On approximation of Markov binomial distributions

For a Markov chain $\mathbf{X}=\{X_i,i=1,2,...,n\}$ with the state space $\{0,1\}$, the random variable $S:=\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\mathcal{L}S$ when $\mathbf{X}$ is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\mathcal{L}S$ when $\operatorname {Var}S$ is greater than and less than $\mathbb{E}S$, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ194 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

In this paper we extend the consumption-investment life cycle model for an uncertain-lived agent, proposed by Richard (1974), to allow for exible labor supply. We further study the consumption, labor supply and portfolio decisions of an agent facing age-dependent mortality risk, as presented by UK actuarial life tables spanning the time period from 1951-2060 (including mortality forecasts). We find that historical changes in mortality produces significant changes in portfolio investment (more risk taking), labour (decrease of hours) and consumption level (shift to higher level) contributing up to 5% to GDP growth during the period from 1980 until 2010

Switching and Rectification of a Single Light-sensitive Diarylethene Molecule Sandwiched between Graphene Nanoribbons

The 'open' and 'closed' isomers of the diarylethene molecule that can be converted between each other upon photo-excitation are found to have drastically different current-voltage characteristics when sandwiched between two graphene nanoribbons (GNRs). More importantly, when one GNR is metallic and another one is semiconducting, strong rectification behavior of the 'closed' diarylethene isomer with the rectification ratio >10^3 is observed. The surprisingly high rectification ratio originates from the band gap of GNR and the bias-dependent variation of the lowest unoccupied molecular orbital (LUMO) of the diarylethene molecule, the combination of which completely shuts off the current at positive biases. Results presented in this paper may form the basis for a new class of molecular electronic devices.Comment: The Journal of Chemical Physics 135 (2011

Optimal management and inflation protection for defined contribution pension plans

Due to the increasing risk of inflation and diminishing pension benefits, insurance companies have started selling in°ation-linked products. Selling such products the insurance company takes over some or all of the inflation risk from their customers. On the other side financial derivatives which are linked to inflation such as inflation linked bonds are traded on financial markets and appear to be of increasing popularity. The insurance company can use these products to hedge its own inflation risk. In this article we study how to optimally manage a pension fund taking positions in a money market account, a stock and an inflation linked bond, while financing investments through a continuous stochastic income stream such as the plan member's contributions. We use the martingale method in order to compute an analytic expression for the optimal strategy and express it in terms of observable market variables.Pension mathematics; in°ation; long-term investment; stochastic optimal control; martingale method

On the asymptotics of locally dependent point processes

AbstractWe investigate a family of approximating processes that can capture the asymptotic behaviour of locally dependent point processes. We prove two theorems presented to accommodate respectively the positively and negatively related dependent structures. Three examples are given to illustrate that our approximating processes can circumvent the technical difficulties encountered in compound Poisson process approximation (see Barbour and Månsson (2002) [10]) and our approximation error bound decreases when the mean number of the random events increases, in contrast to the increasing of bounds for compound Poisson process approximation

Progress in Pathogenesis of Proteinuria

Aims. Proteinuria not only is a sign of kidney damage, but also is involved in the progression of renal diseases as an independent pathologic factor. Clinically, glomerular proteinuria is most commonly observed, which relates to structural and functional anomalies in the glomerular filtration barrier. The aim of this paper was to describe the pathogenesis of glomerular proteinuria. Data Sources. Articles on glomerular proteinuria retrieved from Pubmed and MEDLINE in the recent 5 years were reviewed. Results. The new understanding of the roles of glomerular endothelial cells and the glomerular basement membrane (GBM) in the pathogenesis of glomerular proteinuria was gained. The close relationships of slit diaphragm (SD) molecules such as nephrin, podocin, CD2-associated protein (CD2AP), a-actinin-4, transient receptor potential cation channel 6 (TRPC6), Densin and membrane-associated guanylate kinase inverted 1 (MAGI-1), α3β1 integrin, WT1, phospholipase C epsilon-1 (PLCE1), Lmx1b, and MYH9, and mitochondrial disorders and circulating factors in the pathogenesis of glomerular proteinuria were also gradually discovered. Conclusion. Renal proteinuria is a manifestation of glomerular filtration barrier dysfunction. Not only glomerular endothelial cells and GBM, but also the glomerular podocytes and their SDs play an important role in the pathogenesis of glomerular proteinuria

Robust Fault Tolerant Control for Discrete-Time Dynamic Systems With Applications to Aero Engineering Systems

Unexpected faults in actuators and sensors may degrade the reliability and safety of aero engineering systems. Therefore, there is motivation to develop integrated fault tolerant control techniques with applications to aero engineering systems. In this paper, discrete-time dynamic systems, in the presence of simultaneous actuator/sensor faults, partially decoupled unknown input disturbances, and sensor noises, are investigated. A jointly state/fault estimator is formulated by integrating an unknown input observer, augmented system approach, and optimization algorithm. Unknown input disturbances can be either decoupled by an unknown input observer, or attenuated by a linear matrix inequality optimization, enabling the estimation error to be input-to-state stable. Estimator-based signal compensation is then implemented to mitigate adverse effects from the unanticipated actuator and sensor faults. A pre-designed controller, which maintains normal system behaviors under a fault-free scenario, is allowed to work along with the presented fault tolerant mechanism of the signal compensations. The fault-tolerant closed-loop system can be ensured to mitigate the effects from the faults, guarantee the input-to-state stability, and satisfy the required robustness performance. The proposed fault estimation and fault tolerant control methods are developed for both discrete-time linear and discrete-time Lipschitz nonlinear systems. Finally, the proposed techniques are applied to a jet engine system and a flight control system for simulation validation

Electrical transport across metal/two-dimensional carbon junctions: Edge versus side contacts

Metal/two-dimensional carbon junctions are characterized by using a nanoprobe in an ultrahigh vacuum environment. Significant differences were found in bias voltage (V) dependence of differential conductance (dI/dV) between edge- and side-contact; the former exhibits a clear linear relationship (i.e., dI/dV \propto V), whereas the latter is characterized by a nonlinear dependence, dI/dV \propto V3/2. Theoretical calculations confirm the experimental results, which are due to the robust two-dimensional nature of the carbon materials under study. Our work demonstrates the importance of contact geometry in graphene-based electronic devices