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A comprehensive workflow to analyze ensembles of globally inverted 2D electrical resistivity models
(2022)
Electrical resistivity tomography (ERT) aims at imaging the subsurface resistivity distribution and provides valuable information for different geological, engineering, and hydrological applications. To obtain a subsurface resistivity model from measured apparent resistivities, stochastic or deterministic inversion procedures may be employed. Typically, the inversion of ERT data results in non-unique solutions; i.e., an ensemble of different models explains the measured data equally well. In this study, we perform inference analysis of model ensembles generated using a well-established global inversion approach to assess uncertainties related to the nonuniqueness of the inverse problem. Our interpretation strategy starts by establishing model selection criteria based on different statistical descriptors calculated from the data residuals. Then, we perform cluster analysis considering the inverted resistivity models and the corresponding data residuals. Finally, we evaluate model uncertainties and residual distributions for each cluster. To illustrate the potential of our approach, we use a particle swarm optimization (PSO) algorithm to obtain an ensemble of 2D layer-based resistivity models from a synthetic data example and a field data set collected in Loon-Plage, France. Our strategy performs well for both synthetic and field data and allows us to extract different plausible model scenarios with their associated uncertainties and data residual distributions. Although we demonstrate our workflow using 2D ERT data and a PSObased inversion approach, the proposed strategy is general and can be adapted to analyze model ensembles generated from other kinds of geophysical data and using different global inversion approaches.
According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.
River-valley morphology preserves information on tectonic and climatic conditions that shape landscapes. Observations suggest that river discharge and valley-wall lithology are the main controls on valley width. Yet, current models based on these observations fail to explain the full range of cross-sectional valley shapes in nature, suggesting hitherto unquantified controls on valley width. In particular, current models cannot explain the existence of paired terrace sequences that form under cyclic climate forcing. Paired river terraces are staircases of abandoned floodplains on both valley sides, and hence preserve past valley widths. Their formation requires alternating phases of predominantly river incision and predominantly lateral planation, plus progressive valley narrowing. While cyclic Quaternary climate changes can explain shifts between incision and lateral erosion, the driving mechanism of valley narrowing is unknown. Here, we extract valley geometries from climatically formed, alluvial river-terrace sequences and show that across our dataset, the total cumulative terrace height (here: total valley height) explains 90%–99% of the variance in valley width at the terrace sites. This finding suggests that valley height, or a parameter that scales linearly with valley height, controls valley width in addition to river discharge and lithology. To explain this valley-width-height relationship, we reformulate existing valley-width models and suggest that, when adjusting to new boundary conditions, alluvial valleys evolve to a width at which sediment removal from valley walls matches lateral sediment supply from hillslope erosion. Such a hillslope-channel coupling is not captured in current valley-evolution models. Our model can explain the existence of paired terrace sequences under cyclic climate forcing and relates valley width to measurable field parameters. Therefore, it facilitates the reconstruction of past climatic and tectonic conditions from valley topography.
Dynamic pricing is considered a possibility to gain an advantage over competitors in modern online markets. The past advancements in Reinforcement Learning (RL) provided more capable algorithms that can be used to solve pricing problems. In this paper, we study the performance of Deep Q-Networks (DQN) and Soft Actor Critic (SAC) in different market models. We consider tractable duopoly settings, where optimal solutions derived by dynamic programming techniques can be used for verification, as well as oligopoly settings, which are usually intractable due to the curse of dimensionality. We find that both algorithms provide reasonable results, while SAC performs better than DQN. Moreover, we show that under certain conditions, RL algorithms can be forced into collusion by their competitors without direct communication.
Beyond humanitarianism
(2022)
In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task (“Is it a number or a letter?”). In Experiment 2, we used a deeper semantic task (“Is this number larger or smaller than five?”). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500–700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).
A conundrum of trends
(2022)
This comment is meant to reiterate two warnings: One applies to the uncritical use of ready-made (openly available) program packages, and one to the estimation of trends in serially correlated time series. Both warnings apply to the recent publication of Lischeid et al. about lake-level trends in Germany.
Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude.
Transform2Open
(2022)