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.

Directional persistence and the optimality of run-and-tumble chemotaxis

E. coli does chemotaxis by performing a biased random walk composed of alternating periods of swimming (runs) and reorientations (tumbles). Tumbles are typically modelled as complete directional randomisations but it is known that in wild type E. coli, successive run directions are actually weakly correlated, with a mean directional difference of ∼63°. We recently presented a model of the evolution of chemotactic swimming strategies in bacteria which is able to quantitatively reproduce the emergence of this correlation. The agreement between model and experiments suggests that directional persistence may serve some function, a hypothesis supported by the results of an earlier model. Here we investigate the effect of persistence on chemotactic efficiency, using a spatial Monte Carlo model of bacterial swimming in a gradient, combined with simulations of natural selection based on chemotactic efficiency. A direct search of the parameter space reveals two attractant gradient regimes, (a) a low-gradient regime, in which efficiency is unaffected by directional persistence and (b) a high-gradient regime, in which persistence can improve chemotactic efficiency. The value of the persistence parameter that maximises this effect corresponds very closely with the value observed experimentally. This result is matched by independent simulations of the evolution of directional memory in a population of model bacteria, which also predict the emergence of persistence in high-gradient conditions. The relationship between optimality and persistence in different environments may reflect a universal property of random-walk foraging algorithms, which must strike a compromise between two competing aims: exploration and exploitation. We also present a new graphical way to generally illustrate the evolution of a particular trait in a population, in terms of variations in an evolvable parameter.

Supporting sleep in early care and education: An assessment of observed sleep-times using a sleep practices optimality index

Aim: The aim was to investigate whether the sleep practices in early childhood education (ECE) settings align with current evidence on optimal practice to support sleep. Background: Internationally, scheduled sleep times are a common feature of daily schedules in ECE settings, yet little is known about the degree to which care practices in these settings align with the evidence regarding appropriate support of sleep. Methods: Observations were conducted in 130 Australian ECE rooms attended by preschool children (Mean = 4.9 years). Of these rooms, 118 had daily scheduled sleep times. Observed practices were scored against an optimality index, the Sleep Environment and Practices Optimality Score, developed with reference to current evidence regarding sleep scheduling, routines, environmental stimuli, and emotional climate. Cluster analysis was applied to identify patterns and prevalence of care practices in the sleep time. Results: Three sleep practices types were identified. Supportive rooms (36%) engaged in practices that maintained regular schedules, promoted routine, reduced environmental stimulation, and maintained positive emotional climate. The majority of ECE rooms (64%), although offering opportunity for sleep, did not engage in supportive practices: Ambivalent rooms (45%) were emotionally positive but did not support sleep; Unsupportive rooms (19%) were both emotionally negative and unsupportive in their practices. Conclusions: Although ECE rooms schedule sleep time, many do not adopt practices that are supportive of sleep. Our results underscore the need for education about sleep supporting practice and research to ascertain the impact of sleep practices in ECE settings on children’s sleep health and broader well-being.

Altruism, Trade Policy, and the Optimality of Foreign Aid

There are many studies in the literature that deal with the welfare effects of income transfers between nations in a general equilibrium setting. An important impetus for this extensive literature was the demonstration of the transfer paradox; that the donor country could actually gain from a transfer of income to another, and that the recipient could lose as a result of the gift. The reason for this paradoxical result is that the transfer gives rise to a terms-of-trade effect that may be especially beneficial to the donor and detrimental to the recipient. Subsequently, many papers have established conditions under which this paradox will or will not occur. Early work by Samuelson (1954) was followed by demonstrations of paradoxes by Gale (1974), Ohyama (1974), Brecher and Bhagwati (1982) and Bhagwati, Brecher and Hatta 1983, 1985, and Dixit (1983)) among others.1 More recently, many studies have examined whether or not foreign aid — tied and untied — can be welfare improving for both the donor and the recipient (see, for example, Turunen-Red and Woodland (1988), Kemp and Wong (1993), Schweinberger (1990), Hatzipanayotou and Michael (1995), Lahiri and Raimondos-Moller 1995, 1997, Djajić, Lahiri and Raimondos-Møller 1996a, 1996b, and Lahiri, Raimondos-Møller, Wong and Woodland 1997.2

Measuring tax efficiency: A tax optimality index

This paper introduces an index of tax optimality that measures the distance of some current tax structure from the optimal tax structure in the presence of public goods. This index is defined on the [0, 1] interval and measures the proportion of the optimal tax rates that will achieve the same welfare outcome as some arbitrarily given initial tax structure. We call this number the Tax Optimality Index. We also show how the basic methodology can be altered to derive a revenue equivalent uniform tax, which measures the tax burden implied by the public sector. A numerical example is used to illustrate the method developed, and extensions of the analysis to handle models with multiple households and nonlinear taxation structures are undertaken.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion

In the paper, the flow-shop scheduling problem with parallel machines at each stage (machine center) is studied. For each job its release and due date as well as a processing time for its each operation are given. The scheduling criterion consists of three parts: the total weighted earliness, the total weighted tardiness and the total weighted waiting time. The criterion takes into account the costs of storing semi-manufactured products in the course of production and ready-made products as well as penalties for not meeting the deadlines stated in the conditions of the contract with customer. To solve the problem, three constructive algorithms and three metaheuristics (based one Tabu Search and Simulated Annealing techniques) are developed and experimentally analyzed. All the proposed algorithms operate on the notion of so-called operation processing order, i.e. the order of operations on each machine. We show that the problem of schedule construction on the base of a given operation processing order can be reduced to the linear programming task. We also propose some approximation algorithm for schedule construction and show the conditions of its optimality.

Design optimisation using advanced artificial intelligent system coupled to hybrid-game strategies

One of the main aims in artificial intelligent system is to develop robust and efficient optimisation methods for Multi-Objective (MO) and Multidisciplinary Design (MDO) design problems. The paper investigates two different optimisation techniques for multi-objective design optimisation problems. The first optimisation method is a Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The second method combines the concepts of Nash-equilibrium and Pareto optimality with Multi-Objective Evolutionary Algorithms (MOEAs) which is denoted as Hybrid-Game. Numerical results from the two approaches are compared in terms of the quality of model and computational expense. The benefit of using the distributed hybrid game methodology for multi-objective design problems is demonstrated.

Railway junction traffic control by heuristic methods

Traffic conflicts at railway junctions are very conmon, particularly on congested rail lines. While safe passage through the junction is well maintained by the signalling and interlocking systems, minimising the delays imposed on the trains by assigning the right-of-way sequence sensibly is a bonus to the quality of service. A deterministic method has been adopted to resolve the conflict, with the objective of minimising the total weighted delay. However, the computational demand remains significant. The applications of different heuristic methods to tackle this problem are reviewed and explored, elaborating their feasibility in various aspects and comparing their relative merits for further studies. As most heuristic methods do not guarantee a global optimum, this study focuses on the trade-off between computation time and optimality of the resolution.

The conflict resolution in connected railway junctions

Purpose of study: Traffic conflicts occur when trains on different routes approach a converging junction in a railway network at the same time. To prevent collisions, a right-of-way assignment is needed to control the order in which the trains should pass the junction. Such control action inevitably requires the braking and/or stopping of trains, which lengthens their travelling times and leads to delays. Train delays cause a loss of punctuality and hence directly affect the quality of service. It is therefore important to minimise the delays by devising a suitable right-of-way assignment. One of the major difficulties in attaining the optimal right-of-way assignment is that the number of feasible assignments increases dramatically with the number of trains. Connected-junctions further complicate the problem. Exhaustive search for the optimal solution is time-consuming and infeasible for area control (multi-junction). Even with the more intelligent deterministic optimisation method revealed in [1], the computation demand is still considerable, which hinders real-time control. In practice, as suggested in [2], the optimality may be traded off by shorter computation time, and heuristic searches provide alternatives for this optimisation problem.

Optimisation of a class of transportation problems using genetic algorithms

This paper presents a Genetic Algorithms (GA) approach to search the optimized path for a class of transportation problems. The formulation of the problems for suitable application of GA will be discussed. Exchanging genetic information in the sense of neighborhoods will be introduced for generation reproduction. The performance of the GA will be evaluated by computer simulation. The proposed algorithm use simple coding with population size 1 converged in reasonable optimality within several minutes.

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.