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We review a class of energy landscape analysis method that uses the Ising model and takes multivariate time series data as input. The method allows one to capture dynamics of the data as trajectories of a ball from one basin to a different basin to yet another, constrained on the energy landscape specified by the estimated Ising model. While this energy landscape analysis has mostly been applied to functional magnetic resonance imaging (fMRI) data from the brain for historical reasons, there are emerging applications outside fMRI data and neuroscience. To inform such applications in various research fields, this review paper provides a detailed tutorial on each step of the analysis, terminologies, concepts underlying the method, and validation, as well as recent developments of extended and related methods. 

Heavy metal cations such as Ag+, Pb2+, and Hg2+ can accumulate in living organisms, posing severe risks to biological systems, including humans. Therefore, removing heavy metal cations from wastewater is crucial before discharging them to the environment. However, trace levels and high-capacity removal of the heavy metals remain a critical challenge. This work demonstrates the synthesis and characterization of [Mo2S12]2− intercalated cobalt aluminum-layered double hydroxide, CoAl―Mo2S12―LDH (CoAl―Mo2S12), and its remarkable sorption properties for heavy metals. This material shows high efficiency for removing over 99.9% of Ag+, Cu2+, Hg2+, and Pb2+ from 10 ppm aqueous solutions with a distribution constant, Kd, as high as 107 mL/g. The selectivity order for removing these ions, determined from the mixed ion state experiment, was Pb2+ < Cu2+ ≪ Hg2+ < Ag+. This study also suggests that CoAl―Mo2S12 is not selective for Ni2+, Cd2+, and Zn2+ cations. CoAl―Mo2S12 is an efficient sorbent for Ag+, Cu2+, Hg2+, and Pb2+ ions at pH~12, with the removal performance of both Ag+ and Hg2+ cations retaining > 99.7% across the pH range of ~2 to 12. Our study also shows that the CoAl―Mo2S12 is a highly competent silver cation adsorbent exhibiting removal capacity (qm) as high as ~918 mg/g compared with the reported data. A detailed mechanistic analysis of the post-treated solid samples with Ag+, Hg2+, and Pb2+ reveals the formation of Ag2S, HgS, and PbMoO4, respectively, suggesting the precipitation reaction mechanism. 

Abstract Electroencephalogram (EEG) microstate analysis entails finding dynamics of quasi-stable and generally recurrent discrete states in multichannel EEG time series data and relating properties of the estimated state-transition dynamics to observables such as cognition and behavior. While microstate analysis has been widely employed to analyze EEG data, its use remains less prevalent in functional magnetic resonance imaging (fMRI) data, largely due to the slower timescale of such data. In the present study, we extend various data clustering methods used in EEG microstate analysis to resting-state fMRI data from healthy humans to extract their state-transition dynamics. We show that the quality of clustering is on par with that for various microstate analyses of EEG data. We then develop a method for examining test–retest reliability of the discrete-state transition dynamics between fMRI sessions and show that the within-participant test–retest reliability is higher than between-participant test–retest reliability for different indices of state-transition dynamics, different networks, and different data sets. This result suggests that state-transition dynamics analysis of fMRI data could discriminate between different individuals and is a promising tool for performing fingerprinting analysis of individuals. 

Water constitutes an indispensable resource for global life but remains susceptible to pollution from diverse human activities. To mitigate this issue, researchers are committed to purifying water using a variety...