Search Results (1,010)

Despite the introduction of novel therapeutic options, the prognosis of advanced endometrial cancer remains poor. In recent years, increasing attention has been directed toward the molecular characterization of endometrial cancer. However, data specifically focusing on advanced-stage disease are still limited. In our single-center, retrospective, exploratory study with a limited sample size, we analyzed 32 patients with advanced or recurrent endometrial cancer treated at the Modena Cancer Center. Comprehensive molecular profiling was performed to assess DNA mutations, copy number variations, and RNA expression. We characterized the molecular landscape of this cohort, evaluated selected genomic alterations across predefined clinical subgroups, and explored their association with overall survival. Consistent with previous reports, a high prevalence of PTEN and PIK3CA mutations were observed. Patients experiencing relapse more than six months after diagnosis were more likely to harbor CTNNB1 mutations. KRAS mutations were more frequently detected in younger patients and in those with endometrioid histology, whereas PPP2R1A and TP53 mutations were enriched in tumors with non-endometrioid histology. Notably, CTNNB1 mutations were associated with a favorable prognostic impact, while KRAS mutations correlated with poorer overall survival. Our findings underscore the need for further investigation into the molecular landscape of advanced endometrial cancer, particularly in the context of therapeutic implications. Combinatorial treatment strategies targeting specific molecular alterations, such as KRAS, in combination with other targeted agents or therapeutic approaches, warrant further exploration. Full article

This article presents a hybrid optimization model designed to determine the optimal location and operation of capacitor banks in medium-voltage distribution networks, aiming to reduce energy losses and enhance the system’s economic efficiency. The use of reactive power compensation through fixed-step capacitor banks is highlighted as an effective and cost-efficient solution; however, their optimal placement and sizing pose a mixed-integer nonlinear programming optimization challenge of a combinatorial nature. To address this issue, a multi-objective optimization methodology based on the Sine Cosine Algorithm (SCA) is proposed to identify the ideal location and capacity of capacitor banks within distribution networks. This model simultaneously focuses on minimizing technical losses while reducing both investment and operational costs, thereby producing a Pareto front that facilitates the analysis of trade-offs between technical performance and economic viability. The methodology is validated through comprehensive testing on the 33- and 69-bus reference systems. The results demonstrate that the proposed SCA-based approach is computationally efficient, easy to implement, and capable of effectively exploring the search space to identify high-quality Pareto-optimal solutions. These characteristics render the approach a valuable tool for the planning and operation of efficient and resilient distribution networks. Full article

We develop a topological-combinatorial framework applying classical Ramsey theory to systems of arcs connecting points on Jordan curves and their higher-dimensional analogues. A Jordan curve Λ partitions the plane into interior and exterior regions, enabling a canonical two-coloring of every arc connecting points on Λ according to whether its interior lies in Int(Λ) or Ext(Λ). Using this intrinsic coloring, we prove that any configuration of six points on Λ necessarily contains a monochromatic triangle, and that this property is invariant under all homeomorphisms of the plane. Extending the construction by including arcs lying on Λ itself yields a natural three-coloring, from which the classical value $R\left(3,3.3\right)=17$ guarantees the appearance of monochromatic triangles for sufficiently large point sets. For infinite point sets on Λ, the infinite Ramsey theorem ensures the existence of infinite monochromatic cliques, which we likewise show to be preserved under arbitrary topological deformations. The framework extends to Jordan surfaces and Jordan–Brouwer hypersurfaces in higher dimensions, where interior, exterior, and boundary regions again generate canonical colorings and Ramsey-type constraints. These results reveal a general principle: the separation properties of codimension-one topological boundaries induce universal combinatorial structures—such as monochromatic triangles and infinite monochromatic subsets—that are stable under continuous deformations. The approach offers new links between geometric topology, extremal combinatorics, and the analysis of constrained networks and interfaces. Full article

Open data makes it possible to gain insights into the transaction patterns of blockchain projects. These patterns can be modeled as transaction networks, which support a wide range of analytical techniques. Depending on the trade-off between information preservation and complexity reduction, various graph representations can be used to capture additional features, temporal changes, and interoperability between protocols. Different analytical approaches, including calculating graph metrics or applying graph neural networks, can reveal hidden structures, uncover unusual activities, detect anomalies, and provide a clearer picture of the dynamics of blockchain projects. While network science metrics and machine learning methods have been extensively applied to transaction networks, graph combinatorial optimization problems remain largely underexplored in this domain, despite their potential to identify critical nodes, hidden substructures, and flow patterns. The goal of this paper is to assess the applicability of graph combinatorial optimization problems to blockchain transaction networks, systematically review existing analytics approaches, discuss their respective strengths and limitations, and explore how combining different techniques can yield deeper insights into the structural and functional properties of blockchain ecosystems. Full article

Previous studies, constrained by the overly rigid stability requirements, often fail to adapt to complex systems and struggle to identify stable outcomes that align with the practical context of multi-agent resource allocation. To address the three-sided matching problem in complex socio-technical and business management systems, this paper proposes a fuzzy stable matching method for three-sided agents under a framework of combinatorial preference relations, integrating network and decision theory. First, we construct a membership function to measure the degree of preference satisfaction between elements of different agents, and then define the concept of fuzzy stability. By incorporating preference satisfaction, we introduce the notion of fuzzy blocking strength and derive the generation conditions for blocking triples and fuzzy stability under the fuzzy stable criterion. Furthermore, we abstract the three-sided matching problem with combined preference relations into a shortest path problem. Second, we prove the equivalence between the shortest path solution and the stable matching outcome. We adopt Dijkstra’s algorithm for problem-solving and derive the time complexity of the algorithm under the pruning strategy. Finally, we apply the proposed model and algorithm to a case study of project assignment in software companies, thereby verifying the feasibility and effectiveness of this three-sided matching method. Compared with existing approaches, the fuzzy stable matching method developed in this study demonstrates distinct advantages in handling preference uncertainty and system complexity. It provides a more universal theoretical tool and computational approach for solving flexible resource allocation problems prevalent in real-world scenarios. Full article

Pareto local search (PLS) serves as an important component in multi-objective combinatorial optimization. Nevertheless, achieving a balance between convergence and diversity remains a challenge, as few studies have leveraged knowledge from the search archive to effectively guide the PLS process. This paper proposes an archive entropy-guided Pareto local search algorithm (AEG-PLS). In the proposed method, the objective space is partitioned into subregions using a set of reference vectors. The archive entropy is then computed for each subregion to assess population diversity. To enhance diversity in less explored areas, a PLS is initiated using a well-performing solution selected from the subregion with the lowest entropy, thus indicating the weakest diversity. This approach promotes a more balanced trade-off between convergence and diversity throughout the optimization process. Experimental results on 25 multi-objective combinatorial optimization benchmark instances demonstrate that the proposed AEG-PLS achieves competitive performance in terms of both Inverted Generational Distance and Hypervolume metrics when compared to nine state-of-the-art multi-objective evolutionary algorithms. Full article

Petroleum coke quality strongly influences refinery economics and downstream energy use, yet real-time control is constrained by slow quality assays and a 24–48 h lag in laboratory results. This study introduces a physics-informed combinatorial digital twin for value-optimized coking, aimed at improving energy efficiency and environmental performance through adaptive quality forecasting. The approach builds a modular library of 32 candidate equations grouped into eight quality parameters and links them via cross-parameter dependencies. A two-level optimization scheme is applied: a genetic algorithm selects the best model combination, while a secondary loop tunes parameters under a multi-objective fitness function balancing accuracy, interpretability, and computational cost. Validation on five clustered operating regimes (industrial patterns augmented with noise-perturbed synthetic data) shows that optimal model ensembles outperform single best models, achieving typical cluster errors of ~7–13% NMAE. The developed digital twin framework enables accurate prediction of coke quality parameters that are critical for its energy applications, such as volatile matter and sulfur content, which serve as direct proxies for estimating the net calorific value and environmental footprint of coke as a fuel. Full article

Let R be an axis-aligned rectangle. We define a floorplan as a partition of R into rectangular regions (rooms) such that each vertex is shared by at most three rooms. Following the approach of Nakano et al.,we also assume the presence of a set of points that impose constraints on the walls passing through them, allowing only horizontal or vertical segments. These constraints can be encoded by a permutation matrix whose entries are labeled H and V, which we refer to as a pattern matrix. In this work, we characterize the well-known classes of guillotine, diagonal, and diagonal–guillotine floorplans in terms of the presence of specific families of pattern matrices. In this way, we translate a purely geometric characterization into a combinatorial one. Full article

The design of aircraft components is a complex process that must simultaneously account for environmental impact, manufacturability, cost and structural performance to meet modern regulatory requirements and sustainability objectives. When these factors are integrated from the early design stages, the approach transcends traditional eco-design and becomes a genuinely sustainability-oriented design methodology. This study proposes a sustainability-driven design framework for aircraft components and demonstrates its application to a fuselage panel consisting of a curved skin, four frames, seven stringers, and twenty-four clips. The design variables investigated include the material selection, joining methods, and subcomponent thicknesses. The design space is constructed through a combinatorial generation process coupled with compatibility and feasibility constraints. Sustainability criteria are evaluated using a combination of parametric Life Cycle Assessment (LCA) and Life Cycle Costing (LCC) regression models, parametric Finite Element Analysis (FEA), and Random Forest surrogate modeling trained on a stratified set of simulation results. Two methodological pathways are introduced: 1. Cluster-based optimization, involving customized clustering followed by multi-criteria decision-making (MCDM) within each cluster. 2. Global optimization, performed across the full decision matrix using Pareto front analysis and MCDM techniques. A stability analysis of five objective-weighting methods and four normalization techniques is conducted to identify the most robust methodological configuration. The results—based on a full cradle-to-grave assessment that includes the use phase over a 30-year A319 aircraft operational lifetime—show that the thermoplastic CFRP panel joined by welding emerges as the most sustainable design alternative. Full article

The nonholonomic constraints of fixed-wing UAVs, characterized by coupled heading-curvature feasibility and asymmetric costs, fundamentally deviate from classical Euclidean routing assumptions. While standard neural combinatorial optimization (NCO) architectures could theoretically incorporate Dubins costs via reward signals, such naive adaptations lack the capacity to explicitly model the intrinsic SE(2) geometric invariance and directional asymmetry of fixed-wing motion, leading to suboptimal generalization. To bridge this gap, we propose a Dubins-Aware NCO framework. We design a dual-channel embedding to decouple asymmetric physical distances from rotation-stable geometric features. Furthermore, we introduce a Rotary Phase Encoding (RoPhE) mechanism that theoretically guarantees strict SO(2) equivariance within the attention layer. Extensive sensitivity, ablation, and cross-distribution generalization experiments are conducted on tasks spanning varying turning radii and problem variants with instance scales of 10, 20, 36, and 52 nodes. The results consistently validate the superior optimality and stability of our approach compared with state-of-the-art DRL and NCO baselines, while maintaining significant computational efficiency advantages over classical heuristics. Our results highlight the importance of explicitly embedding geometry-physics consistency, rather than relying on scalar reward signals, for real-world fixed-wing autonomous scheduling. Full article

This paper introduces novel subfamilies of analytic and bi-univalent functions in $\mathrm{\Omega }=\left\{\varsigma \in \mathbb{C}:\left|\varsigma \right|<1\right\}$, defined by applying a linear operator associated with the Mittag–Leffler function and requiring subordination to domains related to generalized bivariate Fibonacci polynomials. The proposed framework provides a unified treatment that generalizes numerous earlier studies by incorporating parameters controlling both the operator’s fractional calculus features and the domain’s combinatorial geometry. For these subfamilies, we establish initial coefficient bounds ($\left|d_2\right|$, $\left|d_3\right|$) and solve the Fekete–Szegö problem ($\left|d_3-\xi d_2^2\right|$). The derived inequalities are interesting, and their proofs leverage the intricate interplay between the series expansions of the Mittag–Leffler function and the generating function of the Fibonacci polynomials. By specializing the parameters governing the operator and the polynomial domain, we show how our main theorems systematically recover and extend a wide range of known results from the literature, thereby demonstrating the generality and unifying power of our approach. Full article

The computational tractability of Integrated Information Theory (IIT) is fundamentally constrained by the exponential cost of identifying the Minimum Information Partition (MIP), which is required to quantify integrated information (Φ). Existing approaches become impractical beyond ~15–20 variables, limiting IIT analyses on realistic neural and complex systems. We introduce GeoMIP, a geometric–topological framework that recasts the MIP search as a graph-based optimization problem on the n-dimensional hypercube graph: discrete system states are modeled as graph vertices, and Hamming distance adjacency defines edges and shortest-path structures. Building on a tensor-decomposed representation of the transition probabilities, GeoMIP constructs a transition-cost (ground cost) structure by dynamic programming over graph neighborhoods and BFS-like exploration by Hamming levels, exploiting hypercube symmetries to reduce redundant evaluations. We validate GeoMIP against PyPhi, ensuring reliability of MIP identification and Φ computation. Across multiple implementations, GeoMIP achieves 165–326× speedups over PyPhi while maintaining 98–100% agreement in partition identification. Heuristic extensions further enable analyses up to ~25 variables, substantially expanding the practical IIT regime. Overall, by leveraging the hypercube’s explicit graph structure (vertices, edges, shortest paths, and automorphisms), GeoMIP turns an intractable combinatorial search into a scalable graph-based procedure for IIT partitioning. Full article

Grammar induction runs into a serious problem due to the exponential growth of the number of possible derivation trees as sentence length increases, which makes unsupervised parsing both computationally demanding and highly indeterminate. This paper proposes a mathematics-based approach that alleviates this combinatorial complexity by introducing structural constraints based on Catalan and Fuss–Catalan numbers. By limiting the depth of the tree, the degree of branching and the form of derivation, the method significantly narrows the search space, while retaining the full generative power of context-free grammars. A filtering algorithm guided by Catalan structures is developed that incorporates these combinatorial constraints directly into the execution process, with formal analysis showing that the search complexity, under realistic assumptions about depth and richness, decreases from exponential to approximately polynomial. Experimental results on synthetic and natural-language datasets show that the Catalan-constrained model reduces candidate derivation trees by approximately 60%, improves F1 accuracy over unconstrained and depth-bounded baselines, and nearly halves average parsing time. Qualitative evaluation further indicates that the induced grammars exhibit more balanced and linguistically plausible structures. These findings demonstrate that Catalan-based structural constraints provide an elegant and effective mechanism for controlling ambiguity in grammar induction, bridging formal combinatorics with practical syntactic learning. Full article

Emergency supplies allocation is a critical task in post-disaster response, as ineffective or delayed decisions can directly lead to increased human suffering and loss of life. In practice, emergency managers must make rapid allocation decisions over multiple periods under incomplete information and highly unpredictable demand, making robust and adaptive decision support essential. However, existing allocation approaches face several challenges: (1) Those traditional approaches rely heavily on predefined uncertainty sets or probabilistic models, and are inherently static, making them unsuitable for multi-period, dynamically allocation problems; and (2) while reinforcement learning (RL) technique is inherently suitable for dynamic decision-making, most existing RL-base approaches assume fixed demand, making them unable to cope with the non-stationary demand patterns seen in real disasters. To address these challenges, we first establish a multi-period and multi-objective emergency supplies allocation problem with demand uncertainty and then formulate it as a two-player zero-sum Markov game (TZMG). Demand uncertainty is modeled through an adversary rather than predefined uncertainty sets. We then propose RESA, a novel RL framework that uses adversarial training to learn robust allocation policies. In addition, RESA introduces a combinatorial action representation and reward clipping methods to handle high-dimensional allocations and nonlinear objectives. Building on RESA, we develop RESA_PPO by employing proximal policy optimization as its policy optimizer. Experiment results with realistic post-disaster data show that RESA_PPO achieves near-optimal performance, with an average gap of only 3.7% in terms of the objective value of the formulated problem, from the theoretical optimum derived by exact solvers. Moreover, RESA_PPO outperforms all baseline methods, including heuristic and standard RL methods, by at least 5.25% on average. Full article

High-entropy alloys (HEAs) have attracted significant attention due to their exceptional physical, chemical, and mechanical properties. The current development of HEAs primarily depends on time-consuming and costly trial-and-error approaches, which not only hinder the efficient exploration of new compositions but also result in unnecessary resource and energy consumption, thereby negatively affecting sustainable development and production. To address this challenge, this study introduces a machine learning-based methodology for predicting the yield strengths of various HEA compositions. The model was trained using 181 data points and achieved an R² performance score of 0.85. To further assess its reliability and generalization capability, the model was validated using external data not included in the collected dataset. The validation was performed across four categories: modified Cantor alloys, refractory HEAs, eutectic HEAs, and other HEAs. The predicted yield strength trends were found to align with the actual experimental trends, demonstrating the model’s robust performance across various categories of HEAs. The proposed machine learning approach is expected to facilitate the combinatorial design of HEAs, thereby enabling efficient optimization of compositions and accelerating the development of novel alloys. Moreover, it has the potential to serve as a guideline for sustainable alloy design and environmentally conscious production in future HEA development. Full article