Anomalous Behavior of the Zero Field Susceptibility of the Ising Model on the Cayley Tree

It is found that the zero field susceptibility chi of the Ising model on the Cayley tree exhibits unusually weak divergence at the critical point Tc. The susceptibility amplitude is found to diverge at Tc proportionally to the tree generation level n, while the behavior of chi is otherwise analytic in the vicinity of Tc, with the critical exponent gamma=0.Comment: 3 pages, 2 figure

Analysis of Daily Streamflow Complexity by Kolmogorov Measures and Lyapunov Exponent

Analysis of daily streamflow variability in space and time is important for water resources planning, development, and management. The natural variability of streamflow is being complicated by anthropogenic influences and climate change, which may introduce additional complexity into the phenomenological records. To address this question for daily discharge data recorded during the period 1989-2016 at twelve gauging stations on Brazos River in Texas (USA), we use a set of novel quantitative tools: Kolmogorov complexity (KC) with its derivative associated measures to assess complexity, and Lyapunov time (LT) to assess predictability. We find that all daily discharge series exhibit long memory with an increasing downflow tendency, while the randomness of the series at individual sites cannot be definitively concluded. All Kolmogorov complexity measures have relatively small values with the exception of the USGS (United States Geological Survey) 08088610 station at Graford, Texas, which exhibits the highest values of these complexity measures. This finding may be attributed to the elevated effect of human activities at Graford, and proportionally lesser effect at other stations. In addition, complexity tends to decrease downflow, meaning that larger catchments are generally less influenced by anthropogenic activity. The correction on randomness of Lyapunov time (quantifying predictability) is found to be inversely proportional to the Kolmogorov complexity, which strengthens our conclusion regarding the effect of anthropogenic activities, considering that KC and LT are distinct measures, based on rather different techniques

Three-dimensional multifractal analysis of trabecular bone under clinical computed tomography

Purpose: An adequate understanding of bone structural properties is critical for predicting fragility conditions caused by diseases such as osteoporosis, and in gauging the success of fracture prevention treatments. In this work we aim to develop multiresolution image analysis techniques to extrapolate high-resolution images predictive power to images taken in clinical conditions. Methods: We performed multifractal analysis (MFA) on a set of 17 ex vivo human vertebrae clinical CT scans. The vertebræ failure loads (FFailure) were experimentally measured. We combined bone mineral density (BMD) with different multifractal dimensions, and BMD with multiresolution statistics (e.g., skewness, kurtosis) of MFA curves, to obtain linear models to predict FFailure. Furthermore we obtained short- and long-term precisions from simulated in vivo scans, using a clinical CT scanner. Ground-truth data - high-resolution images - were obtained with a High-Resolution Peripheral Quantitative Computed Tomography (HRpQCT) scanner. Results: At the same level of detail, BMD combined with traditional multifractal descriptors (Lipschitz-Hölder exponents), and BMD with monofractal features showed similar prediction powers in predicting FFailure (87%, adj. R2). However, at different levels of details, the prediction power of BMD with multifractal features raises to 92% (adj. R2) of FFailure. Our main finding is that a simpler but slightly less accurate model, combining BMD and the skewness of the resulting multifractal curves, predicts 90% (adj. R2) of FFailure. Conclusions: Compared to monofractal and standard bone measures, multifractal analysis captured key insights in the conditions leading to FFailure. Instead of raw multifractal descriptors, the statistics of multifractal curves can be used in several other contexts, facilitating further research.Fil: Baravalle, Rodrigo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Thomsen, Felix Sebastian Leo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; ArgentinaFil: Delrieux, Claudio Augusto. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lu, Yongtao. Dalian University of Technology; ChinaFil: Gómez, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Stošić, Borko. Universidade Federal Rural Pernambuco; BrasilFil: Stošić, Tatijana. Universidade Federal Rural Pernambuco; Brasi

Rainfall dynamics in an ecologically vulnerable area using applied algebraic topology methods

Applied algebraic topology is employed in this work to shed new light on the rainfall dynamics in the Pernambuco state, Brazil. Historical data from the NASA's Tropical Rainfall Measuring Mission (TRMM) precipitation processing system, for the period 1998 to 2020 with a spatial resolution of 0.25° and temporal resolution of 3 h is used to construct correlation matrices in different time frames. Matrices are then analyzed in terms of topological constructs of network theory to yield novel insights into this highly complex phenomenon in this semiarid, ecologically vulnerable area. The outcomes of the algebraic topological analysis reveal clustering patterns of areas and are related to natural climate phenomena. Together with the generality of the applied methodology, the results suggest a broad scope of future applications for the extraction of patterns in datasets related to the changes in the climate system

Automated Traffic and the Finite Size Resonance

We investigate in detail what one might call the canonical (automated) traffic problem: A long string of N+1 cars (numbered from 0 to N) moves along a one-lane road “in formation” at a constant velocity and with a unit distance between successive cars. Each car monitors the relative velocity and position of only its neighboring cars. This information is then fed back to its own engine which decelerates (brakes) or accelerates according to the information it receives. The question is: What happens when due to an external influence—a traffic light turning green—the ‘zero’th’ car (the “leader”) accelerates? As a first approximation, we analyze linear(ized) equations and show that in this scenario the traffic flow has a tendency to be stop-and-go. We give approximate solutions for the global traffic as function of all the relevant parameters (the feed back parameters as well as cruise velocity and so on). We discuss general design principles for these algorithms, that is: how does the choice of parameters influence the performance

The Choice of an Appropriate Information Dissimilarity Measure for Hierarchical Clustering of River Streamflow Time Series, Based on Calculated Lyapunov Exponent and Kolmogorov Measures

The purpose of this paper was to choose an appropriate information dissimilarity measure for hierarchical clustering of daily streamflow discharge data, from twelve gauging stations on the Brazos River in Texas (USA), for the period 1989⁻2016. For that purpose, we selected and compared the average-linkage clustering hierarchical algorithm based on the compression-based dissimilarity measure (NCD), permutation distribution dissimilarity measure (PDDM), and Kolmogorov distance (KD). The algorithm was also compared with K-means clustering based on Kolmogorov complexity (KC), the highest value of Kolmogorov complexity spectrum (KCM), and the largest Lyapunov exponent (LLE). Using a dissimilarity matrix based on NCD, PDDM, and KD for daily streamflow, the agglomerative average-linkage hierarchical algorithm was applied. The key findings of this study are that: (i) The KD clustering algorithm is the most suitable among others; (ii) ANOVA analysis shows that there exist highly significant differences between mean values of four clusters, confirming that the choice of the number of clusters was suitably done; and (iii) from the clustering we found that the predictability of streamflow data of the Brazos River given by the Lyapunov time (LT), corrected for randomness by Kolmogorov time (KT) in days, lies in the interval from two to five days

Periodic series of otolith contour fluctuations.

<p>(A) Schematic representation of the superposition of the standard circular shape on an otolith of <i>M. merlucius</i>. The otolith radius was used to define the periodic series of the otolith contour fluctuations, derived from the normalized radius of the contour at the angle for (B) <i>M. curema</i> and (C) <i>M. merlucius</i>, obtained from the image catalog of the project AFORO.</p