Papers by Gerardo L Febres
Complexity, Mar 29, 2014
We compared entropy for texts written in natural languages (English, Spanish) and artificial lang... more We compared entropy for texts written in natural languages (English, Spanish) and artificial languages (computer software) based on a simple expression for the entropy as a function of message length and specific word diversity. Code text written in artificial languages showed higher entropy than text of similar length expressed in natural languages. Spanish texts exhibit more symbolic diversity than English ones. Results showed that algorithms based on complexity measures differentiate artificial from natural languages, and that text analysis based on complexity measures allows the unveiling of important aspects of their nature. We propose specific expressions to examine entropy related aspects of tests and estimate the values of entropy, emergence, self-organization and complexity based on specific diversity and message length.
Axioms, Aug 1, 2019
This document introduces a method to solve linear optimization problems. The method's strategy is... more This document introduces a method to solve linear optimization problems. The method's strategy is based on the bounding condition that each constraint exerts over the dimensions of the problem. The solution of a linear optimization problem is at the intersection of the constraints defining the extreme vertex. The method decomposes the n-dimensional linear problem into n-1 two-dimensional problems. After studying the role of constraints in these two-dimensional problems, we identify the constraints intersecting at the extreme vertex. We then formulate a linear equation system that directly leads to the solution of the optimization problem. The algorithm is remarkably different from previously existing linear programming algorithms in the sense that it does not iterate; it is deterministic. A fully c-sharp-coded algorithm is made available. We believe this algorithm and the methods applied for classifying constraints according to their role open up a useful framework for studying complex linear problems through feasible-space and constraint analysis.
Synergy is phenomenon found everywhere in nature at all levels of organization in physics, chemis... more Synergy is phenomenon found everywhere in nature at all levels of organization in physics, chemistry, biology, social sciences, and the arts. The English Wikipedia defines Synergy as "the creation of a whole that is greater than the simple sum of its parts. The term synergy comes from the Attic Greek word συνεργία synergia from synergos, συνεργός, meaning working together". Synergy is an important concept that is difficult to define precisely and even more difficult to quantify. Entropy on the other hand has been used as a way to measure order or complexity. Here we explore the changes in entropy induced by diverse process described as synergistic. The paper uses seven examples reported in the literature to quantify synergy in different settings. The result shows that synergistic processes are associated to large decreases in entropy and slightly less large increases in work output of the system where they occur. Systems which suffer changes in entropy that are not associated to synergistic processes show a different pattern These results open the door to use entropy measures to identify and classify synergistic processes.
Systems, Sep 2, 2022
More than two years after the declaration of the COVID-19 pandemic, we are still experiencing con... more More than two years after the declaration of the COVID-19 pandemic, we are still experiencing contagious waves. As this is a long-lasting process, it becomes relevant to have a predictive tool to identify the intensively active places within a region. This study presents the development of a forecasting model applied to foresee the progress of the contagious process in Mexico and its regions. The method comprehends aspects of deterministic and probabilistic modeling. The deterministic part comprises the classical SIR model with some adjustments. The probabilistic part builds and populates a three-dimensional array, which is then used to describe and recall the probabilities of going from one status to another after some time, very much like a Markovian process. The process status is modeled as the combination of two conditions: the infection exponential growth parameter and a proxy variable we named "permissiveness" that accounts for all combined social activity factors affecting COVID-19 propagation. The results offer projections of the exponential growth parameter and the number of newly infected individuals for three weeks into the future. The proposed method's capabilities allow for predicting newly COVID-19-infected individuals with reasonable precision while capturing the characteristic dynamics and behavior of the modeled system.
Axioms, Feb 13, 2018
When considering perceptions, the observation scale and resolution are closely related properties... more When considering perceptions, the observation scale and resolution are closely related properties. There is consensus on considering resolution as the density of the elementary pieces of information in a specified information space. On the other hand, with the concept of scale, several conceptions compete for a consistent meaning. Scale is typically regarded as a way to indicate the degree of detail in which an observation is performed. Surprisingly, there is not a unified definition of scale as a description's property. This paper offers a precise definition of scale and a method to quantify it as a property associated with the interpretation of a description. To complete the parameters needed to describe the perception of a description, the concepts of scope and resolution are also revealed with an exact meaning. A model describing a recursive process of interpretation, based on evolving steps of scale, scope and resolution, is introduced. The model relies on the conception of observation scale and its association to the selection of symbols. Five experiments illustrate the application of these concepts, showing that resolution, scale and scope integrate the set of properties to define any point of view from which an observation is performed and interpreted. The results obtained for descriptions expressed in one and two dimensions, are the basis for a comparison of the perceivable symbolic information from different interpretations of the same descriptions. In conclusion, this study provides a framework for building models of our interpretation process and suggests ways to understand some mechanisms in the formation of information from initially meaningless symbols.
Journal of Bacteriology & Parasitology, 2021
The COVID-19 pandemic has globally impacted the behavior of the social patterns affecting the dis... more The COVID-19 pandemic has globally impacted the behavior of the social patterns affecting the disease's contagiousness. This effect deviates the classical SIR model from reproducing the data of COVID-19 in most countries. This study incorporates a non-constant permissiveness function to the SIR model. The resulting model is computationally solved to obtain a likely permissiveness time-function. To solve the adjusted model, a technique based on a proportional-integral controller is applied. The resulting models are compared with previous results obtained by a manual iterative adjusting method.
Science Trends, Dec 6, 2017
Resumen-La medición de la gestión de conocimiento (GC) se realiza a través del uso de técnicas es... more Resumen-La medición de la gestión de conocimiento (GC) se realiza a través del uso de técnicas estadísticas y de optimización bajo dos perspectivas identificadas en la literatura acerca del tema. Este artículo presenta un método para el diagnóstico de la gestión de conocimiento en individuos pertenecientes a un sector productivo en la ciudad de Bogotá D.C., entendiendo los flujos de conocimiento como el factor de coordinación de los demás factores productivos. Para ello, se construye un modelo basado en circuitos de realimentación en el que se representan las trasferencias de conocimiento por parte de individuos laboralmente activos sobre el factor de materiales, materia prima e insumos. Mediante la observación de coeficientes de correlación entre variables asociadas al conocimiento en distintas etapas de un proceso productivo, se detectan 'discontinuidades' (o roturas) de los ciclos de conocimiento. Así, es posible elaborar un estado actual de las condiciones de transformación de conocimiento tácito a explícito en los individuos de organizaciones dedicadas al curtido de cuero en Bogotá D.C., Finalmente, se deja como trabajo futuro la discusión de cómo estos resultados pueden ser utilizados en la elaboración de un modelo de optimización de la gestión de conocimiento. Palabras Clavesgestión de conocimiento, flujos de conocimiento, diagnóstico de GC Abstract-The assessment of knowledge management is performed by means of statistical and optimization techniques under two perspectives identified in the literature of this field. This article presents a method for the diagnosis of knowledge management in individuals belonging to productive sector in the Bogota D.C. We consider the flow of knowledge as the coordinating factor within all the others production factors of the industry. In this study we build a model based on feedback circuits that represent the transfer of knowledge among active workers on the factor of materials, raw material and inputs on the productive chain for tanning leather. We identified and detected breaks of knowledge cycles by using the correlation coefficients of the variables associated with the stages of the productive process. This we elaborated a current state of the conditions of transformation of tacit to explicit knowledge of the workers of the referenced production chain. Later, we propose as future work the discussion of how these results can be used in the elaboration of an optimization model of knowledge management.
Urban science, Aug 5, 2019
In a highly and rapidly urbanized world, the effect of the action of urban development is determi... more In a highly and rapidly urbanized world, the effect of the action of urban development is determinant for the physical, social, and economic conditions of its citizens, among which is inequality. It is even more crucial for developing regions such as Latin America on which this research is conducted. Therefore, the focus of the investigation was to determine the existence of significant statistical relationships between urban development and economic inequality in the region. For this purpose, it was sought to define urban development from the perspective of the praxis of multilateral organizations measured by indicators of extensive use among them. A hierarchical multiple linear regression model was built with six urban development variables predictors of the Gini coefficient as an indicator of economic inequality, in which data of 49 Latin American cities was used. The application of the method allowed us to discover a stochastic behavior of interaction between those multidimensional systems and confirmed the statistical relation. The research allows having a tool for the formulation of public policies that seek to strengthen local governance, promote community organization and participation, and assert urban planning as an agent for concerted efforts to achieve common goals.
Complexity, Dec 31, 2015
We evaluated the impact of changing the observation scale over the entropy measures for text desc... more We evaluated the impact of changing the observation scale over the entropy measures for text descriptions. MIDI coded Music, computer code and two human natural languages were studied at the scale of characters, words, and at the Fundamental Scale resulting from adjusting the symbols length used to interpret each text-description until it produced minimum entropy. The results show that the Fundamental Scale method is comparable with the use of words when measuring entropy levels in written texts. However, this method can also be used in communication systems lacking words such as music. Measuring symbolic entropy at the fundamental scale allows to calculate quantitatively, relative levels of complexity for different communication systems. The results open novel vision on differences among the structure of the communication systems studied.
This study presents a multivariable probabilistic model of the spread of COVID-19 in the area of ... more This study presents a multivariable probabilistic model of the spread of COVID-19 in the area of 58 counties in California State, USA. The model produces an estimate of the cumulative number of cases and duration of the wave over a certain area and General comments The approach of a model of COVID-19's spreading by obtaining expressions for cumulative cases and wave duration is interesting. Such a model may produce highly useful results for decision-making regarding any attempt to control the infection's spread. Considering the impact of several factors is also a good idea. I would, however, provide a better justification for the factors selected. Also, the manuscript regards Population (P), Density (D), and Size (S) as independent parameters. They are not independent, since D=P/S. Fixing this problem is important not for semantic reasons, but because it arguably distorts the results the model may offer. Final remarks Overall this is a simple but well-conceived approach. After improving some minor aspects of the manuscript, the study may deserve publication.
Entropy, Mar 25, 2015
The complexity of the description of a system is a function of the entropy of its symbolic descri... more The complexity of the description of a system is a function of the entropy of its symbolic description. Prior to computing the entropy of the system's description, an observation scale has to be assumed. In texts written in artificial and natural languages, typical scales are binary, characters, and words. However, considering languages as structures built around certain preconceived set of symbols, like words or characters, limits the level of complexity that can be revealed analytically. This study introduces the notion of the fundamental description scale to analyze the essence of the structure of a language. The concept of Fundamental Scale is tested for English and musical instrument digital interface (MIDI) music texts using an algorithm developed to split a text in a collection of sets of symbols that minimizes the observed entropy of the system. This Fundamental Scale reflects more details of the complexity of the language than using bits, characters or words. Results show that this Fundamental Scale allows to compare completely different languages, such as English and MIDI coded music regarding its structural entropy. This comparative power facilitates the study of the complexity of the structure of different communication systems.
Complexity, Jun 15, 2016
Synergy is often defined as the creation of a whole that is greater than the sum of its parts. It... more Synergy is often defined as the creation of a whole that is greater than the sum of its parts. It is found at all levels of organization in physics, chemistry, biology, social sciences, and the arts. Synergy occurs in open irreversible thermodynamic systems making it difficult to quantify. Negative entropy or negentropy (N) has been related to order and complexity, and so has work efficiency, information content, Gibbs Free Energy in equilibrium thermodynamics, and useful work efficiency in general (W). To define synergy in thermodynamic terms, we use the quantitative estimates of changes in N and W in seven different systems that suffer process described as synergistic. The results show that synergistic processes are characterized by an increase in N coupled to an increase in W. Processes not associated to synergy show a different pattern. The opposite of synergy are dissipative processes such as combustion where both N and W decrease. The synergistic processes studied showed a relatively greater increase in N compared to W opening ways to quantify energy-or information-dissipation due to the second law of thermodynamics in open irreversible systems. As a result, we propose a precise thermodynamic definition of synergy and show the potential of thermodynamic measurements in identifying, classifying and analysing in detail synergistic processes. V
arXiv (Cornell University), Jun 7, 2021
This document aims to estimate and describe the effects of the social distancing measures impleme... more This document aims to estimate and describe the effects of the social distancing measures implemented in several countries with the expectancy of controlling the spread of COVID-19. The procedure relies on the classic Susceptible-Infected-Removed (SIR) model, which is modified to incorporate a permissiveness index, representing the isolation achieved by the social distancing and the future development of vaccination campaigns, allowing the math model to reproduce more than one infection wave. Simulating the contagious process attaining various stages with constant permissiveness connected with short transitions, allowed estimating the shape of the social permissiveness curve for 38 countries. The adjusted SIR models are used to study the compromise between the economy's reactivation and the resulting infection spreading increase. The document presents a graphical abacus that describes the convenience of progressively relax social distancing measures while a feasible vaccination campaign develops.
arXiv (Cornell University), Dec 29, 2014
The complexity of a system description is a function of the entropy of its symbolic description. ... more The complexity of a system description is a function of the entropy of its symbolic description. Prior to computing the entropy of the system description, an observation scale has to be assumed. In natural language texts, typical scales are binary, characters, and words. However, considering languages as structures built around certain preconceived set of symbols, like words or characters, is only a presumption. This study depicts the notion of the Description Fundamental Scale as a set of symbols which serves to analyze the essence a language structure. The concept of Fundamental Scale is tested using English and MIDI music texts by means of an algorithm developed to search for a set of symbols, which minimizes the system observed entropy, and therefore best expresses the fundamental scale of the language employed. Test results show that it is possible to find the Fundamental Scale of some languages. The concept of Fundamental Scale, and the method for its determination, emerges as an interesting tool to facilitate the study of languages and complex systems.
arXiv (Cornell University), Jan 15, 2017
This work presents some characteristics of MoNet, a digital platform for the modeling and visuali... more This work presents some characteristics of MoNet, a digital platform for the modeling and visualization of complex systems. Emphasis is on the ideas that allowed the successful progressive development of this modeling platform, which goes along with the implementation of applications to the modeling of several studied systems. The platform can represent different aspects of systems modeled at different observation scales. This tool offers advantages in the sense of favoring the perception of the phenomenon of the emergence of information, associated with changes of scale. This paper also includes some criteria used for the construction of this modeling platform. The power of current computers has made practical representing graphic resources such as shapes, line thickness, overlaying-text tags, colors, and transparencies, in the graphical modeling of systems. By visualizing diagrams conveniently designed to highlight contrasts, these modeling platforms allow the recognition of patterns that drive our understanding of systems and their structure. Graphs reflecting the benefits of the tool regarding the visualization of systems at different scales of observation are presented to illustrate the application of the platform.
arXiv (Cornell University), Sep 20, 2018
This document introduces a new strategy to solve linear optimization problems. The strategy is ba... more This document introduces a new strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is located at the intersection of the constraints defining the extreme vertex. By identifying the constraints that limit the growth of the objective function value, we formulate linear equations system leading to the optimization problem's solution. The most complex operation of the algorithm is the inversion of a matrix sized by the number of dimensions of the problem. Therefore, the algorithm's complexity is comparable to the corresponding to the classical Simplex method and the more recently developed Linear Programming algorithms. However, the algorithm offers the advantage of being non-iterative.
arXiv (Cornell University), Jan 15, 2017
This work presents some characteristics of MoNet, a digital platform for the modeling and visuali... more This work presents some characteristics of MoNet, a digital platform for the modeling and visualization of complex systems. Emphasis is on the ideas that allowed the successful progressive development of this modeling platform, which goes along with the implementation of applications to the modeling of several studied systems. The platform can represent different aspects of systems modeled at different observation scales. This tool offers advantages in the sense of favoring the perception of the phenomenon of the emergence of information, associated with changes of scale. This paper also includes some criteria used for the construction of this modeling platform. The power of current computers has made practical representing graphic resources such as shapes, line thickness, overlaying-text tags, colors, and transparencies, in the graphical modeling of systems. By visualizing diagrams conveniently designed to highlight contrasts, these modeling platforms allow the recognition of patterns that drive our understanding of systems and their structure. Graphs reflecting the benefits of the tool regarding the visualization of systems at different scales of observation are presented to illustrate the application of the platform.
arXiv (Cornell University), Jan 28, 2014
We measured entropy and symbolic diversity of texts written in English and Spanish. We included t... more We measured entropy and symbolic diversity of texts written in English and Spanish. We included texts by Literature Nobel laureates and other famous authors. We formed four groups of texts according to the combinations of language used and the author's Literature Nobel Prize condition. Entropy, symbol diversity and symbol frequency profiles were compared for these four groups. We also built a scale sensitive to the quality of writing and evaluated its relationship with the Flesch´s readability index for English and the Szigriszt´s perspicuity index for Spanish. Results suggest a correlation between entropy and word diversity with quality of writing. Text genre also influences the resulting entropy and diversity of the text. Results suggest the plausibility of automated quality assessment of texts.
PLOS ONE, Oct 17, 2017
Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy D... more Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy Description, which we call the Fundamental Scale. This allowed us to create a novel space to represent music pieces by developing: (a) a method to adjust a textual description from its original scale of observation to an arbitrarily selected scale, (b) a method to model the structure of any textual description based on the shape of the symbol frequency profiles, and (c) the concept of higher order entropy as the entropy associated with the deviations of a frequency-ranked symbol profile from a perfect Zipfian profile. We call this diversity index the '2nd Order Entropy'. Applying these methods to a variety of musical pieces showed how the space of 'symbolic specific diversity-entropy' and that of '2nd order entropy' captures characteristics that are unique to each music type, style, composer and genre. Some clustering of these properties around each musical category is shown. These methods allow us to visualize a historic trajectory of academic music across this space, from medieval to contemporary academic music. We show that the description of musical structures using entropy, symbol frequency profiles and specific symbolic diversity allows us to characterize traditional and popular expressions of music. These classification techniques promise to be useful in other disciplines for pattern recognition and machine learning.
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Papers by Gerardo L Febres