How to Perform AMP? Cubic Adjustments for Improving the QoE

[EN] Adaptive Media Playout (AMP) consists of smoothly and dynamically adjusting the media playout rate to recover from undesired (e.g., buffer overflow/underflow or out-of-sync) situations. The existing AMP solutions are mainly characterized by two main aspects. The first one is their goal (e.g., keeping the buffers¿ occupancy into safe ranges or enabling media synchronization). The second one is the criteria that determine the need for triggering the playout adjustments (e.g., buffer fullness or asynchrony levels). This paper instead focuses on a third key aspect, which has not been sufficiently investigated yet: the specific adjustment strategy to be performed. In particular, we propose a novel AMP strategy, called Cubic AMP, which is based on employing a cubic interpolation method to adjust a deviated playout point to a given reference. On the one hand, mathematical analysis and graphical examples show that our proposal provides superior performance than other existing linear and quadratic AMP strategies in terms of the smoothness of the playout curve, while significantly outperforming the quadratic AMP strategy regarding the duration of the adjustment period and without increasing the computational complexity. It has also been proved and discussed that higher-order polynomial interpolation methods are less convenient than cubic ones. On the other hand, the results of subjective tests confirm that our proposal provides better Quality of Experience (QoE) than the other existing AMP strategies.This work has been funded, partially, by the “Fondo Europeo de Desarrollo Regional (FEDER)” and the Spanish Ministry of Economy and Competitiveness, under its R&D&I Support Program, in project with Ref. TEC2013-45492-R.Montagud, M.; Boronat, F.; Roig, B.; Sapena Piera, A. (2017). How to Perform AMP? Cubic Adjustments for Improving the QoE. Computer Communications. 103:61-73. https://doi.org/10.1016/j.comcom.2017.01.017S617310

On completeness in metric spaces and fixed point theorems

[EN] Complete ultrametric spaces constitute a particular class of the so called, recently, G-complete metric spaces. In this paper we characterize a more general class called weak G-complete metric spaces, by means of nested sequences of closed sets. Then, we also state a general fixed point theorem for a self-mapping of a weak G-complete metric space. As a corollary, every asymptotically regular self-mapping of a weak G-Complete metric space has a fixed point.V. Gregori acknowledges the support of the Ministry of Economy and Competitiveness of Spain under Grant MTM2015-64373-P (MINECO/Feder, UE). J.J. Minana acknowledges financial support from the Spanish Ministry of Economy and Competitiveness under Grants TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds, by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by Project Ref. PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears), and by project ROBINS. The latter has received research funding from the EU H2020 framework under GA 779776. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.Gregori Gregori, V.; Miñana, J.; Roig, B.; Sapena Piera, A. (2018). On completeness in metric spaces and fixed point theorems. Results in Mathematics. 73(4):1-13. https://doi.org/10.1007/s00025-018-0896-4113734Bourbaki, N.: Topologie Générale II. Herman, Paris (1974)Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–469 (1969)Browder, F.E., Petryshyn, W.V.: The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Am. Math. Soc. 72, 571–575 (1966)Edelstein, M.: On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, 74–79 (1962)Fang, J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46(1), 107–113 (1992)Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)Gregori, V., Sapena, A.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 245–252 (2002)Gregori, V., Miñana, J.-J., Morillas, S., Sapena, A.: Cauchyness and convergence in fuzzy metric spaces. RACSAM 111(1), 25–37 (2017)Gregori, V., Miñana, J-J., Sapena, A.: On Banach contraction principles in fuzzy metric spaces. Fixed Point Theory (to appear)Kelley, J.: General Topology. Van Nostrand, Princeton (1955)Matkowski, J.: Integrable solutions of functional equations. Dissertationes Mathematicae (Rozprawy Matematyczne) 127, 1–63 (1975)Mihet, D.: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 8431–439 (2004)Steen, L.A., Seebach, J.A.: Counterexamples in Topology, 2nd edn. Springer, Berlin (1978)Tirado, P.: On compactness and G-completeness in fuzzy metric spaces. Iran. J. Fuzzy Syst. 9(4), 151–158 (2012)Tirado, P.: Contraction mappings in fuzzy quasimetric spaces and $$[0,1]$$ [ 0 , 1 ] -fuzzy posets. Fixed Point Theory 13(1), 273–283 (2012)Vasuki, R., Veeramani, P.: Fixed points theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets Syst. 135(3), 415–417 (2003

A Characterization of Strong Completeness in Fuzzy Metric Spaces

[EN] Here, we deal with the concept of fuzzy metric space(X,M,*), due to George and Veeramani. Based on the fuzzy diameter for a subset ofX, we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory.Juan-Jose Minana acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion/Proyecto PGC2018-095709-B-C21, and by Spanish Ministry of Economy and Competitiveness under contract DPI2017-86372-C3-3-R (AEI, FEDER, UE). This work was also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears), and by projects ROBINS and BUGWRIGHT2. These two latest projects have received funding from the European Union's Horizon 2020 research and innovation program under grant agreements Nos. 779776 and 871260, respectively. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.Gregori Gregori, V.; Miñana, J.; Roig, B.; Sapena Piera, A. (2020). A Characterization of Strong Completeness in Fuzzy Metric Spaces. Mathematics. 8(6):1-11. https://doi.org/10.3390/math8060861S11186Menger, K. (1942). Statistical Metrics. Proceedings of the National Academy of Sciences, 28(12), 535-537. doi:10.1073/pnas.28.12.535George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399. doi:10.1016/0165-0114(94)90162-7Gregori, V., & Romaguera, S. (2000). Some properties of fuzzy metric spaces. Fuzzy Sets and Systems, 115(3), 485-489. doi:10.1016/s0165-0114(98)00281-4Gregori, V. (2002). On completion of fuzzy metric spaces. Fuzzy Sets and Systems, 130(3), 399-404. doi:10.1016/s0165-0114(02)00115-xAtanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. doi:10.1016/s0165-0114(86)80034-3Gregori, V., Romaguera, S., & Veeramani, P. (2006). A note on intuitionistic fuzzy metric spaces☆. Chaos, Solitons & Fractals, 28(4), 902-905. doi:10.1016/j.chaos.2005.08.113Gregori, V., & Sapena, A. (2018). Remarks to «on strong intuitionistic fuzzy metrics». Journal of Nonlinear Sciences and Applications, 11(02), 316-322. doi:10.22436/jnsa.011.02.12Abu-Donia, H. M., Atia, H. A., & Khater, O. M. A. (2020). Common fixed point theorems in intuitionistic fuzzy metric spaces and intuitionistic (ϕ,ψ)-contractive mappings. Journal of Nonlinear Sciences and Applications, 13(06), 323-329. doi:10.22436/jnsa.013.06.03Gregori, V., & Miñana, J.-J. (2016). On fuzzy ψ -contractive sequences and fixed point theorems. Fuzzy Sets and Systems, 300, 93-101. doi:10.1016/j.fss.2015.12.010Miheţ, D. (2007). On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets and Systems, 158(8), 915-921. doi:10.1016/j.fss.2006.11.012Wardowski, D. (2013). Fuzzy contractive mappings and fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 222, 108-114. doi:10.1016/j.fss.2013.01.012Gregori, V., Miñana, J.-J., Morillas, S., & Sapena, A. (2016). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111(1), 25-37. doi:10.1007/s13398-015-0272-0Gregori, V., & Miñana, J.-J. (2017). Strong convergence in fuzzy metric spaces. Filomat, 31(6), 1619-1625. doi:10.2298/fil1706619gGrabiec, M. (1988). Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 27(3), 385-389. doi:10.1016/0165-0114(88)90064-4George, A., & Veeramani, P. (1997). On some results of analysis for fuzzy metric spaces. Fuzzy Sets and Systems, 90(3), 365-368. doi:10.1016/s0165-0114(96)00207-2Miheţ, D. (2008). Fuzzy -contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets and Systems, 159(6), 739-744. doi:10.1016/j.fss.2007.07.006Vasuki, R., & Veeramani, P. (2003). Fixed point theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets and Systems, 135(3), 415-417. doi:10.1016/s0165-0114(02)00132-xGregori, V., & Romaguera, S. (2004). Characterizing completable fuzzy metric spaces. Fuzzy Sets and Systems, 144(3), 411-420. doi:10.1016/s0165-0114(03)00161-1Gregori, V., Miñana, J.-J., & Morillas, S. (2012). Some questions in fuzzy metric spaces. Fuzzy Sets and Systems, 204, 71-85. doi:10.1016/j.fss.2011.12.008Ricarte, L. A., & Romaguera, S. (2014). A domain-theoretic approach to fuzzy metric spaces. Topology and its Applications, 163, 149-159. doi:10.1016/j.topol.2013.10.014Gregori, V., López-Crevillén, A., Morillas, S., & Sapena, A. (2009). On convergence in fuzzy metric spaces. Topology and its Applications, 156(18), 3002-3006. doi:10.1016/j.topol.2008.12.043Sherwood, H. (1966). On the completion of probabilistic metric spaces. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 6(1), 62-64. doi:10.1007/bf00531809Shukla, S., Gopal, D., & Sintunavarat, W. (2018). A new class of fuzzy contractive mappings and fixed point theorems. Fuzzy Sets and Systems, 350, 85-94. doi:10.1016/j.fss.2018.02.010Beg, I., Gopal, D., Došenović, T., … Rakić, D. (2018). α-type fuzzy H-contractive mappings in fuzzy metric spaces. Fixed Point Theory, 19(2), 463-474. doi:10.24193/fpt-ro.2018.2.37Zheng, D., & Wang, P. (2019). Meir–Keeler theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 370, 120-128. doi:10.1016/j.fss.2018.08.014Rakić, D., Došenović, T., Mitrović, Z. D., de la Sen, M., & Radenović, S. (2020). Some Fixed Point Theorems of Ćirić Type in Fuzzy Metric Spaces. Mathematics, 8(2), 297. doi:10.3390/math802029

Matlab, matrices y transformaciones geométricas en el plano y en el espacio

Este texto está pensado para la realización de prácticas informáticas matriciales y de geometría para alumnos de primer curso con Matlab u Octave. Aparte de exponer las bases operativas y matriciales, también quiere ayudar a la comprensión de lo que son las transformaciones semejantes con un conjunto ágil y estructurado de comandos. En el primer capítulo realiza una introducción general al entorno de cálculo. En el segundo se tratan las matrices, su operatividad y aplicaciones. En el tercero se realiza una representación de curvas y figuras sencillas en el plano euclídeo utilizando distintos tipos de coordenadas (cartesianas y polares) mientras que en el quinto se realiza en el espacio (en cartesianas, cilíndricas y esféricas). En los capítulos cuarto y sexto se presentan las transformaciones geométricas en el plano y en el espacio euclídeo, respectivamente, desde una perspectiva de cálculo e interpretación geométrica. Finalmente se incluyen las soluciones de los ejercicios de autoevaluación propuestos en cada capítulo.Gregori Gregori, V.; Roig Sala, B. (2021). Matlab, matrices y transformaciones geométricas en el plano y en el espacio. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/172798EDITORIA

The polysemy of the words that children learn over time

Here we study polysemy as a potential learning bias in vocabulary learning in children. We employ a massive set of transcriptions of conversations between children and adults in English, to analyze the evolution of mean polysemy in the words produced by children whose ages range between 10 and 60 months. Our results show that mean polysemy in children increases over time in two phases, i.e. a fast growth till the 31st month followed by a slower tendency towards adult speech. In contrast, no dependency with time is found in adults. This may suggest that children have a preference for non-polysemous words in their early stages of vocabulary acquisition. Our hypothesis is twofold: (a) polysemy is a standalone bias or (b) polysemy is a side-effect of other biases. Interestingly, the bias for low polysemy above weakens when controlling by syntactic category (noun, verb, adjective or adverb). The pattern of the evolution of polysemy suggests that both hypotheses may apply to some extent, and that (b) would originate from a combination of the well-known preference for nouns and the lower polysemy of nouns with respect to other syntactic categories.Peer ReviewedPostprint (author's final draft

Lecciones breves de Estadística

El presente libro es un texto elemental de Estadística concebido para alumnos de primer curso de grados técnicos. En cada capítulo, se encuentran argumentaciones detalladas del contenido con una terminología sencilla y un buen número de ejemplos, seguidos de una colección de ejercicios resueltos y propuestos. Los 6 capítulos que constituyen esta obra son: estadística descriptiva, distribuciones bidimensionales, probabilidad, variables aleatorias, distribuciones discretas y distribuciones continuas. La ausencia de demostraciones, en un sentido estricto, permite una lectura fluida del texto y que el alumno afronte el aprendizaje siguiendo un proceso inductivo natural. No obstante, la redacción matemática del texto es rigurosa en la exposición. Para la comprensión del libro solo se requieren conceptos matemáticos de bachilleratoEstruch Miñana, C.; Gregori Gregori, V.; Roig Sala, B.; Sapena Piera, A. (2022). Lecciones breves de Estadística. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/184936EDITORIA

Reforzar la enseñanza de las matemáticas desde el primer curso de grado con proyectos

[EN] The way to build mathematical knowledge of a scientist / engineer differs from that corresponding to the student who accesses a degree in mathematics or other sciences. Learning based on the process of establishing, analyze and validate mathematical models allows the effective acquisition of math skills. In addition, activities based on mathematical modeling can be motivating elements in the teaching / learning process, arousing student interest to cognitive basis on which fundamental mathematical concepts are developed in the mathematical training of future scientist or engineer.[ES] La manera de construir el conocimiento matemático de un científico/ingeniero difiere de la que corresponde al estudiante que accede a un grado en matemáticas o en otras ciencias. El aprendizaje en base al proceso de establecer, analizar y validar modelos matemáticos permite la adquisición efectiva de competencias matemáticas. Pero además, las actividades basadas en la modelización matemática pueden constituir elementos motivadores en el proceso de enseñanza/aprendizaje, despertando el interés del alumno hacia bases cognitivas sobre las cuáles se desarrollan conceptos matemáticos fundamentales en la formación matemática del futuro científico o ingeniero.Boigues Planes, FJ.; Estruch, VD.; Vidal Meló, A.; Roig, B. (2014). Reforzar la enseñanza de las matemáticas desde el primer curso de grado con proyectos. Editorial Universitat Politècnica de València. 741-752. http://hdl.handle.net/10251/168744S74175

Un modelo de transmisión de plagas para la enseñanza del álgebra lineal en el contexto de estudios en ciencias ambientales

[EN] Applied Mathematics appears as a basic subject in the curricula of degree titles within the European Higher Education Area. This fact is not directly or strictly linked to the new structure, but the need to enhance aspects like the teaching in context or to use mathematical modelling to improve educational performance is generally accepted. We present a model of transmission of pests, for students of the first year degree in Environmental Sciences, as a motivating element that also integrates many concepts and topics that are discussed in Linear Algebra in a meaningful environment of mathematics. For the instrumental genesis of the model, the program MatlabQc is used. The actual results obtained in the classroom indicate that the introduction of modelling in the teaching of Applied Mathematics reinforces the perception of students in the sense that mathematics is useful in addressing other disciplines.[ES] La Matemática Aplicada aparece como materia básica en los planes de estudio de los títulos de Grado en el marco del Espacio Europeo de Educación Superior. Aunque el hecho no esté directa y estrictamente ligado a la nueva estructura de las enseñanzas, por diversas razones se impone la dinámica de potenciar aspectos tales como la enseñanza en contexto o recurrir a la modelización matemática desde perspectivas de mejora del rendimiento docente. En este trabajo presentamos un modelo de transmisión de plagas, dirigido a estudiantes de primer curso del Grado en Ciencias Ambientales, como elemento motivador que, además, integra numerosas nociones y tópicos que se estudian en el Algebra Lineal dentro de un entorno significativo de las matemáticas. Para la génesis instrumental del modelo se recurre al programa MatlabQc ). Los resultados concretos obtenidos en el aula indican que la introducción de la modelización en la enseñanza de la Matemática Aplicada refuerza el que los estudiantes perciban que las matemáticas son útiles para afrontar otras disciplinas.Boigues, FJ.; Estruch, VD.; Roig, B.; Vidal, A. (2011). Un modelo de transmisión de plagas para la enseñanza del álgebra lineal en el contexto de estudios en ciencias ambientales. Modelling in Science Education and Learning. 4:105-117. doi:10.4995/msel.2011.3058SWORD1051174Amelkin, V. 1987. Ecuaciones Diferenciales Aplicadas a la Práctica. Editorial Mir Moscu.Artigue, M., Batanero C. y Kent, P.(2007), Mathematics thinking and learning at post secondary level. In Fr. Lester (ed.), Second Handbook of research on Mathematics Teaching and learning. NCTM-IAP; Charlotte, NC. pp. 1011-1045.Camacho, M., Depool, R. y Garbin, S. (2008). Integral definida en diversos contextos. Un estudio de casos. Educación Matemática, 20(3), pp. 33-57.Drijvers, P., Kieran C. y Mariotti, M. (2010) Integrating Technology into Mathematics Education: Theoretical Perspectives. In C. Hoyles y L.B. Lagrange (eds.), Mathematics Education, pp. 89-132. New York: Springer.Gómez-Chacón, I.M, 2000. Matemática Emocional. Los efectos en el aprendizaje matemático. Ed. Narcea, Madrid.Shannon, R., & Johannes, J. D. (1976). Systems Simulation: The Art and Science. IEEE Transactions on Systems, Man, and Cybernetics, SMC-6(10), 723-724. doi:10.1109/tsmc.1976.430943

Una propuesta de Recorrido de Estudio e Investigación (REI): Diseño, simulación y decisión de una estrategia de pesca sostenible

[EN] In ecology and fisheries management, growth models are very important. We present a proposal of a Research and Study Course (RSI) for the subject Mathematics of first course of the Environmental Science Degree in the Polytechnic School of Gandia, in which modeling is used to propose a sustainable policy for fisheries from data collected during initial growth period of close season. The aim is: i) Establishing a mathematical model for the evolution of the population throughout the study period (close season). ii) Fixed a minimum population to ensure a sustainable development of fisheries resources, proposing a fishing quota that can be maintained over the years.[ES] En ecología y en gestión pesquera son muy importantes los modelos de crecimiento. Se plantea una propuesta de Recorrido de Estudio e Investigación (REI) para que en la asignatura Matemáticas, los estudiantes de primero del Grado en Ciencias Ambientales de la Escuela Politécnica Superior de Gandia utilicen la modelización para proponer una política de pesca sostenible a partir de datos de crecimiento iniciales recogidos durante cierto periodo de parada biológica. Se pretende: i) Establecer un modelo matemático para la evolución de la población a lo largo del periodo de estudio (parada biológica). ii) Fijada una población mínima que asegure una evolución sostenible de los recursos pesqueros, proponer una cuota de pesca que pueda mantenerse a lo largo de los años.Boigues Planes, FJ.; Estruch Fuster, VD.; Roig, B.; Vidal Meló, A. (2013). Una propuesta de Recorrido de Estudio e Investigación (REI): Diseño, simulación y decisión de una estrategia de pesca sostenible. Modelling in Science Education and Learning. 6(2):5-19. https://doi.org/10.4995/msel.2013.1851SWORD51962B. Barquero. Els Recorreguts d'Estudi i Investigació (REI) i l'ensenyament de la modelització matemática en el primer curs universitari de Ciències. Trabajo de Investigación. Departament de Matemátiques. Universitat Autónoma de Barcelona. (2006).Boigues, F. J., Estruch, V. D., Roig, B., & Vidal, A. (2011). Un modelo de transmisión de plagas para la enseñanza del álgebra lineal en el contexto de estudios en ciencias ambientales. Modelling in Science Education and Learning, 4, 105. doi:10.4995/msel.2011.3058R. Cabassut, N. G. Mousoulides. Theoretical Considerations for Designing and Implementing a Teacher Training Course on Mathematical Modeling: Insights from a French-Cypriot Comparison. Cyprus and France Research in mathematics education. Lefkosia (2009).Y. Chevallard. Steps towards a new epistemology in mathematics education. In BOSCH, M. (ed.) Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (CERME 4), 21-30 (2006)

A gymkhana to discover and generate curves in a cooperative work

[EN] The student who access the University understands a curve as a function represented by an equality involving the Cartesian variables x and y. But he does not know another great set of curves such as those described by parametric equations and polar coordinates. We show an experience developed in two consecutive courses in the first course of a bachelor's degree, which allows the students to discover and create many curves in parametric or polar representation, working in group. Also the experience facilitate the students to achieve several generic skills.Vidal Meló, A.; Roig Sala, B.; Estruch Fuster, VD.; Boigues Planes, FJ. (2014). A gymkhana to discover and generate curves in a cooperative work. Multidisciplinary Journal for Education, Social and Technological Sciences. 1(1):53-68. doi:10.4995/muse.2014.2192SWORD536811Alamar, M., Roig, B., Vidal, A. (2008). Fonaments Matemàtics: pràctiques de laboratori, Valencia: UPV.Bradley, G.L. and Smith, K.J. (1998). Cálculo de varias variables (vol. 2). Ed. Prentice Hall.Edwards and Penney. (1996). Cálculo con geometría analítica. Ed. Prentice Hall.Fallows, S. and Steven, C. (2000). Integrating key skills in higher education- Employability, transferable skills and learning for life. London: Kogan Page.Larson, R. and Edwards, B.H. (2006). Cálculo (vol. 2). McGraw Hill.Larson, R. and Edwards, B.H. (2010). Cálculo 2 de varias variables. McGraw Hill.Larson, R., Hostetler, R.P., Edwards, B.H. (2006). Cálculo II. PirámideStewart, J. (1999). Cálculo multivariable. ThomsonStewart, J. (2003). Cálculo de una variable. Thomson.Stewart, J. (2005). Cálculo: conceptos y contextos. ThomsonThomas and Finney. (1999). Varias variables. Addison Wesley Longman