Codificación de información mediante códigos de barras

Se presentan en este artículo varios sistemas de codificación de información mediante códigos de barras. En particular se detalla la forma de elaborar el código de barras EAN13, posiblemente el más utilizado en la actualidad, y su relación con otro de los códigos más empleados: el ISBN para la catalogación de libros. Se incluyen y comentan los procesos matemáticos empleados para elaborar tales códigosPeer reviewe

Desarrollo y uso de materiales docentes para la enseñanza de las Matemáticas elaborados mediante software de cálculo numérico y simbólico

Memoria ID12-0216. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2012-2013

eMAT2e: Elaboración de Materiales Matemáticos Electrónicos

Memoria ID-093. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2013-2014

Simulación de la propagación del malware: modelos continuos vs. modelos discretos

La gran mayoría de modelos matemáticos propuestos hasta la fecha para simular la propagación del malware están basados en el uso de ecuaciones diferenciales. Dichos modelos son analizados de manera crítica en este trabajo, determinando las principales deficiencias que presentan y planteando distintas alternativas para su subsanación. En este sentido, se estudia el uso de los autómatas celulares como nuevo paradigma en el que basar los modelos epidemiológicos, proponiendo una alternativa explícita basada en ellos a un reciente modelo continuo.Este trabajo ha sido subvencionado por el Ministerio de Economía y Competitividad bajo el proyecto TUERI (TIN2011-25452) y por la Consejería de Educación de la Junta de Castilla y León

Reversibility of Symmetric Linear Cellular Automata with Radius r = 3

The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius r = 3 and null boundary conditions. The main result obtained is the explicit computation of the local transition functions of the inverse cellular automata. This allows introduction of possible and interesting applications in digital image encryption.This research was funded by Ministerio de Ciencia, Innovación y Universidades (MCIU, Spain), Agencia Estatal de Investigación (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project TIN2017-84844-C2-2-R (MAGERAN) and project SA054G18 supported by Consejería de Educación (Junta de Castilla y León, Spain)

On the Optimal Control of a Malware Propagation Model

An important way considered to control malware epidemic processes is to take into account security measures that are associated to the systems of ordinary differential equations that governs the dynamics of such systems. We can observe two types of control measures: the analysis of the basic reproductive number and the study of control measure functions. The first one is taken at the beginning of the epidemic process and, therefore, we can consider this to be a prevention measure. The second one is taken during the epidemic process. In this work, we use the theory of optimal control that is associated to systems of ordinary equations in order to find a new function to control malware epidemic through time. Specifically, this approach is evaluate on a particular compartmental malware model that considers carrier devices.This research has been partially supported by Ministerio de Ciencia, Innovación y Universidades (MCIU, Spain), Agencia Estatal de Investigación (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project with reference TIN2017-84844-C2-2-R (MAGERAN) and the project with reference SA054G18 (MASEDECID) supported by Consejería de Educación (Junta de Castilla y León, Spain). J.D. Hernández Guillén is supported by University of Salamanca (Spain) and Banco Santander under a doctoral grant

Malware propagation in Wireless Sensor Networks: global models vs Individual-based models

The main goal of this work is to propose a new framework to design a novel family of mathematical models to simulate malware spreading in wireless sensor networks (WSNs). An analysis of the proposed models in the scientific literature reveals that the great majority are global models based on systems of ordinary differential equations such that they do not consider the individual characteristics of the sensors and their local interactions. This is a major drawback when WSNs are considered. Taking into account the main characteristics of WSNs (elements and topologies of network, life cycle of the nodes, etc.) it is shown that individual-based models are more suitable for this purpose than global ones. The main features of this new type of malware propagation models for WSNs are stated

Numerical schemes for general Klein–Gordon equations with Dirichlet and nonlocal boundary conditions

In this work, we address the problem of solving nonlinear general Klein–Gordon equations (nlKGEs). Different fourth- and sixth-order, stable explicit and implicit, finite difference schemes are derived. These new methods can be considered to approximate all type of Klein–Gordon equations (KGEs) including phi-four, forms I, II, and III, sine-Gordon, Liouville, damped Klein–Gordon equations, and many others. These KGEs have a great importance in engineering and theoretical physics.The higher-order methods proposed in this study allow a reduction in the number of nodes, which might also be very interesting when solving multi-dimensional KGEs. We have studied the stability and consistency of the proposed schemes when considering certain smoothness conditions of the solutions. Additionally, both the typical Dirichlet and some nonlocal integral boundary conditions have been studied. Finally, some numerical results are provided to support the theoretical aspects previously considered

Autonomous use of a computer algebra system for learning linear algebra

A Computer Algebra System (CAS) can be defined as mathematical software with numerical, graphic and symbolic capacities. Many studies have addressed the teaching of mathematics in a CAS environment. This paper describes a teaching experience carried out in a linear algebra course, for engineering students, with methodologies adapted to the European Higher Education Area. Generic competences such as self-learning, team work or use of technology have been enhanced through autonomous work of students, who had worked in small groups (2-3 students) using a CAS for solving proposal exercises. The experience was completed with a competition which was announced and promoted between the students with the best grades. They developed a project related to a real problem in science or engineering, where orthogonal transformations are used for modelling and solving the problem. A brief summary of the winner project is included in the paper. The experiment proves that technology provides the students with material for enhancing the apprenticeship and improving the motivation

Smart Buildings IoT Networks Accuracy Evolution Prediction to Improve Their Reliability Using a Lotka–Volterra Ecosystem Model

Internet of Things (IoT) is the paradigm that has largely contributed to the development of smart buildings in our society. This technology makes it possible to monitor all aspects of the smart building and to improve its operation. One of the main challenges encountered by IoT networks is that the the data they collect may be unreliable since IoT devices can lose accuracy for several reasons (sensor wear, sensor aging, poorly constructed buildings, etc.). The aim of our work is to study the evolution of IoT networks over time in smart buildings. The hypothesis we have tested is that, by amplifying the Lotka–Volterra equations as a community of living organisms (an ecosystem model), the reliability of the system and its components can be predicted. This model comprises a set of differential equations that describe the relationship between an IoT network and multiple IoT devices. Based on the Lotka–Volterra model, in this article, we propose a model in which the predators are the non-precision IoT devices and the prey are the precision IoT devices. Furthermore, a third species is introduced, the maintenance staff, which will impact the interaction between both species, helping the prey to survive within the ecosystem. This is the first Lotka–Volterra model that is applied in the field of IoT. Our work establishes a proof of concept in the field and opens a wide spectrum of applications for biology models to be applied in IoT.This paper has been partially supported by the Salamanca Ciudad de Cultura y Saberes Foundation under the Talent Attraction Program (CHROMOSOME project)