Gerardo L. Febres

Mario Franco, Gerardo Febres, Nelson Fernández et al.

Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is ultimately constrained by the intrinsic properties of datasets, independently of computational power or model complexity. In this work, we introduce a formal entropy-based measure of classificability, which quantifies the inherent difficulty of a classification problem by assessing the uncertainty in class assignments given feature representations. This measure captures the degree of class overlap and aligns with human intuition, serving as an upper bound on classification performance for classification problems. Our results establish a theoretical limit beyond which no classifier can improve the classification accuracy, regardless of the architecture or amount of data, in a given problem. Our approach provides a principled framework for understanding when classification is inherently fallible and fundamentally ambiguous.

Gerardo L. Febres

This document focuses on modeling a complex situations to achieve an advantage within a competitive context. Our goal is to devise the characteristics of games to teach and exercise non-easily quantifiable tasks crucial to the math-modeling process. A computerized game to exercise the math-modeling process and optimization problem formulation is introduced. The game is named The Formula 1 Championship, and models of the game were developed in the computerized simulation platform MoNet. It resembles some situations in which team managers must make crucial decisions to enhance their racing cars up to the feasible, most advantageous conditions. This paper describes the game's rules, limitations, and five Formula 1 circuit simulators used for the championship development. We present several formulations of this situation in the form of optimization problems. Administering the budget to reach the best car adjustment to a set of circuits to win the respective races can be an approach. Focusing on the best distribution of each Grand Prix's budget and then deciding how to use the assigned money to improve the car is also the right approach. In general, there may be a degree of conflict among these approaches because they are different aspects of the same multi-scale optimization problem. Therefore, we evaluate the impact of assigning the highest priority to an element, or another, when formulating the optimization problem. Studying the effectiveness of solving such optimization problems turns out to be an exciting way of evaluating the advantages of focusing on one scale or another. Another thread of this research directs to the meaning of the game in the teaching-learning process. We believe applying the Formula 1 Game is an effective way to discover opportunities in a complex-system situation and formulate them to finally extract and concrete the related benefit to the context described.

Gerardo L. Febres

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.

Gerardo Febres, Klaus Jaffe

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 description from its original scale of observation to a general scale, b) the concept of higher order entropy as the entropy associated to the deviations of a frequency ranked symbol profile from a perfect Zipf profile. We called 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. This method allows to visualize a historic trajectory of academic music across this space, from medieval to contemporary academic music. We show that description of musical structures using entropy and symbolic diversity allows to characterize traditional and popular expressions of music. These classification techniques promise to be useful in other disciplines for pattern recognition and machine learning, for example.

Gerardo Febres, Klaus Jaffe

We measured entropy and symbolic diversity for English and Spanish texts including literature Nobel laureates and other famous authors. 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.

Gerardo Febres, Klaus Jaffe, Carlos Gershenson

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.