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One of the most significant challenges facing society is the development of effective mechanisms that can ensure the security of citizens while facilitating comprehensive economic and social advancement. This study identifies the commercial areas of Bogotá, Colombia, which are critical points in terms of security, and proposes a strategic allocation of police resources in order to optimise their coverage and response times. The methodological process was executed in accordance with the guidelines set forth in the Cross-Industry Standard Process for Data Mining. Geospatial analysis techniques were employed, including the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to identify commercial zones and the graph theory to model the security network. Additionally, data from the Special Administrative Unit of Land Registry and the locations of National Police stations and precincts were utilised. The results demonstrate the identification of 241 commercial zones in Bogotá and propose a strategic allocation of police resources based on degree centrality and a stable matching algorithm. The integration of related techniques allowed for the generation of an innovative approach that combines the accurate identification of critical commercial zones with a data-driven optimisation of police resources. This not only increases the understanding of security dynamics in urban commercial areas, but also provides a robust public safety decision-making tool for the city. [ABSTRACT FROM AUTHOR]

Computational thinking emerges as a field of knowledge due to the increasing importance of technology and computing in today's society. It has been demonstrated that computational thinking can enhance problem-solving abilities by employing techniques from computer science to develop solutions for complex problems. It often involves the application of mathematical principles, such as algebra, geometry, and statistics. Mathematics is fundamental to computational thinking as it provides the theoretical and conceptual foundation for many computer science techniques. Mathematical concepts like functions, sets, and graph theory are essential for understanding algorithms and data structures. The aim of this study was to analyze the integration of mathematics and computational thinking and how this relationship has been measured using both connected and disconnected activities in primary school students. A total of 302 articles were reviewed, applying inclusion and exclusion criteria related to the study's variables of interest. The review found that most articles integrate mathematics and computational thinking based on their interconnectedness, using classroom strategies that support both fields of knowledge. Eleven articles propose activities encompassing four mathematical components (geometric, metric, spatial, and numeric) to address computational thinking, with the geometric component being the most commonly utilized. Only seven articles included students at the 0th grade level, and only two articles worked with populations from Central (Panama) and South America (Uruguay), suggesting that computational thinking is in its early stages in our continent, excluding North American countries where a higher number of articles are reported. [ABSTRACT FROM AUTHOR]

Copyright of Revista Entramado is the property of Universidad Libre Seccional Cali and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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Copyright of Ciencias Psicológicas is the property of Universidad Catolica del Uruguay Damaso Antonio Larranaga and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bistua: Revista de la Facultad de Ciencias Básicas is the property of Facultad de Ciencias Basicas de la Universidad de Pamplona and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study is about knowledge transfer and innovation in Mexico. Consider the hypothesis that one of the fundamental inputs of innovation is the ability to create and transfer knowledge. Thus, innovation depends on the way in which knowledge is created and flows within National Innovation Systems (NIS). Using graph theory, econometrics and cluster analysis, it is shown that Mexico has a limited capacity to generate and transfer knowledge and its NIS is disjointed, and in consequence its rate of technological innovation is low. However, this does not imply that there is no innovation, but rather that it is focused on some technologically advanced and highproductivity sectors, giving rise to different styles of innovation. It is concluded that without an industrial policy oriented to the articulation of the NIS, which considers higher spending on Innovation and Technological Development (ITD), Mexico will continue with poor economic growth in the long term. [ABSTRACT FROM AUTHOR]

The research describes and explains the patterns, costs and limits of daily mobility caused by the urban structure of Ciudad Juarez. The concatenation of classical and contemporary theories of location, urban structure and mobility underpinned the analysis processes and results of this study. Methodologically, Moran's I and Getis-Ord's G spatial autocorrelation techniques were implemented for the analysis of INEGI's economic censuses, which spatially identified the subcenters of total, manufacturing and tertiary employment in the periods 1993, 2004, 2009 and 2014. On the other hand, a two-stage data survey was conducted throughout the city by means of origin-destination surveys, which showed, from a macro scale, mobility patterns in terms of time, distance, origins, destinations, number of trips, transportation preferences, motives, ages and economic costs. At a micro scale, graph theory and network analysis allowed spatial modeling of each intra-urban trip, the results of which are detailed in a Mobility Atlas that includes each of the 64 territorial units into which the city was divided. The research proposes a replicable methodology and provides relevant and current information about the city, useful for other studies, decision making and public policies on urban structuring and mobility. [ABSTRACT FROM AUTHOR]

Optimal distribution networks reconfiguration is very important in reducing losses and operating costs and in improving networks security, stability and reliability indicators. The work objective is reprogramming an algorithm that improves results obtained previously. Paper presents non-dominated classification genetic algorithm II parts adaptation and reprogramming, with a new coding that, unlike previous authors, avoids modified genetic operators and take better advantage of algorithm's potentialities. In addition, graph theory is used to transform non-feasible individuals and avoid new generations of them, dispensing with annoying mesh checking and reducing the search space and computational burden. Proposal's effectiveness was tested with 33 and 70 bars test distribution systems, showing promising results and better than previous proposals. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative methodology to optimally design an electrical distribution system in a real urban area. A medium voltage (MV) network polygon is extracted from the web page of a distribution company (GIS platform), which serves as a comparison pattern. A redesign of the medium voltage network is made to the extracted polygon. Taking as a premise that it is a new urbanization that needs to be provided with electric power, with all the technical requirements imposed by the regulating entity, good power quality and at minimum cost. To achieve this goal, two mathematical optimization models are used. The methodology begins by delimiting the project area in a geo-referenced manner; in this area 36 possible sites are located where the distribution transformers that will provide electricity to the new urbanization can be placed. The first optimization model determines how many transformers will be installed, by means of a minimization objective function, the constraints of the model are: transformer capacity (KVA) and coverage (number of subscribers connected to the low voltage network of each transformer). Once the number of transformers to be installed and their respective geo-referenced optimal locations are determined, the model is run. The second heuristic optimization model, based on graph theory, calculates the mine spanning tree for the connection of the medium voltage electrical network, thus interconnecting the transformers of the project with the minimum distance, thus optimizing the construction cost. These optimization models are implemented and solved with Matlab and LpSolve software. The topology found with the two proposed models is electrically evaluated by running power flows with CYMEDIST software. Finally, the proposed model is evaluated by comparing the electrical parameters obtained with the electrical parameters of the polygon extracted from the GIS system of the distribution company. [ABSTRACT FROM AUTHOR]

Copyright of Electronic Journal of Educational Research, Assessment & Evaluation / Revista Electrónica de Investigación y Evaluación Educativa is the property of RELIEVE - Revista Electonica de Investigacion y Evaluacion Educativa and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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Copyright of Revista de Ingenieria, Matematicas y Ciencias de la Informacion is the property of Corporacion Universitaria Republicana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This document presents a Bibliometric Analysis and Identification of Trends on the topic of public sector corruption, with the use of the Scopus database in a time range of years 2000-2021. From the methodological technical perspective, scientific mapping and network analysis were used. For the scientific map, the most relevant works in the area are addressed, with citations, co-occurrence of words, cocitations, co-authorships and bibliographic coupling. For the analysis of Red was used software R, according to graph theory, with an image of a tree figuratively, which distributes the information in three large groups of categories: root, for classic documents, trunk for cited and cited documents and sheets, which refer to the most current trends. The results show the existence of mechanisms that have proven to be effective in the fight against corruption, although these mechanisms are exposed with a certain level of restrictions in different countries. [ABSTRACT FROM AUTHOR]

The article presents reviews of three undergraduate works carried out by students from the National University of Colombia. The topics addressed include combinatorial optimization in an industrial printing press, a predictive model for the study of personal theft, and the analysis of Wolfram's hypergraph in relation to physics. Additionally, the article presents several research abstracts in mathematics and computer science, addressing topics such as graph theory, optimization of paid search campaigns, and fraud prevention in the online market. A guide for back-end web development using mathematical skills acquired in the study of Computer Science is also provided. [Extracted from the article]

The article presents reviews of various undergraduate works carried out at the National University of Colombia, addressing topics such as solving the early-late production problem, quantifying the benefit of predictive security models, modeling and solving the problem of sterilization of prepackaged foods, and studying the homotopy type theory. The works were carried out by students under the guidance of university professors. In addition, summaries of degree works in mathematics are presented, dealing with topics such as the distribution of Catalan words, the impact of human activity on roadside ecosystems, rational consumer choice, lattice topology, the prime number theorem, and Ramsey's theory on graphs. Each summary provides a brief description of the topic and the main results of the study. [Extracted from the article]

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Copyright of Contaduría y Administración is the property of Facultad de Contaduria y Administracion-Universidad Nacional Autonoma de Mexico and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents, from an introductory point of view and oriented to non-experts in network theory, the fundamentals of graphs and networks that allow projecting information about cultural networks in a formal context. It also describes some of the most common measures and tools to design quantitative mechanisms for the subsequent analysis of these networks. This article does not pretend to be a complete course or tutorial on network theory, for that the reader can refer to any of the references listed at the end, but rather it is an introduction oriented to go through, in a single document, some of the details that are considered more important and that are usually leTh out of the initial explanations on the subject. [ABSTRACT FROM AUTHOR]

Copyright of CIRCULO de Linguistica Aplicada a la Comunicacion is the property of Universidad Complutense de Madrid and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Estudios Gerenciales is the property of Universidad ICESI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The introduction of new loads to the traditional electrical distribution systems can lead to the overloading in the power equipment. This on the sizing makes the useful life of the power equipment decrease considerably, in addition, the reliability and stability of the system begins to be compromised. Therefore, through the present investigation it is possible to solve the problem of the planning of electrical distribution networks by integrating the possibility of migrating from the concept of traditional electric networks to smart electric networks, the same ones that only electrical distribution systems of robust networks are achieved heterogeneous bidirectional communication. The present work focused on the development of a model capable of locating the distribution transformers in the best sites to satisfy the majority of users of the electrical network and obtain the best topology by applying the theory of graphs In addition, the presented model contemplates the development of a heuristic capable of executing georeferenced planning processes through the management and use of geolocated information from OpenStreetMap through the .osm file that this free platform offers us. The heuristic proposed in the present document is modeled using the Matlab software and to validate the information, the Cymdist software is required. [ABSTRACT FROM AUTHOR]

The Gröbner Basis constitute a central axis in the theory of Computational Algebra. Its versatility and large number of applications have allowed these to be used for research in various branches of mathematics, such as Commutative Algebra, Algebraic Geometry, Graph Theory, Code Theory, Cryptography, to mention only some of them. The present document has an introductory purpose towards the Gröbner basis, taking as reference some of its applications. [ABSTRACT FROM AUTHOR]

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Copyright of Ciencia, Tecnología y Salud is the property of Ciencia, Tecnologia y Salud and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista Espacios is the property of Talleres de Impresos Oma and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Ensayos de Economia is the property of Universidad Nacional de Colombia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The research focused on proposing an educational tool to introduce Graph Theory in teaching mathematics, in 5th year of Highschool of Liceo Bolivariano Mariscal Sucre Cumaná, Sucre state, Venezuela. The tool is proposed as a pedagogical strategy to provide both teachers and students, a different approach to teaching and learning mathematics, in correspondence with the sociocultural context where they live, trying to make visible the multiple applications of mathematics in everyday life. The sample under study consisted of eight (8) teachers and seventy-seven (77) students. Among the conclusions, it is highlighted the fact that despite the lack of knowledge about Graph Theory by students and some teachers, the latter are willing to use the didactic proposal in the development of classroom activity, as a necessary mechanism to help learners to visualize the applicability of mathematics in everyday life events. [ABSTRACT FROM AUTHOR]

In Colombia, public policies about quality of higher education involve student assessment systems as a relevant characteristic. These systems should have clear and transparent institutional policies requiring comprehensive identification of attitudinal and academic conditions about examinee performance. Consequently, on the way of continuous improvement of academic services offered by institutions of higher education, an assessment process adequately technified allowing valid inferences about academic achievement is required. In this sense, the Rasch measurement model of Item Response Theory is a modern alternative to strengthen educational measurement estimating the ability of the student and the difficulty of the item on a comparable scale. Unidimensionality, local independence and internal consistency are assumptions made in Rasch measurement model. Unidimensionality assumption has several definitions, one of them is the occurrence of a dominant factor influencing test performance. Another definition is considered in the present study. Here, unidimensionality was interpreted as scalar and criterial homogeneity for the order relations defined by domination for items and assessed applicants. Graph Theory is an ideal mathematical modelling approach to this assumption inasmuch as represent intangible interactions as required. In order to achieve this, Graph Theory and Item Response Theory were combined to examine the qualifying test for the Basic Mathematics subject at Jorge Tadeo Lozano University as a case study. This test was composed by 45 items divided in three blocks. With several combinations of these blocks, three virtual booklets were obtained each one comprising 30 of them. From the application of June 2011, a test sample of 509 responses chains was obtained. Three data bases were processed one for each booklet, the first spanned 175 responses chains, the second 170 and the third one 164. To begin with the exmination on the Rasch measurement model, the parameters reliability, separation, Cronbach Alpha and item residual correlation were estimated to gauge and determine performance test for getting acceptable values in each booklet applied. Tatsuoka was followed to undertake the path to unidimensionality from Graph Theory gathering a real case experience processed with suitable software. Additionally, the sensitivity of the order relation was verified through: 1) ordering by number of correct responses per item (1I order) and items difficulty (2I order); 2) ordering by number of correct responses per applicant (1E order) and estimated ability (2E order). Furthermore, the linear models were obtained collating these orders. In like manner, three Guttman scales and their adjacency matrices were schematized one for each booklet. Subsequently, the respective graphs were processed and represented using Gephi just as a specialized tool that enables running some algorithms like Force Atlas. Afterwards, the second power of each adjacency matrix was found using Matlab 2014b and domination matrices were calculated for both items and applicants in the aforementioned orders for a total of 12 matrices. Consistency index developed by Cliff was computed for the domination matrices. As a result, moderate consistency was observed. Significant domination for the entries of these matrices was analyzed through McNemar test in order to have an asymmetric dominance relation. Moreover, a reachable matrix was calculated for each one of these significant domination matrices as a limit of a sequence of boolean powers. Finally, dominance hierarchies were illustrated with vertex degrees and compared with student maps by the means of Winsteps 3.73. The combination of Graph Theory and Item Response Theory allowed a deeper comprehension of unidimensionality assumption. Thereupon, universities can optimize their resources offering to applicant differential academic options per individual position in the ability scale. The results can be used to outline advantages for the applicants who can evidence their position in the ability scale and identify the different areas to improve. [ABSTRACT FROM AUTHOR]

Copyright of Analítika: Journal of Statistical Analysis / Revista de Análisis Estadístico is the property of Analitika: Journal of Statistical Analysis / Revista de Analisis Estadistico and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The strong penetration of information and communication technologies have redefined the interaction of human beings. Internet as a medium and social networks as disruptive elements in communication have forced all subjects and political structures to adapt to a digital environment with new rules for interaction and collective participation. This paper analyzes the structure of relationships among political parties in a local government election. Based on graph theory , relationships between players in political communication in the twitter sphere are analyzed. Using the social graph of each political party we found an asymmetric communication that reveals different ways of persuading the electorate. [ABSTRACT FROM AUTHOR]

With the purpose of addressing the several challenges that humanitarian logistics faces, the configuration of the humanitarian aid of Manizales city (Colombia) was identified and graph theory as a component of social network analysis was used. Humanitarian logistics faces these challenges due to adverse circumstances in which it takes place. In particular, coordination between actors has been identified as one of the biggest problems in this field of study. As a result, the overall structure and some particular network characteristics were determined. Also, the three most important actors and the existence of four communities were identified. The low network density was detected as one of the main problems, which constitutes an important aspect to consider in public policy formulation on disaster remediation. [ABSTRACT FROM AUTHOR]

This article studies the problem of locating surveillance cameras in the context of a public transportation system. A network of stops or stations is considered which is interconnected by a set of predetermined bus routes. The studied problem is to choose the set of stations to be monitored by cameras in order to simultaneously optimize two objectives: the expected number of crimes detected by the cameras, and the image quality of the entire surveillance system. Two mathematical models based on integer programming are proposed for this problem, considering multiple periods, budget constraints, and connectivity constraints which ensure that at least a surveillance camera is assigned to one station for each pair of directly connected stations. A comparison of the performance of the proposed mathematical models using a commercial optimizer is performed using a set of randomly generated instances with 20-200 stations. The computational results show the capability of the proposed mathematical models to find optimal solutions and the required computational resources. [ABSTRACT FROM AUTHOR]

This article shows an application of the Petri nets for the establishment of inverse logistics, by means of the reuse. Following this guideline the simulation of the reuse of containers in an ice creams production line comes into question, by means of the study of the dynamic behavior of the process, as well as the validation of its behavior. As a result, stands out the improvement of the reuse in the logistic process of the dairy services enterprise Rafael Freyre of Holguín, Cuba, increasing their benefits, such as productivity and utilities. [ABSTRACT FROM AUTHOR]

The hypothesis that the brain works using glial-neuronal networks that are responsible for sensory, motor and cognitive processes has been proposed in the neuroscience literature. Graph theory offers mathematical models to describe these complex networks from simple abstractions such as nodes and connecting edges. In this work, usign signal processing techniques to the analysis of functional connectivity between neuronal emsembles derived from EEG measurements through theory graph. Procedures for the analysis of connectivity are described, from multichannel record processing and conditioning, computation of wideband power spectral density, determination of connectivity measures between electrodes, and parameter estimation of the resulting complex networks. EEG recordings from fifty subjects were analyzed in intervals before (pre) and during repeated photostimulation (Rph). Based on the statistical significance of the response during Rph, desynchronization/synchronization (D/S) in alfa band, and its wide distribution in corticals areas, the participants were divided into three groups: G1, G2 and G3. The slope D/S in alfa band was significant in 16 of 16 regions (G1), 12 of 16 (G2) and 5 of 16 (G3). The functional connectivity depicted the same trend as these changes, whereas in the delta, theta and beta bands occurred no modifications. D is related to activation and S with inhibition, supporting the hypothesis of alfa-band's participation in the cognitive process of habituation to photostimulation. [ABSTRACT FROM AUTHOR]

The problem under study is to find k node-disjoint paths between two terminals of a network. The network has cost in the links, and the goal is to build k node-disjoint paths at the minimum cost, with the additional requirement that the length of each path must not exceed a fixed positive integer d, called the diameter. This combinatorial problem belongs to the NP-Complete class, and as a consequence there is no exact solution available with polynomial time. In the related literature there are particular solutions to the problem when the diameter is not a constraint, such as Suurballe and Bhandari algorithms. Other authors either work with planar, acyclic graphs or study the case where k = 2. In this work we introduce a GRASP heuristic, named CADILAC, for the general problem. The algorithm combines andomization and adaptive diversity to build paths, and it is inspired by Bhandari and DIMCRA algorithms. The latter was considered to build two link-disjoint paths in a graph with multidimensional costs in the links. Randomization is added to Bhandari' s algorithm during the construction search phase. It also includes some ingredients from DIMCRA. The local search phase has a sub-path replacement strategy to explore the seach space. Finally, we compare the performance of CADILAC versus a Greedy resolution. We remark that Greedy presents lower computational requirements, but CADILAC achieves both feasible and cheaper solutions. [ABSTRACT FROM AUTHOR]

The reconfiguration of distribution electric systems constitutes an optimization problem of the electric power systems operation. The genetic algorithms (GA) present numerous applications in the field of the optimization. The main advantage resides in its relative simplicity to formulate problems mathematically complex. It also has been thought that the methods based on GA are better than the traditional heuristic algorithms in the global optimum obtainment. However, when the GA is applied to the reconfiguration problem appears the necessity of carrying out radiality verifications that recharge their mathematical algorithm notably. The random nature of the variants generation process makes that many of them should be rejected by not fulfilling the connection premises imposed to the problem. In this work a formulation is presented based on certain principles of the graph theory that avoids the inconveniences of the realization of these checkups. [ABSTRACT FROM AUTHOR]

Copyright of Ensayos - Revista de Economía is the property of Ensayos Revista de Economia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista de Ciencias Sociales (13159518) is the property of Revista de Ciencias Sociales de la Universidad del Zulia Venezuela and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An Investment Project Portfolio in an Electric Power System (IPPEPS) is considered in this article as a set of enhancement projects to increase the installed capacity of an Electric Power System (EPS). These enhancement projects can consist of the installed capacity of power plants or transmission lines of the EPS. This paper develops a methodology to improve the IPPEPS. This consists in estimating the time where the investment projects should be carried out, and the amount of average active energy that each investment project must enter to the EPS, in order to improve the economic balance of the electric utility and decrease the forecasted not covered consumption of average active energy. Since the improvement of the IPPEPS falls into an optimization problem, this paper uses the Integer Mixed Simplex Algorithm (IMSA) to solve this problem. The methodology developed in this article uses Monte Carlo simulation to model the randomness of the EPS. This methodology is formulated in pseudocodes and is implemented in a numeric example whose results are analyzed by some statistical tools. [ABSTRACT FROM AUTHOR]

Graph theory offers methodological tools that allow the description of different kinds of interactions, as well as describe their emergent properties such as the conformation of modules. The objective of this study was to detect and visualize modules for a graph constructed from the Neotropical butterfly fauna and their geographic localities using two optimization methods. Depending on the method used, seven to eight modules were obtained, which corresponded in part to the major biogeographic regions proposed. The resultant graph showed communities patterns of reduction in species richness and an increase in isolation toward the periphery; this was true for either the general graph as well as some modules expressing a core-periphery pattern. The potential role of dispersal and the usefulness of graphs to explain the balance between local and regional richness and speciation at the community level are discussed. [ABSTRACT FROM AUTHOR]