The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible

Linear chaos for the Quick-Thinking-Driver model

The final publication is available at Springer via http://dx.doi.org/10.1007/s00233-015-9704-6In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car).Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.The authors were supported by a grant from the FPU program of MEC and MEC Project MTM2013-47093-P.Conejero, JA.; Murillo Arcila, M.; Seoane-Sepúlveda, JB. (2016). Linear chaos for the Quick-Thinking-Driver model. Semigroup Forum. 92(2):486-493. https://doi.org/10.1007/s00233-015-9704-6S486493922Aroza, 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 Série 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., Lachowicz, M., Moszyński, M.: Topological chaos: when topology meets medicine. Appl. Math. Lett. 16(3), 303–308 (2003)Banasiak, J., Moszyński, M.: A generalization of Desch–Schappacher–Webb criteria for chaos. Discret. Contin. Dyn. Syst. 12(5), 959–972 (2005)Banasiak, J., Moszyński, M.: Dynamics of birth-and-death processes with proliferation–stability and chaos. Discret. Contin. Dyn. Syst. 29(1), 67–79 (2011)Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s definition of chaos. Am. Math. Mon. 99(4), 332–334 (1992)Barrachina, X., Conejero, J.A.: Devaney chaos and distributional chaos in the solution of certain partial differential equations. Abstr. Appl. Anal. 457,019, 11 (2012)Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li-Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373(1), 83–93 (2011)Brackstone, M., McDonald, M.: Car-following: a historical review. Transp. Res. Part F 2(4), 181–196 (1999)Brzeźniak, Z., Dawidowicz, A.L.: On periodic solutions to the von Foerster–Lasota equation. Semigroup Forum 78, 118–137 (2009)Chandler, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Op. Res. 6, 165–184 (1958)Chung, C.C., Gartner, N.: Acceleration noise as a measure of effectiveness in the operation of traffic control systems. Operations Research Center. Massachusetts Institute of Technology. Cambridge (1973)CNN (2014) Driverless car tech gets serious at CES. http://edition.cnn.com/2014/01/09/tech/innovation/self-driving-cars-ces/ . Accessed 7 Apr 2014Conejero, J.A., Rodenas, F., Trujillo, M.: Chaos for the hyperbolic bioheat equation. Discret. Contin. Dyn. Syst. 35(2), 653–668 (2015)DARPA Grand Challenge. http://en.wikipedia.org/wiki/2005_DARPA_Grand_Challenge#2005_Grand_Challengede Laubenfels, R., Emamirad, H., Protopopescu, V.: Linear chaos and approximation. J. Approx. Theory 105(1), 176–187 (2000)Desch, W., Schappacher, W., Webb, G.F.: Hypercyclic and chaotic semigroups of linear operators. Ergod. Theory Dyn. Syst. 17(4), 793–819 (1997)El Mourchid, S.: The imaginary point spectrum and hypercyclicity. Semigroup Forum 73(2), 313–316 (2006)El Mourchid, S., Metafune, G., Rhandi, A., Voigt, J.: On the chaotic behaviour of size structured cell populations. J. Math. Anal. Appl. 339(2), 918–924 (2008)El Mourchid, S., Rhandi, A., Vogt, H., Voigt, J.: A sharp condition for the chaotic behaviour of a size structured cell population. Differ. Integral Equ. 22(7–8), 797–800 (2009)Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics, vol. 194. Springer, New York, 2000. With contributions by Brendle S., Campiti M., Hahn T., Metafune G., Nickel G., Pallara D., Perazzoli C., Rhandi A., Romanelli S., and Schnaubelt RGodefroy, G., Shapiro, J.H.: Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98(2), 229–269 (1991)Greenshields, B.D.: The photographic method of studying traffic behavior. In: Proceedings of the 13th Annual Meeting of the Highway Research Board, pp. 382–399 (1934)Greenshields, B.D.: A study of traffic capacity. In: Proceedings of the 14th Annual Meeting of the Highway Research Board, pp. 448–477 (1935)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear Chaos. Universitext. Springer, London (2011)Herman, R., Montroll, E.W., Potts, R.B., Rothery, R.W.: Traffic dynamics: analysis of stability in car following. Op. Res. 7, 86–106 (1959)Helly, W.: Simulation of Bottleneckes in Single-Lane Traffic Flow. Research Laboratories, General Motors. Elsevier, New York (1953)Li, T.: Nonlinear dynamics of traffic jams. Phys. D 207(1–2), 41–51 (2005)Lo, S.C., Cho, H.J.: Chaos and control of discrete dynamic traffic model. J. Franklin Inst. 342(7), 839–851 (2005)Martínez-Giménez, F., Oprocha, P., Peris, A.: Distributional chaos for backward shifts. J. Math. Anal. Appl. 351(2), 607–615 (2009)Pipes, L.A.: An operational analysis of traffic dynamics. J. Appl. Phys. 24, 274–281 (1953

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. Semigroup Forum (2015). doi: 10.1007/s00233-015-9704-6Conejero, J.A., Peris, A., Trujillo, M.: Chaotic asymptotic behavior of the hyperbolic heat transfer equation solutions. Int. J. Bifur. Chaos Appl. Sci. Eng. 20(9), 2943–2947 (2010)Conejero, J.A., Rodenas, F., Trujillo, M.: Chaos for the hyperbolic bioheat equation. Discrete Contin. Dyn. Syst. 35(2), 653–668 (2015)Desch, W., Schappacher, W., Webb, G.F.: Hypercyclic and chaotic semigroups of linear operators. Ergod. Theory Dyn. Syst. 17(4), 793–819 (1997)Engel, K.-J., Nagel, R.: One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194. Springer, New York (2000). With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. SchnaubeltGrosse-Erdmann, K.-G., Peris Manguillot, A.: Linear Chaos. Universitext. Springer, London (2011)Herzog, G.: On a universality of the heat equation. Math. 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. RACSAM 109(1), 101–115 (2015)Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44. Springer, New York (1983)Protopopescu, V., Azmy, Y.Y.: Topological chaos for a class of linear models. Math. Models Methods Appl. Sci. 2(1), 79–90 (1992)Richards, P.I.: Shock waves on the highway. Oper. Res. 4, 42–51 (1956

Gendering subtitles? Evidence from a Netflix corpus

We start from the observation that language pairs like Polish and English display an intriguing asymmetry: Polish has the structural resources to express grammatical gender in nouns while English predominantly leaves these under-determined. Therefore, a speaker of English can conventionally say “I am a nurse” irrespective of the speaker’s gender, while in Polish male/female/non-binary speakers would likely use variable forms. This asymmetry leads to nuanced translation choices which this paper aims to explore. Based on a newly compiled corpus of English-to-Polish Netflix subtitles – amounting to 3.5 million words – we examine how 113 different occupation-related feminatives are deployed by translators. We address three main research questions (RQ1-RQ3). RQ1 is about the frequency of the relevant feminatives in our corpus. RQ2 deals with how the feminatives are distributed across the 284 productions analysed in the dataset. Finally, RQ3 addresses the relationship between the frequency of feminatives in Netflix subtitles and the acceptability of these feminatives, as judged by speakers.Partimos de la observación de que pares de lenguas como el polaco y el inglés muestran una asimetría muy atractiva: el polaco tiene los recursos estructurales para expresar el género gramatical en los sustantivos, mientras que el inglés los deja predominantemente indeterminados. Por lo tanto, un hablante de inglés puede decir convencionalmente «I am a nurse» (soy enfermera) independientemente del género del hablante, mientras que en polaco los hablantes masculinos/femeninos/no binarios probablemente utilizarían formas variables. Esta asimetría da lugar a opciones de traducción matizadas que este artículo pretende explorar. A partir de un corpus recién compilado de subtítulos de Netflix del inglés al polaco –que asciende a 3,5 millones de palabras–, examinamos cómo los traductores emplean 113 feminativos diferentes relacionados con la ocupación. Abordamos tres preguntas principales de investigación (RQ1-RQ3). La RQ1 se refiere a la frecuencia de los feminativos relevantes en nuestro corpus. La RQ2 trata de cómo se distribuyen los femeninos en las 284 producciones analizadas en el conjunto de datos. Por último, la RQ3 aborda la relación entre la frecuencia de los feminativos en los subtítulos de Netflix y la aceptabilidad de estos feminativos, a juicio de los hablantes

Hypercapnic Chemosensitivity in Patients with Heart Failure: Relation to Shifts in Type-1 Insulin-Like Growth Factor and Sex Hormone-Binding Globulin Levels

In patients suffering from heart failure (HF), autonomic imbalance develops even at early stages along with derangements of cardiopulmonary reflex control and abnormalities in metabolism of several hormones. In 34 men with stable systolic HF, we investigated hypercapnic chemosensitivity (HCS, liter/min·mm Hg) measured using the rebreathing method and defined as the slope of the regression line relating minute ventilation (VE, liter/min) to end­tidal carbon dioxide concentration (PETCO₂ , mm Hg). Serum levels of testosterone, dehydroepiandrosterone sulfate, type­1 insulin­like growth factor (IGF­1), sex hormonebinding globulin (SHBG), estradiol, and cortisol were measured using immunoassays. We found that there were no associations between HCS and clinical variables, applied therapy, and co­morbidities (all P > 0.2). Augmented HCS was accompanied by increased serum SHBG (when expressed in nM, r = 0.43, P < 0.05; when expressed as percentage of the agematched reference values, r = 0.62, P < 0.001) and the reduced serum IGF­1 (when expressed in ng/ml and as percentage of the above­mentioned values, r = –0.49, P < 0.05, and r = = –0.47, P = 0.007, respectively). The HCS was not related to serum levels of all the remaining analyzed hormones (all P > 0.2). Thus, it may be suggested that the hormone stimuli can noticeably modify the reflex mechanisms in cardiorespiratory control in the clinical setting of cardiovascular pathology.У пацієнтів із серцевою недостатністю (СН) навіть на ранніх стадіях захворювання розвивається автономний дисбаланс паралельно з розладами контролю серцево­судинної системи та відхиленнями метаболізму деяких гормонів від норми. Ми досліджували хемочутливість до гіперкапнії (HCS) у 34 чоловіків із СН, використовуючи метод зворотного дихання. Така чутливість визначалась як нахил лінії регресії при співставленні хвилинного об’єму вентиляції (л/хв) та кінцевої концентрації двооксиду вуглецю (мм рт. ст.). Рівні тестостерону, дигідроепіандростерону сульфату, інсулінподібного фактора росту типу 1 (IGF­1), глобуліну, що зв’язує статеві гормони (SHBG), естрадіолу та кортизолу визначали в сироватці крові, використовуючи імунологічні методики. Як виявилося, зв’язки між рівнем HCS, з одного боку, та клінічними показниками, застосованою терапією та супутніми захворюваннями – з другого, були відсутніми (в усіх випадках P > 0.2). Підвищена HCS супроводжувалася підвищеними рівнями SHBG (для концентрацій у наномолях на 1 л r = 0.43, P < 0.05, а для нормованих значень, наведених щодо певної вікової групи, r = 0.62, P < 0.001) та низькими рівнями IGF­1 (для концентрацій у нанограмах на 1 мл та для наведених нормованих значень r = –0.49, P < 0.05 та r = –0.47, P = 0.007 відповідно). Значення HCS не виявляли будь­яких зв’язків з рівнями всіх досліджених гормонів у сироватці. Це дозволяє думати, що гормональні стимули можуть помітно модифікувати рефлекторні механізми контролю серцево­судинної системи у клінічних випадках її патологій