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The duopoly market research has a long history. Due to such reasons as material supply, product pa-tent right and concession of the government, development of many economic industries is similar to the process of duopoly. In game theory, the Bertrand model which considers price to be a strategic variable is closer to reality and provides the market with more references, especially for retail market and electricity market, as the competitive world develops.Firstly, we analyze the classical Bertrand model and the Nash equilibrium in the model.Secondly, multi-agent technology is applied and the Bertrand duopoly game bidding process is con-ducted; meanwhile, in order to help agents find the optimal solutions, genetic algorithm based on multi-agent Bertrand model is chosen as the main algorithm for the research; and we finish with software im-plementation of the algorithm and with example analysis. In the end, oligopoly market bidding is also modelled in MATLAB simulation, which provides us with more accuracies and flexibilities.It is evidently shown in the model that when none of the two companies are able to meet all the de-mands in the market, the bigger the price gap, the more oscillated it is in the process; thus, the pure stra-tegic Nash equilibrium doesn't exist. However, when one of the two can offer the demands independent-ly, Nash equilibrium appears and is shown as the calculated results in Bertrand-Edgeworth model where the equilibrium reaches the cost price. Further, the reason for no pure strategic Nash Equilibrium is also discussed. ; The duopoly market research has a long history. Due to such reasons as material supply, product pa-tent right and concession of the government, development of many economic industries is similar to the process of duopoly. In game theory, the Bertrand model which considers price to be a strategic variable is closer to reality and provides the market with more references, especially for retail market and electricity market, as the competitive world develops.Firstly, we analyze the classical Bertrand model and the Nash equilibrium in the model.Secondly, multi-agent technology is applied and the Bertrand duopoly game bidding process is con-ducted; meanwhile, in order to help agents find the optimal solutions, genetic algorithm based on multi-agent Bertrand model is chosen as the main algorithm for the research; and we finish with software im-plementation of the algorithm and with example analysis. In the end, oligopoly market bidding is also modelled in MATLAB simulation, which provides us with more accuracies and flexibilities.It is evidently shown in the model that when none of the two companies are able to meet all the de-mands in the market, the bigger the price gap, the more oscillated it is in the process; thus, the pure stra-tegic Nash equilibrium doesn't exist. However, when one of the two can offer the demands independent-ly, Nash equilibrium appears and is shown as the calculated results in Bertrand-Edgeworth model where the equilibrium reaches the cost price. Further, the reason for no pure strategic Nash Equilibrium is also discussed

Abstract. Geoelectric time series (TS) have long been studied for their
potential for probabilistic earthquake forecasting, and a recent model
(GEMSTIP) directly used the skewness and kurtosis of geoelectric TS to
provide times of increased probability (TIPs) for earthquakes for several
months in the future. We followed up on this work by applying the hidden Markov
model (HMM) to the correlation, variance, skewness, and kurtosis TSs to
identify two hidden states (HSs) with different distributions of these
statistical indexes. More importantly, we tested whether these HSs could
separate time periods into times of higher/lower earthquake probabilities.
Using 0.5 Hz geoelectric TS data from 20 stations across Taiwan over 7 years, we first computed the statistical index TSs and then applied the
Baum–Welch algorithm with multiple random initializations to obtain a
well-converged HMM and its HS TS for each station. We then divided the map
of Taiwan into a 16-by-16 grid map and quantified the forecasting skill,
i.e., how well the HS TS could separate times of higher/lower earthquake
probabilities in each cell in terms of a discrimination power measure that we defined. Next, we
compare the discrimination power of empirical HS TSs against those of 400 simulated HS TSs and then
organized the statistical significance values from this cellular-level
hypothesis testing of the forecasting skill obtained into grid maps of
discrimination reliability. Having found such significance values to be high for many grid cells for
all stations, we proceeded with a statistical hypothesis test of the
forecasting skill at the global level to find high statistical significance
across large parts of the hyperparameter spaces of most stations. We
therefore concluded that geoelectric TSs indeed contain earthquake-related
information and the HMM approach is capable of extracting this
information for earthquake forecasting.

Abstract
Acute lung injury (ALI) is a serious adverse event in the management of acute type A aortic dissection (ATAAD). Using a large-scale cohort, we applied artificial intelligence-driven approach to stratify patients with different outcomes and treatment responses. A total of 2,499 patients from China 5A study database (2016–2022) from 10 cardiovascular centers were divided into 70% for derivation cohort and 30% for validation cohort, in which extreme gradient boosting algorithm was used to develop ALI risk model. Logistic regression was used to assess the risk under anti-inflammatory strategies in different risk probability. Eight top features of importance (leukocyte, platelet, hemoglobin, base excess, age, creatinine, glucose, and left ventricular end-diastolic dimension) were used to develop and validate an ALI risk model, with adequate discrimination ability regarding area under the receiver operating characteristic curve of 0.844 and 0.799 in the derivation and validation cohort, respectively. By the individualized treatment effect prediction, ulinastatin use was significantly associated with significantly lower risk of developing ALI (odds ratio [OR] 0.623 [95% CI 0.456, 0.851]; P = 0.003) in patients with a predicted ALI risk of 32.5–73.0%, rather than in pooled patients with a risk of <32.5 and >73.0% (OR 0.929 [0.682, 1.267], P = 0.642) (Pinteraction = 0.075). An artificial intelligence-driven risk stratification of ALI following ATAAD surgery were developed and validated, and subgroup analysis showed the heterogeneity of anti-inflammatory pharmacotherapy, which suggested individualized anti-inflammatory strategies in different risk probability of ALI.