A Physarum-inspired multi-agent system to solve maze

Physarum Polycephalum is a primitive unicellular organism. Its foraging behavior demonstrates a unique feature to form a shortest path among food sources, which can be used to solve a maze. This paper proposes a Physarum-inspired multi-agent system to reveal the evolution of Physarum transportation networks. Two types of agents – one type for search and the other for convergence – are used in the proposed model, and three transition rules are identified to simulate the foraging behavior of Physarum. Based on the experiments conducted, the proposed multiagent system can solve the two possible routes of maze, and exhibits the reconfiguration ability when cutting down one route. This indicates that the proposed system is a new way to reveal the intelligence of Physarum during the evolution process of its transportation networks.

On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

Fast algorithm for the cutting angle method of global optimization

The cutting angle method for global optimization was proposed in 1999 by Andramonov et al. (Appl. Math. Lett. 12 (1999) 95). Computer implementation of the resulting algorithm indicates that running time could be improved with appropriate modifications to the underlying mathematical description. In this article, we describe the initial algorithm and introduce a new one which we prove is significantly faster at each stage. Results of numerical experiments performed on a Pentium III 750 Mhz processor are presented.

Psychometric data on the mathematics self-efficacy scale

Descriptive measurement reliability and validity data are reported on scores from the Mathematics Self-Efficacy Scale (MSES) in two contexts—class and test—for a sample of 302 Australian high school students. Summated scores on the MSES correlated r = .74, and together these items yielded one component that explained 49% of the variance. MSES scores demonstrated internal reliability for both class and test (Cronbach alphas = .86 and .90). Statistically significant correlations between MSES scores, past mathematics grades, and Marsh’s Self-Description Questionnaire III (Math) were used to indicate the convergent validity of scores for the MSES. Discriminant validity of the MSES scores was suggested by the lack of significant correlations between the MSES measures and students’ desired English grades. Statistically significant correlations between MSES scores and students’ desired mathematics grades indicated concurrent validity of the MSES measures. A statistically significant difference between class and test scores supported Bandura’s prescription for context specificity in efficacy research.

The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ_ABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ_ABCD, its conjugate ψ_ȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

Achilles tendinopathy

Achilles tendon injury (tendinopathy) and pain occur in active individuals, when the tendon is subject to high or unusual load. Achilles tendinopathy can be resistant to treatment, and symptoms may persist despite both conservative and surgical intervention. The pathology of overuse tendinopathy is non-inflammatory, with a degenerative or failed healing tendon response. The diagnosis of Achilles tendinopathy requires excellent differential diagnosis and an understanding of the role of tendon imaging. Conservative treatment must include exercise, with a bias to eccentric contractions. Surgical treatment is effective after complete tendon rupture, but may not assist recovery from overuse tendinopathy. Further research into the clinical aspects of Achilles tendinopathy is required.

Impetus to explore: approaching operational deficiency optimistically

‘Impetus to explore’ is studied through post-lesson video-stimulated student interviews. This impetus focuses ‘spontaneous’ decisions to explore unfamiliar mathematics. Uncertainty, quests for elegance and curiosity have been found to contribute to this impetus. This study identified other contributing factors: inability to undertake the teacher’s task, ‘optimistic explanatory style’ (Seligman, 1995), and identifying relevant complexities (Williams, 2002). Explanatory style affects how a person perceives successes and failures. Enactment of optimism in this study illuminated its role in creating an impetus to explore. Re-conceptualising ‘operational deficiency’ (Chen & Siegler, 2000) to include absence of resources to undertake a task illuminated a task design feature that can increase exploration.

Determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. III. mixed invariants of arbitrary degree in the Ricci Spinor

In this paper, we rigorously prove that the complete set of Riemann tensor invariants given by Sneddon [J. Math. Phys. 40, 5905 (1999)] is both minimal and complete. Furthermore, we provide a two-stage algorithm for the explicit construction of polynomial syzygies relating any dependent Riemann tensor invariant to members of the complete set.

Design of linear functional observers for time-delay systems of the neutral-type

This paper presents the design of reduced-order linear functional observers for a class of linear time-delay systems of the neutral-type. The type of the observer proposed in this paper is without internal delay and its order is the same as the number of linear functions to be estimated. First, conditions for the existence of the reduced-order functional observers that are capable of asymptotically estimating any given function of the state vector are derived. Then, based on the newly derived existence conditions, a procedure is given for the determination of the observer parameters. The results derived in this paper include a range of linear systems and extend some existing results of linear functional observers to linear neutral delay systems. A numerical example is given to illustrate the design procedure.

Diversions

The article highlights various books that integrates mathematics in activities and solving problems. The author stated that the novel "The Dice Man" of Luke Rhinehart describes a person who decides to use rolling a dice to make important decisions. Meanwhile, the "Casino Royale" of Ian Fleming highlights the character as an extremely experienced gambler. On the other hand, the "Lieutenant Hornblower" of C. S. Forester highlights the character who support himself by playing whist.