Short communication: Forward and inverse models relating river long profile to monotonic step-changes in tectonic rock uplift rate history: A theoretical perspective under a nonlinear slope-erosion dependency

The long profile of rivers is widely considered as a recorded of tectonic uplift rate. Knickpoints form in response to rate changes and faster rates produce steeper channel segments. However, when the exponent relating fluvial incision to river slope, n, is not unity, the links between tectonic rates and channel profile are complicated by channel dynamics that consume and form river segments. Here, we explore non-linear cases leading to channel segment consumption and develop a Lagrangian analytic model for knickpoint migration. We derive a criterion for knickpoint preservation and merging, and develop a forward analytic model that resolves knickpoint and long profile evolution before and after knickpoint merging. We further propose a linear inverse scheme to infer tectonic history from river profiles when all knickpoints are preserved. Our description provides a new framework to explore the links between tectonic uplift rates and river profile evolution when n is not unity.

Cognitive Science as a Source of Forward and Inverse Models of Human Decisions for Robotics and Control

Those designing autonomous systems that interact with humans will invariably face questions about how humans think and make decisions. Fortunately, computational cognitive science offers insight into human decision-making using tools that will be familiar to those with backgrounds in optimization and control (e.g., probability theory, statistical machine learning, and reinforcement learning). Here, we review some of this work, focusing on how cognitive science can provide forward models of human decision-making and inverse models of how humans think about others’ decision-making. We highlight relevant recent developments, including approaches that synthesize black box and theory-driven modeling, accounts that recast heuristics and biases as forms of bounded optimality, and models that characterize human theory of mind and communication in decision-theoretic terms. In doing so, we aim to provide readers with a glimpse of the range of frameworks, methodologies, and actionable insights that lie at the intersection of cognitive science and control research. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Zircon (U-Th)/He thermochronology of Grand Canyon resolves 1250 Ma unroofing at the Great Unconformity and <20 Ma canyon carving

Our study used zircon (U-Th)/He (ZHe) thermochronology to resolve cooling events of Precambrian basement below the Great Unconformity surface in the eastern Grand Canyon, United States. We combined new ZHe data with previous thermochronometric results to model the &lt;250 °C thermal history of Precambrian basement over the past &gt;1 Ga. Inverse models of ZHe date-effective uranium (eU) concentration, a relative measure of radiation damage that influences closure temperature, utilize He diffusion and damage annealing and suggest that the main phase of Precambrian cooling to &lt;200 °C was between 1300 and 1250 Ma. This result agrees with mica and potassium feldspar 40Ar/39Ar thermochronology showing rapid post–1400 Ma cooling, and both are consistent with the 1255 Ma depositional age for the Unkar Group. At the young end of the timescale, our data and models are also highly sensitive to late-stage reheating due to burial beneath ~3–4 km of Phanerozoic strata prior to ca. 60 Ma; models that best match observed date-eU trends show maximum temperatures of 140–160 °C, in agreement with apatite (U-Th)/He and fission-track data. Inverse models also support multi-stage Cenozoic cooling, with post–20 Ma cooling from ~80 to 20 °C reflecting partial carving of the eastern Grand Canyon, and late rapid cooling indicated by 3–7 Ma ZHe dates over a wide range of high eU. Our ZHe data resolve major basement exhumation below the Great Unconformity during the Mesoproterozoic (1300–1250 Ma), and “young” (20–0 Ma) carving of Grand Canyon, but show little sensitivity to Neoproterozoic and Cambrian basement unroofing components of the composite Great Unconformity.

The hydrochemical signature of incongruent weathering in Iceland

Basaltic watersheds such as those found in Iceland are thought to be important sites of CO₂ sequestration via silicate weathering. However, determining the magnitude of CO₂ uptake depends on accurately interpreting river chemistry. Here, we compile geochemical data from Iceland and use them to constrain weathering processes. Specifically, we use a newly developed inverse model to quantify solute supply from rain and hydrothermal fluids as well as allow for different mineral phases within basalts to react at different rates, solutes to be removed via clay formation, and some Ca to be sourced from carbonate dissolution. While some of these processes have been considered previously, they have not been considered together allowing us to newly determine their relative contributions.We find that weathering in Iceland is incongruent in two ways. Firstly, solute release from primary silicates is characterized by a higher proportion of Na than would be expected from bulk basalts, which may reflect preferential weathering or some contribution from rhyolites. This Na enrichment is further enhanced by preferential Mg and K uptake by clays. No samples in our dataset (n=537) require carbonate dissolution even if isotopic data (δ26Mg, δ30Si, δ44Ca, and/or 87Sr/86Sr) are included. While some carbonate weathering is allowable, silicate weathering likely dominates. The complexity we observe in Iceland underscores the need for inverse models to account for a wide range of processes and end-members. Given that riverine fluxes from Iceland are more Na-rich than expected for congruent basalt weathering, the characteristic timescale of CO₂ drawdown is likely affected.

Quantification of Sub-Solar Star Ages from the Symmetry of Conjugate Histograms of Spin Period and Angular Velocity

Empirical laws proposed for the decline in star spin with time have heretofore been tested using ambiguous fitting models. We develop an analytical inverse model that uses histogram data to unequivocally determine the physical law governing how dwarf star spin depends on time (t) and mass (M). We analyze shapes of paired histograms of axial rotation period (П) and angular velocity (ω = 2π/П) to utilize the fact that a variable and its reciprocal are governed by the same physics. Copious data on open clusters are used to test the formula ∂ω/∂t ∝ − ωn where n is unrestricted, and thus covers diverse possibilities. Histogram conjugates for each of 15 clusters with 120 to 812 measurements provide n = 1.13 ± 0.19. Results are independent of initial spin rate, bin size, cluster parameters, and star mass. Notably, 11 large clusters with mostly M-types yield fits with n = 1.07 ± 0.12. Associations behave similarly. Only exponential decay (n = 1) explains the similar shapes of the conjugate histograms for the spin period and angular velocity, despite the asymmetric (inverse) relationship of these variables. This rate law is consistent with viscous dissipation. Forward modeling confirms that n is near unity and further shows that coeval formation of all stars in a cluster does not occur. We therefore explore a constant rate of star production, which is reasonable for tiny stars. Inverse models show that episodic production increases with mass, but is unimportant below ~0.55 MSun. We infer star and cluster ages, and find that star production becomes less regular with time, as interstellar gas and dust are progressively depleted. Our new analytical approach of extracting a physical law from conjugate histograms is general and widely applicable.