Computing Groebner Fans

This paper presents algorithms for computing the Groebner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Groebner bases of the ideal. Our algorithms are based on a uniform definition of the Groebner fan that applies to both homogeneous and non-homogeneous ideals and a proof that this object is a polyhedral complex. We show that the cells of a Groebner fan can easily be oriented acyclically and with a unique sink, allowing their enumeration by the memory-less reverse search procedure. The significance of this follows from the fact that Groebner fans are not always normal fans of polyhedra in which case reverse search applies automatically. Computational results using our implementation of these algorithms in the software package Gfan are included.Comment: 26 page

Polygons on a Rotating Fluid Surface

We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously break the axial symmetry and assume the form of a polygon rotating rigidly with a speed different from that of the plate. With water we have observed polygons with up to 6 corners. It has been known for many years that such flows are prone to symmetry breaking, but apparently the polygonal surface shapes have never been observed. The creation of rotating internal waves in a similar setup was observed for much lower rotation rates, where the free surface remains essentially flat. We speculate that the instability is caused by the strong azimuthal shear due to the stationary walls and that it is triggered by minute wobbling of the rotating plate. The slight asymmetry induces a tendency for mode-locking between the plate and the polygon, where the polygon rotates by one corner for each complete rotation of the plate

The Circuit Ideal of a Vector Configuration

The circuit ideal, \ica, of a configuration \A = \{\a_1, ..., \a_n\} \subset \Z^d is the ideal generated by the binomials {\x}^{\cc^+} - {\x}^{\cc^-} \in \k[x_1, ..., x_n] as \cc = \cc^+ - \cc^- \in \Z^n varies over the circuits of \A. This ideal is contained in the toric ideal, \ia, of \A which has numerous applications and is nontrivial to compute. Since circuits can be computed using linear algebra and the two ideals often coincide, it is worthwhile to understand when equality occurs. In this paper we study \ica in relation to \ia from various algebraic and combinatorial perspectives. We prove that the obstruction to equality of the ideals is the existence of certain polytopes. This result is based on a complete characterization of the standard pairs/associated primes of a monomial initial ideal of \ica and their differences from those for the corresponding toric initial ideal. Eisenbud and Sturmfels proved that \ia is the unique minimal prime of \ica and that the embedded primes of \ica are indexed by certain faces of the cone spanned by \A. We provide a necessary condition for a particular face to index an embedded prime and a partial converse. Finally, we compare various polyhedral fans associated to \ia and \ica. The Gr\"obner fan of \ica is shown to refine that of \ia when the codimension of the ideals is at most two.Comment: 25 page

Fish schooling as a basis for vertical axis wind turbine farm design

Most wind farms consist of horizontal axis wind turbines (HAWTs) due to the high power coefficient (mechanical power output divided by the power of the free-stream air through the turbine cross-sectional area) of an isolated turbine. However when in close proximity to neighbouring turbines, HAWTs suffer from a reduced power coefficient. In contrast, previous research on vertical axis wind turbines (VAWTs) suggests that closely-spaced VAWTs may experience only small decreases (or even increases) in an individual turbine's power coefficient when placed in close proximity to neighbours, thus yielding much higher power outputs for a given area of land. A potential flow model of inter-VAWT interactions is developed to investigate the effect of changes in VAWT spatial arrangement on the array performance coefficient, which compares the expected average power coefficient of turbines in an array to a spatially-isolated turbine. A geometric arrangement based on the configuration of shed vortices in the wake of schooling fish is shown to significantly increase the array performance coefficient based upon an array of 16x16 wind turbines. Results suggest increases in power output of over one order of magnitude for a given area of land as compared to HAWTs.Comment: Submitted for publication in BioInspiration and Biomimetics. Note: The technology described in this paper is protected under both US and international pending patents filed by the California Institute of Technolog

Age-related differences in adaptation during childhood: The influences of muscular power production and segmental energy flow caused by muscles

Acquisition of skillfulness is not only characterized by a task-appropriate application of muscular forces but also by the ability to adapt performance to changing task demands. Previous research suggests that there is a different developmental schedule for adaptation at the kinematic compared to the neuro-muscular level. The purpose of this study was to determine how age-related differences in neuro-muscular organization affect the mechanical construction of pedaling at different levels of the task. By quantifying the flow of segmental energy caused by muscles, we determined the muscular synergies that construct the movement outcome across movement speeds. Younger children (5-7 years; n = 11), older children (8-10 years; n = 8), and adults (22-31 years; n = 8) rode a stationary ergometer at five discrete cadences (60, 75, 90, 105, and 120 rpm) at 10% of their individually predicted peak power output. Using a forward dynamics simulation, we determined the muscular contributions to crank power, as well as muscular power delivered to the crank directly and indirectly (through energy absorption and transfer) during the downstroke and the upstroke of the crank cycle. We found significant age × cadence interactions for (1) peak muscular power at the hip joint [Wilks' Lambda = 0.441, F(8,42) = 2.65, p = 0.019] indicating that at high movement speeds children produced less peak power at the hip than adults, (2) muscular power delivered to the crank during the downstroke and the upstroke of the crank cycle [Wilks' Lambda = 0.399, F(8,42) = 3.07, p = 0.009] indicating that children delivered a greater proportion of the power to the crank during the upstroke when compared to adults, (3) hip power contribution to limb power [Wilks' Lambda = 0.454, F(8,42) = 2.54, p = 0.023] indicating a cadence-dependence of age-related differences in the muscular synergy between hip extensors and plantarflexors. The results demonstrate that in spite of a successful performance, children construct the task of pedaling differently when compared to adults, especially when they are pushed to their performance limits. The weaker synergy between hip extensors and plantarflexors suggests that a lack of inter-muscular coordination, rather than muscular power production per se, is a factor that limits children's performance ranges

How to Improve University Orientation: Seven Good Practice Strategies for South Africa

There is a great deal of variability in the practice of orientation across the country at South Africa’s universities, and there is limited knowledge of what exactly constitutes good practice in orientation.  Many areas of enquiry remain unexplored, and remain blind spots for South Africa’s higher education sector. The article addresses this central question: What constitutes good practice for orientation programmes in South Africa? The article argues that a structured and informed orientation strategy is critical in terms of matters of student retention and, in fact, may serve as the key linchpin of students’ decision to stay or exit the higher education system. Accordingly, seven strategies to improve nationalorientation practice are proposed in this article

Grey-box Modeling of Reversible Solid Oxide Cell Stack’s Electrical Dynamics Based on Electrochemical Impedance Spectroscopy

This paper aims to design a lumped-capacity modelof a reversible solid oxide cell stack for hydrogen electrolysis.The lumped-capacity model needs to have an adequate representationof the electrical dynamics over a wide operatingrange and a model structure suitable for the design of a physicalemulator. The grey-box model is based on data obtained by electrochemicalimpedance spectroscopy conducted on a commercialsolid oxide cell stack for four different gas compositions at sixaging stages. In addition, a comparison of the experimental andsimulated voltage response of the reversible solid oxide cell stackin cyclic reversible operation mode was conducted at differentaging levels of the stack

Radiomics for Everyone: A New Tool Simplifies Creating Parametric Maps for the Visualization and Quantification of Radiomics Features

Aim was to develop a user-friendly method for creating parametric maps that would provide a comprehensible visualization and allow immediate quantification of radiomics features. For this, a self-explanatory graphical user interface was designed, and for the proof of concept, maps were created for CT and MR images and features were compared to those from conventional extractions. Especially first-order features were concordant between maps and conventional extractions, some even across all examples. Potential clinical applications were tested on CT and MR images for the differentiation of pulmonary lesions. In these sample applications, maps of Skewness enhanced the differentiation of non-malignant lesions and non-small lung carcinoma manifestations on CT images and maps of Variance enhanced the differentiation of pulmonary lymphoma manifestations and fungal infiltrates on MR images. This new and simple method for creating parametric maps makes radiomics features visually perceivable, allows direct feature quantification by placing a region of interest, can improve the assessment of radiological images and, furthermore, can increase the use of radiomics in clinical routine