Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Tessellations, Restricted Isometric Embeddings, and One Bit
  Sensing   We obtain mproved bounds for one bit sensing. For instance, let $ K_s$ denote
the set of $ s$-sparse unit vectors in the sphere $ \mathbb S ^{n}$ in
dimension $ n+1$ with sparsity parameter $ 0 < s < n+1$ and assume that $ 0 <
\delta < 1$. We show that for $ m \gtrsim \delta ^{-2} s \log \frac ns$, the
one-bit map $$ x \mapsto \bigl[ {sgn} \langle x,g_j \rangle \bigr] _{j=1} ^{m},
$$ where $ g_j$ are iid gaussian vectors on $ \mathbb R ^{n+1}$, with high
probability has $ \delta $-RIP from $ K_s$ into the $ m$-dimensional Hamming
cube. These bounds match the bounds for the {linear} $ \delta $-RIP given by $
x \mapsto \frac 1m[\langle x,g_j \rangle ] _{j=1} ^{m} $, from the sparse
vectors in $ \mathbb R ^{n}$ into $ \ell ^{1}$. In other words, the one bit and
linear RIPs are equally effective. There are corresponding improvements for
other one-bit properties, such as the sign-product RIP property.

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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat