The pair correlation function, g( r 1, r 2), of an intercalated fluid is rigorously defined on the basis of the spatially varying singlet densities, n (1) ( r 1), n (1) ( r 2) by the equation g( r 1, r 2)= n (2) ( r 1, r 2)/ n (1) ( r 1) n (1) ( r 2...
Indeed, if the pair correlation function \(\Phi (x,y)\) fulfills the condition $$\begin{aligned} \left[ \frac{\partial \Phi (x,y)}{\partial x}-\frac{\partial \Phi (x,y)}{\partial y}\right] \Bigr \vert _{x=y^{+}}-\left[ \frac{\partial \Phi (x,y)}{\partial x}-...
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SHAP has specific support for natural language models like those in the Hugging Face transformers library. By adding coalitional rules to traditional Shapley values we can form games that explain large modern NLP model using very few function evaluations. Using this functionality is as simple as pass...
(V)iμ≈(WH)iμ=∑a=1kWiaHaμEq. 4 The objective function, based on the Poisson distribution, can be defined using the following divergence function, which the factorization process needs to minimize: D(V,WH)=∑i=1p∑j=1n(VijlnVij(W...
and filling up the leaf tree nodes with points that define IMLS function in the second stage. To train the two-stage neural network, researchers incorporated loss functions that supervised the octree structure, signed distance values of IMLS function, point s...
aggregates in the soil will generally (but now always) be less strongly bound. Since this improvement increases the sensitivity of emissions tou*t, it shifts those emissions to the world’s most erodible regions, whereu*tis lowest. This eliminates the need to use a source function to shift ...
On the Pair Correlation of Zeros ofDirichlet L-Functions Ali E. Özlük In the course of investigating the vertical distribution of zeros of the Riemann Zeta Function ζ(ί ) on the critical line, Montgomery [5] introduced the form function ...
The paper presents results on the dynamics of bubbles in a mono- and in a bi-disperse bubble swarm. The radial pair correlation function provides insight into the characteristic bubble clustering length. The angular pair correlation function shows that for small distances the most probable alignment...
We will begin by listing the steps to the calculation of the correlation coefficient. The data we are working with arepaired data, each pair of which will be denoted by (xi,yi). We begin with a few preliminary calculations. The quantities from these calculations will be used in subsequent ...