Stable Set Research Articles

Shape and stability of rotation sets for incompressible flows on the torus

AbstractIn this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus $$\mathbb{T}^{d}$$ T d , d ⩾ 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on $$\mathbb{T}^{2}$$ T 2 . We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in ℤd. If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is C0-open and dense among those having proper rotation cones.

Efficient heuristics to compute minimal and stable feedback arc sets

Given a directed graph G=(V,A)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G=(V,A)$$\\end{document}, we tackle the Minimum Feedback Arc Set (MFAS) Problem by designing an efficient algorithm to search for minimal and stable Feedback Arc Sets, i.e. such that none of the arcs can be reintroduced in the graph without disrupting acyclicity and such that for each vertex the number of eliminated outgoing (resp. incoming) arcs is not bigger than the number of remaining incoming (resp. outgoing) arcs. Our algorithm has a good polynomial upper bound and can therefore be applied even on large graphs. We also introduce an algorithm to generate strongly connected graphs with a known upper bound on their feedback arc set, and on such graphs we test our algorithm.

Socio-legal instabilities in Ukraine’s wartime Compensation Law for damaged and destroyed residential property

Abstract Laws seeking to resolve war-related problems face a significant dilemma. While the legal establishment in a war-affected country drafts laws based on normative approaches suited to peacetime and stable settings, the civilian population pursues crises livelihoods that are markedly unsuited to compliance with or use of such laws. What emerges are socio-legal instabilities that aggravate instead of resolve wartime problems. With a socio-legal examination of Ukraine’s wartime housing Compensation Law, this article describes six sets of instabilities that compromise the utility of the law and aggravate or create additional problems: (1) the case-by-case approach, (2) administrative and institutional capacities, (3) legal vs. available evidence, (4) the timeframe for claims submission and awareness raising, (5) excluded segments of civil society and (6) prohibitions on selling properties. Approaches from international best practice that may be able to attend to these instabilities are then suggested.

The First Discovery of Archean Dolerite Dikes in the Western Part of the Aldan Shield

Dolerite dikes were studied in the western part of the Aldan terrane, in the middle reaches of the Tokko River. These dolerite dikes form a swarm of submeridional trend about 1 km wide. The dolerites of the thickest dike preserve their primary textural and structural features and mineral composition: plagioclase + pigeonite + augite + titanomagnetite. Dolerite in the chilled margins and central parts of the dike are homogeneous in composition, corresponds to low-Mg tholeiites, has low contents of Ti and other HFSE, with weak enrichment in light REE and small negative Nb anomalies. Sm–Nd isotope data on magmatic minerals of dolerite from the central part of the dike yield a good linear regression in an isochron diagram that gives to an age of 2510 ± 64 Ma, which probably corresponds to the crystallization age of the basalt. Metadolerites in a thin dike retain plagioclase porphyritic structures, but the pyroxenes are completely replaced by amphibole and chlorite. The metadolerites are contrastingly different in low contents of MgO, Cr, and Ni and in higher contents of TiO2, Fe2O3, P2O5, Nb, and all REE. The differences in the composition of the dikes may be explained by the longterm (about 65%) crystallization differentiation of the initial melt and the emplacement of the residual melt from a shallow intermediate magma chamber via opening cracks. Such conditions probably may have existed in tectonically stable intraplate settings. The age of the dolerites of the dike swarm is comparable to that of the anorogenic granites of the Nelyuki complex (~2.4–2.5 Ga), which are widespread in the western part of Aldan granulite–gneiss terrane. Our data bridge some gaps in characteristics of intraplate anorogenic magmatism that occurred in the western Aldan Shield in the Late Archean and marked the final consolidation of a large block of Archean crust in the Chara–Olekma granite–greenstone area.

Adapting stable matchings to forced and forbidden pairs

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Given a stable matching M1, a set Q of forced pairs, and a set P of forbidden pairs, we want to find a stable matching that includes all pairs from Q, no pair from P, and is as close as possible to M1. We study this problem in four classic stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). Our main contribution is a polynomial-time algorithm, based on the theory of rotations, for adapting Stable Roommates matchings to forced pairs. In contrast, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs. Moreover, we study the setting where preferences contain ties: Some of our algorithmic results can be extended while other problems become intractable.

Decentralized pure exchange processes on networks

AbstractWe define a class of pure exchange Edgeworth trading processes that under minimal assumptions converge to a stable set in the space of allocations, and characterise the Pareto set of these processes. Choosing a specific process belonging to this class, that we define fair trading, we analyse the trade dynamics between agents located on a weighted network. We determine the conditions under which there always exists a one-to-one map between the set of networks and the set of limit points of the dynamics, and derive an analog of the Second Welfare Theorem for networks. This result is used to explore what is the effect of the network topology on the trade dynamics and on the final allocation.

Early Warning Models Using Machine Learning to Predict Sepsis-Associated Chronic Critical Illness: A Study Based on the Medical Information Mart for Intensive Care Database.

Background Patients with chronic critical illness (CCI) experience poor prognoses and incur high medical costs. However, there is currently limited clinical awareness of sepsis-associated CCI, resulting in insufficient vigilance.Therefore, it is necessary to build a machine learning model that can predict whether sepsis patients will developCCI. Methods Clinical data on19,077 sepsis patients from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database were analyzed. Predictive factors were identified using the Student's t-test, Mann-Whitney Utest, or χ 2test. Six machine learning classification models, namely, the logistic regression, support vector machine, decision tree, random forest, extreme gradient enhancement, and artificial neural network, were established. The optimal model was selected on the basis of its performance. Calibration curves wereused to evaluate the accuracy of model classification, while the external validation dataset was used to evaluate the performance of the model. Results Thirty-seven characteristics,such as elevated alanine aminotransferase, rapid heart rate, and high Logistic Organ Dysfunction System scores, were identified as risk factors for developingCCI. The area under the receiver operating characteristic curve (AUROC) values forall models were above 0.73 onthe internal test set. Among them, the extreme gradient enhancement model exhibited superior performance (F1score=0.91, AUROC=0.91, Brierscore=0.052). It alsoexhibited stable prediction performance onthe external validation set (AUROC =0.72). Conclusion A machine learning model was established to predict whether sepsis patients will develop CCI. It can provide useful predictive information for clinical decision-making.

A weak box-perfect graph theorem

A graph G is called perfect if ω(H)=χ(H) for every induced subgraph H of G, where ω(H) is the clique number of H and χ(H) its chromatic number. The Weak Perfect Graph Theorem of Lovász states that a graph G is perfect if and only if its complement G‾ is perfect. This does not hold for box-perfect graphs, which are the perfect graphs whose stable set polytope is box-totally dual integral.We prove that both G and G‾ are box-perfect if and only if G‾+ is box-perfect, where G+ is obtained by adding a universal vertex to G. Consequently, G+ is box-perfect if and only if G‾+ is box-perfect. As a corollary, we characterize when the complete join of two graphs is box-perfect.

Supporting Carers to Coregulate With Children in Care: Learnings From Action Research With Caseworkers

ABSTRACTTrauma negatively impacts on the ability of children in out‐of‐home care to experience safety in their relationships. Trauma rearousal can continue to occur even when children are living in a safe and stable setting due to environmental triggers. Carers who are emotionally regulated themselves can model and support emotional regulation (known as coregulation) when their child becomes dysregulated. To do this, carers need agencies to provide trauma‐informed and therapeutic models of care, so they in turn can offer an emotionally secure experience for their child. This article reports on participatory action research with caseworkers from two nongovernment and one government organisation who supported foster and kinship carers to coregulate with children in long‐term care. Reflective practice meetings were held over an eight‐month period to capture the perspectives and experiences of 16 caseworkers who trialled practice changes for coregulation. An inductive analysis approach was used to elicit themes. Findings revealed a three‐phase process took place for caseworkers and carers to (1) acknowledge the presence of trauma and stress, (2) become aware of their own emotional capacity and (3) apply coregulation strategies. This process was possible when organisations promoted trauma awareness and relational safety, thereby creating a ‘holding environment’ for their caseworkers and allowing coregulation to be experienced by carers and their children.

Optimizing construction supplier selection in conflict-affected regions: a hybrid multi-criteria framework

AbstractConflicts and wars profoundly impact infrastructure, exacerbating the adversity already caused by natural disasters. Therefore, it is imperative that the reconstruction process be both effective and efficient to expedite a return to normalcy. This study aims to enhance the efficacy of reconstruction efforts through improved construction supplier evaluation and selection. It introduces an innovative hybrid multi-objective decision-making model that integrates a broad spectrum of economic, technical, and humanitarian criteria. The model is designed to optimally select and assign construction suppliers in regions affected by human and natural conflicts and crises. Fifteen criteria have been incorporated into the evaluation process to validate its effectiveness and maximize its contribution to local communities. This methodology streamlines decision-making and enhances transparency in conflict zones, aligning with the interests of all stakeholders. The study incorporates advanced methodologies, including Fuzzy Goal Programming (F-GP), Geographic Information System (GIS)-based Risk Assessment, and Fuzzy Analytic Hierarchy Process (F-AHP), leveraging real-world data and a case study. Additionally, a sensitivity analysis examines the impact of varying inputs on the model's output. The findings attest to the model's utility in conflict-affected regions and its potential applicability in stable settings.

A Schur-Weyl type duality for twisted weak modules over a vertex algebra

Let V V be a vertex algebra of countable dimension, G G a subgroup of A u t V AutV of finite order, V G V^{G} the fixed point subalgebra of V V under the action of G G , and S \mathscr {S} a finite G G -stable set of inequivalent irreducible twisted weak V V -modules associated with possibly different automorphisms in G G . We show a Schur–Weyl type duality for the actions of A α ( G , S ) \mathscr {A}_{\alpha }(G,\mathscr {S}) and V G V^G on the direct sum of twisted weak V V -modules in S \mathscr {S} where A α ( G , S ) \mathscr {A}_{\alpha }(G,\mathscr {S}) is a finite dimensional semisimple associative algebra associated with G , S G,\mathscr {S} , and a 2 2 -cocycle α \alpha naturally determined by the G G -action on S \mathscr {S} . It follows as a natural consequence of the result that for any g ∈ G g\in G every irreducible g g -twisted weak V V -module is a completely reducible weak V G V^G -module.

Back to the future: re-examining John Mearsheimer’s idea of hypernationalism in the context of the Russian–Ukrainian war

ABSTRACT Russia’s ‘special military operation’ in Ukraine is an opportunity for readdressing a crucial theoretical question: How to understand the role of hypernationalism in the run-up to war? Given the participation of Ukrainian ultranationalist militias and Russia’s goal of de-Nazifying Ukraine, a need emerges to provide a greater understanding of hypernationalism and its relation to this war’s origins. By going back to John Mearsheimer’s 1990 article ‘Back to the future: Instability in Europe after the Cold War’, this article examines Mearsheimer’s idea of hypernationalism and the problem of how states can signify other nations most negatively in the run-up to war. Drawing on a problem-driven strategy, it tackles this problem by applying ‘Essex School’ poststructuralist discourse theory. It argues that Ukrainian hypernationalism played a vital role in the genesis of this war, although not as a stable set of principles that possess a causal force but as a political subjectivity that the Russian government signified as a threat to its national identity. I use this distinction to theorise the role of hypernationalism by examining Russian official statements about Ukrainian neo-Nazism.

The total matching polytope of complete bipartite graphs

The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant description in the original space and a compact description in an extended space of the total matching polytope of complete bipartite graphs.

Homogeneous Ensemble Feature Selection for Mass Spectrometry Data Prediction in Cancer Studies

The identification of important proteins is critical for the medical diagnosis and prognosis of common diseases. Diverse sets of computational tools have been developed for omics data reduction and protein selection. However, standard statistical models with single-feature selection involve the multi-testing burden of low power with limited available samples. Furthermore, high correlations among proteins with high redundancy and moderate effects often lead to unstable selections and cause reproducibility issues. Ensemble feature selection in machine learning (ML) may identify a stable set of disease biomarkers that could improve the prediction performance of subsequent classification models and thereby simplify their interpretability. In this study, we developed a three-stage homogeneous ensemble feature selection (HEFS) approach for both identifying proteins and improving prediction accuracy. This approach was implemented and applied to ovarian cancer proteogenomics datasets comprising (1) binary putative homologous recombination deficiency (HRD)- positive or -negative samples; (2) multiple mRNA classes (differentiated, proliferative, immunoreactive, mesenchymal, and unknown samples). We conducted and compared various ML methods with HEFS including random forest (RF), support vector machine (SVM), and neural network (NN) for predicting both binary and multiple-class outcomes. The results indicated that the prediction accuracies varied for both binary and multiple-class classifications using various ML approaches with the proposed HEFS method. RF and NN provided better prediction accuracies than simple Naive Bayes or logistic models. For binary outcomes, with a sample size of 122 and nine selected prediction proteins using our proposed three-stage HEFS approach, the best ensemble ML (Treebag) achieved 83% accuracy, 85% sensitivity, and 81% specificity. For multiple (five)-class outcomes, the proposed HEFS-selected proteins combined with Principal Component Analysis (PCA) in NN resulted in prediction accuracies for multiple-class classifications ranging from 75% to 96% for each of the five classes. Despite the different prediction accuracies of the various models, HEFS identified consistent sets of proteins linked to the binary and multiple-class outcomes.

On two variants of split graphs: 2-unipolar graph and k-probe-split graph

A graph is called split if its vertex set can be partitioned into a stable set and a clique. In this article, we studied two variants of split graphs. A graph G is polar if its vertex set can be partitioned into two sets A and B such that G[A] is a complete multipartite graph and G[B] is a disjoint union of complete graphs. A 2-unipolar graph is a polar graph G such that G[A] is a clique and G[B] is the disjoint union of complete graphs with at most two vertices. We present a minimal forbidden induced subgraph characterization for 2-unipolar graphs. In addition, we show that they can be represented as an intersection of substars of special cacti. Let G be a graph class, the G-width of a graph G is the minimum positive integer k such that there exist k independent sets N1, … , Nk such that a set F of nonedges of G, whose endpoints belong to some Ni with i = 1, … , k, can be added so that the resulting graph G′ belongs to G. We say that a graph G is k-probe-G if it has G-width at most k and when G is the class of split graphs it is denominated k-probe-split. We prove that deciding, given a graph G and a positive integer k, whether G is a h-probe-split graph for some h ≤ k is NP-complete. Besides, a characterization by minimal forbidden induced subgraphs for 2-probe-split cographs is presented.

Stable set reformulations for the degree preserving spanning tree problem

Let G=(V,E) be a connected undirected graph and assume that a spanning tree is available for it. Any vertex in this tree is called degree preserving if it has the same degree in the graph and in the tree. Building upon this concept, the Degree Preserving Spanning Tree Problem (DPSTP) asks for a spanning tree of G with as many degree preserving vertices as possible. DPSTP is very much intertwined with the most important application for it, so far, i.e., the online monitoring of arc flows in a water distribution network, what serves us as an additional motivation for our investigation. We show that degree preserving vertices correspond to a stable set of a properly defined DPSTP conflict graph. This, in turn, allows us to use valid inequalities for the Stable Set Polytope (SSP) and thus strengthen the DPSTP formulations previously suggested in the literature. In doing so, the Branch-and-cut and Benders Decomposition algorithms suggested for these formulations are greatly enhanced. Additionally, as a further contribution, we also introduce a new and very challenging set of DPSTP test instances, given by graphs that closely resemble water distribution networks. For these instances, the new algorithms very clearly outperform all previous DPSTP algorithms. They not only run faster than their competitors but are also less dependent on good initial DPSTP primal bounds. For previous DPSTP test sets, the new algorithms lag behind the best existing algorithm for them, which is based on Lagrangian relaxation. However, as compared to additional DPSTP previous algorithms that do not benefit from SSP inequalities, the new ones come much closer to the Lagrangian relaxation one.

Behavioral and cortical dynamics underlying superior accuracy in short-distance passes

Improved pass accuracy is a prominent determinant of success in football. It demands an effective interaction of complex behavioral and cortical dynamics. Exploring differences in the ability to sustain an accurate pass behavior in a stable setting and the associated cortical dynamics at different expertise levels may provide an insight into skilled strategies contributing to superior accuracy in football. The aim of this study is to compare trial-to-trial variability of pass biomechanics and the corresponding cortical dynamics during short-distance passes between novices and experienced football players. Thirty participants (15 novices, 15 football players) performed 90 short-distance passes. The intertrial variability of pass biomechanics (foot acceleration, range of hip flexion, knee flexion and foot rotation) was assessed by means of multiscale entropy. The task-related cortical dynamics were analyzed via source-derived event-related spectral perturbations. Experienced players demonstrated higher accuracy and overall lower entropy values across multiple time scales which was significant for hip flexion. The electroencephalography data revealed group differences in parieto-occipital alpha desynchronization and frontal theta synchronization in successive phases of passes. The current findings suggest that experienced football players may show a skilled ability to recruit and retain pass biomechanics promoting higher accuracy, whereas novices may show an explorative behavior with higher spatial variability. This difference may be associated with distinctive visuospatial and attentional strategies acquired with expertise in football. Our study provides an insight into expertise-specific behavioral and cortical dynamics of superior accuracy in football and a basis for its prospective investigation in enriched contexts.

Paleolithic portable art in the collections of the Irkutsk Regional Art Museum (Buret’ site)

The collection of Buret’ site is one of the most important archaeological complexes of the Upper Paleolithic of Siberia. The decorative elements on the mobile art found at the site marks the “classical stage” of the Upper Paleolithic. Field research was carried out in 1936-1940, under the general leadership of A.P. Okladnikov. In the 2000s, due to new research methods and data obtained on the stratigraphy and archeology of cultural remains, the comprehension of the object changed. This article examines the issues of morphology, manufacturing technology and decoration of ivory sculptures in the collection of the V.P. Sukachev Irkutsk Regional Art Museum, excavated in 1940. During the research it was established that in the materials of Buret’, as in the “classic” Mal’ta’s Paleolithic collection, there were various technological methods for making anthropomorphic and zoomorphic figures, using a stable set of tools and technological standards. The technology for producing portable art objects on the territory of the Buret’ site is in many ways similar to that used at the Mal’ta site. The research revealed the main patterns of production for each of the identified morphological types of items at both sites. For each of the types of mobile art objects studied, the basic technology of their production was adapted and acquired characteristic features, manifested in the specifics of using the main tools. Systematization of the data obtained during the analysis of the material made it possible to exclude the version of a random, chaotic selection of the tools used. It should be noted that among the relatively low-quality production of most objects of Buret’s portable art, one example of ornithomorphic sculpture stands out, distinguished by the skill and care of its production, based on the use of more advanced technology and careful processing of ivory tusk. We assume that the production of portable art at the Buret’ site was serial in nature and did not have the features of individual craftsman creativity. The use of universal tools of production indicates the priority of mass production over individual motives.

On the Topological Nature of the Stable Sets Associated to the Second Invariant of the Order $q$ Standard Lyness’ Equation

On the Topological Nature of the Stable Sets Associated to the Second Invariant of the Order $q$ Standard Lyness’ Equation

An interpretability model for syndrome differentiation of HBV-ACLF in traditional Chinese medicine using small-sample imbalanced data

ObjectiveClinical medical record data associated with hepatitis B-related acute-on-chronic liver failure (HBV-ACLF) generally have small sample sizes and a class imbalance. However, most machine learning models are designed based on balanced data and lack interpretability. This study aimed to propose a traditional Chinese medicine (TCM) diagnostic model for HBV-ACLF based on the TCM syndrome differentiation and treatment theory, which is clinically interpretable and highly accurate. MethodsWe collected medical records from 261 patients diagnosed with HBV-ACLF, including three syndromes: Yang jaundice (214 cases), Yang-Yin jaundice (41 cases), and Yin jaundice (6 cases). To avoid overfitting of the machine learning model, we excluded the cases of Yin jaundice. After data standardization and cleaning, we obtained 255 relevant medical records of Yang jaundice and Yang-Yin jaundice. To address the class imbalance issue, we employed the oversampling method and five machine learning methods, including logistic regression (LR), support vector machine (SVM), decision tree (DT), random forest (RF), and extreme gradient boosting (XGBoost) to construct the syndrome diagnosis models. This study used precision, F1 score, the area under the receiver operating characteristic (ROC) curve (AUC), and accuracy as model evaluation metrics. The model with the best classification performance was selected to extract the diagnostic rule, and its clinical significance was thoroughly analyzed. Furthermore, we proposed a novel multiple-round stable rule extraction (MRSRE) method to obtain a stable rule set of features that can exhibit the model’s clinical interpretability. ResultsThe precision of the five machine learning models built using oversampled balanced data exceeded 0.90. Among these models, the accuracy of RF classification of syndrome types was 0.92, and the mean F1 scores of the two categories of Yang jaundice and Yang-Yin jaundice were 0.93 and 0.94, respectively. Additionally, the AUC was 0.98. The extraction rules of the RF syndrome differentiation model based on the MRSRE method revealed that the common features of Yang jaundice and Yang-Yin jaundice were wiry pulse, yellowing of the urine, skin, and eyes, normal tongue body, healthy sublingual vessel, nausea, oil loathing, and poor appetite. The main features of Yang jaundice were a red tongue body and thickened sublingual vessels, whereas those of Yang-Yin jaundice were a dark tongue body, pale white tongue body, white tongue coating, lack of strength, slippery pulse, light red tongue body, slimy tongue coating, and abdominal distension. This is aligned with the classifications made by TCM experts based on TCM syndrome differentiation and treatment theory. ConclusionOur model can be utilized for differentiating HBV-ACLF syndromes, which has the potential to be applied to generate other clinically interpretable models with high accuracy on clinical data characterized by small sample sizes and a class imbalance.