Minimal Subset Research Articles

Determining the Identity of Nucleotides and the Energy of Binding of tRNAs to Their Aminoacyl-tRNA Synthetases Using a Simple Logistic Model

This study showed that the predictor in logistic regression can be applied to estimating the Gibbs free energy of tRNAs’ recognition of and binding to their aminoacyl-tRNA synthetases. Then, 24 linear logistic regression models predicting different classes of tRNAs loaded with a corresponding amino acid were trained in a machine learning classification method, reducing the misclassification error to zero. The models were based on minimal subsets of Boolean explanatory variables describing the favorite presence of nucleotides or nucleosides localized in the different parts of the tRNA. In 90% of cases, they agree with the components of the consensus strand in a class of tRNAs loaded by a given amino acid. According to the proposed theoretical model, the values of the free energy for the entry of the recognition state in the process of tRNA charging were obtained, and the inputs from identity nucleotides and the tRNA strand backbone were distinguished. Almost all the resulting models indicated leading anticodon tandems defining the first and second positions of the anticodon (positions 35 and 36 of the tRNA strand) and the small sets (up to six positions) of the other nucleotides as the natural identity nucleotides most influential in the free energy balance. The magnitude of their input to this energy depends on the position in the strand, favoring positions −1, 35, and 36. The role of position 34 is relatively smaller. These identity attributes may not always be fully arranged in a real single adaptor molecule but were comprehensively present in a given tRNA class. A detailed analysis of the resulting models showed that the absolute value of the energy of binding the tandem 35–36 decreases with the number of identity positions, as well as with the decreasing number of possible hydrogen bonds. On the other hand, in these conditions, the absolute value of the energy of binding of other identity nucleotides increases. All the models indicate that the nucleotide-independent energy of the repulsion tRNA backbone decreases with the number of identity nucleotides. It was also shown that the total free energy change in entering the recognition state increases with the amino acid mass, making this process less spontaneous, which may have an evolutionary reference.

A deep reinforcement learning approach towards distributed Function as a Service (FaaS) based edge application orchestration in cloud-edge continuum

Serverless computing has emerged as a new cloud computing model which in contrast to IoT offers unlimited and scalable access to resources. This paradigm improves resource utilization, cost, scalability and resource management specifically in terms of irregular incoming traffic. While cloud computing has been known as a reliable computing and storage solution to host IoT applications, it is not suitable for bandwidth limited, real time and secure applications. Therefore, shifting the resources of the cloud-edge continuum towards the edge can mitigate these limitations. In serverless architecture, applications implemented as Function as a Service (FaaS), include a set of chained event-driven microservices which have to be assigned to available instances. IoT microservices orchestration is still a challenging issue in serverless computing architecture due to IoT dynamic, heterogeneous and large-scale environment with limited resources. The integration of FaaS and distributed Deep Reinforcement Learning (DRL) can transform serverless computing by improving microservice execution effectiveness and optimizing real-time application orchestration. This combination improves scalability and adaptability across the edge-cloud continuum. In this paper, we present a novel Deep Reinforcement Learning (DRL) based microservice orchestration approach for the serverless edge-cloud continuum to minimize resource utilization and delay. This approach, unlike existing methods, is distributed and requires a minimum subset of realistic data in each interval to find optimal compositions in the proposed edge serverless architecture and is thus suitable for IoT environment. Experiments conducted using a number of real-world scenarios demonstrate improvement of the number of successfully composed applications by 18%, respectively, compared to state-of-the art methods including Load Balance, Shortest Path algorithms.

Feature selection via robust weighted score for high dimensional binary class-imbalanced gene expression data

In this paper, a robust weighted score for unbalanced data (ROWSU) is proposed for selecting the most discriminative features for high dimensional gene expression binary classification with class-imbalance problem. The method addresses one of the most challenging problems of highly skewed class distributions in gene expression datasets that adversely affect the performance of classification algorithms. First, the training dataset is balanced by synthetically generating data points from minority class observations. Second, a minimum subset of genes is selected using a greedy search approach. Third, a novel weighted robust score, where the weights are computed by support vectors, is introduced to obtain a refined set of genes. The highest scoring genes based on this approach are combined with the minimum subset of genes selected by the greedy search approach to form the final set of genes. The novel method ensures the selection of the most discriminative genes, even in the presence of skewed class distribution, thereby improving the performance of the classifiers. The performance of the proposed ROWSU method is evaluated on 7 gene expression datasets. Classification accuracy, sensitivity and F1-score are used as performance metrics to compare the proposed ROWSU algorithm with several other state-of-the-art methods. Boxplots and stability plots are also constructed for a better understanding of the results. The results show that the proposed method outperforms the existing feature selection procedures based on classification performance from k nearest neighbors (kNN) and random forest (RF) classifiers.

Prediction of Acrylonitrile-Butadiene-Styrene Mechanical Properties through Compressed-Sensing Techniques.

One of the challenges in the plastic industry is the cost and time spent on the characterization of different grades of polymers. Compressed sensing is a data reconstruction method that combines linear algebra with optimization schemes to retrieve a signal from a limited set of measurements of that signal. Using a data set of signal examples, a tailored basis can be constructed, allowing for the optimization of the measurements that should be conducted to provide the highest and most robust signal reconstruction accuracy. In this work, compressed sensing was used to predict the values of numerous properties based on measurements for a small subset of those properties. A data set of 21 fully characterized acrylonitrile-butadiene-styrene samples was used to construct a tailored basis to determine the minimal subset of properties to measure to achieve high reconstruction accuracy for the remaining nonmeasured properties. The analysis showed that using only six measured properties, an average reconstruction error of less than 5% can be achieved. In addition, by increasing the number of measured properties to nine, an average error of less than 3% was achieved. Compressed sensing enables experts in academia and industry to substantially reduce the number of properties that must be measured to fully and accurately characterize plastics, ultimately saving both costs and time. In future work, the method should be expanded to optimize not only individual properties but also entire tests used to simultaneously measure multiple properties. Furthermore, this approach can also be applied to recycled materials, of which the properties are more difficult to predict.

Predicting invasion in early-stage ground-glass opacity pulmonary adenocarcinoma: a radiomics-based machine learning approach

BackgroundTo design a pulmonary ground-glass nodules (GGN) classification method based on computed tomography (CT) radiomics and machine learning for prediction of invasion in early-stage ground-glass opacity (GGO) pulmonary adenocarcinoma.MethodsThis retrospective study included pulmonary GGN patients who were histologically confirmed to have adenocarcinoma in situ (AIS), minimally invasive adenocarcinoma (MIA), or invasive adenocarcinoma cancer (IAC) from 2020 to 2023. CT images of all patients were automatically segmented and 107 radiomic features were obtained for each patient. Classification models were developed using random forest (RF) and cross-validation, including three one-versus-others models and one three-class model. For each model, features were ranked by normalized Gini importance, and a minimal subset was selected with a cumulative importance exceeding 0.9. These selected features were then used to train the final models. The models’ performance metrics, including area under the curve (AUC), accuracy, sensitivity, and specificity, were computed. AUC and accuracy were compared to determine the final optimal method.ResultsThe study comprised 193 patients (mean age 54 ± 11 years, 65 men), including 65 AIS, 54 MIA, and 74 IAC, divided into one training cohort (N = 154) and one test cohort (N = 39). The final three-class RF model outperformed three individual one-versus-others models in distinguishing each class from the other two. For the multiclass classification model, the AUC, accuracy, sensitivity, and specificity were 0.87, 0.79, 0.62, and 0.88 for AIS; 0.90, 0.79, 0.54, and 0.89 for MIA; and 0.87, 0.69, 0.73, and 0.67 for IAC, respectively.ConclusionsA radiomics-based multiclass RF model could effectively differentiate three types of pulmonary GGN, which enabled early diagnosis of GGO pulmonary adenocarcinoma.

62 Prognostic biomarker development using deep learning and spatial proteomics in papillary renal cell carcinoma

Abstract Background Papillary renal cell carcinoma (pRCC) is a prevalent but understudied kidney cancer pathology, constituting 15-20% of cases. While many patients achieve curative therapy using nephrectomy, others go on to develop progressive, metastatic disease with poor overall prognosis. In order to improve the current standards of care for pRCC patients, it is critical to identify new methods to identify high-risk patients likely to require more intense and risk-modulated follow-up. Our goals in this project are two-fold: (1) to identify prognostic patient clusters based on spatial architecture of tumor tissue, and (2) to identify a minimal subset of markers to accurately predict the defined clusters for clinical translation. Methods A tissue microarray of 100 pRCC patients was assayed using multiplex immunofluorescence with a 31-antibody panel with immune- and cancer-related proteins. We have developed novel algorithms to identify spatial neighborhoods and features. These features are then used to identify unsupervised clusters of patients. This new approach to classifying patients allows for a more specific and comprehensive description of each patient tumor’s spatial composition and association with diverse clinical outcomes. Next, we developed attention-based deep learning models capable of predicting these spatially-defined clusters directly from the underlying immunofluorescence images and subsequently profiled these for interpretability by retraining based on individual channels. We assessed each model iteratively on a validation set and a held-out test set for final model selection. We focussed on developing an accurate model with the minimal number of channels to enable development of a cost-efficient biomarker assay for the clinic. Results We performed a systematic analysis of the cellular and spatial phenotypes for each patient in our cohort and identified six (6) major spatial clusters. These clusters are based on the spatial neighborhood composition of the tumors (Fig 1A) and describe the composite effects of cell-cell interactions within a patient tumor. We identified one cluster in particular (cluster #6, mainly associated with spatial interaction of CD163+ macrophages) with a significantly worse prognosis than the other clusters. Using our advanced deep learning models, we have been able to achieve excellent validation accuracy in predicting a variety of clinical phenotypes and spatial features, including patient clusters and histological grade. We wished to then reduce the set of required features and began our efforts in predicting tumor vs. normal based on individual immunofluorescence channels and identified 6 channels with >75% individual predictive accuracy (Fig. 1B). Compositing all 6 markers further improves our accuracy to 90%. This success paves the way for exciting future prospects as we work to extend these efforts to identify a minimal clinically-applicable subset of protein markers. Conclusions The combination of computational spatial proteomics and deep learning models has the potential to identify new biomarkers specific to the spatial organization of patient tumors. We have identified a particular patient cluster with multiple associations with CD163+ macrophages demonstrating poor prognosis; selecting these patients may allow for tailored and more informed patient care. We are also working to enhance our deep learning models to circumvent the need for stepwise spatial analysis and, instead, allow for direct-from-image assessment of patients for particular spatial features indicative of various prognostic indicators. Our identified set of 6 markers serves as a basis for further refinements as we work to identify a minimal set of relevant markers able to predict various clinical outcomes from immunofluorescence imaging, offering a promising new avenue in the field of cancer pathology and biomarker development. DOD CDMRP Funding: yes

Diagnosing infeasible optimization problems using large language models

Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields, such as economics, engineering, transportation, and health care. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat’s reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.

Fast Robust Point Cloud Registration Based on Compatibility Graph and Accelerated Guided Sampling

Point cloud registration is a crucial technique in photogrammetry, remote sensing, etc. A generalized 3D point cloud registration framework has been developed to estimate the optimal rigid transformation between two point clouds using 3D key point correspondences. However, challenges arise due to the uncertainty in 3D key point detection techniques and the similarity of local surface features. These factors often lead to feature descriptors establishing correspondences containing significant outliers. Current point cloud registration algorithms are typically hindered by these outliers, affecting both their efficiency and accuracy. In this paper, we propose a fast and robust point cloud registration method based on a compatibility graph and accelerated guided sampling. By constructing a compatible graph with correspondences, a minimum subset sampling method combining compatible edge sampling and compatible vertex sampling is proposed to reduce the influence of outliers on the estimation of the registration parameters. Additionally, an accelerated guided sampling strategy based on preference scores is presented, which effectively utilizes model parameters generated during the iterative process to guide the sampling toward inliers, thereby enhancing computational efficiency and the probability of estimating optimal parameters. Experiments are carried out on both synthetic and real-world data. The experimental results demonstrate that our proposed algorithm achieves a significant balance between registration accuracy and efficiency compared to state-of-the-art registration algorithms such as RANSIC and GROR. Even with up to 2000 initial correspondences and an outlier ratio of 99%, our algorithm achieves a minimum rotation error of 0.737° and a minimum translation error of 0.0201 m, completing the registration process within 1 s.

Efficient and Intelligent Feature Selection via Maximum Conditional Mutual Information for Microarray Data

The challenge of analyzing microarray datasets is significantly compounded by the curse of dimensionality and the complexity of feature interactions. Addressing this, we propose a novel feature selection algorithm based on maximum conditional mutual information (MCMI) to identify a minimal feature subset that is maximally relevant and non-redundant. This algorithm leverages a greedy search strategy, prioritizing both feature quality and classification performance. Experimental results on high-dimensional microarray datasets demonstrate our algorithm’s superior ability to reduce dimensionality, eliminate redundancy, and enhance classification accuracy. Compared to existing filter feature selection methods, our approach exhibits higher adaptability and intelligence.

GraphSlimmer: Preserving Read Mappability with the Minimum Number of Variants.

Modern genomic datasets, like those generated under the 1000 Genome Project, contain millions of variants belonging to known haplotypes. Although these datasets are more representative than a single reference sequence and can alleviate issues like reference bias, they are significantly more computationally burdensome to work with, often involving large-indexed genome graph data structures for tasks such as read mapping. The construction, preprocessing, and mapping algorithms can require substantial computational resources depending on the size of these variant sets. Moreover, the accuracy of mapping algorithms has been shown to decrease when working with complete variant sets. Therefore, a drastically reduced set of variants that preserves important properties of the original set is desirable. This work provides a technique for finding a minimal subset of variants such that for given parameters α and δ, all substrings up to length α in the haplotypes are guaranteed to be still alignable to the appropriate locations with either Hamming or edit distance at most δ, using only . Our contributions include showing the NP-hardness and inapproximability of these optimization problems and providing Integer Linear Programming (ILP) formulations. Our edit distance ILP formulation carefully decomposes the problem according to variant locations, which allows it to scale to support all of chromosome 22's variants from the 1000 Genome Project. Our experiments also demonstrate a significant reduction in the number of variants. For example, for moderately long reads, e.g., α = 1000, over 75% of the variants can be removed while preserving read mappability with edit distance at most one.

Fecal calprotectin and platelet count predict histologic disease activity in pediatric ulcerative colitis: results from a projection-predictive feature selection

Especially for pediatric patients, proxies of mucosal inflammation are needed. The Pediatric Ulcerative Colitis Activity Index (PUCAI) has been established to predict clinical and endoscopic disease activity. However, histologic inflammation might persist. We applied a special variable selection technique to predict histologic healing in pediatric ulcerative colitis (UC) as parsimoniously (but still as precisely) as possible. The retrospective analysis included data from two study cohorts, comprising 91 visits from 59 pediatric patients with UC. A Bayesian ordinal regression model was used in combination with a projection-predictive feature selection (PPFS) to identify a minimal subset of clinical and laboratory parameters sufficient for the prediction of histologic disease activity. Following the PPFS, CEDATA-GPGE patient registry data were analyzed to investigate the relevance of the selected predictors in relation to PUCAI and Physician Global Assessment (PGA) in up to 6697 patient visits. Fecal calprotectin (FC) and platelet count were identified as the minimal subset of predictors sufficient for prediction of histologic disease activity in pediatric UC. FC and platelet count also appeared to be associated with increasing disease activity as measured by PUCAI and PGA in the CEDATA-GPGE registry. Based on the selected model, predictions can be performed with a Shiny web app. Conclusion: Our statistical approach constitutes a reproducible and objective tool to select a minimal subset of the most informative parameters to predict histologic inflammation in pediatric UC. A Shiny app shows how physicians may predict the histologic activity in a user-friendly way using FC and platelet count. To generalize the findings, further prospective studies will be needed.What is Known:• Histologic healing is a major endpoint in the therapy of ulcerative colitis (UC).• The PUCAI score has been established to predict disease activity in pediatric UC but is not suitable for the prediction of histologic healing.What is New:• Our Bayesian ordinal regression model in combination with a projection-predictive feature selection is a reproducible and objective tool to select the minimal subset of clinical and laboratory parameters to predict histologic inflammation in pediatric UC.• Histologic inflammation in pediatric UC can be non-invasively predicted based on the combination of fecal calprotectin levels and platelet count.

COUNTING IN UNCOUNTABLY CATEGORICAL PSEUDOFINITE STRUCTURES

Abstract We show that every definable subset of an uncountably categorical pseudofinite structure has pseudofinite cardinality which is polynomial (over the rationals) in the size of any strongly minimal subset, with the degree of the polynomial equal to the Morley rank of the subset. From this fact, we show that classes of finite structures whose ultraproducts all satisfy the same uncountably categorical theory are polynomial R-mecs as well as N-dimensional asymptotic classes, where N is the Morley rank of the theory.

Generating Minimal Training Sets for Machine Learned Potentials.

This Letter presents a novel approach for identifying uncorrelated atomic configurations from extensive datasets with a nonstandard neural network workflow known as random network distillation (RND) for training machine-learned interatomic potentials (MLPs). This method is coupled with a DFT workflow wherein initial data are generated with cheaper classical methods before only the minimal subset is passed to a more computationally expensive abinitio calculation. This benefits training not only by reducing the number of expensive DFT calculations required but also by providing a pathway to the use of more accurate quantum mechanical calculations. The method's efficacy is demonstrated by constructing machine-learned interatomic potentials for the molten salts KCl and NaCl. Our RND method allows accurate models to be fit on minimal datasets, as small as 32 configurations, reducing the required structures by at least 1 order of magnitude compared to alternative methods. This reduction in dataset sizes not only substantially reduces computational overhead for training data generation but also provides a more comprehensive starting point for active-learning procedures.

Granular computing in zero-divisor graphs of [formula omitted]

In this article, we study the zero-divisor graphs Γ(Zn) of rings of integers modulo n as information systems I(Γ(Zn)) using equivalence classes and rough sets. Equivalence classes are referred as granules and partitions are referred as indiscernible partitions. We define an indiscernibility relation on the vertex set and identify different sets of attributes that induce the same indiscernibility partition. A reduct is a minimal subset of attributes which yields the same partition as the original attribute set. We compute all reducts of the defined information system and classify them in to two types including: (i) the set P of all prime divisors of n and (ii) the set consisting of P∖pi, prime powers of pi in the prime factorization of n and the elements of the form pipj, where pj∈P∖pi. Moreover, we give the structures and the cardinalities of the attribute subsets whose removal yields a different indiscernibility partition than that of the set of all attributes, referred as essential sets. We prove that the essential sets of I(Γ(Zn)) either consist of two prime divisors of n or one prime divisor pi combined with prime powers of pi. Further, we determine the lower and upper approximations of various vertex subsets to study the properties of the zero-divisor graphs. We also study properties of the rough membership function for Γ(Zn). Furthermore, we introduce the class-based discernibility matrix induced by indiscernibility classes of zero divisors and determine general form of its entries. We also prove that the minimal entries of the class-based discernibility matrix coincide with the essential sets of Γ(Zn). Based on these results, we determine information-granularity measures corresponding to the notable partitions of Γ(Zn) and provide an example to establish consistency of the proved results with these well-known measures. Thus, starting from introducing an information system, we investigate the components of granular computing and utilize our findings to compute information granularity measures, contributing to a deeper understanding of the zero divisor graphs via rough set theory.

A recursive framework for improving the performance of multi-objective differential evolution algorithms for gene selection

Gene selection is a pivotal process in machine-learning-driven medical diagnostics, where the goal is to identify a subset of genes from microarray expression profiles that can enhance the predictive accuracy of classifiers for disease diagnosis. The two key objectives of gene selection are to reduce the dimensionality of the data and to improve the accuracy of disease diagnosis, which is typically a multi-objective optimization problem. In recent years, multi-objective evolutionary algorithms (MOEAs) have gained wide attention in feature selection research, and several related algorithms have been produced. However, most algorithms tend to get stuck in local optimality when searching for solutions from a high-dimensional space. To solve the gene selection problem effectively, this study introduces a recursive multi-objective differential evolution algorithm with elite recursive strategy (RMODE-E) and a recursive multi-objective differential evolution algorithm with Pareto front recursive strategy (RMODE-P). RMODE-E amalgamates the features selected by the top E elite individuals, RMODE-P consolidates the features selected by the Pareto front set, and the combined features then serve as the foundation for subsequent recursive rounds of searching. The proposed feature subspace combination strategy not only reduces the recursive search space but also improves the capacity to find globally optimal feature subsets. Extensive experiments were conducted to compare our proposed algorithms with eight state-of-the-art evolutionary algorithms to validate their effectiveness. Experimental results demonstrate that RMODE-P has better global search capability as it achieves better best classification accuracy, mean classification accuracy, and minimal gene subset size.

Detecting k-Vertex Cuts in Sparse Networks via a Fast Local Search Approach

The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -vertex cut ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -VC) problem belongs to the family of the critical node detection problems, which aims to find a minimum subset of vertices whose removal decomposes a graph into at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> connected components. It is an important NP-hard problem with various real-world applications, e.g., vulnerability assessment, carbon emissions tracking, epidemic control, drug design, emergency response, network security, and social network analysis. In this article, we propose a fast local search (FLS) approach to solve it. It integrates a two-stage vertex exchange strategy based on neighborhood decomposition and cut vertex, and iteratively executes operations of addition and removal during the search. Extensive experiments on both intersection graphs of linear systems and coloring/DIMACS graphs are conducted to evaluate its performance. Empirical results show that it significantly outperforms the state-of-the-art (SOTA) algorithms in terms of both solution quality and computation time in most of the instances. To evaluate its generalization ability, we simply extend it to solve the weighted version of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -VC problem. FLS also demonstrates its excellent performance.

Axiomatic Aggregations of Abductive Explanations

The recent criticisms of the robustness of post hoc model approximation explanation methods (like LIME and SHAP) have led to the rise of model-precise abductive explanations. For each data point, abductive explanations provide a minimal subset of features that are sufficient to generate the outcome. While theoretically sound and rigorous, abductive explanations suffer from a major issue --- there can be several valid abductive explanations for the same data point. In such cases, providing a single abductive explanation can be insufficient; on the other hand, providing all valid abductive explanations can be incomprehensible due to their size. In this work, we solve this issue by aggregating the many possible abductive explanations into feature importance scores. We propose three aggregation methods: two based on power indices from cooperative game theory and a third based on a well-known measure of causal strength. We characterize these three methods axiomatically, showing that each of them uniquely satisfies a set of desirable properties. We also evaluate them on multiple datasets and show that these explanations are robust to the attacks that fool SHAP and LIME.

Threshold-Based Responsive Simulated Annealing for Directed Feedback Vertex Set Problem

As a classical NP-hard problem and the topic of the PACE 2022 competition, the directed feedback vertex set problem (DFVSP) aims to find a minimum subset of vertices such that, when vertices in the subset and all their adjacent edges are removed from the directed graph, the remainder graph is acyclic. In this paper, we propose a threshold-based responsive simulated annealing algorithm called TRSA for solving DFVSP. First, we simplify the problem instances with two new reduction rules proposed in this paper and eight reduction rules from the literature. Then, based on a new solution representation, TRSA solves DFVSP with a fast local search procedure featured by a swap-based neighborhood structure and three neighborhood acceleration strategies. Finally, all these strategies are incorporated into a threshold-based responsive simulated annealing framework. Computational experiments on 140 benchmark instances show that TRSA is highly competitive compared to the state-of-the-art methods. Specifically, TRSA can improve the best known results for 53 instances, while matching the best known results for 79 ones. Furthermore, some important features of TRSA are analyzed to identify its success factors.

On denseness of horospheres in higher rank homogeneous spaces

Abstract Let $ G $ be a connected semisimple real algebraic group and $\Gamma &lt;G$ be a Zariski dense discrete subgroup. Let N denote a maximal horospherical subgroup of G, and $P=MAN$ the minimal parabolic subgroup which is the normalizer of N. Let $\mathcal E$ denote the unique P-minimal subset of $\Gamma \backslash G$ and let $\mathcal E_0$ be a $P^\circ $ -minimal subset. We consider a notion of a horospherical limit point in the Furstenberg boundary $ G/P $ and show that the following are equivalent for any $[g]\in \mathcal E_0$ : (1) $gP\in G/P$ is a horospherical limit point; (2) $[g]NM$ is dense in $\mathcal E$ ; (3) $[g]N$ is dense in $\mathcal E_0$ . The equivalence of items (1) and (2) is due to Dal’bo in the rank one case. We also show that unlike convex cocompact groups of rank one Lie groups, the $NM$ -minimality of $\mathcal E$ does not hold in a general Anosov homogeneous space.

Optimal Coloring Strategies for the Max k-Cut Game

We explore strong Nash equilibria in the max k-cut game on an undirected and unweighted graph with a set of k colors. Here, the vertices represent players, and the edges denote their relationships. Each player, v, selects a color as its strategy, and its payoff (or utility) is determined by the number of neighbors of v who have chosen a different color. Limited findings exist on the existence of strong equilibria in max k-cut games. In this paper, we make advancements in understanding the characteristics of strong equilibria. Specifically, our primary result demonstrates that optimal solutions are seven-robust equilibria. This implies that for a coalition of vertices to deviate and shift the system to a different configuration, i.e., a different coloring, a number of coalition vertices greater than seven is necessary. Then, we establish some properties of the minimal subsets concerning a robust deviation, revealing that each vertex within these subsets will deviate toward the color of one of its neighbors.