1,002 research outputs found
The polymer mat: Arrested rebound of a compressed polymer layer
Compression of an adsorbed polymer layer distorts its relaxed structure.
Surface force measurements from different laboratories show that the return to
this relaxed structure after the compression is released can be slowed to the
scale of tens of minutes and that the recovery time grows rapidly with
molecular weight. We argue that the arrested state of the free layer before
relaxation can be described as a Guiselin brush structure1, in which the
surface excess lies at heights of the order of the layer thickness, unlike an
adsorbed layer. This brush structure predicts an exponential falloff of the
force at large distance with a decay length that varies as the initial
compression distance to the 6/5 power. This exponential falloff is consistent
with surface force measurements. We propose a relaxation mechanism that
accounts for the increase in relaxation time with chain length.Comment: 24 pages, 5 figre
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers that store the dataset. In this paper it is shown that Lagrange encoding, a recently suggested powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers that collude in attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to non-linear polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in
which a user is able to compute a function on a distributed dataset without
revealing the identity of that function to the servers. In this paper it is
shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon
codes, enables private computation in many cases of interest. In particular, we
present a scheme that enables private computation of polynomials of any degree
on Lagrange encoded data, while being robust to Byzantine and straggling
servers, and to servers colluding to attempt to deduce the identities of the
functions to be evaluated. Moreover, incorporating ideas from the well-known
Shamir secret sharing scheme allows the data itself to be concealed from the
servers as well. Our results extend private computation to high degree
polynomials and to data-privacy, and reveal a tight connection between private
computation and coded computation.Comment: To appear in Transactions on Information Forensics and Securit
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers that store the dataset. In this paper it is shown that Lagrange encoding, a recently suggested powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers that collude in attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to non-linear polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
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