Contribution of higher-order structure to perception of mirror symmetry: Role of shapes and corners

Visual mirror symmetry is a global feature that is dependent on specific low-level relationships between component elements. Initially conceptualized as virtual lines between paired elements, it has been suggested that higher-order structure between pairs of symmetric elements forming virtual four cornered shapes may also be important for strengthening the percept of mirror symmetry. We utilize corner elements, formed by joining two Gabor elements along a central midline creating vertices with variable internal angles, in a temporal integration paradigm. This allows us to specifically manipulate the presence and type of higher-order versus lower-order structure in patterns with symmetrically placed elements. We show a significant contribution of higher-order structure to the salience of visual symmetries compared with patterns with only lower-order structures. We also find that although we are more sensitive to patterns with higher-order structure, there is no difference in the temporal processing of higher-order versus lower-order patterns. These findings have important implications for existing spatial filter models of symmetry perception that rely on lower-order structures alone and reinforces the need for elaborated models that can more readily capture the complexities of real-world symmetries.

Corner Flows Induced by Surfactant-Producing Bacteria Bacillus subtilis and Pseudomonas fluorescens

A mechanistic understanding of bacterial spreading in soil, which has both air and water in angular pore spaces, is critical to control pathogenic contamination of soil and to design bioremediation projects. A recent study (J. Q. Yang, J. E. Sanfilippo, N. Abbasi, Z. Gitai, et al., Proc Natl Acad Sci U S A 118:e2111060118, 2021, https://doi.org/10.1073/pnas.2111060118) shows that Pseudomonas aeruginosa can self-generate flows along sharp corners by producing rhamnolipids, a type of biosurfactants that change the hydrophobicity of solid surfaces. We hypothesize that other types of biosurfactants and biosurfactant-producing bacteria can also generate corner flows. Here, we first demonstrate that rhamnolipids and surfactin, biosurfactants with different chemical structures, can generate corner flows. We identify the critical concentrations of these two biosurfactants to generate corner flow. Second, we demonstrate that two common soil bacteria, Pseudomonas fluorescens and Bacillus subtilis (which produce rhamnolipids and surfactin, respectively), can generate corner flows along sharp corners at the speed of several millimeters per hour. We further show that a surfactin-deficient mutant of B. subtilis cannot generate corner flow. Third, we show that, similar to the finding for P. aeruginosa, the critical corner angle for P. fluorescens and B. subtilis to generate corner flows can be predicted from classic corner flow theories. Finally, we show that the height of corner flows is limited by the roundness of corners. Our results suggest that biosurfactant-induced corner flows are prevalent in soil and should be considered in the modeling and prediction of bacterial spreading in soil. The critical biosurfactant concentrations we identify and the mathematical models we propose will provide a theoretical foundation for future predictions of bacterial spreading in soil. IMPORTANCE The spread of bacteria in soil is critical in soil biogeochemical cycles, soil and groundwater contamination, and the efficiency of soil-based bioremediation projects. However, the mechanistic understanding of bacterial spreading in soil remains incomplete due to a lack of direct observations. Here, we simulate confined spaces of hydrocarbon-covered soil using a transparent material with similar hydrophobicity and visualize the spread of two common soil bacteria, Pseudomonas fluorescens and Bacillus subtilis. We show that both bacteria can generate corner flows at the velocity of several millimeters per hour by producing biosurfactants, soap-like chemicals. We provide quantitative equations to predict the critical corner angle for bacterial corner flow and the maximum distance of the corner spreading. We anticipate that bacterial corner flow is prevalent because biosurfactant-producing bacteria and angular pores are common in soil. Our results will help improve predictions of bacterial spreading in soil and facilitate the design of soil-related bioremediation projects.

A regularized phase-field model for faceting in a kinetically controlled crystal growth

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen-Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in t , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.

Landmark-Based Drift Compensation Algorithm for Inertial Pedestrian Navigation

The navigation of pedestrians based on inertial sensors, i.e., accelerometers and gyroscopes, has experienced a great growth over the last years. However, the noise of medium- and low-cost sensors causes a high error in the orientation estimation, particularly in the yaw angle. This error, called drift, is due to the bias of the z-axis gyroscope and other slow changing errors, such as temperature variations. We propose a seamless landmark-based drift compensation algorithm that only uses inertial measurements. The proposed algorithm adds a great value to the state of the art, because the vast majority of the drift elimination algorithms apply corrections to the estimated position, but not to the yaw angle estimation. Instead, the presented algorithm computes the drift value and uses it to prevent yaw errors and therefore position errors. In order to achieve this goal, a detector of landmarks, i.e., corners and stairs, and an association algorithm have been developed. The results of the experiments show that it is possible to reliably detect corners and stairs using only inertial measurements eliminating the need that the user takes any action, e.g., pressing a button. Associations between re-visited landmarks are successfully made taking into account the uncertainty of the position. After that, the drift is computed out of all associations and used during a post-processing stage to obtain a low-drifted yaw angle estimation, that leads to successfully drift compensated trajectories. The proposed algorithm has been tested with quasi-error-free turn rate measurements introducing known biases and with medium-cost gyroscopes in 3D indoor and outdoor scenarios.

On the solution of the Helmholtz equation on regions with corners

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.