The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.Comment: Accepted for publication in Astrophysics & Space Scienc

Integrable generalizations of oscillator and Coulomb systems via action-angle variables

Oscillator and Coulomb systems on N-dimensional spaces of constant curvature can be generalized by replacing their angular degrees of freedom with a compact integrable (N-1)-dimensional system. We present the action-angle formulation of such models in terms of theradial degree of freedom and the action-angle variables of the angular subsystem. As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz and by Post and Winternitz. We demonstrate the superintegrability of these systems and give their hidden constant of motion.Comment: 10 pages; v2: formulae for hidden integrals and two refs. added, typos fixed, published versio

Tracing the Dark Matter Sheet in Phase Space

The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single valued in velocity space. Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics, and count the number of streams as well as their individual contributions to any point in configuration-space. We calculate the bulk velocity, local velocity dispersions, and densities from the sheet - all without averaging over control volumes. This gives a wealth of new information about dark matter fluid flow which had previously been thought of as inaccessible to N-body simulations. We outline how this mapping may be used to create new accurate collisionless fluid simulation codes that may be able to overcome the sparse sampling and unphysical two-body effects that plague current N-body techniques.Comment: MNRAS submitted; 17 pages, 19 figures; revised in line with referee's comments, results unchange

Minimum Energy Configurations in the NN-Body Problem and the Celestial Mechanics of Granular Systems

Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for $N=1,2,3$ and develops hypotheses on the relative equilibria and minimum energy configurations for $N\gg 1$ bodies.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

Amplified EPOR/JAK2 Genes Define a Unique Subtype of Acute Erythroid Leukemia

ゲノム解析から急性赤白血病の変異プロファイルと治療標的を解明 --特定の遺伝子変異群の組み合わせと、特徴となる遺伝子の増幅が鍵--. 京都大学プレスリリース. 2022-08-05.Acute erythroid leukemia (AEL) is a unique subtype of acute myeloid leukemia characterized by prominent erythroid proliferation whose molecular basis is poorly understood. To elucidate the underlying mechanism of erythroid proliferation, we analyzed 121 AEL using whole-genome/exome and/or targeted-capture sequencing, together with transcriptome analysis of 21 AEL samples. Combining publicly available sequencing data, we found a high frequency of gains/amplifications involving EPOR/JAK2 in TP53-mutated cases, particularly those having >80% erythroblasts designated as pure erythroid leukemia (10/13). These cases were frequently accompanied by gains/amplifications of ERG/ETS2 and associated with a very poor prognosis, even compared with other TP53-mutated AEL. In addition to activation of the STAT5 pathway, a common feature across all AEL cases, these AEL cases exhibited enhanced cell proliferation and heme metabolism and often showed high sensitivity to ruxolitinib in vitro and in xenograft models, highlighting a potential role of JAK2 inhibition in therapeutics of AEL

Chaos, decoherence and quantum cosmology

In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler - DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the Wave function of the Universe adopting a Wentzel - Kramers - Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet.Comment: 40 page

Increase in the number of cataract surgeries performed under the cross-border directive of 2016

Niewydolny system organizacji leczenia zaćmy w Polsce oraz gwarantowana przepisami unijnymi swoboda w realizacji zabiegów usunięcia zaćmy poza Polską stymulują chorych do leczenia w innych państwach członkowskich Unii Europejskiej. Dynamikę tego procesu najlepiej oddaje miesięczna liczba wniosków o refundację kosztów leczenia składanych w oddziałach wojewódzkich Narodowego Funduszu Zdrowia (NFZ). Liczba wniosków złożonych przez chorych w styczniu 2015 r. wzrosła ze 100 do ponad 1200 w grudniu 2016 r. Wzrost zainteresowania polskich pacjentów leczeniem zaćmy poza granicami kraju zaowocował ponad 100-procentowym wzrostem budżetu publicznego transferowanego przez Narodowy Fundusz Zdrowia do placówek medycznych w Czechach i innych krajach Unii Europejskiej. W ciągu ostatnich 2 lat wydatki wzrosły z blisko 12 mln PLN w 2015 r. do ponad 27,5 mln PLN w 2016 r.The inefficient system of cataract treatment in Poland motivates patients to look for cataract surgery treatments in the neighbouring countries within the European Union. The dynamics of the process is best reflected by the number of monthly applications for reimbursement of the treatment submitted to each provincial National Health Fund branch. There were 100 applications submitted by patients in January 2015, and the number grew to more than 1200 in December 2016. The patients’ interest in obtaining cataract treatment outside of Poland resulted in 100% increase in the public budget, which was transferred by the National Health Service to the medical facilities primarily located in the Czech Republic and other EU member states. In the past two years, spending has increased from 12 million PLN in 2015 to over 27.5 million PLN in 2016

The social costs of deferred cataract surgery with implantation of the intraocular lens

W Polsce wykonuje się ponad 200 tys. operacji usunięcia zaćmy rocznie. Niestety, liczba zabiegów jest stale niewystarczająca. Pomimo działań podejmowanych przez Narodowy Fundusz Zdrowia kolejka pacjentów oczekujących na leczenie systematycznie się wydłuża. Obecnie na zabieg usunięcia zaćmy z jednoczesnym wszczepieniem soczewki oczekuje ponad 500 tys. chorych. Wśród nich są nie tylko osoby w zaawansowanym wieku, lecz także osoby aktywne zawodowo. Obie grupy chorych generują koszty pośrednie, które – jak się wydaje – nie są uwzględniane przez Ministerstwo Zdrowia. Wskazują one na konieczność stworzenia ułatwień w dostępie do operacji zaćmy dla pacjentów w wieku produkcyjnym.In Poland, there are more than 200,000 cataract surgeries performed annually. Unfortunately the number of patients waiting for the operation surpasses the amount of surgeries offered. Despite attempts by the National Health Fund, the number of patients waiting for the procedure is gradually increasing. Currently, more than 500,000 people are awaiting cataract surgery with concurrent intraocular lens implantation. The demographics for the aforementioned population include the elderly along with those actively working. Both groups of patients however generate indirect costs, which do not seem to be taken into account by the Ministry of Health. They indicate the necessity to increase the access of cataract surgery for actively working people