Generalized Log-Normal Chain-Ladder

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder based bootstrap. We embed the log normal chain-ladder model in a class of infinitely divisible distributions called the generalized log normal chain-ladder model. The asymptotic theory uses small $\sigma$ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application

Identification of the age-period-cohort model and the extended chain-ladder model

We consider the identification problem that arises in the age-period-cohort models as well as in the extended chain-ladder model. We propose a canonical parameterization based on the accelerations of the trends in the three factors. This parameterization is exactly identified and eases interpretation, estimation and forecasting. The canonical parameterization is applied to a class of index sets which have trapezoidal shapes, including various Lexis diagrams and the insurance-reserving triangles

Understanding the newly observed Y(4008) by Belle

Very recently a new enhancement around 4.05 GeV was observed by Belle experiment. In this short note, we discuss some possible assignments for this enhancement, i.e. $\psi(3S)$ and $D^*\bar{D}^*$ molecular state. In these two assignments, Y(4008) can decay into $J/\psi\pi^0\pi^0$ with comparable branching ratio with that of $Y(4008)\to J/\psi\pi^+\pi^-$. Thus one suggests high energy experimentalists to look for Y(4008) in $J/\psi\pi^0\pi^0$ channel. Furthermore one proposes further experiments to search missing channel $D\bar{D}$, $D\bar{D}^*+h.c.$ and especially $\chi_{cJ}\pi^+\pi^-\pi^0$ and $\eta_c\pi^+\pi^-\pi^0$, which will be helpful to distinguish $\psi(3S)$ and $D^*\bar{D}^*$ molecular state assignments for this new enhancement.Comment: 4 pages, 5 figures. Typos correcte

Feedback system for divertor impurity seeding based on real-time measurements of surface heat flux in the Alcator C-Mod tokamak

Mitigation of the intense heat flux to the divertor is one of the outstanding problems in fusion energy. One technique that has shown promise is impurity seeding, i.e., the injection of low-Z gaseous impurities (typically N2 or Ne) to radiate and dissipate the power before it arrives to the divertor target plate. To this end, the Alcator C-Mod team has created a first-of-its-kind feedback system to control the injection of seed gas based on real-time surface heat flux measurements. Surface thermocouples provide real-time measurements of the surface temperature response to the plasma heat flux. The surface temperature measurements are inputted into an analog computer that "solves" the 1-D heat transport equation to deliver accurate, real-time signals of the surface heat flux. The surface heat flux signals are sent to the C-Mod digital plasma control system, which uses a proportional-integral-derivative (PID) algorithm to control the duty cycle demand to a pulse width modulated piezo valve, which in turn controls the injection of gas into the private flux region of the C-Mod divertor. This paper presents the design and implementation of this new feedback system as well as initial results using it to control divertor heat flux

Calculation of the Chiral Lagrangian Coefficients from the Underlying Theory of QCD: A Simple Approach

We calculate the coefficients in the chiral Lagrangian approximately from QCD based on a previous study of deriving the chiral Lagrangian from the first principles of QCD in which the chiral Lagrangian coefficients are defined in terms of certain Green's functions in QCD. We first show that, in the large N(c)-limit, the anomaly part contributions to the coefficients are exactly cancelled by certain terms in the normal part contributions, and the final results of the coefficients only concern the remaining normal part contributions depending on QCD interactions. We then do the calculation in a simple approach with the approximations of taking the large-N(c) limit, the leading order in dynamical perturbation theory, and the improved ladder approximation, thereby the relevant Green's functions are expressed in terms of the quark self energy. By solving the Schwinger-Dyson equation for the quark self energy, we obtain the approximate QCD predicted coefficients and the quark condensate which are consistent with the experimental values.Comment: Further typos corrected, to appear in Phys. Rev.

Conceptual design study for heat exhaust management in the ARC fusion pilot plant

The ARC pilot plant conceptual design study has been extended beyond its initial scope [B. N. Sorbom et al., FED 100 (2015) 378] to explore options for managing ~525 MW of fusion power generated in a compact, high field (B_0 = 9.2 T) tokamak that is approximately the size of JET (R_0 = 3.3 m). Taking advantage of ARC's novel design - demountable high temperature superconductor toroidal field (TF) magnets, poloidal magnetic field coils located inside the TF, and vacuum vessel (VV) immersed in molten salt FLiBe blanket - this follow-on study has identified innovative and potentially robust power exhaust management solutions.Comment: Accepted by Fusion Engineering and Desig

Decoherence in ion traps due to laser intensity and phase fluctuations

We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with recent experiments and predict that the decoherence rate will depend on vibrational quantum number in different ways depending on which vibrational excitation sideband is used.Comment: 2 figures, submitted to PR

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure

Mutational signatures in tumours induced by high and low energy radiation in Trp53 deficient mice.

Ionising radiation (IR) is a recognised carcinogen responsible for cancer development in patients previously treated using radiotherapy, and in individuals exposed as a result of accidents at nuclear energy plants. However, the mutational signatures induced by distinct types and doses of radiation are unknown. Here, we analyse the genetic architecture of mammary tumours, lymphomas and sarcomas induced by high (56Fe-ions) or low (gamma) energy radiation in mice carrying Trp53 loss of function alleles. In mammary tumours, high-energy radiation is associated with induction of focal structural variants, leading to genomic instability and Met amplification. Gamma-radiation is linked to large-scale structural variants and a point mutation signature associated with oxidative stress. The genomic architecture of carcinomas, sarcomas and lymphomas arising in the same animals are significantly different. Our study illustrates the complex interactions between radiation quality, germline Trp53 deficiency and tissue/cell of origin in shaping the genomic landscape of IR-induced tumours