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In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these data is necessary. Compressed sensing is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, by using a minimum number of nonadaptive linear measurements. After this compressed sensing process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose, in this work, a compressed sensing reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by using an augmented Lagrangian that avoids the difficult problem of nonlinearity and nondifferentiability of the regularization terms. The proposed algorithm, called denoising-compressed sensing by regularization (DCSR) terms, will not only perform image reconstruction but also denoising. To evaluate the performance of the proposed algorithm, we compare its performance with state-of-the-art methods, such as Nesterov’s algorithm, group-based sparse representation and wavelet-based methods, in terms of denoising and preservation of edges, texture and image details, as well as from the point of view of computational complexity. Our approach permits a gain up to 25% in terms of denoising efficiency and visual quality using two metrics: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).

In this article, we extend, with a great deal of generality, many results regarding the Hausdorff dimension of certain dynamical Diophantine coverings and shrinking target sets associated with a conformal iterated function system (IFS) previously established under the so-called open set condition. The novelty of the result we present is that it holds regardless of any separation assumption on the underlying IFS and thus extends to a large class of IFSs the previous results obtained by Beresnevitch and Velani [A mass transference principle and the Duffin–Schaeffer conjecture for Hausdorff measures. Ann. of Math. (2) 164(3) (2006), 971–992] and by Barral and Seuret [The multifractal nature of heterogeneous sums of Dirac masses. Math. Proc. Cambridge Philos. Soc. 144(3) (2008), 707–727]. Moreover, it will be established that if S is conformal and satisfies mild separation assumptions (which are, for instance, satisfied for any self-similar IFS on \\( R\\) with algebraic parameters, no exact overlaps and similarity dimension smaller than \\(1\\)), then the classical result of Hill–Velani regarding the shrinking target problem associated with a conformal IFS satisfying the open set condition (and for which the Hausdorff measure was later computed by Allen and Barany [On the Hausdorff measure of shrinking target sets on self-conformal sets. Mathematika 67 (2021), 807–839]) can be extended.

Dynamical solutions to the vacuum Einstein equations for Bianchi IX cosmologies are examined using Ellis-MacCallum-Wainwright (expansion normalized) variables. An iterative map, representing the transition from Kasner state to another, is shown to have period-3 solutions. The evolution of the remaining three variables, for initial conditions consistent with those determined by the period-3 iterative map, leads to discrete self-similar solutions where the golden ratio Φ appears as a parameter in many of the properties of the full dynamics. The oscillatory behaviour of three curvature variables produce self-similar golden rectangles with scaling parameters determined by Φ. The existence of the 3-cycles satisfy necessary and sufficient condition for the Bianchi-IX dynamics to exhibit deterministic chaos.

When particles in a quantum mechanical system are entangled, a measurement performed on one part of the system can affect the results of the same type of measurement performed on another part—even if these subsystems are physically separated. Kunkel et al. , Fadel et al. , and Lange et al. achieved this so-called distributed entanglement in a particularly challenging setting: an ensemble of many cold atoms (see the Perspective by Cavalcanti). In all three studies, the entanglement was first created within an atomic cloud, which was then allowed to expand. Local measurements on the different, spatially separated parts of the cloud confirmed that the entanglement survived the expansion. Science , this issue p. 413 , p. 409 , p. 416 ; see also p. 376 Local measurements on spatially separated parts of a cold atom cloud confirm entanglement between the subsystems. A key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. However, the robust generation and detection of entanglement between spatially separated regions of an ultracold atomic system remain a challenge. We used spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this entanglement can be spatially distributed by self-similar expansion of the atomic cloud. We used spatially resolved spin read-out to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Based on the strength of EPR steering, we constructed a witness, which confirmed genuine 5-partite entanglement.

Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is sufficient to capture a great deal of low-level image statistics prior to any learning. In order to do so, we show that a randomly-initialized neural network can be used as a handcrafted prior with excellent results in standard inverse problems such as denoising, super-resolution, and inpainting. Furthermore, the same prior can be used to invert deep neural representations to diagnose them, and to restore images based on flash-no flash input pairs. Apart from its diverse applications, our approach highlights the inductive bias captured by standard generator network architectures. It also bridges the gap between two very popular families of image restoration methods: learning-based methods using deep convolutional networks and learning-free methods based on handcrafted image priors such as self-similarity (Code and supplementary material are available at https://dmitryulyanov.github.io/deep_image_prior).

For the DCF protocol model at the data link layer and in a saturated network, the self-similar structure of the probabilistic distribution of a data transmission time is studied, and both exact and approximate expressions for the distribution are obtained. A comparison with the simulation results is carried out.

Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This paper proposes a novel tensor based approach to handle the problem of HSI spatial super-resolution by modeling such three underlying characteristics. Specifically, a noncovex tensor penalty is used to exploit the former two intrinsic characteristics hidden in several 4D tensors formed by nonlocal similar patches within the 3D HSI. In addition, the local smoothness in both spatial and spectral modes of the HSI cube is characterized by a 3D total variation (TV) term. Then, we develop an effective algorithm for solving the resulting optimization by using the local linear approximation (LLA) strategy and the alternative direction method of multipliers (ADMM). A series of experiments are carried out to illustrate the superiority of the proposed approach over some state-of-the-art approaches.

Photothermal superhydrophobic coatings are supposed promising to prevent ice accumulation on infrastructures but often experience significant performance degradation in real icing conditions and lack mechanical robustness. Here, we report design of robust photothermal superhydrophobic coatings with three-tier hierarchical micro-/nano-/nanostructures by deposition of nanosized MOFs on natural attapulgite nanorods, fluorination, controlled phase separation of a hydrophobic adhesive and spraying assembly. Phase separation degree and adhesive content significantly influence the coatings’ properties by regulating the structural parameters and morphology. In simulated/real icing environments, the coatings simultaneously show (i) high superhydrophobicity and stable Cassie-Baxter states due to their low-surface-energy, three-tier micro-/nano-/nanostructure, (ii) excellent photothermal effect primarily due to nanosized MOFs, and (iii) good mechanical robustness by the phase-separated adhesive, reinforcement with attapulgite and the coatings’ self-similar structure. Accordingly, combined with low thermal conductivity, the coatings exhibit remarkable anti-icing/frosting (e.g., no freezing in at least 150 min and almost free of frost in 25 min) and de-icing/frosting performances (e.g., fast de-icing in 12.7 min and fast de-frosting in 16.7 min) in such environments. Furthermore, we realize large-scale preparation of the coatings at reasonable costs. The coatings have great application potential for anti-icing and de-icing in the real world by efficiently using natural sunlight. Photothermal superhydrophobic coatings show poor anti-icing performance and mechanical stability in real conditions. Here, authors report on robust photothermal superhydrophobic coatings with self-similar low-surface-energy three-tier micro-/nano- /nanostructures.

Self-similarity refers to the image prior widely used in image restoration algorithms that small but similar patterns tend to occur at different locations and scales. However, recent advanced deep convolutional neural network-based methods for image restoration do not take full advantage of self-similarities by relying on self-attention neural modules that only process information at the same scale. To solve this problem, we present a novel Pyramid Attention module for image restoration, which captures long-range feature correspondences from a multi-scale feature pyramid. Inspired by the fact that corruptions, such as noise or compression artifacts, drop drastically at coarser image scales, our attention module is designed to be able to borrow clean signals from their “clean” correspondences at the coarser levels. The proposed pyramid attention module is a generic building block that can be flexibly integrated into various neural architectures. Its effectiveness is validated through extensive experiments on multiple image restoration tasks: image denoising, demosaicing, compression artifact reduction, and super resolution. Without any bells and whistles, our PANet (pyramid attention module with simple network backbones) can produce state-of-the-art results with superior accuracy and visual quality. Our code is available at https://github.com/SHI-Labs/Pyramid-Attention-Networks

For each $n\\geq 2$ , we investigate a family of iterated function systems which is parameterized by a common contraction ratio $s\\in \\mathbb{D}^{\\times }\\equiv \\{s\\in \\mathbb{C}:0<|s|<1\\}$ and possesses a rotational symmetry of order $n$ . Let ${\\mathcal{M}}_{n}$ be the locus of contraction ratio $s$ for which the corresponding self-similar set is connected. The purpose of this paper is to show that ${\\mathcal{M}}_{n}$ is regular-closed, that is, $\\overline{\\text{int}\\,{\\mathcal{M}}_{n}}={\\mathcal{M}}_{n}$ holds for $n\\geq 4$ . This gives a new result for $n=4$ and a simple geometric proof of the previously known result by Bandt and Hung [Fractal $n$ -gons and their Mandelbrot sets. Nonlinearity 21 (2008), 2653–2670] for $n\\geq 5$ .