Beware the second offer!

In conveyancing of all types, it is very common that a contract will only be formed after often lengthy negotiations which may involve a counter-offer or multiple counter-offers. At common law, the laws of contract that govern these arrangements are well known and well understood. However, the legislative overlay imposed by the requirements of the Property Agents and Motor Dealers Act 2000 (Qld) (‘PAMDA’) can create difficulties as illustrated by the result in Rice v Ray [2009] QDC 275.

Interaction in a Paired Speaking Test : the Rater's Perspective

Paired speaking tests are increasingly used in both low-and high-stakes second language assessment contexts. Until recently, very little was known about the way in which raters interpret and apply descriptors relating to interactional competence to a performance that is co-constructed. This book presents a study which explores the interactional features of a paired speaking test that were sailient to raters and the extent to which raters viewed the performance as separable. The study shows that raters use their own frames of reference to interpret descriptors and that they viewed certain features of the performance as mutual accomplishments. The book takes us 'beyond scores', and in doing so, contributes to the growing body of research on paired speaking tests.

Reflections, successes and pitfalls of coordinating online discussion forums in a foreign language

The advent of e-learning has seen the adaptation and use of a plethora of educational techniques. Of these, online discussion forums have met with success and been used widely in both undergraduate and postgraduate education. The authors of this paper, having previously used online discussion forums in the postgraduate arena with success, adopted this approach for the design and subsequent delivery of a learning and teaching subject. This learning and teaching subject, however, was part of an international collaboration and designed for nurse academics in another country – Vietnam. With the nursing curriculum in Vietnam currently moving to adopt a competency based approach, two learning and teaching subjects were designed by an Australian university for Vietnamese nurse academics. Subject materials constituted a DVD which arrived by post and access to an online platform. Assessment for the subject included (but was not limited to) mandatory participation in online discussion with the other nurse academics enrolled in the subject. The purpose behind the online discussion was to generate discourse between the Vietnamese nurse academics located across Vietnam. Consequently the online discussions occurred in both Vietnamese and English; the Australian academic moderating the discussion did so in Australia with a Vietnamese translator. For the Australian University delivering this subject the difference between this and past online discussions were twofold: delivery was in a foreign language; and the teaching experience of the Vietnamese nurse teachers was mixed and frequently very limited. This paper will provide a discussion addressing the design of an online learning environment for foreign correspondents, the resources and translation required to maximise the success of the online discussion, the lessons learnt and consequent changes made, as well as the rationale of delivering complex content in a foreign language. While specifically addressing the first iteration of the first learning module designed, this paper will also address subsequent changes made for the second iteration of the first module and comment on their success. While a translator is clearly a key component of success, the elements of simplicity and clarity in hand with supportive online moderation must not be overlooked.

On the optimality of sample-based estimates of the expectation of the empirical minimizer

We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates expectations to sample averages. Second, we show that these structural upper bounds can be loose, compared to previous bounds. In particular, we demonstrate a class for which the expectation of the empirical minimizer decreases as O(1/n) for sample size n, although the upper bound based on structural properties is Ω(1). Third, we show that this looseness of the bound is inevitable: we present an example that shows that a sharp bound cannot be universally recovered from empirical data.

Shifting : one-inclusion mistake bounds and sample compression

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d=VC(F) bound on the graph density of a subgraph of the hypercube—one-inclusion graph. The first main result of this report is a density bound of n∙choose(n-1,≤d-1)/choose(n,≤d) < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d-contractible simplicial complexes, extending the well-known characterization that d=1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VC-dimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(log n) and is shown to be optimal up to a O(log k) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout

Adaptive online gradient descent

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between [square root T] and [log T]. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

Margin-adaptive model selection in statistical learning

A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning framework. Actually, we consider a weaker version of this condition that allows one to take into account that learning within a small model can be much easier than within a large one. Requiring this “strong margin adaptivity” makes the model selection problem more challenging. We first prove, in a general framework, that some penalization procedures (including local Rademacher complexities) exhibit this adaptivity when the models are nested. Contrary to previous results, this holds with penalties that only depend on the data. Our second main result is that strong margin adaptivity is not always possible when the models are not nested: for every model selection procedure (even a randomized one), there is a problem for which it does not demonstrate strong margin adaptivity.