, use
/
for subsections if there's a long text. (There's only one paragraph here, so I'll just wrap it in
, or maybe split it logically? The prompt says "每个自然段落用
包裹" (Wrap each natural paragraph with
). The input is one big paragraph. I will wrap it in
or maybe split it into smaller
s if it feels like multiple paragraphs, but it's safer to keep it as one
or properly segment it. Actually, it looks like one cohesive abstract paragraph.) Wait, let's look at the sentences. It's one paragraph of plain text. Let's just use one `
` tag for the whole text, or maybe break it into a few `
` tags to make it readable, but the prompt says "不得增删改内容" (must not add, delete, or modify content). Breaking into paragraphs might be considered adding structure, but "每个自然段落用
包裹" means each natural paragraph. The input is one natural paragraph. So `
...
` is appropriate. Wait, let's look closer at the text. It has some math formulas. "$\*\*\*\[n+s_+^2/(m^{-1}+τ^2)\]^{-1}\*\*\*$" wait, the user text has: `$[n+s_+^2/(m^{-1}+τ^2)]^{-1}$` - no, it says `$ [n+s_+^2/(m^{-1}+τ^2)]^{-1} $` (with spaces around math). Let's check the exact text: `A source can make a training mixture easier to learn while making its accuracy less valuable for the target. We study how the training problem a source creates and the finite-sample error of learning it jointly determine target-risk guarantees under reweighting. For binary classification, for each pair of laws and each positive target weight, we derive the sharpest target excess hinge-risk bound implied by mixture excess alone, uniformly over clipped predictors. This exact conversion curve is determined by density-weighted local votes. A two-sample oracle inequality for weighted support vector machines supplies the mixture excess, and the composition becomes explicit for Gaussian kernels. On a tilted-boundary class, we establish the all-procedure minimax classification rate [n+s_+^2/(m^{-1}+τ^2)]^{-1} in the transferable strength s_+ and the tilt τ, separating source sampling uncertainty (m^{-1}) from relation uncertainty (τ^2). A target-checked Gaussian-SVM selector adapts to unknown s_+ and τ up to a logarithmic factor for fixed dimension, and retains the target-only rate up to the same factor against arbitrary independent sources under the stated target model. On a separate smooth opposition class, the minimax risk within the family of exact Gaussian SVMs fitted to the original labels with nonnegative weights is exponentially larger than the unrestricted minimax risk whenever the target sample is at most half the source sample, despite arbitrary data-dependent weighting and tuning. The value of a source thus depends on the training problem it creates, on what accuracy there means for the target, and on whether the permitted use of the source can implement the needed correction.` Wait, the math in the text: `$ [n+s_+^2/(m^{-1}+τ^2)]^{-1} $` - actually the user text says: `$[n+s_+^2/(m^{-1}+τ^2)]^{-1}$` (without spaces inside the dollars, wait, let me check the prompt: `$[n+s_+^2/(m^{-1}+τ^2)]^{-1}$`). Prompt text: `...minimax classification rate $[n+s_+^2/(m^{-1}+τ^2)]^{-1}$ in the transferable strength $s_+$ and the tilt $τ$...` I should preserve the `$...$` or just keep it as is. The prompt says "不得增删改内容" (do not add, delete, or modify content). So I must keep the `$` and the exact characters. Wait, the prompt has: `$[n+s_+^2/(m^{-1}+τ^2)]^{-1}$` (with a leading space before $ in the prompt? Let me check: `rate $[n+s_+^2/(m^{-1}+τ^2)]^{-1}$ in`). Actually, I will just copy the text exactly inside the `` tag. Wait, are there any lists, quotes, or code blocks? No. Can I use `` for important sentences? The prompt says "重要句子可用" (important sentences can use ). Which sentences are important? - "The value of a source thus depends on the training problem it creates, on what accuracy there means for the target, and on whether the permitted use of the source can implement the needed correction." -> This is the concluding sentence, could be ``. - "On a tilted-boundary class, we establish the all-procedure minimax classification rate..." -> Could be `` for the main result. - "On a separate smooth opposition class, the minimax risk within the family of exact Gaussian SVMs fitted to the original labels with nonnegative weights is exponentially larger than the unrestricted minimax risk whenever the target sample is at most half the source sample, despite arbitrary data-dependent weighting and tuning." -> Another main result. Let's read the rule again: "重要句子可用" - "Important sentences can use ". It's optional but good to use. Let's split the text into paragraphs? The input is just one block of text. "每个自然段落用
包裹" means if there are multiple paragraphs. Here there is only one natural paragraph. I will wrap it in a single `
` or maybe split it into logical paragraphs to make it look like a news article? No, "不得增删改内容" means I shouldn't artificially change the paragraph breaks if there are none. I will just use one `
` tag. Wait, is there any possibility to use `