Search Results (123)

The subset-sum problem, a foundational NP-hard problem in theoretical computer science, serves as a critical building block for cryptographic constructions. This work introduces novel classical and quantum heuristic algorithms for the random subset-sum problem at density $d=1$, where exactly one solution is expected. Classically, we propose the first algorithm based on a ternary tree representation structure, inspired by recent advances in lattice-based cryptanalysis. Through numerical optimization, our method achieves a time complexity of $\widetilde{𝒪}\left(2^{0.2400n}\right)$ and space complexity of $\widetilde{𝒪}\left(2^{0.2221n}\right)$, improving upon the previous best classical heuristic result of $\widetilde{𝒪}\left(2^{0.2830n}\right)$. In the quantum setting, we develop a corresponding algorithm by integrating the classical ternary representation technique with a quantum walk search framework. The optimized quantum algorithm attains a time and space complexity of $\widetilde{𝒪}\left(2^{0.1843n}\right)$, surpassing the prior state-of-the-art quantum heuristic of $\widetilde{𝒪}\left(2^{0.2182n}\right)$. Furthermore, we apply our algorithms to information set decoding in code-based cryptography. For half-distance decoding, our classical algorithm improves the time complexity to $\widetilde{𝒪}\left(2^{0.0453n}\right)$, surpassing the previous best of $\widetilde{𝒪}\left(2^{0.0465n}\right)$. For full-distance decoding, we achieve a quantum complexity of $\widetilde{𝒪}\left(2^{0.058326n}\right)$, advancing beyond the prior best quantum result of $\widetilde{𝒪}\left(2^{0.058696n}\right)$. These findings demonstrate the broad applicability and efficiency of our ternary representation technique across both classical and quantum computational models. Full article

Selecting an appropriate Multi-Criteria Decision-Making (MCDM) algorithm for optimizing marine diesel engine operation presents a complex challenge due to the diversity in mathematical formulations, normalization schemes, and trade-off resolutions across methods. This study systematically evaluates fourteen MCDM algorithms, which are grouped into five primary methodological categories: Scoring-Based, Distance-Based, Pairwise Comparison, Outranking, and Hybrid/Intelligent System-Based methods. The goal is to identify the most suitable algorithm for real-time performance optimization of two stroke marine diesel engines. Using Diesel-RK software, calibrated for marine diesel applications, simulations were performed on a variant of the MAN-B&W-S60-MC-C8-8 engine. A refined five-dimensional parameter space was constructed by systematically varying five key control variables: Start of Injection (SOI), Dwell Time, Fuel Mass Fraction, Fuel Rail Pressure, and Exhaust Valve Timing. A subset of 4454 high-potential alternatives was systematically evaluated according to three equally important criteria: Specific Fuel Consumption (SFC), Nitrogen Oxides (NO_x), and Particulate Matter (PM). The MCDM algorithms were evaluated based on ranking consistency and stability. Among them, Proximity Indexed Value (PIV), Integrated Simple Weighted Sum Product (WISP), and TriMetric Fusion (TMF) emerged as the most stable and consistently aligned with the overall consensus. These methods reliably identified optimal engine control strategies with minimal sensitivity to normalization, making them the most suitable candidates for integration into automated marine engine decision-support systems. The results underscore the importance of algorithm selection and provide a rigorous basis for establishing MCDM in emission-constrained maritime environments. This study is the first comprehensive, simulation-based evaluation of fourteen MCDM algorithms applied specifically to the optimization of two stroke marine diesel engines using Diesel-RK software. Full article

The problem of graph-based X-secure T-private linear computation (GXSTPLC) is to allow a user to retrieve a linear combination of K messages from a set of N distributed servers that store the messages in a graph-based fashion, i.e., each message is restricted to be distributed among a subset of servers. T-privacy requires that the coefficients of the linear combination are not revealed to any group of up to T colluding servers, and X-security guarantees that any set of up to X colluding servers learns nothing about the messages. In this paper, we propose an achievability scheme for GXSTPLC that enables a storage–communication trade-off by exploiting non-replicated storage codes. Novel aspects of our achievability scheme include the usage of the idea of cross-subspace alignment null shaper that addresses various challenges posed by the graph-based storage structure. In addition, unlike previous works, our scheme allows a direct transformation into a quantum one to achieve a superdense coding gain by leveraging the idea of N-Sum Box abstraction of quantum “over-the-air” computing. Full article

Background: Myocardial perfusion scintigraphy (MPS) is an important tool for evaluating ischemia in diabetic populations. However, applications of advanced predictive models like multivariate adaptive regression splines (MARS) to estimate summed stress scores (SSS) are lacking. Methods: In this study, 1028 diabetic women undergoing Thallium-201 MPS were analyzed. The dataset was split into training (80%) and testing (20%) subsets. MARS and multiple linear regression (MLR) models were constructed to predict SSS, and their performance was evaluated using root mean square error (RMSE), relative absolute error (RAE), root relative squared error (RRSE), Mean Absolute Percentage Error (MAPE), and Symmetric Mean Absolute Percentage Error (SMAPE). Results: On the testing dataset, the MARS model outperformed the MLR model across all metrics, with an RMSE of 3.25 compared to 3.89 for MLR, an RAE of 0.52 vs. 0.64, and an RRSE of 0.53 vs. 0.67. Similar trends were observed in MAPE (18.7% vs. 22.1%) and SMAPE (17.3% vs. 20.5%). Conclusions: The superior predictive accuracy of the MARS model suggests its potential to enhance non-invasive myocardial risk stratification in diabetic women. Full article

Sandy beaches are vital geomorphic units with ecological, social, and economic significance, playing a key role in coastal protection and ecosystem regulation. However, they are increasingly threatened by climate change and human activities, highlighting the need for large-scale, high-precision monitoring to support sustainable management. Existing remote-sensing-based sandy beach extraction methods face challenges such as suboptimal feature selection and reliance on single data sources, limiting their generalization and accuracy. This study proposes a novel sandy beach extraction framework that integrates multi-source data, feature optimization, and collaborative modeling, with Fujian Province, China, as the study area. The framework combines Sentinel-1/2 imagery, nighttime light data, and terrain data to construct a comprehensive feature set containing 44 spectrum, index, polarization, texture, and terrain variables. The optimal feature subsets are selected using the Recursive Feature Elimination (RFE) algorithm. Six machine learning models—Random Forest (RF), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LGBM), Gradient Boosting Machine (GBM), Adaptive Boosting (AdaBoost), and Categorical Boosting (CatBoost)—along with an ensemble learning model, are employed for comparative analysis and performance optimization. The results indicate the following. (1) All models achieved the best performance when integrating all five types of features, with the average overall F1-score and accuracy reaching 0.9714 and 0.9733, respectively. (2) The number of optimal features selected by RFE varied by model, ranging from 19 to 36. The ten most important features across models were Band 2 (B2), Elevation, Band 3 (B3), VVVH_SUM, Spatial Average (SAVG), VH, Enhanced Water Index (EWI), Slope, Variance (VAR), and Normalized Difference Vegetation Index (NDVI). (3) The ensemble learning model outperformed all others, achieving an average overall accuracy, precision, recall, and F1-score of 0.9750, 0.9733, 0.9725, and 0.9734, respectively, under the optimal feature subset. A total of 555 sandy beaches were extracted in Fujian Province, covering an area of 43.60 km² with a total perimeter of 1263.59 km. This framework demonstrates strong adaptability and robustness in complex coastal environments, providing a scalable solution for intelligent sandy beach monitoring and refined resource management. Full article

Introduction: Haglund’s deformity, characterized by bony enlargement at the back of the heel, often coincides with Achilles tendon pathology due to impingement on the retrocalcaneal bursa and tendon insertion. Surgical management of Haglund’s deformity with a preexisting Achilles tendon rupture is complex, and understanding the outcomes of this subset of patients is essential for optimizing treatment strategies. Methods: This retrospective study reviewed patients undergoing open surgical management for Haglund’s syndrome between January 2015 and December 2023. Patients with chronic degenerative changes secondary to Haglund’s deformity and a preoperative Achilles tendon rupture were compared to those without. Data on demographics, surgical techniques, weightbearing protocols, and complications were collected. Univariate analysis was performed using χ² or Fisher’s exact test for categorical variables, and the T-test or Wilcoxon rank-sum test for continuous and ordinal variables, with normality assessed via the Shapiro–Wilk test. Results: Four hundred and three patients were included, with 13 having a preoperative Achilles tendon rupture. There was a higher incidence of preoperative ruptures among males. Surgical repair techniques and postoperative weightbearing protocols varied, though were not randomized. Complications included persistent pain, wound breakdown, infection, plantar flexion weakness, and revision surgery. While patients with Haglund’s deformity and a preoperative Achilles tendon rupture demonstrated a trend toward higher complication rates, including postoperative rupture and wound breakdown, these differences were not statistically significant in our analysis. Conclusions: A cautious approach is warranted in managing these patients, with careful consideration of surgical planning and postoperative rehabilitation. While our findings provide valuable insights into managing patients with Haglund’s deformity and preoperative Achilles tendon rupture, the retrospective design, limited sample size of the rupture group, and short duration of follow-up restrict generalizability and the strength of the conclusions by limiting the power of the analysis and underestimating the incidence of long-term complications. Therefore, the results of this study should be interpreted with caution. Further studies with larger patient cohorts, validated functional outcome measures, and comparable follow-up durations between groups are needed to confirm these results and optimize treatment approaches. Full article

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, and $C(K, X)$ is the Banach space of all continuous X-valued functions (with the supremum norm). We will study some strongly bounded operators $T:C(K, X)\to Y$ with representing measures $m:\Sigma \to L(X,Y)$, where $L(X,Y)$ is the Banach space of all operators $T:X\to Y$ and $\Sigma$ is the $\sigma$-algebra of Borel subsets of K. The classes of operators that we will discuss are the Grothendieck, p-limited, p-compact, limited, operators with completely continuous, unconditionally converging, and p-converging adjoints, compact, and absolutely summing. We give a characterization of the limited operators (resp. operators with completely continuous, unconditionally converging, p-convergent adjoints) in terms of their representing measures. Full article

Here all rings have identities. Let R be a ring and let R-mod denote the additive category of left finitely generated R-modules. Note that if R is a noetherian ring, then R-mod is an abelian category and every R-module is a finite direct sum of indecomposable R-modules. Finite Group Modular Representation Theory concerns the study of left finitely generated $\mathcal{O}G$-modules where G is a finite group and $\mathcal{O}$ is a complete discrete valuation ring with $\mathcal{O}/J\left(\mathcal{O}\right)$ a field of prime characteristic p. Thus $\mathcal{O}G$ is a noetherian $\mathcal{O}$-algebra. The Green Theory in this area yields for each isomorphism type of finitely generated indecomposable (and hence for each isomorphism type of finitely generated simple $\mathcal{O}G$-module) a theory of vertices and sources invariants. The vertices are derived from the set of p-subgroups of G. As suggested by the above, in Basic Definition and Main Results for Rings Section, let $\mathrm{\Sigma }$ be a fixed subset of subrings of the ring R and we develop a theory of $\mathrm{\Sigma }$-vertices and sources for finitely generated R-modules. We conclude Basic Definition and Main Results for Rings Section with examples and show that our results are compatible with a ring isomorphic to R. For Idempotent Morita Equivalence and Virtual Vertex-Source Pairs of Modules of a Ring Section, let e be an idempotent of R such that $R=ReR$. Set $B=eRe$ so that B is a subring of R with identity e. Then, the functions $eR{\otimes }_R\ast :R-\mathrm{mod}\to B-\mathrm{mod}$ and $Re{\otimes }_B\ast :B-\mathrm{mod}\to R-\mathrm{mod}$ form a Morita Categorical Equivalence. We show, in this Section, that such a categorical equivalence is compatible with our vertex-source theory. In Two Applications with Idemptent Morita Equivalence Section, we show such compatibility for source algebras in Finite Group Block Theory and for naturally Morita Equivalent Algebras. Full article

In this cross-disciplinary investigation, we uncover a suite of previously unexamined factors and their intricate interplay that hold causal relationships with the distribution of Trachurus japonicus in the northern reaches of the South China Sea, thereby extending the existing research paradigms. Leveraging advanced machine learning algorithms and causal inference, our robust experimental design uncovered nine key global and regional factors affecting the distribution of T. japonicus density. A robust experimental design identified nine key factors significantly influencing this density: mean sea-level pressure (msl-0, msl-4), surface pressure (sp-0, sp-4), Summit ozone concentration (Ozone_sum), F10.7 solar flux index (F10.7_index), nitrate concentration at 20 m depth (N3M20), sonar-detected effective vertical range beneath the surface (Height), and survey month (Month). Crucially, stable causal relationships were identified among Ozone_sum, F10.7_index, Height, and N3M20. Variations in Ozone_sum likely impact surface UV radiation levels, influencing plankton dynamics (a primary food source) and potentially larval/juvenile fish survival. The F10.7_index, reflecting solar activity, may affect geomagnetic fields, potentially influencing the migration and orientation behavior of T. japonicus. N3M20 directly modulates primary productivity by limiting phytoplankton growth, thereby shaping the availability and distribution of prey organisms throughout the food web. Height defines the vertical habitat range acoustically detectable, intrinsically linking directly to the vertical distribution and availability of the fish stock itself. Surface pressures (msl-0/sp-0) and their lagged effects (msl-4/sp-4) significantly influence sea surface temperature profiles, ocean currents, and stratification, all critical determinants of suitable habitats and prey aggregation. The strong influence of Month predominantly reflects seasonal changes in water temperature, reproductive cycles, and associated shifts in nutrient supply and plankton blooms. Rigorous robustness checks (Data Subset and Random Common Cause Refutation) confirmed the reliability and consistency of these causal findings. This elucidation of the distinct biological and physical pathways linking these diverse factors leading to T. japonicus density provides a significantly improved foundation for predicting distribution patterns globally and offers concrete scientific insights for sustainable fishery management strategies. Full article

Background: Diabetic foot ulcers (DFUs) are a severe complication of diabetes and are characterized by impaired wound healing and a high amputation risk. Exosomes—which are nanovesicles carrying proteins, RNAs, and lipids—mediate intercellular communication in wound microenvironments, yet their biomarker potential in DFUs remains underexplored. Methods: We analyzed transcriptomic data from GSE134431 (13 DFU vs. 8 controls) as a training set and validated findings in GSE80178 (6 DFU vs. 3 controls). A sum of 7901 differentially expressed genes (DEGs) of DFUs were detected and intersected with 125 literature-curated exosome-related genes (ERGs) to yield 51 candidates. This was followed by GO/KEGG analyses and a PPI network construction. Support vector machine–recursive feature elimination (SVM-RFE) and the Boruta random forest algorithm distilled five biomarkers (DIS3L, EXOSC7, SDC1, STX11, SYT17). Expression trends were confirmed in both datasets. Analyses included nomogram construction, functional and correlation analyses, immune infiltration, GSEA, gene co-expression and regulatory network construction, drug prediction, molecular docking, and RT-qPCR validation in clinical samples. Results: A nomogram combining these markers achieved an acceptable calibration (Hosmer–Lemeshow p = 0.0718, MAE = 0.044). Immune cell infiltration (CIBERSORT) revealed associations between biomarker levels and NK cell and neutrophil subsets. Gene set enrichment analysis (GSEA) implicated IL-17 signaling, proteasome function, and microbial infection pathways. A GeneMANIA network highlighted RNA processing and vesicle trafficking. Transcription factor and miRNA predictions uncovered regulatory circuits, and DGIdb-driven drug repurposing followed by molecular docking identified Indatuximab ravtansine and heparin as high-affinity SDC1 binders. Finally, RT-qPCR validation in clinical DFU tissues (n = 5) recapitulated the bioinformatic expression patterns. Conclusions: We present five exosome-associated genes as novel DFU biomarkers with diagnostic potential and mechanistic links to immune modulation and vesicular transport. These findings lay the groundwork for exosome-based diagnostics and therapeutic targeting in DFU management. Full article

Background/Objectives: Lymph node metastases (LNM) undetected by standard hematoxylin and eosin (H&E) have been associated with unfavorable prognosis in colorectal cancer. The One-Step Nucleic Acid Amplification (OSNA) assay has demonstrated superior sensitivity in detecting LNM compared to H&E. We aimed to assess the performance of OSNA in detecting LNM, as well as its prognostic value in rectal cancer (RC) patients. Methods: Lymph nodes (LNs) of patients from 15 centers were analyzed by both H&E and OSNA. The total tumor load (TTL) was defined as the sum of cytokeratin 19 mRNA copies/µL in all LNs from a surgical specimen, using a threshold of 250 copies/μL for OSNA positivity. Cox proportional hazard regression was used to assess the effect of TTL ≥ 250 or 6000 copies/μL on cancer-specific survival (CSS) and recurrence-free survival (RFS), with Firth’s method applied to account for low event rate. Results: A total of 97 RC patients were included. Of these, 84 patients were eligible for survival analysis. The sensitivity and specificity of OSNA, compared to H&E, were 91.7% and 84.7%, respectively. TTL ≥ 6000 versus <6000 copies/μL was related to worse CSS and RFS. When dividing TTL into three groups: ≤250, 250–6000, and >6000 copies/μL, only TTL ≥ 6000 copies/μL was significantly associated with worse CSS and RFS. Conclusions: The OSNA assay is highly sensitive for detecting LNM in RC patients. A TTL of ≥6000 copies/μL could identify a subset of RC patients with worse CSS and RFS who might benefit from adjuvant treatment or intensive surveillance. Full article

Benzo[a]pyrene is an important indicator of polycyclic aromatic hydrocarbons pollution that exhibits complex atmospheric dynamics influenced by meteorological factors and suspended particulate matter (SPM). Herein, the factors influencing B(a)P concentration were elucidated by analyzing the monthly environmental data for Kyoto, Japan, from 2001 to 2021 using an improved association rule algorithm. Results revealed that B(a)P concentrations were 1.3–3 times higher in cold seasons than in warm seasons and SPM concentrations were lower in cold seasons. The clustering performance was enhanced by optimizing the K-means method using the sum of squared error. The efficiency and reliability of the traditional Apriori algorithm were enhanced by restructuring its candidate itemset generation process, specifically by (1) generating C₂ exclusively from frequent itemset L₁ to avoid redundant database scans and (2) implementing the iterative pruning of nonfrequent subsets during L_k → C_k+1 transitions, adding the lift parameter, and eliminating invalid rules. Strong association rules revealed that B(a)P concentrations ≤ 0.185 ng/m³ were associated with specific meteorological conditions, including humidity ≤ 58%, wind speed ≥ 2 m/s, temperature ≥ 12.3 °C, and pressure ≤ 1009.2 hPa. Among these, changes in pressure had the most substantial impact on the confidence of the association rules, followed by humidity, wind speed, and temperature. Under the influence of high SPM concentrations, favorable meteorological conditions further accelerated pollutant dispersion. B(a)P concentration increased with increasing pressure, decreasing temperature, and decreasing wind speed. Principal component analysis confirmed the robustness and accuracy of our optimized association rule approach in quantifying complex, nonlinear relationships, while providing granular, interpretable insights beyond the traditional methods. Full article

In machine learning, when the labeled portion of data needs to be processed, a semi-supervised learning algorithm is used. A dataset with missing attribute values or labels is referred to as an incomplete information system. Addressing incomplete information within a system poses a significant challenge, which can be effectively tackled through the application of rough set theory (R-theory). However, R-theory has its limits: It fails to consider the frequency of an attribute value and then cannot the distribution of attribute values appropriately. If we consider partially labeled data and replace a missing attribute value with the multiset of all possible attribute values under the same attribute, this results in the emergence of partially labeled multiset-valued data. In a semi-supervised learning algorithm, in order to save time and costs, a large number of redundant features need to be deleted. This study proposes semi-supervised attribute selection algorithms for partially labeled multiset-valued data. Initially, a partially labeled multiset-valued decision information system (p-MSVDIS) is partitioned into two distinct systems: a labeled multiset-valued decision information system (l-MSVDIS) and an unlabeled multiset-valued decision information system (u-MSVDIS). Subsequently, using the indistinguishable relation, distinguishable relation, and dependence function, two types of attribute subset importance in a p-MSVDIS are defined: the weighted sum of l-MSVDIS and u-MSVDIS determined by the missing rate of labels, which can be considered an uncertainty measurement (UM) of a p-MSVDIS. Next, two adaptive semi-supervised attribute selection algorithms for a p-MSVDIS are introduced, which leverage the degrees of importance, allowing for automatic adaptation to diverse missing rates. Finally, experiments and statistical analyses are conducted on 11 datasets. The outcome indicates that the proposed algorithms demonstrate advantages over certain algorithms. Full article

The subset sum problem is a classical NP-hard problem. Various methods have been developed to address this issue, including backtracking techniques, dynamic programming approaches, branch-and-bound strategies, and Monte Carlo methods. In recent years, researchers have proposed several neural network-based methods for solving combinatorial optimization problems, which have shown commendable performance. However, there has been limited research on the performance guarantees of recurrent neural networks (RNNs) when applied to the subset sum problem. In this paper, we conduct a novel investigation into the performance guarantees of RNNs to solve the subset sum problem for the first time. A construction method for RNNs is developed to compute both exact and approximate solutions of subset sum problems, and the mathematical model of each hidden layer in RNNs is rigorously defined. Furthermore, the correctness of the proposed RNNs is strictly proven through mathematical reasoning, and their performance is thoroughly analyzed. In particular, we prove $w^{NN}\ge w^{OPT}(1-\epsilon )$ mathematically, i.e., the errors between the approximate solutions obtained by the proposed ASS-NN model and the actual optimal solutions are relatively small and highly consistent with theoretical expectations. Finally, the validity of RNNs is verified through a series of examples, where the actual error value of the approximate solution aligns closely with the theoretical error value. Additionally, our research reveals that recurrence relations in dynamic programming can effectively simulate the process of constructing solutions. Full article

This paper presents a combinatorial perspective on evaluating the permanent for a rectangular matrix. It proves that the permanent can be computed using the permanents of its largest square submatrices. The proof employs a structured combinatorial method and reveals a connection to the subset-sum problem, known as the grid shading problem. Furthermore, this study uncovers an inherent symmetry in the distribution of terms, highlighting structured patterns within permanent computation. This perspective bridges combinatorial principles with matrix theory, offering new insights into their interplay. Full article