Exact multi-parameter persistent homology of time-series data: one-dimensional reduction of multi-parameter persistence theory

In various applications of data classification and clustering problems, multi-parameter analysis is effective and crucial because data are usually defined in multi-parametric space. Multi-parameter persistent homology, an extension of persistent homology of one-parameter data analysis, has been developed for topological data analysis (TDA). Although it is conceptually attractive, multi-parameter persistent homology still has challenges in theory and practical applications. In this study, we consider time-series data and its classification and clustering problems using multi-parameter persistent homology. We develop a multi-parameter filtration method based on Fourier decomposition and provide an exact formula and its interpretation of one-dimensional reduction of multi-parameter persistent homology. The exact formula implies that the one-dimensional reduction of multi-parameter persistent homology of the given time-series data is equivalent to choosing diagonal ray (standard ray) in the multi-parameter filtration space. For this, we first consider the continuousization of time-series data based on Fourier decomposition towards the construction of the exact persistent barcode formula for the Vietoris-Rips complex of the point cloud generated by sliding window embedding. The proposed method is highly efficient even if the sliding window embedding dimension and the length of time-series data are large because the method precomputes the exact barcode and the computational complexity is as low as the fast Fourier transformation of $O(N \log N)$. Further the proposed method provides a way of finding different topological inferences by trying different rays in the filtration space in no time.Comment: 29 page

Supervised low-rank semi-nonnegative matrix factorization with frequency regularization for forecasting spatio-temporal data

We propose a novel methodology for forecasting spatio-temporal data using supervised semi-nonnegative matrix factorization (SSNMF) with frequency regularization. Matrix factorization is employed to decompose spatio-temporal data into spatial and temporal components. To improve clarity in the temporal patterns, we introduce a nonnegativity constraint on the time domain along with regularization in the frequency domain. Specifically, regularization in the frequency domain involves selecting features in the frequency space, making an interpretation in the frequency domain more convenient. We propose two methods in the frequency domain: soft and hard regularizations, and provide convergence guarantees to first-order stationary points of the corresponding constrained optimization problem. While our primary motivation stems from geophysical data analysis based on GRACE (Gravity Recovery and Climate Experiment) data, our methodology has the potential for wider application. Consequently, when applying our methodology to GRACE data, we find that the results with the proposed methodology are comparable to previous research in the field of geophysical sciences but offer clearer interpretability.Comment: 34 page

Fault Log Recovery Using an Incomplete-data-trained FDA Classifier for Failure Diagnosis of Engineered Systems

In the 2015 PHM Data Challenge Competition, the goal of the competition problem was to diagnose failure of industrial plant systems using incomplete data. The available data consisted of sensor measurements, control reference signals, and fault logs. A detailed description of the plant system of interest was not revealed, and partial fault logs were eliminated from the dataset. This paper presents a fault log recovery method using a machine-learning-based fault classification approach for failure diagnosis. For optimal performance, it was critical to be able to utilize a set of incomplete data and to select relevant features. First, physical interpretation of the given data was performed to select proper features for a fault classifier. Second, Fisher discriminant analysis (FDA) was employed to minimize the effect of outliers in the incomplete data sets. Finally, the type of the missing fault logs and the duration of the corresponding faults were recovered. The proposed approach, based on the use of an incomplete-data-trained FDA classifier, led to the second-highest score in the 2015 PHM Data Challenge Competition

Topological domain walls and quantum valley Hall effects in silicene

Silicene is a two-dimensional honeycomb lattice made of silicon atoms, which is considered to be a new Dirac fermion system. Based on first-principles calculations, we examine the possibility of the formation of solitonlike topological domain walls (DWs) in silicene. We show that the DWs between regions of distinct ground states of the buckled geometry should bind electrons when a uniform electric field is applied in the perpendicular direction to the sheet. The topological origin of the electron confinement is demonstrated based on numerical calculations of the valley-specific Hall conductivities, and possible experimental signatures of the quantum valley Hall effects are discussed using simulated scanning tunneling microscopy images. Our results strongly suggest that silicene could be an ideal host for the quantum valley Hall effect, thus providing a pathway to the valleytronics in silicon-based technology.close12

Exact Multi-parameter Persistent Homology of Time-series Data: One-dimensional Reduction of Multi-parameter Persistence Theory

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A Noise-Robust Feature Extraction Method for Rolling Element Bearing Diagnosis: Linear Power-Normalized Cepstral Coefficients (LPNCC)

One of the most critical challenges in rolling bearing diagnosis is dealing with weak fault signals that are buried in noises arising from environmental effects. To overcome this problem, the research described in this paper aims to develop a noise-robust feature extraction method, namely linear power-normalized cepstral coefficients (LPNCC), inspired by speech recognition based on auditory physiology. In this approach, for the cepstra from a feature extraction process, the squared envelope spectra are computed to find bearing characteristic frequencies. The performance of the proposed method is examined by studying simulation data in the presence of various levels of Gaussian background noises and through study of two experimental cases from the Case Western University dataset in the presence of impulsive noise and with a low signal-to-noise ratio (SNR), respectively. It can be concluded from the results that the proposed method has the potential to be utilized for robust bearing diagnosis in various noisy environments.N

Progress on first-principles-based materials design for hydrogen storage

This article briefly summarizes the research activities in the field of hydrogen storage in sorbent materials and reports our recent works and future directions for the design of such materials. Distinct features of sorption-based hydrogen storage methods are described compared with metal hydrides and complex chemical hydrides. We classify the studies of hydrogen sorbent materials in terms of two key technical issues: (i) constructing stable framework structures with high porosity, and (ii) increasing the binding affinity of hydrogen molecules to surfaces beyond the usual van der Waals interaction. The recent development of reticular chemistry is summarized as a means for addressing the first issue. Theoretical studies focus mainly on the second issue and can be grouped into three classes according to the underlying interaction mechanism: electrostatic interactions based on alkaline cations, Kubas interactions with open transition metals, and orbital interactions involving Ca and other nontransitional metals. Hierarchical computational methods to enable the theoretical predictions are explained, from ab initio studies to molecular dynamics simulations using force field parameters. We also discuss the actual delivery amount of stored hydrogen, which depends on the charging and discharging conditions. The usefulness and practical significance of the hydrogen spillover mechanism in increasing the storage capacity are presented as well.close14

Efficient, stable solar cells by using inherent bandgap of alpha-phase formamidinium lead iodide

In general, mixed cations and anions containing formamidinium (FA), methylammonium (MA), caesium, iodine, and bromine ions are used to stabilize the black alpha-phase of the FA-based lead triiodide (FAPbI(3)) in perovskite solar cells. However, additives such as MA, caesium, and bromine widen its bandgap and reduce the thermal stability. We stabilized the alpha-FAPbI(3) phase by doping with methylenediammonium dichloride (MDACl(2)) and achieved a certified short-circuit current density of between 26.1 and 26.7 milliamperes per square centimeter. With certified power conversion efficiencies (PCEs) of 23.7%, more than 90% of the initial efficiency was maintained after 600 hours of operation with maximum power point tracking under full sunlight illumination in ambient conditions including ultraviolet light. Unencapsulated devices retained more than 90% of their initial PCE even after annealing for 20 hours at 150 degrees C in air and exhibited superior thermal and humidity stability over a control device in which FAPbI(3) was stabilized by MAPbBr(3)

Controlling the Structural Robustness of Zirconium-Based Metal Organic Frameworks for Efficient Adsorption on Tetracycline Antibiotics

Tetracyclines (TCs) are the most widely used antibiotics for the prevention and treatment of livestock diseases, but they are toxic to humans and have frequently been detected in water bodies. In this study, the physical and chemical properties of the zirconium-based metal organic framework (MOF) UiO-66 and its NH2-functionalized congener UiO-66-NH2 were investigated along with batch TC adsorption tests to determine the effect of functionalization on TC removal. TC removal was highest at pH 3 and decreased with increasing pH. Pseudo-1st and pseudo-2nd-order kinetic models were used to study the adsorption equilibrium times, and Langmuir isotherm model was found to be more suitable than Freundlich model. The maximum uptake for UiO-66 and UIO-66-NH2 was measured to be 93.6 and 76.5 mg/g, respectively. Unexpectedly, the TC adsorption capacity of UiO-66-NH2 was observed to be lower than that of UiO-66. Density functional theory calculations revealed that the pore structures are irrelevant to TC adsorption, and that the -NH2 functional group could weaken the structural robustness of UiO-66-NH2, causing a reduction in TC adsorption capacity. Accordingly, robust MOFs with zirconium-based metal clusters can be effectively applied for the treatment of antibiotics such as TC in water