Intermediate Level Of Complexity Research Articles

Comparing Perceptual and Computational Complexity for Short Rhythmic Patterns

According to Leibniz ‘Music is the hidden arithmetical exercise of a mind unconscious that it is calculating.’ The perception or experience of time is an essential aspect of listeners’ engagement with music. As such listeners’ experience of rhythmic patterns and their aesthetic response can enhance our understanding of the perception of time. Studies by Berlyne suggest that aesthetic evaluations are low for stimuli that are too simple or too complex with a preference for intermediate level of complexity. In musical terms we would expect listeners to respond negatively to music that is purely repetitive or to music that seems incomprehensibly random and to prefer music that manages to balance familiarity with variation. We present a study that aims to match listeners’ evaluation of rhythmic complexity with computational measures of complexity. We selected five measures derived from information theory - Shannon's entropy, entropy rate, excess entropy, transient information, and Kolmogorov complexity. Rhythmic sequences, covering a wide spectrum of complexity levels according to these measures, were generated algorithmically as binary sequences. These sequences were synthesized as drum patterns with 1s as hits and 0s as rests. 32 participants were asked to guess whether the last beat of each sequence was supposed to be a drum hit or a rest. We averaged the participants’ scores in order to assign an implicit rating of rhythm complexity to each sequence. We also obtained an explicit rating of complexity by asking the participants to rate the perceived difficulty of guessing the last beat for each sequence. Finally, the participants completed the Gold-MSI questionnaire and a shortened version of the Raven's matrices, in order to investigate the effects of musicality and visual pattern identification on the perception of rhythm complexity. The Kolmogorov complexity of the sequences was correlated with the scores on the explicit task (r=.973, p<.001), and the entropy rate of the sequences was correlated with the scores on both implicit (r=.670, p=.012) and explicit tasks (r=.909, p<.001). There was also a Kolmogorov complexity-by-musicality interaction (F=5.498, p=.026), confirming the influence of musical expertise in the perception of rhythm complexity. There was no effect of the scores on the Raven's matrices, showing that auditory sequence perception and visual pattern identification seem to be different abilities. These results show that information-theoretical concepts capture some salient features of rhythm perception, and provide the framework for further studies on the aesthetic perception of rhythm.

Including cetaceans in multi-species assessment models using strandings data: why, how and what can we do about it?

Including cetaceans in multi-species assessment models using strandings data: why, how and what can we do about it?

The application of an enhanced Brute Force algorithm to minimise energy costs and train delays for differing railway train control systems

This paper demonstrates an enhanced Brute Force algorithm application for optimising the driving speed curve by trading off reductions in energy usage against increases in delay penalty. A simulator is used to compare the train operation performance with different train control system configurations when implemented on a section of high-speed line operating with two trains, including differences in journey time and train energy consumption. Results are presented using six different train control system configurations combined with three different operating priorities. Analysis of the results shows that the operation performance can be improved by eliminating the interactions between trains using advanced control systems or optimal operating priorities. The algorithm is shown to achieve the objectives efficiently and accurately. Control system configurations with intermediate levels of complexity (e.g. European Train Control System Levels 2 and 1 with in-fill) when coupled with the optimisation process have been shown to have similar performance to the more advanced control system.

Dominant controls on pesticide transport from tile to catchment scale: Lessons from a minimalist model

This paper proposes a minimalist modeling approach for characterizing pesticide concentrations in runoff from agricultural catchments across spatial scales. The model proposed is of an intermediate level of complexity between traditional chromatographic separation models and the more complex dual‐domain models. Parsimony in the model is achieved by assuming stationarity of catchment travel time distributions and by coupling a dual‐domain source zone model that describes near‐surface pesticide dynamics with the mass response function (MRF) approach, which describes catchment‐scale solute transport. The model is evaluated by comparing predicted atrazine concentrations with measured values over a 5 yr period at two spatial scales (tile drain: 3–5 ha; river station: 69 km2) within an intensively managed agricultural catchment in Illinois, United States. Pesticide dynamics within the source zone provided the strongest control on leaching. Two parameters were calibrated at the tile scale, Γ, which describes partitioning in the dual‐domain surficial source zone, and ke, which describes the mass transfer rate constant between the two domains. The initial peak of concentration was found to be sensitive to Γ, while the later peaks were sensitive to ke. The calibrated parameters at the tile stations were used to predict atrazine dynamics at the river station. Prediction errors are examined and related to the lack of detailed information about anthropogenic forcings across scales (e.g., land‐use or soil/crop management practices).

Cryo-EM Structure of the Archaeal 50S Ribosomal Subunit in Complex with Initiation Factor 6 and Implications for Ribosome Evolution

Translation of mRNA into proteins by the ribosome is universally conserved in all cellular life. The composition and complexity of the translation machinery differ markedly between the three domains of life. Organisms from the domain Archaea show an intermediate level of complexity, sharing several additional components of the translation machinery with eukaryotes that are absent in bacteria. One of these translation factors is initiation factor 6 (IF6), which associates with the large ribosomal subunit. We have reconstructed the 50S ribosomal subunit from the archaeon Methanothermobacter thermautotrophicus in complex with archaeal IF6 at 6.6 Å resolution using cryo-electron microscopy (EM). The structure provides detailed architectural insights into the 50S ribosomal subunit from a methanogenic archaeon through identification of the rRNA expansion segments and ribosomal proteins that are shared between this archaeal ribosome and eukaryotic ribosomes but are mostly absent in bacteria and in some archaeal lineages. Furthermore, the structure reveals that, in spite of highly divergent evolutionary trajectories of the ribosomal particle and the acquisition of novel functions of IF6 in eukaryotes, the molecular binding of IF6 on the ribosome is conserved between eukaryotes and archaea. The structure also provides a snapshot of the reductive evolution of the archaeal ribosome and offers new insights into the evolution of the translation system in archaea.

Complexity theory and engaged research: Critical incidents in the Sydney rail system

This article reports on a study of Sydney's rail system to argue that engaged research requires a problem-oriented complexity framework. This needs a richer method drawing on ideas from more scientific and mathematical forms of complexity/chaos theory to complement cultural studies understandings of complexity. The paper develops the idea of critical incidents as a bridge between science, cultural studies and business, and uses it to analyse small and large problems of Sydney rail, from loose roof-hatch bolts to communication problems in the organization. It also proposes a strategy, virtual trialogues, to construct a manageable intermediate level of complexity and analyse it by adapting digital software.

An intracranial event-related potential study on transformational apparent motion. Does its neural processing differ from real motion?

How the brain processes visual stimuli has been extensively studied using scalp surface electrodes and magnetic resonance imaging. Using these and other methods, complex gratings have been shown to activate the ventral visual stream, whereas moving stimuli preferentially activate the dorsal stream. In the current study, a first experiment assessed brain activations evoked by complex gratings using intracranial electroencephalography in 10 epileptic patients implanted with subdural electrodes. These stimuli of intermediate levels of complexity were presented in such a way that transformational apparent motion (TAM) was perceived. Responses from both the ventral and the dorsal pathways were obtained. The response characteristics of visual area 4 and the fusiform cortex were of similar amplitudes, suggesting that both ventral areas are recruited for the processing of complex gratings. On the other hand, TAM-induced responses of dorsal pathway areas were relatively noisier and of lower amplitudes, suggesting that TAM does not activate motion-specific structures to the same extent as does real motion. To test this hypothesis, we examined the activity evoked by TAM in comparison to the one produced by real motion in a patient implanted with the same subdural electrodes. Findings demonstrated that neural response to real motion was much stronger than that evoked by TAM, in both the primary visual cortex (V1) and other motion-sensitive areas within the dorsal pathway. These results support the conclusion that apparent motion, even if perceptually similar to real motion, is not processed in a similar manner.

Spatial relationships between surface sedimentary facies distribution and topography using remotely sensed data: Example from the Ganghwa tidal flat, Korea

Spatial relationships between surface sedimentary facies distribution and topography, including channel networks and an intertidal digital elevation model (DEM), were estimated for the Ganghwa tidal flat, Korea. Tidal channels were extracted from high spatial resolution satellite data and used to derive maps of channel density and distance from channels. The intertidal DEM was generated by a waterline method using Landsat Enhanced Thematic Mapper Plus (ETM+) images, and the map of surface sedimentary facies distribution was produced from grain-size data on sediment samples. A GIS-based frequency ratio model was applied to quantify the relationships between the surface sediment facies and topographic factors. The result indicated that the fine-grained mud flat facies occurs mainly in areas of complex tidal channels and in elevated areas that have a high spectral reflectance in the Landsat ETM+ image. The coarse-grained sand flat facies is concentrated in areas of sparse tidal channels, and the mixed flat facies is distributed where tidal channels have an intermediate level of complexity. The results demonstrate a significant spatial relationship between the distribution of surface sediment in a tidal flat and topographic features. We conclude that tidal channels should be considered an important factor in mapping surface sedimentary facies in tidal flat environments, and that patterns of tidal topography are a useful adjunct to spectral reflectance in classifying sedimentary facies from remotely sensed data with high spatial resolution.

The Analysis of Simple and Complex Auditory Signals in Human Auditory Cortex: Magnetoencephalographic Evidence From M100 Modulation

Ecologically valid signals (e.g., vowels) have multiple components of substantially different frequencies and amplitudes that may not be equally cortically represented. In this study, we investigate a relatively simple signal at an intermediate level of complexity, two-frequency composite tones, a stimulus lying between simple sinusoids and ecologically valid signals such as speech. We aim to characterize the cortical response properties to better understand how complex signals may be represented in auditory cortex. Using magnetoencephalography, we assessed the sensitivity of the M100/N100m auditory-evoked component to manipulations of the power ratio of the individual frequency components of the two-frequency complexes. Fourteen right-handed subjects with normal hearing were scanned while passively listening to 10 complex and 12 simple signals. The complex signals were composed of one higher frequency and one lower frequency sinusoid; the lower frequency sinusoidal component was at one of the five loudness levels relative to the higher frequency one: -20, -10, 0, +10, +20 dB. The simple signals comprised all the complex signal components presented in isolation. The data replicate and extend several previous findings: (1) the systematic dependence of the M100 latency on signal intensity and (2) the dependence of the M100 latency on signal frequency, with lower frequency signals ( approximately 100 Hz) exhibiting longer latencies than higher frequency signals ( approximately 1000 Hz) even at matched loudness levels. (3) Importantly, we observe that, relative to simple signals, complex signals show increased response amplitude-as one might predict-but decreased M100 latencies. : The data suggest that by the time the M100 is generated in auditory cortex ( approximately 70 to 80 msecs after stimulus onset), integrative processing across frequency channels has taken place which is observable in the M100 modulation. In light of these data models that attribute more time and processing resources to a complex stimulus merit reevaluation, in that our data show that acoustically more complex signals are associated with robust temporal facilitation, across frequencies and signal amplitude level.

Users' Evaluations of House FaÇades: Preference, Complexity and Impressivenes

This research solicits the opinions of the residents of the Keçiören district of Ankara, Turkey, in order to learn their preferences about their local postmodern environment where the municipality forces all contractors and architects to adhere to strict planning laws requiring Turkish folk and Islamic architectural references. The Municipality of Keçiören, as an agent of civil power, manages the architectural and urban transformation of the area from a district formerly composed of squatter housing to one comprised of, in the words of Robert Venturi, “decorated sheds,” in an effort to create a different looking environment rich in nostalgia and excitement. In this research, a total of 7 different sets of apartment façades were analyzed, with each set comprising three examples each of minimum complexity (representing the former condition of the district), intermediate complexity (representing “high” architecture designed by an architect, which does not exist in the district) and maximum complexity (representing the present postmodern condition of the district). The main hypothesis of the study was that preference rates would be high for intermediately altered “high style” houses by showing the existence of a U-shaped relationship between preference and complexity. That is, façades representing an intermediate level of complexity would be favored over less complex and more complex façades. It was also assumed that there would be a difference in the ratings of different age groups. A questionnaire was carried out with 50 adults (aged 30-45) and 50 high school students (aged 18-20) of Keçiören, who were asked to rate a total of 21 photographs from 7 apartment complexes with the help of a five-point semantic differential scales under three headings: preference, complexity and impressiveness. The results proved the existence of a U-shaped relationship between preference and complexity. On the other hand, younger respondents, compared to older respondents, gave more favorable ratings to the physical qualities of the photographed buildings.

Sensitivity Study of Four Land Surface Schemes in the WRF Model

The Weather Research and Forecasting (WRF) model version 3.0 developed by the National Center for Atmospheric Research (NCAR) includes three land surface schemes: the simple soil thermal diffusion (STD) scheme, the Noah scheme, and the Rapid Update Cycle (RUC) scheme. We have recently coupled the sophisticated NCAR Community Land Model version 3 (CLM3) into WRF to better characterize land surface processes. Among these four land surface schemes, the STD scheme is the simplest in both structure and process physics. The Noah and RUC schemes are at the intermediate level of complexity. CLM3 includes the most sophisticated snow, soil, and vegetation physics among these land surface schemes. WRF simulations with all four land surface schemes over the western United States (WUS) were carried out for the 1 October 1995 through 30 September 1996. The results show that land surface processes strongly affect temperature simulations over the (WUS). As compared to observations, WRF‐CLM3 with the highest complexity level significantly improves temperature simulations, except for the wintertime maximum temperature. Precipitation is dramatically overestimated by WRF with all four land surface schemes over the (WUS) analyzed in this study and does not show a close relationship with land surface processes.

Functional–structural plant modelling in crop production. Wageningen UR Frontis Series, vol. 22

Functional–structural plant modelling in crop production. Wageningen UR Frontis Series, vol. 22

Architecture and engineering students' evaluations of house façades: Preference, complexity and impressiveness

In this study, five different sets of single-family house façades from private suburban cooperative housing developments in Ankara, Turkey, were analyzed; with each set comprising one example each of minimum, intermediate and maximum complexity. Although the houses in each set had the same appearance when they were first built, their façades have since been altered by their owners. The main hypothesis of the study was that preference rates would be high for intermediately altered houses by showing the existence of a U-shaped relationship. On the other hand, it was hypothesized that perceived complexity and perceived impressiveness would have a linear relationship, with perceived complexity increasing and perceived impressiveness decreasing as the complexity level changed. In terms of these two basic hypotheses, it was also assumed that there would be a difference in the ratings of particular respondent groups with different backgrounds. Thus, a questionnaire was given to 100 undergraduate students of the Architecture and Engineering Departments of Gazi University, Ankara (41 from architecture and 59 from engineering). These students were asked to rate a total of 15 photographs from five housing sites with the help of five-point semantic differential scales under three headings; namely: Preference: beautiful – ugly, warm – cold, pleasant – unpleasant; Complexity: unimposing – imposing, simple – complex; and Impressiveness: impressive – unimpressive. The results proved the existence of a U-shaped relationship between complexity and preference criteria. That is, façades representing an intermediate level of complexity were favored over less and more complex ones. The façades that seemed the most impressive were the most complex ones, but these, however, were not the most preferred. Amongst these results, it was also noted that the architecture students replied in a more critical way than the engineering students as they criticized what they saw as negative design decisions.

Enveloped viruses understood via multiscale simulation: computer-aided vaccine design

Enveloped viruses are viewed as an opportunity to understand how highly organized and functional biosystems can emerge from a collection of millions of chaotically moving atoms. They are an intermediate level of complexity between macromolecules and bacteria. They are a natural system for testing theories of self-assembly and structural transitions, and for demonstrating the derivation of principles of microbiology from laws of molecular physics. As some constitute threats to human health, a computer-aided vaccine and drug design strategy that would follow from a quantitative model would be an important contribution. However, current molecular dynamics simulation approaches are not practical for modeling such systems. Our multiscale approach simultaneously accounts for the outer protein net and inner protein/genomic core, and their less structured membranous material and host fluid. It follows from a rigorous multiscale deductive analysis of laws of molecular physics. Two types of order parameters are introduced: (1) those for structures wherein constituent molecules retain long-lived connectivity (they specify the nanoscale structure as a deformation from a reference configuration) and (2) those for which there is no connectivity but organization is maintained on the average (they are field variables such as mass density or measures of preferred orientation). Rigorous multiscale techniques are used to derive equations for the order parameters dynamics. The equations account for thermal-average forces, diffusion coefficients, and effects of random forces. Statistical properties of the atomic-scale fluctuations and the order parameters are co-evolved. By combining rigorous multiscale techniques and modern supercomputing, systems of extreme complexity can be modeled.

Congruent epidemic models for unstructured and structured populations: Analytical reconstruction of a 2003 SARS outbreak

Both the threat of bioterrorism and the natural emergence of contagious diseases underscore the importance of quantitatively understanding disease transmission in structured human populations. Over the last few years, researchers have advanced the mathematical theory of scale-free networks and used such theoretical advancements in pilot epidemic models. Scale-free contact networks are particularly interesting in the realm of mathematical epidemiology, primarily because these networks may allow meaningfully structured populations to be incorporated in epidemic models at moderate or intermediate levels of complexity. Moreover, a scale-free contact network with node degree correlation is in accord with the well-known preferred mixing concept. The present author describes a semi-empirical and deterministic epidemic modeling approach that (a) focuses on time-varying rates of disease transmission in both unstructured and structured populations and (b) employs probability density functions to characterize disease progression and outbreak controls. Given an epidemic curve for a historical outbreak, this modeling approach calls for Monte Carlo calculations (that define the average new infection rate) and solutions to integro-differential equations (that describe outbreak dynamics in an aggregate population or across all network connectivity classes). Numerical results are obtained for the 2003 SARS outbreak in Taiwan and the dynamical implications of time-varying transmission rates and scale-free contact networks are discussed in some detail.

A new fast stratospheric ozone chemistry scheme in an intermediate general‐circulation model. II: Application to effects of future increases in greenhouse gases

AbstractWhile chlorine loadings in the atmosphere are expected to decrease towards pre‐ozone‐hole levels by 2060, the greenhouse gases (GHGs) burden is rising continuously and may in turn significantly modify the stratospheric ozone layer.In this study, use is made of the new interactively coupled chemistry–general‐circulation model IGCMFASTOC to investigate in detail the response of stratospheric ozone to a specified increase in GHG concentrations between 1979 and 2060.The Intermediate General Circulation Model (IGCM) is a relatively fast general‐circulation model with parametrizations of an intermediate level of complexity, and the new chemistry scheme Fast STratospheric Ozone Chemistry (FASTOC) is an efficient input‐output model composed of pre‐computed nonlinear functions.A total of seven 14‐year time‐slice simulations are performed to allow for the separation of individual processes and the analysis of sensitivity to methane and stratospheric water‐vapour scenarios.In a basic scenario where all GHG concentrations increase (except stratospheric H2O) the total ozone column is found to increase at a global rate of 0.27 DU decade−1 with maxima in late winter–spring poles. This increase is merely the result of two opposing effects: (i) An increase of ozone concentration in the summer and tropical stratospheric region near 30–40 km which is passively advected into the polar‐night vortex between 40 and 20 km. This ozone increase is due to the slowing down of the NOx catalytic cycle caused by the cooling of the stratosphere resulting from increased GHG concentrations in the stratosphere. (ii) A decrease of ozone concentration in the same region which is also advected into the polar‐night vortex, due to enhanced NOx concentrations caused by the increased N2O concentrations. These two opposing effects are additive to a large degree, i.e. the sum of their individual effects is a good approximation of their total effect when the processes are acting together.A significant deviation from this additivity occurs inside the northern polar‐night vortex and to a lesser extent in the southern polar‐night vortex. Our analysis suggests that methane is mainly responsible for this feature. The impact of methane increase on ozone is confined to the high latitudes and is found to have a negative sign in the northern polar vortex when the stratospheric cooling is taken into account, and a positive sign when no stratospheric cooling is taken into account.The scenario where methane is kept at its 1979 level produces a global rate of increase of the ozone column of 9% above the basic scenario. The scenario where stratospheric H2O is increased by 50% leads to a global rate of increase of the ozone column of 70% above the basic scenario. Finally, in a scenario where CO2 is reduced to its 1979 level and the other GHGs involved in the ozone chemistry are increased as in the basic scenario, the global effect of GHGs on the ozone layer is to decrease it at a rate of 0.37 DU decade−1. Copyright © 2005 Royal Meteorological Society

Conditional Akaike information for mixed-effects models

SUMMARY This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the AIC in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional AIC, CAIC. The penalty term in CAIC is related to the effective degrees of freedom p for a linear mixed model proposed by Hodges & Sargent (2001); p reflects an intermediate level of complexity between a fixed-effects model with no cluster effect and a corresponding model with fixed cluster effects. The CAIC is defined for both maximum likelihood and residual maximum likelihood estimation. A pharmacokinetics data appli cation is used to illuminate the distinction between the two inference settings, and to illustrate the use of the conditional AIC in model selection.

Bioclimatic model of tree radial growth: application to the French Mediterranean Aleppo pine forests

The potential effects of global changes on forests are of increasing concern. Dendrochronology, which deals with long-term records of tree growth under natural environmental conditions, can be used to evaluate the impact of climatic change on forest productivity. However, assessment of climatic change impacts must be supported by accurate and reliable models of the relationships between climate and tree growth. In this study, a bioclimatic model is used to explore the relationships between tree radial growth and bioclimatic variables closely related to the biological functioning of a tree. This model is at an intermediate level of complexity between purely empirical and process-based models. The method is illustrated with data for 21 Aleppo pine (Pinus halepensis Mill.) stands grown under a Mediterranean climate in south-east France. The results show that Aleppo pine growth is mainly controlled by soil water availability during the growing season. The bioclimatic variable which best expresses the observed inter-annual tree growth variations is the actual evapotranspiration (AET). Four parameters were adjusted to simulate dendrochronological data: the soil water capacity, the wilting point, the minimum temperature for photosynthesis, and the end of the growing season. The bioclimatic model gives better results than the standard response function and provides better insight into the functional processes involved in tree growth. The convincing results obtained by the bioclimatic model as well as the limited numbers of parameters it requires demonstrate the feasibility of using it to explore future climatic change impacts on Aleppo pine forests.

Numerical Forward Modeling of Carbonate Platform Dynamics: An Evaluation of Complexity and Completeness in Carbonate Strata

ABSTRACT It is clear that carbonate strata are complex and incomplete, but the nature and origins of the complexity, and the origin and distribution of hiatuses remain poorly understood. A three-dimensional numerical forward model of carbonate platform systems has been used to investigate how variations in complexity and completeness arise in carbonate strata. The model includes depth-dependent carbonate production occurring as a stochastic mosaic of producing elements across a topographic surface. It also includes depth-dependent sediment erosion, transport, and deposition governed by a regional transport direction that can vary stochastically through time, and by wave refraction that causes local variations in transport direction. Combined mosaic production and variable sediment transport create a complex distribution of prograding islands, generating self-organizing, shallowing-upward parasequences of variable thickness and variable lateral extent. Hiatuses occur throughout the parasequences, not just at the base and top, generated by nondeposition due to mosaic production, and by erosional scour. This erosion is triggered by variations in water depth and fetch distance, created by complex island morphologies. Preserved strata represent between 15 and 60% of total elapsed time measured at a 2 ky resolution, and much of the preserved thickness represents punctuated deposition, with depositional events spanning only a few thousand years. Stratigraphic completeness depends on subsidence rate and sediment transport rate, so that completeness generally increases with increasing subsidence rate and decreasing transport rate, but shows a nonlinear relationship with subsidence rate. This suggests that reliable estimates of completeness of ancient carbonate strata require more than knowledge of subsidence rate and sea-level change, particularly because the real situation is likely to be considerably more complex than represented in this model. The stochastic production mosaic and stochastic variations in regional transport direction create complex strata, whereas the self-organizing island progradation process creates simpler, ordered strata. A combination of the two processes creates an intermediate level of complexity, producing strata consisting of laterally impersistent parasequences with numerous erosion surfaces and complex stacking patterns and complex thickness distributions. This has important implications for parasequence correlation in outcrop and the subsurface.

Equivalence relationships between stage-structured population models

Matrix population models are widely applied in conservation ecology to help predict future population trends and guide conservation effort. Researchers must decide upon an appropriate level of model complexity, yet there is little theoretical work to guide such decisions. In this paper we present an analysis of a stage-structured model, and prove that the model's structure can be simplified and parameterised in such a way that the long-term growth rate, the stable-stage distribution and the generation time are all invariant to the simplification. We further show that for certain structures of model the simplified models require less effort in data collection. We also discuss features of the models which are not invariant to the simplification and the implications of our results for the selection of an appropriate model. We illustrate the ideas using a population model for short-tailed shearwaters ( Puffinus tenuirostris). In this example, model simplification can increase parameter elasticity, indicating that an intermediate level of complexity is likely to be preferred.