Zipf-scaling behavior in the immune system

Burgos, Javier de; Moreno-Tovar, Pedro

doi:10.1016/0303-2647(96)01618-8

Cited by 49 publications

(53 citation statements)

References 11 publications

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“…They have been discovered in 1949 by Zipf (Zipf 1949) in written English texts and Zipf distributions have been found in every natural language such as the Chinese language (Lua 1994) and the Russian language (Kalinin 1964); it was verified also that several areas in real life phenomena follow a power law distributions such as the characterization of immune system (Burgos and Moreno-Tovar 1996), demography (Gan et al 2006 G.PÉ ROT (1972), with her customary intuition, thought that this law does not apply only to the linguistic messages, but also to the iconic messages (including images); she concluded that in the analyzed corpuses, the iconic language verifies the law of Zipf, with a precision better than in linguistics. However, it is only in 2002 in the works of (Caron et al 2002) that the laws of Zipf and inverse Zipf were applied to images.…”

Section: The Laws Of Zipf and Inverse Zipfmentioning

confidence: 97%

The power laws: Zipf and inverse Zipf for automated segmentation and classification of masses within mammograms

2014

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Breast cancer is becoming the leading form of cancer among women worldwide, indeed, there are no effective ways to prevent this disease at present, therefore, it's early screening and detection is the key to rise the success of treatment, hence, the reduce of the associated mortality rates. This work aims to improve the performance of the current computer-aided detection and diagnosis approaches (CADe/CADx) of breast cancer which involve the application of the computer technology in mammograms analysis and understanding; for this purpose, we deal with the power laws: Zipf and inverse Zipf. The originality of this research lays in the contribution of the power laws for mammograms analysis; it is the first attempt to use them in the field of mammograms masses segmentation and classification, indeed, these laws characterize the structural complexity of texture within mammograms and provide the curves of Zipf and inverse Zipf which carry significant information that could be used to mammograms masses detection and classification along a new set of textural features extracted from the curves of Zipf and inverse Zipf. According to our experiments conducted on a mammogram database used in the framework of a bilateral project between our university and the hospital CHU at Algeria, we can assert that our approach based Zipf's and inverse Zipf's laws is a powerful and efficient approach for automated mammograms masses detection and classification.

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Section: The Laws Of Zipf and Inverse Zipfmentioning

confidence: 97%

The power laws: Zipf and inverse Zipf for automated segmentation and classification of masses within mammograms

2014

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“…Although there are a lot of methods to extrapolate an underlying dynamics from a given time series such as the embedding dimension (e.g., Taken, 1981), the number of attempt to estimate the regime change of dynamics is relatively small. Since it was found that a power law results from a critical phenomenon or self-organized criticality (Bak and Sneppen, 1993;Bak, 1996), the power law is studied not only in evolution (Bak and Boettcher, 1997;Kauffman and Johnsen, 1991;Takachi and Gunji, 2004) and systematic biology (Burlando, 1993) but in biochemical processes, e.g., oligonucleotide frequency in DNA (Martindale and Konopka, 1996;Voss, 1996), RNA structure realization (Schuster, 1995), immune systems (Burgos and Moreno-Tovar, 1996). However, these studies did not uncover the regime change and/or detection of the emergent event.…”

Section: Introductionmentioning

confidence: 97%

Event detection by forward- and backward-prediction, illustrating the analysis for behaviors of black larder beetle Dermestes haemorrhoidalis Küster

2004

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“…Así defi nió el concepto de dimensión fractal, que es la medida de la irregularidad de los objetos fractales (3) . Existen diferentes ti pos de fractales, como los abstractos (6) , los fractales salvajes (7) y los fractales estadísti cos (8)(9)(10) .…”

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Ley caótica exponencial de los sistemas dinámicos cardiacos para evaluación del Holter: 16 horas

Rodríguez

Jattin

Mendoza³

et al. 2017

An Fac med

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Fac med. 2017;78(3):292-297 DOI: http://dx.doi.org/10.15381/anales.v78i3.13761 Resumen Introducción. En un estudio previo se realizó una reducción a 16 horas en la evaluación de la ley exponencial de la dinámica cardiaca caótica, mostrando su efectividad en la caracterización de enfermedad y normalidad. Objetivo. Confirmar la aplicabilidad clínica de la ley matemática exponencial para evaluar la dinámica cardiaca caótica a partir de los registros Holter en 16 horas, observando su utilidad diagnóstica al disminuir su tiempo de evaluación. Diseño. Estudio observacional de corte trasversal donde se avaluó los parámetros electrocardiográficos mediante metodologías físico matemáticas inductivas con una confirmación estadística. Metodología. Se tomaron 100 registros Holter con diferentes tipos de patología, y 40 Holter que fueron diagnosticados como normales. Para cada Holter se construyó un atractor caótico, y midiendo sus espacios de ocupación y dimensión fractal se aplicó la evaluación matemática para diferenciar normalidad de enfermedad. Finalmente se realizaron medidas de concordancia diagnostica respecto al estándar de oro. Resultados. La ocupación espacial de todos los atractores estuvieron dentro de los valores esperados; los registros normales presentaron en la rejilla Kp valores entre 205 y 423. Para los registros con enfermedad aguda, estos valores oscilaron entre 21 y 65; y para los registros de enfermedad crónica estos valores estuvieron entre 104 y 195. Los valores de sensibilidad y especificidad fueron de 100% y el coeficiente Kappa fue de 1. Conclusión. El presente estudio muestra la aplicabilidad clínica de esta metodología para la evaluación en 16 horas de registros electrocardiográficos continuos o Holter. Palabras clave: Ley; Caos; Ley Caótica; Fractal; Dinámica Cardiaca; Diagnóstico. Abstract Introduction: In a previous study, a 16-hour reduction in the evaluation of the exponential law of chaotic cardiac dynamics was done, showing its effectiveness in the characterization of disease and normality. Objective: To confirm the clinical applicability of the exponential mathematical law to evaluate chaotic cardiac dynamics from the Holter registers in 16 hours, observing its diagnostic utility when reducing its evaluation time. Design: Cross-sectional observational study where the electrocardiographic parameters were evaluated using inductive mathematical methodologies with statistical confirmation. Methodology: We obtained 100 Holter records from patients with different types of pathology, and 40 Holter that were diagnosed as normal. For each Holter, a chaotic attractor was constructed, and measuring their spaces of occupation and fractal dimension, the mathematical evaluation to differentiate normality of disease was applied. Finally, we calculated measures of diagnostic concordance in accordance with the gold standard.

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Zipf-scaling behavior in the immune system

Cited by 49 publications

References 11 publications

The power laws: Zipf and inverse Zipf for automated segmentation and classification of masses within mammograms

The power laws: Zipf and inverse Zipf for automated segmentation and classification of masses within mammograms

Event detection by forward- and backward-prediction, illustrating the analysis for behaviors of black larder beetle Dermestes haemorrhoidalis Küster

Ley caótica exponencial de los sistemas dinámicos cardiacos para evaluación del Holter: 16 horas

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