CFD simulations are widely used to quantify the mixing performance of stirred tanks for various applications in chemical engineering and biotechnology. Due to advances in GPU computing, these simulations increasingly employ Large Eddy Simulation (LES), which explicitly resolves the dynamics of large-scale turbulence. Although such simulations are fully deterministic and therefore theoretically reproducible, small numerical variations induced by round-off errors, floating-point arithmetic, and differences in the distribution and ordering of operations in parallel computing lead to separation of trajectories i.e., different flow-field evolutions and consequently to significant run-to-run variability in predicted mixing times, even on the same hardware architecture. This work investigates the impact of repeated simulations, in the form of a case study, on the mixing-time distribution observed in a 30 L stirred tank reactor using two commercial CFD packages operating with representative, production-level solver configurations. The analysis does not aim to assess the general performance of numerical method classes, but rather to quantify run-to-run variability under fixed solver settings and to compare the resulting numerical distributions to experimental variability. The results demonstrate that numerical variability is of comparable magnitude to the experimental spread, highlighting the necessity to treat LES-derived metrics as statistical ensembles rather than deterministic values. It is concluded that the reporting of confidence intervals is essential for methodological rigour in LES-based mixing studies.

Shape heterogeneity and surface sp2 carbon in high-pressure high-temperature nanodiamonds (HPHT NDs) compromise nitrogen-vacancy (NV) sensing and imaging capabilities. Rapid molten-nitrate etching is investigated on a ∼gram preparative scale to round off HPHT NDs while removing sp2 carbon. Subsequent centrifugal fractionation narrows size distribution, yielding more homogenized samples. Etching conditions of 567°C and 6min maximize particle circularity at an acceptable mass yield. The rounding of ND particles is quantified by transmission electron microscopy (TEM), high-resolution TEM with electron energy loss (EELS), and Raman spectroscopy, which confirm atomically stepped surfaces with markedly reduced sp2 content. After separation, the rounded NDs exhibit a number-weighted maximum at ∼35-40nm (mean: 34nm) and substantially reduced dispersity. Aqueous colloids retain negative ζ-potential and are colloidally stable. After irradiation and annealing, the rounded NDs show an increased proportion of luminescent particles (66% vs. 24% for angular controls) and more than twofold greater single-particle photoluminescence under identical excitation conditions. Additionally, the NV- charge state and NV spin longitudinal relaxation (T1) are preserved after the etching. Furthermore, the process is compatible with further scale-up and provides shape-controlled, low-sp2, narrowly size-dispersed NDs with enhanced optical properties, bringing improved reproducibility to bioimaging and quantum sensing.

<bold></bold> A quaternion n × n matrix Q is Hermitian R -conjugate if R Q R = Q ¯ , Q ∗ = Q for some orthogonal symmetric matrix R ≠ ± I . This paper presents finite iterative algorithms for solving two-sided k -conjugate quaternion matrix equations with Hermitian R -conjugate solution. When the equation is consistent, the convergence theorem guarantees a solution within a finite number of iterations, assuming no round-off errors, for any initial arbitrary Hermitian R -conjugate solution. Finally, two numerical instances demonstrate the theoretical results and impact of the proposed algorithms.

Enhancing the inner heterogeneous surface functionality of laser powder bed fused W-Cu minichannels by combining abrasive flow machining and electroless nickel deposition

ABSTRACT This work investigated the geometrical shape of the holes by measuring diameter (D) and roundness error (R e ) along the drilling direction, evaluated surface quality by measuring roughness (R a ), and studied machining defects induced by abrasive waterjet drilling (AWJD). The SEM and X-ray CT confirmed that the machining damage with predrilling was significantly less severe than that of the two constituents without it. Minor delamination occurred in some holes, while abrasives did not contaminate any holes. The empirical quantitative relationship between the drilling variables and delamination was established by introducing a new parameter, named “index of impact force.” The relationship was used to predict delamination, representing a novelty. Several key hole-quality parameters, including D, R e , ΔD (the difference in D at the two ends of the hole), and P erp (perpendicularity), can meet the requirements of aviation holes, illustrating that predrilling, followed by AWJD, can produce high-quality holes in flax FMLs, which also represents a novelty.

At microwave frequencies, the electromagnetic (EM) characterization of materials is not possible through direct measurements. In this case, the Nicholson-Ross-Weir (NRW) algorithm is the standard phenomenological analytical approach for the inverse problem. The algorithm finds the equivalent complex permittivity and permeability, starting from scattering parameters at two terminals of a waveguide structure containing the material. To be successful, NRW needs a material sample thin enough, and careful operations with complex valued logarithm. When successful, extracted parameters have round-off errors, but when not, the results are wrong. Thus, the inverse problem of the EM material characterization at microwave frequencies is an interesting benchmark for optimization algorithms and machine learning alternatives. A neural network alternative is investigated in this paper for the case of non-magnetic materials, operating at a fixed frequency. This is a necessary first step before approaching neural network (NN) models valid for whole frequency ranges and magneto-dielectric materials. A feed forward NN with one hidden layer was used, its hyperparameters being tuned by employing a multi-objective optimization procedure. Numerical results show that a NN carefully chosen can provide accurate results for a relatively large domain of complex permittivity components, being successful in areas where NRW fails. The implementation, carried out in python with Optuna module, is available for free download.

Security is the main attribute when dealing with information exchange. Confidential information theft, data loss, and data manipulation are conceivable results of security events. Different forms of data hiding are Cryptography and Steganography. Cryptography converts information into an unreadable form, and steganography hides the existence of information. The proposed work experiments with Advanced Blowfish Encryption based on an extended round function integrity with Chaotic Image Quantization (ABECIQ) as a security mechanism. ABECIQ aims to introduce a novel security mechanism that combines cryptography and steganography with the key generation scenario using a genetic algorithm. Initially, using a genetic algorithm and real-time clock values, the secret keys are created. The Blowfish algorithm’s round function ‘F’ is modified by adding crossover and mutation functions. The generated ciphertext is embedded in an image using the chaotic-quant technique. The proposed work is analysed using parameters of the Avalanche effect, Entropy values, Execution time, Attack scenario, Correlation coefficient, and Peak Signal-to-Noise Ratio (PSNR) values. The experiments demonstrate that the ABECIQ algorithm achieves PSNR values within the range of 65 to 74 dB while SSIM values are above 0.999, which indicate high imperceptibility. The generated keys also show entropy values which are close to the theoretic maximum of 8 bits per character. In addition, the proposed algorithm shows high throughput thereby indicating improved computational efficiency compared to the existing algorithm. The analysis shows that ABECIQ provides better results than the existing Chaotic, Blowfish Encryption, as well as AES-RDH algorithm. ABECIQ is evaluated with different text files of sizes 4KB and 12KB demonstrating better PSNR, MSE, SSIM, and Correlation Coefficient. In addition, the time complexity for ABECIQ has also been analyzed for embedding process.

This paper introduces a finite iterative algorithm for solving a single-variable quaternion system of matrix equations. It is theoretically proven that if the system is consistent, the solution can be achieved from any initial quaternion matrix within a finite number of iterations, assuming the absence of round-off errors. A special case of this equation is studied, which contains the k -conjugate of the unknown matrix. Numerical examples are provided to illustrate the effectiveness and computational efficiency of the proposed algorithms.

This paper presents a unified framework for generic attacks on Generalized Feistel Ciphers, with a primary focus on Type 1, Type 2, and unbalanced contracting (U-Type 1) Feistel constructions with non-invertible round functions. In [OBR23], authors reveal a class of vulnerabilities exploitable via key independent multidimensional linear trails for Feistel Ciphers, yielding efficient generic distinguishing and key-recovery attacks. We extend the work of [OBR23] by formalizing the application of generic multidimensional linear cryptanalysis to Generalized Feistel Ciphers. In this way, we improve upon existing results by extending the maximum number of rounds for the generic distinguishing attack to t2 + 2t − 1 for Type 1 and U-Type 1, and to 2t + 3 for Type 2. Moreover, we have the maximum number of rounds for generic key recovery attacks on (U)-Type 1 as t2 + 3t − 2 and Type 2 as 4t. To the best of our knowledge, these findings yield the best results for the maximum number of rounds in key recovery attacks on the corresponding GFC. We further demonstrate the branch-permutation-independence of these attacks, showing that changing internal permutations does not affect the applicability, complexity, or maximum number of rounds of generic attacks. The effectiveness of our attacks is validated through experiments on the first-round AES candidate CAST-256 and the MPC-friendly block cipher GMiMC. Both theoretical and experimental results confirm that our proposed branch-permutation-independent generic attacks enhance the maximum number of rounds for generic attacks for GFC and reduce complexity across various interesting cases.

We present the first known-plaintext attack on up to 25 rounds of the tweakable block cipher Craft. These attacks require only two known plaintextciphertext pairs to recover the full key, and work independent of the used tweaks. Given the state and key size of 64 and 128 bits, respectively, this is the minimal data complexity an attack recovering the full key can have.At the basis of this attack is the observation that Craft can be decomposed into two loosely dependent functions: the state can be split in half such that the round function mixes only 4 bits of each half into the other. Since the key schedule does not provide mixing between these parts either, we can guess these 4 bits per round to mount a meet-in-the-middle attack on up to 25 rounds.While the best attacks on Craft by M’Foukh et al. cover up to 26 rounds, they are in the chosen-ciphertext setting and require (up to) the full code book. In fact, we show that their attacks (implicitly) use a similar decomposition, and therefore present the other end of a time-data trade-off for the same family of attacks.

To meet the strict non-contact measurement requirements for the assembly of aircraft engine pipelines and to overcome the limitations of the traditional three-dimensional laser scanning workflow, this study proposes an automated pipeline point cloud processing and deviation analysis framework. Through a standardized three-dimensional laser scanning procedure, high-resolution pipeline point clouds are obtained and preprocessed. Based on the geometric characteristics of the pipeline, automated algorithms for point cloud feature segmentation, axis extraction, and model registration are developed. Particularly, the three-dimensional extended Douglas-Peucker (DP) algorithm is introduced to achieve efficient point cloud downsampling while retaining necessary geometric and structural features. These algorithms are fully integrated into a unified software platform, supporting one-click operation, and can automatically analyze and obtain five key types of pipeline deviations: angular deviation, radial deviation, axial deviation, roundness error, and diameter error. The platform also provides intuitive visualization effects and comprehensive report generation functions to facilitate quantitative inspection and analysis. Test results show that the proposed method significantly improves the processing efficiency and measurement reliability of complex pipeline systems. The developed framework provides a powerful practical solution for the automated geometric inspection of aircraft engine pipelines and lays a solid foundation for subsequent quality assessment tasks.

It is well known that bipolar disorder (BD) and epilepsy (EP) are common neurological diseases. The objective of this study was to screen for potential biomarkers applicable to the diagnosis of EP and BD. The gene expression profiles from both the BD and EP datasets were sourced from the Gene Expression Omnibus database. To pinpoint the core shared genes, we conducted differential expression analysis as well as weighted gene co-expression network analysis. Additionally, we leveraged protein–protein interaction, Gene Ontology, and Kyoto Encyclopedia of Genes and Genomes pathway enrichment to uncover the pathogenic genes of BD and EP, as well as their underlying mechanisms. Using least absolute shrinkage and selection operator regression, support vector machine–recursive feature elimination, and random forest, hub genes were determined via rigorous examination. Subsequently, predictive nomograms and receiver operating characteristic curves were crafted to forecast BD and EP. A single-gene set enrichment analysis was executed meticulously on every diagnostic gene, aiming to identify shared signaling pathways. To round things off, the cell-type identification by estimating relative subsets of RNA transcripts algorithm analysis explored immune cell infiltration within BD and EP samples. After analyzing the intersection of weighted gene co-expression network analysis significant module genes and the differentially expressed genes, we pinpointed 113 genes of interest. Our protein–protein interaction analysis revealed 3 pivotal modules, each harboring 14 genes, which are considered pivotal for diagnosing BD and EP. The machine learning models consistently highlighted 2 genes – Regulators of G-protein signaling 4 and gamma-aminobutyric acid type A receptor subunit alpha1 – as universal diagnostic biomarkers. Furthermore, the immune infiltration analysis disclosed that activated M2 macrophages and mast cells are integral players in the onset of BD and EP.

The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion method extends well beyond this constraint: It remains valid across the entire complex plane and is thus suitable for arbitrary non-Hermitian matrices. We identify numerical rounding errors as the primary source of errors encountered when applying the method outside the conventional spectral bounds, and they are not caused by fundamental limitations. By carefully selecting the spectral radius and the time step, we show how these errors can be effectively suppressed, enabling accurate time evolution calculations in non-Hermitian systems. We derive an analytic upper bound for the rounding error, which serves as a practical guideline for selecting time steps in numerical simulations. As an application, we illustrate the performance of the method by computing the time evolution of wave packets in the Hatano-Nelson model.

As wind turbines trend toward larger sizes, higher rotational speeds, and extended service lives, higher demands are emerging for the dimensional accuracy, mechanical properties, and service reliability of the main shaft bearings. The hot bulging process is a critical process in bearing ring manufacturing. The stress-strain and dimensional evolution during the hot bulging process are crucial for the fatigue life and dimensional accuracy of rings with non-circular cross-sections. Therefore, based on the residual stress field from rolling as an initial condition, this paper established a coupled finite element model for the entire rolling-to-bulging process of GCr15SiMn bearing steel rings and verified the accuracy of the model. A stepwise rotation hot bulging process was innovatively designed. The stresses, strains, and deformation rates of the rings were thoroughly evaluated at different steps of the bulging process. Additionally, the effect of the bulge amount on the stress-strain uniformity and dimensional accuracy of the fabricated rings was also evaluated. Results indicate that based on the stepwise rotation hot bulging process conducted at 870-930 °C, when the first-step bulging amount is 1.50 mm, the secondary and third-step amounts are both 0.50 mm, and the bulging speed is 1.00 mm/s, while the roundness error of ring #3 stabilizes within 0.28-0.35 mm. The standard deviation of the axial equivalent strain was decreased by 92%, and the stress peak was also decreased by 39%. Above all, the stepwise rotation hot bulging process is an effective approach to improve the distribution uniformity of the stress-strain and the dimensional consistency of the bearing rings. This paper provides theoretical foundations and process guidance for the precision forming of large wind turbine bearing rings with non-standard sections.

Abstract The use of artificial neural networks is now becoming widespread across a wide variety of tasks. In this context of very rapid development issues related to the storage and computational performance of these models emerge, since networks are sometimes very deep and comprise up to trillions of parameters. For all these reasons the use of reduced precision is increasingly being considered, although, until now, its accuracy and robustness had been approached mostly from a practical standpoint or verified by software. The aim of this work is to provide formal tools to better understand, explain and predict the accuracy and stability of neural networks when using floating-point arithmetic. To this end, we apply a rounding error analysis based on existing tools in numerical linear algebra to obtain both forward and backward error bounds. This includes both deterministic worst-case bounds as well as probabilistic bounds that are sharper on average. Since the exact backward error is not directly computable the backward error bounds are validated experimentally through a linearized backward error. These bounds both ensure the proper functioning of neural networks once trained and provide recommendations on architectures and training methods to enhance the robustness of neural networks.

Ultra-precision grinding is widely used in fields such as precision instrumentation, military industry, and aerospace. Focusing on a grinding system based on hydrostatic support, this paper investigates the formation mechanism and variation patterns of roundness error during grinding. The dynamic equations are derived based on the structural characteristics of a vertical grinding system. The uncut chip thickness is formulated, enabling the prediction of grinding forces through mathematical expressions. The dynamic equations are solved using a fully discrete algorithm to obtain the surface profile of the workpiece after machining, and roundness error is extracted using the least squares method. As the speed ratio of the grinding wheel to the workpiece increases, the grinding accuracy improves, and the roundness error can be controlled within 0.2 μm. The farther the grinding force application point is from the center of the slider, the greater the roundness error. Under the condition of meeting the processing range, a shorter grinding wheel contact rod should be selected.

Real-time evaluation method for roundness error in grinding process based on data optimization

MotivationPhylogenetic trees describe the evolutionary history among biological species based on their genomic data. Maximum likelihood (ML) based phylogenetic inference tools search for the tree and evolutionary model that best explain the observed genomic data. Given the independence of likelihood score calculations between different genomic sites, parallel computation is commonly deployed. This is followed by a parallel summation over the per-site scores to obtain the overall likelihood score of the tree. However, basic arithmetic operations on IEEE 754 floating-point numbers, such as addition and multiplication, inherently introduce rounding errors. Consequently, the order by which floating-point operations are executed affects the exact resulting likelihood value since these operations are not associative. Moreover, parallel reduction algorithms in numerical codes re-associate operations as a function of the core count and cluster network topology, inducing different round-off errors. These low-level deviations can cause heuristic searches to diverge and induce high-level result discrepancies (e.g. yield topologically distinct phylogenies). This effect has also been observed in multiple scientific fields beyond phylogenetics.ResultsWe observe that varying the degree of parallelism results in diverging phylogenetic tree searches (high-level results) for over 31% out of 10 179 empirical datasets. More importantly, 8% of these diverging datasets yield trees that are statistically significantly worse than the best-known ML tree for the dataset (AU-test, P < .05). To alleviate this, we develop a variant of the widely used phylogenetic inference tool RAxML-NG, which does yield bit-reproducible results under varying core-counts, with a slowdown of only 0%–12.7% (median 0.8%) on up to 768 cores. For this, we introduce the ReproRed reduction algorithm, which yields bit-identical results under varying core-counts, by maintaining a fixed operation order that is independent of the communication pattern. ReproRed is thus applicable to all associative reduction operations—in contrast to competitors, which are confined to summation. Our ReproRed reduction algorithm only exchanges the theoretical minimum number of messages, overlaps communication with computation, and utilizes fast base-cases for local reductions. ReproRed is able to all-reduce (via a subsequent broadcast) operands across 48–768 cores in 19.7–48.61 μs, thereby exhibiting a slowdown of 13%–93% over a non-reproducible all-reduce algorithm. ReproRed outperforms the state-of-the-art reproducible all-reduction algorithm ReproBLAS (offers summation only) beyond 10 000 elements per core. In summary, we re-assess non-reproducibility in parallel phylogenetic inference, present the first bit-reproducible parallel phylogenetic inference tool, as well as introduce a general algorithm and open-source code for conducting reproducible associative parallel reduction operations.Availability and implementationReproRed: https://doi.org/10.5281/zenodo.15004918 (LGPL)—Reproducible RAxML-NG version https://doi.org/10.5281/zenodo.15017407 (GPL)

Tapered roller bearings are widely employed in mechanical structures such as automotive wheel hub units, transmissions, and machine tool spindles, and they have a direct impact on the performance and stability of the equipment. The shape error and surface quality of the bearing raceway, as its working interface, directly affect its service performance. Grinding is an important process in a machining bearing raceway, and the formed roundness error and surface roughness of a raceway affect the workload of subsequent precision polishing processes. In order to reveal the effect of workpiece rotational speed, grinding wheel linear velocity, and grinding depth on the machining quality of the bearing outer ring inner raceway, single-factor experiments and surface roughness orthogonal experiments were conducted. The results were analyzed for range and variance using surface roughness Ra as the evaluation index, and we developed a mathematical model using a regression method for Ra. It has been found that the roundness error and surface roughness of the bearing raceway are improved with the increase in the grinding wheel linear velocity and the decrease in the grinding depth and workpiece rotational speed. The grinding depth has the greatest impact on surface roughness and the most significant effect. Next are the grinding wheel linear velocity and the workpiece rotational speed, while the effect of changes in workpiece rotational speed on roughness is relatively insignificant. The lowest surface roughness obtained under the optimized grinding parameter combination is 0.205 μm.

Abstract Gustav Krug (1844–1902). Nietzsche’s Childhood Friend and Musical Companion. Following Martin Pernet’s genealogical and biographical study, this article focuses on the composer and jurist Gustav Krug as a musical advisor and discussion partner to Nietzsche. Starting out from the function of music in Nietzsche’s philosophical thinking, I examine Nietzsche’s and Krug’s joint music-making and exchanges about their own works as well as questions of compositional aesthetics and technique, before I offer a stylistic analysis of Krug’s surviving compositions. This allows us to round off our picture of Nietzsche’s childhood friend from a new perspective.