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Abstract Apertures are specialized regions on the pollen surface that receive little to no exine deposition, forming distinct structures important for pollen function. Aperture number, shape, and positions vary widely across species, resulting in diverse, species-specific patterns that make apertures fascinating from both cell biological and evolutionary perspectives. Aperture formation requires developing pollen to establish polarity and define specific regions of the plasma membrane as aperture domains. In the decade or so since the discovery of the first aperture factor, INAPERTURATE POLLEN1 (INP1), pollen apertures have become a powerful model for investigating how cells form distinct plasma membrane domains. Recent studies in Arabidopsis and rice, two species with contrasting aperture patterns, have identified key molecular players that regulate aperture domain specification and development. In this review, we summarize these advances and discuss directions for future studies on the molecular mechanisms controlling aperture formation. 

Abstract We introduce a distributional Jacobian determinant $detD{V}_{\beta }\left(Dv\right)$\det DV_{\beta}(Dv)in dimension two for the nonlinear complex gradient $V_{\beta }\left(Dv\right)={\left|Dv\right|}^{\beta }(v_{x_1},-v_{x_2})$V_{\beta}(Dv)=\lvert Dv\rvert^{\beta}(v_{x_{1}},-v_{x_{2}})for any $\beta >-1$\beta>-1, whenever $v\in W_{\mathrm{loc}}^{1,2}$v\in W^{1\smash{,}2}_{\mathrm{loc}}and $\beta {\left|Dv\right|}^{1+\beta }\in W_{\mathrm{loc}}^{1,2}$\beta\lvert Dv\rvert^{1+\beta}\in W^{1\smash{,}2}_{\mathrm{loc}}.This is new when $\beta \ne 0$\beta\neq 0.Given any planar ∞-harmonic function 𝑢, we show that such distributional Jacobian determinant $detD{V}_{\beta }\left(Du\right)$\det DV_{\beta}(Du)is a nonnegative Radon measure with some quantitative local lower and upper bounds.We also give the following two applications. Applying this result with $\beta =0$\beta=0, we develop an approach to build up a Liouville theorem, which improves that of Savin.Precisely, if 𝑢 is an ∞-harmonic function in the whole ${\mathbb{R}}^2$\mathbb{R}^{2}with $\underset{R\to \mathrm{\infty }}{lim\; inf}\underset{c\in \mathbb{R}}{inf}\frac{1}{R}{⨍}_{B(0,R)}\left|u\left(x\right)-c\right|dx<\mathrm{\infty },$\liminf_{R\to\infty}\inf_{c\in\mathbb{R}}\frac{1}{R}\barint_{B(0,R)}\lvert u(x)-c\rvert\,dx<\infty,then $u=b+a\cdot x$u=b+a\cdot xfor some $b\in \mathbb{R}$b\in\mathbb{R}and $a\in {\mathbb{R}}^2$a\in\mathbb{R}^{2}.Denoting by $u_p$u_{p}the 𝑝-harmonic function having the same nonconstant boundary condition as 𝑢, we show that $detD{V}_{\beta }\left(D{u}_p\right)\to detD{V}_{\beta }\left(Du\right)$\det DV_{\beta}(Du_{p})\to\det DV_{\beta}(Du)as $p\to \mathrm{\infty }$p\to\inftyin the weak-⋆ sense in the space of Radon measure.Recall that $V_{\beta }\left(D{u}_p\right)$V_{\beta}(Du_{p})is always quasiregular mappings, but $V_{\beta }\left(Du\right)$V_{\beta}(Du)is not in general. 

Modern machine learning frameworks support very large models by incorporating parallelism and optimization techniques. Yet, these very techniques add new layers of complexity in ensuring the correctness of the computation. An incorrect implementation of these techniques might lead to compile-time or runtime errors that can easily be observed and fixed, but it might also lead to silent errors that will result in incorrect computations in training or inference, which do not exhibit any obvious symptom until the model is used later. These subtle errors not only waste computation resources, but involve significant developer effort to detect and diagnose. In this work, we propose Aerify, a framework to automatically expose silent errors by verifying semantic equivalence of models with equality saturation. Aerify constructs equivalence graphs (e-graphs) from intermediate representations of tensor programs, and incrementally applies rewriting rules---derived from generic templates and refined via domain-specific analysis---to prove or disprove equivalence at scale. When discrepancies remain unproven, Aerify pinpoints the corresponding graph segments and maps them back to source code, simplifying debugging and reducing developer overhead. Our preliminary results show strong potentials of Aerify in detecting real-world silent errors. 

Neuromorphic vision sensors or event cameras have made the visual perception of extremely low reaction time possible, opening new avenues for high-dynamic robotics applications. These event cameras’ output is dependent on both motion and texture. However, the event camera fails to capture object edges that are parallel to the camera motion. This is a problem intrinsic to the sensor and therefore challenging to solve algorithmically. Human vision deals with perceptual fading using the active mechanism of small involuntary eye movements, the most prominent ones called microsaccades. By moving the eyes constantly and slightly during fixation, microsaccades can substantially maintain texture stability and persistence. Inspired by microsaccades, we designed an event-based perception system capable of simultaneously maintaining low reaction time and stable texture. In this design, a rotating wedge prism was mounted in front of the aperture of an event camera to redirect light and trigger events. The geometrical optics of the rotating wedge prism allows for algorithmic compensation of the additional rotational motion, resulting in a stable texture appearance and high informational output independent of external motion. The hardware device and software solution are integrated into a system, which we call artificial microsaccade–enhanced event camera (AMI-EV). Benchmark comparisons validated the superior data quality of AMI-EV recordings in scenarios where both standard cameras and event cameras fail to deliver. Various real-world experiments demonstrated the potential of the system to facilitate robotics perception both for low-level and high-level vision tasks.