Node-Max-Cut and the Complexity of Equilibrium in Linear Weighted Congestion Games

In this work, we seek a more refined understanding of the complexity of local optimum computation for Max-Cut and pure Nash equilibrium (PNE) computation for congestion games with weighted players and linear latency functions. We show that computing a PNE of linear weighted congestion games is PLS-complete either for very restricted strategy spaces, namely when player strategies are paths on a series-parallel network with a single origin and destination, or for very restricted latency functions, namely when the latency on each resource is equal to the congestion. Our results reveal a remarkable gap regarding the complexity of PNE in congestion games with weighted and unweighted players, since in case of unweighted players, a PNE can be easily computed by either a simple greedy algorithm (for series-parallel networks) or any better response dynamics (when the latency is equal to the congestion). For the latter of the results above, we need to show first that computing a local optimum of a natural restriction of Max-Cut, which we call Node-Max-Cut, is PLS-complete. In Node-Max-Cut, the input graph is vertex-weighted and the weight of each edge is equal to the product of the weights of its endpoints. Due to the very restricted nature of Node-Max-Cut, the reduction requires a careful combination of new gadgets with ideas and techniques from previous work. We also show how to compute efficiently a (1+?)-approximate equilibrium for Node-Max-Cut, if the number of different vertex weights is constant

Σχεδιασμός μηχανισμών, κοινωνική επιλογή και υπολογισμός ισορροπιών σε περιορισμένα πεδία

Abstract: The work in this thesis primarily revolves around efficient algorithmic frameworks for settings where information is not readily available. Specifically, we look at limitations of provided information from three main angles: (1) Information is difficult to quantify. In this line of work we focused on distortion in voting (JAIR ’22, AAAI ’22), which is the notion that quantifies the impact of being able to use only limited information on the social welfare of the outcome (i.e. in terms of approximation). Here 1 we study both the effects of various forms of limited information on metric distortion and also the distortion of a very popular mechanism, STV, in relation to the dimensionality of the underlying metric space. (2) Information is private to strategic agents and needs to be revealed to the algorithm through properly designed incentives. This area is commonly referred to as mechanism design and my related work focuses on fighting strong impossibility results by restricting our analysis in “natural” sub-classes of the general instance space (WINE ’21). In this setting we have studied the approximability of the facility location problem by truthful mechanisms, whose allocation is aligned with the agent incentives. (3) Communication is expensive. Combining this restriction along with the strategic environment described previously, we show that known mechanisms have implementations with asymptotically optimal communication complexity (SAGT ’20). In most of our works, our objective is to maximize the social welfare. Furthermore, some work has been focused on a classical aspect of algorithmic game theory, that of equilibrium computation, where we study the complexity of computing a Pure Nash Equilibrium in linear weighted congestion games and also show an efficient algorithm for computing approximate equilibria in a natural subclass of Max-Cut games (ICALP ’20).Η παρούσα διδακτορική διατριβή μελετάει αποδοτικά αλγοριθμικά πλαίσια για περιβάλλοντα στα οποία η πληροφορία δεν είναι άμεσα διαθέσιμη. Πιο συγκεκριμένα μελετάει περιορισμούς στην πρόσβαση στην πληροφορία από τρεις διαφορετικές γωνίες: (1) Η πληροφορία είναι προσωπική (και ιδιωτική) σε στρατηγικούς παίκτες και χρειάζεται να αποκαλυφθεί στον αλγόριθμο μέσα από κατάλληλα σχεδιασμένα κίνητρα: Αυτή η περιοχή συνήθως αναφέρεται ως «αλγοριθμικός σχεδιασμός μηχανισμών». Η έρευνα στα πλαίσια της διατριβής επικεντρώνεται στην αντιμετώπιση ισχυρών αρνητικών αποτελεσμάτων περιορίζοντας την ανάλυση σε «φυσιολογικά» υποσύνολα στιγμιότυπων του προβλήματος, μια πρακτική από την περιοχή της ανάλυσης πέραν της χειρότερης περίπτωσης στη θεωρία αλγορίθμων. Συγκεκριμένα, αναλύεται η προσεγγισιμότητα του προβλήματος χωροθέτησης εγκαταστάσεων από φιλαλήθεις μηχανισμούς. (2) Η επικοινωνία είναι ακριβή: Μελετώντας αυτόν τον περιορισμό σε περιβάλλοντα με στρατηγικούς παίκτες αποδεικνύεται ότι απλοί μηχανισμοί για κλασσικά προβλήματα μπορούν να υλοποιηθούν με ασυμπτωτικά βέλτιστη πολυπλοκότητα επικοινωνίας (ανάμεσα στον μηχανισμό και τους παίκτες). (3) Η πληροφορία που χρησιμοποιείται από τον μηχανισμό είναι περιορισμένη: η διατριβή εστιάζει στην παραμόρφωση στο πρόβλημα της ψηφοφορίας, που είναι η έννοια που ποσοτικοποιεί την επίπτωση της πρόσβασης σε περιορισμένη πληροφορία στην κοινωνική ωφέλεια του αποτελέσματος ενός αλγορίθμου (σε όρους προσέγγισης της βέλτιστης λύσης). Εδώ μελετώνται και οι επιπτώσεις διάφορων μορφών περιορισμένης πληροφορίας στην μετρική παραμόρφωση αλλά και η παραμόρφωση ενός πολύ διαδεδομένου μηχανισμού, του STV, σε σχέση με την διαστασιμότητα του σχετικού μετρικού χώρου. Επιπλέον, στα πλαίσια της διατριβής διερευνάται η κλασική πτυχή της αλγοριθμικής θεωρίας παιγνίων που αφορά την πολυπλοκότητα υπολογισμού αμιγών ισορροπιών. Μελετάται το πρόβλημα αυτό στο πλαίσιο των βεβαρυμμένων παιγνίων συμφόρησης με γραμμικές συναρτήσεις καθυστέρησης, και παρουσιάζεται ένας αποδοτικός αλγόριθμος για τον υπολογισμό προσεγγιστικών ισορροπιών σε μια ενδιαφέρουσα κλάση των Max-Cut παιγνίων

Association of VEGF Gene Polymorphisms with the Development of Heart Failure in Patients after Myocardial Infarction

Objectives: Vascular endothelial growth factor (VEGF) is upregulated in vivo in the ischemic human myocardium. Since several polymorphisms have been shown to influence VEGF expression, we evaluated the contribution of such polymorphisms to the clinical outcome of patients after an acute myocardial infarction (AMI). Methods: PCR and restriction fragment length polymorphism analysis was performed to genotype 10 VEGF polymorphisms in 102 patients who had suffered an AMI and in 98 age- and sex-matched healthy individuals. Distribution of these polymorphisms was assessed by logistic regression analysis. Results: No significant differences were found between patients and normal individuals. However, when patients were subdivided into 2 groups based on the development of heart failure after their AMI judged by heart ultrasound measurements (ejection fraction <40%), the distribution of the -634 polymorphism differed significantly (p = 0.016). Specifically, patients with a CC genotype had 7 times higher risk of developing heart failure. Additionally, the co-inheritance of -634 with other VEGF polymorphisms was found to be significant for the development of heart failure between these 2 groups. Conclusions: Our data indicate that the -634 polymorphism and its co-inheritance with genotypes of other VEGF polymorphisms might be considered as risk factors playing a role in the clinical outcome of AMI patients. Copyright (C) 2009 S. Karger AG, Base

Cohort profile. the ESC-EORP chronic ischemic cardiovascular disease long-term (CICD LT) registry

The European Society of cardiology (ESC) EURObservational Research Programme (EORP) Chronic Ischemic Cardiovascular Disease registry Long Term (CICD) aims to study the clinical profile, treatment modalities and outcomes of patients diagnosed with CICD in a contemporary environment in order to assess whether these patients at high cardiovascular risk are treated according to ESC guidelines on prevention or on stable coronary disease and to determine mid and long term outcomes and their determinants in this population

Lipoprotein(a) and Benefit of PCSK9 Inhibition in Patients With Nominally Controlled LDL Cholesterol

International audienceBackground: Guidelines recommend nonstatin lipid-lowering agents in patients at very high risk for major adverse cardiovascular events (MACE) if low-density lipoprotein cholesterol (LDL-C) remains ≥70 mg/dL on maximum tolerated statin treatment. It is uncertain if this approach benefits patients with LDL-C near 70 mg/dL. Lipoprotein(a) levels may influence residual risk.Objectives: In a post hoc analysis of the ODYSSEY Outcomes (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab) trial, the authors evaluated the benefit of adding the proprotein subtilisin/kexin type 9 inhibitor alirocumab to optimized statin treatment in patients with LDL-C levels near 70 mg/dL. Effects were evaluated according to concurrent lipoprotein(a) levels.Methods: ODYSSEY Outcomes compared alirocumab with placebo in 18,924 patients with recent acute coronary syndromes receiving optimized statin treatment. In 4,351 patients (23.0%), screening or randomization LDL-C was 13.7 mg/dL or ≤13.7 mg/dL; corresponding adjusted treatment hazard ratios were 0.82 (95% CI: 0.72-0.92) and 0.89 (95% CI: 0.75-1.06), with Pinteraction = 0.43.Conclusions: In patients with recent acute coronary syndromes and LDL-C near 70 mg/dL on optimized statin therapy, proprotein subtilisin/kexin type 9 inhibition provides incremental clinical benefit only when lipoprotein(a) concentration is at least mildly elevated. (ODYSSEY Outcomes: Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab; NCT01663402)

Risk Categorization Using New American College of Cardiology/American Heart Association Guidelines for Cholesterol Management and Its Relation to Alirocumab Treatment Following Acute Coronary Syndromes

10.1161/CIRCULATIONAHA.119.042551CIRCULATION140191578-158

Effect of Alirocumab on Mortality After Acute Coronary Syndromes An Analysis of the ODYSSEY OUTCOMES Randomized Clinical Trial

10.1161/CIRCULATIONAHA.118.038840CIRCULATION1402103-11