Article
Computer Science, Theory & Methods
Wei Yao, Yueli Yue
Summary: The paper demonstrates that the collections of open filters of T-0 L-topological spaces form a monad, and concludes that the Eilenberg-Moore algebras of the open filter monad are precisely L-continuous lattices. Additionally, it shows that the category of L-continuous lattices is strictly monadic over the category of T-0 L-topological spaces.
FUZZY SETS AND SYSTEMS
(2021)
Article
Materials Science, Multidisciplinary
Sean Carey, Ciaran McHale, Vincenzo Oliveri, Paul M. Weaver
Summary: By replacing traditional mechanical fasteners with magnets in the helical lattice structure, enhanced morphing capabilities and new functionality were achieved, allowing a linear actuator to be converted into a curved one.
MATERIALS & DESIGN
(2021)
Article
Computer Science, Artificial Intelligence
Saeed Rasouli, Amin Dehghani
Summary: This paper applies a combination of algebraic and topological methods to study Gelfand residuated lattices. It shows the strong connection between Gelfand residuated lattices and the hull-kernel topology. The paper introduces the class of soft residuated lattices and characterizes them in terms of being Gelfand and semisimple.
Article
Engineering, Mechanical
Seyed Ardalan Nejat, Navid Changizi, Mazdak Tootkaboni, Alireza Asadpoure
Summary: This study advances the design of light, stiff lattice materials by considering stability factors and employing Timoshenko beam theory for accurate evaluation. By using analytical sensitivities and specific design variables, the study minimizes relative density while meeting stiffness and stability constraints.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Multidisciplinary Sciences
Ahmad F. Al Musawi, Satyaki Roy, Preetam Ghosh
Summary: This study investigates the indicators that make complex networks vulnerable to attacks and finds that high modularity and disassortativity are the main indicators of vulnerability. The individual contribution of the indicators on network protection is quantified using partial least squares discriminant analysis. The findings are important for defending against strategic attacks on critical infrastructures.
SCIENTIFIC REPORTS
(2023)
Article
Engineering, Multidisciplinary
Weisheng Si, Balume Mburano, Wei Xing Zheng, Tie Qiu
Summary: Infrastructure networks are crucial for our daily lives, but they are vulnerable to cyber-attacks. This paper proposes a robustness metric called Average Network Flow (ANF) and demonstrates its effectiveness through comparisons with other metrics.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2022)
Article
Computer Science, Theory & Methods
Tatsuji Kawai
Summary: The notion of strong proximity join-semilattice is introduced as a predicative notion of continuous lattice, characterized by coalgebras of the powerlocale on proximity posets. Locally compact locales can also be characterized in terms of strong proximity join-semilattices. A logical characterization of a strong proximity join-semilattice, known as a strong continuous finitary cover, using an entailment relation is also provided, making the notion of continuous lattice in point-free topology more explicit.
LOGICAL METHODS IN COMPUTER SCIENCE
(2021)
Article
Computer Science, Interdisciplinary Applications
Hesaneh Kazemi, Julian A. Norato
Summary: This work presents a topology optimization method for designing programmable lattice materials, which can activate/deactivate struts through an actuation mechanism. The method simultaneously determines the spatial layout of the struts and corresponding programs for their open/close states to achieve desired effective properties. The geometry projection method is used to analyze the cylindrical struts, while material symmetries are imposed through reflections with respect to symmetry planes. The open/close state of the struts is modeled using state variables, and a no-cut constraint is imposed for manufacturability.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Mathematics
Jozef Pocs, Jana Pocsova
Summary: The paper investigates intercontextual relationships using the concept of bonds to explore the connections between different formal contexts. A composition of bonds is defined, and it is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. Furthermore, the category of formal contexts with bonds is proven to be equivalent to the category of complete lattices with supremum preserving mappings as morphisms.
Article
Materials Science, Multidisciplinary
Xikun Li, Mani Chandra Jha, Anne E. B. Nielsen
Summary: This article investigates the density, correlation, and entanglement properties of Laughlin states on fractal lattices compared to two-dimensional systems. It is found that the connected particle-particle correlation function follows an exponential decay. However, unlike two-dimensional systems, the entanglement entropy does not follow the area law on fractal lattices. Additionally, the topological entanglement entropy cannot be extracted using the Kitaev-Preskill or the Levin-Wen methods. The entanglement spectrum for different partitions is also studied, and the number of states below the entanglement gap is found to be robust and the same as for Laughlin states on two-dimensional lattices.
Article
Computer Science, Interdisciplinary Applications
Hesaneh Kazemi, Julian A. Norato
Summary: This study proposes a method for optimizing the topology structure using anisotropic materials for lattice struts, achieving better effective properties. The focus is on optimizing the shape and material of the lattice struts.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Theory & Methods
Longchun Wang, Xiangnan Zhou, Qingguo Li
Summary: This article discusses the representation theory of continuous semi-lattices and bounded complete domains using information systems. The first problem of representing continuous semi-lattices is solved by introducing SL-information systems, which are a special case of continuous information systems. The second problem of representing bounded complete domains is correctly solved by strengthening the conditions of SL-information systems.
THEORETICAL COMPUTER SCIENCE
(2022)
Article
Mathematics, Applied
Yang Deng, Marcel de Jeu
Summary: The study investigates the construction of a Hausdorff uo-Lebesgue topology from a Hausdorff (o)-Lebesgue topology on an order dense ideal, and examines the properties of the obtained topologies. When a vector lattice has an order dense ideal with a separating order continuous dual, it can always be equipped with such a topology, and the restriction of this topology to a regular sublattice is also a Hausdorff uo-Lebesgue topology. If a vector lattice not only has an order dense ideal with a separating order continuous dual, but also has the countable sup property, every net in a regular vector sublattice that converges in its Hausdorff uo-Lebesgue topology contains a sequence that is uo-convergent to the same limit.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Gianni Bosi, Laura Franzoi, Gabriele Sbaiz
Summary: We investigate the properties of strongly useful topologies, proving that a topology is strongly useful if the topology generated by every family of separable systems is countable. Focusing on normal Hausdorff topologies, we show that strongly useful topologies are hereditarily separable on closed sets and identify a simple condition for the Lindelof property to hold.
Article
Computer Science, Artificial Intelligence
Lingjuan Yao, Shengwen Wang, Qingguo Li, Mingjie Cai
Summary: This paper introduces the concepts of augmented formal contexts and generalized approximable concepts, and proves that in an augmented formal context, the generalized approximable concepts generate a continuous lattice, and vice versa. Furthermore, the notion of C-mappings is proposed to describe the relationships between augmented formal contexts, and it is shown that this category is equivalent to the category of continuous lattices with morphisms being Scott continuous functions.
Article
Mathematics
Behrouz Emamizadeh, Amin Farjudian, Mohsen Zivari-Rezapour
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
(2016)
Article
Operations Research & Management Science
Behrouz Emamizadeh, Amin Farjudian, Hayk Mikayelyan
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2017)
Article
Mathematics, Applied
Behrouz Emamizadeh, Amin Farjudian, Yichen Liu
APPLIED MATHEMATICS AND COMPUTATION
(2018)
Article
Computer Science, Theory & Methods
Eugenio Moggi, Amin Farjudian, Adam Duracz, Walid Taha
THEORETICAL COMPUTER SCIENCE
(2018)
Article
Mathematics, Applied
Tilak Bhattacharya, Behrouz Emamizadeh, Amin Farjudian
ACTA APPLICANDAE MATHEMATICAE
(2020)
Article
Computer Science, Information Systems
Filippo Savi, Amin Farjudian, Giampaolo Buticchi, Davide Barater, Giovanni Franceschini
Summary: This paper proposes a method to assess the numerical stability of control algorithms using interval analysis, with a case study on electric drive systems. The results show that resonant control is more robust in terms of numerical stability compared to vector space decomposition, making it the preferred choice for mission-critical electric drive control.
Article
Education, Scientific Disciplines
Amin Farjudian
Summary: This article presents a project using threshold concepts as the framework for curriculum design, which includes transformative concepts from mathematics and computer science, providing important knowledge for modern machine learning. Student projects effectively facilitate interdisciplinary research between mathematics and computer science. This project allows students from computer science and mathematics to gain a deeper understanding of each other beyond the school curriculum.
IEEE TRANSACTIONS ON EDUCATION
(2023)
Article
Computer Science, Theory & Methods
Can Zhou, Razin A. Shaikh, Yiran Li, Amin Farjudian
Summary: A domain-theoretic framework is proposed for validated robustness analysis of neural networks. Global and local robustness of networks are analyzed using this framework. A validated algorithm for estimation of Lipschitz constant is developed within this framework. The algorithm is implemented using arbitrary-precision interval arithmetic and handles floating-point errors.
MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
(2023)
Article
Computer Science, Artificial Intelligence
Heshan Du, Natasha Alechina, Amin Farjudian, Brian Logan, Can Zhou, Anthony G. Cohn
Summary: We propose a logic system called LEW for describing direction relations in 1D Euclidean space, including east (E), west (W), and indeterminate east/west (Iew). It has a parameter T that represents the level of indeterminacy in directions. For each T, we provide a complete axiomatisation of LEW and prove its NP-completeness. The finite axiomatisability of LEW depends on T: finite axiomatisation exists for T = 2 or T = 3, but not for T > 3. LEW can be extended to higher-dimensional Euclidean spaces, which is useful for reasoning about imperfectly aligned representations of spatial objects in different datasets, such as crowd-sourced digital maps.
JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
(2023)
Proceedings Paper
Computer Science, Information Systems
Zeyu Xiong, Pei-Chun Lin, Amin Farjudian
Summary: This study proposes a method for generating music from an image through three stages of translation. The model retains the semantics of the input image and the results show that users with composition experience are able to match the generated music with the input image more accurately.
2022 IEEE INTERNATIONAL SYMPOSIUM ON MULTIMEDIA (ISM)
(2022)
Proceedings Paper
Computer Science, Theory & Methods
Abbas Edalat, Amin Farjudian, Mina Mohammadian, Dirk Pattinson
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
(2020)
Article
Computer Science, Cybernetics
Eugenio Moggi, Walid Taha, Johan Thunberg