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1. Mimicking Complexity of Structured Data Matrix’s Information Content: Categorical Exploratory Data Analysis

   https://doi.org/10.3390/e23050594  

   Hsieh, Fushing; Chou, Elizabeth P.; Chen, Ting-Li (May 2021, Entropy)

   null (Ed.)

   We develop Categorical Exploratory Data Analysis (CEDA) with mimicking to explore and exhibit the complexity of information content that is contained within any data matrix: categorical, discrete, or continuous. Such complexity is shown through visible and explainable serial multiscale structural dependency with heterogeneity. CEDA is developed upon all features’ categorical nature via histogram and it is guided by all features’ associative patterns (order-2 dependence) in a mutual conditional entropy matrix. Higher-order structural dependency of k(≥3) features is exhibited through block patterns within heatmaps that are constructed by permuting contingency-kD-lattices of counts. By growing k, the resultant heatmap series contains global and large scales of structural dependency that constitute the data matrix’s information content. When involving continuous features, the principal component analysis (PCA) extracts fine-scale information content from each block in the final heatmap. Our mimicking protocol coherently simulates this heatmap series by preserving global-to-fine scales structural dependency. Upon every step of mimicking process, each accepted simulated heatmap is subject to constraints with respect to all of the reliable observed categorical patterns. For reliability and robustness in sciences, CEDA with mimicking enhances data visualization by revealing deterministic and stochastic structures within each scale-specific structural dependency. For inferences in Machine Learning (ML) and Statistics, it clarifies, upon which scales, which covariate feature-groups have major-vs.-minor predictive powers on response features. For the social justice of Artificial Intelligence (AI) products, it checks whether a data matrix incompletely prescribes the targeted system. 

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2. Topological data analysis of zebrafish patterns

   https://doi.org/10.1073/pnas.1917763117  

   McGuirl, Melissa R.; Volkening, Alexandria; Sandstede, Björn (March 2020, Proceedings of the National Academy of Sciences)

   Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior capture only macroscopic features or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agent-level features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides an approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale. 

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3. Diffusiophoresis-enhanced Turing patterns

   https://doi.org/10.1126/sciadv.adj2457  

   Alessio, Benjamin M.; Gupta, Ankur (November 2023, Science Advances)

   Turing patterns are fundamental in biophysics, emerging from short-range activation and long-range inhibition processes. However, their paradigm is based on diffusive transport processes that yield patterns with shallower gradients than those observed in nature. A complete physical description of this discrepancy remains unknown. We propose a solution to this phenomenon by investigating the role of diffusiophoresis, which is the propulsion of colloids by a chemical gradient, in Turing patterns. Diffusiophoresis enables robust patterning of colloidal particles with substantially finer length scales than the accompanying chemical Turing patterns. A scaling analysis and a comparison to recent experiments indicate that chromatophores, ubiquitous in biological pattern formation, are likely diffusiophoretic and the colloidal Péclet number controls the pattern enhancement. This discovery suggests that important features of biological pattern formation can be explained with a universal mechanism that is quantified straightforwardly from the fundamental physics of colloids. 

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4. Investigating Fire–Atmosphere Interaction in a Forest Canopy Using Wavelets

   https://doi.org/10.1007/s10546-024-00862-0  

   Desai, Ajinkya; Guilloteau, Clément; Heilman, Warren E; Charney, Joseph J; Skowronski, Nicholas S; Clark, Kenneth L; Gallagher, Michael R; Foufoula-Georgiou, Efi; Banerjee, Tirtha (May 2024, Boundary-Layer Meteorology)

   Abstract Wildland fire–atmosphere interaction generates complex turbulence patterns, organized across multiple scales, which inform fire-spread behaviour, firebrand transport, and smoke dispersion. Here, we utilize wavelet-based techniques to explore the characteristic temporal scales associated with coherent patterns in the measured temperature and the turbulent fluxes during a prescribed wind-driven (heading) surface fire beneath a forest canopy. We use temperature and velocity measurements from tower-mounted sonic anemometers at multiple heights. Patterns in the wavelet-based energy density of the measured temperature plotted on a time–frequency plane indicate the presence of fire-modulated ramp–cliff structures in the low-to-mid-frequency band (0.01–0.33 Hz), with mean ramp durations approximately 20% shorter and ramp slopes that are an order of magnitude higher compared to no-fire conditions. We then investigate heat- and momentum-flux events near the canopy top through a cross-wavelet coherence analysis. Briefly before the fire-front arrives at the tower base, momentum-flux events are relatively suppressed and turbulent fluxes are chiefly thermally-driven near the canopy top, owing to the tilting of the flame in the direction of the wind. Fire-induced heat-flux events comprising warm updrafts and cool downdrafts are coherent down to periods of a second, whereas ambient heat-flux events operate mainly at higher periods (above 17 s). Later, when the strongest temperature fluctuations are recorded near the surface, fire-induced heat-flux events occur intermittently at shorter scales and cool sweeps start being seen for periods ranging from 8 to 35 s near the canopy top, suggesting a diminishing influence of the flame and increasing background atmospheric variability thereat. The improved understanding of the characteristic time scales associated with fire-induced turbulence features, as the fire-front evolves, will help develop more reliable fire behaviour and scalar transport models. 

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5. Understanding the impact of temporal scale on human movement analytics

   https://doi.org/10.1007/s10109-021-00370-6  

   Su, Rongxiang; Dodge, Somayeh; Goulias, Konstadinos G. (January 2022, Journal of Geographical Systems)

   Movement is manifested through a series of patterns at multiple spatial and temporal scales. Movement data today are becoming available at increasingly fine-grained temporal granularity. These observations often represent multiple behavioral modes and complex patterns along the movement path. However, the relationships between the observation scale of movement data and the analysis scales at which movement patterns are captured remain understudied. This article aims at investigating the role of temporal scale in movement data analytics. It takes up an important question of “how do decisions surrounding the scale of movement data and analyses impact our inferences about movement patterns?” Through a set of computational experiments in the context of human movement, we take a systematic look at the impact of varying temporal scales on common movement analytics techniques including trajectory analytics to calculate movement parameters (e.g., speed, path tortuosity), estimation of individual space usage, and interactions analysis to detect potential contacts between multiple mobile individuals. 

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