Measuring order in the isotropic packing of elastic rods

The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic two-dimensional confinement of a rod by a central force. We seek to measure how ordered is a folded configuration and we identify two key quantities. A geometrical characterization is given by the number of superposed layers in the configuration. Using temporal modulations of the confining force, we probe the mechanical properties of the configuration and we define and measure its effective compressibility. These two quantities may be used to build a statistical framework for packed elastic systems.Comment: 4 pages, 5 figure

On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Securitization outside of the West:conceptualizing the securitization–neo-patrimonialism nexus in Africa

Securitization is arguably the most successful theoretical framework to analyse security beyond the military confines with the nation state as the dominant actor within the international system. Amongst the critical voices, securitization has become the gold standard for analysing emerging challenges, such as migration, terrorism, human security, intra-state and cross-border issues, as well as environmental challenges. Yet, despite its broadening agenda, the framework has also been accused of a Western bias with a Western political context and democratic governance structure at its heart. This article aims to re-conceptualize the framework in a way that suits a non-Western context better, notably by re-conceptualizing the securitization–neo-patrimonialism nexus in Africa, which gives us significant new insights into non-Western political contexts. It analyses the securitization processes among the political elites in a neo-patrimonial statehood. It further stretches the conceptualization of securitization into African statehood, characterized by a blurred line between the leader and the state.</p

Military business and the business of the military

Contrary to dominant approaches that locate the causes for military entrepreneurialism in eastern Democratic Republic of the Congo predominantly in criminal military elites, this article highlights the importance of the Congolese military’s (FARDC) civilian context for understanding military revenue-generation. It analyses how the latter is shaped by structures of domination, signification and legitimisation that drive and are driven by the FARDC’s governance, private protection and security practices. It argues that these practices contribute to bestowing a degree of legitimacy on both the FARDC’s position of power and some of its revenue-generation activities. Furthermore, by emphasising that the FARDC’s regulatory and protection practices are partly the product of popular demands and the routine actions of civilians, the article contends that the causes of military revenue-generation are co-located in the military’s civilian environment. In this manner, it offers a more nuanced conceptualisation of military entrepreneurialism, thus opening up new perspectives on policy interventions in this area

Recurrence properties of hypercyclic operators

[EN] We generalize the notions of hypercyclic operators, U-frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics, namely A-hypercyclicity. We then state an A-hypercyclicity criterion, inspired by the hypercyclicity criterion and the frequent hypercyclicity criterion, and we show that this criterion characterizes the A-hypercyclicity for weighted shifts. We also investigate which density properties can the sets N(x, U) = {n is an element of N; T-n x is an element of U} have for a given hypercyclic operator, and we study the new notion of reiteratively hypercyclic operators.This work is supported in part by MEC and FEDER, Project MTM2013-47093-P, and by GVA, Projects PROMETEOII/2013/013 and ACOMP/2015/005. The second author was a postdoctoral researcher of the Belgian FNRS.Bès, JP.; Menet, Q.; Peris Manguillot, A.; Puig-De Dios, Y. (2016). Recurrence properties of hypercyclic operators. Mathematische Annalen. 366(1):545-572. https://doi.org/10.1007/s00208-015-1336-3S5455723661Badea, C., Grivaux, S.: Unimodular eigenvalues, uniformly distributed sequences and linear dynamics. Adv. Math. 211, 766–793 (2007)Bayart, F., Grivaux, S.: Frequently hypercyclic operators. Trans. Amer. Math. Soc. 358, 5083–5117 (2006)Bayart, F., Grivaux, S.: Invariant Gaussian measures for operators on Banach spaces and linear dynamics. Proc. Lond. Math. Soc. 94, 181–210 (2007)Bayart, F., Matheron, É.: Dynamics of linear operators, Cambridge Tracts in Mathematics, 179. Cambridge University Press, Cambridge (2009)Bayart, F., Matheron, É.: (Non-)weakly mixing operators and hypercyclicity sets. Ann. Inst. Fourier 59, 1–35 (2009)Bayart, F., Ruzsa, I.: Difference sets and frequently hypercyclic weighted shifts. Ergodic Theory Dynam. Syst. 35, 691–709 (2015)Bergelson, V.: Ergodic Ramsey Theory- an update, Ergodic Theory of $$\mathbb{Z}^d$$ Z d -actions. Lond. Math. Soc. Lecture Note Ser. 28, 1–61 (1996)Bernal-González, L., Grosse-Erdmann, K.-G.: The Hypercyclicity Criterion for sequences of operators. Studia Math. 157, 17–32 (2003)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors. Ergodic Theory Dynam. Syst. 27, 383–404 (2007)Bonilla, A., Grosse-Erdmann, K.-G.: Erratum: Ergodic Theory Dynam. Systems 29, 1993–1994 (2009)Chan, K., Seceleanu, I.: Hypercyclicity of shifts as a zero-one law of orbital limit points. J. Oper. Theory 67, 257–277 (2012)Costakis, G., Sambarino, M.: Topologically mixing hypercyclic operators. Proc. Amer. Math. Soc. 132, 385–389 (2004)Furstenberg, H.: Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton (1981)Giuliano, R., Grekos, G., Mišík, L.: Open problems on densities II, Diophantine Analysis and Related Fields 2010. AIP Conf. Proc. 1264, 114–128 (2010)Grosse-Erdmann, K.-G.: Hypercyclic and chaotic weighted shifts. Studia Math. 139, 47–68 (2000)Grosse-Erdmann, K.-G., Peris, A.: Frequently dense orbits. C. R. Math. Acad. Sci. Paris 341, 123–128 (2005)Grosse-Erdmann, K.G., Peris, A.: Weakly mixing operators on topological vector spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 104, 413–426 (2010)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos, Universitext. Springer, London (2011)Menet, Q.: Linear chaos and frequent hypercyclicity. Trans. Amer. Math. Soc. arXiv:1410.7173Puig, Y.: Linear dynamics and recurrence properties defined via essential idempotents of $$\beta {\mathbb{N}}$$ β N (2014) arXiv:1411.7729 (preprint)Salas, H.N.: Hypercyclic weighted shifts. Trans. Amer. Math. Soc. 347, 993–1004 (1995)Salat, T., Toma, V.: A classical Olivier’s theorem and statistical convergence. Ann. Math. Blaise Pascal 10, 305–313 (2003)Shkarin, S.: On the spectrum of frequently hypercyclic operators. Proc. Am. Math. Soc. 137, 123–134 (2009

PLK1 facilitates chromosome biorientation by suppressing centromere disintegration driven by BLM-mediated unwinding and spindle pulling

Centromeres provide a pivotal function for faithful chromosome segregation. They serve as a foundation for the assembly of the kinetochore complex and spindle connection, which is essential for chromosome biorientation. Cells lacking Polo-like kinase 1 (PLK1) activity suffer severe chromosome alignment defects, which is believed primarily due to unstable kinetochore-microtubule attachment. Here, we reveal a previously undescribed mechanism named ‘centromere disintegration’ that drives chromosome misalignment in PLK1-inactivated cells. We find that PLK1 inhibition does not necessarily compromise metaphase establishment, but instead its maintenance. We demonstrate that this is caused by unlawful unwinding of DNA by BLM helicase at a specific centromere domain underneath kinetochores. Under bipolar spindle pulling, the distorted centromeres are promptly decompacted into DNA threadlike molecules, leading to centromere rupture and whole-chromosome arm splitting. Consequently, chromosome alignment collapses. Our study unveils an unexpected role of PLK1 as a chromosome guardian to maintain centromere integrity for chromosome biorientation

L'Afrique du Sud à la veille d'une consultation décisive

En dépit de ses succès, le modèle démocratique sud-africain traverse une phase délicate. La succession du président Nelson Mandela annonce une possible crispation du pouvoir, en raison notamment des tendances autoritaires de Thabo Mbeki. Incapable de s'affirmer sur la scène continentale comme une puissance modératrice, l'Afrique du Sud pourrait devenir un État "tricheur" (trickster) comme un autre dans la zone australe, profitant des interstices criminels de l'économie internationale. Les auteurs décrivent les différents éléments de ce scénario: une certaine dérive autoritaire du régime sud-africain qui aurait tendance à se présidentialiser encore davantage; la criminalisation croissante de l'État, que faciliteraient la corruption avérée de la police, des douanes, de l'armée, de l'administration, mais aussi l'héritage du régime de l'apartheid et de la lutte armée contre celui-ci; l'informalisation croissante de l'insertion de l'économie sud-africaine dans son environnement régional. ASC – Publicaties niet-programma gebonde

L'Afrique du Sud à la veille d'une consultation décisive

En dépit de ses succès, le modèle démocratique sud-africain traverse une phase délicate. La succession du président Nelson Mandela annonce une possible crispation du pouvoir, en raison notamment des tendances autoritaires de Thabo Mbeki. Incapable de s'affirmer sur la scène continentale comme une puissance modératrice, l'Afrique du Sud pourrait devenir un État "tricheur" (trickster) comme un autre dans la zone australe, profitant des interstices criminels de l'économie internationale. Les auteurs décrivent les différents éléments de ce scénario: une certaine dérive autoritaire du régime sud-africain qui aurait tendance à se présidentialiser encore davantage; la criminalisation croissante de l'État, que faciliteraient la corruption avérée de la police, des douanes, de l'armée, de l'administration, mais aussi l'héritage du régime de l'apartheid et de la lutte armée contre celui-ci; l'informalisation croissante de l'insertion de l'économie sud-africaine dans son environnement régional. ASC – Publicaties niet-programma gebonde

Editorial: African women's struggles in a gender perspective

International audienc