Project description:We derive a theoretical model for studying SPM feedback in the context of control theory. Previous models presented in the literature that apply standard models for proportional-integral-derivative controllers predict a highly unstable feedback environment. This model uses features specific to the SPM implementation of the proportional-integral controller to give realistic feedback behaviour. As such the stability of SPM feedback for a wide range of feedback gains can be understood. Further consideration of mechanical responses of the SPM system gives insight into the causes of exciting mechanical resonances of the scanner during feedback operation.
Project description:Empirical evidence for diminishing fitness returns of beneficial mutations supports Fisher's geometric model. We show that a similar pattern emerges through the phenomenon of regression to the mean and that few studies correct for it. Although biases are often small, regression to the mean has overemphasized diminishing returns and will hamper cross-study comparisons unless corrected for.
Project description:The under-representation of women on faculties of science and engineering is ascribed in part to demographic inertia, which is the lag between retirement of current faculty and future hires. The assumption of demographic inertia implies that, given enough time, gender parity will be achieved. We examine that assumption via a semi-Markov model to predict the future faculty, with simulations that predict the convergence demographic state. Our model shows that existing practices that produce gender gaps in recruitment, retention, and career progression preclude eventual gender parity. Further, we examine sensitivity of the convergence state to current gender gaps to show that all sources of disparity across the entire faculty career must be erased to produce parity: we cannot blame demographic inertia.
Project description:A continental-scale model of Holocene Australian hunter-gatherer demography and mobility is generated using radiocarbon data and geospatial techniques. Results show a delayed expansion and settlement of much of Australia following the termination of the late Pleistocene until after 9,000 years ago (or 9ka). The onset of the Holocene climatic optimum (9-6ka) coincides with rapid expansion, growth and establishment of regional populations across ~75% of Australia, including much of the arid zone. This diffusion from isolated Pleistocene refugia provides a mechanism for the synchronous spread of pan-continental archaeological and linguistic attributes at this time (e.g. Pama-Nyungan language, Panaramitee art style, backed artefacts). We argue longer patch residence times were possible at the end of the optimum, resulting in a shift to more sedentary lifestyles and establishment of low-level food production in some parts of the continent. The onset of El Niño - Southern Oscillation (ENSO; 4.5-2ka) restricted low-level food production, and resulted in population fragmentation, abandonment of marginal areas, and reduction in ranging territory of ~26%. Importantly, climate amelioration brought about by more pervasive La Niña conditions (post-2ka), resulted in an intensification of the mobility strategies and technological innovations that were developed in the early- to mid-Holocene. These changes resulted in population expansion and utilization of the entire continent. We propose that it was under these demographically packed conditions that the complex social and religious societies observed at colonial contact were formed.
Project description:The diversity of life on Earth raises the question of whether it is possible to have a single theoretical description of the quantitative aspects of the organization of metabolism for all organisms. However, similarities between organisms, such as von Bertalanffy's growth curve and Kleiber's law on metabolic rate, suggest that mechanisms that control the uptake and use of metabolites are common to all organisms. These and other widespread empirical patterns in biology should be the ultimate test for any metabolic theory that hopes for generality. The present study (i) collects empirical evidence on growth, stoichiometry, feeding, respiration and energy dissipation and exhibits it as stylized biological facts; (ii) formalizes assumptions and propositions in a metabolic theory that is fully consistent with the Dynamic Energy Budget theory; and (iii) proves that these assumptions and propositions are consistent with the stylized facts.
Project description:Background: E-cigarettes have become the most commonly used tobacco products among youth in the United States (US) recently. It is not clear whether there is a causal relationship between e-cigarette use and the onset of cigarette smoking. The "common liability" theory postulates that the association between e-cigarette use and cigarette smoking can be attributed to a common risk construct of using tobacco products. This study aims to investigate the relationship between ever e-cigarette use and cigarette smoking onset in the US using a structural equation modeling approach guided by the "common liability" theory. Methods: The study population is non-institutionalized civilian adolescents living in the US, sampled in the longitudinal Population Assessment of Tobacco and Health study. Information about tobacco product use was obtained via confidential self-report. A structural equation modeling approach was used to estimate the relationship between e-cigarette use at wave 1 and the onset of cigarette smoking at wave 2 after controlling for a latent construct representing a "common liability to use tobacco products." Results: After controlling for a latent construct representing a "common liability to use tobacco products", ever e-cigarette use does not predict the onset of cigarette smoking (?=0.13, 95% CI= -0.07, 0.32, p=0.204). The latent "common liability to use tobacco products" is a robust predictor for the onset of cigarette smoking (?=0.38; 95% CI=0.07, 0.69; p=0.015). Conclusions: Findings from this study provide supportive evidence for the 'common liability' underlying observed associations between e-cigarette use and smoking onset.
Project description:The number of neurons under a square millimeter of cortical surface has been reported to be the same across five cortical areas and five species [Rockel et al. (1980) Brain 103(2):221-244] despite differences in cortical thickness between the areas. Although the accuracy of this result has been the subject of sharp debate since its publication approximately 30 y ago, the experiments of Rockel et al. have never been directly replicated with modern stereological methods. We have replicated these experiments and confirm the accuracy of the original report. In addition, we have observed that the number of glial cells under a square millimeter of cortical surface depends on cortical thickness, but not on cortical area or species.
Project description:Carbon uptake by the land is a key determinant of future climate change. Unfortunately, Dynamic Global Vegetation Models have many unknown internal parameters which leads to significant uncertainty in projections of the future land carbon sink. By contrast, observed forest inventories in both Amazonia and the USA show strikingly common tree-size distributions, pointing to a simpler modelling paradigm. The curvature of these size-distributions is related to the ratio of mortality to growth in Demographic Equilibrium Theory (DET). We extend DET to include recruitment limited by competitive exclusion from existing trees. From this, we find simultaneous maxima of tree density and biomass in terms of respectively the ratio of mortality to growth and the proportion of primary productivity allocated to reproduction, an idea we call Demographic Optimality (DO). Combining DO with the ratio of mortality to growth common to the US and Amazon forests, results in the prediction that about an eighth of productivity should be allocated to reproduction, which is broadly consistent with observations. Another prediction of the model is that seed mortality should decrease with increasing seed size, such that the advantage of having many small seeds is nullified by the higher seed mortality. Demographic Optimality is therefore consistent with the common shape of tree-size distributions seen in very different forests, and an allocation to reproduction that is independent of seed size.
Project description:Online communities, which have become an integral part of the day-to-day life of people and organizations, exhibit much diversity in both size and activity level; some communities grow to a massive scale and thrive, whereas others remain small, and even wither. In spite of the important role of these proliferating communities, there is limited empirical evidence that identifies the dominant factors underlying their dynamics. Using data collected from seven large online platforms, we observe a relationship between online community size and its activity which generally repeats itself across platforms: First, in most platforms, three distinct activity regimes exist-one of low-activity and two of high-activity. Further, we find a sharp activity phase transition at a critical community size that marks the shift between the first and the second regime in six out of the seven online platforms. Essentially, we argue that it is around this critical size that sustainable interactive communities emerge. The third activity regime occurs above a higher characteristic size in which community activity reaches and remains at a constant and higher level. We find that there is variance in the steepness of the slope of the second regime, that leads to the third regime of saturation, but that the third regime is exhibited in six of the seven online platforms. We propose that the sharp activity phase transition and the regime structure stem from the branching property of online interactions.
Project description:Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran.