Bayes correlated equilibria and no-regret dynamics

This paper explores equilibrium concepts for Bayesian games, which are fundamental models of games with incomplete information. We aim at three desirable properties of equilibria. First, equilibria can be naturally realized by introducing a mediator into games. Second, an equilibrium can be computed efficiently in a distributed fashion. Third, any equilibrium in that class approximately maximizes social welfare, as measured by the price of anarchy, for a broad class of games. These three properties allow players to compute an equilibrium and realize it via a mediator, thereby settling into a stable state with approximately optimal social welfare. Our main result is the existence of an equilibrium concept that satisfies these three properties. Toward this goal, we characterize various (non-equivalent) extensions of correlated equilibria, collectively known as Bayes correlated equilibria. In particular, we focus on communication equilibria (also known as coordination mechanisms), which can be realized by a mediator who gathers each player's private information and then sends correlated recommendations to the players. We show that if each player minimizes a variant of regret called untruthful swap regret in repeated play of Bayesian games, the empirical distribution of these dynamics converges to a communication equilibrium. We present an efficient algorithm for minimizing untruthful swap regret with a sublinear upper bound, which we prove to be tight up to a multiplicative constant. As a result, by simulating the dynamics with our algorithm, we can efficiently compute an approximate communication equilibrium. Furthermore, we extend existing lower bounds on the price of anarchy based on the smoothness arguments from Bayes Nash equilibria to equilibria obtained by the proposed dynamics

The Secretary Problem with Predictions

The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values are provided in advance. We propose an algorithm that achieves a nearly optimal value if the predictions are accurate and results in a constant-factor competitive ratio otherwise. We also show that the worst-case competitive ratio of an algorithm cannot be higher than some constant $< 1/\mathrm{e}$, which is the best possible competitive ratio when we ignore predictions, if the algorithm performs nearly optimally when the predictions are accurate. Additionally, for the multiple-choice secretary problem, we propose an algorithm with a similar theoretical guarantee. We empirically illustrate that if the predictions are accurate, the proposed algorithms perform well; meanwhile, if the predictions are inaccurate, performance is comparable to existing algorithms that do not use predictions

Complications Associated With Spine Surgery in Patients Aged 80 Years or Older: Japan Association of Spine Surgeons with Ambition (JASA) Multicenter Study

Study Design:Retrospective study of registry data.Objectives:Aging of society and recent advances in surgical techniques and general anesthesia have increased the demand for spinal surgery in elderly patients. Many complications have been described in elderly patients, but a multicenter study of perioperative complications in spinal surgery in patients aged 80 years or older has not been reported. Therefore, the goal of the study was to analyze complications associated with spine surgery in patients aged 80 years or older with cervical, thoracic, or lumbar lesions.Methods:A multicenter study was performed in patients aged 80 years or older who underwent 262 spinal surgeries at 35 facilities. The frequency and severity of complications were examined for perioperative complications, including intraoperative and postoperative complications, and for major postoperative complications that were potentially life threatening, required reoperation in the perioperative period, or left a permanent injury.Results:Perioperative complications occurred in 75 of the 262 surgeries (29%) and 33 were major complications (13%). In multivariate logistic regression, age over 85 years (hazard ratio [HR] = 1.007, P = 0.025) and estimated blood loss ≥500 g (HR = 3.076, P = .004) were significantly associated with perioperative complications, and an operative time ≥180 min (HR = 2.78, P = .007) was significantly associated with major complications.Conclusions:Elderly patients aged 80 years or older with comorbidities are at higher risk for complications. Increased surgical invasion, and particularly a long operative time, can cause serious complications that may be life threatening. Therefore, careful decisions are required with regard to the surgical indication and procedure in elderly patients

Risk Factors for Delirium After Spine Surgery in Extremely Elderly Patients Aged 80 Years or Older and Review of the Literature: Japan Association of Spine Surgeons with Ambition Multicenter Study

Study Design:Retrospective database analysis.Objective:Spine surgeries in elderly patients have increased in recent years due to aging of society and recent advances in surgical techniques, and postoperative complications have become more of a concern. Postoperative delirium is a common complication in elderly patients that impairs recovery and increases morbidity and mortality. The objective of the study was to analyze postoperative delirium associated with spine surgery in patients aged 80 years or older with cervical, thoracic, and lumbar lesions.Methods:A retrospective multicenter study was performed in 262 patients 80 years of age or older who underwent spine surgeries at 35 facilities. Postoperative complications, incidence of postoperative delirium, and hazard ratios of patient-specific and surgical risk factors were examined.Results:Postoperative complications occurred in 59 of the 262 spine surgeries (23%). Postoperative delirium was the most frequent complication, occurring in 15 of 262 patients (5.7%), and was significantly associated with hypertension, cerebrovascular disease, cervical lesion surgery, and greater estimated blood loss (P < .05). In multivariate logistic regression using perioperative factors, cervical lesion surgery (odds ratio = 4.27, P < .05) and estimated blood loss ≥300 mL (odds ratio = 4.52, P < .05) were significantly associated with postoperative delirium.Conclusions:Cervical lesion surgery and greater blood loss were perioperative risk factors for delirium in extremely elderly patients after spine surgery. Hypertension and cerebrovascular disease were significant risk factors for postoperative delirium, and careful management is required for patients with such risk factors

INFRARED SPECTROSCOPIC INVESTIGATION ON HIGH ACIDITY OF DIETHYLETHER CATION

Author Institution: Depertment of Chemistry, Graduate School of Science,Tohoku University, Sendi 980-8578, Japan; Institute of Atomic and Molecular Sciences, Academia Sinca,Taipei 10617, TaiwanWe performed infrared spectroscopy of a diethylether cation which was generated by the vacuum-ultraviolet photoionization. In the observed spectrum, the stretch vibration of the CH bond next to the oxygen atom appears with high intensity in the lower frequency region than ordinary alkyl CH stretches. Comparison of infrared spectroscopic results and theoretical calculations reveals that the low frequency of the CH stretch originates from hyperconjugation between the CH bonding orbital and the nonbonding orbital of the oxygen atom. This hyperconjugation also induces the increase of the acidity of the CH bond as well as its stretch band intensity

Selecting molecules with diverse structures and properties by maximizing submodular functions of descriptors learned with graph neural networks

Selecting diverse molecules from unexplored areas of chemical space is one of the most important tasks for discovering novel molecules and reactions. This paper proposes a new approach for selecting a subset of diverse molecules from a given molecular list by using two existing techniques studied in machine learning and mathematical optimization: graph neural networks (GNNs) for learning vector representation of molecules and a diverse-selection framework called submodular function maximization. Our method, called SubMo-GNN, first trains a GNN with property prediction tasks, and then the trained GNN transforms molecular graphs into molecular vectors, which capture both properties and structures of molecules. Finally, to obtain a subset of diverse molecules, we define a submodular function, which quantifies the diversity of molecular vectors, and find a subset of molecular vectors with a large submodular function value. This can be done efficiently by using the greedy algorithm, and the diversity of selected molecules measured by the submodular function value is mathematically guaranteed to be at least 63% of that of an optimal selection. We also introduce a new evaluation criterion to measure the diversity of selected molecules based on molecular properties. Computational experiments confirm that our SubMo-GNN successfully selects diverse molecules from the QM9 dataset regarding the property-based criterion, while performing comparably to existing methods regarding standard structure-based criteria. We also demonstrate that SubMo-GNN with a GNN trained on the QM9 dataset can select diverse molecules even from other MoleculeNet datasets whose domains are different from the QM9 dataset. The proposed method enables researchers to obtain diverse sets of molecules for discovering new molecules and novel chemical reactions, and the proposed diversity criterion is useful for discussing the diversity of molecular libraries from a new property-based perspective