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1. A Flip‐book of Knot Diagrams for Visualizing Surfaces in 4‐Space

   https://doi.org/10.1111/cgf.14545  

   Liu, Huan; Zhang, Hui (August 2022, Computer Graphics Forum)

   Abstract Just as 2D shadows of 3D curves lose structure where lines cross, 3D graphics projections of smooth 4D topological surfaces are interrupted where one surface intersects itself. They twist, turn, and fold back on themselves, leaving important but hidden features behind the surface sheets. In this paper, we propose a smart slicing tool that can read the 4D surface in its entropy map and suggest the optimal way to generate cross‐sectional images — or “slices” — of the surface to visualize its underlying 4D structure. Our visualization thinks of a 4D‐embedded surface as a collection of 3D curves stacked in time, very much like a flip‐book animation, where successive terms in the sequence differ at most by a critical change. This novel method can generate topologically meaningful visualization to depict complex and unfamiliar 4D surfaces, with the minimum number of cross‐sectional diagrams. Our approach has been successfully used to create flip‐books of diagrams to visualize a range of known 4D surfaces. In this preliminary study, our results show that the new visualization and slicing tool can help the viewers to understand and describe the complex spatial relationships and overall structures of 4D surfaces. 

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2. 4D Printed Actuation with Spatially-Varying Lattices

   https://doi.org/10.26153/tsw/58032  

   Delgado_Ramos, Katia L; Aranzola, Ana Paola; Akbar, Ijaz; Cervantes, Aaron; Martínez, Ana C; Maurel, Alexis; MacDonald, Eric; Castellanos, Alejandra G; El_Mansori, Mohamed; Roberson, David A (January 2024, Texas ScholarWorks/ University of Texas Libraries)

   Creating 3D printed structures from materials with shape memory properties allows these structures to change form, modifying configuration or function over time in response to external stimuli such as temperature, light, electrical current, etc. This area of additive manufacturing has come to be known as 4D printing. A variety of geometries have been previously explored in the context of 4D printing, including foldable surfaces (e.g. Origami), lattices, and bio-inspired shapes. However, with advances in solid modeling software tools, more sophisticated spatially- varying lattices are now easily generated to further optimize the mechanical performance and functionality of a 4D printed structure. In this work, complex lattices are created to bend at specific locations with intentionally-reduced stiffness and improved compliance based on locally-reduced strut dimensions. By experimentally demonstrating more complex geometries in the study of 4D printing, new applications can be considered that were not previously possible, with tailored performance allowing for balancing between weight and actuation. 

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3. A hybrid adjacency and time-based data structure for analysis of temporal networks

   https://doi.org/10.1007/s41109-022-00489-5  

   Hilsabeck, Tanner; Arastuie, Makan; Xu, Kevin_S (July 2022, Applied Network Science)

   Abstract Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus quickly retrieve all edges between two sets of nodes (anode-based slice) but cannot quickly retrieve all edges that occur within a given time interval (atime-based slice). We propose a hybrid data structure for storing temporal networks that stores edges in both an adjacency dictionary, enabling rapid node-based slices, and an interval tree, enabling rapid time-based slices. Our hybrid structure also enablescompound slices, where one needs to slice both over nodes and time, either by slicing first over nodes or slicing first over time. We further propose an approach for predictive compound slicing, which attempts to predict whether a node-based or time-based compound slice is more efficient. We evaluate our hybrid data structure on many real temporal network data sets and find that they achieve much faster slice times than existing data structures with only a modest increase in creation time and memory usage. 

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4. OnSlicing: online end-to-end network slicing with reinforcement learning

   https://doi.org/10.1145/3485983.3494850  

   Liu, Qiang; Choi, Nakjung; Han, Tao (December 2021, Proceedings of the 17th International Conference on Emerging Networking EXperiments and Technologies)

   Network slicing allows mobile network operators to virtualize infrastructures and provide customized slices for supporting various use cases with heterogeneous requirements. Online deep reinforcement learning (DRL) has shown promising potential in solving network problems and eliminating the simulation-to-reality discrepancy. Optimizing cross-domain resources with online DRL is, however, challenging, as the random exploration of DRL violates the service level agreement (SLA) of slices and resource constraints of infrastructures. In this paper, we propose OnSlicing, an online end-to-end network slicing system, to achieve minimal resource usage while satisfying slices' SLA. OnSlicing allows individualized learning for each slice and maintains its SLA by using a novel constraint-aware policy update method and proactive baseline switching mechanism. OnSlicing complies with resource constraints of infrastructures by using a unique design of action modification in slices and parameter coordination in infrastructures. OnSlicing further mitigates the poor performance of online learning during the early learning stage by offline imitating a rule-based solution. Besides, we design four new domain managers to enable dynamic resource configuration in radio access, transport, core, and edge networks, respectively, at a timescale of subseconds. We implement OnSlicing on an end-to-end slicing testbed designed based on OpenAirInterface with both 4G LTE and 5G NR, OpenDayLight SDN platform, and OpenAir-CN core network. The experimental results show that OnSlicing achieves 61.3% usage reduction as compared to the rule-based solution and maintains nearly zero violation (0.06%) throughout the online learning phase. As online learning is converged, OnSlicing reduces 12.5% usage without any violations as compared to the state-of-the-art online DRL solution. 

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5. Surface-Toolpath Twins of Shell Components in 3D Concrete Printing for Optimized Buildability and Surface Quality

   ZHI, Y; AKBARZADEH, M (October 2025, Proceedings of the IASS Annual Symposium 2025)

   Gerardo_Oliva, J; Ignacio_del_Cueto, J; Drago, E (Ed.)

   This paper directly links the abstract geometry of structural form-finding to the fabrication-aware design of discrete shells and spatial structures for 3D concrete printing through a bidirectional approach, where it creates surface-toolpath twins for the components, optimizing the buildability of the parts and their surface quality. The design-to-production process of efficient structural systems for 3D printing is often a top-down unidirectional process involving form-finding, segmentation, and slicing, where results face printability challenges due to incompatibility between the initial geometry and the printing system, as well as material constraints. We introduce surface-toolpath twins that can be interconverted and synchronized through efficient slicing and surface reconstruction algorithms to allow the combination of optimizations and modifications on either part of the twin in flexible orders. We provide two core methods for fabrication rationalization: (1) global buildability optimization on the surface mesh by normal-driven shape stylization and (2) local surface quality optimization on toolpath curves through intra-layer iterative adjustments. The result is a bidirectional design-to-production process where one can plug and play different form-finding results, assess and optimize their fabrication schemes, or leverage knowledge in fabrication design, model toolpath curves as sections, reconstruct surfaces, and merge them into form-finding and segmentation in an inverse way. The proposed framework enables the integration of form-finding expertise with fabrication-oriented design, allowing the realization of spatial shell structures with complex topologies or extreme geometrical features through 3D concrete printing. 

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