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Kleidon A, Gozzi C, Buccianti A, Sauro Graziano R. Type of probability distribution reflects how close mixing dynamics in river chemistry are to thermodynamic equilibrium. THE SCIENCE OF THE TOTAL ENVIRONMENT 2024; 941:173409. [PMID: 38810755 DOI: 10.1016/j.scitotenv.2024.173409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Revised: 05/10/2024] [Accepted: 05/19/2024] [Indexed: 05/31/2024]
Abstract
The distribution of geochemical species are typically either (log)normally distributed or follow power laws. Here we link these types of distributions to the dynamics of the system that generates these distributions, showing that power laws can emerge in dissipative systems far from equilibrium while (log)normal distributions are found for species for which the concentrations are close to equilibrium. We use observations of the chemical composition of river water from the sampling space in central Italy as well as discharge data to test this interpretation. We estimate the dissipation rate that results when groundwater drains into the river and the dissolved chemical species mix with the river water. We show that calcium (Ca2+) and bicarbonate (HCO3-) concentrations are close to saturation along most of the downstream length of the Arno river, with decreasing dissipation rates and a lognormal distribution, while sodium (Na+) and chloride (Cl-) concentrations increase substantially downstream, show increased dissipation rates, and are power-law distributed. This supports our hypothesis that power law distributions appear to be indicative of dissipative systems far from thermodynamic equilibrium, while (log)normal distributions indicate weakly dissipative systems close to equilibrium. What this implies is that probability distributions are likely to be indicative of the thermodynamics of the system and the magnitude of disequilibrium constrains the range over which power-law scaling may be observed. This should help us to better identify the generalities and mechanisms that result in these common types of distributions and to better classify variability in systems according to how dissipative these are.
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Affiliation(s)
- Axel Kleidon
- Max Planck Institute for Biogeochemistry, Jena, Germany
| | - Caterina Gozzi
- University of Florence, Department of Earth Sciences, Firenze, Italy.
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Livi L, Sadeghian A, Di Ieva A. Fractal Geometry Meets Computational Intelligence: Future Perspectives. ADVANCES IN NEUROBIOLOGY 2024; 36:983-997. [PMID: 38468072 DOI: 10.1007/978-3-031-47606-8_48] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
Characterizations in terms of fractals are typically employed for systems with complex and multiscale descriptions. A prominent example of such systems is provided by the human brain, which can be idealized as a complex dynamical system made of many interacting subunits. The human brain can be modeled in terms of observable variables together with their spatio-temporal-functional relations. Computational intelligence is a research field bridging many nature-inspired computational methods, such as artificial neural networks, fuzzy systems, and evolutionary and swarm intelligence optimization techniques. Typical problems faced by means of computational intelligence methods include those of recognition, such as classification and prediction. Although historically conceived to operate in some vector space, such methods have been recently extended to the so-called nongeometric spaces, considering labeled graphs as the most general example of such patterns. Here, we suggest that fractal analysis and computational intelligence methods can be exploited together in neuroscience research. Fractal characterizations can be used to (i) assess scale-invariant properties and (ii) offer numeric, feature-based representations to complement the usually more complex pattern structures encountered in neurosciences. Computational intelligence methods could be used to exploit such fractal characterizations, considering also the possibility to perform data-driven analysis of nongeometric input spaces, therby overcoming the intrinsic limits related to Euclidean geometry.
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Affiliation(s)
- Lorenzo Livi
- Department of Computer Science, University of Manitoba, Winnipeg, MB, Canada
| | - Alireza Sadeghian
- Department of Computer Science, Faculty of Science, Ryerson University, Toronto, Canada
| | - Antonio Di Ieva
- Computational NeuroSurgery (CNS) Lab & Macquarie Neurosurgery, Macquarie Medical School, Faculty of Medicine, Human and Health Sciences, Macquarie University, Sydney, NSW, Australia.
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Davidson JM, Zhang L, Yue GH, Di Ieva A. Fractal Dimension Studies of the Brain Shape in Aging and Neurodegenerative Diseases. ADVANCES IN NEUROBIOLOGY 2024; 36:329-363. [PMID: 38468041 DOI: 10.1007/978-3-031-47606-8_17] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
The fractal dimension is a morphometric measure that has been used to investigate the changes of brain shape complexity in aging and neurodegenerative diseases. This chapter reviews fractal dimension studies in aging and neurodegenerative disorders in the literature. Research has shown that the fractal dimension of the left cerebral hemisphere increases until adolescence and then decreases with aging, while the fractal dimension of the right hemisphere continues to increase until adulthood. Studies in neurodegenerative diseases demonstrated a decline in the fractal dimension of the gray matter and white matter in Alzheimer's disease, amyotrophic lateral sclerosis, and spinocerebellar ataxia. In multiple sclerosis, the white matter fractal dimension decreases, but conversely, the fractal dimension of the gray matter increases at specific stages of disease. There is also a decline in the gray matter fractal dimension in frontotemporal dementia and multiple system atrophy of the cerebellar type and in the white matter fractal dimension in epilepsy and stroke. Region-specific changes in fractal dimension have also been found in Huntington's disease and Parkinson's disease. Associations were found between the fractal dimension and clinical scores, showing the potential of the fractal dimension as a marker to monitor brain shape changes in normal or pathological processes and predict cognitive or motor function.
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Affiliation(s)
- Jennilee M Davidson
- Centre for Motor Neuron Disease Research, Macquarie Medical School, Faculty of Medicine, Health and Human Sciences, Macquarie University, Sydney, NSW, Australia
| | | | - Guang H Yue
- Center for Mobility and Rehabilitation Engineering Research, Kessler Foundation, West Orange, NJ, USA
- Department of Physical Medicine and Rehabilitation, Rutgers New Jersey Medical School, Rutgers, The State University of New Jersey, Newark, NJ, USA
| | - Antonio Di Ieva
- Computational Neurosurgery (CNS) Lab, Macquarie Medical School, Faculty of Medicine, Health and Human Sciences, Macquarie University, Macquarie Park, NSW, Australia
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Karaca Y, Baleanu D, Karabudak R. Hidden Markov Model and multifractal method-based predictive quantization complexity models vis-á-vis the differential prognosis and differentiation of Multiple Sclerosis’ subgroups. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.108694] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Seely AJE. Optimizing Our Patients' Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology. ENTROPY 2020; 22:e22101095. [PMID: 33286863 PMCID: PMC7597192 DOI: 10.3390/e22101095] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Revised: 09/21/2020] [Accepted: 09/25/2020] [Indexed: 02/01/2023]
Abstract
Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature's drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients' entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.
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Affiliation(s)
- Andrew J. E. Seely
- Faculty of Medicine, University of Ottawa, Ottawa, ON K1H 8M5, Canada;
- Ottawa Hospital Research Institute, University of Ottawa, ON K1Y 4E9, Canada
- Thoracic Surgery and Critical Care Medicine, University of Ottawa, ON K1H 8L6, Canada
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Hedderich DM, Bäuml JG, Menegaux A, Avram M, Daamen M, Zimmer C, Bartmann P, Scheef L, Boecker H, Wolke D, Gaser C, Sorg C. An analysis of MRI derived cortical complexity in premature-born adults: Regional patterns, risk factors, and potential significance. Neuroimage 2020; 208:116438. [DOI: 10.1016/j.neuroimage.2019.116438] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2019] [Revised: 11/18/2019] [Accepted: 12/03/2019] [Indexed: 01/20/2023] Open
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Metze K, Adam R, Florindo JB. The fractal dimension of chromatin - a potential molecular marker for carcinogenesis, tumor progression and prognosis. Expert Rev Mol Diagn 2019; 19:299-312. [DOI: 10.1080/14737159.2019.1597707] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Konradin Metze
- Department of Pathology, Faculty of Medical Sciences, State University of Campinas (UNICAMP), Campinas, Brazil
| | - Randall Adam
- Department of Pathology, Faculty of Medical Sciences, State University of Campinas (UNICAMP), Campinas, Brazil
| | - João Batista Florindo
- Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas, Campinas, Brazil
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Singh SS, Khundrakpam B, Reid AT, Lewis JD, Evans AC, Ishrat R, Sharma BI, Singh RKB. Scaling in topological properties of brain networks. Sci Rep 2016; 6:24926. [PMID: 27112129 PMCID: PMC4845066 DOI: 10.1038/srep24926] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Accepted: 04/05/2016] [Indexed: 01/14/2023] Open
Abstract
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure, which reveals the self-similar rules governing the network structure. Further, the calculated fractal dimensions of brain networks of different species are found to decrease when one goes from lower to higher level species which implicates the more ordered and self-organized topography at higher level species. The sparsely distributed hubs in brain networks may be most influencing nodes but their absence may not cause network breakdown, and centrality parameters characterizing them also follow one parameter scaling law indicating self-similar roles of these hubs at different levels of organization in brain networks. The local-community-paradigm decomposition plot and calculated local-community-paradigm-correlation co-efficient of brain networks also shows the evidence for self-organization in these networks.
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Affiliation(s)
- Soibam Shyamchand Singh
- Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, New Delhi-110025, India.,School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India
| | - Budhachandra Khundrakpam
- McConnell Brain Imaging Center, Montreal Neurological Institute, McGill University, Montreal, QC H3A 2B4, Canada
| | - Andrew T Reid
- Institute of Neuroscience and Medicine (INM-1), Research Centre Jülich, Jülich, Germany
| | - John D Lewis
- McConnell Brain Imaging Center, Montreal Neurological Institute, McGill University, Montreal, QC H3A 2B4, Canada
| | - Alan C Evans
- McConnell Brain Imaging Center, Montreal Neurological Institute, McGill University, Montreal, QC H3A 2B4, Canada
| | - Romana Ishrat
- Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, New Delhi-110025, India
| | - B Indrajit Sharma
- Department of Physics, Assam University, Silchar-788011, Assam, India
| | - R K Brojen Singh
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India
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Oliveira CLN, Araújo AD, Bates JHT, Andrade JS, Suki B. Entropy Production and the Pressure-Volume Curve of the Lung. Front Physiol 2016; 7:73. [PMID: 26973540 PMCID: PMC4771753 DOI: 10.3389/fphys.2016.00073] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Accepted: 02/15/2016] [Indexed: 02/02/2023] Open
Abstract
We investigate analytically the production of entropy during a breathing cycle in healthy and diseased lungs. First, we calculate entropy production in healthy lungs by applying the laws of thermodynamics to the well-known transpulmonary pressure–volume (P–V) curves of the lung under the assumption that lung tissue behaves as an entropic spring similar to rubber. The bulk modulus, B, of the lung is also derived from these calculations. Second, we extend this approach to elastic recoil disorders of the lung such as occur in pulmonary fibrosis and emphysema. These diseases are characterized by particular alterations in the P–V relationship. For example, in fibrotic lungs B increases monotonically with disease progression, while in emphysema the opposite occurs. These diseases can thus be mimicked simply by making appropriate adjustments to the parameters of the P–V curve. Using Clausius's formalism, we show that entropy production, ΔS, is related to the hysteresis area, ΔA, enclosed by the P–V curve during a breathing cycle, namely, ΔS=ΔA∕T, where T is the body temperature. Although ΔA is highly dependent on the disease, such formula applies to healthy as well as diseased lungs, regardless of the disease stage. Finally, we use an ansatz to predict analytically the entropy produced by the fibrotic and emphysematous lungs.
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Affiliation(s)
| | - Ascânio D Araújo
- Departamento de Física, Universidade Federal do Ceará Fortaleza, Brazil
| | - Jason H T Bates
- Department of Medicine, University of Vermont Burlington, VT, USA
| | - José S Andrade
- Departamento de Física, Universidade Federal do Ceará Fortaleza, Brazil
| | - Béla Suki
- Department of Biomedical Engineering, Boston University Boston, MA, USA
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Identify the Rotating Stall in Centrifugal Compressors by Fractal Dimension in Reconstructed Phase Space. ENTROPY 2015. [DOI: 10.3390/e17127848] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Multidimensional Scaling Visualization Using Parametric Similarity Indices. ENTROPY 2015. [DOI: 10.3390/e17041775] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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