Risk management strategies using seasonal climate forecasting in irrigated cotton production: a tale of stochastic dominance.

Decision-making in agriculture is carried out in an uncertain environment with farmers often seeking information to reduce risk. As a result of the extreme variability of rainfall and stream-flows in north-eastern Australia, water supplies for irrigated agriculture are a limiting factor and a source of risk. The present study examined the use of seasonal climate forecasting (SCF) when calculating planting areas for irrigated cotton in the northern Murray Darling Basin. Results show that minimising risk by adjusting plant areas in response to SCF can lead to significant gains in gross margin returns. However, how farmers respond to SCF is dependent on several other factors including irrigators’ attitude towards risk.

On states, on a lattice, with half-integral charge

In certain molecular models, and related one-dimensional field theories, localized objects appear with half-integral expectation values of charge. We consider whether these states are eigenstates of charge, with half-integral eigenvalue. We find that it is indeed so for a suitably diffuse definition of the charge operator in question. This diffuse charge operator has a spectrum which approaches a continuum. The analysis is made on a lattice, to avoid divergence ambiguities, and on a finite length, which is only subsequently made large. The half-integral charge phenomenon is not tied to solitons, but can also arise as an end effect.

Evolution in design of integral leg prosthesis leads to improved outcomes

Developments of surgical attachments for bone-anchored prostheses are slowly but surely winning over the initial disbelief in the orthopedic community. Clearly, this option is becoming accessible to a wide range of individuals with limb loss. Seminal studies have demonstrated that the pioneering procedure relying on screw-type fixation engenders major clinical benefits and acceptable safety. The surgical procedure for press-fit implants, such as the Integral-Leg-Prosthesis (ILP) has been described Dr Aschoff and his team. Some clinical benefits of press-fit implants have been also established. Here, his team is once again taking a leading role by sharing the progression over 15 years of the rate of deep infections for 69 individuals with transfemoral amputation fitted with three successive refined versions of the ILP. By definition, a double-blind randomized clinical trial to test the effect of different fixation’s design is difficult. Alternatively, Juhnke and colleagues are reporting the outcomes of action-research study for a cohort of participants. The first and foremost important outcome of this study is the confirmation that the current design of the IPL and rehabilitation program are altogether leading to an acceptable rate of deep infection and other adverse events (e.g., structural failure of implant, periprosthetic factures). This study is also providing a strong insight onto the effect of major phases in redesign of an implant on the risk of infection. This is an important reminder that the development of a successful osseointegrated implant is unlikely to be immediate but the results of a learning curve made of empirical and sequential changes led by a reflective clinical practice. Clearly, this study provided better understanding of the safety of the ILP surgical and rehabilitation procedure while establishing standards and benchmark data for future studies focusing on design and infection of press-fit implants. Complementary observations of relationship between infection and cofounders such as loading of the prosthesis and prosthetic components used would be beneficial.Further definitive evidences of the clinical benefits with the latest design would be valuable, although an increase in health related quality of life and functional outcomes are likely to be confirmed. Altogether, the authors are providing compelling evidence that bone-anchored attachments particularly those relying on press-fit implants are an established alternative to socket prostheses.

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1. Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity. 2. We analyse a stochastic environment model of the red kangaroo (Macropus rufus), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates. 3. Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate. 4. Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates. 5. Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c. 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c. 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

Efficient implementations of a pseudodynamical stochastic filtering strategy for static elastography

A computationally efficient pseudodynamical filtering setup is established for elasticity imaging (i.e., reconstruction of shear modulus distribution) in soft-tissue organs given statically recorded and partially measured displacement data. Unlike a regularized quasi-Newton method (QNM) that needs inversion of ill-conditioned matrices, the authors explore pseudodynamic extended and ensemble Kalman filters (PD-EKF and PD-EnKF) that use a parsimonious representation of states and bypass explicit regularization by recursion over pseudotime. Numerical experiments with QNM and the two filters suggest that the PD-EnKF is the most robust performer as it exhibits no sensitivity to process noise covariance and yields good reconstruction even with small ensemble sizes.

Stochastic Modeling of an Aircraft Traversing a Runway Using Time Series Analysis

Time series, from a narrow point of view, is a sequence of observations on a stochastic process made at discrete and equally spaced time intervals. Its future behavior can be predicted by identifying, fitting, and confirming a mathematical model. In this paper, time series analysis is applied to problems concerning runwayinduced vibrations of an aircraft. A simple mathematical model based on this technique is fitted to obtain the impulse response coefficients of an aircraft system considered as a whole for a particular type of operation. Using this model, the output which is the aircraft response can be obtained with lesser computation time for any runway profile as the input.

On solitons with half integral charge

Can certain soliton states, with half integral expectation value of charge, be also eigenstates of charge X with half integral eigenvalue? It can be so only with a somewhat sophisticated definition of charge.

Stochastic kinetics of ribosomes: Single motor properties and collective behavior

Syntheses of protein molecules in a cell are carried out by ribosomes.A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a Michaelis-Menten-type'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechanochemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in three-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Stochastic growth of the Eastern King Prawn (melicertus plebejus (hess, 1865)) harvested off Eastern Australia

Stochastic growth models were fitted to length-increment data of eastern king prawns, Melicertus plebejus (Hess, 1865), tagged across eastern Australia. The estimated growth parameters and growth transition matrix are for each sex representative of the species' geographical distribution. Our study explicitly displays the stochastic nature of prawn growth. Capturing length-increment growth heterogeneity for short-lived exploited species such as prawns that cannot be readily aged is essential for length-based modelling and improved management.