Search Results (13)

Simultaneous Localization and Mapping (SLAM) has long been a fundamental and challenging task in robotics literature, where safety and reliability are the critical issues for successfully autonomous applications of robots. Classically, the SLAM problem is tackled via probabilistic or optimization methods (such as EKF-SLAM, Fast-SLAM, and Graph-SLAM). Despite their strong performance in real-world scenarios, these methods may exhibit inconsistency, which is caused by the inherent characteristic of model linearization or Gaussian noise assumption. In this paper, we propose an alternative monocular SLAM algorithm which theoretically relies on interval analysis (iMonoSLAM), to pursue guaranteed rather than probabilistically defined solutions. We consistently modeled and initialized the SLAM problem with a bounded-error parametric model. The state estimation process is then cast into an Interval Constraint Satisfaction Problem (ICSP) and resolved through interval constraint propagation techniques without any linearization or Gaussian noise assumption. Furthermore, we theoretically prove the obtained consistency and propose a versatile method for numerical validation. To the best of our knowledge, this is the first time such a proof has been proposed. A plethora of numerical experiments are carried to validate the consistency, and a preliminary comparison with classical EKF-SLAM in different noisy situations is also presented. Our proposed iMonoSLAM shows outstanding performance in obtaining reliable solutions, highlighting the potential application prospect in safety-critical scenarios of mobile robots. Full article

The zero-error capacity of discrete memoryless channels (DMCs), introduced by Shannon, is a fundamental concept in information theory with significant operational relevance, particularly in settings where even a single transmission error is unacceptable. Despite its importance, no general closed-form expression or algorithm is known for computing this capacity. In this work, we investigate the computability-theoretic boundaries of the zero-error capacity and establish several fundamental limitations. Our main result shows that the zero-error capacity of noisy channels is not Banach–Mazur-computable and therefore is also not Borel–Turing-computable. This provides a strong form of non-computability that goes beyond classical undecidability, capturing the inherent discontinuity of the capacity function. As a further contribution, we analyze the deep connections between (i) the zero-error capacity of DMCs, (ii) the Shannon capacity of graphs, and (iii) Ahlswede’s operational characterization via the maximum-error capacity of 0–1 arbitrarily varying channels (AVCs). We prove that key semi-decidability questions are equivalent for all three capacities, thus unifying these problems into a common algorithmic framework. While the computability status of the Shannon capacity of graphs remains unresolved, our equivalence result clarifies what makes this problem so challenging and identifies the logical barriers that must be overcome to resolve it. Together, these results chart the computational landscape of zero-error information theory and provide a foundation for further investigations into the algorithmic intractability of exact capacity computations. Full article

Accurate address matching is crucial for the analysis, integration, and intelligent management of urban geospatial data and is also a key step in achieving geocoding. However, due to the complexity, diversity, and irregularity of address expression, address matching becomes a challenging task. This paper proposes a multi-semantic feature fusion method for complex address matching of Chinese addresses that formulates address matching as a classification task that directly predicts whether two addresses refer to the same location, without relying on predefined similarity thresholds. First, the address is resolved into address elements, and the Word2vec model is trained to generate word vector representations using these address elements. Then, multi-semantic features of the addresses are extracted using a Text Recurrent Convolutional Neural Network (Text-RCNN) and a Graph Attention Network (GAT). Finally, the Enhanced Sequential Inference Model (ESIM) is used to perform both local inference and inference composition on the multi-semantic features of the addresses to achieve accurate matching of addresses. Experiments were conducted using Points of Interest (POI) address data from Baidu Maps, Tencent Maps, and Amap within the Chengdu area. The results demonstrate that the proposed method outperforms existing address matching methods, with precision, recall, and F1 values all exceeding 95%. In addition, transfer experiments using datasets from five other cities including Beijing, Shanghai, Xi’an, Guangzhou, and Wuhan show that the model maintains strong generalization ability, achieving F1 values above 84% in cities such as Xi’an and Wuhan. Full article

Pesticide registration information is an essential part of the pesticide knowledge base. However, the large amount of unstructured text data that it contains pose significant challenges for knowledge storage, retrieval, and utilization. To address the characteristics of pesticide registration text such as high information density, complex logical structures, large spans between entities, and heterogeneous entity lengths, as well as to overcome the challenges faced when using traditional joint extraction methods, including triplet overlap, exposure bias, and redundant computation, we propose a single-stage entity–relation joint extraction model based on HT-BES multi-dimensional labeling (MD-SERel). First, in the encoding layer, to address the complex structural characteristics of pesticide registration texts, we employ RoBERTa combined with a multi-head self-attention mechanism to capture the deep semantic features of the text. Simultaneously, syntactic features are extracted using a syntactic dependency tree and graph neural networks to enhance the model’s understanding of text structure. Subsequently, we integrate semantic and syntactic features, enriching the character vector representations and thus improving the model’s ability to represent complex textual data. Secondly, in the multi-dimensional labeling framework layer, we use HT-BES multi-dimensional labeling, where the model assigns multiple labels to each character. These labels include entity boundaries, positions, and head–tail entity association information, which naturally resolves overlapping triplets. Through utilizing a parallel scoring function and fine-grained classification components, the joint extraction of entities and relations is transformed into a multi-label sequence labeling task based on relation dimensions. This process does not involve interdependent steps, thus enabling single-stage parallel labeling, preventing exposure bias and reducing computational redundancy. Finally, in the decoding layer, entity–relation triplets are decoded based on the predicted labels from the fine-grained classification. The experimental results demonstrate that the MD-SERel model performs well on both the Pesticide Registration Dataset (PRD) and the general DuIE dataset. On the PRD, compared to the optimal baseline model, the training time is 1.2 times faster, the inference time is 1.2 times faster, and the F1 score is improved by 1.5%, demonstrating its knowledge extraction capabilities in pesticide registration documents. On the DuIE dataset, the MD-SERel model also achieved better results compared to the baseline, demonstrating its strong generalization ability. These findings will provide technical support for the construction of pesticide knowledge bases. Full article

Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {(u₁, σ(u₁)), (u₂, σ(u₂)), …(u_k, σ(u_k))}, |H| ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tuple with regard to H of G. If any two elements of σ − H do not have any distinct representation with regard to H, then this subset is called a fuzzy resolving set (FRS) and the smallest cardinality of this set is known as a fuzzy resolving number (FRN) and it is denoted by Fr(G). Similarly, consider a subset S such that for any u∈S, ∃v∈V − S, then S is called a fuzzy dominating set only if u is a strong arc. Now, again consider a subset F which is both a resolving and dominating set, then it is called a fuzzy resolving domination set (FRDS) and the smallest cardinality of this set is known as the fuzzy resolving domination number (FRDN) and it is denoted by F_γr(G). We have defined a few basic properties and theorems based on this FRDN and also developed an application for social network connection. Moreover, a few related statements and illustrations are discussed in order to strengthen the concept. Full article

Wavelet transforms or wavelet analysis represent a recently created mathematical tool for assistance in resolving various issues. Wavelets can also be used in numerical analysis. In this study, we solve pantograph delay differential equations using the Modified Laguerre Wavelet method (MLWM), an effective numerical technique. Fractional derivatives are defined using the Caputo operator. The convergence of the suggested strategy is carefully examined. The suggested strategy is straightforward, effective, and simple in comparison with previous approaches. Specific examples are provided to demonstrate the current scenario’s reliability and accuracy. Compared with other methodologies, our results show a higher accuracy level. With the aid of tables and graphs, we demonstrate the effectiveness of the proposed approach by comparing results of the actual and suggested methods and demonstrating their strong agreement. For better understanding of the proposed method, we show the pointwise solution in the tables provided which confirm the accuracy at each point of the proposed method. Additionally, the results of employing the suggested method to various fractional-orders are compared, which demonstrates that when a value shifts from fractional-order to integer-order, the result approaches the exact solution. Owing to its novelty and scientific significance, the suggested technique can also be used to solve additional nonlinear delay differential equations of fractional-order. Full article

Predictive graph learning approaches have been bringing significant advantages in many real-life applications, such as social networks, recommender systems, and other social-related downstream tasks. For those applications, learning models should be able to produce a great prediction result to maximize the usability of their application. However, the paradigm of current graph learning methods generally neglects the differences in link strength, leading to discriminative predictive results, resulting in different performance between tasks. Based on that problem, a fairness-aware predictive learning model is needed to balance the link strength differences and not only consider how to formulate it. To address this problem, we first formally define two biases (i.e., Preference and Favoritism) that widely exist in previous representation learning models. Then, we employ modularity maximization to distinguish strong and weak links from the quantitative perspective. Eventually, we propose a novel predictive learning framework entitled ACE that first implements the link strength differentiated learning process and then integrates it with a dual propagation process. The effectiveness and fairness of our proposed ACE have been verified on four real-world social networks. Compared to nine different state-of-the-art methods, ACE and its variants show better performance. The ACE framework can better reconstruct networks, thus also providing a high possibility of resolving misinformation in graph-structured data. Full article

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are $M\left[{\gamma }_s\left(C_l(\sigma ,\varphi ,\eta )\right)\right]=\lceil \frac{l}{3}\rceil$. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization. Full article

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix; and the Laplace transform. The fundamental solution is presented in the form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of an RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations. Full article

A vertex w of a connected graph G strongly resolves two distinct vertices $u,v\in V\left(G\right)$, if there is a shortest $u,w$ path containing v, or a shortest $v,w$ path containing u. A set S of vertices of G is a strong resolving set for G if every two distinct vertices of G are strongly resolved by a vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs. Full article

Herein we are not interested in merely using dynamical systems theory, graph theory, information theory, etc., to model the relationship between brain dynamics and networks, and various states and degrees of conscious processes. We are interested in the question of how phenomenal conscious experience and fundamental physics are most deeply related. Any attempt to mathematically and formally model conscious experience and its relationship to physics must begin with some metaphysical assumption in mind about the nature of conscious experience, the nature of matter and the nature of the relationship between them. These days the most prominent metaphysical fixed points are strong emergence or some variant of panpsychism. In this paper we will detail another distinct metaphysical starting point known as neutral monism. In particular, we will focus on a variant of the neutral monism of William James and Bertrand Russell. Rather than starting with physics as fundamental, as both strong emergence and panpsychism do in their own way, our goal is to suggest how one might derive fundamental physics from neutral monism. Thus, starting with two axioms grounded in our characterization of neutral monism, we will sketch out a derivation of and explanation for some key features of relativity and quantum mechanics that suggest a unity between those two theories that is generally unappreciated. Our mode of explanation throughout will be of the principle as opposed to constructive variety in something like Einstein’s sense of those terms. We will argue throughout that a bias towards property dualism and a bias toward reductive dynamical and constructive explanation lead to the hard problem and the explanatory gap in consciousness studies, and lead to serious unresolved problems in fundamental physics, such as the measurement problem and the mystery of entanglement in quantum mechanics and lack of progress in producing an empirically well-grounded theory of quantum gravity. We hope to show that given our take on neutral monism and all that follows from it, the aforementioned problems can be satisfactorily resolved leaving us with a far more intuitive and commonsense model of the relationship between conscious experience and physics. Full article

We consider in this work a new approach to study the simultaneous strong metric dimension of graphs families, while introducing the simultaneous version of the strong resolving graph. In concordance, we consider here connected graphs G whose vertex sets are represented as $V\left(G\right)$ , and the following terminology. Two vertices $u,v\in V\left(G\right)$ are strongly resolved by a vertex $w\in V\left(G\right)$ , if there is a shortest $w-v$ path containing u or a shortest $w-u$ containing v. A set A of vertices of the graph G is said to be a strong metric generator for G if every two vertices of G are strongly resolved by some vertex of A. The smallest possible cardinality of any strong metric generator (SSMG) for the graph G is taken as the strong metric dimension of the graph G. Given a family $\mathcal{F}$ of graphs defined over a common vertex set V, a set $S\subset V$ is an SSMG for $\mathcal{F}$ , if such set S is a strong metric generator for every graph $G\in \mathcal{F}$ . The simultaneous strong metric dimension of $\mathcal{F}$ is the minimum cardinality of any strong metric generator for $\mathcal{F}$ , and is denoted by ${Sd}_s\left(\mathcal{F}\right)$ . The notion of simultaneous strong resolving graph of a graph family $\mathcal{F}$ is introduced in this work, and its usefulness in the study of ${Sd}_s\left(\mathcal{F}\right)$ is described. That is, it is proved that computing ${Sd}_s\left(\mathcal{F}\right)$ is equivalent to computing the vertex cover number of the simultaneous strong resolving graph of $\mathcal{F}$ . Several consequences (computational and combinatorial) of such relationship are then deduced. Among them, we remark for instance that we have proved the NP-hardness of computing the simultaneous strong metric dimension of families of paths, which is an improvement (with respect to the increasing difficulty of the problem) on the results known from the literature. Full article

The region merging algorithm is a widely used segmentation technique for very high resolution (VHR) remote sensing images. However, the segmentation of post-earthquake VHR images is more difficult due to the complexity of these images, especially high intra-class and low inter-class variability among damage objects. Herein two key issues must be resolved: the first is to find an appropriate descriptor to measure the similarity of two adjacent regions since they exhibit high complexity among the diverse damage objects, such as landslides, debris flow, and collapsed buildings. The other is how to solve over-segmentation and under-segmentation problems, which are commonly encountered with conventional merging strategies due to their strong dependence on local information. To tackle these two issues, an adaptive dynamic region merging approach (ADRM) is introduced, which combines an adaptive spectral-spatial descriptor and a dynamic merging strategy to adapt to the changes of merging regions for successfully detecting objects scattered globally in a post-earthquake image. In the new descriptor, the spectral similarity and spatial similarity of any two adjacent regions are automatically combined to measure their similarity. Accordingly, the new descriptor offers adaptive semantic descriptions for geo-objects and thus is capable of characterizing different damage objects. Besides, in the dynamic region merging strategy, the adaptive spectral-spatial descriptor is embedded in the defined testing order and combined with graph models to construct a dynamic merging strategy. The new strategy can find the global optimal merging order and ensures that the most similar regions are merged at first. With combination of the two strategies, ADRM can identify spatially scattered objects and alleviates the phenomenon of over-segmentation and under-segmentation. The performance of ADRM has been evaluated by comparing with four state-of-the-art segmentation methods, including the fractal net evolution approach (FNEA, as implemented in the eCognition software, Trimble Inc., Westminster, CO, USA), the J-value segmentation (JSEG) method, the graph-based segmentation (GSEG) method, and the statistical region merging (SRM) approach. The experiments were conducted on six VHR subarea images captured by RGB sensors mounted on aerial platforms, which were acquired after the 2008 Wenchuan Ms 8.0 earthquake. Quantitative and qualitative assessments demonstrated that the proposed method offers high feasibility and improved accuracy in the segmentation of post-earthquake VHR aerial images. Full article