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The super Weyl group of a basic classical Lie superalgebra was introduced and studied in \cite{PS}, which turns out to play an important role for the study of representations of the basic classical Lie superalgebras and algebraic supergroups (see \cite{PS, LS}). These groups turn out to be some quotients of Coxeter groups. It is deserved to specially investigate super Weyl groups via revealing the related Coxeter systems. The purpose of this paper is twofold. One is to describe the Coxeter systems for super Weyl groups of basic classical Lie superalgebras. The other one is to introduce defining sequences which are a kind of new descriptions of fundamental root systems for classical Lie superalgebras of type $A,B,C$ and $D$. Based on defining sequences, we decide the Coxeter groups associated with those super Weyl groups via Coxeter graphs.

An explicit gerbe-theoretic description of the super-$σ$-models of the Green-Schwarz type is proposed and its fundamental structural properties, such as equivariance with respect to distinguished isometries of the target supermanifold and $κ$-symmetry, are studied at length for targets with the structure of a homogeneous space of a Lie supergroup. The programme of (super)geometrisation of the Cartan-Eilenberg super-$(p+2)$-cocycles that determine the topological content of the super-$p$-brane mechanics and ensure its $κ$-symmetry, motivated by the successes of and guided by the intuitions provided by its bosonic predecessor, is based on the idea of a (super)central extension of a Lie supergroup in the presence of a nontrivial super-2-cocycle in the Chevalley-Eilenberg cohomology of its Lie superalgebra, the gap between the two cohomologies being bridged by a super-variant of the classic Chevalley-Eilenberg construction. A systematic realisation of the programme is herewith begun with a detailed study of the elementary homogeneous space of the super-Poincaré group, the super-Minkowskian spacetime, whose simplicity affords straightforward identification of the supergeometric mechanis

In this paper, we present a unique multi-functional super-resolution instrument, the SuperNANO system, which integrates real-time super-resolution imaging with direct laser nanofabrication capabilities. Central to the func-tionality of the SuperNANO system is its capacity for simultaneous nanoimaging and nanopatterning, enabling the creation of anti-counterfeiting markings and precision cutting with exceptional accuracy. The SuperNANO system, featuring a unibody superlens objective, achieves a resolution ranging from 50 to 320 nm. We showcase the instrument's versatility through its application in generating high-security anti-counterfeiting features on an aluminum film. These 'invisible' security features, which are nanoscale in dimension, can be crafted with arbi-trary shapes at designated locations. Moreover, the system's precision is further evidenced by its ability to cut silver nanowires to a minimum width of 50 nm. The integrated imaging and fabricating functions of the Su-perNANO make it a pivotal tool for a variety of applications, including nano trapping, sensing, cutting, weld-ing, drilling, signal enhancement, detection, and nano laser treatment.

In this article we define stable supercurves and super stable maps of genus zero via labeled trees. We prove that the moduli space of stable supercurves and super stable maps of fixed tree type are quotient superorbifolds. To this end, we prove a slice theorem for the action of super Lie groups on Riemannian supermanifolds and discuss superorbifolds. Furthermore, we propose a Gromov topology on super stable maps such that the restriction to fixed tree type yields the quotient topology from the superorbifolds and the reduction is compact. This would, possibly, lead to the notions of super Gromov-Witten invariants and small super quantum cohomology to be discussed in sequels.

This paper reviews the NTIRE 2026 challenge on efficient single-image super-resolution with a focus on the proposed solutions and results. The aim of this challenge is to devise a network that reduces one or several aspects, such as runtime, parameters, and FLOPs, while maintaining PSNR of around 26.90 dB on the DIV2K_LSDIR_valid dataset, and 26.99 dB on the DIV2K_LSDIR_test dataset. The challenge had 95 registered participants, and 15 teams made valid submissions. They gauge the state-of-the-art results for efficient single-image super-resolution.

Aligning generative real-world image super-resolution models with human visual preference is challenging due to the perception--fidelity trade-off and diverse, unknown degradations. Prior approaches rely on offline preference optimization and static metric aggregation, which are often non-interpretable and prone to pseudo-diversity under strong conditioning. We propose OARS, a process-aware online alignment framework built on COMPASS, a MLLM-based reward that evaluates the LR to SR transition by jointly modeling fidelity preservation and perceptual gain with an input-quality-adaptive trade-off. To train COMPASS, we curate COMPASS-20K spanning synthetic and real degradations, and introduce a three-stage perceptual annotation pipeline that yields calibrated, fine-grained training labels. Guided by COMPASS, OARS performs progressive online alignment from cold-start flow matching to full-reference and finally reference-free RL via shallow LoRA optimization for on-policy exploration. Extensive experiments and user studies demonstrate consistent perceptual improvements while maintaining fidelity, achieving state-of-the-art performance on Real-ISR benchmarks.

We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) with non-symmetrizable Cartan matrix of polynomial growth, (c) Lie (super)algebras of vector fields with polynomial coefficients, (d) stringy a.k.a. superconformal superalgebras, (e) queerifications of simple restricted Lie algebras. Over algebraically closed fields of positive characteristic, we establish when the deform (i.e., the result of deformation) of the known finite-dimensional simple Lie (super)algebra has a NIS. Amazingly, in most of the cases considered, if the Lie (super)algebra has a NIS, its deform has a NIS with the same Gram matrix after an identification of bases of the initial and deformed algebras. We do not consider odd parameters of deformations. Closely related with simple Lie (super)algebras with NIS is the notion of doubly extended Lie (super)algebras of which affine Kac--Moody (super)algebras are the most known examples.

With our previous study, the Super-k algorithm, we have introduced a novel way of piecewise-linear classification. While working on the Super-k algorithm, we have found that there is a similar, and simpler way to explain for obtaining a piecewise-linear classifier based on Voronoi tessellations. Replacing the multidimensional voxelization and expectation-maximization stages of the algorithm with a distance-based clustering algorithm, preferably k-means, works as well as the prior approach. Since we are replacing the voxelization with the clustering, we have found it meaningful to name the modified algorithm, with respect to Super-k, as Supervised k Clusters or in short Super-klust. Similar to the Super-k algorithm, the Super-klust algorithm covers data with a labeled Voronoi tessellation, and uses resulting tessellation for classification. According to the experimental results, the Super-klust algorithm has similar performance characteristics with the Super-k algorithm.

Image segmentation is a fundamental vision task and a crucial step for many applications. In this paper, we propose a fast image segmentation method based on a novel super boundary-to-pixel direction (super-BPD) and a customized segmentation algorithm with super-BPD. Precisely, we define BPD on each pixel as a two-dimensional unit vector pointing from its nearest boundary to the pixel. In the BPD, nearby pixels from different regions have opposite directions departing from each other, and adjacent pixels in the same region have directions pointing to the other or each other (i.e., around medial points). We make use of such property to partition an image into super-BPDs, which are novel informative superpixels with robust direction similarity for fast grouping into segmentation regions. Extensive experimental results on BSDS500 and Pascal Context demonstrate the accuracy and efficency of the proposed super-BPD in segmenting images. In practice, the proposed super-BPD achieves comparable or superior performance with MCG while running at ~25fps vs. 0.07fps. Super-BPD also exhibits a noteworthy transferability to unseen scenes. The code is publicly available at https://github.com/Jianq

This paper provides a comprehensive review of the NTIRE 2024 challenge, focusing on efficient single-image super-resolution (ESR) solutions and their outcomes. The task of this challenge is to super-resolve an input image with a magnification factor of x4 based on pairs of low and corresponding high-resolution images. The primary objective is to develop networks that optimize various aspects such as runtime, parameters, and FLOPs, while still maintaining a peak signal-to-noise ratio (PSNR) of approximately 26.90 dB on the DIV2K_LSDIR_valid dataset and 26.99 dB on the DIV2K_LSDIR_test dataset. In addition, this challenge has 4 tracks including the main track (overall performance), sub-track 1 (runtime), sub-track 2 (FLOPs), and sub-track 3 (parameters). In the main track, all three metrics (ie runtime, FLOPs, and parameter count) were considered. The ranking of the main track is calculated based on a weighted sum-up of the scores of all other sub-tracks. In sub-track 1, the practical runtime performance of the submissions was evaluated, and the corresponding score was used to determine the ranking. In sub-track 2, the number of FLOPs was considered. The score calculated based on the

Non-trivial supergeneralization of the Kerr-Newman solution is considered as representing a combined model of the Kerr-Newman spinning particle and superparticle. We show that the old problem of obtaining non-trivial super black hole solutions can be resolved in supergravity broken by Goldstone fermion. Non-linear realization of broken N=2 supersymmetry specific for the Kerr geometry is considered and some examples of the super-Kerr geometries generated by Goldstone fermion are analyzed. The resulting geometries acquire torsion, Rarita-Schwinger field and extra wave contributions to metric and electromagnetic field caused by Grassmann variables. One family of the self-consistent super-Kerr-Newman solutions to broken N=2 supergravity is selected, and peculiarities of these solutions are discussed. In particular, the appearance of extra `axial' singular line and traveling waves concentrated near `axial' and ring-like singularities.

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion. We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z^k falloff at (Next-to)^k MHV level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z^(k+4) falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to N=8 su

Recently, the methods based on implicit neural representations have shown excellent capabilities for arbitrary-scale super-resolution (ASSR). Although these methods represent the features of an image by generating latent codes, these latent codes are difficult to adapt for different magnification factors of super-resolution, which seriously affects their performance. Addressing this, we design Multi-Scale Implicit Transformer (MSIT), consisting of an Multi-scale Neural Operator (MSNO) and Multi-Scale Self-Attention (MSSA). Among them, MSNO obtains multi-scale latent codes through feature enhancement, multi-scale characteristics extraction, and multi-scale characteristics merging. MSSA further enhances the multi-scale characteristics of latent codes, resulting in better performance. Furthermore, to improve the performance of network, we propose the Re-Interaction Module (RIM) combined with the cumulative training strategy to improve the diversity of learned information for the network. We have systematically introduced multi-scale characteristics for the first time in ASSR, extensive experiments are performed to validate the effectiveness of MSIT, and our method achieves state-of-th

It is known that there exists a natural functor $Φ$ from Lie supergroups to super Harish-Chandra pairs. A functor going backwards, that associates a Lie supergroup with each super Harish-Chandra pair, yielding an equivalence of categories, was found by Koszul [18]; this result was later extended by other authors, to different levels of generality, but always elaborating on Koszul's original idea. In this paper, I provide two new backwards equivalences, i.e. two different functors $Ψ^\circ$ and $Ψ^e$ that construct a Lie supergroup (thought of as a special group-valued functor) out of a given super Harish-Chandra pair, so that any Lie supergroup is recovered from its naturally associated super Harish-Chandra pair; more precisely, both $Ψ^\circ$ and $Ψ^e$ are quasi-inverse to the functor $Φ$.

Most existing super-resolution methods and datasets have been developed to improve the image quality in well-lighted conditions. However, these methods do not work well in real-world low-light conditions as the images captured in such conditions lose most important information and contain significant unknown noises. To solve this problem, we propose a SRRIIE dataset with an efficient conditional diffusion probabilistic models-based method. The proposed dataset contains 4800 paired low-high quality images. To ensure that the dataset are able to model the real-world image degradation in low-illumination environments, we capture images using an ILDC camera and an optical zoom lens with exposure levels ranging from -6 EV to 0 EV and ISO levels ranging from 50 to 12800. We comprehensively evaluate with various reconstruction and perceptual metrics and demonstrate the practicabilities of the SRRIIE dataset for deep learning-based methods. We show that most existing methods are less effective in preserving the structures and sharpness of restored images from complicated noises. To overcome this problem, we revise the condition for Raw sensor data and propose a novel time-melding condition

With the emergence of image super-resolution (SR) algorithm, how to blindly evaluate the quality of super-resolution images has become an urgent task. However, existing blind SR image quality assessment (IQA) metrics merely focus on visual characteristics of super-resolution images, ignoring the available scale information. In this paper, we reveal that the scale factor has a statistically significant impact on subjective quality scores of SR images, indicating that the scale information can be used to guide the task of blind SR IQA. Motivated by this, we propose a scale guided hypernetwork framework that evaluates SR image quality in a scale-adaptive manner. Specifically, the blind SR IQA procedure is divided into three stages, i.e., content perception, evaluation rule generation, and quality prediction. After content perception, a hypernetwork generates the evaluation rule used in quality prediction based on the scale factor of the SR image. We apply the proposed scale guided hypernetwork framework to existing representative blind IQA metrics, and experimental results show that the proposed framework not only boosts the performance of these IQA metrics but also enhances their gen

The overabundance of super-early (redshift $z>10$), luminous ($M_{\rm UV} < -20$), and blue galaxies detected by JWST has been explained (Ferrara et al. 2023) as due to negligible dust attenuation in these systems. We show that such model correctly reproduces the UV luminosity function at $z>10$, and the star formation rate (SFR) density evolution. The model also predicts, in agreement with data, that the cosmic specific SFR grows as ${\rm sSFR} \propto (1+z)^{3/2}$. At $z \simeq 10$ the cosmic sSFR crosses the critical value $\rm sSFR^\star = 25\, \rm Gyr^{-1}$ and $\approx 45$% of the galaxies become super-Eddington driving outflows reaching velocities of $\approx 830 \,(ε_\star/f_M)^{1/2}\, {\rm km\, s}^{-1}$, where $ε_\star$ and $f_M$ are the SF efficiency and fraction of the halo gas expelled in the outflow, respectively. This prediction is consistent with the outflow velocities measured in 12 super-Eddington galaxies of the JWST/JADES sample. Such outflows clear the dust, thus boosting the galaxy luminosity. They also dramatically enhance the visibility of the Ly$α$ line from $z>10$ galaxies, by introducing a velocity offset. The observed Ly$α$ properties in GN-z1

Benefited from the deep learning, image Super-Resolution has been one of the most developing research fields in computer vision. Depending upon whether using a discriminator or not, a deep convolutional neural network can provide an image with high fidelity or better perceptual quality. Due to the lack of ground truth images in real life, people prefer a photo-realistic image with low fidelity to a blurry image with high fidelity. In this paper, we revisit the classic example based image super-resolution approaches and come up with a novel generative model for perceptual image super-resolution. Given that real images contain various noise and artifacts, we propose a joint image denoising and super-resolution model via Variational AutoEncoder. We come up with a conditional variational autoencoder to encode the reference for dense feature vector which can then be transferred to the decoder for target image denoising. With the aid of the discriminator, an additional overhead of super-resolution subnetwork is attached to super-resolve the denoised image with photo-realistic visual quality. We participated the NTIRE2020 Real Image Super-Resolution Challenge. Experimental results show th

Wetting phenomena are widespread in both natural and technological contexts. Despite the well-established nature of this scientific field and our extensive knowledge of its underlying principles, wetting remains a dynamic and vibrant area of study. It continues to pose fundamental questions while offering innovative avenues for controlling these phenomena to develop novel applications. By tailoring the wetting properties of surfaces, researchers and engineers can design materials with specific functionalities, such as self-cleaning surfaces, anti-fog coatings, and enhanced slipperiness. Recent years have witnessed significant advancements in wetting research, owing to the exquisite control achieved in surface topography and chemistry and to the development of novel experimental techniques. Additionally, simulations and theory have played a crucial role in these advancements. They provid the fundamental knowledge and quantitative tools to control wettability and design surfaces with enhanced properties. Given these recent breakthroughs, this special collection Chemical Physics of Controlled Wettability and Super Surfaces becomes particularly timely and significant. It serves as a pl