We applied the unsupervised ‘K-means’ clustering machine learning algorithm implemented in Wolfram Mathematica 12.1 [50 ] to estimate a cut-off value for each taxonomic level using the datasets of genetic distance values. The number of clusters that we selected was pre-determined based on the taxonomic levels of the genetic distance values (e.g. four clusters represent ‘species,’ ‘genus,’ ‘family’ and ‘order’). In the ‘K-means’ method, the centroids of each cluster are initially guided by an agglomerative hierarchical algorithm, and each data point is then assigned to the nearest centroid [51 , 52 ]. The ‘K-means’ clustering aims to partition the data points to minimize the within-cluster sum of squares in order to minimize the pairwise squared deviations of points in the same cluster until the centroids are stable [51 –53 (link)]. Statistical analyses and plots were also performed using Wolfram Mathematica 12.1 [50 ], and the script and data used in this study for ‘K-means’ clustering analysis are available at https://github.com/slphy/Chan-HelminthMarkers .
Mathematica 12
Manufactured by Wolfram
Sourced in United States, United Kingdom
Mathematica 12 is a computational software package developed by Wolfram Research. It provides a wide range of mathematical capabilities, including numerical and symbolic computation, visualization, and programming. Mathematica 12 can be used for tasks such as data analysis, scientific research, and educational purposes.
Automatically generated - may contain errors
Lab products found in correlation
Nanodrop 1000, by Thermo Fisher Scientific (2 mentions)
Prism 9, by GraphPad (1 mentions)
Nanolab 650, by Thermo Fisher Scientific (1 mentions)
Sigmaplot 14, by Grafiti LLC (1 mentions)
Matlab r2018a, by MathWorks (1 mentions)
Ccd detector, by Horiba (1 mentions)
M per protein extraction reagent, by Thermo Fisher Scientific (1 mentions)
Complete inhibitor cocktail, by Roche (1 mentions)
Stain free technology, by Bio-Rad (1 mentions)
Miniprotean tgx stain free gels, by Bio-Rad (1 mentions)
Chemidoc mp imaging system, by Bio-Rad (1 mentions)
Spark 20m, by Tecan (1 mentions)
Liquid nitrogen cooledccd detector, by Horiba (1 mentions)
Spss 20, by IBM (1 mentions)
Matlab r2020b, by MathWorks (1 mentions)
785 nm diode laser, by Toptica (1 mentions)
42 protocols using mathematica 12
1
K-means Clustering for Taxonomic Cutoffs
2
Mathematica-Powered Research Protocol
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
All numerical calculations, including the analyses, were performed using Mathematica 12.3.1.0 (Wolfram Research, Champaign, IL, USA).
3
Mathematica 12.3.1.0 Numerical Analyses
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
All numerical calculations, including the analyses, were performed using Mathematica 12.3.1.0 (Wolfram Research, Champaign, IL, USA).
4
Macintosh-Based Mathematica Development Protocol
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
The following development environment was used: A Macintosh running OS X 10.14.5 (Apple, Inc.) and Mathematica 12.0.0.0 (Wolfram Research, Inc.).
5
Comparative Analysis of Lab and AI Classifier
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
The laboratory and AI classifier data were compared using Mathematica 12.0.0.0 (Wolfram Research, Inc.). The Cochran Armitage test, Cohen's κ, χ2 test and Fisher's exact test were used. P<0.05 was considered to indicate a statistically significant difference.
6
Statistical Analysis of Research Data
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
Statistical tests performed were described in the text and calculated using Prism 9 (GraphPad Software, San Diego, CA, United States), Excel (Microsoft, Redmond, WA, United States), and Mathematica 12.1.1.0 (Wolfram Research, Inc., Champaign, IL, United States).
7
Wolfram Mathematica for Figures Analysis
8
3D Hair-Bundle Modeling and Mechanics
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
We used Mathematica 12.1.1.0 (Wolfram Research, Inc., Champaign, IL, United States) to create the 3-D hair-bundle model (Figures 6B,C ), to calculate the effects of morphology on mechanics (Figure 7 ), and to create Supplementary Figures 4 , 6 .
9
Rigid Registration for Vascular Imaging
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
Given the coordinates (x, y, z) of the points of maximum ILT thickness, PWS, and PWRI in CT1, linear transformation (also known as rigid registration or affine transformation) was used to predict said points in CT2. Minimizing the error through least square optimization of the x, y, and z coordinates of up to nine corresponding points (left and right renal arteries, superior mesenteric artery, aortic bifurcation, proximal left and right common iliac arteries, and one to three lumbar arteries if available) in CT1 and CT2 determined the transformation matrix (MATHEMATICA 12.0, Wolfram, Champaign, IL). An additional point (ie, calcified plaque or inferior mesenteric artery) clearly visible in both CTAs validated the transformation matrix. The applied linear transformation was considered successful if the distance between the predicted position and the actual position of the validation point in CT2 was less than 15 mm.
All measurements, including biomechanical parameters and the linear transformation, were performed by an experienced analyzer (D.Z.) and reviewed by an experienced vascular surgeon and analyzer (A.B., T.C.G.). Upon discrepant results, all three investigators performed a joint analysis.
All measurements, including biomechanical parameters and the linear transformation, were performed by an experienced analyzer (D.Z.) and reviewed by an experienced vascular surgeon and analyzer (A.B., T.C.G.). Upon discrepant results, all three investigators performed a joint analysis.
10
Modeling Biphasic Lamellae Screw Dislocations
Check if the same lab product or an alternative is used in the 5 most similar protocols
+ Expand
The screw dislocations of biphasic lamellae were modeled by the equation of helicoid in cylindrical coordinates (r, ϕ, and z), which can be expressed in terms of three parameters, r, ϕ, and t by where f is the fraction of one of the lamellar domains [we take f = 0.15 (PS), therefore 1 − f = 0.85 (corresponding to 6:1 swollen QP2VP)]. The parameters r, ϕ, and t are in the range of
Here, D is the outer diameter of helicoid and n is the number of turns, and 2cπ is the pitch of the helicoid. The screw dislocation of biphasic lamellae shown inFig. 2B is depicted using Mathematica 12.0 (Wolfram Research Inc.) with the values of D = 4, n = 3, c = 1/3, and f = 0.15.
Here, D is the outer diameter of helicoid and n is the number of turns, and 2cπ is the pitch of the helicoid. The screw dislocation of biphasic lamellae shown in
About PubCompare
Our mission is to provide scientists with the largest repository of trustworthy protocols and intelligent analytical tools, thereby offering them extensive information to design robust protocols aimed at minimizing the risk of failures.
We believe that the most crucial aspect is to grant scientists access to a wide range of reliable sources and new useful tools that surpass human capabilities.
However, we trust in allowing scientists to determine how to construct their own protocols based on this information, as they are the experts in their field.
Ready to get started?
Sign up for free.
Registration takes 20 seconds.
Available from any computer
No download required
Revolutionizing how scientists
search and build protocols!