Asymptotic diophantine approximation:the multiplicative case

Let $\alpha$ and $\beta$ be irrational real numbers and 0<\F<1/30. We prove a precise estimate for the number of positive integers $q\leq Q$ that satisfy \|q\alpha\|\cdot\|q\beta\|<\F. If we choose \F as a function of $Q$ we get asymptotics as $Q$ gets large, provided \F Q grows quickly enough in terms of the (multiplicative) Diophantine type of $(\alpha,\beta)$, e.g., if $(\alpha,\beta)$ is a counterexample to Littlewood's conjecture then we only need that \F Q tends to infinity. Our result yields a new upper bound on sums of reciprocals of products of fractional parts, and sheds some light on a recent question of L\^{e} and Vaaler.Comment: To appear in Ramanujan Journa

On Spectral Properties of the L Operator in the Lax Pair of the sine-Gordon Equation

We analyze the periodic spectrum of the L operator in the Lax pair of the sine-Gordon equation in terms of the regularity of the potential.Ми аналiзуємо перiодичний спектр оператора L у парi Лакса рiвняння sine-Гордона в термiнах регулярностi потенцiалу

Fragility, Stokes-Einstein violation, and correlated local excitations in a coarse-grained model of an ionic liquid

Dynamics of a coarse-grained model for the room-temperature ionic liquid, 1-ethyl-3-methylimidazolium hexafluorophosphate, couched in the united-atom site representation are studied via molecular dynamics simulations. The dynamically heterogeneous behavior of the model resembles that of fragile supercooled liquids. At or close to room temperature, the model ionic liquid exhibits slow dynamics, characterized by nonexponential structural relaxation and subdiffusive behavior. The structural relaxation time, closely related to the viscosity, shows a super-Arrhenius behavior. Local excitations, defined as displacement of an ion exceeding a threshold distance, are found to be mainly responsible for structural relaxation in the alternating structure of cations and anions. As the temperature is lowered, excitations become progressively more correlated. This results in the decoupling of exchange and persistence times, reflecting a violation of the Stokes-Einstein relation.Comment: Published on the Phys. Chem. Chem. Phys. websit

The steps to therapeutic drug monitoring: A structured approach illustrated with imatinib

Pharmacometric methods have hugely benefited from progress in analytical and computer sciences during the past decades, and play nowadays a central role in the clinical development of new medicinal drugs. It is time that these methods translate into patient care through therapeutic drug monitoring (TDM), due to become a mainstay of precision medicine no less than genomic approaches to control variability in drug response and improve the efficacy and safety of treatments. In this review, we make the case for structuring TDM development along five generic questions: 1) Is the concerned drug a candidate to TDM? 2) What is the normal range for the drug's concentration? 3) What is the therapeutic target for the drug's concentration? 4) How to adjust the dosage of the drug to drive concentrations close to target? 5) Does evidence support the usefulness of TDM for this drug? We exemplify this approach through an overview of our development of the TDM of imatinib, the very first targeted anticancer agent. We express our position that a similar story shall apply to other drugs in this class, as well as to a wide range of treatments critical for the control of various life-threatening conditions. Despite hurdles that still jeopardize progress in TDM, there is no doubt that upcoming technological advances will shape and foster many innovative therapeutic monitoring methods

Suivi thérapeutique de l'imatinib

* Le monitoring (suivi) joue un rôle important pour un traitement et son évaluation - pour autant qu'il se base sur la mesure de marqueurs cliniques adéquats ou de substituts validés. * Pour ce qui est du traitement d'imatinib, le «therapeutic drug monitoring» (TDM) semble être une option utile pour le contrôle du traitement de la LMC. Il utilise la concentration plasmatique de ce médicament comme marqueur. * Les concentrations plasmatiques d'imatinib varient considérablement d'un patient à l'autre sous un même schéma posologique, en raison de la variabilité interindividuelle de sa pharmacocinétique. Il a été démontré que l'exposition plasmatique était en corrélation avec le résultat clinique des patients LMC - aussi bien pour la réponse au traitement que pour le profil d'effets indésirables. * Il n'est pas encore établi si le TDM de l'imatinib doit être utilisé que dans le cas de problèmes cliniques ou si les patients LMC peuvent déjà profiter d'un contrôle préventif systématique «de routine» - de manière à garder la concentration plasmatique dans des marges thérapeutiques. Cela est toujours plus recommandé ces derniers temps. * Pour répondre à cette question, une étude suisse prospective, randomisée et contrôlée recrute des patients LMC traités par imatinib depuis moins de 5 ans et propose en outre le TDM pour tous les patients en cas de problèmes cliniques. - * Monitoring spielt eine wichtige Rolle zur Therapieevaluierung und Behandlungsentscheidung - solange es auf der Basis der Messung von entsprechenden klinischen oder validierten Surrogat-Markern stattfindet. * Im Hinblick auf die Imatinib-Therapie scheint das «Therapeutische Drug-Monitoring» (TDM) ein nützlicher Ansatz zum Therapie-Monitoring der CML-Behandlung zu sein, welches die Plasmakonzentration des Arzneimittels als Marker zur Therapieüberwachung verwendet. * Imatinib-Plasmakonzentrationen variieren beträchtlich von Patient zu Patient unter dem gleichen Dosierungsschema, aufgrund der interindividuell unterschiedlichen Pharmakokinetik des Arzneimittels. Für die Plasmaexposition wurde gezeigt, dass sie mit dem klinischen Outcome von CML-Patienten korreliert - sowohl im Bezug auf das Therapieansprechen als auch auf das Nebenwirkungsprofil. * Es ist noch unklar, ob das TDM von Imatinib nur im Falle von klinischen Problemen Verwendung finden sollte oder ob CML-Patienten bereits von einem systematischen, präventiven «Routine»-Monitoring zur Therapieindividualisierung - zur Steuerung der Plasmakonzentration in einen therapeutischen Bereich - profitieren könnten, welches in letzter Zeit immer häufiger empfohlen wird. * Um diese Fragestellung zu beantworten, nimmt eine prospektive, randomisiert kontrollierte Schweizer Studie CML-Patienten auf, die seit weniger als 5 Jahren mit Imatinib behandelt werden, und bietet das TDM zudem für alle Patienten im Falle von klinischen Problemen an

The Problem of Marginality in Model Reductions of Turbulence

Reduced quasilinear (QL) and nonlinear (gradient-driven) models with scale separations, commonly used to interpret experiments and to forecast turbulent transport levels in magnetised plasmas are tested against nonlinear models without scale separations (flux-driven). Two distinct regimes of turbulence -- either far above threshold or near marginal stability -- are investigated with Boltzmann electrons. The success of reduced models especially hinges on the reproduction of nonlinear fluxes. Good agreement between models is found above threshold whilst reduced models would significantly underpredict fluxes near marginality, overlooking mesoscale flow organisation and turbulence self-advection. Constructive prescriptions whereby to improve reduced models is discussed