Critical Thickness Ratio for Buckled and Wrinkled Fruits and Vegetables

Fruits and vegetables are usually composed of exocarp and sarcocarp and they take a variety of shapes when they are ripe. Buckled and wrinkled fruits and vegetables are often observed. This work aims at establishing the geometrical constraint for buckled and wrinkled shapes based on a mechanical model. The mismatch of expansion rate between the exocarp and sarcocarp can produce a compressive stress on the exocarp. We model a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. The derived bifurcation condition contains both geometrical and material constants. However, a careful analysis on this condition leads to the finding of a critical thickness ratio which separates the buckling and wrinkling modes, and remarkably, which is independent of the material stiffnesses. More specifically, it is found that if the thickness ratio is smaller than this critical value a fruit/vegetable should be in a buckling mode (under a sufficient stress); if a fruit/vegetable in a wrinkled shape the thickness ratio is always larger than this critical value. To verify the theoretical prediction, we consider four types of buckled fruits/vegetables and four types of wrinkled fruits/vegetables with three samples in each type. The geometrical parameters for the 24 samples are measured and it is found that indeed all the data fall into the theoretically predicted buckling or wrinkling domains. Some practical applications based on this critical thickness ratio are briefly discussed.Comment: 11 pages 9 figures 2 table

Polynomial Roots and Calabi-Yau Geometries

The examination of roots of constrained polynomials dates back at least to Waring and to Littlewood. However, such delicate structures as fractals and holes have only recently been found. We study the space of roots to certain integer polynomials arising naturally in the context of Calabi-Yau spaces, notably Poincare and Newton polynomials, and observe various salient features and geometrical patterns.Comment: 22 pages, 13 Figure

Quiver Gauge Theories: Finitude and Trichotomoty

D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of standard techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, conformality and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then, we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N < 2 Yang-Mills theories in four dimensions

Query expansion with naive bayes for searching distributed collections

The proliferation of online information resources increases the importance of effective and efficient distributed searching. However, the problem of word mismatch seriously hurts the effectiveness of distributed information retrieval. Automatic query expansion has been suggested as a technique for dealing with the fundamental issue of word mismatch. In this paper, we propose a method - query expansion with Naive Bayes to address the problem, discuss its implementation in IISS system, and present experimental results demonstrating its effectiveness. Such technique not only enhances the discriminatory power of typical queries for choosing the right collections but also hence significantly improves retrieval results

Self-Similar kk-Graph C*-Algebras

In this paper, we introduce a notion of a self-similar action of a group $G$ on a $k$-graph $\Lambda$, and associate it a universal C*-algebra \O_{G,\Lambda}. We prove that \O_{G,\Lambda} can be realized as the Cuntz-Pimsner algebra of a product system. If $G$ is amenable and the action is pseudo free, then \O_{G,\Lambda} is shown to be isomorphic to a "path-like" groupoid C*-algebra. This facilitates studying the properties of \O_{G,\Lambda}. We show that \O_{G,\Lambda} is always nuclear and satisfies the Universal Coefficient Theorem; we characterize the simplicity of \O_{G,\Lambda} in terms of the underlying action; and we prove that, whenever \O_{G,\Lambda} is simple, there is a dichotomy: it is either stably finite or purely infinite, depending on whether $\Lambda$ has nonzero graph traces or not. Our main results generalize the recent work of Exel and Pardo on self-similar graphs.Comment: 28 pages; minor change

Hierarchical classification for multiple, distributed web databases

The proliferation of online information resources increases the importance of effective and efficient distributed searching. Our research aims to provide an alternative hierarchical categorization and search capability based on a Bayesian network learning algorithm. Our proposed approach, which is grounded on automatic textual analysis of subject content of online web databases, attempts to address the database selection problem by first classifying web databases into a hierarchy of topic categories. The experimental results reported demonstrate that such a classification approach not only effectively reduces the class search space, but also helps to significantly improve the accuracy of classification performance