Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur

Implementasi Lean Sigma Untuk Penurunan Nilai Cost of Poor Quality Kain Ekspor Kelas a (Studi Kasus : Departemen Finishing PT Mertex Indonesia)

Departemen Finishing PT Mertex Indonesia bertugas mengolah kain mentah menjadi produk kain jadi. Dalam menjalankan produksinya, Departemen Finishing masih mengalami pemborosan. Pemborosan (waste) sebagai internal failure menyebabkan cost of poor quality yang membuat Perusahaan kehilangan kesempatan untuk mendapatkan keuntungan. Tujuan penelitian ini adalah agar Perusahaan dapat meningkatkan kualitas proses produksi dan menurunkan nilai cost of poor quality dengan menggunakan pendekatan lean sigma. Tahap awal dalam penelitian adalah mengidentifikasi alur proses produksi dan menggambarkan hasilnya melalui value stream mapping (VSM). Kemudian melakukan klasifikasi aktivitas dan melakukan identifikasi waste. Jenis waste yang dipertimbangkan dalam penelitian ini adalah seven waste. Setelah itu dicari nilai cost of poor quality (COPQ) dari masing-masing waste untuk mendapatkan waste berpengaruh berdasarkan nilai COPQ yang terbesar. Setelah itu dicari akar penyebab permasalahan dengan root cause analysis (RCA) dan prioritas waste yang harus diperbaiki dengan failure mode and effect analysis (FMEA). Dari alternatif perbaikan dipilih yang terbaik menggunakan value based management berdasarkan nilai value yang tertinggi. Melalui konsep value based management didapatkan alternatif perbaikan terpilih yaitu mengganti proses pengemasan manual dengan proses pengemasan otomatis dengan membeli mesin pengemas otomatis, menjaga kestabilan rolling mesin, melakukan preventive maintenance secara teratur dan melakukan pemasangan expander roll pada roll mesin. Setelah dilakukan rekomendasi perbaikan diharapkan nilai sigma dapat meningkat dan cost of poor quality dapat menurun

Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v

Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

Application of Numerical Newton-Raphson Method in Calculation of Emitter Water Discharge of Drip Irrigation System in “Mutis Cemerlang” Coffee Plantation

Based on the slope class, the shape of the area and the elevation of dry land in Nusa Tenggara, agricultural land in Noepesu Village is suitable for planting coffee plants with an agroforestry scheme. To overcome the problem of limited water, drip irrigation system technology can be applied. The use of drip irrigation as an agricultural technology in Noepesu village has been carried out by many farmer groups. Still, the installation process does not consider the pipe specifications (pipe length and pipe diameter) and the condition of agricultural land. This causes the service life of drip irrigation to be not long. If this continues, of course, it will increase system installation costs. To optimize service life, a hydraulics analysis method is needed for drip irrigation pipe network systems that take into account pipe specifications and agricultural land conditions.The hydraulics analysis of the drip irrigation network system determines the emitter’s water flow rate. The emitter flow rate forms a nonlinear equation known as the closed pipe equation. In the process of solving these equations, numerical methods can be used, specifically the Newton-Raphson method. This study focuses on applying the Newton-Raphson method to calculate the amount of water discharge from each emitter of the drip irrigation network system on the farmland of the Mutis Cemerlang Farmer Group in Noepesu Village. The drip irrigation system is designed with 250 nodes, 275 pipes, 26 loops, and 86 outlets divided into two sides, with the left side containing 84 outlets with one emitter and the right side containing 102 outlets with two emitters. The amount of water discharge for each emitter is 0,0008 ml/second≤Q≤2,6 ml/second for the left side and 0,001 ml/second≤Q≤1,1 ml/second for the right side, as determined by simulation calculations utilizing the Newton-Raphson method and Matlab software. The simulation results show that the amount of water discharge at each emitter is ideal in the first iteration because it has a discharge correction value (∆Q)≈0

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

Inflammatory biomarkers in Alzheimer's disease plasma

Introduction: Plasma biomarkers for Alzheimer's disease (AD) diagnosis/stratification are a \u201cHoly Grail\u201d of AD research and intensively sought; however, there are no well-established plasma markers. Methods: A hypothesis-led plasma biomarker search was conducted in the context of international multicenter studies. The discovery phase measured 53 inflammatory proteins in elderly control (CTL; 259), mild cognitive impairment (MCI; 199), and AD (262) subjects from AddNeuroMed. Results: Ten analytes showed significant intergroup differences. Logistic regression identified five (FB, FH, sCR1, MCP-1, eotaxin-1) that, age/APO\u3b54 adjusted, optimally differentiated AD and CTL (AUC: 0.79), and three (sCR1, MCP-1, eotaxin-1) that optimally differentiated AD and MCI (AUC: 0.74). These models replicated in an independent cohort (EMIF; AUC 0.81 and 0.67). Two analytes (FB, FH) plus age predicted MCI progression to AD (AUC: 0.71). Discussion: Plasma markers of inflammation and complement dysregulation support diagnosis and outcome prediction in AD and MCI. Further replication is needed before clinical translation