Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure

Ultradiscretization of the solution of periodic Toda equation

A periodic box-ball system (pBBS) is obtained by ultradiscretizing the periodic discrete Toda equation (pd Toda eq.). We show the relation between a Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula for the fundamental cycle of the pBBS is obtained as a colloraly.Comment: 41 pages; 7 figure

Rab8a and Rab8b are essential for several apical transport pathways but insufficient for ciliogenesis

The small GTP-binding protein Rab8 is known to play an essential role in intracellular transport and cilia formation. We have previously demonstrated that Rab8a is required for localising apical markers in various organisms. Rab8a has a closely related isoform, Rab8b. To determine whether Rab8b can compensate for Rab8a, we generated Rab8b-knockout mice. Although the Rab8b-knockout mice did not display an overt phenotype, Rab8a and Rab8b double-knockout mice exhibited mislocalisation of apical markers and died earlier than Rab8a-knockout mice. The apical markers accumulated in three intracellular patterns in the double-knockout mice. However, the localisation of basolateral and/or dendritic markers of the double-knockout mice seemed normal. The morphology and the length of various primary and/or motile cilia, and the frequency of ciliated cells appeared to be identical in control and double-knockout mice. However, an additional knockdown of Rab10 in double-knockout cells greatly reduced the percentage of ciliated cells. Our results highlight the compensatory effect of Rab8a and Rab8b in apical transport, and the complexity of the apical transport process. In addition, neither Rab8a nor Rab8b are required for basolateral and/or dendritic transport. However, simultaneous loss of Rab8a and Rab8b has little effect on ciliogenesis, whereas additional loss of Rab10 greatly affects ciliogenesis

A crystal theoretic method for finding rigged configurations from paths

The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.Comment: 24 pages, version for publicatio

Box-ball system: soliton and tree decomposition of excursions

We review combinatorial properties of solitons of the Box-Ball system introduced by Takahashi and Satsuma in 1990. Starting with several definitions of the system, we describe ways to identify solitons and review a proof of the conservation of the solitons under the dynamics. Ferrari, Nguyen, Rolla and Wang 2018 proposed a soliton decomposition of a configuration into a family of vectors, one for each soliton size. Based on this decompositions, the authors have proposed a family of measures on the set of excursions which induces invariant distributions for the Box-Ball System. In this paper, we propose a new soliton decomposition which is equivalent to a branch decomposition of the tree associated to the excursion, see Le Gall 2005. A ball configuration distributed as independent Bernoulli variables of parameter $\lambda<1/2$ is in correspondence with a simple random walk with negative drift $2\lambda-1$ and infinitely many excursions over the local minima. In this case the authors have proven that the soliton decomposition of the walk consists on independent double-infinite vectors of iid geometric random variables. We show that this property is shared by the branch decomposition of the excursion trees of the random walk and discuss a corresponding construction of a Geometric branching process with independent but not identically distributed Geometric random variables.Comment: 47 pages, 33 figures. This is the revised version after addressing referee reports. This version will be published in the special volume of the XIII Simposio de Probabilidad y Procesos Estoc\'asticos, UNAM Mexico, by Birkhause

Deployment Adviser Tool for Wireless Sensor Networks

This paper presents a system for the purpose of field deployment of nodes in wireless sensor networks. We propose a mobile phone based deployment adviser tool which is robust as well as practically implementable. The tool advises a layman deployer to create a optimized wireless sensor network by placing of the nodes according to application requirements. The tool is presented here as logically linked sub-modules. Each sub-modules are described in detail. Also we propose an algorithm which helps in distributing the power consumption among the nodes in the network, thus, increasing the network lifetime. The adviser tool has been verified by implementing it in IITH mote. The tool we propose has significant implication since it greatly eases, but more importantly extracts the best performance possible while deploying the wireless sensor network

The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function

Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value problem is solved in terms of an ultradiscrete analogue of the Riemann theta function whose period matrix originates in the Bethe ansatz at q=0.Comment: 11 pages, 1 figur

Natural attenuation of Fukushima-derived radiocesium in soils due to its vertical and lateral migration

Processes of vertical and lateral migration lead to gradual reduction in contamination of catchment soil, particularly its top layer. The reduction can be considered as natural attenuation. This, in turn, results in a gradual decrease of radiocesium activity concentrations in the surface runoff and river water, in both dissolved and particulate forms. The purpose of this research is to study the dynamics of Fukushima-derived radiocesium in undisturbed soils and floodplain deposits exposed to erosion and sedimentation during floods. Combined observations of radiocesium vertical distribution in soil and sediment deposition on artificial lawn-grass mats on the Niida River floodplain allowed us to estimate both annual mean sediment accumulation rates and maximum sedimentation rates corresponding to an extreme flood event during Tropical Storm Etau, 6-11 September 2015. Dose rates were reduced considerably for floodplain sections with high sedimentation because the top soil layer with high radionuclide contamination was eroded and/or buried under cleaner fresh sediments produced mostly due to bank erosion and sediments movements. Rate constants of natural attenuation on the sites of the Takase River and floodplain of Niida River was found to be in range 0.2-0.4 year-1. For the site in the lower reach of the Niida River, collimated shield dose readings from soil surfaces slightly increased during the period of observation from February to July 2016. Generally, due to more precipitation, steeper slopes, higher temperatures and increased biological activities in soils, self-purification of radioactive contamination in Fukushima associated with vertical and lateral radionuclide migration is faster than in Chernobyl. In many cases, monitored natural attenuation along with appropriate restrictions seems to be optimal option for water remediation in Fukushima contaminated areas

Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics

The U_q(\hat{sl}_2) vertex model at q=0 with periodic boundary condition is an integrable cellular automaton in one-dimension. By the combinatorial Bethe ansatz, the initial value problem is solved for arbitrary states in terms of an ultradiscrete analogue of the Riemann theta function with rational characteristics.Comment: 9 page

3D Localization Technique with Mobile Robot for Improving Operability of Remote-Control Devices

Electrical devices which are controlled remotely by a smartphone have recently been spreading. With some typical existing systems, a user needs to identify a target device to control with only its less user-friendly ID. A system for association between actual position of the device and its position on smartphone display would allow the user to identify it easily. We call such a system "Smart Interaction System". One of the key technologies for Smart Interaction System is localization of the device. Localization technique using some anchors with the given position to measure received signal strength indication (RSSI) of a device have been developed. They incur user burden to deploy the anchors and measure their positions. Thus alleviating the burden is still a technical challenge. As a solution to the challenge, this paper proposes a new 3D localization technique with a mobile robot including a floor cleaning robot. The mobile robot would reduce the burden by measuring RSSI while cleaning floor instead of the anchors. The proposed localization technique has been implemented with a floor cleaning robot. Experimental results show that the proposed localization technique provides the position of the device with approximately 1000mm of estimation error and is useful for Smart Interaction System