Undecidability of the Spectral Gap in One Dimension by Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia

“…However, there are many indications that one-dimensional spin systems are simpler than their higher-dimensional counterparts: For example, they cannot have thermal phase transitions or topological order, and there exist highly effective numerical algorithms such as the density matrix renormalization group—and even provably polynomial-time ones—for gapped 1D systems, exploiting the fact that such systems obey an entropy area law. …”
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Numerical investigation of burning reserve fuel in combustion chamber of boiler BKZ-420-140 by Andrey Gil, Aleksandr Zavorin, Dmitry Lebed, Aleksandr Starchenko

“…The main aim of the research is to analyze physical and chemical processes in the furnace volume of boiler BKZ-210-140 operating on reserve fuel and rated load when using the Euler and Euler combined and Lagrangian modeling approaches; to construct the mathematical models of the object of study, taking into account the number of rational settlement areas and application of modern numerical algorithms and approaches; to compare numerical results obtained by using different software packages and different representations of the combustion of liquid fuel in the power boiler furnace; to evaluate temperature fields in the volume of the combustion chamber, the concentration of chemical elements of the combustion products, formation of a wind flow patterns and efficiency of backup fuel burn. …”
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Certifiable Robustness to Adversarial State Uncertainty in Deep Reinforcement Learning by Everett, Michael, Lutjens, Bjorn, How, Jonathan P

“…In light of these dangers, numerous algorithms have been developed as defensive mechanisms from these adversarial inputs, some of which provide formal robustness guarantees or certificates. …”
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Circulant preconditioning in the volume integral equation method for silicon photonics by Groth, Samuel P, Polimeridis, Athanasios G, Tambova, Alexandra, White, Jacob K

“…In this paper, we describe an effective circulant preconditioning strategy based on the multilevel circulant preconditioner of Chan and Olkin [Numer. Algorithms 6, 89 (1994)]. We show that this approach proves ideal in the canonical photonics problem of propagation within a uniform waveguide, in which the flow is unidirectional. …”
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Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework by Birkisson, A

“…Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are considered as maps from one function space to another, common numerical algorithms for ODEs discretise problems early on in the solution process. …”

Central limit model checking by Bortolussi, L, Cardelli, L, Kwiatkowska, M, Laurenti, L

“…We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a time-bounded fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical algorithms for CSL model checking based on uniformisation are limited to finite CTMCs and suffer from exponential growth of the state space with respect to the number of species. …”

Extensions to the K-AMH algorithm for numerical clustering by Seman, Ali, Mohd Sapawi, Azizian

“…The significance of this study lies in that the k-AMH numeric algorithms have been demonstrated as potential solutions for clustering numerical objects.…”
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A review of perovskite solar cell (PSC) : Its revolution and mathematical modelling by Yao, Lee Jin, Rahifa, Ranom, Kyairul Azmi, Baharin, Norhafizah, Md Sarif

“…This paper also summarizes the numerical algorithms and modelling simulations used such as SCAPS, AFORS-HET, COMSOL Multiphysics, MATLAB to evaluate PSC model performance. …”
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Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel by Nurul Asyiqin, Mat Yaman, Nur Asiah, Mohd Makhatar, Mohd Rijal, Ilias, Abdul Rahman, Mohd Kasim, Nurul Farahain, Mohammad

“…The generated numerical algorithms are programmed in MATLAB for velocity, temperature and the local Nusselt number analysis. …”
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Microgrid Management Strategies for Economic Dispatch of Electricity Using Model Predictive Control Techniques: A Review by Juan Moreno-Castro, Victor Samuel Ocaña Guevara, Lesyani Teresa León Viltre, Yandi Gallego Landera, Oscar Cuaresma Zevallos, Miguel Aybar-Mejía

“…However, implementing controllers and algorithms for optimizing ED requires the independent handling of constraints. Numerous algorithms and solutions have been proposed for the ED of MGs. …”
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GS-DeepNet: mastering tokamak plasma equilibria with deep neural networks and the Grad–Shafranov equation by Semin Joung, Y.-C. Ghim, Jaewook Kim, Sehyun Kwak, Daeho Kwon, C. Sung, D. Kim, Hyun-Seok Kim, J. G. Bak, S. W. Yoon

“…Here, we introduce GS-DeepNet, which learns plasma equilibria through solely unsupervised learning, without using traditional numerical algorithms. GS-DeepNet includes two neural networks and teaches itself. …”
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Numerical Approach Based on Solving 3D Navier–Stokes Equations for Simulation of the Marine Propeller Flow Problems by Andrey Kozelkov, Vadim Kurulin, Andrey Kurkin, Andrey Taranov, Kseniya Plygunova, Olga Krutyakova, Aleksey Korotkov

“…The specific features of the numerical algorithms in use are described. The method validation results are given; they were obtained because of the problems of finding the performance curves of model-scale propellers in open water, namely the problems of finding the performance of propellers KP505 and IB without consideration of cavitation and the performance of propellers VP1304 and C5 under cavitation conditions. …”
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Explicit and Implicit Finite -Volume Methods for Depth Averaged Free-Surface Flows by Evangelia D. Farsirotou, Alexander D. Panagiotopoulos, Johannes V. Soulis

“…Computational results and convergence acceleration of two different (explicit and implicit numerical techniques) finite-volume based numerical algorithms, for depth-averaged subcritical and/or supercritical, free-surface, steady flows in channels, are presented. …”
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Predicting Respiratory Rate from Electrocardiogram and Photoplethysmogram Using a Transformer-Based Model by Qi Zhao, Fang Liu, Yide Song, Xiaoya Fan, Yu Wang, Yudong Yao, Qian Mao, Zheng Zhao

“…Due to the challenges of direct measurement, RR is still predominantly measured through the traditional manual counting-breaths method in clinic practice. Numerous algorithms and machine learning models have been developed to predict RR using physiological signals, such as electrocardiogram (ECG) or/and photoplethysmogram (PPG) signals. …”
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The Gradient-Boosting Method for Tackling High Computing Demand in Underwater Acoustic Propagation Modeling by Dominic Lagrois, Tyler R. Bonnell, Ankita Shukla, Clément Chion

“…A mean error of 3.23 ± 3.76(1<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>) dB on received sound pressure levels was predicted when compared to ground truth values that were processed using rigorous, although time-consuming, numerical algorithms. The computing time gain was significant, i.e., it was estimated to be 10-fold higher than the ground truth simulation, whilst maintaining the original temporal resolution.…”
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The credibility challenge for global fluvial flood risk analysis by M A Trigg, C E Birch, J C Neal, P D Bates, A Smith, C C Sampson, D Yamazaki, Y Hirabayashi, F Pappenberger, E Dutra, P J Ward, H C Winsemius, P Salamon, F Dottori, R Rudari, M S Kappes, A L Simpson, G Hadzilacos, T J Fewtrell

“…Global flood hazard models are now a practical reality, thanks to improvements in numerical algorithms, global datasets, computing power, and coupled modelling frameworks. …”
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Partitioning Graph Clustering With User-Specified Density by Rohi Tariq, Kittichai Lavangnananda, Pascal Bouvry, Pornchai Mongkolnam

“…It presents a challenging NP-class problem, and as a result, numerous algorithms have been developed, each tailored to specific objectives and quality metrics for evaluation. …”
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A comparative study for the impact performance of shaped charge JET on UHPC targets by Hao Wu, Feng Hu, Qin Fang

“…Finally, based on the validated numerical algorithms, constitutive models and the corresponding parameters, the influences of target material (UHPC, NSC and 45# steel), standoff distance, target configuration (stacked and spaced) and weight efficiency on the impact performance of jet are further discussed. …”
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Computing molecular excited states on a D-Wave quantum annealer by Alexander Teplukhin, Brian K. Kendrick, Susan M. Mniszewski, Yu Zhang, Ashutosh Kumar, Christian F. A. Negre, Petr M. Anisimov, Sergei Tretiak, Pavel A. Dub

“…Towards this direction, numerous algorithmic advances have been made in the last five years. …”
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N-YOLO: A SAR Ship Detection Using Noise-Classifying and Complete-Target Extraction by Gang Tang, Yichao Zhuge, Christophe Claramunt, Shaoyang Men

“…High-resolution images provided by synthetic aperture radar (SAR) play an increasingly important role in the field of ship detection. Numerous algorithms have been so far proposed and relative competitive results have been achieved in detecting different targets. …”
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