Strongly mixing convolution operators on Fr\'echet spaces of holomorphic functions

A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on $\mathbb{C}^n$ are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy-Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.Comment: 16 page

Decolonizing the Imagination in Times of Crisis. Gestures for Speculative Thinking-Feeling: Interview with Martin Savransky

In this interview, Savransky analyzes the implications of thinking and creating through a pragmatist perspective aiming at the challenges that experimental research faces in the turbulent times we live in. Through key concepts and authors that have marked his intellectual work, he invites us to conceive thinking exercises as practices of experimen-tality, through which the uncertain and unstable situations of current problems would raise new questions rather than closed answers. English translation of Spanish Original: http://ojs.uc.cl/index.php/Disena/article/view/41503/3347

Chaotic exchange of solid material between planetary systems: implications for lithopanspermia

We examine a low energy mechanism for the transfer of meteoroids between two planetary systems embedded in a star cluster using quasi-parabolic orbits of minimal energy. Using Monte Carlo simulations, we find that the exchange of meteoroids could have been significantly more efficient than previously estimated. Our study is relevant to astrobiology as it addresses whether life on Earth could have been transferred to other planetary systems in the solar system's birth cluster and whether life on Earth could have been transferred here from beyond the solar system. In the solar system, the timescale over which solid material was delivered to the region from where it could be transferred via this mechanism likely extended to several hundred million years (as indicated by the 3.8-4.0 Ga epoch of the Late Heavy Bombardment). This timescale could have overlapped with the lifetime of the Solar birth cluster (~100-500 Myr). Therefore, we conclude that lithopanspermia is an open possibility if life had an early start. Adopting parameters from the minimum mass solar nebula, considering a range of planetesimal size distributions derived from observations of asteroids and Kuiper Belt Objects and theoretical coagulation models, and taking into account Oort Cloud formation models, the expected number of bodies with mass > 10 kg that could have been transferred between the Sun and its nearest cluster neighbor could be of the order of 1E14-3E16, with transfer timescales of 10s Myr. We estimate that of the order of 3E8 x l(km) could potentially be life-bearing, where l(km) is the depth of the Earth crust in km that was ejected as the result of the early bombardment.Comment: Accepted by Astrobiology. Submitted: Sep. 21, 2011. Accepted: May 2, 2012. 39 pages. 21 figures. arXiv admin note: substantial text overlap with arXiv:0808.326

Hypercyclicity in spaces of holomorphic functions and pseudo orbits of linear operators

En esta tesis estudiamos distintos problemas sobre densidad de órbitas de operadores lineales. Un operador lineal se dice hipercíclico si admite una órbita densa. Podemos decir que el centro de atención es el comportamiento de las sucesivas iteraciones de un operador lineal. En otras palabras, se estudian sistemas dinámicos discretos asociados a operadores lineales. En el contexto finito dimensional este problema se puede resolver a través del estudio de la forma de Jordan asociada a una matriz, y los comportamientos son relativamente simples (de ahí que el caos se asocia naturalmente a sistemas no lineales). Sin embargo, en espacios de dimensión infinita los sistemas lineales pueden ser caóticos, ya que aparecen fenómenos nuevos, como por ejemplo la existencia de órbitas densas en todo el espacio. Los primeros ejemplos de operadores hipercíclicos surgieron en el contexto de la teoría de funciones analíticas. Así, en 1929, G. D. Birkhoff [Bir29] probó que para todo aϵC, a≠0, el operador traslación en el espacio de funciones enteras de variable compleja (H(C),τ) con la topología compacto-abierta, Ta : H(C)→H(C) definido por Taf(z)=f(z+a) es hipercíclico, y en 1952, G. R. MacLane [Mac52], demostró que lo mismo ocurre con el operador de diferenciación en H(C). Estos resultados fueron generalizados por G. Godefroy y J. H. Shapiro en 1991 [GS91] quienes probaron que todo operador lineal y continuo T : H(C)→H(C) que conmute con las traslaciones y no sea un múltiplo de la identidad es hipercíclico. Esta familia de operadores se conoce por el nombre de operadores de convolución. En esta tesis estudiamos operadores de convolución definidos en espacios de funciones holomorfas sobre espacios de Banach. Así como también damos ejemplos de operadores fuera de la clase de la familia de los operadores de convolución que resultan hipercíclicos. Estos ejemplos se presentan tanto en espacios de funciones holomorfas de finitas variables complejas y también en espacios de funciones holomorfas definidas en espacios de Banach de dimensión infinita. Por otro lado, estudiamos pseudo órbitas de opeadores lineales. Decimos que {Xn}nϵN es una (εn)-pseudo órbita para T si d(xn+1,T(xn)) ≤ εn para todo nϵN. Esta definición cobra sentido cuando se permite cometer un error en cada paso de la iteración del sistema. Notemos que si εn = 0 para todo nϵN, una (εn)-pseudo órbita es una órbita. Decimos que el operador T es (εn)-hipercíclico si existe una pseudo órbita densa para la sucesión de errores (εn). Estudiamos este concepto enmarcado dentro de la teoría de sistemas dinámicos lineales.In this thesis we study several problems on the density of orbits of linear operators. A linear operator is said hypercyclic if admits a dense orbit. We can say that the spotlight is the behavior of successive iterations of a linear operator. In other words, dynamical systems associated to linear operators are studied. In the finite dimensional context the problem is relatively simple and it can be solved through the canonical Jordan form of a matrix. Hence, chaos is usually associated to non linear systems. However, in infinite dimensional spaces linear operators can be chaotic since new phenomena appears, such as the existence of dense orbits. The first examples of hypercyclic operators came out in the context of analytic functions. Birkhoff in [Bir29] proved that for every aϵC, a≠0, the translation operator on the space of one complex variable functions (H(C),τ) with the compact-open topology, Ta : H(C)→H(C) defined by Taf(z)=f(z+a) is hypercyclic. MacLane in [Mac52], proved that the same occurs with the derivative operator on the space H(C). Both results were generalized by a remarkable theorem due to Godefroy and Shapiro [GS91], who proved that every linear operator that commutes with the translation on H(C^N) and is not a scalar multiple of the identity is hypercyclic. This family of operators is known as the class of (non trivial) "convolution operators". In this thesis we study convolution operators defined on spaces of holomorphic functions on Banach spaces. In addition, we show examples of non convolution hypercyclic operators defined on spaces of holomorphic functions of finite complex variables and also for spaces of holomorphic functions defined on infinite dimensional Banach spaces. On other side, we deal with pseudo orbits of linear operators. We say that {Xn}nϵN is a (εn)-pseudo orbit of T if d(xn+1,T(xn)) ≤ εn for any nϵN. This definition becomes meaningful when a small measurement error is committed in each step of the iteration. We say that an operator T is (εn)-hypercyclic if admits a dense pseudo orbit for the error sequence (εn)nϵN. We study this new concept framed on the theory of linear dynamical systems.Fil:Savransky, Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Decolonizing the Imagination in Times of Crisis. Gestures for Speculative Thinking-Feeling: Interview with Martin Savransky

In this interview, Savransky analyzes the implications of thinking and creating through a pragmatist perspective aiming at the challenges that experimental research faces in the turbulent times we live in. Through key concepts and authors that have marked his intellectual work, he invites us to conceive thinking exercises as practices of experimen­tality, through which the uncertain and unstable situations of current problems would raise new questions rather than closed answers

A randomized trial of planned cesarean or vaginal delivery for twin pregnancy

Background: Twin birth is associated with a higher risk of adverse perinatal outcomes than singleton birth. It is unclear whether planned cesarean section results in a lower risk of adverse outcomes than planned vaginal delivery in twin pregnancy.\ud \ud Methods: We randomly assigned women between 32 weeks 0 days and 38 weeks 6 days of gestation with twin pregnancy and with the first twin in the cephalic presentation to planned cesarean section or planned vaginal delivery with cesarean only if indicated. Elective delivery was planned between 37 weeks 5 days and 38 weeks 6 days of gestation. The primary outcome was a composite of fetal or neonatal death or serious neonatal morbidity, with the fetus or infant as the unit of analysis for the statistical comparison.\ud \ud Results: A total of 1398 women (2795 fetuses) were randomly assigned to planned cesarean delivery and 1406 women (2812 fetuses) to planned vaginal delivery. The rate of cesarean delivery was 90.7% in the planned-cesarean-delivery group and 43.8% in the planned-vaginal-delivery group. Women in the planned-cesarean-delivery group delivered earlier than did those in the planned-vaginal-delivery group (mean number of days from randomization to delivery, 12.4 vs. 13.3; P = 0.04). There was no significant difference in the composite primary outcome between the planned-cesarean-delivery group and the planned-vaginal-delivery group (2.2% and 1.9%, respectively; odds ratio with planned cesarean delivery, 1.16; 95% confidence interval, 0.77 to 1.74; P = 0.49).\ud \ud Conclusion: In twin pregnancy between 32 weeks 0 days and 38 weeks 6 days of gestation, with the first twin in the cephalic presentation, planned cesarean delivery did not significantly decrease or increase the risk of fetal or neonatal death or serious neonatal morbidity, as compared with planned vaginal delivery

Intravenous immunoglobulin treatment for mild Guillain-Barré syndrome. An international observational study

Objective: To compare the disease course in patients with mild Guillain-Barré syndrome (GBS) who were treated with intravenous immunoglobulin (IVIg) or supportive care only. Methods: We selected patients from the prospective observational International GBS Outcome Study (IGOS) who were able to walk independently at study entry (mild GBS), treated with one IVIg course or supportive care. The primary endpoint was the GBS disability score four weeks after study entry, assessed by multivariable ordinal regression analysis. Results: Of 188 eligible patients, 148 (79%) were treated with IVIg and 40 (21%) with supportive care. The IVIg group was more disabled at baseline. IVIg treatment was not associated with lower GBS disability scores at 4 weeks (adjusted OR (aOR) 1.62, 95% CI 0.63 to 4.13). Nearly all secondary endpoints showed no benefit from IVIg, although the time to regain full muscle strength was shorter (28 vs 56 days, p=0.03) and reported pain at 26 weeks was lower (n=26/121, 22% vs n=12/30, 40%, p=0.04) in the IVIg treated patients. In the subanalysis with persistent mild GBS in the first 2 weeks, the aOR for a lower GBS disability score at 4 weeks was 2.32 (95% CI 0.76 to 7.13). At 1 year, 40% of all patients had residual symptoms. Conclusion: In patients with mild GBS, one course of IVIg did not improve the overall disease course. The certainty of this conclusion is limited by confounding factors, selection bias and wide confidence limits. Residual symptoms were often present after one year, indicating the need for better treatments in mild GBS