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Hi HN, We’re Adeel and Umair, co-founders of Unlayer (https://unlayer。 We let you add content creation to your applications without having to build an entire editor, renderer, template, and export stack yourself。 Unlayer lets you create emails, web pages, and documents inside your app, in three different ways: in code, visually, or with AI
For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for which any spanner on $O(n)$ edges must increase a pairwise distance by $+Ω(n^{1/7})$. This improves on a recent lower bound of $+Ω(n^{1/10.5})$ by Lu, Wein, Vassilevska Williams, and Xu [SODA '22]. 2) A classic result by Coppersmith and Elkin [SODA '05] proves that for any $n$-node graph $G$ and set of $p = O(n^{1/2})$ demand pairs, one can exactly preserve all pairwise distances among demand pairs using a spanner on $O(n)$ edges. They also provided a lower bound construction, establishing that that this range $p = O(n^{1/2})$ cannot be improved. We strengthen this lower bound by proving that, for any constant $k$, this range of $p$ is still unimprovable even if the spanner is allowed $+k$ additive error among the demand pairs. This negatively resolves an open question asked by Coppersmith and Elkin [SODA '05] and again by Cygan, Grandoni, and Kavitha [STACS '13] and Abboud and Bodwin [SODA '16]. At a technical level, our lower bounds are obtain
Electron diffraction, imaging, and energy loss provide evidence for unlayered graphene sheets in the core of certain interstellar graphite onions (from the meteorite Murchison) whose isotopes indicate formation in the atmosphere of late-stage asymptotic giant branch stars (like those which nucleo-synthesized much of the earth's carbon). The data are compared to structural models loosely associated with atom-by-atom, molecule-by-molecule, and dendritic-droplet solidification processes. In this context the observed density, diffraction peak-shapes, and edge-on sheet patterns, along with theoretical limits on time for growth in the presence of outgoing radiation pressure, suggest nucleation of hexagonal sheets from pentagons, perhaps from a supercooled melt. These results warrant a closer examination of specimen structure, the energetics of unlayered graphene nucleation, and processes such as jets in late star atmospheres.
Fluoride (F-) stress is one of the major environmental pollutant, affecting plant growth, development and production, globally. Acquisition of eco-friendly F- stress reliever seems to be the major concern these days. Consequently, application of engineered nanomaterials (ENMs) has been increasing to improve agri-economy. However, the impact of silicon nanoparticles (Si NPs) on mitigation of F- stress has not been investigated yet. Thus, the present study was conducted to compare their protective roles against F- stress by improving diurnal photosynthetic efficiency of sugarcane plant leaves. An ability of sugarcane (Saccharum officinarum cv. GT44) plants to ameliorate F- toxicity assessed through soil culture medium. After an adaptive growth phase, 45 days old plants select to examine F- mitigative efficacy of silicon nanoparticles (SiNPs: 0, 100, 300 and 500 ppm) on sugarcane plants, irrigated by F- contaminated water (0, 100, 200 and 500 ppm). Our results strongly favour that SiNPs enhanced diurnally leaf photosynthetic gas exchange viz., photosynthesis (∼1.0-29%), stomatal conductance (∼3.0-90%), and transpiration rate (∼0.5-43%), significantly, as revealed by increments in photochemical chlorophyll fluorescence efficiency of PS II linked with performance index and photosynthetic pigments during F- stress. To the best of our knowledge, this is the first investigation to explore the impact of SiNPs improving and/or maintaining the diurnal photosynthetic responses in sugarcane plants in response to F- stress. It may also precisely unlayer action of molecular mechanism(s) mediated by SiNPs, found essential for mitigation of F--toxicity to explore nano-phytoremediation approach for crop improvement and agri-economy as well.
As generative models expand the possibilities of visual content creation, layered image synthesis has emerged as a promising direction for controllable and creative editing. However, existing methods struggle to fully realize this potential. Decomposition-based methods often struggle with clean separation, while generation-based methods suffer from difficulty in training data acquisition, reducing quality and scene diversity. In this paper, we propose BFS, a novel generation-based framework for layered image synthesis. Specifically, given a background image and user guidance, BFS synthesizes a foreground layer that incorporates not only a foreground object but also its associated visual effects, such as shadows and reflections, while seamlessly harmonizing with the background to produce a coherent composite. To enable diverse and high-quality foreground layer synthesis while overcoming data scarcity, we leverage the comparatively easy-to-learn knowledge of unlayered image synthesis for the foreground synthesis. To this end, we adopt a dual-branch diffusion framework in which two interconnected branches generate a composite image and a foreground layer, respectively, enabling bidire
We study the free part of the Bernoulli action of $\mathbb{Z}^n$ for $n\geq 2$ and the Borel combinatorics of the associated Schreier graphs. We construct orthogonal decompositions of the spaces into marker sets with various additional properties. In general, for Borel graphs $Γ$ admitting weakly orthogonal decompositions, we show that $χ_B(Γ)\leq 2χ(Γ)-1$ under some mild assumptions. As a consequence, we deduce that the Borel chromatic number for $F(2^{\mathbb{Z}^n})$ is $3$ for all $n\geq 2$. Weakly orthogonal decompositions also give rise to Borel unlayered toast structures. We also construct orthogonal decompositions of $F(2^{\mathbb{Z}^2})$ with strong topological regularity, in particular with all atoms homeomorphic to a disk. This allows us to show that there is a Borel perfect matching for $F(2^{\mathbb{Z}^n})$ for all $n\geq 2$ and that there is a Borel lining of $F(2^{\mathbb{Z}^2})$.
In this paper we improve the lower bound of Chatterjee et al.\ (ECCC 2019) to an $Ω(n^2)$ lower bound for unlayered Algebraic Branching Programs. We also study the impact layerization has on Algebraic Branching Programs. We exhibit a polynomial that has an unlayered ABP of size $O(n)$ but any layered ABP has size at least $Ω(n\sqrt{n})$. We exhibit a similar dichotomy in the non-commutative setting where the unlayered ABP has size $O(n)$ and any layered ABP has size at least $Ω(n\log n -\log^2 n)$.
K2-18b is one of the most promising worlds for the search for extraterrestrial life, so astronomers conducted an unusually powerful radio survey using both the VLA and MeerKAT telescopes。 Advanced software analyzed millions of signals, filtering out Earth-based interference and other false positives。 No convincing artificial radio transmissions wer
Ultra-fine bubbles may offer a cleaner way to perfect inkjet printing for next-generation electronics。 By simply changing the number of bubbles in each droplet, researchers were able to dramatically reshape the final printed pattern without leaving behind unwanted chemical residues
NASA has chosen 41 commercial technology projects that could solve critical challenges for future missions to the Moon and Mars。 From powering lunar outposts to protecting spacecraft from Moon dust, the innovations are designed to push both space exploration and the commercial space economy forward
NASA's PACE satellite captured the Black Sea glowing turquoise during its annual phytoplankton bloom。 The vivid color comes from massive numbers of coccolithophores, microscopic organisms whose reflective shells brighten the water enough to be seen from space。 An astronaut aboard the International Space Station also photographed the bloom spreading
Ronald Fischer, aka Richard Graydon, was arrested in New York last week
Four nearby white dwarf stars have been discovered hiding in plain sight beside brighter red dwarf companions。 Hubble's ultraviolet observations finally revealed the long-hidden stellar remnants, including one just 25 light-years away that took nearly three decades to confirm。 The findings match long-standing predictions and suggest our corner of t
The asteroid that wiped out the dinosaurs was likely an exceptionally rare CO chondrite from a distant region of the solar system。 Its unusual chemistry suggests that planet-cooling dust and debris, rather than sulfur inside the asteroid, may have delivered the deadliest blow