Rare event simulation for processes generated via stochastic fixed point equations

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$, where $f(v)=A\max\{v,D\}+B$ for $(A,B,D)\in(0,\infty)\times {\mathbb{R}}^2$. This paper is concerned with computational methods for evaluating these tail probabilities. We introduce a novel importance sampling algorithm, involving an exponential shift over a random time interval, for estimating these rare event probabilities. We prove that the proposed estimator is: (i) consistent, (ii) strongly efficient and (iii) optimal within a wide class of dynamic importance sampling estimators. Moreover, using extensions of ideas from nonlinear renewal theory, we provide a precise description of the running time of the algorithm. To establish these results, we develop new techniques concerning the convergence of moments of stopped perpetuity sequences, and the first entrance and last exit times of associated Markov chains on $\mathbb{R}$. We illustrate our methods with a variety of numerical examples which demonstrate the ease and scope of the implementation.Comment: Published in at http://dx.doi.org/10.1214/13-AAP974 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fractures of the proximal femur in the elderly in a sub-Saharan country

Background: The aim of this study was to describe the epidemiological, radiographic and therapeutic profile of the fractures of the proximal femur in the elderly in a sub-Saharan country.Methods: A retrospective longitudinal study was carried out at the orthopedic trauma department of Idrissa Pouye Hospital in Senegal. Sixty-six patients recruited were aged at least 90 years; and treated for proximal femur fracture between 2008 and 2017.Results: The median age of the patients was 91 years (90-107). Females represented 54.5%. The fracture was located in the right 65.2%. Femoral neck fractures were 53% predominant with 94.3% type IV according to Garden’s classification. Concerning the 31 patients with a pertrochanteric fractures, 61.3% were stable and 38.7% unstable. The time taken for seeking hospital care was an average of 5.8±9.7 days. All patients had a preoperative anesthesic score less than 4 according to the American society of anesthesiologists (ASA). The therapeutic indication was functional in 15.1% of cases, surgical by internal fixation in 39.2% and by arthroplasty in 45.7% of cases. Pertrochanteric fractures were managed by a dynamic hip screw (DHS) in 68.2% and by gamma nail in 18.2%. Femoral neck fractures were managed by Moore's arthroplasty in 93.3% and by bipolar hip prothesis (BHP) in 6.7%.Conclusions: Fractures of the proximal femur represent a growing problem in sub-Saharan Africa. For patients above 90 years, the management remains essentially surgical by internal fixation in pertrochanteric fractures or by arthroplasty in cervical fractures

Fatigue strengthening of damaged steel members using wire arc additive manufacturing

In this study, a directed energy deposition (DED) process called wire arc additive manufacturing (WAAM) is employed for the fatigue strengthening of damaged steel members. Three steel specimens with central cracks were tested under a high-cycle fatigue loading (HCF) regime: (1) the reference specimen; (2) the WAAM-repaired specimen with an as-deposited profile, and (3) the WAAM-repaired specimen machined to reduce stress concentration factors (SCF). The corresponding finite element (FE) simulation of the WAAM process was calibrated using static experimental results, which revealed the main mechanism. The process was found to introduce compressive residual stresses at the crack tip owing to the thermal contraction of the repair. The FE results also revealed that stress concentration exists at the root of the as-deposited WAAM; this stress concentration can be mitigated by machining the WAAM to a pyramid-like shape. The fractography analysis indicated that the cracks were initiated at the WAAM-steel interface, and microscopic observations revealed that the microcracks were arrested by the porosities in the melted interface. The results of this pioneering study suggest that WAAM repair is a promising technique for combating fatigue damage in steel structures

DECOUPLED PAYMENTS IN A CHANGING POLICY SETTING

The studies in this report analyze the effects of decoupled payments in the Federal Agriculture Improvement and Reform (FAIR) Act on recipient households, and assess land, labor, risk management, and capital market conditions that can lead to links between decoupled payments and production choices. Each study contributes a different perspective to understanding the response of U.S. farm households and production to decoupled income transfers. Some use new microdata on farm households collected through USDA's Agricultural Resource Management Survey (ARMS), initiated in 1996, and its predecessor survey. These data are used to compare household and producer behavior and outcomes before and after the FAIR Act. Other studies use applied or conceptual models to characterize the impact of introducing decoupled payments. Collectively, the chapters represent an early stage in the empirical analysis of decoupled payments. The studies address many aspects of the payments' household impacts but remaining issues call for additional analysis. As the analytical paradigm changes with the evolution of farm programs, the development of appropriate data and models will improve our understanding of farm program impacts on the behavior and well-being of U.S. farm households, and the agricultural sector.Agricultural and Food Policy,

4-[(4-Benzyl­oxybenzyl­idene)amino]-1,5-dimethyl-2-phenyl-1H-pyrazol-3(2H)-one

In the title mol­ecule, C25H23N3O2, two terminal phenyl rings are twisted by 50.20 (6) and 71.26 (5)° from the mean plane (r.m.s. deviation = 0.032 Å) of the central benzyl­idene–amino–pyrazolone fragment. The N atoms of the pyrazole ring have a pyramidal environment, the sums of the valence angles around them being 353.5 (2) and 347.3 (2)°. The crystal structure is stabilized by C—H⋯O interactions

Geographical interdependence, international trade and economic dynamics: the Chinese and German solar energy industries

The trajectories of the German and Chinese photovoltaic industries differ significantly yet are strongly interdependent. Germany has seen a rapid growth in market demand and a strong increase in production, especially in the less developed eastern half of the country. Chinese growth has been export driven. These contrasting trajectories reflect the roles of market creation, investment and credit and the drivers of innovation and competitiveness. Consequent differences in competiveness have generated major trade disputes

Integrated photonics on silicon with wide bandgap GaN semiconductor

We report on GaN self-supported photonic structures consisting in freestanding waveguides coupled to photonic crystal waveguides and cavities operating in the near-infrared. GaN layers were grown on Si (111) by metal organic vapor phase epitaxy. E-beam lithography and dry etching techniques were employed to pattern the GaN layer and undercut the substrate. The combination of low-absorption in the infrared range and improved etching profiles results in cavities with quality factors as high as $5400. The compatibility with standard Si technology should enable the development of low cost photonic devices for optical communications combining wide-bandgap III-nitride semiconductors and silicon