Linear regression model for metal–organic frameworks with CO2 adsorption based on topological data analysis

BackgroundAttention-deficit/hyperactivity disorder (ADHD) is currently diagnosed by a diagnostic interview, mainly based on subjective reports from parents or teachers. It is necessary to develop methods that rely on objectively measureable neurobiological data to assess brain-behavior relationship in patients with ADHD. We investigated the application of a topological data analysis tool, Mapper, to analyze the brain functional connectivity data from ADHD patients.MethodsTo quantify the disease severity using the neuroimaging data, the decomposition of individual functional networks into normal and disease components by the healthy state model (HSM) was performed, and the magnitude of the disease component (MDC) was computed. Topological data analysis using Mapper was performed to distinguish children with ADHD (n = 196) from typically developing controls (TDC) (n = 214).ResultsIn the topological data analysis, the partial clustering results of patients with ADHD and normal subjects were shown in a chain-like graph. In the correlation analysis, the MDC showed a significant increase with lower intelligence scores in TDC. We also found that the rates of comorbidity in ADHD significantly increased when the deviation of the functional connectivity from HSM was large. In addition, a significant correlation between ADHD symptom severity and MDC was found in part of the dataset.ConclusionsThe application of HSM and topological data analysis methods in assessing the brain functional connectivity seem to be promising tools to quantify ADHD symptom severity and to reveal the hidden relationship between clinical phenotypic variables and brain connectivity.

In this paper we develop an alternative topological data analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale representation of the graph that can distinguish between dynamic states such as periodic and chaotic behavior. We show the approach for two graph constructions obtained from the time series. In the first approach the time series is embedded into a point cloud which is then used to construct an undirected k-nearest-neighbor graph. The second construct relies on the recently developed ordinal partition framework. In either case, a pairwise distance matrix is then calculated using the shortest path between the graph's nodes, and this matrix is utilized to define a filtration of a simplicial complex that enables tracking the changes in homology classes over the course of the filtration. These changes are summarized in a persistence diagram's two-dimensional summary of changes in the topological features. We then extract existing as well as new geometric and entropy point summaries from the persistence diagram and compare to other commonly used network characteristics. Our results show that persistence-based point summaries yield a clearer distinction of the dynamic behavior and are more robust to noise than existing graph-based scores, especially when combined with ordinal graphs.

Detecting structural changes in time-series data is crucial in many applications. However, the changes in the data may appear as global structural changes that cannot be detected by conventional methods. In recent years, Topological Data Analysis (TDA) has been used to detect such global structural changes. In TDA, information on connected components or holes of data is encoded into a two-dimensional plot called a persistence diagram (PD), which can be used to detect global changes in time-series. However, only a few studies on TDA conducted change detection assuming probabilistic structure on PDs. In this paper, we introduce probability structures into PD, with which we conduct change detection on the basis of the minimum description length principle. We propose the following two methods: (1) A parametric method: We employ the Gaussian mixture model for PD modeling and then detect global changes by tracking the changes in the optimal number of mixture components. (2) A non-parametric method: We employ kernel densities for PD modeling and then detect changes by tracking changes in their global complexity. These methods not only improve the detection accuracy of global structural changes but also provide the explainability of global changes. We showcase the effectiveness of the proposed methods using synthetic data and real-world financial time-series data.

Topological data analysis is an approach to study the shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions. Multiple data sets can be compared by the similarity of their diagrams to understand their behaviors relative to each other. The bottleneck and Wasserstein distances are often used as a tool to indicate the similarity. In this paper, we introduce the cosine similarity as a new indicator for the similarity between persistence diagrams and investigate its properties. Furthermore, it leads to the new notion of orthogonality between persistence diagrams. It turns out that the orthogonality refers to perfect dissimilarity between persistence diagrams under the cosine similarity. Through data demonstration, the cosine similarity is shown to be more accurate than the standard distances to measure the similarity between persistence diagrams.

Diagnosing neuropsychiatric systemic lupus erythematosus (NPSLE) and differentiating it from systemic lupus erythematosus (SLE) without neuropsychiatric manifestations remains a substantial clinical challenge due to the absence of specific biomarkers. Topological data analysis (TDA) is a novel computational technique that enables the visualization, exploration, and analysis of complex data structures. This study aimed to identify distinct neuroimaging biomarkers in patients with NPSLE (NPSLE group) and differentiate them from patients with SLE without neuropsychiatric symptoms (non-NPSLE group) by employing TDA. We conducted a retrospective cohort study involving 30 patients with NPSLE and 30 without neuropsychiatric symptoms between 2005 and 2020. TDA was utilized to extract topological features, specifically connected components and holes, from fluid-attenuated inversion recovery (FLAIR) sequences obtained via brain magnetic resonance imaging (MRI). Summary statistics, including critical point count, persistence lifetime, centroid coordinates, perimeter, area, and filamentarity, were derived from persistence diagrams. Multiple logistic regression analyses, adjusted for age, cerebrovascular comorbidities, and 50% hemolytic unit of complement levels, demonstrated a significant association between NPSLE and the perimeter of the holes (odds ratio [OR]: 1.67, 95% confidence interval [CI]: 1.07-2.63, p = 0.025) and the area of the holes (OR: 4.42, 95% CI: 1.35-19.6, p = 0.026) of the identified topological features. Additionally, both areas under the receiver operating characteristic curve (AUC) exceeded 0.8, indicating good diagnostic accuracy. This study identified novel neuroimaging biomarkers for the diagnosis of NPSLE. The application of TDA to brain MRI features in patients with SLE proved to be a valuable diagnostic tool, particularly through the analysis of persistence diagrams.

Metal-organic framework thin films with diverse redox-active/inactive components for enhanced optical modulation and coloration efficiency

We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback-Leibler divergence, which is commonly used for comparing text and images, and the Itakura-Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized Cech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized Cech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory.

Continuation of point clouds via persistence diagrams

The synthesis and characterization of PTCDA-Co(II), and PTCDA-La(III) fluorescent MOFs

The Vietoris–Rips filtration is a versatile tool in topological data analysis. It is a sequence of simplicial complexes built on a metric space to add topological structure to an otherwise disconnected set of points. It is widely used because it encodes useful information about the topology of the underlying metric space. This information is of-ten extracted from its so-called persistence diagram. Unfortunately, this filtration is often too large to construct in full. We show how to construct an O(n)-size filtered simplicial complex on an n-point metric space such that its persistence diagram is a good approximation to that of the Vietoris–Rips filtration. This new filtration can be constructed in O(n log n) time. The constant factors in both the size and the run-ning time depend only on the doubling dimension of the metric space and the desired tightness of the approximation. For the first time, this makes it computationally tractable to approximate the persistence di-agram of the Vietoris–Rips filtration across all scales for large data sets. We describe two different sparse filtrations. The first is a zigzag filtration that removes points as the scale increases. The second is a (non-zigzag) filtration that yields the same persistence diagram. Both methods are based on a hierarchical net-tree and yield the same guar-antees.

Introduction. Metal-Organic frameworks (MOFs), which have a high surface area, flexibility, and designability, are highly porous materials formed from a combination with metal ion and organic ligand. Therefore, MOFs are widely studied and expected to apply them to gas storages, separations, and catalysts [1]. Moreover, MOFs are expected as not only bulk materials but also composite materials, such as electronic and photo devices, by constructing MOF thin films on various solid substrates. Layer-by-layer (LbL) fashion can control a growth orientation, thickness, and morphology without losing bulk phase properties on oxide substrates, semiconductors, and self-assembled monolayers (SAMs) on metals [1-3]. However, their structures were not completely matched to those of their bulk. For understanding the growth mechanism of MOFs films to construct the same structures of their bulk, in this study, we have examined the structure of [Cu2(bdc)2dabco]n [4]; (bdc = 1,4-benzdicarboxylate, dabco = 1,4-diaza bicyclo[2.2.2]octane) thin films on a single-crystal Au(100) surface, which was modified by 4-mercaptobenzoic acid (4-MBA) SAMs. In order to investigate the preparation process of this MOF thin films, polarization modulation – fourier transform infrared reflectance absorption spectroscopy (PM-FTIR-RAS), x-ray photoelectron spectroscopy (XPS), and x-ray absorption fine structure (XAFS) [5], were performed. Experimentals. The Au(100) substrates were pre-treated via annealing/quenching to clean those surface. For [Cu2(bdc)2dabco]n thin films on Au(100) ([Cu2(bdc)2dabco]n / 4-MBA / Au(100) ), pre-treated Au(100) was initially immersed in an ethanol solution containing 1 mM 4-MBA for 10 min. The substrate was then alternatively immersed in the ethanol solutions containing 1 mM Cu(CH3COO)2 for 30 min, 0.1 mM bdc for 1 h, and 0.1 mM dabco for 1 h at room temperature to fabricate thin films. After every immersion, the sample substrates were thoroughly rinsed with ethanol and dried in a stream of N2 gas. The structures of the samples at each step were investigated by PM-FTIR-RAS, XPS and XAFS. Results and Discussion. The XP spectra in the Cu2p 2/3 region showed the construction of [Cu2(bdc)2dabco]n on the Au(100) substrate modified by the 4-MBA SAM successively by LbL fashion immersed in each solution. The PM-FTIR-RA spectra showed more details for initial formation process of [Cu2(bdc)2dabco]n thin films on Au(100) modified by the 4-MBA SAM. The peak of C=O stretching vibration of terminal carboxyl group of the 4-MBA SAM for 4-MBA SAM / Au(100) was observed at 1724 cm-1, indicating the presence of a monomer hydrogen bonding of a couple of the carboxyl group. After immersion of 4-MBA SAM / Au(100) into 1 mM Cu(CH3COO)2, this peak observed at 1724 cm-1 for [Cu(CH3COO)2] / 4-MBA SAM / Au(100) was disappeared. Instead of this peak, another peak was observed at 1763 cm-1, indicating the disappearance of a hydrogen bond. Therefore, carboxyl-terminals for the 4-MBA SAM were partially coordinated to Cu(CH3COO)2. After immersion into 0.1 mM bdc, in addition of the coordination of the bdc molecules as a bridging legand, the peak due to C=O stretching vibration for [Cu(bdc)2]n / 4-MBA SAM / Au(100) was observed at 1698 cm-1. This result shows the presence of a dimer hydrogen bonding. After immersion into 0.1 mM dabco, the peak intensity of COO stretching vibration of a carboxylate group for [Cu2(bdc)2dabco]n / 4-MBA SAM / Au(100) decreased, as compared to that for [Cu(bdc)2]n / 4-MBA SAM / Au(100), suggesting that the direction of COO stretching vibration became parallel to the substrate surface. References. [1] D. Zacher et al., Chem. Soc. Rev., 38, 1418-1429 (2009). [2] O. Shekhah et al., J. Am. Chem. Soc., 129, 15118-15119 (2007). [3] H. Gliemann et al., Materials Today, 15, 110-116 (2012). [4] K. Seki et al., Chem Lett., 30, 332 (2001). [5] W.-J. Chun et al., J. Phys. Chem. B, 102, 9006-9014 (1998).

This application paper presents a comprehensive experimental eval-uation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the max-ima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypothe-ses by two comparison measures: (i) a standard distance used in scientific imaging (the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{2}$</tex> norm) and (ii) an established topological distance between persistence diagrams (the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{2}$</tex> -Wasserstein metric). Extensive experiments on the input ensemble demonstrate the supe-riority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.

We propose to use Topological Data Analysis (TDA) to characterize the morphological development of brain organoids. We combine TDA with clustering strategies to characterize the morphology of three developmental stages of segmented brain organoid images. We calculate a linear regression of the H1 feature diagrams as well as entropy, dispersion, and average persistence of H0 and H1 features separately for each developmental stage. We also compute pairwise average Wasserstein distances between features, and within and inter clusters for each developmental stage. To explore all feature vectors from each group, we calculate K-L divergence on the t-SNE reduction of the TDA results.Early stages are characterized by a persistence diagram with a low slope and intercept, a high entropy within features, and a high Wasserstein distance between clusters near and far from the origin. The opposite is true for later stages. K-L divergences are particularly high between mid-stages and early or late stages, and punctually between some clusters. Results highlight specific morphological patterns at 14 days, corresponding to neuroepithelial formations.KeywordsBrain organoidCharacterisationTDA-clustering

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis. In these applications, the online detection of changes is of crucial importance, but this can be highly challenging since such changes often occur in low-dimensional embeddings within high-dimensional data streams. We thus propose a new method, called PERsistence diagram-based ChangE-PoinT detection (PERCEPT), which leverages the learned topological structure from TDA to sequentially detect changes. PERCEPT follows two key steps: it first learns the embedded topology as a point cloud via persistence diagrams, then applies a nonparametric monitoring approach for detecting changes in the resulting point cloud distributions. This yields a nonparametric, topology-aware framework which can efficiently detect online geometric changes. We investigate the effectiveness of PERCEPT over existing methods in a suite of numerical experiments where the data streams have an embedded topological structure. We then demonstrate the usefulness of PERCEPT in two applications on solar flare monitoring and human gesture detection.

Background: Anthropogenic carbon dioxide (CO₂) emissions have risen significantly due to the extensive use of fossil fuels, necessitating the development of effective CO₂ capture and conversion techniques. Adsorption using Metal-Organic Frameworks (MOFs) has shown great potential due to their high CO₂ adsorption capacity, particularly Ni-based MOFs. Enhancing their adsorption efficiency remains a key research focus to improve sustainability in CO₂ capture applications. Methods: Ni-based MOF (Ni-DOBDC) was synthesized using the solvothermal method, employing DMF as the solvent and 2,5-dihydroxyterephthalic acid (DOBDC) as the organic ligand. To enhance CO₂ adsorption capacity, Ni-DOBDC was further modified with ethylenediamine (EDA) via post-synthetic modification. Structural characterization was performed using XRD, confirming similarity to the Ni-DOBDC reference (CCDC 288477), and FTIR, which showed enhanced absorbance peaks. SEM-EDX analysis revealed a flower-like morphology with an average particle size of 0.75 μm. CO₂ adsorption tests were conducted on Ni-DOBDC and EDA/Ni-DOBDC (10%) using the titration method under controlled conditions. Findings: The CO₂ adsorption capacity of Ni-DOBDC and EDA/Ni-DOBDC was tested at 70°C with a CO₂ concentration of 50% in N₂. EDA modification significantly improved CO₂ adsorption capacity, with EDA/Ni-DOBDC achieving 9.95 mmol g⁻¹ compared to pristine Ni-DOBDC’s 6.44 mmol g⁻¹. However, Ni-DOBDC exhibited better regeneration ability in a three-cycle reusability test, likely due to EDA leaching during regeneration. Conclusion: EDA-modified Ni-DOBDC demonstrates enhanced CO₂ adsorption capacity, making it a promising material for CO₂ capture applications. However, its reduced regeneration stability suggests the need for further optimization to improve long-term performance. Future studies should explore strategies to minimize EDA leaching while maintaining high adsorption efficiency. Novelty/Originality of this article: This study provides new insights into improving Ni-based MOF performance for CO₂ capture through post-synthetic modification with EDA. The findings highlight a trade-off between increased adsorption capacity and material stability, emphasizing the need for further refinement in MOF functionalization strategies.