Clustering Kualitas Kinerja Karyawan Pada Perusahaan Bahan Kimia Menggunakan Algoritma K-Means

Assessment of the quality of employee performance is one of the important things and is very much needed by the company, however, PT Clariant Adsorbents Indonesia does not currently have an employee performance quality system. This study aims to see the productivity of an employee and the effectiveness of an employee's performance in the future. Employee performance appraisal is divided into several clusters that are highly productive, moderately productive and less productive. The method used in this study is the K-means method, where the k-means method is the most popular method in the clustering algorithm. The k-means method looks for some of the most optimal partitions of the processed data by minimizing the error of the criteria using the optimal iteration. The variables used consist of employee names, work quality scores, responsibility values, cooperation values, attendance values, and discipline values. This research in processing data using Rapidminer Version 7.6.0.0.1 using the K-means method. The final result of this research is to get the grouping of the assessment into several categories that are very productive, quite productive and less productive and the clustering results are 0.42% for cluster 1, very productive category, which consists of 16 employee data, 0.47% for cluster 2 quite productive category, which consists of 18 employee data, 0.11% for cluster 3, less productive category, which consists of 4 employee data.

Critical polyharmonic systems and optimal partitions

<p style='text-indent:20px;'>We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula> which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling parameters tend to <inline-formula><tex-math id="M2">\begin{document}$ -\infty $\end{document}</tex-math></inline-formula>. We show that the supports of the limiting profiles of their components are pairwise disjoint smooth domains and solve a nonlinear optimal partition problem of <inline-formula><tex-math id="M3">\begin{document}$ \mathbb R^N $\end{document}</tex-math></inline-formula>. We give a detailed description of the shape of these domains.</p>

Yamabe systems and optimal partitions on manifolds with symmetries

<p style='text-indent:20px;'>We prove the existence of regular optimal <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula>-invariant partitions, with an arbitrary number <inline-formula><tex-math id="M2">\begin{document}$ \ell\geq 2 $\end{document}</tex-math></inline-formula> of components, for the Yamabe equation on a closed Riemannian manifold <inline-formula><tex-math id="M3">\begin{document}$ (M,g) $\end{document}</tex-math></inline-formula> when <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math></inline-formula> is a compact group of isometries of <inline-formula><tex-math id="M5">\begin{document}$ M $\end{document}</tex-math></inline-formula> with infinite orbits. To this aim, we study a weakly coupled competitive elliptic system of <inline-formula><tex-math id="M6">\begin{document}$ \ell $\end{document}</tex-math></inline-formula> equations, related to the Yamabe equation. We show that this system has a least energy <inline-formula><tex-math id="M7">\begin{document}$ G $\end{document}</tex-math></inline-formula>-invariant solution with nontrivial components and we show that the limit profiles of its components separate spatially as the competition parameter goes to <inline-formula><tex-math id="M8">\begin{document}$ -\infty $\end{document}</tex-math></inline-formula>, giving rise to an optimal partition. For <inline-formula><tex-math id="M9">\begin{document}$ \ell = 2 $\end{document}</tex-math></inline-formula> the optimal partition obtained yields a least energy sign-changing <inline-formula><tex-math id="M10">\begin{document}$ G $\end{document}</tex-math></inline-formula>-invariant solution to the Yamabe equation with precisely two nodal domains.</p>

Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.

Phase Separation, Optimal Partitions, and Nodal Solutions to the Yamabe Equation on the Sphere

We study an optimal $M$-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least energy sign-changing symmetric solutions to the Yamabe equation on the sphere with precisely $M$ nodal domains. The existence of an optimal partition is established through the study of the limit profiles of least energy solutions to a weakly coupled competitive elliptic system on the sphere.