Continuation of connecting orbits in 3D-ODEs: (I) Point-to-cycle connections

We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are formulated using an eigenfunction of the associated adjoint variational equation, avoiding costly and numerically unstable computations of the monodromy matrix. The equations for the eigenfunction are included in the defining boundary-value problem, allowing a straightforward implementation in AUTO, in which only the standard features of the software are employed. Homotopy methods to find connecting orbits are discussed in general and illustrated with several examples, including the Lorenz equations. Complete AUTO demos, which can be easily adapted to any autonomous 3-dimensional ODE system, are freely available.Comment: 18 pages, 10 figure

Twinkling pulsar wind nebulae in the synchrotron cut-off regime and the gamma-ray flares in the Crab Nebula

Synchrotron radiation of ultra-relativistic particles accelerated in a pulsar wind nebula may dominate its spectrum up to gamma-ray energies. Because of the short cooling time of the gamma-ray emitting electrons, the gamma-ray emission zone is in the immediate vicinity of the acceleration site. The particle acceleration likely occurs at the termination shock of the relativistic striped wind, where multiple forced magnetic field reconnections provide strong magnetic fluctuations facilitating Fermi acceleration processes. The acceleration mechanisms imply the presence of stochastic magnetic fields in the particle acceleration region, which cause stochastic variability of the synchrotron emission. This variability is particularly strong in the steep gamma-ray tail of the spectrum, where modest fluctuations of the magnetic field lead to strong flares of spectral flux. In particular, stochastic variations of magnetic field, which may lead to quasi-cyclic gamma-ray flares, can be produced by the relativistic cyclotron ion instability at the termination shock. Our model calculations of the spectral and temporal evolution of synchrotron emission in the spectral cut-off regime demonstrate that the intermittent magnetic field concentrations dominate the gamma-ray emission from highest energy electrons and provide fast, strong variability even for a quasi-steady distribution of radiating particles. The simulated light curves and spectra can explain the very strong gamma-ray flares observed in the Crab nebula and the lack of strong variations at other wavelengths. The model predicts high polarization in the flare phase, which can be tested with future polarimetry observations.Comment: 5 pages, 3 figures, MNRAS in pres

Electroconvulsive Therapy as a Corrector for Certain Side Effects of Antipsychotic Therapy

The discovery of the first typical antipsychotics in the 1950s had revolutionized the treatment of many severe mental illnesses. This discovery opened the door for radical humanization and deinstitutionalization of the whole psychiatry. It also served as an impetus for the emergence of a new science, called psychopharmacology. This signaled the beginning of an era of widespread use of psychopharmacotherapy in psychiatry. However, the use of typical antipsychotics has been associated with many side effects, including severe ones, such as severe extrapyramidal syndrome, neuroleptic-induced deficit syndrome, cognitive impairment, and neuroleptic malignant syndrome. This necessitated the development of methods for correction or treatment of such side effects.Over the past decades, a number of new antipsychotics have been synthesised and approved for clinical use. Those new drugs are considered to belong to the group of so-called «atypical antipsychotics». This group, as a whole, has an improved tolerance and safety profile compared to older, conventional antipsychotics. In particular, these new drugs less often cause exactly the aforementioned side effects. Nevertheless, the problem of antipsychotic side effects and their correction is still far from being resolved. Some patients experiencing certain side effects from antipsychotic therapy do not get adequate relief from the standard pharmacological correction of those side effects.This fact stimulated our interest in the study of the possibilities of using electroconvulsive therapy as an alternative or adjuvant method for the correction of some side effects that can arise during antipsychotic therapy. In this article, we thoroughly discuss the existing evidence base regarding the effectiveness and safety of the use of electroconvulsive therapy as a corrector for certain side effects that can occur during antipsychotic therapy

Lithium Preparations in Psychiatry, Addiction Medicine and Neurology. Part II. Biochemical Mechanisms of Its Action

Lithium is the first and the lightest in the series of alkali metals, to which, in addition to lithium, two very biologically important elements – sodium and potassium, as well as trace elements rubidium and cesium, belong. Despite its formal affiliation to the group of alkali metals, lithium, like many other chemical elements of the «atypical» second period of the periodic table (for example, boron), is more similar in its chemical properties not to its counterparts in the group, but to its «diagonal brother» – magnesium. As we will show in this article, the diagonal chemical similarity between lithium and magnesium is of great importance for understanding the mechanisms of its intracellular biochemical action. At the same time, the intragroup chemical similarity of lithium with sodium and potassium is more important for understanding the mechanisms of its absorption, its distribution in the body and its excretion. Despite the 70 years that have passed since John Cade’s discovery of the antimanic effect of lithium, the mechanisms of its therapeutic action are still not completely understood. In the end, it turns out that the mechanism of the therapeutic action of lithium is extremely complex, multicomponent, unique and not imitable. Certain aspects of the mechanism of its action may be compatible with the mechanisms of action of other mood stabilizers, or with the mechanisms of action of so-called «lithium-mimetics», such as ebselen. However, no other drug to date failed to fully reproduce the biochemical effect of lithium on the body