On the Gromov width of polygon spaces

For generic $r=(r_1,\ldots,r_n) \in \mathbb{R}^n_+$ the space $\mathcal{M}(r)$ of $n$--gons in $\mathbb{R}^3$ with edges of lengths $r$ is a smooth, symplectic manifold. We investigate its Gromov width and prove that the expression $$2\pi \min \{2 r_j, (\sum_{i \neq j} r_i) - r_j\,\,|\, j=1,\ldots,n\}$$ is the Gromov width of all (smooth) $5$--gon spaces and of $6$--gon spaces, under some condition on $r \in \mathbb{R}^6_+$. The same formula constitutes a lower bound for all (smooth) spaces of $6$--gons. Moreover, we prove that the Gromov width of $\mathcal{M}(r)$ is given by the above expression when $\mathcal{M}(r)$ is symplectomorphic to $\mathbb{C}\mathbb{P}^{n-3}$, for any $n \geq 4$.Comment: 39 pages, 14 figures, to appear on Transformation Group

Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1

Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with the natural involution defined by (E,\Phi)\mapsto (E,-\Phi). We study the fixed point locus of this involution. In [GM], this moduli space with involution was identified with the moduli space of hyperpolygons equipped with a certain natural involution. Here we identify the fixed point locus with the moduli spaces of polygons in Minkowski 3-space. This identification yields information on the connected components of the fixed point locus.Comment: 22 page

Symplectic form on hyperpolygon spaces

In [GM], a family of parabolic Higgs bundles on $CP^1$ has been constructed and identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative construction of this family. This enables us to compute the Higgs symplectic form for this family and show that the isomorphism of [GM] is a symplectomorphism.Comment: 9 page

Quasi-parabolic Higgs bundles and null hyperpolygon spaces

We introduce the moduli space of quasi-parabolic S ⁢ L ⁡ ( 2 , C ) -Higgs bundles over a compact Riemann surface Σ and consider a natural involution, studying its fixed point locus when Σ is C ⁢ P 1 and establishing an identification with a moduli space of null polygons in Minkowski 3 -space

SPATIAL MACHINE LEARNING FOR MONITORING TEA LEAVES AND CROP YIELD ESTIMATION USING SENTINEL-2 IMAGERY, (A Case of Gunung Mas Plantation, Bogor)

Indonesia's tea production and export volume have fluctuated with a downward trend in the last five years, partly due to the increasingly competitive world tea quality. Crop yield estimation is part of the management of tea plucking, affecting tea quality and quantity. The constraint in estimating crop yields requires technology that can make the process more effective and efficient. Remote sensing technology and machine learning have been widely used in precision agriculture. Recently, big data processing, especially remote sensing data, machine learning, and deep learning have been carried out using a cloud computing platform. Therefore, we propose using GeoAI, a combination of Sentinel-2A imagery, machine learning, and Google Collaboratory, to predict ready for plucking tea leaves at optimal plucking time at Gunung Mas Plantation Bogor. We used selected bands of Sentinel-2A and extracted more features (i.e., NDVI) as a training set. Then we utilized the tea blocks boundary and tea plucking data to generate labels using Random Forest (RF) and Support Vector Machine (SVM). The classification results were further used to estimate the production of crop tea yield. The RF classifier is able to achieve overall accuracy at 51% and SVM at 54%. Meanwhile, accuracy at optimally aged tea blocks is able to achieve at 75.62% for RF and 52.88% for SVM. Thus, the SVM classifier is better in terms of overall accuracy. Meanwhile, the RF classifier is superior in predicting ready for plucking tea at optimally aged tea blocks

Monitoring functional capacity in heart failure.

This document reflects the key points of a consensus meeting of the Heart Failure Association of European Society of Cardiology (ESC) held to provide an overview the role of physiological monitoring in the complex multimorbid heart failure (HF) patient. This article reviews assessments of the functional ability of patients with HF. The gold standard measurement of cardiovascular functional capacity is peak oxygen consumption obtained from a cardiopulmonary exercise test. The 6-min walk test provides an indirect measure of cardiovascular functional capacity. Muscular functional capacity is assessed using either a 1-repetition maximum test of the upper and lower body or other methods, such as handgrip measurement. The short physical performance battery may provide a helpful, indirect indication of muscular functional capacity