggested by the Tsallis statistics. The specific values of the variable $q$ at which the $q$-phase transitions take place are identified with the specific values for the Tsallis entropic index $q$ in the corresponding $\xi_{t}$. We describe too the bifurcation gap induced by external noise and show that its properties exhibit the characteristic elements of glassy dynamics close to vitrification in supercooled liquids, e.g. two-step relaxation, aging and a relationship between relaxation time and entropy.Comment: Proceedings of: Verhulst 200 on Chaos, Brussels 16-18 September 2004, Springer Verlag, in pres