Stable Set Research Articles

"This is Not the 90s": Myanmar and Change in ASEAN's Normative Order

In this article, we examine the contours of the Association of Southeast Asian Nations' (ASEAN) response to the latest regional challenge from Myanmar, the 2021 coup. Scholars and practitioners alike often portray ASEAN as a relatively cohesive community of states united in adherence to a long-held and comparatively stable set of norms within the so-called "ASEAN way." Core among these norms has been domestic non-interference. However, we argue that rather than being determined by a coherent set of agreed norms, ASEAN's response to this crisis has been shaped by intra-regional contestation and division around how ASEAN ought to enact its particular "way" of regional governance. More narrowly, we show that the ASEAN response has been shaped by contestation over competing normative impulses in the organization—centrality and non-interference—which have developed in increasing tension since the humanitarian disaster after Cyclone Nargis in 2008 and the Rohingya crisis after 2016. We show that in response to these crises, officials from the organization and its member states advanced divergent accounts of what ASEAN ought to do and why, given competing normative commitments to centrality and non-interference. By showing how ASEAN's response to the 2021 coup is the result of internal contestation within the organization, we support accounts of regional governance in Southeast Asia that stress less the fixity of ASEAN norms than their contestation in practice. To make our argument we analyze more than 250 documents and draw on interviews with regional officials.

Flow Rate Determination of the Nanoflow Sheath Liquid CE-MS-Coupling Applying the nanoCEasy Interface.

In recent years, nanoflow sheath liquid (nanoSL) interfaces have been used more commonly for capillary electrophoresis-mass spectrometry (CE-MS) coupling due to their high sensitivity combined with flexibility in CE separation conditions. So far, the exact amount of sheath liquid (SL) and, thus, the dilution effect remain unknown due to the self-supplying type of the nanoSL interfaces. To quantify the SL flow rates, we present here an approach for the determination of the flow rate based on isotopically labeled standards using the nanoCEasy interface. SL and pumped CE flow are spiked with atrazine and d5-atrazine, respectively, enabling the determination of the total flow rate for different electrospray (ES) conditions. Generally, flow rates increase with higher ES voltages. Only at high ES voltages, larger emitter sizes lead to higher flow rates; for low voltages, flow rates are independent of emitter size. Additionally, smaller emitter sizes can generally be operated at lower ES voltages. Visualizing the ES, higher flow rates lead to a larger spray angle. Higher flow rates may decrease the signal intensity by diluting the CE-separated analytes. Indeed, this effect is observed for the flow-injected atrazine analytes and in the CE-MS analysis of an amino acid standard mix under aqueous acidic separation conditions. Therefore, lower flow rates are preferred for low electroosmotic flow (EOF) applications. However, in high EOF applications, higher voltages are required to prevent the accumulation of aqueous background electrolyte (BGE) at the emitter tip, which otherwise leads to peak broadening and inefficient ionization. Overall, the presented data enable the selection of stable and sensitive settings for nanoSL interfaces.

EGS SO28 - Management of oesophageal diverticulitis in a 71-year-old female: Case report and review of management approaches

Abstract Background Oesophageal diverticulitis is a rare condition with fewer than ten reports in the literature. We present a case of oesophageal diverticulitis in a 71-year-old female with a history of COPD, TIA, and known oesophageal diverticulum. She was managed conservatively with NBM, total parenteral nutrition and intravenous antibiotics requiring a 16-day inpatient stay. The rarity of this condition poses challenges in its diagnosis and management, necessitating a thorough understanding of both conservative and surgical interventions. This case highlights the complexity involved in treating oesophageal diverticulitis, especially in patients with significant comorbidities. Method Patient presented with a 6-day history of upper abdominal pain and sepsis (elevated inflammatory markers; CRP 320, WCC 11.1, temperature 38.0, pulse 104). Abdomen was soft with upper abdominal tenderness. Imaging was consistent with diverticulitis of a 5.9cm lower oesophageal diverticulum without perforation. Initial management included making the patient nil by mouth, total parenteral nutrition, and intravenous antibiotics (vancomycin and metronidazole). The patient’s condition was closely monitored with serial blood tests and clinical assessments. Opinion was sought from a tertiary upper GI centre. Discharge was planned once the patient safely transitioned to oral diet and was apyrexial for 48 hours. Results Inflammatory markers improved over five days (CRP from 320 to 51, WCC from 11.1 to 9). She remained intermittently pyrexial until day 8 of admission. Clinical improvement allowed transition from intravenous to oral therapy, and she was discharged on day 16 with double dose oral PPI therapy. Patient has been followed up by tertiary upper GI services with plans for consideration of surgical resection of the oesophageal diverticulum. The patient’s successful discharge without surgical intervention during the acute phase underscores the effectiveness of a conservative management approach initially, with a plan for definitive surgical treatment in a stable outpatient setting. Conclusion Oesophageal diverticulitis, though rare, requires a nuanced approach to management, especially in patients with significant comorbidities. This case demonstrates the importance of an awareness of thorough history taking and review of previous examinations to prevent delayed diagnosis of a rare pathology not demonstrated on a CT abdomen and pelvis. This approach highlights the importance of individualised treatment plans and the potential for conservative management to provide stabilisation, followed by elective surgical management. The paucity of cases of oesophageal diverticulitis has prevented development of evidence based guidelines, underscoring the importance of seeking advice from tertiary centers when managing rare presentations.

Abstract 4124289: Changes in high-sensitivity cardiac troponin I and associated cardiovascular risk: Analyses From the FOURIER Trial

Background: Circulating high-sensitivity cardiac troponin I (hs-cTnI) is associated with the risk of future cardiovascular (CV) events in stable patients (pts). Data are scarce regarding changes of hs-cTnI in a stable setting. Aims: To study baseline and changes of hs-cTnI in pts with atherosclerotic CV disease (ASCVD), and the association with risk of major CV events. Methods: We measured hs-cTnI (Abbott ARCHITECT) at baseline (BL) and 24 weeks (wks) in 20,718 pts enrolled in a nested biomarker study of the FOURIER trial, which tested the PCSK9i evolocumab vs. placebo in pts with ASCVD on statin and LDL > 70 or non-HDL > 100 mg/dL. The primary endpoint was an adjudicated composite of CV death, MI, stroke, hosp. for unstable angina, or coronary revascularization. The HR (95% CI) across percent-change of hs-cTnI was investigated in pts with quantifiable hs-cTnI at BL and 24 wks (lower limit of quantification (LLOQ) 3.6ng/L) using restricted-cubic splines and Cox-PH models, adjusted for sex, age, LDL at BL, prior MI, randomized treatment, eGFR, DM, HTN, prior HF, and BMI. A Generalized Additive Model was used to predict event rates as a function of hs-cTnI BL and absolute change, flexibly evaluated with a non-linear interaction. All models were based on 3-year follow-up using landmark analysis from 24 wks. Results: Median age was 63 yrs (25 th , 75 th percentiles: 56, 69), 75.5% were male, 86.1% had CAD, 13.7% PAD, and 19.0% a prior stroke. Of these pts, 11,021 (46.8%) had hs-cTnI > LLOQ at BL and 24 wks. The median hs-cTnI at 24 wks was 6.6ng/L (5 th , 25 th , 75 th , 95 th percentiles are: 3.7, 4.7, 11.9, 51.1 ng/L). The absolute event rate of the primary endpoint across hs-cTnI BL and depending on absolute hs-cTnI change to 24 wks is shown in Fig. A . Higher Hs-cTnI BL was associated with higher event rates (p < 0.001). Additionally, absolute reductions and increases of hs-cTnI from BL to 24 wks resulted in reduced and increased event rates, respectively, across hs-cTnI BL . Additionally, relative decrease and increase of hs-cTnI from BL to 24 wks were associated with reduced and increased relative risk, respectively (p for overall effect < 0.001, Fig. B ). Conclusion: Changes in hs-cTnI are associated with the risk of future CV events. Serial measurements of hs-cTnI may aid in reclassification of CV risk and the identification of pts whose CV risk changes with time.

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

Conflicts 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.