Prediction Model For Wordle Game Results With High Robustness

In this study, we delve into the dynamics of Wordle using data analysis and machine learning. Our analysis initially focused on the correlation between the date and the number of submitted results. Due to initial popularity bias, we modeled stable data using an ARIMAX model with coefficient values of 9, 0, 2, and weekdays/weekends as the exogenous variable. We found no significant relationship between word attributes and hard mode results. To predict word difficulty, we employed a Backpropagation Neural Network, overcoming overfitting via feature engineering. We also used K-means clustering, optimized at five clusters, to categorize word difficulty numerically. Our findings indicate that on March 1st, 2023, around 12,884 results will be submitted and the word "eerie" averages 4.8 attempts, falling into the hardest difficulty cluster. We further examined the percentage of loyal players and their propensity to undertake daily challenges. Our models underwent rigorous sensitivity analyses, including ADF, ACF, PACF tests, and cross-validation, confirming their robustness. Overall, our study provides a predictive framework for Wordle gameplay based on date or a given five-letter word. Results have been summarized and submitted to the Puzzle Editor of the New York Times.Comment: 25 Pages, 28 Figure

Mean Li-Yorke chaos along any infinite sequence for infinite-dimensional random dynamical systems

In this paper, we study the mean Li-Yorke chaotic phenomenon along any infinite positive integer sequence for infinite-dimensional random dynamical systems. To be precise, we prove that if an injective continuous infinite-dimensional random dynamical system $(X,\phi)$ over an invertible ergodic Polish system $(\Omega,\mathcal{F},\mathbb{P},\theta)$ admits a $\phi$-invariant random compact subset $K$ with $h_{top}(K,\phi)>0$, then given a positive integer sequence $\mathbf{a}=\{a_i\}_{i\in\mathbb{N}}$ with $\lim_{i\to+\infty}a_i=+\infty$, for $\mathbb{P}$-a.s. $\omega\in\Omega$ there exists an uncountable subset $S(\omega)\subset K(\omega)$ and $\epsilon(\omega)>0$ such that for any distinct points $x_1$, $x_2\in S(\omega)$ with following properties \begin{align*} \liminf_{N\to+\infty}\frac{1}{N}\sum_{i=1}^{N} d\big(\phi(a_i, \omega)x_1, \phi(a_i, \omega)x_2\big)=0,\quad\limsup_{N\to+\infty}\frac{1}{N}\sum_{i=1}^{N} d\big(\phi(a_i, \omega)x_1, \phi(a_i, \omega)x_2\big)>\epsilon(\omega), \end{align*} where $d$ is a compatible complete metric on $X$.Comment: 22 page

Measurement Models For Sailboats Price vs. Features And Regional Areas

In this study, we investigated the relationship between sailboat technical specifications and their prices, as well as regional pricing influences. Utilizing a dataset encompassing characteristics like length, beam, draft, displacement, sail area, and waterline, we applied multiple machine learning models to predict sailboat prices. The gradient descent model demonstrated superior performance, producing the lowest MSE and MAE. Our analysis revealed that monohulled boats are generally more affordable than catamarans, and that certain specifications such as length, beam, displacement, and sail area directly correlate with higher prices. Interestingly, lower draft was associated with higher listing prices. We also explored regional price determinants and found that the United States tops the list in average sailboat prices, followed by Europe, Hong Kong, and the Caribbean. Contrary to our initial hypothesis, a country's GDP showed no direct correlation with sailboat prices. Utilizing a 50% cross-validation method, our models yielded consistent results across test groups. Our research offers a machine learning-enhanced perspective on sailboat pricing, aiding prospective buyers in making informed decisions.Comment: 20 pages, 17 figure

Adaptation of Rice to the Nordic Climate Yields Potential for Rice Cultivation at Most Northerly Site and the Organic Production of Low-Arsenic and High-Protein Rice

There is an urgent demand for low-arsenic rice in the global market, particularly for consumption by small children. Soils in Uppsala, Sweden, contain low concentrations of arsenic (As). We hypothesize that if certain japonica paddy rice varieties can adapt to the cold climate and long day length in Uppsala and produce normal grains, such a variety could be used for organic production of low-arsenic rice for safe rice consumption. A japonica paddy rice variety, "Heijing 5," can be cultivated in Uppsala, Sweden, after several years' adaptation, provided that the rice plants are kept under a simple plastic cover when the temperature is below 10 degrees C. Uppsala-adapted "Heijing 5" has a low concentration of 0.1 mg per kg and high protein content of 12.6% per dry weight in brown rice grain, meaning that it thus complies with all dietary requirements determined by the EU and other countries for small children. The high protein content is particularly good for small children in terms of nutrition. Theoretically, Uppsala-adapted "Heijing 5" can produce a yield of around 5100 kg per ha, and it has a potential for organic production. In addition, we speculate that cultivation of paddy rice can remove nitrogen and phosphorus from Swedish river water and reduce nutrient loads to the Baltic Sea and associated algae blooms

Prognostic value of inflammation biomarkers for 30-day mortality in critically ill patients with stroke

ObjectiveTo explore the values of neutrophil to lymphocyte ratio (NLR), platelet to lymphocyte ratio (PLR), neutrophil to albumin ratio (NAR), prognostic nutritional index (PNI), systemic immune inflammatory index (SII) and red cell distribution width to albumin ratio (RA) for evaluating the risk of 30-day mortality of ischemic stroke or hemorrhagic stroke patients.MethodsIn this cohort study, the data of 1,601 patients diagnosed with stroke were extracted from the Medical Information Mart for Intensive Care III (MIMIC-III) database. Among them, 908 were hemorrhagic stroke patients and 693 were ischemic stroke patients. Demographic and clinical variables of patients were collected. Univariate and multivariable Cox regression were performed to evaluate the predictive values of NLR, PLR, SII, NAR, RA, and PNI for 30-day mortality in hemorrhagic stroke or ischemic stroke patients. The receiver operator characteristic (ROC) curves were plotted to assess the predictive values of NLR, NAR, and RA for 30-day mortality of hemorrhagic stroke patients.ResultsAt the end of follow-up, 226 hemorrhagic stroke patients and 216 ischemic stroke patients died. The elevated NLR level was associated with increased risk of 30-day mortality in hemorrhagic stroke [hazard ratio (HR) = 1.17, 95% confidence interval (CI): 1.06–1.29]. The increased NAR level was associated with elevated risk of 30-day mortality in hemorrhagic stroke (HR = 1.16, 95% CI: 1.02–1.30). The high RA level was linked with increased risk of 30-day mortality (HR = 1.44, 95% CI: 1.23–1.69). No significant correlation was observed in these inflammation biomarkers with the risk of 30-day mortality in ischemic stroke patients. The area under the curves (AUCs) of NLR, RA, and NAR for evaluating the risk of 30-day mortality of hemorrhagic stroke patients were 0.552 (95% CI: 0.503–0.601), 0.644 (95% CI: 0.590–0.699) and 0.541 (95% CI: 0.490–0.592).ConclusionNLR, NAR, and RA were potential prognostic biomarkers for predicting 30-day mortality of hemorrhagic stroke patients, which might provide clinicians an easy and cheap way to quickly identify patients with high risk of mortality

Balancing public and private interests through optimization of concession agreement design for user-pay PPP projects

In user-pay public private partnership (PPP) projects, private sectors collect user fees to cover cost and reap revenue. For projects that cannot be self-financed, public sectors usually invest public funds to make them financially feasible. The concession agreement allocates revenues and risks, and lies in the center of balancing public and private interests. However, stakeholders may have contrary opinions regarding the optimization of concession agreement. While private sectors are concerned about earning money, public sectors pay more attention to the efficient use of public funds. To address this challenge, this paper firstly identifies several key concessionary items, including concession period, concession price, capital structure and government subsidy. Then, a multi-objective optimization model is presented using discounted cash flow method, in which key concessionary items act as decision variables and public and private interests are represented by two sub-objectives. Subsequently, the model is solved using non-dominated sorting genetic algorithm-II (NSGA-II). Furthermore, a numerical case based on Beijing No. 4 Metro Line is provided to demonstrate the application of the model. Results show that the proposed model can produce a series of viable combinations of concessionary items that balance public and private interests, which provides practical references for relative decision making activities