### Table 1: Classical radial basis functions 16 Classical RBF Equation

2003

"... In PAGE 4: ... (35) Some of the classical radial functions used in multivariate interpolation are presented in Table 1. Note that the shape parameter c in the radial basis functions in Table1 is user-defined and can be adjusted Table 1: Classical radial basis functions 16 Classical RBF Equation ... ..."

Cited by 2

### Table 1. Boolean functions and constants in SHA-1

2005

"... In PAGE 9: ... Suppose we would like to correct 10 conditions from step 17 to 22 by modifying the last 6 message words m10; m11; :::m15. From Table1 2, we know there are 32 chaining variable conditions, together with total 47 message equations from step 11 to step 16, the total number of conditions is 79 in step 11-16. Intuitively, this leaves a message space of size 2113, which is large enough for modifying some message bits to correct 10 conditions.... In PAGE 11: ... We use step 23 to step 80 of the disturbance vector in Table 5 to construct a 58-step differential path that leads to a collision. The specific path for the first 16 steps is given in Table1 0, and the rest of the path consists of the usual local collisions. As we discussed before, there are two major complications that we need to deal with in constructing a valid differential path in the first 16 steps.... ..."

Cited by 63

### Table 1: Best bounds to date on strong and weak PTF degrees of n-variable Boolean functions. Lower bounds for every function mean that some function has this as a lower bound. Boldface entries are new bounds proved in this paper.

2003

Cited by 10

### Table 1: Best bounds to date on strong and weak PTF degrees of n-variable Boolean functions. Lower bounds for \every function quot; mean that some function has this as a lower bound. Entries marked with (y) are new bounds proved in this paper.

2007

### Table 2 Relation of Higher Order Nonlinearity, Partial Higher Order Nonlinearity, Algebraic Immunity and Degree for Some Balanced Boolean Function f of 6 Arguments

### Table 1. Distribution of the Walsh-Hadamard spectra for Boolean functions of n variables.

"... In PAGE 3: ... Each of them has different and unique spectra. Table1 shows distribution of spectral coefficients for some Boolean functions of n -variables. Table 1.... In PAGE 6: ... Mentioned functions are balanced. It is possible to construct of Boolean functions of n 3 = variables with eight nonzero spectral coefficients but such functions are not balanced ( Table1 and Table 2). For and , it is possible to construct balanced Boolean functions f with algebraic degree .... ..."

Cited by 1

### Table 3: Best bounds to date on density and degree for -approximating polynomials for n-variable Boolean functions. Lower bounds for \every function quot; mean that some function has this as a lower bound. Entries marked with (y) are new bounds proved in this paper | for the range of for which they hold, please see the relevant theorems. For (z), we in fact show that every set of (1 ( 2 n )) 2n monomials can serve as an -approximating polynomial support for almost every Boolean function.

2007

### Table 1: Functions C for the M, S, RMCD and classical estimator of the covariance matrix.

2000

"... In PAGE 7: ... Examples of the function C for some robust estimators. corresponding functions C are given in Table1 and are plotted in Figure 1. The functions S and M are smooth while RMCD is a step-function with two discontinuities: one at pq which is due to the initial estimator and the other one at pq resulting from the weighting scheme.... ..."

Cited by 8

### Table 5.1: Basic functionality annotations for naming concept responsibilities

### Table 1: Rules for Transforming Boolean Operations to Probability Expressions FUNCTION BOOLEAN EXPRESSION PROBABILITY EXPRESSION Inversion

"... In PAGE 7: ... It is possible to compute the OPE for a given circuit by transforming its Boolean equation representation or by calculating the OPE from a schematic diagram representation [21]. The rules for transforming a Boolean equation to its equivalent OPE are given in Table1 . In this table, the rules are given for 2-input logic gates only, but the expressions for functions with more than 2-inputs or with di erent gate types may be easily derived.... In PAGE 7: ... In this OPE calculation technique, each primary input, each internal interconnection, and the output is assigned a unique variable name. Using the rules in Table1 , each internal node is expressed as a function of the primary inputs. This step is performed through subsequent substitutions until an expression is derived for the output variable in terms of the primary input variables thus forming the OPE.... In PAGE 7: ... This step is performed through subsequent substitutions until an expression is derived for the output variable in terms of the primary input variables thus forming the OPE. As an example, consider the logic diagram illustrated in Figure 2 that is a realization of the Boolean equation: f(x) = x1x2x3x4 + x1x2x3x4 + x1x2x3x4 + x1x2x3x4 + x1x2x3x4 (5) Using the variables assigned to each interconnection as shown in Figure 2 and the rules in Table1 , the OPE is derived as follows.... In PAGE 10: ...OPE of the original circuit may be computed initially and stored. Then all that is required is the computation of the OPE of each constituent function and the two OPEs are combined using quot;AND-operation quot; rule given in Table1 . If the constituent functions are simple then the corresponding computation of each spectral coe cient is e cient.... In PAGE 10: ... First the composite OPE will be formulated by ANDing the OPE for fc (denoted by OP Ec) with that of the original function, f. This composite OPE (denoted by OP Ecomp) is given by multiplying Equation 12 by OP Ec = X3 and obeying the idempotence rule in Table1 . The result is: OP Ecomp = X3 ? X2X3 ? X1X3X4 + X1X2X3X4 (18) To determine the pm1 value associated with the constituent function, fc = x3, the value of 0.... In PAGE 11: ... In the worst case, there can be 2n product terms since all possible combinations of the input variables may be used to formulate a single term. Fortunately, due to the idempotence rule in Table1 , there are no variables present in the OPE with a power greater than unity. In addition, most logic circuits have OPEs with signi cantly fewer product terms than the maximum possible number of 2n.... ..."