Linear Trade-off Research Articles

Data quality and query cost in pervasive sensing systems

This research is motivated by large-scale pervasive sensing applications. We examine the benefits and costs of caching data for such applications. We propose and evaluate several approaches to querying for, and then caching data in a sensor field data server. We show that for some application requirements (i.e., when delay drives data quality), policies that emulate cache hits by computing and returning approximate values for sensor data yield a simultaneous quality improvement and cost saving. This win–win is because when system delay is sufficiently important, the benefit to both query cost and data quality achieved by using approximate values outweighs the negative impact on quality due to the approximation. In contrast, when data accuracy drives quality, a linear trade-off between query cost and data quality emerges. We also identify caching and lookup policies for which the sensor field query rate is bounded when servicing an arbitrary workload of user queries. This upper bound is achieved by having multiple user queries share the cost of a single sensor field query. Finally, we demonstrate that our results are robust to the manner in which the environment being monitored changes using models for two different sensing systems.

The BUMP model of response planning: Variable horizon predictive control accounts for the speed–accuracy tradeoffs and velocity profiles of aimed movement

The BUMP model is a comprehensive discrete-time computational model of response planning. Developed within the Adaptive Model Theory framework, it is based on intermittent optimal control. The theory posits a basic unit of motor production (BUMP) that is determined by a planning system that operates intermittently at fixed intervals of time. Given sensory information about the position and velocity of the actual response as well as the predicted future state of the target, the response planning system generates an optimal response trajectory to reach the predicted future state of the target and to compensate for executional error. The ability to vary the duration, or prediction horizon, of the trajectory gives rise to the concept of variable horizon predictive control. We propose that the combination of signal-dependent noise in the nervous system and variable horizon predictive control accounts for the well-known speed–accuracy tradeoffs and velocity profiles in aimed movements. Conducting a simulation study, we found that on one extreme of variable horizon control, a receding horizon strategy reproduced Fitts’ law and corresponding asymmetrical velocity profiles. On the other extreme, a fixed horizon strategy reproduced the linear tradeoff and corresponding symmetrical velocity profiles. We conclude that the BUMP model provides a unifying theoretical bridge between speed–accuracy tradeoffs and the accompanying velocity profiles of aimed movement.

SINK-LIMITATION AND THE SIZE-NUMBER TRADE-OFF OF ORGANS: PRODUCTION OF ORGANS USING A FIXED AMOUNT OF RESERVES

Abstract To analyze the nature of size-number trade-off of organs, we develop models in which the effects of sink-limitation in the growth of organs and the loss of resources by maintenance respiration are taken into consideration. In these models, the resource absorption rate of an organ is proportional to either its absolute size or its surface area and either the initial size of an organ or the total initial size of the organs produced is fixed. In all models, organs are produced using a fixed amount of reserved resources and no additional resources become newly available for their growth. We theoretically show that size-number trade-offs are nonlinear if the resource absorption rate of an organ is proportional to the absolute size of the organ and the initial size of the individual organs is fixed or if the resource absorption rate of an organ is proportional to the surface area of the organ. In these nonlinear size-number trade-offs, the size of individual organs increases less rapidly than in linear trade-offs with a decrease in the number of organs and the total size of organs is an increasing function of the number of organs produced. This implies that increasing the number of organs produced is advantageous in terms of resource-use efficiency. In contrast, size-number trade-off is linear if the resource absorption rate of an organ is proportional to the absolute size of the organ and there is a linear trade-off between the initial size of organs and their number. To exemplify the effects of those size-number trade-offs on the life-history evolution, we calculate the optimal offspring sizes that maximize the number of offspring successfully being established. In the case of nonlinear size-number trade-offs, the optimal offspring sizes are smaller than the optimal offspring size in the case of linear size-number trade-offs, namely, that in the model of Smith and Fretwell (1974). Our optimal offspring size depends on the metabolism of organ development; the optimal offspring size decreases with an increase in maintenance respiration rate relative to the growth coefficient of organs.

The evolution of crypsis in replicating populations of web‐based prey

To investigate the evolution of background matching (crypsis) when prey are viewed against uniform and heterogeneous (alternating) backgrounds, we conducted some web‐based experiments. Visitors to our experimental web site were rewarded for finding artificial prey, thereby providing a measure of their detectability. We first compared the “survivorship” of a range of pixilated prey phenotypes presented against both light green and dark green pixilated backgrounds and found clear evidence for a concave tradeoff curve, indicating that specialism on one or the other background would maximise their overall survivorship. We then compared the survivorship of a range of spotted prey phenotypes presented against backgrounds with small spots and large spots and found evidence for a more linear tradeoff curve, indicating that both intermediates and specialists would have approximately equal survivorship. Replicated evolutionary experiments were then conducted in which the survivors in any given system automatically reproduced themselves (subject to occasional mutation) when their population size was depleted to a critical threshold. Here close background matching readily evolved when prey were presented against a single uniform pixilated environment and when prey were presented against a single uniform spotted environment. As expected, the background matching that evolved in alternating light and dark green environments involved specialism on one or other background, and no intermediate forms evolved. By contrast, a more polymorphic range of phenotypes evolved in the alternating small and large spotted environments. To our knowledge this is the first time that automatically regenerating populations of web based prey have been set up to address evolutionary questions. Our findings have clearly shown conditions under which jack‐of‐all‐trades cryptic forms survive poorly, and, although more work is needed, it may also help explain why background matching frequently appears so specialized in natural systems.

The role of trade-off shapes in the evolution of parasites in spatial host populations: An approximate analytical approach

Given the substantial changes in mixing in many populations, there is considerable interest in the role that spatial structure can play in the evolution of disease. Here we examine the role of different trade-off shapes in the evolution of parasites in a spatially structured host population where infection can occur locally or globally. We develop an approximate adaptive dynamic analytical approach, to examine how the evolutionarily stable (ES) virulence depends not only on the fraction of global infection/transmission but also on the shape of the trade-off between transmission and virulence. Our analysis can successfully predict the ES virulence found previously by simulation of the full system. The analysis confirms that when there is a linear trade-off between transmission and virulence spatial structure may lead to an ES virulence that increases as the proportion of global transmission increases. However, we also show that the ESS disappears above a threshold level of global infection, leading to maximization. In addition just below this threshold, there is the possibility of evolutionary bi-stabilities. When we assume the realistic trade-off between transmission and virulence that results in an ESS in the classical mixed model, we find that spatial structure can increase or decrease the ES virulence. A relatively high proportion of local infection reduces virulence but intermediate levels can select for higher virulence. Our work not only emphasizes the importance of spatial structure to the evolution of parasites, but also makes it clear that situations between the local and the global need to be considered. We also emphasize the key role that the shape of trade-offs plays in evolutionary outcomes.

Spectral and Temporal Cues in Cochlear Implant Speech Perception

Taking advantage of the flexibility in the number of stimulating electrodes and the stimulation rate in a modern cochlear implant, the present study evaluated relative contributions of spectral and temporal cues to cochlear implant speech perception. Four experiments were conducted by using a Research Interface Box in five MED-EL COMBI 40+ cochlear implant users. Experiment 1 varied the number of electrodes from four to twelve or the maximal number of available active electrodes while keeping a constant stimulation rate at 1000 Hz per electrode. Experiment 2 varied the stimulation rate from 1000 to 4000 Hz per electrode on four pairs of fixed electrodes. Experiment 3 covaried the number of stimulating electrodes and the stimulation rate to study the trade-off between spectral and temporal cues. Experiment 4 studied the effects of envelope extraction on speech perception and listening preference, including half-wave rectification, full-wave rectification, and the Hilbert transform. Vowels, consonants, and HINT sentences in quiet, as well as with a competing female voice served as test materials. Experiment 1 found significant improvement in all speech tests with a higher number of stimulating electrodes. Experiment 2 found a significant advantage of the high stimulation rate only on consonant recognition and sentence recognition in noise. Experiment 3 found an almost linear trade-off between the number of stimulation electrodes and the stimulation rate for consonant and sentence recognition in quiet, but not for vowel and sentence recognition in noise. Experiment 4 found significantly better performance with the Hilbert transform and the full-wave rectification than the half-wave rectification. In addition, envelope extraction with the Hilbert transform produced the highest rating on subjective judgment of sound quality. Consistent with previous studies, the present result from the five MED-EL subjects showed that (1) the temporal envelope cues from a limited number of channels are sufficient to support high levels of phoneme and sentence recognition in quiet but not for speech recognition in a competing voice, (2) consonant recognition relies more on temporal cues while vowel recognition relies more on spectral cues, (3) spectral and temporal cues can be traded to some degree to produce similar performance in cochlear implant speech recognition, and (4) the Hilbert envelope improves both speech intelligibility and quality in cochlear implants.

Production of offspring using current income and reserves: size-number trade-off and optimal offspring size

To analyse the effects of current income on the nature of size-number trade-off and optimal offspring size, we developed a model in which offspring grow by absorbing current income and reserves. The offspring continue to grow while the current income is available or the reserves exist, and they cease to grow when the reserves are depleted and the current income ceases. We showed that the size-number trade-off is nonlinear in the region where the number of offspring is smaller than the critical number and linear in the region where the number of offspring is greater than the critical number. In the former region, the reserves are not depleted by the time the current income ceases and the offspring cease to grow when the reserves are depleted, whereas in the latter region, the reserves are depleted before the current income ceases and the offspring production is completed when the current income ceases. The optimal offspring size is the same as that shown in Sakai and Harada (Evolution 55 (2001) 467) if this optimal size is realized in the region of nonlinear trade-off, whereas the optimal offspring size is the same as that shown in Smith and Fretwell (Am. Natur. 108 (1974) 499) if this optimal size is realized in the region of linear trade-off.

Theoretical derivation of SNR, CNR and spatial resolution for a local adaptive strain estimator for elastography

Conventional techniques in elastography estimate the axial strain as the gradient of the displacement (time-delay) estimates obtained using cross-correlation of pre- and temporally stretched postcompression radiofrequency (RF) A-line segments. The use of a constant stretch factor for stretching the postcompression A-line is not adequate in the presence of heterogeneous targets that are commonly encountered. This led to the development of several adaptive strain estimation techniques in elastography. Yet, a theoretical framework for the image quality of adaptive strain estimation has not been established. In this work, we develop theoretical expressions for the image quality [measured in terms of the signal-to-noise ratio (SNR), contrrast-to-noise ratio (CNR) and spatial resolution] of elastograms obtained using an adaptive strain estimator developed by Alam et al. (1998). We show a linear trade-off between the SNR and axial resolution of the strain elastogram with respect to the window length used for strain estimation. The CNR shows a quadratic tradeoff with the axial resolution with respect to the window length. The SNR, CNR and axial resolution are shown to improve with the ultrasonic bandwidth. (E-mail: jonathan.ophir@uth.tmc.edu)

Perceived transparency of neutral density filters across dissimilar backgrounds.

We examine how the luminance distributions of overlaid surfaces affect the perception of transparency of neutral density filters. Pairs of neutral density filters were generated overlying variegated backgrounds of varying luminance distributions, and observers adjusted a single parameter of one filter until the pair appeared equally transparent. Physically identical filters appeared equally transparent on similar backgrounds, but did not appear equally transparent when backgrounds differed in luminance or contrast. Reducing luminance or contrast of the background decreased perceived transparency of the overlaying filter by a multiplicative factor. Observers matched perceived transparency of physically dissimilar filters by applying a linear trade-off between reflectivity and inner transmittance. In a second experiment, filters had their spatial structure altered in order to abolish the perception of transparency and appeared as patterned opaque disks, and observers equated perceived contrast of the two overlaid areas. Match settings gave results similar to the previous experiment, indicating that, in general, perceived transparency corresponds closely to the perceived contrast of the overlaid region.

Sensory and physical determinants of perceived achromatic transparency.

What are the physical and sensory determinants of perceived transparency? To explore this question, we simulated pairs of physically different neutral density filters on a CRT and asked observers to match their perceived transparency. Matching was accomplished by adjusting one of two physically independent filter properties, reflectivity and inner transmittance. Results show that observers can make reliable matches through a linear trade-off of these two properties. In a separate experiment, observers matched the perceived contrast of the overlaid regions. The reflectivity and inner transmittance values for contrast matches are similar to those of perceived transparency matches, suggesting that perceived image contrast is the sensory determinant of perceived transparency. In variegated displays, neither Michelson contrast nor other standard contrast metrics predicts contrast appearance. When perceived transparency is plotted in terms of filter reflectance and filter transmittance, perceived transparency corresponds closely to filter transmittance.

The evolution of trade-offs: testing predictions on response to selection and environmental variation.

The concept of phenotypic trade-offs is a central element in evolutionary theory. In general, phenotypic models assume a fixed trade-off function, whereas quantitative genetic theory predicts that the trade-off function will change as a result of selection. For a linear trade-off function selection will readily change the intercept but will have to be relatively stronger to change the slope. We test these predictions by examining the trade-off between fecundity and flight capability, as measured by dorso-longitudinal muscle mass, in four different populations of the sand cricket, Gryllus firmus. Three populations were recently derived from the wild, and the fourth had been in the laboratory for 19 years. We hypothesized that the laboratory population had most likely undergone more and different selection from the three wild populations and therefore should differ from these in respect to both slope and intercept. Because of geographic variation in selection, we predicted a general difference in intercept among the four populations. We further tested the hypothesis that this intercept will be correlated with proportion macropterous and that this relationship will itself vary with environmental conditions experienced during both the nymphal and adult period. Observed variation in the phenotypic trade-off was consistent with the predictions of the quantitative genetic model. These results point to the importance of modeling trade-offs as dynamic rather than static relationships. We discuss how phenotypic models can incorporate such variation. The phenotypic trade-off between fecundity and dorso-longitudinal muscle mass is determined in part by variation in body size, illustrating the necessity of considering trade-offs to be multi factorial rather than simply bivariate relationships.

Guidance in evolutionary multi-objective optimization

Many real world design problems involve multiple, usually conflicting optimization criteria. Often, it is very difficult to weight the criteria exactly before alternatives are known. Multi-Objective Evolutionary Algorithms based on the principle of Pareto optimality are designed to explore the complete set of non-dominated solutions, which then allows the user to choose among many alternatives. However, although it is very difficult to exactly define the weighting of different optimization criteria, usually the user has some notion as to what range of weightings might be reasonable. In this paper, we present a novel, simple, and intuitive way to integrate the user's preference into the evolutionary algorithm by allowing to define linear maximum and minimum trade-off functions. On a number of test problems we show that the proposed algorithm efficiently guides the population towards the interesting region, allowing a faster convergence and a better coverage of this area of the Pareto optimal front.

Sink-limitation and the size-number trade-off of organs: production of organs using a fixed amount of reserves.

To analyze the nature of size-number trade-off of organs, we develop models in which the effects of sink-limitation in the growth of organs and the loss of resources by maintenance respiration are taken into consideration. In these models, the resource absorption rate of an organ is proportional to either its absolute size or its surface area and either the initial size of an organ or the total initial size of the organs produced is fixed. In all models, organs are produced using a fixed amount of reserved resources and no additional resources become newly available for their growth. We theoretically show that size-number trade-offs are nonlinear if the resource absorption rate of an organ is proportional to the absolute size of the organ and the initial size of the individual organs is fixed or if the resource absorption rate of an organ is proportional to the surface area of the organ. In these nonlinear size-number trade-offs, the size of individual organs increases less rapidly than in linear trade-offs with a decrease in the number of organs and the total size of organs is an increasing function of the number of organs produced. This implies that increasing the number of organs produced is advantageous in terms of resource-use efficiency. In contrast, size-number trade-off is linear if the resource absorption rate of an organ is proportional to the absolute size of the organ and there is a linear trade-off between the initial size of organs and their number. To exemplify the effects of those size-number trade-offs on the life-history evolution, we calculate the optimal offspring sizes that maximize the number of offspring successfully being established. In the case of nonlinear size-number trade-offs, the optimal offspring sizes are smaller than the optimal offspring size in the case of linear size-number trade-offs, namely, that in the model of Smith and Fretwell (1974). Our optimal offspring size depends on the metabolism of organ development; the optimal offspring size decreases with an increase in maintenance respiration rate relative to the growth coefficient of organs.

Size-number trade-off and allocation to flower production in animal-pollinated flowers

The evolutionarily stable size of attractive structures of a flower was analyzed theoretically to examine the factors that select for the differences in the size of attractive structures of a flower depending on the sexuality and self-fertilization rate. In the first analysis, it was assumed that the size–number trade-off for flowers is non-linear (the size of individual flowers increases less rapidly than in a linear trade-off with a decrease in the number of flowers, as would occur during a linear trade-off) and the frequency of pollinator visits per flower depends on the size of attractive structures of individual flowers, but is independent of the number of flowers on the plant. In this case the size of attractive structures is larger in male flowers than in female flowers in dioecious plants, and this size decreases with an increase in the self-fertilization rate for hermaphroditic plants (where both are consistent with the general trends observed). In the second analysis, it was assumed that the size–number trade-off for flowers is linear and the frequency of pollinator visits per flower depends not only on the size of attractive structures of individual flowers, but also on the number of flowers on the plant. However, the results were inconsistent with the general trends in this case; namely, that the size of the attractive structures is smaller in male flowers than in female flowers in dioecious plants, and this size increases with an increase in self-fertilization rate for hermaphroditic plants. I therefore conclude that the non-linearity in size–number trade-offs for flowers is a more useful factor to use to explain the general trends in the size of attractive structures of a flower. This also suggests that the attractive function hypothesis, that is, the differences in fitness gains through allocation to attractive structures between males and females and among plants with different self-fertilization rates, are important factors, but alone cannot explain the general trends.

The Shape of the Trade-Off Function Between Egg Production and Life Span in the Parasitoid Asobara Tabida

Despite a large number of studies on the cost of reproduction, the shape of the trade-off between reproduction and survival is still unresolved. In this paper, two prominent alternatives with respect to this problem are compared in the parasitoid Asobara tabida (Nees): a linear relationship between egg production and physiological life span, and a linear relationship between egg production and intrinsic mortality rate. This is the first study that directly assesses the shape of the trade-off function between reproduction and survival in an insect parasitoid. We manipulated egg production to be low, medium or high and measured the associated life span under laboratory conditions. The results showed a decrease in mean life span with increasing egg production. The data differed significantly from a trade-off function between egg production and mortality rate, while a linear trade-off function between egg production and physiological life span produced an accurate description of the data.

Short- vs. Long-range Disperser: the Evolutionarily Stable Allocation in a Lattice-Structured Habitat

The population dynamics of two types of organisms in a lattice-structured habitat are studied and the evolutionarily stable allocation between short- and long-range disperser is calculated. Offsprings of short-range dispersal stay in the vicinity of their parent and cause local competition. Using pair approximation, I derive a closed system of ordinary differential equations of global and local densities (or mean crowding), and calculate the condition for one type to invade the population dominated by the other type. The evolutionarily stable strategy (ESS) of resource allocation is derived for the case in which there is a linear trade-off between short- and long-range dispersers. The maximum equilibrium abundance of the population may be achieved by a mixture of both types of dispersers, but it is in general different from the ESS resource allocation calculated from the invasibility condition. For the same parameter values, the ESS invests a larger fraction of resources to short-range disperser than the optimal allocation which maximizes the equilibrium population density. This difference can be explained by the fact that long-range disperser is more effective in the preoccupation of space than short-range disperser. The predictions are confirmed by the direct computer simulations of the lattice stochastic models.

Micromagnetic modelling of nanocrystalline magnets and structures

Numerical micromagnetic 3D simulation of nanocrystalline magnetic materials and structures determine the microstructural factors controlling the magnetisation reversal process. Predictions for size and shape of grains and elements in order to obtain optimum magnetic properties are made. The micromagnetic predictions of coercivity and remanence for composite hard magnets cover the range of (H c , J r )=(0.34, 1.4 T) to (0.61 MA/m, 1.1 T), assuming a grain size of 20 nm and an Nd 2Fe 14B content of 40%. The calculations reveal a linear trade off of remanence and coercivity as a function of the α-Fe to Fe 3B ratio. Increasing Fe 3B content improves the coercive field, but reduces the remanence and deteriorates the squareness of the hysteresis loop. The coercive field shows a maximum at a grain size of about D=15–20 nm. Intergrain exchange interactions override the magnetocrystalline anisotropy of the ND 2Fe 14B grains for smaller grains, whereas exchange hardening of the soft phases becomes less effective for larger grains. The magnetisation distribution shows a vortex-like structure within soft magnetic regions with an extension greater than 80 nm. The vortices have zero net magnetisation and act as nucleation sites, reducing remanence and coercivity. The shape of the grains considerably influences the squareness of the demagnetisation curve. Our simulation shows that the magnetisation reversal starts with reversible rotations of the magnetisation within the soft magnetic phase followed by irreversible switching of the hard magnetic grains. The minimum size and the domain wall jaggedness of nanocrystalline Co/Pt multilayered films strongly depend on the average size and misorientation of grains. Switching fields in patterned NiFe and Co elements are also influenced and the formation of a multidomain structure is suppressed on the type of anisotropy and the size and shape of the elements containing nanocrystalline grains.

Leadtime-Inventory Trade-Offs in Assemble-to-Order Systems

This paper studies the trade-off between inventory levels and the delivery leadtime offered to customers in achieving a target level of service. It addresses the question of how much a delivery leadtime can be reduced, per unit increase in inventory, at a fixed fill rate. We show that for a class of assemble-to-order models with stochastic demands and production intervals there is a simple linear trade-off between inventory and delivery leadtime, in a limiting sense, at high fill rates. The limiting slope is easy to calculate and can be interpreted as the approximate marginal rate for trading off inventory against leadtime at a constant level of service. We also investigate how various model features affect the trade-off—in particular, the impact of orders for multiple units of a single item and of orders for multiple units of different items.

Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem

Due to its obvious practical relevance, the Time-Cost Tradeoff Problem has attracted the attention of many researchers over the last forty years. While the Linear Time-Cost Tradeoff Problem can be solved in polynomial time, its discrete variant is known to be NP-hard. We present the first approximation algorithms for the Discrete Time-Cost Tradeoff Problem. Specifically, given a fixed budget we consider the problem of finding a shortest schedule for a project. We give an approximation algorithm with performance ratio 3/2 for the class of projects where all feasible durations of activities are either 0, 1, or 2. We extend our result by giving approximation algorithms with performance guarantee O(log l), where l is the ratio of the maximum duration of any activity to the minimum nonzero duration of any activity. Finally, we discuss bicriteria approximation algorithms which compute schedules for a given deadline or budget such that both project duration and cost are within a constant factor of the duration and cost of an optimum schedule for the given deadline or budget.

Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem

Due to its obvious practical relevance, the Time-Cost Tradeoff Problem has attracted the attention of many researchers over the last forty years. While the Linear Time-Cost Tradeoff Problem can be ...