Výsledky vyhledávání - "Mendelson, S"

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Catalytic Embeddings of Quantum Circuits

Autor: Amy, M., Crawford, M., Glaudell, A. N., Macasieb, M. L., Mendelson, S. S., Ross, N. J.

If a set $\mathbb{G}$ of quantum gates is countable, then the operators that can be exactly represented by a circuit over $\mathbb{G}$ form a strict subset of the collection of all unitary operators. When $\mathbb{G}$ is universal, one circumvents th

Externí odkaz: http://arxiv.org/abs/2305.07720

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Remarks on the geometry of coordinate projections in R^n

Autor: Mendelson, S., Vershynin, R.

Publikováno v: Israel Journal of Mathematics 140 (2004), 203--220

We study geometric properties of coordinate projections. Among other results, we show that if a body K in R^n has an "almost extremal" volume ratio, then it has a projection of proportional dimension which is close to the cube. We compare type 2 and

Externí odkaz: http://arxiv.org/abs/math/0306314

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Entropy and the Combinatorial Dimension

Autor: Mendelson, S., Vershynin, R.

Publikováno v: Invent. Math. 152 (2003), 37-55

We solve Talagrand's entropy problem: the L_2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley's theorem on classes of {0,1}-valued functions, for which the shattering dim

Externí odkaz: http://arxiv.org/abs/math/0203275

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Entropy, dimension and the Elton-Pajor Theorem

Autor: Mendelson, S., Vershynin, R.

The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a num

Externí odkaz: http://arxiv.org/abs/math/0201048

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