Mathematical Programs for Belief Propagation and Consensus

This paper develops methods of distributed Bayesian hypothesis tests for fault detection and diagnosis that are based on belief propagation and optimization in graphical models. The main challenges in developing distributed statistical estimation algorithms are i) difficulties in ensuring convergence and consensus for solutions of distributed inference problems, ii) increasing computational costs due to lack of scalability, and iii) communication constraints for networked multi-agent systems. To cope with those challenges, this manuscript considers i) belief propagation and optimization in graphical models of complex distributed systems, ii) decomposition methods of optimization for parallel and iterative computations, and iii) distributed decision-making protocols.Comment: 25 pages, 2 figures, technical repor

A Note on the Convexity of log⁡det⁡(I+KX−1)\log \det ( I + KX^{-1} ) and its Constrained Optimization Representation

This note provides another proof for the {\em convexity} ({\em strict convexity}) of $\log \det ( I + KX^{-1} )$ over the positive definite cone for any given positive semidefinite matrix $K \succeq 0$ (positive definite matrix $K \succ 0$) and the {\em strictly convexity} of $\log \det (K + X^{-1})$ over the positive definite cone for any given $K \succeq 0$. Equivalent optimization representation with linear matrix inequalities (LMIs) for the functions $\log \det ( I + KX^{-1} )$ and $\log \det (K + X^{-1})$ are presented. Their optimization representations with LMI constraints can be particularly useful for some related synthetic design problems

Roles of Direct Break-up Reaction on Neutrino Scattering off 12^{12}C near Nucleon Threshold Region

Neutrino (antineutrino) scattering off $^{12}$C is one of various important key reactions for $\nu$-process in the nucleosysnthesis of light nuclei. Most of neutrino-nucleus scattering are considered through indirect processes within the energy range from a few to tens of MeV. Target nuclei are excited by incident neutrino (antineutrino) through various transitions, and subsequently decay into other nuclei with emitting particles. But, direct processes are also feasible, in which incident neutrino (antineutrino) strips directly one nucleon from target nuclei. Consequently, direct processes may affect abundances of $^{11}$C and $^{11}$B additionally to indirect processes. We investigate direct neutrino (antineutrino) quasi-elastic scattering off $^{12}$C around the energy region liberating one nucleon and discuss implications of direct processes in the nucleosynthesis. The direct processes might be comparable to the indirect processes if the final state interaction is taken into account.Comment: 9 pages, 3 figure

Stability Analysis of Discrete-time Lure Systems with Slope-restricted Odd Monotonic Nonlinearities

Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global asymptotic stability analysis of discrete-time Lure systems in which the nonlinearities have restricted slope and/or are odd, which is the usual case in real applications. A Lure-Postnikov-type Lyapunov function is proposed that is used to derive sufficient analysis conditions in terms of linear matrix inequalities (LMIs). The derived stability critera are provably less conservative than criteria published in the literature, with numerical examples indicating that conservatism can be reduced by orders of magnitude

General limit on the relation between abundances of D and 7^7Li in big bang nucleosynthesis with nucleon injections

The injections of energetic hadrons could have occurred in the early universe by decays of hypothetical long-lived exotic particles. The injections induce the showers of nonthermal hadrons via nuclear scattering. Neutrons generated at these events can react with $^7$Be nuclei and reduce $^7$Be abundance solving a problem of the primordial $^7$Li abundance. We suggest that thermal neutron injection is a way to derive a model independent conservative limit on the relation between abundances of D and $^7$Li in a hadronic energy injection model. We emphasize that an uncertainty in cross sections of inelastic $n+p$ scattering affects the total number of induced neutrons, which determines final abundances of D and $^7$Li. In addition, the annihilations of antinucleons with $^4$He result in higher D abundance and trigger nonthermal $^6$Li production. It is concluded that a reduction of $^7$Li abundance from a value in the standard big bang nucleosynthesis (BBN) model down to an observational two $\sigma$ upper limit is necessarily accompanied by an undesirable increase of D abundance up to at least an observational 12 $\sigma$ upper limit from observations of quasi-stellar object absorption line systems. The effects of antinucleons and secondary particles produced in the hadronic showers always lead to a severer constraint. The BBN models involving any injections of extra neutrons are thus unlikely to reproduce a small $^7$Li abundance consistent with observations.Comment: 14 pages, 6 figure

High-lying Gamow-Teller excited states in the deformed nuclei, 76Ge^{76}\textrm{Ge} and 82Se^{82}\textrm{Se}, by the smearing of the Fermi surface in Deformed Quasi-particle RPA (DQRPA)

With the advent of high analysis technology in detecting the Gamow-Teller (GT) excited states beyond one nucleon emission threshold, the quenching of the GT strength to the Ikeda sum rule seems to be recovered by the high-lying GT states. Moreover, in some nuclei, the stronger GT peaks than any other peaks appear explicitly in the high-lying excited states. We address that these high-lying GT excited states stems from the smearing of the Fermi surface by the increase of the chemical potential owing to the deformation within a framework of the deformed quasi-particle random phase approximation (DQRPA). Detailed mechanism leading to the smearing is discussed, and comparisons to the available experimental data are shown to explain the strong peaks on the high-lying GT excited states in a satisfactory manner.Comment: 8 figures. arXiv admin note: substantial text overlap with arXiv:1205.456

Effects of the density-dependent weak form factors on the neutrino reaction via neutral current for the nucleon in nuclear medium and 12^{12}C

The nucleon form factors in free space are usually thought to be modified when a nucleon is bound in a nucleus or immersed in a nuclear medium. We investigate effects of the density-dependent axial and weak-vector form factors on the electro-neutrino ($\nu_e$) and anti-electro-neutrino $({\bar \nu_e})$ reactions via neutral current (NC) for a nucleon in nuclear medium or $^{12}$C. For the density-dependent form factors, we exploit the quark-meson-coupling (QMC) model, and apply them to the $\nu_e$ and ${\bar \nu_e}$ induced reactions by NC. About 12% decrease of the total cross section by $\nu_e$ reaction on the nucleon is obtained at normal density, $\rho = \rho_0 \sim 0.15 {fm}^{-3}$, as well as about 18% reduction of total ${\nu}_e$ cross section on $^{12}$C, by the modification of the weak form factors of the bound nucleon. However, similarly to the charged current reaction, effects of the nucleon property change in the ${\bar \nu}_e$ reaction reduce significantly the cross sections about 30% for the nucleon in matter and $^{12}$C cases. Such a large asymmetry in the ${\bar \nu}_e$ cross sections is addressed to originate from the different helicities of ${\bar \nu}_e$ and ${\nu}_e$

The Axial Current in Electromagnetic Interaction

We discussed the possibility that the charged axial currents of matter fields could be non-conserved in electromagnetic interaction at $O(e)$ order. It means that chiral symmetry is broken explicitly by electromagnetic interaction. This explicit symmetry breaking of chiral symmetry is shown to lead the mass differences between the charged and neutral particles of matter fields.Comment: 8 page

A Role of the Axial Vector Mesons on the Photon Production in Heavy Ion Collisions and Their Relevant Decays

A role of the axial vector mesons, such as $K_1$ and $a_1$, on the emitted photon spectrum in hot hadronic matter is studied through the channels $\pi \rho \to a_1 \to \pi \gamma$ and $K \rho \to K_1 \to K \gamma$. They are shown to be dominant channels in this spectrum. This study is carried out with an effective chiral lagrangian which includes vector and axial-vector mesons and explains well their relevant decays simultaneously.Comment: 12 pages, 2 figure

Corrected constraints on big bang nucleosynthesis in a modified gravity model of f(R)∝Rnf(R) \propto R^n

Big bang nucleosynthesis in a modified gravity model of $f(R)\propto R^n$ is investigated. The only free parameter of the model is a power-law index $n$. We find cosmological solutions in a parameter region of $1< n \leq (4+\sqrt{6})/5$. We calculate abundances of $^4$He, D, $^3$He, $^7$Li, and $^6$Li during big bang nucleosynthesis. We compare the results with the latest observational data. It is then found that the power-law index is constrained to be $(n-1)=(-0.86\pm 1.19)\times 10^{-4}$ (95 % C.L.) mainly from observations of deuterium abundance as well as $^4$He abundance.Comment: 6 pages, 2 figures, Published by APS at http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.10402