Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Australian water mass variations from GRACE data linked to Indo-Pacific climate variability

Time-variable gravity data from the Gravity Recovery And Climate Experiment (GRACE) mission are used to study total water content over Australia for the period 2002–2010. A time-varying annual signal explains 61% of the variance of the data, in good agreement with two independent estimates of the same quantity from hydrological models. Water mass content variations across Australia are linked to Pacific and Indian Ocean variability, associated with El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), respectively. From 1989, positive (negative) IOD phases were related to anomalously low (high) precipitation in southeastern Australia, associated with a reduced (enhanced) tropical moisture flux. In particular, the sustained water mass content reduction over central and southern regions of Australia during the period 2006–2008 is associated with three consecutive positive IOD events.

Advanced interpretation of subsidence in Murcia (SE Spain) using A-DInSAR data – modelling and validation

Subsidence is a natural hazard that affects wide areas in the world causing important economic costs annually. This phenomenon has occurred in the metropolitan area of Murcia City (SE Spain) as a result of groundwater overexploitation. In this work aquifer system subsidence is investigated using an advanced differential SAR interferometry remote sensing technique (A-DInSAR) called Stable Point Network (SPN). The SPN derived displacement results, mainly the velocity displacement maps and the time series of the displacement, reveal that in the period 2004–2008 the rate of subsidence in Murcia metropolitan area doubled with respect to the previous period from 1995 to 2005. The acceleration of the deformation phenomenon is explained by the drought period started in 2006. The comparison of the temporal evolution of the displacements measured with the extensometers and the SPN technique shows an average absolute error of 3.9±3.8 mm. Finally, results from a finite element model developed to simulate the recorded time history subsidence from known water table height changes compares well with the SPN displacement time series estimations. This result demonstrates the potential of A-DInSAR techniques to validate subsidence prediction models as an alternative to using instrumental ground based techniques for validation.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Detection and mapping of burnt areas from time series of MODIS-derived NDVI data in a Mediterranean region

Moderate resolution remote sensing data, as provided by MODIS, can be used to detect and map active or past wildfires from daily records of suitable combinations of reflectance bands. The objective of the present work was to develop and test simple algorithms and variations for automatic or semiautomatic detection of burnt areas from time series data of MODIS biweekly vegetation indices for a Mediterranean region. MODIS-derived NDVI 250m time series data for the Valencia region, East Spain, were subjected to a two-step process for the detection of candidate burnt areas, and the results compared with available fire event records from the Valencia Regional Government. For each pixel and date in the data series, a model was fitted to both the previous and posterior time series data. Combining drops between two consecutive points and 1-year average drops, we used discrepancies or jumps between the pre and post models to identify seed pixels, and then delimitated fire scars for each potential wildfire using an extension algorithm from the seed pixels. The resulting maps of the detected burnt areas showed a very good agreement with the perimeters registered in the database of fire records used as reference. Overall accuracies and indices of agreement were very high, and omission and commission errors were similar or lower than in previous studies that used automatic or semiautomatic fire scar detection based on remote sensing. This supports the effectiveness of the method for detecting and mapping burnt areas in the Mediterranean region.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.