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Two lower bounds for branching programs
, 1986
"... The first result concerns branching programs having width (log n) °{*). We give an fl(n log n ~ log log n) lower bound for the size of such branching programs computing almost any symmetric Boolean function and in particular the following explicit function: "the sum of the input variables is a ..."
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Cited by 19 (1 self)
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The first result concerns branching programs having width (log n) °{*). We give an fl(n log n ~ log log n) lower bound for the size of such branching programs computing almost any symmetric Boolean function and in particular the following explicit function: "the sum of the input variables is a quadratic residue mod p " where p is any given prime between n 1/4 and n 1/3. This is a strengthening of previous nonlinear lower bounds obtained by Chandra, Furst, Lipton and by Pudlak. We mention that by iterating our method the result can be further strengthened to lfl(nlog n). The second result is a C " lower bound for readonceonly branching programs computing an explicit Boolean function. For n = (~), the function computes the parity of the number of triangles in a graph on v vertices. This improves previous exp(cx/n) lower bounds for other graph functions by Wegener and Z£k. The result implies a linear lower bound for the space complexity of this Boolean function on "eraser machines", i.e. machines that erase each input bit immediately after having read it.
On the Use of High Order Ambiguity Function for Multicomponent Polynomial Phase Signals
 Signal Processing, submitted
, 1998
"... Nonstationary signals appear often in reallife applications and many of them can be modeled as polynomial phase signals (PPS). Highorder ambiguity function (HAF) was first introduced to estimate the parameters of a single component PPS, but has not been widely used for multicomponent PPS because ..."
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Cited by 2 (1 self)
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Nonstationary signals appear often in reallife applications and many of them can be modeled as polynomial phase signals (PPS). Highorder ambiguity function (HAF) was first introduced to estimate the parameters of a single component PPS, but has not been widely used for multicomponent PPS because of its nonlinearity. Multicomponent PPS arise for example, in Doppler radar applications when multiple objects are tracked simultaneously. In this paper, we show that HAF is virtually additive for multicomponent PPS and suggest an algorithm to estimate their parameters. Numerical examples are presented to illustrate the theories. Keywords: Polynomial phase signal, chirp signal, highorder ambiguity function, radar, Weyl sum. Original manuscript was submitted to Signal Processing 6/96; revised 12/96, 12/97. y Research supported in part by the National Science Foundation, grant DMS9307601. 1 1 Introduction Signals encountered in engineering applications such as communications, radar,...
Numerical simulation of nonlinear dispersive quantization, preprint 2012
"... Abstract. When posed on a periodic domain in one space variable, linear dispersive evolution equations with integral polynomial dispersion relations exhibit strikingly different behaviors depending upon when the time is rational or irrational relative to the length of the interval, producing the Tal ..."
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Cited by 1 (0 self)
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Abstract. When posed on a periodic domain in one space variable, linear dispersive evolution equations with integral polynomial dispersion relations exhibit strikingly different behaviors depending upon when the time is rational or irrational relative to the length of the interval, producing the Talbot effect of dispersive quantization and fractalization. The goal here is to show that these remarkable phenomena extend to nonlinear dispersive evolution equations. We will present numerical simulations, based on operator splitting methods, of the nonlinear Schrödinger and Korteweg–deVries equations with step function initial data and periodic boundary conditions. For the integrable nonlinear Schrödinger equation, our observations have been rigorously confirmed in a recent paper of Erdoğan and Tzirakis, [10]. 1.
Hua Loo Keng’s Problem Involving Primes of a Special Type
, 812
"... Let η be a quadratic irrationality. The variant of Hua Loo Keng’s problem involving primes such that a < {ηp 2} < b, where a and b are arbitrary real numbers of the interval (0,1), solved in this paper. 1. Introduction Suppose that k ..."
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Let η be a quadratic irrationality. The variant of Hua Loo Keng’s problem involving primes such that a < {ηp 2} < b, where a and b are arbitrary real numbers of the interval (0,1), solved in this paper. 1. Introduction Suppose that k
1992 Birkh&user Verlag, Basel UNIFORM
"... Every sufficiently large finite set X in [0,1) has a dilation nX rood 1 with small maximal gap and even small discrepancy. We establish a sharp quantitative version of this principle, which puts into a broader perspective some classical results on the distribution of power residues. The proof is bas ..."
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Every sufficiently large finite set X in [0,1) has a dilation nX rood 1 with small maximal gap and even small discrepancy. We establish a sharp quantitative version of this principle, which puts into a broader perspective some classical results on the distribution of power residues. The proof is based on a secondmoment argument which reduces the problem to an estimate on the number of edges in a certain graph. Cycles in this graph correspond to solutions of a simple Diophantine equation: The growth asymptotics of these solutions, which can be determined from properties of lattices in Euclidean space, yield the required estimate. 1.
DISCRETE ANALOGUES IN HARMONIC ANALYSIS, I: ` 2 ESTIMATES FOR SINGULAR RADON TRANSFORMS
"... Abstract. This paper studies the discrete analogues of singular Radon transforms. We prove the ` 2 boundedness for those operators that are “quasitranslationinvariant. ” The approach used is related to the “circlemethod ” of Hardy and Littlewood, and requires multidimensional extensions of Weyl ..."
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Abstract. This paper studies the discrete analogues of singular Radon transforms. We prove the ` 2 boundedness for those operators that are “quasitranslationinvariant. ” The approach used is related to the “circlemethod ” of Hardy and Littlewood, and requires multidimensional extensions of Weyl sums and Gauss sums, as well as variants that replace scalar sums by operator sums. 1. Introduction. The
Continued Fractions and the Convergence of a Double Trigonometric Series
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