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[ "<thought>\nThe cut occurs mid-identifier in the distribution definition $\\widehat{P}_{W,Z_i}=$, with the next token being the start of a distribution name or expression. Given the context of the corollary and the previous theorems, the most plausible next content is the completion of the distribution definition, ...
[ 0 ]
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[ "<thought>\nThe text cuts off mid-equation at the beginning of the align environment in Corollary \\ref{corollary: Subgaussian and Jensen}. The next few tokens must continue the left-hand side of the inequality or define the bound that follows from the assumed subgaussianity. Given the structure of previous bounds ...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence inside an equation label and is about to define or reference a specific information-theoretic quantity. The equation is incomplete, and the next few tokens must continue the definition in the equation. The immediate next content is most likely the full name or symbol of the quan...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence, having begun a new clause with \"That correlations\". Given the prior discussion about bias and cancellation of errors in summation, the next 8 tokens likely continue this clause, introducing a noun or noun phrase that is correlated with the errors or quantities in question. Th...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence, having just introduced the comparison of edge weights $w$, computed from $\\mat{E}$. The next tokens will likely complete this clause by specifying the source or method of computing $w$, likely involving $\\hat{\\mat{E}}$ or a related quantity, and may include a comparison to a...
[ 0 ]
[ false ]
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[ "<thought>\nThe next 8 tokens are likely to continue the caption by introducing or labeling the figure panels, possibly with a phrase such as “The top row shows...” or “Each panel displays...”, or by specifying the axes or metrics of the scatterplots, such as “true vs. estimated weights” or “correlation coefficient...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence, having introduced a second post-recovery task as \"to extract a network's\". The next 8 tokens will almost certainly begin the completion of this noun phrase, likely specifying a structural or functional property of the network being extracted. Given the context of network anal...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-citation at the end of the sentence: \"Our second example of a post-recovery task is to extract a network's multiscale backbone~\\cite{serr\". The next token must be the completion of the citation key, likely \"serre\" or \"serrano\", followed by the closing brace. Given the context a...
[ 0 ]
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[ "<thought>\nThe text cuts off mid-sentence, inside a clause about the \"local distribution\" of some quantity related to the network's structure. Given the context of multiscale backbones and edge centrality, the next tokens will likely specify what is being distributed locally—most likely a centrality measure, edg...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence, having just cited Serrano *et al.* and left an open parenthesis from a citation command. The next tokens will almost certainly close the citation with a closing parenthesis and continue the explanation of the multiscale backbone criterion. The next 8 tokens will likely be \"ser...
[ 0 ]
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[ -47.78303527832031 ]
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[ "<thought>\nThe text is mid-sentence, inside a clause that begins \"To do so\" and is about to introduce a method or procedure for comparing backbones. The next tokens will likely introduce a specific action or define a metric, possibly involving computing or evaluating the overlap, similarity, or performance of th...
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[ -45.949485778808594 ]
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[ "<thought>\nThe cut occurs mid-phrase in the middle of the sentence \"as the multiscale backbone method depends on parameter $\\alpha\", with the LaTeX math mode open and the symbol $\\alpha$ just introduced. The next tokens must close the math mode and likely introduce a subscript or context for $\\alpha$, such as...
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[ -61.63092803955078 ]
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[ "<thought>\nThe text is mid-sentence, with the last token being the opening quote of \"true\". The next few tokens will complete the phrase \"the ``true'' solution\", likely followed by a clarification of what this solution refers to, such as a specific method or baseline. Given the context of comparing recovered d...
[ 0 ]
[ false ]
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[ -8.542613983154297 ]
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[ "<thought>\nThe next 8 tokens will almost certainly begin with the phrase \"used on $\\ensuremath{\\hat{\\mat{E}}}$\", continuing the definition of $\\alpha_B^{\\prime}$ as the parameter value applied to the recovered matrix. This follows the prior grammatical structure, which uses parallel phrasing to distinguish ...
[ 0 ]
[ false ]
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[ -74.07695770263672 ]
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false
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