Search Results (116)

This paper develops a geometric framework for analyzing the ideal structure of the bipolar semigroup $B=\{(-a,b)\mid a,b\in {\mathbb{R}}_0^{+}\}$ under coordinate-wise addition. Subsets of B are interpreted as planar regions, allowing ideals to be described in terms of boundary behavior. In particular, we prove that the complement of a simply connected region is an ideal of the commutative additive semigroup $(B,+)$ if and only if its boundary contains no strictly decreasing segment. This provides a direct and visually verifiable criterion for ideality, linking algebraic structure to geometric shape. Each ideal can be written as a union of translates of the form $z+B$, with minimal generating sets determined by boundary structure. Potential applications to modeling bipolar system states, including cybersecurity contexts, are also discussed. These results uncover an intrinsic symmetry between algebraic closure and geometric monotonicity, offering a new perspective on semigroup ideals through spatial structure. In contrast to our previous work on the semiring $(B,+,·)$, where ideals necessarily exhibit symmetry with respect to the line $y=-x$, we show that removing the multiplicative operation leads to a fundamentally different geometric behavior: ideals in the semigroup $(B,+)$ no longer possess symmetric shapes. This demonstrates that the multiplicative structure is the key mechanism enforcing geometric symmetry. Full article

Nicotinamide mononucleotide (NMN) plays vital physiological roles as a vitamin B derivative, with nicotinamide riboside kinase (NRK) serving as a key enzyme for its efficient and environmentally friendly synthesis. In this study, semi-rational design was employed to modify the Hi-NRK enzyme at the molecular level, leading to the identification of a critical mutant, Hi-NRK^G8S. This variant exhibited a twofold increase in enzymatic activity and significantly enhanced thermal stability, extending its half-life at 40 °C from 4 to 8 h. By optimizing reaction conditions, NMN yield reached 94.17% at a nicotinamide riboside (NR) substrate concentration of 50 g/L. Further addition of adenylate kinase (ADK) to facilitate ATP recycling increased the yield to 97.24% at 75 g/L NR. This study establishes a foundation for industrial-scale, efficient, and green NMN production. Full article

Aiming at the problems with traditional transformer winding deformation detection, requiring power outages, low signal-to-noise ratios for online monitoring, and insufficient feature extraction, this paper proposes a live monitoring and intelligent diagnosis method based on pulse-coupled injection. At the hardware level, a semi-ring capacitive coupling sensor is developed and designed, which realizes non-contact injection of high-frequency pulse signals and high-SNR extraction without a power outage. The reliability of the system under complex working conditions is verified by field experiments on multiple actual 110 kV transformers. At the algorithm level, an innovative MSCNN–Transformer–PGA deep composite model fused with prior electromagnetic physical knowledge is constructed and combined with the transformer equivalent circuit model. The model uses a multi-scale convolution to extract local details of frequency response signals, adopts Transformer to establish the global sequence dependence, and introduces a Physics-Guided Attention mechanism (PGA) to adaptively focus on the key fault physical frequency bands. The experimental results show that the proposed method effectively overcomes electromagnetic noise interference, and the fault classification accuracy of single-modal pulse frequency response data reaches 97.6%, providing a high-precision online monitoring solution for the safe operation and maintenance of transformers. Full article

This review comprehensively examines the structural architecture, catalytic mechanisms, and targeted molecular engineering of α-amylase (primarily the GH13 family), a pivotal biocatalyst in the food industry. We highlight diverse microbial sources of α-amylases and their cost-effective heterologous expression in well-characterized hosts like Bacillus subtilis and Escherichia coli. To overcome extreme operational bottlenecks—such as elevated temperatures and acidic environments—recent advances in protein engineering are critically evaluated. These strategies, including directed evolution, semi-rational design, and advanced immobilization on nanomaterials, synergistically enhance the enzyme’s thermostability, catalytic efficiency, and reusability. Furthermore, this paper synthesizes the state-of-the-art applications of engineered α-amylases across key food processing sectors, including baking, sugar refining, and brewing. By integrating structural biology with advanced material science, this review provides a targeted roadmap for developing next-generation, high-performance α-amylases to address current and future challenges in sustainable food processing. Full article

Loop-mediated isothermal amplification (LAMP) is a widely used nucleic acid detection method, but its application is often limited by the suboptimal performance of wild-type Bacillus stearothermophilus (Bst) DNA polymerase. This study employed a combined deep learning and semi-rational design strategy to engineer Bst DNA polymerase. High-throughput screening identified the A0A150MFP3 sequence and the L105M mutation, which increased enzymatic activity by 32.92%. Fusion with the CL7 protein generated a CL7-Bst mutant with enhanced thermal stability and tolerance to common inhibitors, including 7% (v/v) ethanol, 0.18‰ (w/v) SDS, 80 mmol/L NaCl, and 0.8 mmol/L EDTA. Systematic optimization of the LAMP reaction system determined the optimal pH (9.0), enzyme concentration (0.20 U/μL), and temperature (64 °C). When applied to Escherichia coli O157:H7 detection, the CL7-Bst mutant achieved Tt values of 15.13 and 12.78 for crude and purified DNA, respectively, with a limit of detection of 1 × 10³ CFU/mL. In summary, integrating deep learning with semi-rational design and fusion protein engineering yielded a high-performance DNA polymerase that facilitates rapid, sensitive, and field-deployable LAMP-based pathogen detection. Full article

Extreme low-light image enhancement (ELLIE) targets the restoration of visual quality under ultra-dim environments (<0.1 lux). Conventional image signal processing (ISP) pipelines often fail in such scenarios due to the limitations of heuristic, hand-crafted algorithms. While deep learning has advanced the field via end-to-end mapping, existing models suffer from constrained generalization and suboptimal perceptual fidelity, primarily stemming from the scarcity of large-scale, high-diversity datasets. To bridge this gap, we present the Day and Night (DaN) dataset, a semi-synthetic benchmark synthesized through a rigorous physics-based noise model. This approach effectively captures authentic noise characteristics while enabling the scalable generation of paired samples across multifaceted illumination conditions and scenes. Furthermore, we propose No Longer Vigil (NLV), a fully differentiable AI-ISP framework. By replacing traditional rigid blocks with adaptive non-linear networks, NLV facilitates scene-dependent transformations without requiring manual priors. Comprehensive evaluations demonstrate that our method significantly outshines state-of-the-art approaches, yielding a 4.15 dB gain in PSNR and a 0.026 improvement in SSIM. Full article

Multi-campus AI data centers procure identical hardware and service SKUs across geographically heterogeneous locations, yet finance and operations require a single system-level benchmark (“world price”) per SKU for budgeting, chargeback, and capacity planning. Naive deployment-weighted aggregation preserves total cost but can induce Simpson-type aggregation bias, where heterogeneous location mixes reverse global SKU rankings and weaken managerial decision signals. This study formalizes the problem of location-robust, cost-preserving aggregation and develops two mathematically structured operators for production cost pipelines. The first operator applies a two-way fixed-effects decomposition to separate global SKU effects from campus-specific premia, followed by normalization to guarantee exact cost preservation. This yields an interpretable benchmark that performs well when campus coverage is sufficiently broad and location effects remain approximately additive. The second operator solves a constrained convex common-weight optimization, producing a unified set of non-negative campus weights that preserves total cost while providing the strongest protection against dominance reversals in the ordered setting. Simulation experiments and a semi-real calibrated AI datacenter OPEX illustration show that both operators substantially improve ranking stability relative to naive blending, while the convex operator serves as the more conservative safeguard under adverse heterogeneity. The resulting detect–correct–validate workflow provides a scalable decision-support framework for robust cost aggregation in distributed AI infrastructure and illustrates how symmetry-preserving aggregation operators can stabilize benchmarking in large heterogeneous systems. Full article

We introduce the transitive closure operator $\mathrm{\Gamma }$ on the set of square matrices over a class of semirings, and then define the transitive closure of a matrix. We characterize the surjective linear transformations of matrices preserving (strongly preserving) transitive closures, and show that a surjective linear transformation preserves the transitive closures if and only if it commutes with $\mathrm{\Gamma }$, which is equivalent to preserving the kernel of $\mathrm{\Gamma }$. We also deduce that the strong linear preservers of transitive closure on $2\times 2$ matrices over certain inclines are surjective. In particular, we provide a complete characterization of strong linear preservers of transitive closure on $n\times n$ matrices over the binary Boolean semiring. Full article

Aflatoxin B1 (AFB1) poses a serious threat to global food and feed safety. Laccase-based enzymatic degradation represents a promising green strategy for AFB1 removal; however, its industrial application is severely limited by the rapid thermal inactivation of wild-type enzymes under high-temperature processing conditions (>70 °C). Here, we engineered the thermal stability of a laccase from Bacillus amyloliquefaciens B10 through an integrated strategy combining computational structural biology with semi-rational design. By coupling molecular dynamics (MD) simulations with folding free-energy (ΔΔG) calculations, we identified key flexible regions associated with thermal instability and subsequently implemented iterative saturation mutagenesis. The best single mutant, R196C, retained more than 96% relative activity after heat treatment at 80 °C for 10 min. Further iterative mutational stacking progressively enhanced thermostability: the R90E/R196C double mutant showed 1.25-fold higher activity at 80 °C than R196C, and the R90E/R196C/H54F triple mutant showed a further 1.16-fold increase over the double mutant. The final quadruple mutant, R90E/R196C/H54F/R253I, achieved 86.9% AFB1 degradation at 80 °C after 24 h. High-temperature MD simulations (100 ns at 353.15 K) indicated that the enhanced thermostability was associated with reduced conformational flexibility, lower radius of gyration (Rg) and solvent-accessible surface area (SASA), and a coil-to-β-sheet transition that contributed to stabilization of the protein core. In addition, efficient secretory expression of the engineered enzyme was achieved in Pichia pastoris, reaching 3.0 U/mL, while the crude enzyme maintained more than 70% activity at 80 °C. Collectively, these results provide a practical basis for the rational engineering and scalable production of thermostable biocatalysts for AFB1 detoxification-related applications of AFB1 control, and offer broader insights into the targeted enhancement of thermal stability in industrial enzymes. Full article

Imine reductases (IREDs) have emerged as valuable biocatalysts for the asymmetric synthesis of chiral amines, key intermediates in numerous active pharmaceutical ingredients. Their ability to operate under mild reaction conditions with high chemo- and stereoselectivity provides an attractive alternative to conventional metal-catalyzed or chemical reduction processes. However, the broader industrial application of wild-type IREDs is often constrained by their limited substrate scope and moderate catalytic efficiency. Recent advances in biocatalysis have demonstrated that engineered IREDs can catalyze the reduction of a wide range of natural and non-natural imines, significantly expanding their applicability in pharmaceutical and fine chemical synthesis. In parallel, enzyme immobilization strategies have proven highly effective for improving operational stability, facilitating enzyme reuse, and enabling continuous flow biocatalytic processes. Efficient cofactor regeneration systems have further enhanced the practical implementation of IRED-based transformations. Advances in protein engineering, including structure-guided design, semi-rational mutagenesis, and directed evolution, have generated enzyme variants with improved catalytic activity, stereoselectivity, and substrate tolerance. The integration of high-throughput screening technologies and machine-learning-assisted enzyme design has further accelerated the discovery and optimization of efficient IRED biocatalysts. This review summarizes recent progress in the protein engineering and immobilization of IREDs and discusses future perspectives for their industrial application. Full article

As an isoflavone metabolite with diverse physiological activities, the development of efficient and sustainable manufacturing technologies for (S)-equol holds significant importance. This study focuses on the semi-rational design of daidzein reductase (DZNR), the first key enzyme in the (S)-equol biotransformation pathway. Through multiple sequence alignment and three-dimensional structural analysis, two critical residues, Gly30 and Ala105, were identified in DZNR. A library of single and combinatorial mutants was constructed and screened, yielding the double variant DZNR30S+105S with substantially enhanced catalytic performance. In a whole-cell biocatalytic system, the recombinant E. coli (Escherichia coli) strain harboring this combinatorial mutant achieved a yield of 238.3 mg/L (S)-equol at a substrate concentration of 1 mM daidzein, demonstrating markedly improved catalytic efficiency. Upon increasing the daidzein concentration to 2 mM, the reaction reached equilibrium within 5 h, producing 384.6 mg/L (S)-equol, which highlights the mutant’s excellent potential for high-substrate-concentration applications. This study not only provides novel mechanistic insights into DZNR catalysis but also successfully establishes a DZNR variant with enhanced activity, offering an efficient biocatalytic component for the industrial-scale biomanufacturing of (S)-equol and thereby advancing the development of green biosynthesis technologies for this valuable compound. Full article

In this paper, for any real number λ, we transform the complete max-plus semiring ${\mathbb{R}}_{\infty }$ into a commutative, complete, additively idempotent semiring ${\mathbb{R}}_{\infty }^{\lambda }$, called the lower λ-truncation of ${\mathbb{R}}_{\infty }$. It is obtained by removing from ${\mathbb{R}}_{\infty }$ all real numbers smaller than λ, inheriting the addition operation, shifting the original products by −λ, and appropriately modifying the residuum operation. The purpose of lower truncations is to transfer the iterative procedures for computing the greatest presimulations and prebisimulations between max-plus automata, in cases where they cannot be completed in a finite number of iterations over ${\mathbb{R}}_{\infty }$, to ${\mathbb{R}}_{\infty }^{\lambda }$, where they could terminate in a finite number of iterations. For instance, we prove that this necessarily happens when working with max-plus automata with integer weights. We also show how presimulations and prebisimulations computed over ${\mathbb{R}}_{\infty }^{\lambda }$ can be transformed into presimulations and prebisimulations between the original automata over ${\mathbb{R}}_{\infty }$. Although they do not play a significant role from the standpoint of computing presimulations and prebisimulations, for theoretical reasons we also introduce two types of upper truncations of the complete max-plus semiring ${\mathbb{R}}_{\infty }$. Full article

Background/Objectives: Caffeic acid is a hydroxycinnamic acid that has a wide range of applications in the medical field. The synthesis of caffeic acid using microbial fermentation technology is an environmentally friendly method. Methods: By engaging various enzymes, specifically 4-hydroxyphenylacetate 3-monooxygenase (HpaB), sourced from diverse bacterial strains, we successfully engineered a functional version of this enzyme within Escherichia coli, enabling the production of caffeic acid. In addition to the two common tyrosine ammonia lyases (TAL) and HpaC, different combinations of HpaB demonstrated varying abilities in converting the substrate L-tyrosine into the desired product, caffeic acid. Results: Under shake-flask culture conditions, the highest yield of caffeic acid was achieved with an enzyme mixture containing HpaB from Escherichia coli, reaching 75.88 mg/L. Enhancing the activity of the rate-limiting enzyme through engineering could potentially increase caffeic acid titer. This study aims to conduct a semi-rational design of HpaB through structure-based approaches to screen for mutants that can enhance the production of caffeic acid. Initially, the predicted three-dimensional structure of HpaB was generated using AlphaFold2, and subsequent analysis was conducted to pinpoint the critical mutation sites within the substrate-binding pocket. Five key amino acid residues (R113, Y117, H155, S210 and Y461) located in the vicinity of the flavin adenine dinucleotide binding domain in HpaB from Escherichia coli could be instrumental in modulating enzyme activity. Subsequently, the mutant S210G/Y117A was obtained by iterative saturation mutagenesis, which increased the titer of caffeic acid by 1.68-fold. The caffeic acid titer was further improved to 2335.48 mg/L in a 5 L fermenter. The findings show that the yield of caffeic acid was significantly enhanced through the integration of semi-rational design and fermentation process optimization. Full article

In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of the preservation of positivity or monotonicity of functions for some models in approximation and interpolation theory. The setting in complete semi-vector spaces does not requite additional assumptions but is intrinsically built into the framework. For the purposes of this paper, fractal interpolation in the complete semi-vector spaces $C^{+}$ and $L_p^{+}$ is considered. Full article

Patchoulene, the characteristic sesquiterpene of patchouli essential oil, is highly valued in the perfume industry for its distinctive woody note and fixative properties. Beyond its olfactory applications, patchoulene has demonstrated promising biological activities, including anti-inflammatory, antimicrobial, and neuroprotective effects. Current production relies mainly on extraction from Pogostemon cablin plants, which requires long growth cycles (≥8 months), exhibits low yields, and imposes significant environmental constraints. To overcome these limitations, this study aimed to enhance the Whole-cell yield of patchoulene synthase (PcPTS) through structure-informed protein engineering. A semi-rational design approach was employed, combining homology modeling, molecular docking, evolutionary analysis, and molecular dynamics simulations to identify functional residues within the enzyme active site. Ala-scanning mutagenesis highlighted Thr532 as essential for catalytic activity, and coevolutionary analysis indicated synergistic effects between Phe456 and Thr532. Site-directed mutagenesis was conducted to generate single (F456M, T532Y) and double (F456M/T532Y, designated M2) mutants. The double mutant M2 showed a 3.62-fold increase in patchoulene production compared to the wild-type enzyme. In silico analyses suggested that the enhanced performance of M2 originates from improved substrate positioning, reduced structural flexibility, and strengthened molecular interactions, collectively contributing to a lower energy barrier for catalysis. This study provides an effective strategy for the rapid optimization of terpenoid synthases and facilitates the development of microbial cell factories for sustainable and high-yield production of plant-derived terpenoids. Full article