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Camera-based tactile sensors can provide high-density surface geometry and force information for robots in the interaction process with the target. However, most existing methods cannot achieve accurate reconstruction with high efficiency, impeding the applications in robots. To address these problems, we propose an efficient two-shot photometric stereo method based on symmetric color LED distribution. Specifically, based on the sensing response curve of CMOS channels, we design orthogonal red and blue LEDs as illumination to acquire four observation maps using channel-splitting in a two-shot manner. Subsequently, we develop a two-shot photometric stereo theory, which can estimate accurate surface normal and greatly reduce the computing overhead in magnitude. Finally, leveraging the characteristics of the camera-based tactile sensor, we optimize the algorithm to be a highly efficient, pure addition operation. Simulation and real-world experiments demonstrate the advantages of our approach. Further details are available on: https://github.com/Tacxels/SymmeTac., Comment: This work has been submitted to the IEEE for possible publication

We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the first FPTASes for $q$-colourings on graphs of bounded maximum degree $\Delta\ge 3$, when $q\ge (11/6-\varepsilon_0)\Delta$ for some small $\varepsilon_0\approx 10^{-5}$, or when $\Delta\ge 125$ and $q\ge 1.809\Delta$, and on graphs with sufficiently large (but constant) girth, when $q\geq\Delta+3$. These bounds match the current best randomised approximate counting algorithms by Chen, Delcourt, Moitra, Perarnau, and Postle (2019), Carlson and Vigoda (2024), and Chen, Liu, Mani, and Moitra (2023), respectively.

In this paper, we investigate pure geometric $f(R)$ cosmology branes embedded in five-dimensional spacetime. The form of $f(R)$ is chosen as a polynomial. The Five-dimensional scalar curvature $R$ is assumed to be constant. Based on the value of the four-dimensional cosmological constant $\lambda_4$, the branes can be classified into Minkowski, de Sitter, and de anti-de Sitter cases. Solutions for each case can be calculated. These solutions are stable against linear tensor perturbations in all cases. In the Minkowski brane case, the zero mode of gravity can be localized on the brane. In the de Sitter brane case, the zero mode and one massive Kaluza-Klein mode can be localized on the brane. In the anti-de Sitter brane case, all massive Kaluza-Klein modes can be localized on the brane. The results of the analysis of tensor fluctuations are the same in both the Einstein frame and the Jordan frame., Comment: 16 pages, 8 figures

We show that the flip chain for non-crossing spanning trees of $n+1$ points in convex position mixes in time $O(n^8\log n)$., Comment: 19 pages, 6 figures

We give a deterministic polynomial-time approximation scheme (FPTAS) for the volume of the truncated fractional matching polytope for graphs of maximum degree $\Delta$, where the truncation is by restricting each variable to the interval $[0,\frac{1+\delta}{\Delta}]$, and $\delta\le \frac{C}{\Delta}$ for some constant $C>0$. We also generalise our result to the fractional matching polytope for hypergraphs of maximum degree $\Delta$ and maximum hyperedge size $k$, truncated by $[0,\frac{1+\delta}{\Delta}]$ as well, where $\delta\le C\Delta^{-\frac{2k-3}{k-1}}k^{-1}$ for some constant $C>0$. The latter result generalises both the first result for graphs (when $k=2$), and a result by Bencs and Regts (2024) for the truncated independence polytope (when $\Delta=2$). Our approach is based on the cluster expansion technique., Comment: 12 pages

Face super-resolution aims to reconstruct a high-resolution face image from a low-resolution face image. Previous methods typically employ an encoder-decoder structure to extract facial structural features, where the direct downsampling inevitably introduces distortions, especially to high-frequency features such as edges. To address this issue, we propose a wavelet-based feature enhancement network, which mitigates feature distortion by losslessly decomposing the input feature into high and low-frequency components using the wavelet transform and processing them separately. To improve the efficiency of facial feature extraction, a full domain Transformer is further proposed to enhance local, regional, and global facial features. Such designs allow our method to perform better without stacking many modules as previous methods did. Experiments show that our method effectively balances performance, model size, and speed. Code link: https://github.com/PRIS-CV/WFEN.

Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical challenges. A fundamental property of such structures is their topological self-similarity, which can be quantified by fractal features such as fractal dimension (FD). In this study, we incorporate fractal features into a deep learning model by extending FD to the pixel-level using a sliding window technique. The resulting fractal feature maps (FFMs) are then incorporated as additional input to the model and additional weight in the loss function to enhance segmentation performance by utilizing the topological self-similarity. Moreover, we extend the U-Net architecture by incorporating an edge decoder and a skeleton decoder to improve boundary accuracy and skeletal continuity of segmentation, respectively. Extensive experiments on five tubular structure datasets validate the effectiveness and robustness of our approach. Furthermore, the integration of FFMs with other popular segmentation models such as HR-Net also yields performance enhancement, suggesting FFM can be incorporated as a plug-in module with different model architectures. Code and data are openly accessible at https://github.com/cbmi-group/FFM-Multi-Decoder-Network.

We present NeRSP, a Neural 3D reconstruction technique for Reflective surfaces with Sparse Polarized images. Reflective surface reconstruction is extremely challenging as specular reflections are view-dependent and thus violate the multiview consistency for multiview stereo. On the other hand, sparse image inputs, as a practical capture setting, commonly cause incomplete or distorted results due to the lack of correspondence matching. This paper jointly handles the challenges from sparse inputs and reflective surfaces by leveraging polarized images. We derive photometric and geometric cues from the polarimetric image formation model and multiview azimuth consistency, which jointly optimize the surface geometry modeled via implicit neural representation. Based on the experiments on our synthetic and real datasets, we achieve the state-of-the-art surface reconstruction results with only 6 views as input., Comment: 10 pages

In this paper, we investigate a $q$-form field, represented as $\displaystyle X_{M_1M_2...M_q}$, where $\displaystyle q$ indicates the number of indices, with special cases $\displaystyle q = 0, 1, 2$ corresponding to the scalar fields, vector fields, and Kalb-Ramond fields, respectively. Unlike the duality observed between scalar and vector fields in four-dimensional spacetime, $q$-form fields in higher dimensions correspond to a wider array of particles. We propose a novel localized Kaluza-Klein decomposition approach for the $q$-form field in a five-dimensional spacetime, considering its coupling with gravity and background scalar fields. This methodology enables the successful localization of the $q$-form field on a domain wall brane, leading to the derivation of zero modes, Schr\"{o}dinger-like equations, and a four-dimensional effective action. Additionally, in order to stand for the coupling of the $q$-form field with gravity and scalar fields of the background spacetime, we propose a new coupling function $F(R,\varphi)$. Our analysis highlights the significance of the parameters $\displaystyle C_2$ and $\displaystyle t$ in the localization process., Comment: 14 pages, 9 figures

In the realm of medical 3D data, such as CT and MRI images, prevalent anisotropic resolution is characterized by high intra-slice but diminished inter-slice resolution. The lowered resolution between adjacent slices poses challenges, hindering optimal viewing experiences and impeding the development of robust downstream analysis algorithms. Various volumetric super-resolution algorithms aim to surmount these challenges, enhancing inter-slice resolution and overall 3D medical imaging quality. However, existing approaches confront inherent challenges: 1) often tailored to specific upsampling factors, lacking flexibility for diverse clinical scenarios; 2) newly generated slices frequently suffer from over-smoothing, degrading fine details, and leading to inter-slice inconsistency. In response, this study presents CycleINR, a novel enhanced Implicit Neural Representation model for 3D medical data volumetric super-resolution. Leveraging the continuity of the learned implicit function, the CycleINR model can achieve results with arbitrary up-sampling rates, eliminating the need for separate training. Additionally, we enhance the grid sampling in CycleINR with a local attention mechanism and mitigate over-smoothing by integrating cycle-consistent loss. We introduce a new metric, Slice-wise Noise Level Inconsistency (SNLI), to quantitatively assess inter-slice noise level inconsistency. The effectiveness of our approach is demonstrated through image quality evaluations on an in-house dataset and a downstream task analysis on the Medical Segmentation Decathlon liver tumor dataset., Comment: CVPR accepted paper

Segment anything model (SAM) demonstrates strong generalization ability on natural image segmentation. However, its direct adaption in medical image segmentation tasks shows significant performance drops with inferior accuracy and unstable results. It may also requires an excessive number of prompt points to obtain a reasonable accuracy. For segmenting 3D radiological CT or MRI scans, a 2D SAM model has to separately handle hundreds of 2D slices. Although quite a few studies explore adapting SAM into medical image volumes, the efficiency of 2D adaption methods is unsatisfactory and 3D adaptation methods only capable of segmenting specific organs/tumors. In this work, we propose a comprehensive and scalable 3D SAM model for whole-body CT segmentation, named CT-SAM3D. Instead of adapting SAM, we propose a 3D promptable segmentation model using a (nearly) fully labeled CT dataset. To train CT-SAM3D effectively, ensuring the model's accurate responses to higher-dimensional spatial prompts is crucial, and 3D patch-wise training is required due to GPU memory constraints. For this purpose, we propose two key technical developments: 1) a progressively and spatially aligned prompt encoding method to effectively encode click prompts in local 3D space; and 2) a cross-patch prompt learning scheme to capture more 3D spatial context, which is beneficial for reducing the editing workloads when interactively prompting on large organs. CT-SAM3D is trained and validated using a curated dataset of 1204 CT scans containing 107 whole-body anatomies, reporting significantly better quantitative performance against all previous SAM-derived models by a large margin with much fewer click prompts. Our model can handle segmenting unseen organ as well. Code, data, and our 3D interactive segmentation tool with quasi-real-time responses will be made publicly available.

The scalar fields, $U(1)$ gauge vector fields, and Kalb-Ramond fields are the $0$-form, 1-form, and 2-form fields, respectively. In four-dimensional space-time, free $q$-form fields are equivalent to scalar or vector fields by a duality, however, in higher-dimensional space-time, $q-$form fields correspond to new types of particles. In this paper, with considering a coupling mechanism between the kinetic term of the $q-$form fields and the background spacetime, we investigate the localization of Kaluza-Klein modes for the $q-$form fields on a $D-$dimensional Randall-Sundrum-like brane model. We demonstrate that the zero mode can be localized on the brane, and the massive Kaluza-Klein modes could be localized or quasi-localized on the brane when with certain value of parameters. Then, we present the localization of the scalar fields, $U(1)$ gauge vector fields, and 2-form Kalb-Ramond fields within a five-dimensional bulk spacetime. For a massless scalar field, an interesting characteristic emerges: When the parameter $t_2$ is negative, the zero mode is localized on both sides of the brane, whereas the massive Kaluza-Klein modes can be quasi-localized at the center of the brane., Comment: 39 pages, 20figures, 4 tables

In this paper, we consider a coupling mechanism between the kinetic term and the gravity, in which a coupling function $F(R)$ is introduced into the kinetic term of the five-dimensional scalar field. Based on this scenario, we investigate the localization of scalar fields in three specific braneworld models: the Minkowski brane, the de Sitter brane, and the Anti-de Sitter brane. The brane models considered here are regular with no singularity for scalar curvature. For the Minkowshi brane case, the zero mode can always be localized on the brane, and the massive modes can be localized or quasi-localized on the brane. For the dS$_4$ brane case, two forms of factor $F(R)$ is considered. The zero mode can always be localized, and the massive modes could be quasi-localized on the brane. Besides, with the second coupling factor, the scalar zero mode could be localized on the both sides of the origin of extra dimension, while the massive modes could be quasi-localized on the origin. Lastly, for the AdS$_4$ brane case, the localization of the scalar zero mode requires the consideration of a coupling potential $V(\Phi,\varphi)$, while the massive modes can still be localized on the brane with an infinite number., Comment: 34pages, 17 figures, 2 tables,published in JHEP

We give a fully polynomial-time randomized approximation scheme (FPRAS) for two terminal reliability in directed acyclic graphs (DAGs). In contrast, we also show the complementing problem of approximating two terminal unreliability in DAGs is #BIS-hard., Comment: 30 pages. v3: improved presentation

In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their ranks and maxima.linearly independent groups are verified.The initial motivation to study double cyclic matrices is to study the quasi cyclic codes of the fractional index. In this paper, the generalized form of the quasi cyclic codes, i.e. the {\phi}-quasi cyclic codes. and the construction of the generated matrix are given by the double ideal matrix.

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one $\mathcal X= -\frac12 (\nabla \varphi)^2$, say $\mathcal F(\mathcal X)$, and the kink is generated by a canonical scalar matter field $\phi$. It is found that for arbitrary $\mathcal F(\mathcal X)$, the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schr\"odinger-like equation with factorizable Hamiltonian operator. After choosing appropriate $\mathcal F(\mathcal X)$ and superpotential, we obtain a sine-Gordon type kink solution with pure AdS$_2$ metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value., Comment: 7 pages, 2 figures

We give a $\widetilde{O}(n)$ time almost uniform sampler for independent sets of a matroid, whose ground set has $n$ elements and is given by an independence oracle. As a consequence, one can sample connected spanning subgraphs of a given graph $G=(V,E)$ in $\widetilde{O}(|E|)$ time. This leads to improved running time on estimating all-terminal network reliability. Furthermore, we generalise this near-linear time sampler to the random cluster model with $q\le 1$.

We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $\lambda$ on graphs with maximum degree $\Delta$ when $\lambda=O(\Delta^{-1.5-c_1})$ where $c_1=c/(2-2c)$; (2) for spin systems with strong spatial mixing (SSM) on planar graphs with quadratic growth, such as $\mathbb{Z}^2$. For the hard-core model, Weitz's algorithm (STOC, 2006) achieves sub-quadratic running time when correlation decays faster than the neighbourhood growth, namely when $\lambda = o(\Delta^{-2})$. Our first algorithm does not require this property and extends the range where sub-quadratic algorithms exist. Our second algorithm appears to be the first to achieve sub-quadratic running time up to the SSM threshold, albeit on a restricted family of graphs. It also extends to (not necessarily planar) graphs with polynomial growth, such as $\mathbb{Z}^d$, but with a running time of the form $\widetilde{O}\left(n^2\varepsilon^{-2}/2^{c(\log n)^{1/d}}\right)$ where $d$ is the exponent of the polynomial growth and $c>0$ is some constant., Comment: 19 pages, 3 figures. To appear in ICALP2024

We investigate the gauge invariance of massive vector Kaluza-Klein (KK) modes in different brane models with two extra dimensions. We demonstrate that some additional constraint conditions on the geometry of branes are needed in order to get the gauge invariant effective action of the KK modes. Nevertheless, not all the conditions can be satisfied by the solutions of the branes, which will break the gauge invariance. Moreover, in the branes where the conditions can meet the brane solutions, we calculate mass spectra of vector and scalar KK modes, and the results show that when only one kind of scalar KK modes is found to be massive, the gauge invariance will also be broken., Comment: 14pages, 2 figures

Self-supervised learning (SSL) has recently achieved promising performance for 3D medical image analysis tasks. Most current methods follow existing SSL paradigm originally designed for photographic or natural images, which cannot explicitly and thoroughly exploit the intrinsic similar anatomical structures across varying medical images. This may in fact degrade the quality of learned deep representations by maximizing the similarity among features containing spatial misalignment information and different anatomical semantics. In this work, we propose a new self-supervised learning framework, namely Alice, that explicitly fulfills Anatomical invariance modeling and semantic alignment via elaborately combining discriminative and generative objectives. Alice introduces a new contrastive learning strategy which encourages the similarity between views that are diversely mined but with consistent high-level semantics, in order to learn invariant anatomical features. Moreover, we design a conditional anatomical feature alignment module to complement corrupted embeddings with globally matched semantics and inter-patch topology information, conditioned by the distribution of local image content, which permits to create better contrastive pairs. Our extensive quantitative experiments on three 3D medical image analysis tasks demonstrate and validate the performance superiority of Alice, surpassing the previous best SSL counterpart methods and showing promising ability for united representation learning. Codes are available at https://github.com/alibaba-damo-academy/alice., Comment: This paper has been accepted by ICCV 2023 (oral)

Automatic parsing of human anatomies at instance-level from 3D computed tomography (CT) scans is a prerequisite step for many clinical applications. The presence of pathologies, broken structures or limited field-of-view (FOV) all can make anatomy parsing algorithms vulnerable. In this work, we explore how to exploit and conduct the prosperous detection-then-segmentation paradigm in 3D medical data, and propose a steerable, robust, and efficient computing framework for detection, identification, and segmentation of anatomies in CT scans. Considering complicated shapes, sizes and orientations of anatomies, without lose of generality, we present the nine degrees-of-freedom (9-DoF) pose estimation solution in full 3D space using a novel single-stage, non-hierarchical forward representation. Our whole framework is executed in a steerable manner where any anatomy of interest can be directly retrieved to further boost the inference efficiency. We have validated the proposed method on three medical imaging parsing tasks of ribs, spine, and abdominal organs. For rib parsing, CT scans have been annotated at the rib instance-level for quantitative evaluation, similarly for spine vertebrae and abdominal organs. Extensive experiments on 9-DoF box detection and rib instance segmentation demonstrate the effectiveness of our framework (with the identification rate of 97.0% and the segmentation Dice score of 90.9%) in high efficiency, compared favorably against several strong baselines (e.g., CenterNet, FCOS, and nnU-Net). For spine identification and segmentation, our method achieves a new state-of-the-art result on the public CTSpine1K dataset. Last, we report highly competitive results in multi-organ segmentation at FLARE22 competition. Our annotations, code and models will be made publicly available at: https://github.com/alibaba-damo-academy/Med_Query., Comment: updated version

Multispectral photometric stereo(MPS) aims at recovering the surface normal of a scene from a single-shot multispectral image captured under multispectral illuminations. Existing MPS methods adopt the Lambertian reflectance model to make the problem tractable, but it greatly limits their application to real-world surfaces. In this paper, we propose a deep neural network named NeuralMPS to solve the MPS problem under general non-Lambertian spectral reflectances. Specifically, we present a spectral reflectance decomposition(SRD) model to disentangle the spectral reflectance into geometric components and spectral components. With this decomposition, we show that the MPS problem for surfaces with a uniform material is equivalent to the conventional photometric stereo(CPS) with unknown light intensities. In this way, NeuralMPS reduces the difficulty of the non-Lambertian MPS problem by leveraging the well-studied non-Lambertian CPS methods. Experiments on both synthetic and real-world scenes demonstrate the effectiveness of our method.

We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC) algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of marginal distributions. For the latter task, we introduce a method called coupling towards the past that can, in logarithmic time, evaluate one or a constant number of variables from a stationary Markov chain state. Since there are at most logarithmic random choices, this leads to very simple derandomisation. We provide two applications of this framework, namely efficient deterministic approximate counting algorithms for hypergraph independent sets and hypergraph colourings, under local lemma type conditions matching, up to lower order factors, their state-of-the-art randomised counterparts., Comment: 64 pages

Critical scenario generation requires the ability of sampling critical combinations from the infinite parameter space in the logic scenario. Existing solutions aim to explore the correlation of action parameters in the initial scenario rather than action sequences. How to model action sequences so that one can further consider the effects of different action parameters in the scenario is the bottleneck of the problem. In this paper, we attack the problem by proposing the ECSAS framework. Specifically, we first propose a description language, BTScenario, allowing us to model action sequences of the scenarios. We then use reinforcement learning to search for combinations of critical action parameters. To increase efficiency, we further propose several optimizations, including action masking and replay buffer. We have implemented ECSAS, and experimental results show that it is more efficient than native approaches such as random and combination testing in various nontrivial scenarios.

Accurate and robust abdominal multi-organ segmentation from CT imaging of different modalities is a challenging task due to complex inter- and intra-organ shape and appearance variations among abdominal organs. In this paper, we propose a probabilistic multi-organ segmentation network with hierarchical spatial-wise feature modulation to capture flexible organ semantic variants and inject the learnt variants into different scales of feature maps for guiding segmentation. More specifically, we design an input decomposition module via a conditional variational auto-encoder to learn organ-specific distributions on the low dimensional latent space and model richer organ semantic variations that is conditioned on input images.Then by integrating these learned variations into the V-Net decoder hierarchically via spatial feature transformation, which has the ability to convert the variations into conditional Affine transformation parameters for spatial-wise feature maps modulating and guiding the fine-scale segmentation. The proposed method is trained on the publicly available AbdomenCT-1K dataset and evaluated on two other open datasets, i.e., 100 challenging/pathological testing patient cases from AbdomenCT-1K fully-supervised abdominal organ segmentation benchmark and 90 cases from TCIA+&BTCV dataset. Highly competitive or superior quantitative segmentation results have been achieved using these datasets for four abdominal organs of liver, kidney, spleen and pancreas with reported Dice scores improved by 7.3% for kidneys and 9.7% for pancreas, while being ~7 times faster than two strong baseline segmentation methods(nnUNet and CoTr)., Comment: 12 pages, 6 figures

We give a simple polynomial-time approximation algorithm for the total variation distance between two product distributions.

This paper presents a near-light photometric stereo method that faithfully preserves sharp depth edges in the 3D reconstruction. Unlike previous methods that rely on finite differentiation for approximating depth partial derivatives and surface normals, we introduce an analytically differentiable neural surface in near-light photometric stereo for avoiding differentiation errors at sharp depth edges, where the depth is represented as a neural function of the image coordinates. By further formulating the Lambertian albedo as a dependent variable resulting from the surface normal and depth, our method is insusceptible to inaccurate depth initialization. Experiments on both synthetic and real-world scenes demonstrate the effectiveness of our method for detailed shape recovery with edge preservation.

We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random $k$-SAT model applies when the density $\alpha=m/n$ of the formula is less than $2^{k/300}$ and runs in time $n^{\exp(\Theta(k))}$. Here $n$ is the number of variables and $m$ is the number of clauses. Our algorithm achieves a significantly faster running time of $n^{1 + o_k(1)}$ and samples satisfying assignments up to density $\alpha\leq 2^{0.039 k}$. The main challenge in our setting is the presence of many variables with unbounded degree, which causes significant correlations within the formula and impedes the application of relevant Markov chain methods from the bounded-degree setting. Our main technical contribution is a $o_k(\log n )$ bound of the sum of influences in the $k$-SAT model which turns out to be robust against the presence of high-degree variables. This allows us to apply the spectral independence framework and obtain fast mixing results of a uniform-block Glauber dynamics on a carefully selected subset of the variables. The final key ingredient in our method is to take advantage of the sparsity of logarithmic-sized connected sets and the expansion properties of the random formula, and establish relevant connectivity properties of the set of satisfying assignments that enable the fast simulation of this Glauber dynamics. Our results also allow us to conclude that, with high probability, a random $k$-CNF formula with density at most $2^{0.227 k}$ has a giant component of solutions that are connected in a graph where solutions are adjacent if they have Hamming distance $O_k(\log n)$. We are also able to deduce looseness results for random $k$-CNFs in the same regime., Comment: This is a merger with the independent work arxiv:2207.02841. To appear in SIDMA

We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from $1$., Comment: Major revision and new results