The linear preservers of real diagonalizable matrices

Using a recent result of Bogdanov and Guterman on the linear preservers of pairs of simultaneously diagonalizable matrices, we determine all the automorphisms of the vector space M_n(R) which stabilize the set of diagonalizable matrices. To do so, we investigate the structure of linear subspaces of diagonalizable matrices of M_n(R) with maximal dimension.Comment: 14 page

Patent Foramen Ovale Closure or Anticoagulation vs. Antiplatelets after Stroke

BACKGROUND Trials of patent foramen ovale (PFO) closure to prevent recurrent stroke have been inconclusive. We investigated whether patients with cryptogenic stroke and echocardiographic features representing risk of stroke would benefit from PFO closure or anticoagulation, as compared with antiplatelet therapy. METHODS In a multicenter, randomized, open-label trial, we assigned, in a 1:1:1 ratio, patients 16 to 60 years of age who had had a recent stroke attributed to PFO, with an associated atrial septal aneurysm or large interatrial shunt, to transcatheter PFO closure plus long-term antiplatelet therapy (PFO closure group), antiplatelet therapy alone (antiplatelet-only group), or oral anticoagulation (anticoagulation group) (randomization group 1). Patients with contraindications to anticoagulants or to PFO closure were randomly assigned to the alternative noncontraindicated treatment or to antiplatelet therapy (randomization groups 2 and 3). The primary outcome was occurrence of stroke. The comparison of PFO closure plus antiplatelet therapy with antiplatelet therapy alone was performed with combined data from randomization groups 1 and 2, and the comparison of oral anticoagulation with antiplatelet therapy alone was performed with combined data from randomization groups 1 and 3. RESULTS A total of 663 patients underwent randomization and were followed for a mean (+/- SD) of 5.3 +/- 2.0 years. In the analysis of randomization groups 1 and 2, no stroke occurred among the 238 patients in the PFO closure group, whereas stroke occurred in 14 of the 235 patients in the antiplatelet-only group (hazard ratio, 0.03; 95% confidence interval, 0 to 0.26; P<0.001). Procedural complications from PFO closure occurred in 14 patients (5.9%). The rate of atrial fibrillation was higher in the PFO closure group than in the antiplatelet-only group (4.6% vs. 0.9%, P = 0.02). The number of serious adverse events did not differ significantly between the treatment groups (P = 0.56). In the analysis of randomization groups 1 and 3, stroke occurred in 3 of 187 patients assigned to oral anticoagulants and in 7 of 174 patients assigned to antiplatelet therapy alone. CONCLUSIONS Among patients who had had a recent cryptogenic stroke attributed to PFO with an associated atrial septal aneurysm or large interatrial shunt, the rate of stroke recurrence was lower among those assigned to PFO closure combined with antiplatelet therapy than among those assigned to antiplatelet therapy alone. PFO closure was associated with an increased risk of atrial fibrillation

Mahler functional equations and applications to p-regular sequences

Le concept de suite p-régulière, introduit par Allouche et Shallit, généralise celui de suite p-automatique. La série génératrice d'une telle suite est considérée, tantôt comme une série formelle, tantôt comme une fonction holomorphe (dans le cas complexe) ; elle vérifie une équation fonctionnelle linéaire, dite de Mahler. Ce travail étudie ces équations fonctionnelles de façon générale, pour les appliquer au cas particulier des suites p-régulières.Le cadre formel est celui des chapitres 1, 2 et 3. On y étudie certaines structures mahlériennes. Le chapitre 4 montre la transcendance des solutions non rationnelles, par l'étude de leurs singularités. On étend ainsi un résultat bien connu dans le cas automatique. Le chapitre 5, répondant à une question posée par Rubel, montre que, dans un cas, les solutions non rationnelles sont différentiellement transcendantes (ou hypertranscendantes). Le chapitre 7, reprenant des méthodes bien connues, s'appuie sur le chapitre 4 pour établir la transcendance des valeurs prises, s'intéressant ainsi à une question posée par Allouche et Shallit. Le chapitre 8 montre un résultat très partiel en direction d'une conjecture de Loxton et van der Poorten. Le chapitre 6 esquisse une étude dans le cas non linéaire.p-Regular sequences, introduced by Allouche and Shallit, are a generalization of p-automatic sequences. The generating series of such a sequence can be either viewed as a formal power series, or as a holomorphic function (in the complex case); it satisfies a linear functional equation called "Mahler equation". In this work we give general results for these functional equations, that we then apply to the particular case of p-regular sequences.The formal framework is given in Chapters 1 to 3, where Mahlerian structures are studied. Chaper 4 shows transcendency of nonrational solutions through the study of their singularities. We thus extend a result which is well-known in the automatic case. Chapter 5 answers a question asked by Rubel by proving that, in one case, nonrational solutions are differentially transcendental (or hypertranscendental). Chapter 7, using well-known methods, builds on Chapter 4 to establish the transcendency of values of these functions, in connection with a question asked by Allouche and Shallit. Chapter 8 gives a very partial result in the direction of a conjecture by Loxton and van der Poorten. Chapter 6 sketches a study of the non-linear case

Équations fonctionnelles de Mahler et applications aux suites p-régulières

p-Regular sequences, introduced by Allouche and Shallit, are a generalization of p-automatic sequences. The generating series of such a sequence can be either viewed as a formal power series, or as a holomorphic function (in the complex case); it satisfies a linear functional equation called "Mahler equation". In this work we give general results for these functional equations, that we then apply to the particular case of p-regular sequences.The formal framework is given in Chapters 1 to 3, where Mahlerian structures are studied. Chaper 4 shows transcendency of nonrational solutions through the study of their singularities. We thus extend a result which is well-known in the automatic case. Chapter 5 answers a question asked by Rubel by proving that, in one case, nonrational solutions are differentially transcendental (or hypertranscendental). Chapter 7, using well-known methods, builds on Chapter 4 to establish the transcendency of values of these functions, in connection with a question asked by Allouche and Shallit. Chapter 8 gives a very partial result in the direction of a conjecture by Loxton and van der Poorten. Chapter 6 sketches a study of the non-linear case.Le concept de suite p-régulière, introduit par Allouche et Shallit, généralise celui de suite p-automatique. La série génératrice d'une telle suite est considérée, tantôt comme une série formelle, tantôt comme une fonction holomorphe (dans le cas complexe) ; elle vérifie une équation fonctionnelle linéaire, dite de Mahler. Ce travail étudie ces équations fonctionnelles de façon générale, pour les appliquer au cas particulier des suites p-régulières.Le cadre formel est celui des chapitres 1, 2 et 3. On y étudie certaines structures mahlériennes. Le chapitre 4 montre la transcendance des solutions non rationnelles, par l'étude de leurs singularités. On étend ainsi un résultat bien connu dans le cas automatique. Le chapitre 5, répondant à une question posée par Rubel, montre que, dans un cas, les solutions non rationnelles sont différentiellement transcendantes (ou hypertranscendantes). Le chapitre 7, reprenant des méthodes bien connues, s'appuie sur le chapitre 4 pour établir la transcendance des valeurs prises, s'intéressant ainsi à une question posée par Allouche et Shallit. Le chapitre 8 montre un résultat très partiel en direction d'une conjecture de Loxton et van der Poorten. Le chapitre 6 esquisse une étude dans le cas non linéaire

Diuretics in normotensive patients with acute pulmonary embolism and right ventricular dilatation.: Diuretics in Pulmonary Embolism

International audienceBACKGROUND: The benefit of load expansion is controversial in acute pulmonary embolism (PE). The aim of this study was to evaluate the benefit of furosemide in cases of normotensive acute PE. METHODS AND RESULTS: We retrospectively included 70 consecutive normotensive patients (systolic blood pressure ≥ 90 mmHg) admitted for acute PE with right ventricular dilation. Overall, 40 patients were treated during the first 24h by repeated bolus of furosemide (78 ± 42 mg, range 40-160 mg) and 30 patients received isotonic saline solution (1.6 ± 0.9L). Severity of hemodynamic status was similar in both groups, but patients in the furosemide group were older and had a greater creatinine level. At 24h, only the furosemide group had a decreased shock index (0.82 ± 0.22 vs. 0.63 ± 0.16, P<0.0001) with improved systolic blood pressure (118 ± 18 vs. 133 ± 17 mmHg, P<0.0001), and creatinine levels. After treatment, there were fewer patients with simplified pulmonary embolism severity index ≥ 1 in the diuretic group (45% vs. 55%, P=0.03) than in the fluid expansion group (47% vs. 40%, P<0.0001). Finally, oxygen requirement at 24h decreased only in the diuretic group (75% to 47%, P=0.0004), and in-hospital survival without death and PE-related shock were similar between the 2 groups. CONCLUSIONS: In normotensive PE with RV dilatation, diuretics may improve hemodynamics and oxygenation requirement.