Bijective Map Research Articles

Robust Shared Control With Stable Contact Servoing for Enhanced Object Transportation by Telerobotic Bimanual Mobile Manipulators

ABSTRACTBimanual mobile manipulation significantly enhances the capabilities of field robots that interact with diverse dynamic environments and expands the range of possible manipulation actions. This paper introduces a robust shared control architecture for remote manipulation of the Collaborative Dual‐arm Robot Manipulator (CURI), aimed at stable object transportation. Given that stable contact is pivotal for successful object transportation, our focus is on stabilizing the contact between the robot end‐effectors and the object using a contact servoing strategy. To maintain stable contact, it is essential that the contact wrenches consistently stay within the predefined friction cones throughout the task. We propose a novel shared control strategy to stabilize the contact using the contact parameterization model. This model formulates the contact stability manifold using a set of unconstrained reparameterized variables through a bijective mapping function, ensuring that the controller derived from these unconstrained reparameterized variables consistently maintains contact stability. The efficacy of the proposed approach is convincingly demonstrated through a series of experiments involving representative bimanual transportation tasks within a logistics context. Both theoretical analysis and experimental validations confirm that our proposed control strategy not only ensures the stable transportation of objects by CURI but also substantially enhances the overall robustness of the shared control system.

Hom-actions and Class Equation for Hom-groups

The notion of Hom-groups is defined as a generalization of a non-associative group. They can be obtained by twisting the associative operation with a compatible bijection mapping. In this article, we provide some constructions by twisting and also discuss properties related to Hom-groups. We introduce different notions of actions concerning Hom-groups. We then present a theorem for a class equation, which is proven. Following that, we illustrate some applications for p-Hom groups.

Arithmetic Sequential Graceful Labeling For Arrow Graphs

Let G be a simple, finite, connected, undirected, non-trivial graph with 𝑝 vertices and 𝑞 edges. 𝑉(𝐺) be the vertex set and 𝐸(𝐺) be the edge set of 𝐺. Let 𝑓: 𝑉(𝐺) → {𝑎, 𝑎 + 𝑑, 𝑎 + 2𝑑, 𝑎 + 3𝑑, … , 𝑎 + 2𝑞𝑑} where a ≥ 0 and 𝑑 ≥ 1 is an injective function. If for each edge 𝑢𝑣 ∈ 𝐸(𝐺) , 𝑓 ∗ : 𝐸(𝐺) → {𝑑, 2𝑑, 3𝑑, 4𝑑, … , 𝑞𝑑} defined by 𝑓 ∗ (𝑢𝑣) = |𝑓(𝑢)− 𝑓(𝑣)| is a bijective function then the function 𝑓 is called arithmetic sequential graceful labeling. The graph with arithmetic sequential graceful labeling is called arithmetic sequential graceful graph. In this paper, we prove that one side arrow graphs 𝐴𝑅𝜂 2 , 𝐴𝑅𝜂 3 , 𝐴𝑅𝜂 5 and double-sided arrow graphs 𝐷(𝐴𝑅𝜂 2 ),𝐷(𝐴𝑅𝜂 3 ) are arithmetic sequential graceful graph

Results on super edge magic deficiency of somewell-known classes of finite graphs

A graph Ω(Λ, Γ) is considered super edge magic if there exists a bijective function ϕ:Λ(Ω)∪Γ(Ω)→ {1, 2, 3, …,|Λ(Ω)|+|Γ(Ω)|} such that ϕ(τ1)+(τ1τ2)+ ϕ(τ2) is a constant for every edge τ1τ2 ∈ Γ(Ω), and ϕ(Λ(Ω))= {1, 2, 3, …,|Λ(Ω)|}. Furthermore, the super edge magic deficiency of a graph Ω, denoted as μs (Ω), is either the minimum non-negative integer η such that Ω∪ηK1 is a super edge magic graph or +∞ if such an integer η does not exist. In this paper, we investigate the super edge magic deficiency of certain families of graphs.

Novel non‐involutive solutions of the Yang–Baxter equation from (skew) braces

AbstractWe produce novel non‐involutive solutions of the Yang–Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew braces, and surprisingly in the case of braces, they are not necessarily involutive. In the case of two‐sided (skew) braces, one can assign such solutions to every element of the set. Novel bijective maps associated to the inverse solutions are also introduced. Moreover, we show that the recently derived Drinfeld twists of the involutive case are still admissible in the non‐involutive frame, and we identify the twisted ‐matrices and twisted coproducts. We observe, as in the involutive case, that the underlying quantum algebra is not a quasi‐triangular bialgebra, as one would expect, but a quasi‐triangular quasi‐bialgebra. The same applies to the quantum algebra of the twisted ‐matrices, contrary to the involutive case.

Closing duality gaps of SDPs completely through perturbation when singularity degree is one

Let ( P , D ) be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, P and D are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal value function v as a function of the perturbation is not well-defined at zero (i.e. at the unperturbed data). Nevertheless, under the assumption that both P and D have singularity degree one, we show that a limiting version v a of v is a well-defined monotone decreasing continuous bijective function with domain [ 0 , π / 2 ] and image [ v ( P ) , v ( D ) ] , where v ( P ) and v ( D ) are the optimal values of P and D , respectively. The domain [ 0 , π / 2 ] corresponds to directions of perturbation defined in a certain manner. Thus, v a ‘completely fills’ the nonzero duality gap under a mild regularity condition. Our result is tight in that there exists an instance with singularity degree two for which v a is not continuous.

Uni-to-Multi Modal Knowledge Distillation for Bidirectional LiDAR-Camera Semantic Segmentation.

Combining LiDAR points and images for robust semantic segmentation has shown great potential. However, the heterogeneity between the two modalities (e.g. the density, the field of view) poses challenges in establishing a bijective mapping between each point and pixel. This modality alignment problem introduces new challenges in network design and data processing for cross-modal methods. Specifically, 1) points that are projected outside the image planes; 2) the complexity of maintaining geometric consistency limits the deployment of many data augmentation techniques. To address these challenges, we propose a cross-modal knowledge imputation and transition approach. First, we introduce a bidirectional feature fusion strategy that imputes missing image features and performs cross-modal fusion simultaneously. This allows us to generate reliable predictions even when images are missing. Second, we propose a Uni-to-Multi modal Knowledge Distillation (U2MKD) framework, leveraging the transfer of informative features from a single-modality teacher to a cross-modality student. This overcomes the issues of augmentation misalignment and enables us to train the student effectively. Extensive experiments on the nuScenes, Waymo, and SemanticKITTI datasets demonstrate the effectiveness of our approach. Notably, our method achieves an 8.3 mIoU gain over the LiDAR-only baseline on the nuScenes validation set and achieves state-of-the-art performance on the three datasets.

On Computing the k -Shortcut Fréchet Distance

The Fréchet distance is a popular measure of dissimilarity for polygonal curves. It is defined as a min–max formulation that considers all orientation-preserving bijective mappings between the two curves. Because of its susceptibility to noise, Driemel and Har-Peled introduced the shortcut Fréchet distance in 2012, where one is allowed to take shortcuts along one of the curves, similar to the edit distance for sequences. We analyse the parameterised version of this problem, where the number of shortcuts is bounded by a parameter \(k\) . The corresponding decision problem can be stated as follows: Given two polygonal curves \(T\) and \(B\) of at most \(n\) vertices, a parameter \(k\) and a distance threshold \(\delta\) , is it possible to introduce \(k\) shortcuts along \(B\) such that the Fréchet distance of the resulting curve and the curve \(T\) is at most \(\delta\) ? We study this problem for polygonal curves in the plane. We provide a complexity analysis for this problem with the following results: (1) there exists a decision algorithm with running time in \(\mathcal{O}(kn^{2k+2}\log n)\) ; (2) assuming the exponential-time hypothesis (ETH), there exists no algorithm with running time bounded by \(n^{o(k)}\) . In contrast, we also show that efficient approximate decider algorithms are possible, even when \(k\) is large. We present a \((3+\varepsilon)\) -approximate decider algorithm with running time in \(\mathcal{O}(kn^{2}\log^{2}n)\) for fixed \(\varepsilon\) . In addition, we can show that, if \(k\) is a constant and the two curves are \(c\) -packed for some constant \(c\) , then the approximate decider algorithm runs in near-linear time.

Hierarchical disentangled representation for image denoising and beyond

Image denoising is a typical ill-posed problem due to complex degradation. Leading methods based on normalizing flows have tried to solve this problem with an invertible transformation instead of a deterministic mapping. However, it is difficult to construct feasible bijective mapping to remove spatial-variant noise while recovering fine texture and structure details due to latent ambiguity in inverse problems. Inspired by a common observation that noise tends to appear in the high-frequency part of the image, we propose a fully invertible denoising method that injects the idea of disentangled learning into a general invertible architecture to split noise from the high-frequency part. More specifically, we decompose the noisy image into clean low-frequency and hybrid high-frequency parts with an invertible transformation and then disentangle case-specific noise and high-frequency components in the latent space. In this way, denoising is made tractable by inversely merging noiseless low and high-frequency parts. Furthermore, we construct a flexible hierarchical disentangling framework, which aims to decompose most of the low-frequency image information while disentangling noise from the high-frequency part in a coarse-to-fine manner. Extensive experiments on real image denoising, JPEG compressed artifact removal, and medical low-dose CT image restoration have demonstrated that the proposed method achieves competitive performance on both quantitative metrics and visual quality, with significantly less computational cost.

Model order reduction by convex displacement interpolation

We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure introduced in [Iollo, Taddei, J. Comput. Phys., 2022] to multi-dimensional parameter domains and to datasets of several snapshots. Given a library of high-fidelity simulations, we rely on a scalar testing function and on a point set registration method to identify coherent structures of the solution field in the form of sorted point clouds. Given a new parameter value, we exploit a regression method to predict the new point cloud; then, we resort to a boundary-aware registration technique to define bijective mappings that deform the new point cloud into the point clouds of the neighboring elements of the dataset, while preserving the boundary of the domain; finally, we define the estimate as a weighted combination of modes obtained by composing the neighboring snapshots with the previously-built mappings. We present several numerical examples for compressible and incompressible, viscous and inviscid flows to demonstrate the accuracy of the method. Furthermore, we employ the nonlinear interpolation procedure to augment the dataset of simulations for linear-subspace projection-based model reduction: our data augmentation procedure is designed to reduce offline costs — which are dominated by snapshot generation — of model reduction techniques for nonlinear advection-dominated problems.

Integrasi Islam dan Sains: Telaah Terhadap Konsep Matematika dalam Hadits Keutamaan Membaca Shalawat

National education has the goal of shaping the morals of students who are truehearted and dedicated to God. As part of national education, Islamic-integrated mathematics learning becomes a bridge to achieve this goal. This study aims to explore the concept of mathematics in the hadith with the theme of the virtue of reciting shalawat. This research uses a qualitative approach with literature study methods. Data were obtained from hadith books, hadith applications, articles, and relevant documents. The results showed that there are three mathematical concepts in the hadith related to the virtue of reciting shalawat. The mathematical concepts found include the concept of numbers (natural numbers, integers, positive integers, odd numbers, and even numbers), arithmetic operations (addition operations), and the concept of relations and functions (bijective functions). The results of this study can be used as a reference for learning resources related to Islamic integrated mathematics derived from hadith with the theme of the virtue of reading shalawat.

Онтологизация познания: уровни, направления и средства реализации

The article investigates the problem of ontologization of cognition, i.e. increasing the level of conformity between the knowledge system and being. Various levels of ontologization of knowledge are examined depending on the nature of the reflection of reality in the system of knowledge. Four levels of ontology are distinguished: the first level corresponds to the injective and bijective mappings of reality onto the knowledge system; the second level involves surjective mapping; the third level encompasses knowledge formed through isomorphic mapping of relationships between elements from reality onto the knowledge system; the fourth level involves knowledge formed through isomorphic mapping of relationships between elements within the knowledge system. Prospects for the ontologization of cognition are related to the expansion of metaphysical and consequent knowledge, the elevation to the fourth level of knowledge domains that lack ontologicality, and the expansion of knowledge linking secondary laws and properties of objects to patterns. The main tool for ontologizing cognition should be a general theory of systems, extended with a metaphysical component and supplemented with extensive collections of patterns, primitives, secondary properties and laws. The author is working on such a general systems theory, referred to as the “empirico-metaphysical general theory of systems”. In conclusion, development of an empirico-metaphysical theory of systems promises to provide a robust framework for addressing the challenges of cognition representation, synthesis, and application across diverse domains. As researchers continue to delve into the nuances of ontological alignment, the proposed framework offers a promising avenue for fostering interdisciplinary collaboration and advancing our understanding of the fundamental nature of cognition.

Explainable Intelligent Fault Diagnosis for Nonlinear Dynamic Systems: From Unsupervised to Supervised Learning.

The increased complexity and intelligence of automation systems require the development of intelligent fault diagnosis (IFD) methodologies. By relying on the concept of a suspected space, this study develops explainable data-driven IFD approaches for nonlinear dynamic systems. More specifically, we parameterize nonlinear systems through a generalized kernel representation for system modeling and the associated fault diagnosis. An important result obtained is a unified form of kernel representations, applicable to both unsupervised and supervised learning. More importantly, through a rigorous theoretical analysis, we discover the existence of a bridge (i.e., a bijective mapping) between some supervised and unsupervised learning-based entities. Notably, the designed IFD approaches achieve the same performance with the use of this bridge. In order to have a better understanding of the results obtained, both unsupervised and supervised neural networks are chosen as the learning tools to identify the generalized kernel representations and design the IFD schemes; an invertible neural network is then employed to build the bridge between them. This article is a perspective article, whose contribution lies in proposing and formalizing the fundamental concepts for explainable intelligent learning methods, contributing to system modeling and data-driven IFD designs for nonlinear dynamic systems.

Pairs of continuous linear bijective maps preserving fixed products of operators

Let X X be a complex Banach space, and denote by B ( X ) \mathcal {B}(X) the algebra of all bounded linear operators on X X . Let C , D ∈ B ( X ) C,D\in \mathcal {B} \left ( X\right ) be fixed operators. In this paper, we characterize linear, continuous and bijective maps φ \varphi and ψ \psi on B ( X ) \mathcal {B}\left ( X\right ) for which there exist invertible operators T 0 , W 0 ∈ B ( X ) T_0, W_0 \in \mathcal { B}(X) such that φ ( T 0 ) , ψ ( W 0 ) ∈ B ( X ) \varphi (T_0), \psi (W_0) \in \mathcal {B}(X) are both invertible, having the property that φ ( A ) ψ ( B ) = D \varphi \left ( A\right ) \psi \left ( B\right ) =D in B ( X ) \mathcal {B}(X) whenever A B = C AB=C in B ( X ) \mathcal {B}(X) . As a corollary, we deduce the form of linear, bijective and continuous maps φ \varphi on B ( X ) \mathcal {B}(X) having the property that φ ( A ) φ ( B ) = D \varphi \left ( A\right ) \varphi \left ( B\right ) =D in B ( X ) \mathcal {B}(X) whenever A B = C AB=C .

Statistical mirroring: A robust method for statistical dispersion estimation

This study introduces statistical mirroring as an innovative approach to statistical dispersion estimation, drawing inspiration from the Kabirian-based isomorphic optinalysis model, aimed at enhancing robustness and mitigating biases in estimation methods. Beyond scale-invariant characteristics, the proposed estimators emphasize scaloc-invariant robustness, thereby addressing a critical gap in dispersion estimation. By highlighting statistical meanic mirroring, alongside other forms of proposed statistical mirroring, the study underscores the adaptability and customization potential. Through extensive Monte Carlo simulations and real-life applications, in comparison with classical estimators, the results of the performance evaluation of the proposed estimators demonstrate robustness, efficiency, and transformations-invariance. The research offers a paradigm shift in addressing longstanding challenges in dispersion estimation, offering a new category of dispersion estimation and increased resistance to outliers. Notable limitations include selecting and evaluating the proposed statistical meanic mirroring under Gaussian and Gaussian mixture model distributions. This research paper significantly contributes to statistical methodologies, offering avenues for expanding knowledge in dispersion estimation. It recommends further exploration of proposed estimators across various statistical mirroring types and encourages comparative studies to establish their effectiveness, thereby advancing statistical knowledge and tools for precise data analysis.•The proposed methodology involves preprocessing transformations, statistical mirror design, and optimization to transform a univariate set into a bivariate one, facilitating the fitting of an isomorphic optinalysis model.•Estimators rely on a foundational bijective mapping of isoreflective pairs, deducing the probability of proximity or deviation from any defined center. This contrasts with classical estimators that utilize average or median deviations from a mean or median center.

A collection of seminorms linking the A-numerical radius and the operator A-seminorm

We investigate a novel operator seminorm, QA,mλ,f, for an A-bounded operator Q, where A is a positive operator on a complex Hilbert space (K,⟨·,·⟩). This seminorm is defined using a continuous increasing and bijective function f:R+⟶R+ and an interpolational path mλ of the symmetric mean m. Specifically, QA,mλ,f=supf−1fQy,yAmλfQyA:y∈K,yA=1, where f−1 represents the reciprocal function of f, and ⟨·,·⟩A and ·A denote the semi-inner product and seminorm, respectively, induced by A on K. We explore various bounds and relationships associated with this new concept, establishing connections with existing literature.

Multiplicative maps on generalized \(n\)-matrix rings

Let \(\mathfrak{R}\) and \(\mathfrak{R}'\) be two associative rings (not necessarily with identity elements). A bijective map \(\varphi\) of \(\mathfrak{R}\) onto \(\mathfrak{R}'\) is called an \textit{\(m\)-multiplicative isomorphism} if {\(\varphi (x_{1} \cdots x_{m}) = \varphi(x_{1}) \cdots \varphi(x_{m})\)} for all \(x_{1}, \dotsc ,x_{m}\in \mathfrak{R}.\) In this article, we establish a condition on generalized matrix rings, that assures that multiplicative maps are additive. And then, we apply our result for study of \(m\)-multiplicative isomorphisms and \(m\)-multiplicative derivations on generalized matrix rings.

Manifold Constraints for Imperceptible Adversarial Attacks on Point Clouds

Adversarial attacks on 3D point clouds often exhibit unsatisfactory imperceptibility, which primarily stems from the disregard for manifold-aware distortion, i.e., distortion of the underlying 2-manifold surfaces. In this paper, we develop novel manifold constraints to reduce such distortion, aiming to enhance the imperceptibility of adversarial attacks on 3D point clouds. Specifically, we construct a bijective manifold mapping between point clouds and a simple parameter shape using an invertible auto-encoder. Consequently, manifold-aware distortion during attacks can be captured within the parameter space. By enforcing manifold constraints that preserve local properties of the parameter shape, manifold-aware distortion is effectively mitigated, ultimately leading to enhanced imperceptibility. Extensive experiments demonstrate that integrating manifold constraints into conventional adversarial attack solutions yields superior imperceptibility, outperforming the state-of-the-art methods.

A PROPERLY EVEN HARMONIOUS LABELING OF SOME WHEEL GRAPH W_n FOR n IS EVEN

A properly even harmonious labeling of a graph G with q edges is an injective mapping f from the vertices of graph G to the integers from 0 to 2q-1 such that induces a bijective mapping f* from the edges of G to {0,2,...,2q-2} defined by f*(v_iv_j)=(f(v_i)+f(v_j))(mod2q). A graph that has a properly even harmonious labeling is called a properly even harmonious graph. In this research, we will show the existence of a properly even harmonious labeling of some wheel graph W_n for n is even.

Variable augmentation network for invertible MR coil compression

To improve the efficiency of multi-coil data compression and recover the compressed image reversibly, increasing the possibility of applying the proposed method to medical scenarios. A deep learning algorithm is employed for MR coil compression in the presented work. The approach introduces a variable augmentation network for invertible coil compression (VAN-ICC). This network utilizes the inherent reversibility of normalizing flow-based models. The aim is to enhance the readability of the sentence and clearly convey the key components of the algorithm. By applying the variable augmentation technology to image/k-space variables from multi-coils, VAN-ICC trains the invertible network by finding an invertible and bijective function, which can map the original data to the compressed counterpart and vice versa. Experiments conducted on both fully-sampled and under-sampled data verified the effectiveness and flexibility of VAN-ICC. Quantitative and qualitative comparisons with traditional non-deep learning-based approaches demonstrated that VAN-ICC carries much higher compression effects. The proposed method trains the invertible network by finding an invertible and bijective function, which improves the defects of traditional coil compression method by utilizing inherent reversibility of normalizing flow-based models. In addition, the application of variable augmentation technology ensures the implementation of reversible networks. In short, VAN-ICC offered a competitive advantage over other traditional coil compression algorithms.