Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painlev\'{e} equation ($P_{II}$). Here we define two-variable polynomials $Y_{n}(t,h)$ on a lattice with spacing $h$, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when $h=0$. They also provide rational solutions for a particular discretisation of $P_{II}$, namely the so called {\it alternate discrete} $P_{II}$, and this connection leads to an expression in terms of the Umemura polynomials for the third Painlev\'{e} equation ($P_{III}$). It is shown that B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete $P_{II}$, which recovers Jimbo and Miwa's Lax pair for $P_{II}$ in the continuum limit $h\to 0$.Comment: 23 pages, IOP style. Title changed, and connection with Umemura polynomials adde

Combinatorial RNA Design: Designability and Structure-Approximating Algorithm

In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete characterizations for the structures that can be designed using restricted alphabets. Under a classic four-letter alphabet, we provide a complete characterization of designable structures without unpaired bases. When unpaired bases are allowed, we provide partial characterizations for classes of designable/undesignable structures, and show that the class of designable structures is closed under the stutter operation. Membership of a given structure to any of the classes can be tested in linear time and, for positive instances, a solution can be found in linear time. Finally, we consider a structure-approximating version of the problem that allows to extend bands (helices) and, assuming that the input structure avoids two motifs, we provide a linear-time algorithm that produces a designable structure with at most twice more base pairs than the input structure.Comment: CPM - 26th Annual Symposium on Combinatorial Pattern Matching, Jun 2015, Ischia Island, Italy. LNCS, 201

Creating drag and lift curves from soccer trajectories

Trajectory analysis is an alternative to using wind tunnels to measure a soccer balls aerodynamic properties. It has advantages over wind tunnel testing such as being more representative of game play. However, previous work has not presented a method that produces complete, speed -dependent drag and lift coefficients. Four high-speed cameras in stereo-calibrated pairs were used to measure the spatial co-ordinates for 29 separate soccer trajectories. Those trajectories span a range of launch speeds from 9.3 m/s to 29.9 m/s. That range encompasses low-speed laminar flow of air over a soccer ball, through the drag crises where air flow is both laminar and turbulent, and up to high-speed turbulent air flow. Results from trajectory analysis were combined to give speed-dependent drag and lift coefficient curves for the entire range of speeds found in the 29 trajectories. Average root mean square error between measured and modelled trajectory was 0.028 m horizontally and 0.034 m vertically. The drag and lift crises can be observed in the plots of drag and lift coefficients respectively

Numerical Simulation of Fatigue Crack Growth in Microelectronics Solder Joints

An FEA (finite element analysis) program employing a new scheme for crack growth analysis is developed and a prediction method for crack growth life is proposed. The FEA program consists of the subroutines for the automatic element re-generation using the Delaunay Triangulation technique, the element configuration in the near-tip region being provided by a super-element, elasto-inelastic stress analyses, prediction of crack extension path and calculation of fatigue life. The FEA results show that crack extension rate and path are controlled by a maximum opening stress range, Δσθmax, at a small radial distance of r = d, where d is chosen to be a grain diameter's distance, 3.5 μm, in solder material. The experimentally obtained crack extension rate is found to be related to Δσθmax in FEA as da/dN = β[Δσθmax - γ]α, where α = 2.0, β = 4.5 × 10-9 mm5/N2 and γ = 98 M Pa are determined for all test conditions. The calculated values of crack extension life by the FEA using the above equation are in good agreement with the experimental ones and are independent of the joint types

Heavy and light roles: myosin in the morphogenesis of the heart

Myosin is an essential component of cardiac muscle, from the onset of cardiogenesis through to the adult heart. Although traditionally known for its role in energy transduction and force development, recent studies suggest that both myosin heavy-chain and myosin lightchain proteins are required for a correctly formed heart. Myosins are structural proteins that are not only expressed from early stages of heart development, but when mutated in humans they may give rise to congenital heart defects. This review will discuss the roles of myosin, specifically with regards to the developing heart. The expression of each myosin protein will be described, and the effects that altering expression has on the heart in embryogenesis in different animal models will be discussed. The human molecular genetics of the myosins will also be reviewed

Occurrence and impact of delayed cerebral ischemia after coiling and after clipping in the International Subarachnoid Aneurysm Trial (ISAT)

Delayed cerebral ischemia (DCI) is an important cause of poor outcome after aneurysmal subarachnoid hemorrhage (SAH). We studied differences in incidence and impact of DCI as defined clinically after coiling and after clipping in the International Subarachnoid Aneurysm Trial. We calculated odds ratios (OR) for DCI for clipping versus coiling with logistic regression analysis. With coiled patients without DCI as the reference group, we calculated ORs for poor outcome at 2 months and 1 year for coiled patients with DCI and for clipped patients without, and with DCI. With these ORs, we calculated relative excess risk due to Interaction (RERI). Clipping increased the risk of DCI compared to coiling in the 2,143 patients OR 1.24, 95% confidence interval (95% CI 1.01–1.51). Coiled patients with DCI, clipped patients without DCI, and clipped patients with DCI all had higher risks of poor outcome than coiled patients without DCI. Clipping and DCI showed no interaction for poor outcome at 2 months: RERI 0.12 (95% CI −1.16 to 1.40) or 1 year: RERI −0.48 (95% CI −1.69 to 0.74). Only for patients treated within 4 days, coiling and DCI was associated with a poorer outcome at 1 year than clipping and DCI (RERI −2.02, 95% CI −3.97 to −0.08). DCI was more common after clipping than after coiling in SAH patients in ISAT. Impact of DCI on poor outcome did not differ between clipped and coiled patients, except for patients treated within 4 days, in whom DCI resulted more often in poor outcome after coiling than after clipping

Subtropical mode water variability in a climatologically forced model in the northwestern Pacific Ocean

Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 42 (2012): 126–140, doi:10.1175/2011JPO4513.1.A climatologically forced high-resolution model is used to examine variability of subtropical mode water (STMW) in the northwestern Pacific Ocean. Despite the use of annually repeating atmospheric forcing, significant interannual to decadal variability is evident in the volume, temperature, and age of STMW formed in the region. This long time-scale variability is intrinsic to the ocean. The formation and characteristics of STMW are comparable to those observed in nature. STMW is found to be cooler, denser, and shallower in the east than in the west, but time variations in these properties are generally correlated across the full water mass. Formation is found to occur south of the Kuroshio Extension, and after formation STMW is advected westward, as shown by the transport streamfunction. The ideal age and chlorofluorocarbon tracers are used to analyze the life cycle of STMW. Over the full model run, the average age of STMW is found to be 4.1 yr, but there is strong geographical variation in this, from an average age of 3.0 yr in the east to 4.9 yr in the west. This is further evidence that STMW is formed in the east and travels to the west. This is qualitatively confirmed through simulated dye experiments known as transit-time distributions. Changes in STMW formation are correlated with a large meander in the path of the Kuroshio south of Japan. In the model, the large meander inhibits STMW formation just south of Japan, but the export of water with low potential vorticity leads to formation of STMW in the east and an overall increase in volume. This is correlated with an increase in the outcrop area of STMW. Mixed layer depth, on the other hand, is found to be uncorrelated with the volume of STMW.E.M.D. acknowledges support of the Doherty Foundation and National Science Foundation (OCE-0849808). S.R.J was sponsored by the National Science Foundation (OCE-0849808). Participation of S.P. and F.B. was supported by the National Science Foundation by its sponsorship of the National Center for Atmospheric Research.2012-07-0