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Yen PTW, Xia K, Cheong SA. Laplacian Spectra of Persistent Structures in Taiwan, Singapore, and US Stock Markets. ENTROPY (BASEL, SWITZERLAND) 2023; 25:846. [PMID: 37372190 DOI: 10.3390/e25060846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Revised: 04/29/2023] [Accepted: 05/17/2023] [Indexed: 06/29/2023]
Abstract
An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent structures can be identified from the spectra and Fiedler vector of the graph Laplacian at different stages of the topological data analysis (TDA) filtration process for twelve toy models. We then investigated four market crashes, three of which were related to the COVID-19 pandemic. In all four crashes, a persistent gap opens up in the Laplacian spectra when we go from a normal phase to a crash phase. In the crash phase, the persistent structure associated with the gap remains distinguishable up to a characteristic length scale ϵ* where the first non-zero Laplacian eigenvalue changes most rapidly. Before ϵ*, the distribution of components in the Fiedler vector is predominantly bi-modal, and this distribution becomes uni-modal after ϵ*. Our findings hint at the possibility of understanding market crashs in terms of both continuous and discontinuous changes. Beyond the graph Laplacian, we can also employ Hodge Laplacians of higher order for future research.
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Affiliation(s)
- Peter Tsung-Wen Yen
- Center for Crystal Researches, National Sun Yat-sen University, 70 Lienhai Rd., Kaohsiung 80424, Taiwan
| | - Kelin Xia
- School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Siew Ann Cheong
- School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
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D’Addese G, Sani L, La Rocca L, Serra R, Villani M. Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems. ENTROPY 2021; 23:e23040398. [PMID: 33801637 PMCID: PMC8066289 DOI: 10.3390/e23040398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Revised: 03/13/2021] [Accepted: 03/22/2021] [Indexed: 11/16/2022]
Abstract
The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.
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Affiliation(s)
- Gianluca D’Addese
- Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy; (G.D.); (L.L.R.); (R.S.)
| | - Laura Sani
- Department of Engineering and Architecture, University of Parma, 43124 Parma, Italy;
| | - Luca La Rocca
- Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy; (G.D.); (L.L.R.); (R.S.)
| | - Roberto Serra
- Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy; (G.D.); (L.L.R.); (R.S.)
- European Centre for Living Technology, 30123 Venice, Italy
- Institute for Advanced Studies, University of Amsterdam, 1012 GC Amsterdam, The Netherlands
| | - Marco Villani
- Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy; (G.D.); (L.L.R.); (R.S.)
- European Centre for Living Technology, 30123 Venice, Italy
- Correspondence:
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Kitazono J, Kanai R, Oizumi M. Efficient search for informational cores in complex systems: Application to brain networks. Neural Netw 2020; 132:232-244. [PMID: 32919313 DOI: 10.1016/j.neunet.2020.08.020] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Revised: 08/04/2020] [Accepted: 08/23/2020] [Indexed: 11/16/2022]
Abstract
An important step in understanding the nature of the brain is to identify "cores" in the brain network, where brain areas strongly interact with each other. Cores can be considered as essential sub-networks for brain functions. In the last few decades, an information-theoretic approach to identifying cores has been developed. In this approach, interactions between parts are measured by an information loss function, which quantifies how much information would be lost if interactions between parts were removed. Then, a core called a "complex" is defined as a subsystem wherein the amount of information loss is locally maximal. Although identifying complexes can be a novel and useful approach, its application is practically impossible because computation time grows exponentially with system size. Here we propose a fast and exact algorithm for finding complexes, called Hierarchical Partitioning for Complex search (HPC). HPC hierarchically partitions systems to narrow down candidates for complexes. The computation time of HPC is polynomial, enabling us to find complexes in large systems (up to several hundred) in a practical amount of time. We prove that HPC is exact when an information loss function satisfies a mathematical property, monotonicity. We show that mutual information is one such information loss function. We also show that a broad class of submodular functions can be considered as such information loss functions, indicating the expandability of our framework to the class. We applied HPC to electrocorticogram recordings from a monkey and demonstrated that HPC revealed temporally stable and characteristic complexes.
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Affiliation(s)
- Jun Kitazono
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan.
| | | | - Masafumi Oizumi
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan.
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Hattinger CM, Biason P, Iacoboni E, Gagno S, Fanelli M, Tavanti E, Vella S, Ferrari S, Roli A, Roncato R, Giodini L, Scotlandi K, Picci P, Toffoli G, Serra M. Candidate germline polymorphisms of genes belonging to the pathways of four drugs used in osteosarcoma standard chemotherapy associated with risk, survival and toxicity in non-metastatic high-grade osteosarcoma. Oncotarget 2018; 7:61970-61987. [PMID: 27566557 PMCID: PMC5308704 DOI: 10.18632/oncotarget.11486] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Accepted: 07/29/2016] [Indexed: 02/03/2023] Open
Abstract
This study aimed to identify associations between germline polymorphisms and risk of high-grade osteosarcoma (HGOS) development, event-free survival (EFS) and toxicity in HGOS patients treated with neo-adjuvant chemotherapy and surgery. Germline polymorphisms of 31 genes known to be relevant for transport or metabolism of all four drugs used in HGOS chemotherapy (methotrexate, doxorubicin, cisplatin and ifosfamide) were genotyped in 196 patients with HGOS and in 470 healthy age and gender-matched controls. Of these 196 HGOS patients, a homogeneously treated group of 126 patients was considered for survival analyses (survival cohort). For 57 of these, treatment-related toxicity data were available (toxicity cohort). Eleven polymorphisms were associated with increased risk of developing HGOS (p < 0.05). The distribution of polymorphisms in patients was characterized by a higher Shannon entropy. In the survival cohort (n = 126, median follow-up = 126 months), genotypes of ABCC2_1249A/G, GGH_452T/C, TP53_IVS2+38G/C and CYP2B6*6 were associated with EFS (p < 0.05). In the toxicity cohort (n = 57), genotypes of ABCB1_1236T/C, ABCC2_1249A/G, ABCC2_3972A/G, ERCC1_8092T/G, XPD_23591A/G, XRCC3_18067T/C, MTHFR_1298A/C and GGH_16T/C were associated with elevated risk for toxicity development (p < 0.05). The results obtained in this retrospective study indicate that the aforementioned germline polymorphisms significantly impact on the risk of HGOS development, EFS and the occurrence of chemotherapy-related toxicity. These findings should be prospectively validated with the aim of optimizing and tailoring HGOS treatment in the near future.
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Affiliation(s)
- Claudia M Hattinger
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Paola Biason
- National Institute of Health and Medical Research (INSERM), Unity 892, University of Medicine of Angers, Angers, France
| | - Erika Iacoboni
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Sara Gagno
- Experimental and Clinical Pharmacology Unit, National Cancer Institute, Aviano, Italy
| | - Marilù Fanelli
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Elisa Tavanti
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Serena Vella
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Stefano Ferrari
- Chemotherapy Ward of Muscoloskeletal Tumours, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Andrea Roli
- Department of Computer Science and Engineering (DISI), University of Bologna, Cesena, Italy
| | - Rossana Roncato
- Experimental and Clinical Pharmacology Unit, National Cancer Institute, Aviano, Italy
| | - Luciana Giodini
- Experimental and Clinical Pharmacology Unit, National Cancer Institute, Aviano, Italy
| | - Katia Scotlandi
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Piero Picci
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
| | - Giuseppe Toffoli
- Experimental and Clinical Pharmacology Unit, National Cancer Institute, Aviano, Italy
| | - Massimo Serra
- Laboratory of Experimental Oncology, Orthopaedic Rizzoli Institute, Bologna, Italy
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