Approximating high-dimensional dynamics by barycentric coordinates with linear programming

Hirata, Yoshito; Shiro, Masanori; Takahashi, Nobuhiro; Aihara, Kazuyuki; Suzuki, Hideyuki; Más, Paloma Díaz

doi:10.1063/1.4906746

Cited by 8 publications

(8 citation statements)

References 51 publications

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“…The development of a tailor-designed mathematical model using barycentric coordinates for high-dimensional space confirmed this notion. The method has been proven successful for a wide range of uses, from weather forecasting to creation of musical instruments with natural sounds (Hirata et al, 2015). Our studies also revealed that the intercellular coupling or circadian communication among shoot apex clocks confer robustness against genetic mutations and pharmacological perturbations.…”

Section: Discussionmentioning

confidence: 71%

“…Our results indicate that intercellular communication might be important for rhythms at the shoot apex. To mathematically explore the degree of intercellular coupling, we developed a predictive model by using barycentric coordinates for high-dimensional space (Hirata et al, 2015). The model involves the use of linear programming that assigns different weights to neighboring cells and identifies the strength of coupling based on the accuracy of the predictions given the weights.…”

Section: Intercellular Circadian Coupling Among Clock Cells Of the Shoot Apexmentioning

confidence: 99%

“…Mathematical analysis was performed as described in Hirata et al (2015). See further details in the Supplemental Experimental Procedures.…”

Section: Mathematical Analysismentioning

confidence: 99%

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A Hierarchical Multi-oscillator Network Orchestrates the Arabidopsis Circadian System

Takahashi

Hirata

Aihara

et al. 2015

Cell

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156

173

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Short- and long-distance circadian communication is essential for integration of temporal information. However, a major challenge in plant biology is to decipher how individual clocks are interconnected to sustain rhythms in the whole plant. Here we show that the shoot apex is composed of an ensemble of coupled clocks that influence rhythms in roots. Live-imaging of single cells, desynchronization of dispersed protoplasts, and mathematical analysis using barycentric coordinates for high-dimensional space show a gradation in the strength of circadian communication in different tissues, with shoot apex clocks displaying the highest coupling. The increased synchrony confers robustness of morning and evening oscillations and particular capabilities for phase readjustments. Rhythms in roots are altered by shoot apex ablation and micrografting, suggesting that signals from the shoot apex are able to synchronize distal organs. Similarly to the mammalian suprachiasmatic nucleus, shoot apexes play a dominant role within the plant hierarchical circadian structure.

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Section: Discussionmentioning

confidence: 71%

Section: Intercellular Circadian Coupling Among Clock Cells Of the Shoot Apexmentioning

confidence: 99%

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A Hierarchical Multi-oscillator Network Orchestrates the Arabidopsis Circadian System

Takahashi

Hirata

Aihara

et al. 2015

Cell

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156

173

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“…We will use this method to identify the causal relation for oberved short time-series data or small samples, for which most of existing methods may fail due to insufficient information. This method is based on barycentric coordinates obtained by tessellation [ 21 ] which was extended to high-dimensional phase space that can model a high-dimensional time series [ 22 ]. We first make basic assumption for our method, i.e., the observed data of variables are from the same system or share a common attractor.…”

Section: Methodsmentioning

confidence: 99%

Detecting causality from short time-series data based on prediction of topologically equivalent attractors

Zhang

Shi

et al. 2017

BMC Syst Biol

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BackgroundDetecting causality for short time-series data such as gene regulation data is quite important but it is usually very difficult. This can be used in many fields especially in biological systems. Recently, several powerful methods have been set up to solve this problem. However, it usually needs very long time-series data or much more samples for the existing methods to detect causality among the given or observed data. In our real applications, such as for biological systems, the obtained data or samples are short or small. Since the data or samples are highly depended on experiment or limited resource.ResultsIn order to overcome these limitations, here we propose a new method called topologically equivalent position method which can detect causality for very short time-series data or small samples. This method is mainly based on attractor embedding theory in nonlinear dynamical systems. By comparing with inner composition alignment, we use theoretical models and real gene expression data to show the effectiveness of our method.ConclusionsAs a result, it shows our method can be effectively used in biological systems. We hope our method can be useful in many other fields in near future such as complex networks, ecological systems and so on.

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“…The corresponding weight w(t′) for ( ) t  in Equation 15 is optimized based on Hirata et al (2014):…”

Section: Proposed Algorithm To Forecast Unprecedented River Stagesmentioning

confidence: 99%

Practical Data‐Driven Flood Forecasting Based on Dynamical Systems Theory

Okuno

Ikeuchi²,

Aihara³

2021

Water Resources Research

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The severity of climatic natural disasters has been increasing over recent years, and repetitive flooding incidents have led to losses of numerous lives. In Japan, rapid flooding of small and steep rivers (flash floods) is an especially serious problem, and there are many rivers that may flood within several hours after heavy rainfall. For example, in the year 2016, Omoto River flooded in a few hours, leading to the loss of many lives (Nursing home operator failed to act on typhoon advisory before fatal flooding, 2016), and heavy rainfall in northern Kyushu in 2017 killed many people because of the resulting rapid floods in associated small rivers (Hazarika et al., 2020). Short-term rainfall intensity directly affects the river flow in such rivers, and the frequency of the rainfall exceeding 50 mm/h has increased by 1.4 times compared to 30 years ago in Japan (Japan Meteorological Agency, n.d.). Spurred by the flooding damage, the Japan administrative agencies launched a policy to increase inexpensive and maintenance-free water gauges for various rivers (Sato et al., 2019). Simultaneously, owing to the recent progress in "the Internet of Things," the water gauges are increasingly deployed by thousands every year, and we can monitor water levels via website (Ministry of Land, Infrastructure & Tourism, n.d.-a) in real time. Although these inexpensive water gauges have been widely used to monitor water levels in recent years, it is difficult to execute timely and properly evacuation actions using only information on the water level at a specific point in time; this is because water level increases tend to be rapid during flooding events.

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Approximating high-dimensional dynamics by barycentric coordinates with linear programming

Cited by 8 publications

References 51 publications

A Hierarchical Multi-oscillator Network Orchestrates the Arabidopsis Circadian System

A Hierarchical Multi-oscillator Network Orchestrates the Arabidopsis Circadian System

Detecting causality from short time-series data based on prediction of topologically equivalent attractors

Practical Data‐Driven Flood Forecasting Based on Dynamical Systems Theory

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