Sensitivity to geometric shape regularity in humans and baboons: A putative signature of human singularity

Among primates, humans are special in their ability to create and manipulate highly elaborate structures of language, mathematics, and music. Here we show that this sensitivity to abstract structure is already present in a much simpler domain: the visual perception of regular geometric shapes such as squares, rectangles, and parallelograms. We asked human subjects to detect an intruder shape among six quadrilaterals. Although the intruder was always defined by an identical amount of displacement of a single vertex, the results revealed a geometric regularity effect: detection was considerably easier when either the base shape or the intruder was a regular figure comprising right angles, parallelism, or symmetry rather than a more irregular shape. This effect was replicated in several tasks and in all human populations tested, including uneducated Himba adults and French kindergartners. Baboons, however, showed no such geometric regularity effect, even after extensive training. Baboon behavior was captured by convolutional neural networks (CNNs), but neither CNNs nor a variational autoencoder captured the human geometric regularity effect. However, a symbolic model, based on exact properties of Euclidean geometry, closely fitted human behavior. Our results indicate that the human propensity for symbolic abstraction permeates even elementary shape perception. They suggest a putative signature of human singularity and provide a challenge for nonsymbolic models of human shape perception.

Phyllotactic patterning of gerbera flower heads

Phyllotaxis, the distribution of organs such as leaves and flowers on their support, is a key attribute of plant architecture. The geometric regularity of phyllotaxis has attracted multidisciplinary interest for centuries, resulting in an understanding of the patterns in the model plants Arabidopsis and tomato down to the molecular level. Nevertheless, the iconic example of phyllotaxis, the arrangement of individual florets into spirals in the heads of the daisy family of plants (Asteraceae), has not been fully explained. We integrate experimental data and computational models to explain phyllotaxis in Gerbera hybrida. We show that phyllotactic patterning in gerbera is governed by changes in the size of the morphogenetically active zone coordinated with the growth of the head. The dynamics of these changes divides the patterning process into three phases: the development of an approximately circular pattern with a Fibonacci number of primordia near the head rim, its gradual transition to a zigzag pattern, and the development of a spiral pattern that fills the head on the template of this zigzag pattern. Fibonacci spiral numbers arise due to the intercalary insertion and lateral displacement of incipient primordia in the first phase. Our results demonstrate the essential role of the growth and active zone dynamics in the patterning of flower heads.

Trajectory Identification for Moving Loads by Multicriterial Optimization

Moving load is a fundamental loading pattern for many civil engineering structures and machines. This paper proposes and experimentally verifies an approach for indirect identification of 2D trajectories of moving loads. In line with the “structure as a sensor” paradigm, the identification is performed indirectly, based on the measured mechanical response of the structure. However, trivial solutions that directly fit the mechanical response tend to be erratic due to measurement and modeling errors. To achieve physically meaningful results, these solutions need to be numerically regularized with respect to expected geometric characteristics of trajectories. This paper proposes a respective multicriterial optimization framework based on two groups of criteria of a very different nature: mechanical (to fit the measured response of the structure) and geometric (to account for the geometric regularity of typical trajectories). The state-of-the-art multiobjective genetic algorithm NSGA-II is used to find the Pareto front. The proposed approach is verified experimentally using a lab setup consisting of a plate instrumented with strain gauges and a line-follower robot. Three trajectories are tested, and in each case the determined Pareto front is found to properly balance between the mechanical response fit and the geometric regularity of the trajectory.

Geometric estimates for complex Monge–Ampère equations

We prove uniform gradient and diameter estimates for a family of geometric complex Monge–Ampère equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge–Ampère equations. We also prove a uniform diameter estimate for collapsing families of twisted Kähler–Einstein metrics on Kähler manifolds of nonnegative Kodaira dimensions.

Sensitivity to geometric shape regularity in humans and baboons: A putative signature of human singularity

Among primates, humans are special in their ability to create and manipulate highly elaborate structures of language, mathematics or music. Here, we show that this sensitivity to abstract structure is already present in a much simpler domain: the visual perception of regular geometric shapes such as squares, rectangles or parallelograms. We asked human subjects to detect an intruder shape among six quadrilaterals. Although the intruder was always defined by an identical amount of displacement of a single vertex, the results revealed a geometric regularity effect: detection was considerably easier when either the base shape or the intruder was a regular figure comprising right angles, parallelism or symmetry, than a more irregular shape. This effect was replicated in several tasks and in all human populations tested, including uneducated Himba adults and French preschoolers. Baboons, however, showed no such geometric regularity effect, even after extensive training. Baboon behavior was captured by convolutional neural networks (CNNs), but neither CNNs nor a variational auto-encoder captured the human geometric regularity effect. However, a symbolic model, based on exact properties of Euclidean geometry, closely fitted human behavior. Our results indicate that the human propensity for symbolic abstraction permeates even elementary shape perception. They suggest a new putative signature of human singularity, and provide a novel challenge for non-symbolic models of human shape perception.