Local Dimension Research Articles

Tensor network decompositions for absolutely maximally entangled states

Absolutely maximally entangled (AME) states of k qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites/parties. We consider the problem of whether such states can be decomposed into a tensor network with a small number of tensors, such that all physical and all auxiliary spaces have the same dimension D. We find that certain AME states with k=6 can be decomposed into a network with only three 4-leg tensors; we provide concrete solutions for local dimension D=5 and higher. Our result implies that certain AME states with six parties can be created with only three two-site unitaries from a product state of three Bell pairs, or equivalently, with six two-site unitaries acting on a product state on six qudits. We also consider the problem for k=8, where we find similar tensor network decompositions with six 4-leg tensors.

Real-time violence detection and localization through subgroup analysis

Real-time violence detection and localization through subgroup analysis

Trust in healthcare: methodological and conceptual insights from mixed-method research in Lao People’s Democratic Republic

BackgroundGlobal health foregrounds trust as a key requirement for the achievement of international health initiatives, but it remains an elusive concept that is often mobilised without consideration of its dimensions,...

Redefining sustainable urban development: A critical analysis in the wake of COVID‐19

AbstractThis paper critically examines the concept of sustainable development, particularly in the context of urban challenges exacerbated by the COVID‐19 pandemic. Although the concept of sustainable development has been around for more than three decades, it faces ongoing global socio‐environmental crises that have been exacerbated by the rapid spread of COVID‐19 since 2019, which has highlighted the vulnerability of urban and interconnected cities. Our approach includes a comparative literature review to analyze the evolution and critique of sustainable development, focusing on its conceptual foundations, complementary strategies, and political‐economic implications. The paper addresses the urban implications of COVID‐19, emphasizing its direct impact on the Sustainable Development Goals and arguing for a comprehensive reassessment of sustainable urban development practices. We propose a transformative agenda that recognizes local specificities and draws on cities' experiences during the pandemic to build a more equitable and crisis‐resilient global society. This research highlights the urgency to rethink current sustainable development paradigms, especially in light of the human‐environment imbalance and lessons learned from the COVID‐19 crisis. It calls for a reformed global approach that incorporates local dimensions and draws on the experience of cities to address the inequalities and crisis‐prone structures in our societies, with the aim of a fundamental shift toward a more sustainable future in the post‐COVID‐19 era.

Characteristics of urban network and city functions in the Yangtze River Delta Region: A multi-scale perspective

The development of cities and regions emerges from the complex associations at various spatial levels, highlighting the importance of a multi-scale approach to analyzing regional urban networks. This study attempts to establish a new analysis framework encompassing national, regional, and local dimensions by employing a population flow network in the Yangtze River Delta in China. It explores the inter-city connections and spatial structures of regional urban networks as well as the correlations and differentiations of urban functions under multi-scale interaction. The results indicate that: (1) Regional network demonstrates notable multi-scale interactions with an explicit hierarchical structure; (2) The roles and positions of different cities vary significantly across scales due to economic, administrative, locational, and transportation differences; (3) Different city types can drive their evolution by navigating through rescaling in a diverse multi-scale environment; (4) A positive correlation is observed when comparing the functional behaviors of cities across various scales. This study provides insights for cities to identify their strategic roles and adapt development strategies within the wider network framework, offering theoretical and practical contributions to multi-scale urban networks analysis.

Desirable and realistic futures of the university: a mixed-methods study with teachers in Denmark

In this paper, we put in dialogue the local dimension of a nation-state with the global challenges faced by universities worldwide. We focus on the case of Denmark, a nation that was exceptionally active in implementing international university reforms and where digitalisation is a high priority of the public sector governance. The article seeks to contribute to speculative research and critical studies by presenting a mixed-methods study that explores higher education teachers’ views about desirable and realistic future scenarios in Denmark. The study draws on data from a survey applied at a large Danish university, analysed both quantitatively (N = 755) and qualitatively (N = 53). The findings show that teachers share clusters of concern about uncontrolled digitalisation and teaching automation, commodification of education, and modularisation of university courses, the latter being a contested but realistic perspective in the latest political reforms. They reaffirm the mission of the university as preparing students for solving real problems and contributing to the challenges of the present time. The paper concludes with a call for university management to recalibrate future imaginaries to the values expressed by the teachers, and the university they wish to create.

Local Multiset Dimension of Amalgamation Graphs.

Background: One of the topics of distance in graphs is the resolving set problem. Suppose the set W = { s 1, s 2, …, s k} ⊂ V ( G), the vertex representations of ∈ V ( G) is r m( x| W) = { d( x, s 1), d( x, s 2), …, d( x, s k)}, where d( x, s i) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if r m( v| W)≠ r m( u| W) for uv ∈ E( G). The local m-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of G, denoted by md l( G). Thus, if G has an infinite local multiset dimension and then we write . Methods: This research is pure research with exploration design. There are several stages in this research, namely we choose the special graph which is operated by amalgamation and the set of vertices and edges of amalgamation of graphs; determine the set W ⊂ V ( G); determine the vertex representation of two adjacent vertices in G; and prove the theorem. Results: The results of this research are an upper bound of local multiset dimension of the amalgamation of graphs namely md l( Amal( G, v, m)) ≤ m. md l( G) and their exact value of local multiset dimension of some families of graphs namely md l( Amal( P n, v, m)) = 1, , md l( Amal( W n, v, m)) = m. md l( W n), md l( Amal( F n, v, m)) = m. md l( F n) for d( v) = n, . Conclusions: We have found the upper bound of a local multiset dimension. There are some graphs which attain the upper bound of local multiset dimension namely wheel graphs.

Buddhist Higher Learning Horizon and Its Relation to Global Trends : The Trajectory of Global Buddhist Pedagogy

This study aims to dissect the challenges, identify the unique characteristics, and propose viable strategies for the seamless integration of local and global dimensions in higher Buddhist education. This study used the systematic literature review method with a qualitative approach. The research hinged on an extensive review of scholarly articles, primary texts, and reports on Buddhist education in Indonesia and internationally and then analyzed using thematic analysis. Results highlight that Indonesian Buddhist education possesses unique characteristics and mirrors global patterns, albeit with localized interpretations. The study underscored the importance of recognizing and integrating the Buddhayana spirit amidst global Buddhist sectarian diversities. The contribution of this review was twofold: first, it enriches the understanding of the specificities of Indonesian Buddhist higher education and its relation to global trends; second, it advocates for a harmonious blend of local and global in shaping the trajectory of global Buddhist pedagogy.

New approach of local critical dimension uniformity improvement for via/contact hole etch with direct current superposition

New approach of local critical dimension uniformity improvement for via/contact hole etch with direct current superposition

Abstaining from Retaliation: A Story of Restoration Ministry-OEIL in Eastern Congo

Reports of violence flow from everywhere. They make humankind look powerless in front of conflicts and seem inclined to a retaliation culture. Many people prefer to justify retaliation by euphemistic concepts like self-defense, counterattack, letting justice prevail, counteroffensive, etc. This is a mere application of the natural human principle of the lex talionis. In tumultuous zones like the African Great Lakes Region in general and Eastern Congo in particular, one might expect escalation of conflicts if retaliation is the only option. However, the advent of Christianity in our societies has strengthened a new culture of reconciliation among opponent groups as a way out of violent conflicts. In a world immersed in retaliation culture, a message about raising a culture of reconciliation by abstaining from retaliation sounds like naïveté or treason. This paper sets out to respond to this question: How does reconciliation become an antidote to retaliation in the Eastern Congo context? Using Case Study method, the objective of this study is to present biblical, ethical, and practical ways of breaking the circle of violence and building a culture of peace. In Eastern Congo, Restoration Ministry-OEIL is one of the Christian organizations that strive to promote reconciliation among ethnic communities. It raises awareness of the root causes of Eastern Congo crisis from their local, national, regional, and international dimensions. Therefore, its story constitutes historical evidence of the possibility of abstaining from retaliation despite the horrors of violence endured. Its peacemaking method is a good example of a contextual theology of reconciliation from indigenous practices.

Machine Learning Applied to Electron Beam Lithography to Accelerate Process Optimization of a Contact Hole Layer.

Determining the lithographic process conditions with high-resolution patterning plays a crucial role in accelerating chip manufacturing. However, lithography imaging is an extremely complex nonlinear system, and obtaining suitable process conditions requires extensive experimental attempts. This severely creates a bottleneck in optimizing and controlling the lithographic process conditions. Herein, we report a process optimization solution for a contact layer of metal oxide nanoparticle photoresists by combining electron beam lithography (EBL) experiments with machine learning. In this solution, a long short-term memory (LSTM) network and a support vector machine (SVM) model are used to establish the contact hole imaging and process condition classification models, respectively. By combining SVM with the LSTM network, the process conditions that simultaneously satisfy the requirements of the contact hole width and local critical dimension uniformity tolerance can be screened. The verification results demonstrate that the horizontal and vertical contact widths predicted by the LSTM network are highly consistent with the EBL experimental results, and the classification model shows good accuracy, providing a reference for process optimization of a contact layer.

CTM: Cross-time temporal module for fine-grained action recognition

Dynamic contextual attribute information in the time dimension is the key to fine-grained action recognition. Temporal contextual relationships cannot be captured by conventional 2D CNNs; good local time can be obtained by the 3D CNNs, but the 3D CNNs are computationally intensive and lack capability for global time. A parallel cross-time temporal module-CTM is proposed in this article, which aims to efficiently capture dynamic contextual information of both local and global temporal dimensions. With our study, we think that the 2D CNNs can better mine temporal features to enrich the contextual relationships of temporal dimensions. The CTM can be embedded into any existing 2D CNNs baseline in a plug-and-play manner, yielding a feature framework that can capture complex spatio-temporal modeling (CTNet) with a tiny additional computational cost. In the extensive validation experiments on three datasets(i.e., SomethingV1&V2, Jester, Diving48), both action recognition accuracy and runtime inference speed are obviously better than existing temporal contextual baseline optimization schemes with similar computational cost complexity, when the CTM embedded into any 2D CNNs framework to enhance the baseline.

The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems

Qudits with local dimension d>2 can have unique structure and uses that qubits (d=2) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group for any, including composite, d in several ways. To cover composite values of d, we work with modules over commutative rings, which generalize the notion of vector spaces over fields. For any specified set of commutation relations, we construct a set of qudit Paulis satisfying those relations. We also study the maximum size of sets of Paulis that mutually non-commute and sets that non-commute in pairs. Finally, we give methods to find near minimal generating sets of Pauli subgroups, calculate the sizes of Pauli subgroups, and find bases of logical operators for qudit stabilizer codes. Useful tools in this study are normal forms from linear algebra over commutative rings, including the Smith normal form, alternating Smith normal form, and Howell normal form of matrices. Possible applications of this work include the construction and analysis of qudit stabilizer codes, entanglement assisted codes, parafermion codes, and fermionic Hamiltonian simulation.

Moving Forward to a World Free of Nuclear Weapons (?): How Regional Issues Shape Global Non-proliferation and Disarmament Politics

This special issue contributes to the global dialogue on a nuclear weapons ban by evaluating how regional politics enable or hinder a global ban on nuclear weapons. The insights of 17 contributions offer a nuanced and diverse account of the landscape of nuclear disarmament, arguing that understanding the diversity of regional perspectives, lenses, and approaches is crucial for advancing toward a global nuclear weapons ban. This introduction sets the stage for a detailed exploration of common themes, aiming to shed light on the structural elements that characterize regional and global nuclear politics. For that, we employ a Comparative Area Studies Approach to explore venues and patterns across different regions, offering a comprehensive analysis that underscores the importance of considering local, regional, and global dimensions in tandem. We delineate three key elements that either facilitate or impede the implementation of a nuclear weapons ban: (1) Inclusivity: How key actors participate and are included in the policy-making process at the global, regional, and local levels; (2) Inequalities: how power inequalities shape social processes that enable or hinder the continuity of nuclear weapons; (3) Institutions: how networks and institutions are organized and structured between each other.

Literary Translation in the Weekly Periodical Paris-Noticias (1921–1922): Exploring the Intersection of Translation and Periodical Studies

This study opens new avenues for research at the intersection of translation and periodical studies and establishes connections between the two fields. It examines the translations that appeared in the weekly periodical Paris-Noticias (1921–1922) and sheds light on a network of French and Portuguese writers, editors and translators. In contrast to previous assumptions that confined their production to a local dimension, this study shows that male and female writers from Portugal were able to disseminate their work across geographical and cultural borders. To do so, they had to establish collaborations with influential figures such as Paulo Osório who was the editor of Paris-Noticias and a writer in his own right. Osório began building his literary network during the first decades of the twentieth century when he started to collaborate with the translators Philéas Lebesgue and Manoel Gahisto. By examining their contribution to the periodical Paris-Noticias, this study aims to recover translations that have previously been neglected and improve our understanding of Portuguese participation in the French literary scene.

NBS-SNI, an extension of the network-based statistic: Abnormal functional connections between important structural actors.

Elucidating the coupling between the structure and the function of the brain and its development across maturation has attracted a lot of interest in the field of network neuroscience in the last 15 years. Mounting evidence supports the hypothesis that the onset of certain brain disorders is linked with the interplay between the structural architecture of the brain and its functional processes, often accompanied with unusual connectivity features. This paper introduces a method called the network-based statistic-simultaneous node investigation (NBS-SNI) that integrates both representations into a single framework, and identifies connectivity abnormalities in case-control studies. With this method, significance is given to the properties of the nodes, as well as to their connections. This approach builds on the well-established network-based statistic (NBS) proposed in 2010. We uncover and identify the regimes in which NBS-SNI offers a gain in statistical resolution to identify a contrast of interest using synthetic data. We also apply our method on two real case-control studies, one consisting of individuals diagnosed with autism and the other consisting of individuals diagnosed with early psychosis. Using NBS-SNI and node properties such as the closeness centrality and local information dimension, we found hypo- and hyperconnected subnetworks and show that our method can offer a 9 percentage points gain in prediction power over the standard NBS.

Neutralized Local Entropy and Dimension bounds for Invariant Measures

Abstract We introduce a notion of a point-wise entropy of measures (i.e., local entropy) called neutralized local entropy, and compare it with the Brin-Katok local entropy. We show that the neutralized local entropy coincides with Brin-Katok local entropy almost everywhere. Neutralized local entropy is computed by measuring open sets with a relatively simple geometric description. Our proof uses a measure density lemma for Bowen balls, and a version of a Besicovitch covering lemma for Bowen balls. As an application, we prove a lower point-wise dimension bound for invariant measures, complementing the previously established bounds for upper point-wise dimension.

Change Detection in Point Clouds Using 3D Fractal Dimension

The management of large point clouds obtained by LiDAR sensors is an important topic in recent years due to the widespread use of this technology in a wide variety of applications and the increasing volume of data captured. One of the main applications of LIDAR systems is the study of the temporal evolution of the real environment. In open environments, it is important to know the evolution of erosive processes or landscape transformation. In the context of civil engineering and urban environments, it is useful for monitoring urban dynamics and growth, and changes during the construction of buildings or infrastructure facilities. The main problem with change detection (CD) methods is erroneous detection due to precision errors or the use of different capture devices at different times. This work presents a method to compare large point clouds, based on the study of the local fractal dimension of point clouds at multiple scales. Our method is robust in the presence of environmental and sensor factors that produce abnormal results with other methods. Furthermore, it is more stable than others in cases where there is no significant displacement of points but there is a local alteration of the structure of the point cloud. Furthermore, the precision can be adapted to the complexity and density of the point cloud. Finally, our solution is faster than other CD methods such as distance-based methods and can run at O(1) under some conditions, which is important when working with large datasets. All these improvements make the proposed method more suitable than the others to solve complex problems with LiDAR data, such as storage, time series data management, visualization, etc.

Brain magnetic resonance images segmentation via improved mixtures of factor analyzers based on dynamic co-clustering

The main goal of this paper is to attain accurate and automatic detection of brain tumors in gray magnetic resonance images using reducing the local dimensions. We propose a novel model called Improved Mixtures of Factor Analyzers based on Dynamic Co-Clustering (IMFADCC) for the detection and localization of brain tumors. After image preprocessing and enhancement, the optimal numbers of row clusters and column clusters corresponding to each row cluster, alongside other model parameters, are determined concurrently based on the size of the tumor by our model. Then, using the optimal values obtained, the image is co-clustered by simultaneously clustering rows and columns until the block containing the tumor is identified. The output image is divided into a certain number of blocks, one of which contains the tumor. For post-processing, the identified block is binarized using minimum error thresholding. The proposed model accurately detects and locates the block binarized within the original image while considering the remainder of the image as background. The effectiveness of the proposed method was assessed by evaluating its accuracy, Dice, intersection on union, geometric mean, receiver operating characteristic curve, specificity, and sensitivity criteria on the BraTS2018, BraTS2019, and BraTS2020 datasets. The results show that our method has significant performance and is highly accurate in detecting tumors of different sizes in complex and high-size images. Moreover, our method outperforms the existing diagnostic methods.

On the metric dimension of extended zero divisor graphs

Let R be a commutative ring with unity, the extended zero divisor graph E(R) is defined by considering the non-zero zero divisors Z(R)∗ as the vertices and two distinct vertices x and y of R are adjacent whenever there exist two positive integers m and n such that xmym=0 with xm≠0 and yn≠ 0. In this paper, we investigate metric dimension, fault tolerant metric dimension and local metric dimension of the extended zero divisor graph for the ring of integers modulo m and the ring of Gaussian integers modulo m.