Analyzing the misperception of exponential growth in graphs.

Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants’ math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.

Self-Seeding Procedure for Obtaining Stacked Block Copolymer Lamellar Crystals in Solution

We examined the formation of self-seeded platelet-like crystals from polystyrene-block-polyethylene oxide (PS-b-PEO) diblock copolymers in toluene as a function of polymer concentration (c), crystallization temperature (TC), and self-seeding temperature (TSS). We showed that the number (N) of platelet-like crystals and their mean lateral size (L) can be controlled through a self-seeding procedure. As (homogeneous) nucleation was circumvented by the self-seeding procedure, N did not depend on TC. N increased linearly with c and decayed exponentially with TSS but was not affected significantly by the time the sample was kept at TSS. The solubility limit of PS-b-PEO in toluene (c*), which was derived from the linear extrapolation of Nc→ 0 and from the total deposited mass of the platelets per area (MCc→0), depended on TC. We have also demonstrated that at low N, stacks consisting of a (large) number (η) of uniquely oriented lamellae can be achieved. At a given TC, L was controlled by N and η as well as by ∆c=c−c∗. Thus, besides being able to predict size and number of platelet-like crystals, the self-seeding procedure also allowed control of the number of stacked lamellae in these crystals.

Optimal forecast algorithm based on compatible linear filtration and extrapolation

This work considers the methods of optimal linear extrapolation of the flight path of the aircraft, which provide a minimum of the mean square of the forecast error with different amounts of a priori information. The research is based on the canonical decomposition of a vectorial random process. It is determined that the development of modern technologies entails increasing requirements for quality and accuracy of control. However, since the existing methods of linear extrapolation do not provide for the maximum accuracy of the forecast due to the inherent constraints on the random process that describe the motion of aircraft, this necessitates a further development and improvement of methods for extrapolation of aircraft trajectories. The peculiarity of the developed methods for extrapolation of aircraft trajectory is that they allow within the correlation model to fully take into account the properties of a real random process that describes the motion of aircraft at the landing approach stage. This provides for the maximum possible accuracy of linear extrapolation with a variety of information support conditions. These methods allow improving the safety of flights and the efficiency of aviation. Accordingly, new capabilities of aircraft and other sophisticated technical systems can be further considered.

Fatigue analysis of a bridge deck using the peaks-over-threshold approach with application to the Millau viaduct

Usually, to estimate the fatigue life of structural details in existing bridges, fatigue damage assessed with monitoring data is extrapolated linearly in time. In this study, a methodology is proposed for predicting the numbers of fatigue cycles with the peaks-over-threshold approach. On the other side, this POT approach, which is based on extreme values, is, as usually, also used to predict the load effects of extreme amplitude. This provides an innovative method to predict fatigue damage, which considers the initial distribution of numbers of cycles over time. It may account for traffic growth in volume and mass. This paper shows the comparison between reliability indexes assessed with the proposed method and the linear extrapolation.

The impact of the truck loads on the braking efficiency assessment

The paper deals with possibilities of assessment of braking efficiency during evaluation of braking system at technical inspection of trucks in conditions of the Slovak Republic. The braking efficiency of the vehicle is evaluated by measuring the braking forces at the roller brake tester. The magnitude of these forces also depends on the loads of the measured vehicle. The paper analyses the results of the practical tests of the braking efficiency measurement of a truck of category N3 and of a vehicle combination consisting of vehicles of category N3 and O4. The analysed vehicle combination was gradually loaded in four different ways and a special situation was the measurement of the braking efficiency of the tractor itself. The instantaneous load on each axle was recorded with portable axle weights. The braking efficiency evaluation was carried out in accordance with the valid methodology, which allows the application of the direct evaluation method, the method of linear extrapolation, the method of the reference braking forces and the indicative evaluation. A vehicle with the same braking system may be assessed as roadworthy or not roadworthy. This is due to the application of different methods of evaluating the braking efficiency and different way of loads at the loading area.