Excitation energies, polarizabilities, multipole transition rates, and lifetimes of ions along the francium isoelectronic sequence

Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the 7s, 7p, 6d, and 5f states of Fr-like ions with nuclear charges Z = 87 - 100 are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for 7s - 7p, 7p - 6d, and 6d - 5f electric-dipole transitions; and 7s - 6d, 7s - 5f, and 5f_5/2 - 5f_7/2 multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions Z = 87 - 92 calculations are also carried out using the relativistic all-order single-double method, in which single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. With the aid of the SD wave functions, we obtain accurate values of energies, transition rates, oscillator strengths, and the lifetimes of these six ions. Ground state scalar polarizabilities in Fr I, Ra II, Ac III, and Th IV are calculated using relativistic third-order and all-order methods. Ground state scalar polarizabilities for other Fr-like ions are calculated using a relativistic second-order method. These calculations provide a theoretical benchmark for comparison with experiment and theory.Comment: 13 figures, 11 table

Eclipsing binary statistics - theory and observation

The expected distributions of eclipse-depth versus period for eclipsing binaries of different luminosities are derived from large-scale population synthesis experiments. Using the rapid Hurley et al. BSE binary evolution code, we have evolved several hundred million binaries, starting from various simple input distributions of masses and orbit-sizes. Eclipse probabilities and predicted distributions over period and eclipse-depth (P/dm) are given in a number of main-sequence intervals, from O-stars to brown dwarfs. The comparison between theory and Hipparcos observations shows that a standard (Duquennoy & Mayor) input distribution of orbit-sizes (a) gives reasonable numbers and P/dm-distributions, as long as the mass-ratio distribution is also close to the observed flat ones. A random pairing model, where the primary and secondary are drawn independently from the same IMF, gives more than an order of magnitude too few eclipsing binaries on the upper main sequence. For a set of eclipsing OB-systems in the LMC, the observed period-distribution is different from the theoretical one, and the input orbit distributions and/or the evolutionary environment in LMC has to be different compared with the Galaxy. A natural application of these methods are estimates of the numbers and properties of eclipsing binaries observed by large-scale surveys like Gaia.Comment: 11 pages, 16 figures, accepted for publication in A&

Partition Information and its Transmission over Boolean Multi-Access Channels

In this paper, we propose a novel partition reservation system to study the partition information and its transmission over a noise-free Boolean multi-access channel. The objective of transmission is not message restoration, but to partition active users into distinct groups so that they can, subsequently, transmit their messages without collision. We first calculate (by mutual information) the amount of information needed for the partitioning without channel effects, and then propose two different coding schemes to obtain achievable transmission rates over the channel. The first one is the brute force method, where the codebook design is based on centralized source coding; the second method uses random coding where the codebook is generated randomly and optimal Bayesian decoding is employed to reconstruct the partition. Both methods shed light on the internal structure of the partition problem. A novel hypergraph formulation is proposed for the random coding scheme, which intuitively describes the information in terms of a strong coloring of a hypergraph induced by a sequence of channel operations and interactions between active users. An extended Fibonacci structure is found for a simple, but non-trivial, case with two active users. A comparison between these methods and group testing is conducted to demonstrate the uniqueness of our problem.Comment: Submitted to IEEE Transactions on Information Theory, major revisio

Functional Equivalency Inferred from “Authoritative Sources” in Networks of Homologous Proteins

A one-on-one mapping of protein functionality across different species is a critical component of comparative analysis. This paper presents a heuristic algorithm for discovering the Most Likely Functional Counterparts (MoLFunCs) of a protein, based on simple concepts from network theory. A key feature of our algorithm is utilization of the user's knowledge to assign high confidence to selected functional identification. We show use of the algorithm to retrieve functional equivalents for 7 membrane proteins, from an exploration of almost 40 genomes form multiple online resources. We verify the functional equivalency of our dataset through a series of tests that include sequence, structure and function comparisons. Comparison is made to the OMA methodology, which also identifies one-on-one mapping between proteins from different species. Based on that comparison, we believe that incorporation of user's knowledge as a key aspect of the technique adds value to purely statistical formal methods

Nonlinear vibration of orthotropic shallow shells of the complex shape with variable thickness

Early R-functions theory [1] combined with variational methods have been applied to linear [2] and nonlinear vibration problems [3,4] of the shallow shells theory of the constant thickness. In the present study, we first apply R-functions theory in order to investigate the geometrically nonlinear vibrations of orthotropic shallow shells of complex shape with variable thickness. Mathematical formulation is made in the framework of classical geometrically nonlinear theory of thin shallow shells. For a discretization of the original system in time, approximation of unknown functions is carried out by using a single mode approach. In order to construct a system of basic functions, the proposed algorithm includes sequence of the linear problems such as finding eigen functions of the linear vibrations of shallow shells with variable thickness and auxiliary tasks of the elasticity theory. The linear problems are solved by the R-functions method. The developed approach allows reducing the original problem to the corresponding problem of solving nonlinear ordinary differential equations (ODEs), whose coefficients are presented in analytical form. In order to solve the obtained system of ODEs the Bubnov-Galerkin method is applied. The proposed algorithm is implemented within an automated system POLE-RL [1]. Numerical examples of large-amplitude flexible vibrations of shallow orthotropic shells with complex shape and variable thickness are introduced demonstrating merits and advantages of the R-functions method. Comparison of the obtained results regarding shells with rectangular plans with the other methods confirms the reliability of the proposed method