580 research outputs found
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 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
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