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194
Slices, Slabs, and Sections of the Unit hypercube
 Online Journal of Analytical Combinatorics
, 2008
"... Abstract Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history of these probl ..."
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Cited by 8 (1 self)
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Abstract Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history
Approximation by Superpositions of a Sigmoidal Function
, 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
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Cited by 1248 (2 self)
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In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate
A Short Note On The Efficient Random Sampling Of The MultiDimensional Pyramid Between A Simplex And The Origin Lying In The Unit Hypercube
, 2005
"... When estimating how much better a classifier is than random allocation in Qclass ROC analysis, we need to sample from a particular region of the unit hypercube: specifically the region, in the unit hypercube, which lies between the Q 1 simplex in Q(Q  1) space and the origin. This report ..."
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When estimating how much better a classifier is than random allocation in Qclass ROC analysis, we need to sample from a particular region of the unit hypercube: specifically the region, in the unit hypercube, which lies between the Q 1 simplex in Q(Q  1) space and the origin. This report
MEASURING THE INTERACTIONS AMONG VARIABLES OF FUNCTIONS OVER THE UNIT HYPERCUBE
"... Abstract. By considering a least squares approximation of a given square integrable function f ∶ [0, 1] n → R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f . This definition extends the concept of Banzhaf interactio ..."
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Abstract. By considering a least squares approximation of a given square integrable function f ∶ [0, 1] n → R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f . This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f , as an expected value of the derivatives of f . Finally, we discuss a few applications of the interaction index in aggregation function theory.
MEASURING THE INFLUENCE OF THE kTH LARGEST VARIABLE ON FUNCTIONS OVER THE UNIT HYPERCUBE
"... ar ..."
Convex envelopes of multilinear functions over a unit hypercube and over special discrete sets
 ACTA MATHEMATICA VIETNAMICA
, 1997
"... In this paper, we present some general as well as explicit characterizations of the convex envelope of multilinear functions defined over a unit hypercube. A new approach is used to derive this characterization via a related convex hull representation obtained by applying the ReformulationLineariz ..."
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Cited by 17 (1 self)
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In this paper, we present some general as well as explicit characterizations of the convex envelope of multilinear functions defined over a unit hypercube. A new approach is used to derive this characterization via a related convex hull representation obtained by applying the Reformulation
Measuring the interactions among variables of functions over the unit hypercube. arXiv:0912.1547
"... Abstract. By considering a least squares approximation of a given square integrable function f : [0, ..."
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Cited by 1 (1 self)
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Abstract. By considering a least squares approximation of a given square integrable function f : [0,
DISSECTION OF THE HYPERCUBE INTO SIMPLEXES
"... Abstract. A generalization of Sperner's Lemma is proved and, using extensions of padit valuations to the real numbers, it is shown that the unit hypercube in n dimensions can be divided into m Simplexes all of equal hypervolume if and only if m is a multiple of n!. This extends the correspondi ..."
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Cited by 1 (0 self)
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Abstract. A generalization of Sperner's Lemma is proved and, using extensions of padit valuations to the real numbers, it is shown that the unit hypercube in n dimensions can be divided into m Simplexes all of equal hypervolume if and only if m is a multiple of n!. This extends
Quantum Mechanics on the Hypercube
, 2000
"... We construct quantum evolution operators on the space of states, that is represented by the vertices of the ndimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2, Z2n). By construction this representation acts in a natural way on the coordinates of the n ..."
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We construct quantum evolution operators on the space of states, that is represented by the vertices of the ndimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2, Z2n). By construction this representation acts in a natural way on the coordinates
Cube or hypercube of natural units
 hepph/0112339. JHEP03(2002)023 – 30
"... Max Planck introduced four natural units: h,c,G,k. Only the first three of them retained their status, representing the so called cube of theories, after the theory of relativity and quantum mechanics were created and became the pillars of physics. This short note is a little pebble on the tombstone ..."
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Cited by 1 (1 self)
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Max Planck introduced four natural units: h,c,G,k. Only the first three of them retained their status, representing the so called cube of theories, after the theory of relativity and quantum mechanics were created and became the pillars of physics. This short note is a little pebble
Results 1  10
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194