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Generalized secret sharing and monotone functions
 in Proceedings on Advances in cryptology. SpringerVerlag
, 1990
"... Secret Sharing from the perspective of threshold schemes has been wellstudied over the past decade. Threshold schemes, however, can only handle a small fraction of the secret sharing functions which we may wish to form. For example, if it is desirable to divide a secret among four participants A, ..."
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Cited by 184 (0 self)
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secret sharing function. There is a natural correspondence between the set of “generitlized ” secret sharing functions and the set of monotone functions, and tools developed for simplifying the latter set can be applied equally well t o the former set. 1
Estimating Monotonic Functions and Their
, 2002
"... We present a function estimator, MSQUID, for fitting and bounding noisy data that is known to be monotonic. MSQUID augments a “backpropagation” neural network model with a set of constraints which restrict the model to monotonic functions. Model parameters are estimated using nonlinear constrained o ..."
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We present a function estimator, MSQUID, for fitting and bounding noisy data that is known to be monotonic. MSQUID augments a “backpropagation” neural network model with a set of constraints which restrict the model to monotonic functions. Model parameters are estimated using nonlinear constrained
Completely monotonic functions
"... In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [3], p.450, for example, that a function w is the Laplace transform of ..."
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Cited by 36 (0 self)
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In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [3], p.450, for example, that a function w is the Laplace transform
Weighted inequalities for monotone functions
, 1997
"... We give characterizations of weights for which reverse inequalities of the Hölder type for monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement the results of [2], [6], [7] and [14], [15] for the values of parameters 0 < p ≤ q < ∞. ..."
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Cited by 3 (0 self)
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We give characterizations of weights for which reverse inequalities of the Hölder type for monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement the results of [2], [6], [7] and [14], [15] for the values of parameters 0 < p ≤ q < ∞.
On the Fourier Spectrum of Monotone Functions
, 1996
"... In this paper, monotone Boolean functions are studied using harmonic analysis on the cube. ..."
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Cited by 60 (0 self)
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In this paper, monotone Boolean functions are studied using harmonic analysis on the cube.
Continuity Of Monotone Functions
, 1993
"... . It is shown that a monotone function acting between euclidean spaces R n and R m is continuous almost everywhere with respect to the Lebesgue measure on R n . As well known the set of all points of discontinuity of a real monotone function is at most countable. The paper deals with the se ..."
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Cited by 1 (1 self)
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. It is shown that a monotone function acting between euclidean spaces R n and R m is continuous almost everywhere with respect to the Lebesgue measure on R n . As well known the set of all points of discontinuity of a real monotone function is at most countable. The paper deals
LIMITWISE MONOTONIC FUNCTIONS AND THEIR APPLICATIONS
"... Abstract. We survey what is known about limitwise monotonic functions and sets and discuss their applications in effective algebra and computable model theory. Additionally, we characterize the computably enumerable degrees that are totally limitwise monotonic, show the support strictly increasing 0 ..."
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Abstract. We survey what is known about limitwise monotonic functions and sets and discuss their applications in effective algebra and computable model theory. Additionally, we characterize the computably enumerable degrees that are totally limitwise monotonic, show the support strictly increasing
Separation By Monotonic Functions
, 1996
"... : It is shown that real functions f and g defined on an arbitrary interval I can be separated by a monotonic function iff f \Gamma tx + (1 \Gamma t)y \Delta max \Phi g(x); g(y) \Psi and g \Gamma tx + (1 \Gamma t)y \Delta min \Phi f (x); f (y) \Psi for all x; y 2 I and t 2 [0; 1]. ..."
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: It is shown that real functions f and g defined on an arbitrary interval I can be separated by a monotonic function iff f \Gamma tx + (1 \Gamma t)y \Delta max \Phi g(x); g(y) \Psi and g \Gamma tx + (1 \Gamma t)y \Delta min \Phi f (x); f (y) \Psi for all x; y 2 I and t 2 [0; 1
On the Noise Sensitivity of Monotone Functions
, 2003
"... It is known that for all monotone functions f: {0, 1} n → {0, 1}, if x ∈ {0, 1} n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ɛ = n −α, then P[f(x) � = f(y)] < cn −α+1/2, for some c> 0. Previously, the best constructio ..."
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Cited by 11 (4 self)
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It is known that for all monotone functions f: {0, 1} n → {0, 1}, if x ∈ {0, 1} n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ɛ = n −α, then P[f(x) � = f(y)] < cn −α+1/2, for some c> 0. Previously, the best
Results 1  10
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6,380