Crosscutting, what is and what is not? A Formal definition based on a Crosscutting Pattern

Crosscutting is usually described in terms of scattering and tangling. However, the distinction between these concepts is vague, which could lead to ambiguous statements. Sometimes, precise definitions are required, e.g. for the formal identification of crosscutting concerns. We propose a conceptual framework for formalizing these concepts based on a crosscutting pattern that shows the mapping between elements at two levels, e.g. concerns and representations of concerns. The definitions of the concepts are formalized in terms of linear algebra, and visualized with matrices and matrix operations. In this way, crosscutting can be clearly distinguished from scattering and tangling. Using linear algebra, we demonstrate that our definition generalizes other definitions of crosscutting as described by Masuhara & Kiczales [21] and Tonella and Ceccato [28]. The framework can be applied across several refinement levels assuring traceability of crosscutting concerns. Usability of the framework is illustrated by means of applying it to several areas such as change impact analysis, identification of crosscutting at early phases of software development and in the area of model driven software development

Multiplicative structures of hypercyclic functions for convolution operators

In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given entire function of subexponential type. A certain stability under multiplication is also shown for compositional hypercyclicity on complex domains.Comment: 12 page

Corrected Evolutive Kendall's tau Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists

[EN] Mathematical analysis of rankings is essential for a wide range of scientific, public, and industrial applications (e.g., group decision-making, organizational methods, R&D sponsorship, recommender systems, voter systems, sports competitions, grant proposals rankings, web searchers, Internet streaming-on-demand media providers, etc.). Recently, some methods for incomplete aggregate rankings (rankings in which not all the elements are ranked) with ties, based on the classic Kendall's tau coefficient, have been presented. We are interested in ordinal rankings (that is, we can order the elements to be the first, the second, etc.) allowing ties between the elements (e.g., two elements may be in the first position). We extend a previous coefficient for comparing a series of complete rankings with ties to two new coefficients for comparing a series of incomplete rankings with ties. We make use of the newest definitions of Kendall's tau extensions. We also offer a theoretical result to interpret these coefficients in terms of the type of interactions that the elements of two consecutive rankings may show (e.g., they preserve their positions, cross their positions, and they are tied in one ranking but untied in the other ranking, etc.). We give some small examples to illustrate all the newly presented parameters and coefficients. We also apply our coefficients to compare some series of Spotify charts, both Top 200 and Viral 50, showing the applicability and utility of the proposed measures.This research was funded by the Spanish Government, Ministerio de Economia y Competividad, grant number MTM2016-75963-P.Pedroche Sánchez, F.; Conejero, JA. (2020). Corrected Evolutive Kendall's tau Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists. Mathematics. 8(10):1-30. https://doi.org/10.3390/math8101828S130810Diaconis, P., & Graham, R. L. (1977). Spearman’s Footrule as a Measure of Disarray. Journal of the Royal Statistical Society: Series B (Methodological), 39(2), 262-268. doi:10.1111/j.2517-6161.1977.tb01624.xMoreno-Centeno, E., & Escobedo, A. R. (2015). Axiomatic aggregation of incomplete rankings. IIE Transactions, 48(6), 475-488. doi:10.1080/0740817x.2015.1109737Criado, R., García, E., Pedroche, F., & Romance, M. (2013). A new method for comparing rankings through complex networks: Model and analysis of competitiveness of major European soccer leagues. Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(4), 043114. doi:10.1063/1.4826446Fortune 500https://fortune.com/fortune500/Academic Ranking of World Universities ARWU 2020http://www.shanghairanking.com/ARWU2020.htmlCWTS Leiden Ranking 2020https://www.leidenranking.com/ranking/2020/listThe Hot 100https://www.billboard.com/charts/hot-100Fagin, R., Kumar, R., Mahdian, M., Sivakumar, D., & Vee, E. (2006). Comparing Partial Rankings. SIAM Journal on Discrete Mathematics, 20(3), 628-648. doi:10.1137/05063088xCook, W. D., Kress, M., & Seiford, L. M. (1986). An axiomatic approach to distance on partial orderings. RAIRO - Operations Research, 20(2), 115-122. doi:10.1051/ro/1986200201151Yoo, Y., Escobedo, A. R., & Skolfield, J. K. (2020). A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings. European Journal of Operational Research, 285(3), 1025-1041. doi:10.1016/j.ejor.2020.02.027Pedroche, F., Criado, R., García, E., Romance, M., & Sánchez, V. E. (2015). Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index). Networks and Heterogeneous Media, 10(1), 101-125. doi:10.3934/nhm.2015.10.101Criado, R., García, E., Pedroche, F., & Romance, M. (2016). On graphs associated to sets of rankings. Journal of Computational and Applied Mathematics, 291, 497-508. doi:10.1016/j.cam.2015.03.009KENDALL, M. G. (1938). A NEW MEASURE OF RANK CORRELATION. Biometrika, 30(1-2), 81-93. doi:10.1093/biomet/30.1-2.81Kendall, M. G., & Smith, B. B. (1939). The Problem of $m$ Rankings. The Annals of Mathematical Statistics, 10(3), 275-287. doi:10.1214/aoms/1177732186Bogart, K. P. (1973). Preference structures I: Distances between transitive preference relations†. The Journal of Mathematical Sociology, 3(1), 49-67. doi:10.1080/0022250x.1973.9989823Bogart, K. P. (1975). Preference Structures. II: Distances Between Asymmetric Relations. SIAM Journal on Applied Mathematics, 29(2), 254-262. doi:10.1137/0129023Cicirello, V. (2020). Kendall tau sequence distance: Extending Kendall tau from ranks to sequences. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems, 7(23), 163925. doi:10.4108/eai.13-7-2018.163925Armstrong, R. A. (2019). Should Pearson’s correlation coefficient be avoided? Ophthalmic and Physiological Optics, 39(5), 316-327. doi:10.1111/opo.12636Redman, W. (2019). An O(n) method of calculating Kendall correlations of spike trains. PLOS ONE, 14(2), e0212190. doi:10.1371/journal.pone.0212190Pihur, V., Datta, S., & Datta, S. (2009). RankAggreg, an R package for weighted rank aggregation. BMC Bioinformatics, 10(1). doi:10.1186/1471-2105-10-62Pnueli, A., Lempel, A., & Even, S. (1971). Transitive Orientation of Graphs and Identification of Permutation Graphs. Canadian Journal of Mathematics, 23(1), 160-175. doi:10.4153/cjm-1971-016-5Gervacio, S. V., Rapanut, T. A., & Ramos, P. C. F. (2013). Characterization and Construction of Permutation Graphs. Open Journal of Discrete Mathematics, 03(01), 33-38. doi:10.4236/ojdm.2013.31007Golumbic, M. C., Rotem, D., & Urrutia, J. (1983). Comparability graphs and intersection graphs. Discrete Mathematics, 43(1), 37-46. doi:10.1016/0012-365x(83)90019-5Emond, E. J., & Mason, D. W. (2002). A new rank correlation coefficient with application to the consensus ranking problem. Journal of Multi-Criteria Decision Analysis, 11(1), 17-28. doi:10.1002/mcda.313Spotify Reports Second Quarter 2020 Earningshttps://newsroom.spotify.com/2020-07-29/spotify-reports-second-quarter-2020-earningsCompany infohttps://newsroom.spotify.com/company-info/Bussines Wirehttps://www.businesswire.com/news/home/20200429005216/en/Swanson, K. (2013). A Case Study on Spotify: Exploring Perceptions of the Music Streaming Service. Journal of the Music and Entertainment Industry Educators Association, 13(1), 207-230. doi:10.25101/13.10Microsoft Retires Groove Music Service, Partners with Spotifyhttps://www.theverge.com/2017/10/2/16401898/microsoft-groove-music-pass-discontinued-spotify-partnerSpotify Launches on PlayStation Music Todayhttps://blog.playstation.com/2015/03/30/spotify-launches-on-playstation-music-today/You Can Now Share Music from Spotify to Facebook Storieshttps://techcrunch.com/2019/08/30/you-can-now-share-music-from-spotify-to-facebook-storiesMähler, R., & Vonderau, P. (2017). Studying Ad Targeting with Digital Methods: The Case of Spotify. Culture Unbound, 9(2), 212-221. doi:10.3384/cu.2000.1525.1792212Analyzing Spotify Data. Exploring the Possibilities of User Data from a Scientific and Business Perspective. (Supervised by Sandjai Bhulai). Report from Vrije Universiteit Amsterdamhttps://www.math.vu.nl/~sbhulai/papers/paper-vandenhoven.pdfGreenberg, D. M., Kosinski, M., Stillwell, D. J., Monteiro, B. L., Levitin, D. J., & Rentfrow, P. J. (2016). The Song Is You. Social Psychological and Personality Science, 7(6), 597-605. doi:10.1177/1948550616641473Spotify Charts Regionalhttps://spotifycharts.com/regionalSpotify Charts Launch Globally, Showcase 50 Most Listened to and Most Viral Tracks Weeklyhttps://www.engadget.com/2013-05-21-spotify-charts-launch.htmlSpotify says its Viral-50 chart reaches the parts other charts don’thttps://musically.com/2014/07/15/spotify-says-its-viral-50-chart-reaches-the-parts-other-charts-dont/Spotify Reveals New Viral 50 Charthttps://www.musicweek.com/news/read/spotify-launches-the-viral-50-chart/059027Reports Results for Fiscal Second Quarter Ended 31 March 2020https://www.wmg.com/news/warner-music-group-corp-reports-results-fiscal-second-quarter-ended-march-31-2020-34751COVID-19’s Effect on the Global Music Business, Part 1: Genrehttps://blog.chartmetric.com/covid-19-effect-on-the-global-music-business-part-1-genre/Top 200https://spotifycharts.com/regional/global/weeklySpotify Chartshttps://spotifycharts.com/viral

Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation

[EN] The phenomenon of chaos has been exhibited in mathematical nonlinear models that describe traffic flows, see, for instance (Li and Gao in Modern Phys Lett B 18(26-27):1395-1402, 2004; Li in Phys. D Nonlinear Phenom 207(1-2):41-51, 2005). At microscopic level, Devaney chaos and distributional chaos have been exhibited for some car-following models, such as the quick-thinking-driver model and the forward and backward control model (Barrachina et al. in 2015; Conejero et al. in Semigroup Forum, 2015). We present here the existence of chaos for the macroscopic model given by the Lighthill Whitham Richards equation.The authors are supported by MEC Project MTM2013-47093-P. The second and third authors are supported by GVA, Project PROMETEOII/2013/013Conejero, JA.; Martínez Jiménez, F.; Peris Manguillot, A.; Ródenas Escribá, FDA. (2016). Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation. Nonlinear Dynamics. 84(1):127-133. https://doi.org/10.1007/s11071-015-2245-4S127133841Albanese, A.A., Barrachina, X., Mangino, E.M., Peris, A.: Distributional chaos for strongly continuous semigroups of operators. Commun. Pure Appl. Anal. 12(5), 2069–2082 (2013)Aroza, J., Peris, A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18(4), 647–655 (2012)Banasiak, J., Lachowicz, M.: Chaos for a class of linear kinetic models. C. R. Acad. Sci. Paris Sér. II 329, 439–444 (2001)Banasiak, J., Lachowicz, M.: Topological chaos for birth-and-death-type models with proliferation. Math. Models Methods Appl. Sci. 12(6), 755–775 (2002)Banasiak, J., Moszyński, M.: A generalization of Desch–Schappacher–Webb criteria for chaos. Discrete Contin. Dyn. Syst. 12(5), 959–972 (2005)Banasiak, J., Moszyński, M.: Dynamics of birth-and-death processes with proliferation—stability and chaos. Discrete Contin. Dyn. Syst. 29(1), 67–79 (2011)Barrachina, X., Conejero, J.A.: Devaney chaos and distributional chaos in the solution of certain partial differential equations. Abstr. Appl. Anal. Art. ID 457019, 11 (2012)Barrachina, X., Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Distributional chaos for the forward and backward control traffic model (2015, preprint)Bayart, F., Matheron, É.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bayart, F., Matheron, É.: Mixing operators and small subsets of the circle. J Reine Angew. Math. (2015, to appear)Bermúdez, T., Bonilla, A., Conejero, J.A., Peris, A.: Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Stud. Math. 170(1), 57–75 (2005)Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li-Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373(1), 83–93 (2011)Bernardes Jr, N.C., Bonilla, A., Müller, V., Peris, A.: Distributional chaos for linear operators. J. Funct. Anal. 265(9), 2143–2163 (2013)Brackstone, M., McDonald, M.: Car-following: a historical review. Transp. Res. Part F Traffic Psychol. Behav. 2(4), 181–196 (1999)Conejero, J.A., Lizama, C., Rodenas, F.: Chaotic behaviour of the solutions of the Moore–Gibson–Thompson equation. Appl. Math. Inf. Sci. 9(5), 1–6 (2015)Conejero, J.A., Mangino, E.M.: Hypercyclic semigroups generated by Ornstein-Uhlenbeck operators. Mediterr. J. Math. 7(1), 101–109 (2010)Conejero, J.A., Müller, V., Peris, A.: Hypercyclic behaviour of operators in a hypercyclic $$C_0$$ C 0 -semigroup. J. Funct. Anal. 244, 342–348 (2007)Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Linear chaos for the quick-thinking-driver model. 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Nachr. 188, 169–171 (1997)Li, K., Gao, Z.: Nonlinear dynamics analysis of traffic time series. Modern Phys. Lett. B 18(26–27), 1395–1402 (2004)Li, T.: Nonlinear dynamics of traffic jams. Phys. D Nonlinear Phenom. 207(1–2), 41–51 (2005)Lustri, C.: Continuum Modelling of Traffic Flow. Special Topic Report. Oxford University, Oxford (2010)Lighthill, M.J., Whitham, G.B.: On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A. 229, 317–345 (1955)Maerivoet, S., De Moor, B.: Cellular automata models of road traffic. Phys. Rep. 419(1), 1–64 (2005)Mangino, E.M., Peris, A.: Frequently hypercyclic semigroups. Stud. Math. 202(3), 227–242 (2011)Murillo-Arcila, M., Peris, A.: Strong mixing measures for linear operators and frequent hypercyclicity. J. Math. Anal. Appl. 398, 462–465 (2013)Murillo-Arcila, M., Peris, A.: Strong mixing measures for $$C_0$$ C 0 -semigroups. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. 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A freshmen mentoring program at the Universitat Politècnica de València over the period 2000-2010

Purpose: We quantify the dedication of mentors and mentees in a double-mentor program for freshmen. We also analyze the fulfillment of the expectations of all the participants and the utility of each mentor during the meetings. Design/methodology/approach: A questionnaire addressed to the participants was designed and took to all of them. Findings: We see that the mentees are highly satisfied with the mentoring program. Despite of mentors want mentees to participate more intensively in the program, mentees consider that their participation in the program is sufficient. Student and teacher mentors agree that freshmen could take more profit of the program. We also observe that the student mentor is slightly more implicated in the program than the teacher mentor. Research limitations/implications: Our results depend on the opinion of the mentors and the mentees. It would be fruitful to know the opinion of the freshmen who are not enrolled in the program. Practical implications: Our research confirms the validity of the system. We hope that our conclusions will be fruitful for other institutions that would like to implement a double-mentor program for freshmen. Originality/value: Many mentoring programs have been designed basing on a big brother/sister system. We analyze the development of a double-mentor program. The last law concerning university students, approved in Spain in 2011, indicates that mentoring programs should be designed in the frame of every degree, and they should be conducted by teachers and by technical staff. With our formula, both approaches are combined.Peer Reviewe

Dynamics of multidimensional Césaro operators

[EN] We study the dynamics of the multi-dimensional Cesar degrees integral operator on L-P (I-n), for I the unit interval, 1 = 2, that is defined as C(f)(x(1),...,x(n)) = 1/x(1)x(2)...x(n) integral(x1)(0) ... integral(x1)(0) f(u(1),...,u(n))du(1)...du(n) for f is an element of L-p(I-n). This operator is already known to be bounded. As a consequence of the Eigenvalue Criterion, we show that it is hypercyclic as well. Moreover, we also prove that it is Devaney chaotic and frequently hypercyclic.The first author was supported by MEC, grant MTM201675963-P. The third author was supported by grant MTM2015-65825-P.Conejero, JA.; Mundayadan, A.; Seoane-Sepúlveda, JB. (2019). Dynamics of multidimensional Césaro operators. Bulletin of the Belgian Mathematical Society Simon Stevin. 26(1):11-20. http://hdl.handle.net/10251/159145S112026

Shock wave formation in compliant arteries

[EN] We focus on the problem of shock wave formation in a model of blood flow along an elastic artery. We analyze the conditions under which this phenomenon can appear and we provide an estimation of the instant of shock formation. Numerical simulations of the model have been conducted using the Discontinuous Galerkin Finite Element Method. The results are consistent with certain phenomena observed by practitioners in patients with arteriopathies, and they could predict the possible formation of a shock wave in the aorta.C. Rodero and I. Garcia-Fernandez are supported by Projects TIN2014-59932-JIN (MINECO/FEDER, EU) and CIB16-BM019 (IISCII). J. A. Conejero is supported by MEC, Project MTM2016-75963-P.Rodero, C.; Conejero, JA.; García-Fernández, I. (2019). Shock wave formation in compliant arteries. Evolution Equations and Control Theory (Online). 8(1):221-230. https://doi.org/10.3934/eect.2019012S2212308

Fractional vs. ordinary control systems: What does the fractional derivative provide?

[EN] The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models.Conejero, JA.; Franceschi, J.; Picó-Marco, E. (2022). Fractional vs. ordinary control systems: What does the fractional derivative provide?. Mathematics. 10(15):1-18. https://doi.org/10.3390/math10152719118101