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

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

Intersection theory rules symbology

We propose a novel method to determine the structure of symbols for a family of polylogarithmic Feynman integrals. Using the d log-bases and simple formulas for the first- and second-order contributions to the intersection numbers, we give a streamlined procedure to compute the entries in the coefficient matrices of canonical differential equations, including the symbol letters and the rational coefficients. We also provide a selection rule to decide whether a given matrix element must be zero. The symbol letters are deeply related with the poles of the integrands, and also have interesting connections to the geometry of Newton polytopes. Our method will have important applications in cutting-edge multi-loop calculations. The simplicity of our results also hints at possible underlying structure in perturbative quantum field theories.Comment: 7 pages, 1 figur

Direct measurement of vorticity using tracer particles with internal markers

Current experiment techniques for vorticity measurement suffer from limited spatial and temporal resolution to resolve the small-scale eddy dynamics in turbulence. In this study, we develop a new method for direct vorticity measurement in fluid flows based on digital inline holography (DIH). The DIH system utilizes a collimated laser beam to illuminate the tracers with internal markers and a digital sensor to record the generated holograms. The tracers made of the polydimethylsiloxane (PDMS) prepolymer mixed with internal markers are fabricated using a standard microfluidic droplet generator. A rotation measurement algorithm is developed based on the 3D location reconstruction and tracking of the internal markers and is assessed through synthetic holograms to identify the optimal parameter settings and measurement range (e.g., rotation rate from 0.3 to 0.7 rad/frame under numerical aperture of imaging of 0.25). Our proposed method based on DIH is evaluated by a calibration experiment of single tracer rotation, which yields the same optimal measurement range. Using von K\'arm\'an swirling flow setup, we further demonstrate the capability of the approach to simultaneously measure the Lagrangian rotation and translation of multiple tracers. Our method can measure vorticity in a small region on the order of 100 ${\mu}$m or less and can be potentially used to quantify the Kolmogorov-scale vorticity field in turbulent flows.Comment: 17 pages, 7 figure

Effect of dual co-rotation wheels configuration on aircraft shimmy

A mathematical model is developed to study the shimmy oscillations of aircraft nose landing gear with a dual-wheel co-rotation configuration. This model incorporates the dynamics of the torsional and lateral mode and the non-linear kinematics of the tire. The procedure of different types of shimmy bifurcation analysis is described in detail. The effect of the co-rotation configuration on shimmy oscillation is compared with non-co-rotation wheels. More specifically, the wheel separation distance and wheel moment of inertia are selected as important parameters to study the effect of the co-rotation configuration on the aircraft shimmy. It is concluded that as the wheel separation distance increases, the lateral shimmy becomes more stable, while the torsional mode become less stable. In comparison to the non-co-rotation configuration, dual co-rotation wheels have a petty effect on landing gear with small wheel separations. However, in the condition of a relatively large distance between wheels, the co-rotation configuration has a great positive influence on the anti-torsional shimmy. The wheel moment inertia, within a practical range, affects shimmy oscillation weakly for both the co-rotation and the non-co-rotation configuration

The conditionally studentized test for high-dimensional parametric regressions

This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and conditional studentization approaches to construct a COnditionally Studentized Test (COST). Whether the initial test is global or local smoothing-based; the dimension of the predictor vector and the number of parameters are fixed or diverge at a certain rate, the proposed test always has a normal weak limit under the null hypothesis. When the dimension of the predictor vector diverges to infinity at faster rate than the number of parameters, even the sample size, these results are still available under some conditions. This shows the potential of our method to handle higher dimensional problems. Further, the test can detect the local alternatives distinct from the null hypothesis at the fastest possible rate of convergence in hypothesis testing. We also discuss the optimal sample splitting in power performance. The numerical studies offer information on its merits and limitations in finite sample cases including the setting where the dimension of predictor vector equals the sample size. As a generic methodology, it could be applied to other testing problems.Comment: 35 pages, 2 figure

Addressing Domain Shift via Knowledge Space Sharing for Generalized Zero-Shot Industrial Fault Diagnosis

Fault diagnosis is a critical aspect of industrial safety, and supervised industrial fault diagnosis has been extensively researched. However, obtaining fault samples of all categories for model training can be challenging due to cost and safety concerns. As a result, the generalized zero-shot industrial fault diagnosis has gained attention as it aims to diagnose both seen and unseen faults. Nevertheless, the lack of unseen fault data for training poses a challenging domain shift problem (DSP), where unseen faults are often identified as seen faults. In this article, we propose a knowledge space sharing (KSS) model to address the DSP in the generalized zero-shot industrial fault diagnosis task. The KSS model includes a generation mechanism (KSS-G) and a discrimination mechanism (KSS-D). KSS-G generates samples for rare faults by recombining transferable attribute features extracted from seen samples under the guidance of auxiliary knowledge. KSS-D is trained in a supervised way with the help of generated samples, which aims to address the DSP by modeling seen categories in the knowledge space. KSS-D avoids misclassifying rare faults as seen faults and identifies seen fault samples. We conduct generalized zero-shot diagnosis experiments on the benchmark Tennessee-Eastman process, and our results show that our approach outperforms state-of-the-art methods for the generalized zero-shot industrial fault diagnosis problem

Unmasking Bias and Inequities: A Systematic Review of Bias Detection and Mitigation in Healthcare Artificial Intelligence Using Electronic Health Records

Objectives: Artificial intelligence (AI) applications utilizing electronic health records (EHRs) have gained popularity, but they also introduce various types of bias. This study aims to systematically review the literature that address bias in AI research utilizing EHR data. Methods: A systematic review was conducted following the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guideline. We retrieved articles published between January 1, 2010, and October 31, 2022, from PubMed, Web of Science, and the Institute of Electrical and Electronics Engineers. We defined six major types of bias and summarized the existing approaches in bias handling. Results: Out of the 252 retrieved articles, 20 met the inclusion criteria for the final review. Five out of six bias were covered in this review: eight studies analyzed selection bias; six on implicit bias; five on confounding bias; four on measurement bias; two on algorithmic bias. For bias handling approaches, ten studies identified bias during model development, while seventeen presented methods to mitigate the bias. Discussion: Bias may infiltrate the AI application development process at various stages. Although this review discusses methods for addressing bias at different development stages, there is room for implementing additional effective approaches. Conclusion: Despite growing attention to bias in healthcare AI, research using EHR data on this topic is still limited. Detecting and mitigating AI bias with EHR data continues to pose challenges. Further research is needed to raise a standardized method that is generalizable and interpretable to detect, mitigate and evaluate bias in medical AI.Comment: 29 pages, 2 figures, 2 tables, 2 supplementary files, 66 reference

Effect of bias voltage on the tribological and sealing properties of rubber seals modified by DLC films

Diamond-like carbon (DLC) films were deposited on nitrile butadiene rubber (NBR) by the DC magnetron sputtering under different bias voltages. Raman spectra revealed that the variation of bias voltage could tune the carbon bond structure in DLC films. Both the hardness and Young's modulus increased with the increasing bias voltage. Tribological tests revealed that the DLC-coated NBR prepared at the bias voltage of -200 V exhibited low wear rate due to its high hardness. The sealing property was studied by evaluating the leakage rate of volatile liquid in a simple apparatus. All DLC films resulted in less leakage rate as compared to the raw rubber under large stress. The lowest leakage rate occurred in the DLC-coated NBR prepared with a bias voltage of -200 V, which was associated with the theoretical calculations (Persson's theory). It was attributed to the synergetic effects of the variations of the Young's modulus and root-mean-square (Rms) roughness. The low Young's modulus and Rms, controlled by regulating bias voltage, could enhance actual contact area and reduce the leakage rate