The Perceived Beauty of Convex Polygon Tilings: The Influence of Regularity, Curvature, and Density

Polygon tilings in natural and man-made objects show great variety. Unlike previous studies that have mainly focused on their classification and production methods, this study aimed at exploring factors that may contribute to the perceived beauty of convex polygon tilings. We analyze the dimensions of regularity, curvature, and density, as well as individual differences. Triangle tilings and hexagon tilings were tested in Experiment 1 and 2, respectively. The results showed that the perceived beauty of convex polygon tilings can be enhanced by higher levels of regularity and nonobvious local curvature. Surprisingly, the effect of density appeared to be different, with the dense triangle tilings and the less dense hexagon tilings scoring higher than the reverse. We discuss a possible explanation based on trypophobia caused by different types of polygons, as well as the observers’ personality trait of agreeableness.

Fully Dynamic Earthquake Cycle Simulations on a Nonplanar Fault Using the Spectral Boundary Integral Element Method (sBIEM)

ABSTRACT One of the most suitable methods for modeling fully dynamic earthquake cycle simulations is the spectral boundary integral element method (sBIEM), which takes advantage of the fast Fourier transform (FFT) to make a complex numerical dynamic rupture tractable. However, this method has the serious drawback of requiring a flat fault geometry due to the FFT approach. Here, we present an analytical formulation that extends the sBIEM to a mildly nonplanar fault. We start from a regularized boundary element method and apply a small-slope approximation of the fault geometry. Making this assumption, it is possible to show that the main effect of nonplanar fault geometry is to change the normal traction along the fault, which is controlled by the local curvature along the fault. We then convert this space–time boundary integral equation of the normal traction into a spectral-time formulation and incorporate this change in normal traction into the existing sBIEM methodology. This approach allows us to model fully dynamic seismic cycle simulations on nonplanar faults in a particularly efficient way. We then test this method against a regular BIEM for both rough-fault and seamount-fault geometries and demonstrate that this sBIEM maintains the scaling between the fault geometry and slip distribution.

INFLUENCE OF FEATURES OF THE ELECTRIC FIELD IN THE DIAPHRAGM SYSTEM ON THE TRANSPORTATION OF THE FLOW OF CHARGED PARTICLES AT ATMOSPHERIC PRESSURE

The results of numerical simulation of the ion-optical scheme of ion transport at atmospheric pressure are presented. The possibility of efficient transport of ions in the system under consideration with an increase in the local curvature of the equipotential lines of the electrostatic field in the vicinity of the nozzle by shaping (changing the shape) of this electrode is shown. Shaping the nozzle allows to increase the value of Iсопло by approximately 1.6 times. Taking into account the gas-dynamic effect on the transport of the ion beam through the nozzle makes it possible to obtain the values of the transmission by 70% higher.

The globalization theorem for the Curvature-Dimension condition

The Lott–Sturm–Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition locally: an essentially non-branching metric-measure space $$(X,\mathsf {d},{\mathfrak {m}})$$ ( X , d , m ) (so that $$(\text {supp}({\mathfrak {m}}),\mathsf {d})$$ ( supp ( m ) , d ) is a length-space and $${\mathfrak {m}}(X) < \infty $$ m ( X ) < ∞ ) verifying the local Curvature-Dimension condition $${\mathsf {CD}}_{loc}(K,N)$$ CD loc ( K , N ) with parameters $$K \in {\mathbb {R}}$$ K ∈ R and $$N \in (1,\infty )$$ N ∈ ( 1 , ∞ ) , also verifies the global Curvature-Dimension condition $${\mathsf {CD}}(K,N)$$ CD ( K , N ) . In other words, the Curvature-Dimension condition enjoys the globalization (or local-to-global) property, answering a question which had remained open since the beginning of the theory. For the proof, we establish an equivalence between $$L^1$$ L 1 - and $$L^2$$ L 2 -optimal-transport–based interpolation. The challenge is not merely a technical one, and several new conceptual ingredients which are of independent interest are developed: an explicit change-of-variables formula for densities of Wasserstein geodesics depending on a second-order temporal derivative of associated Kantorovich potentials; a surprising third-order theory for the latter Kantorovich potentials, which holds in complete generality on any proper geodesic space; and a certain rigidity property of the change-of-variables formula, allowing us to bootstrap the a-priori available regularity. As a consequence, numerous variants of the Curvature-Dimension condition proposed by various authors throughout the years are shown to, in fact, all be equivalent in the above setting, thereby unifying the theory.

Boosting Variational Inference With Locally Adaptive Step-Sizes

Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.

Programmable Self-Assembly of Gold Nanoarrows via Regioselective Adsorption

Programing the self-assembly of colloidal nanoparticles into predetermined superstructures represents an attractive strategy to realize functional assemblies and novel nanodevices, but it remains a challenge. Herein, gold nanoarrows (GNAs) showing a distinct convex-concave structure were employed as unique building blocks for programmable self-assembly involving multiple assembly modes. Regioselective adsorption of 1,10-decanedithiol on the vertexes, edges, and facets of GNAs allowed for programmable self-assembly of GNAs with five distinct assembly modes, and regioselective blocking with 1-dodecanethiol followed by adsorption of 1,10-decanedithiol gave rise to programmable self-assembly with six assembly modes including three novel wing-engaged modes. The assembly mode was essentially determined by regioselective adsorption of the dithiol linker dictated by the local curvature together with the shape complementarity of GNAs. This approach reveals how the geometric morphology of nanoparticles affects their regioselective functionalization and drives their self-assembly.

Effect of malaria parasite shape on its alignment at erythrocyte membrane

During the blood stage of malaria pathogenesis, parasites invade healthy red blood cells (RBC) to multiply inside the host and evade the immune response. When attached to RBC, the parasite first has to align its apex with the membrane for a successful invasion. Since the parasite's apex sits at the pointed end of an oval (egg-like) shape with a large local curvature, apical alignment is in general an energetically un-favorable process. Previously, using coarse-grained mesoscopic simulations, we have shown that optimal alignment time is achieved due to RBC membrane deformation and the stochastic nature of bond-based interactions between the parasite and RBC membrane (Hillringhaus et al., 2020). Here, we demonstrate that the parasite's shape has a prominent effect on the alignment process. The alignment times of spherical parasites for intermediate and large bond off-rates (or weak membrane-parasite interactions) are found to be close to those of an egg-like shape. However, for small bond off-rates (or strong adhesion and large membrane deformations), the alignment time for a spherical shape increases drastically. Parasite shapes with large aspect ratios such as oblate and long prolate ellipsoids are found to exhibit very long alignment times in comparison to the egg-like shape. At a stiffened RBC, spherical parasite aligns faster than any other investigated shapes. This study shows that the original egg-like shape performs not worse for parasite alignment than other considered shapes, but is more robust with respect to different adhesion interactions and RBC membrane rigidities.