Recent papers on scalability computational problems dimensional numbers

Sorted by publication year (newest first) via OpenAlex. List regenerates every 24h.

1. Problem Reductions at Scale: Agentic Integration of Computationally Hard Problems

   2026 · ArXiv.org · Pan, Xi-Wei, An, Shi-Wen, Liu, Jin-Guo

   2026

2. High-speed arithmetic units are foundational to modern computing architectures. However, the performance of these units is fundamentally constrained by the carry propagation delay. In conventional architectures, generating an output bit or digit relies on the temporal propagation of a carry signal from less significant positions. For an operand of length N, traditional Ripple Carry Adders (RCA) exhibit a linear time complexity of O(N), while advanced parallel- prefix structures, such as Carry-Lookahead Adders (CLA) or Wallace trees, reduce this delay to a logarithmic bound of O(log N). [12]. This paper challenges the necessity of this tempo- ral dependency in specific arithmetic domains. We in- troduce a novel Radix-10 scalar multiplication architec- ture—multiplying an N-digit operand by a single-digit multiplier (M ∈ {0, 1, . . . , 9})—that operates in strictly constant time, O(1). Rather than treating the carry as a dynamic signal that must ripple through the circuit, our methodology frames multiplication as a localized state-space mapping problem. We demonstrate that for any single-digit multiplier M, the maximum influence of a carry generated at any position i does not propagate beyond position i+2. By establishing this strict mathematical boundary (∆ = 2), the computational dependency of any output digit yi is **spatially truncated** [6]. Consequently, the output digit yi is computed as a direct, parallel combinational function of only three vari- ables: the current input digit (di) and its two immediate less-significant adjacent digits (di−1 and di−2). To handle the boundaries of the operand without breaking the O(1) property, we introduce the concept of **Structural Imaginary Zeros**—fixed zero digits appended at both ends of the digit sequence—which act as static boundary conditions. This localized dependency allows the entire multiplication process to be mapped into parallel Look-Up Tables (LUTs), resolving the N-digit output in a single standard gate delay cycle (tgate), independent of N. The primary contributions of this paper are: • A formal mathematical proof (Section 5) bounding the carry propagation in scalar Radix-10 multiplication to a strict dependency window of ∆ = 2. • The design of a parallel, O(1) hardware architecture using localized combinational mapping (LUTs) to replace sequential carry logic. • Hardware complexity analysis demonstrating O(1) time delay with strictly linear O(N) area scaling.

   2026 · Zenodo (CERN European Organization for Nuclear Research) · Al-Naami, Abdul Raouf

   2026

3. Universal Informational Invariant 0.045 and the "CREATION" (ТВОРЕНИЕ) Framework for Cosmological Constant Resolution Abstract: This paper presents the theoretical foundations of "CREATION" (ТВОРЕНИЕ) technology, based on the discovery of a universal informational invariant,I=0.045cap I equals 0.045 𝐼=0.045. Key Findings: Resolution of the Cosmological Constant Problem: The model eliminates the 120-orders-of-magnitude discrepancy between theoretical vacuum energy and observational data by interpreting baryonic matter ( mc2m c squared 𝑚𝑐2) as a result of resonant compression within the global information field. The 0.045 Invariant: It is mathematically demonstrated that the density of visible matter is a fundamental system efficiency constant (the "Efficiency of the Universe"). Using this parameter, the masses of fundamental particles (Higgs boson, Electron) are calculated as harmonics of the Planck scale. Geometric Adaptation: The framework introduces the concept of informational resonance, where gravity is redefined as the computational load required by the system to maintain the material interface. Technological Potential: The model predicts the possibility of direct space-time navigation through resonant interaction with the "Dark Sector" (95.5% of the total energy density). Research Status: Independent Research / Proprietary Framework. Origin: Ukraine. Author: Serhii Chekaliuk

   2026 · Zenodo (CERN European Organization for Nuclear Research) · Sergiy, Chekalyuk

   2026

4. Higher-order multi-scale computational method and its convergence analysis for hygro-thermo-mechanical coupling problems of quasi-periodic composite structures

   2025 · ArXiv.org · Dong, Hao, Yifei, Ding,, Linghu, Jiale et al.

   2025

5. Guest editorial: Computational modelling of multi-scale, multi-uncertainty and multi-physics problems 2024

   2025 · Engineering Computations · Pires, F.M. Andrade, Li, Chenfeng

   2025

6. Second-order asymptotic analysis and computations for the Dirichlet eigenvalue problem in perforated domains with three-scale cavities

   2025 · Applied Mathematical Modelling · Ye, Shuyu, Ma, Qiang, Cui, Junzhi

   2025

7. Computational runtime of the algorithms across individual problem instances grouped by scale: (a) Small, (b) Medium, (c) Large, (d) Super-Large.

   2025 · Figshare · (22379086), Panfei Li, (22379089), Chongxing Ji

   2025

8. Problems of Practice in Scaling Computational Thinking and Digital Literacies in Pre-service Teacher Education Efforts

   2024 · Proceedings. · Phelps, David, Santo, Rafi, Vogel, Sara et al.

   2024

9. Efficient Computational Algorithm for Solving Two-Scale Problems of Large Deforming Heterogeneous Periodic Structures

   2024 · Engineering Mechanics ... · Lukeš, Vladimír, Rohan, Eduard

   2024

10. Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection Methods

    2024 · SIAM Review · Chung, Julianne, Gazzola, Silvia

    2024

11. Scalable decision fusion algorithm for enabling decentralized computation in distributed, big data clustering problems

    2024 · International Journal of Machine Learning and Cybernetics · Jennath, H. S., Asharaf, S.

    2024

12. Higher-order multi-scale computational approach and its convergence for nonlocal gradient elasticity problems of composite materials

    2024 · Computers & Mathematics with Applications · Dong, Hao, Shi, Jie, Linghu, Jiale

    2024

13. Multigrid methods for large-scale problems: approximate coarsest-level solves and mixed precision computation

    2024 · Digital Repository (National Repository of Grey Literature) · Vacek, Petr

    2024

14. Multi-{Physics, Phase, Scale} Computational Modeling of Interface-Coupled Problems in Redox Flow Battery Design

    2023 · ECS Meeting Abstracts · Barzegari, Mojtaba, Heijden, Maxime van der, Haas, V. et al.

    2023

15. Bridging Computational Theories And AI: A United Framework for Scalable and Ethical Problem-Solving

    2023 · Nanotechnology Perceptions

    2023

16. Balancing the Average Weighted Completion Times in Large-Scale Two-Agent Scheduling Problems: An Evolutionary-Type Computational Study

    2023 · Mathematics · Avolio, Matteo

    2023

17. Data-driven method of solving computationally expensive combined economic/emission dispatch problems in large-scale power systems: an improved kriging-assisted optimization approach

    2023 · Frontiers in Energy Research · Lin, Chenhao, Liang, Huijun, Pang, Aokang et al.

    2023

18. Scalable Computation of Dynamic Flow Problems via Multimarginal Graph-Structured Optimal Transport

    2023 · Mathematics of Operations Research · Haasler, Isabel, Ringh, Axel, Chen, Yongxin et al.

    2023

19. Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers

    2023 · Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas · Saini, Sumit, Das, Pratibhamoy, Kumar, Sunil

    2023

20. The development of computational methods for solving large - scale optimization problems, such as those arising in logistic and supply chain management

    2023 · Namya Press eBooks · Sarkar, Bikramjit

    2023

21. Multi-scale computational method for nonlinear dynamic thermo-mechanical problems of composite materials with temperature-dependent properties

    2022 · Communications in Nonlinear Science and Numerical Simulation · Dong, Hao, Cui, Junzhi, Nie, Yufeng et al.

    2022

22. Computational scaling of SPH simulations for violent sloshing problems in aircraft fuel tanks

    2022 · Acta Mechanica Sinica · Calderón-Sánchez, Javier, Martinez-Carrascal, Jon, Miguel, González Leo

    2022

23. Parallel Multigrid in Time and Space for Extreme-Scale Computational Science: Chaotic and Hyperbolic Problems

    2022 · Schroder, Jacob B.

    2022

24. Quantum computation capability verification protocol for noisy intermediate-scale quantum devices with the dihedral coset problem

    2022 · Physical review. A/Physical review, A · Lin, Ruge, Wen, Weiqiang

    2022

25. The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

    2022 · Mathematics and Mechanics of Solids · Dong, Hao, Nie, Yufeng, Ma, Ruyun et al.

    2022