Saturation mechanisms for multipactors

We study the space complexity of refuting unsatisfiable random k-CNFs in the resolution proof system. We prove that for any large enough /spl Delta/, with high probability a random k-CNF over n variables and /spl Delta/n clauses requires resolution clause space of /spl Omega/(n/spl middot//spl Delta//sup -1+/spl epsiv//k-2-/spl epsiv//), for any 0 >/spl radic/n. This bound is nearly tight. Specifically, we show that with high probability, a random 3-CNF with /spl Delta/n clauses requires tree-like refutation size of exp(/spl Omega/(n//spl Delta//sup 1+/spl epsiv//1-/spl epsiv//)), for any 0</spl epsiv/<1/2. Our space lower bound is the consequence of three main contributions. 1. We introduce a 2-player matching game on bipartite graphs G to prove that there are no perfect matchings in G. 2. We reduce lower bounds for the clause space of a formula F in resolution to lower bounds for the complexity of the game played on the bipartite graph G(F) associated with F. 3. We prove that the complexity of the game is large whenever G is an expander graph. Finally, a simple probabilistic analysis shows that for a random formula F, with high probability G(F) is an expander. We also extend our result to the case of G-PHP, a generalization of the pigeonhole principle based on bipartite graphs G. We prove that the clause space for G-PHP can be reduced to the game complexity on G.

We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model; namely, MM/sub 1/, MM/sub 2/, MM/sub 3/, and compound algorithms C/sub 1/(/spl epsiv/)and C/sub 2/(/spl delta/). Algorithm C/sub 1/(/spl epsiv/) has adjustable time complexity in sublinear level. Algorithm C/sub 2/(/spl delta/) implies that it is feasible to achieve sublogarithmic time using /spl sigma/(N/sup 3/) processors for matrix multiplication on a realistic system. Algorithms MM/sub 3/, C/sub 1/(/spl epsiv/), and C/sub 2/(/spl delta/) all have o(/spl Nscr//sup 3/) cost and, hence, are very processor efficient. Algorithms MM/sub 1/, MM/sub 3/, and C/sub 1/(/spl epsiv/) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM/sub 2/ and C/sub 2/(/spl delta/) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM/sub 2/ and C/sub 2/(/spl delta/) to unbounded integers and reals are also discussed.

We propose a methodology of genetic algorithms (GAs) for the rules searching of model reference fuzzy adaptive control system (MRFACS). We choose a second order reference model as an ideal output, then adjust the proportional sensitivity by using fuzzy adaptive controller to make the plant's output follows the reference signal. We apply modified GAs for rules searching because that the rules set constructed by cut and try works unsatisfactory. In our study, we offer two types of fuzzy controllers (one is constructed with state error /spl epsi/ & change rate of error /spl Delta//spl epsi/ and the other is constructed with state error /spl epsi/ & plant output y/sub p/). The conclusions we get from simulation results are: (1) Modified GAs can find population with higher fitness values since it select better populations by multiple-point crossover and multiple-point mutation, (2) Fuzzy controller with /spl epsi/ and y/sub p/ shows higher performance indices than that with /spl epsi/& /spl Delta//spl epsi/ for the reason that the front controller can avoid using same rules for different time delay constants, and (3) System remains controllable when the time delay constants exceed the expected margin, it proves that our fuzzy controller contains the characteristic of robustness. >

This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X/sup n/}/sub n=1//sup /spl infin// with a finite or countably infinite alphabet. Suppose that for each n /spl ges/ 1 X/sup n/ is encoded to a binary codeword /spl phi//sub n/(X/sup n/) of length l(/spl phi//sub n/(X/sup n/)). Letting /spl epsiv//sub n/ denote the decoding error probability, we consider the following two criteria on FV codes: i) /spl epsiv//sub n/ = 0 for all n /spl ges/ 1 and ii) lim sup/sub n/spl rarr//spl infin///spl epsiv//sub n/ /spl les/ /spl epsiv/ for an arbitrarily given /spl epsiv/ /spl isin/ [0,1). Under criterion i), we show that, if X/sup n/ is encoded by an arbitrary prefix-free FV code asymptotically achieving the entropy, 1/nl(/spl phi//sub n/(X/sup n/)) - 1/nlog/sub 2/ 1/PX/sup n/(X/sup n/) /spl rarr/ 0 in probability as n /spl rarr/ /spl infin/ under a certain condition, where P/sub X//sup n/ denotes the probability distribution of X/sup n/. Under criterion ii), we first determine the minimum rate achieved by FV codes. Next, we show that 1/nl(/spl phi//sub n/(X/sup n/)) of an arbitrary FV code achieving the minimum rate in a certain sense has a property similar to the lossless case.

Robust multivariable controllers for stable infinite-dimensional systems in the Callier-Desoer (CD) algebra are discussed. In particular, the following robust regulation problem is solved. Given reference and disturbance signals, which are linear combinations of signals of the form t/sup j/ sin(/spl omega//sub k/t+/spl phi//sub k/), j/spl ges/0, k=0, /spl middot//spl middot//spl middot/, n, find a low-order finite-dimensional controller so that the outputs asymptotically track the reference signals, asymptotically reject the disturbance signals, and the closed-loop system is stable and robust with respect to a class of perturbations in the plant. The proposed controller consists of a positive scalar gain /spl epsi/ and certain polynomial matrices K/sub k/(s) for k=0, /spl middot//spl middot//spl middot/, n. The main result of the paper shows that the matrices K/sub k/(s) must satisfy certain stability conditions involving the values of the plant transfer function only at the reference and disturbance signal frequencies /spl omega//sub k/ for k=0, /spl middot//spl middot//spl middot/, n. The controller has unstable poles on the imaginary axis. The behavior of these poles as a function of the scalar parameter /spl epsi/ in the form of a Puiseux series is given.

An (n, k)-affine source over a finite field F is a random variable X = (X/sub 1/, ..., X/sub n/) /spl epsi/ F/sub n/, which is uniformly distributed over an (unknown) k-dimensional affine subspace of F/sub n/. We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger than n/sup c/ (where c is a large enough constant). Our main results are as follows: 1. (For arbitrary k): For any n, k and any F of size larger than n/sub 20/, we give an explicit construction for a function D : F/sub n/ /spl rarr/ F/sub k-1/, such that for any (n, k)-affine source X over F, the distribution of D(X) is /spl epsiv/-close to uniform, where /spl epsiv/ is polynomially small in |F|. 2. (For k = 1): For any n and any F of size larger than n/sup c/, we give an explicit construction for a function D : F/sup n/ /spl rarr/ {0,1}/sup (1-/spl sigma/)log//sub 2/|F|, such that for any (n, 1)-affine source X over F, the distribution of D(X) is /spl epsiv/-close to uniform, where /spl epsiv/ is polynomially small in |F|. Here, /spl delta/ > 0 is an arbitrary small constant, and c is a constant depending on /spl delta/.

Summary form only given. About two years ago Bourgain, Katz and Tao (2004) proved the following theorem, essentially stating that in every finite field, a set which does not grow much when we add all pairs of elements, and when we multiply all pairs of elements, must be very close to a subfield. Theorem 1: (Bourgain et al., 2004) For every /spl epsi/ > 0 there exists a /spl delta/ > 0 such that the following holds. Let F be any field with no subfield of size /spl ges/ |F|/sup /spl epsi//. For every set A /spl sube/ F, with |F|/sup /spl epsi// |A|/sup 1 + /spl delta// or the product set |A /spl times/ A| > |A|/sup 1 + /spl delta//. This theorem revealed its fundamental nature quickly. Shortly afterwards it has found many diverse applications, including in number theory, group theory, combinatorial geometry, and the explicit construction of extractors and Ramsey graphs, mostly described in the references below. In my talk I plan to explain some of the applications, as well as to sketch the main ideas of the proof of the sum-product theorem.

We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n+log log(1//spl epsiv/)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2/sup n/ with error bounded by /spl epsiv/. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log(n//spl epsiv/)). As an application of this depth bound, we show that P. Shor's (1997) factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial size, in combination with classical polynomial-time pre- and postprocessing. Next, we prove an /spl Omega/(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically tight (for a reasonable range of values of /spl epsiv/). We also give an upper bound of O(n(log n)/sup 2/ log log n) on the circuit size of the exact QFT modulo 2/sup n/, for which the best previous bound was O(n/sup 2/). Finally, based on our circuits for the QFT with power-of-2 moduli, we show that the QFT with respect to an arbitrary modulus m can be approximated with accuracy /spl epsiv/ with circuits of depth O((log log m)(log log 1//spl epsiv/)) and size polynomial in log m+log(1//spl epsiv/).

We show that for every /spl epsi/ > 0, there is a constant p(/spl epsi/) such that for all integers p /spl ges/ p(/spl epsi/), it is NP-hard to approximate the shortest vector problem in L/sub p/ norm within factor p/sup 1 - /spl epsi// under randomized reductions. For large values of p, this improves the factor 2/sup 1/p/ - /spl delta/ hardness shown by D. Micciancio (1998).

A finite-difference time-domain (FDTD) analysis is presented to simulate, up to the high-frequency regime, transients on multiconductor transmission lines above dissipative earth. Excitation is in the high-frequency regime if the pulse has significant spectral content up to /spl omega//spl ap//spl omega//sub c/, with /spl omega//sub c/ the frequency where the conduction and displacement current densities have equal magnitude. Thus, /spl omega//sub c/=/spl sigma//sub g///spl epsi//sub 0//spl epsi//sub rg/ with /spl sigma//sub g/ and /spl epsi//sub rg/ the ground conductance and relative permittivity. The FDTD algorithm extends the formulation of Agrawal et al. (1980), by incorporating the theory of D'Amore and Sarto for the interaction of wide-band transients with the earth. Careful experimental testing of the new algorithm is presented. The measurement configuration consists of two parallel wires; first suspended above an aluminum sheet to test the code in the low-frequency regime; then above a block of absorbing material for experiments in the high-frequency regime. The end of one of the conductors is driven with a 2-ns synthesized impulse by a stepped-frequency, automatic network analyzer. Reflected and cross-talk signals are presented in the time domain. These show good agreement with the numerically predicted common mode, differential mode and mode-converted pulses.

Summary form only given. We present the reflectance spectra of conducting polyaniline film protonated with sulfuric acid (PANI-H/sub 2/SO/sub 4/) and of newly processed film protonated with camphor sulfonic acid (PANI-CSA) over a wide spectral range (0.006 eV-6 eV) at room temperature. The reflectance of PANI-H/sub 2/SO/sub 4/reveals the signatures of the intraband excitations in the infrared (IR), including increasing reflectance approaching to far-IR and a reflectance minimum around 1.7 eV. However, the corresponding optical conductivity (/spl sigma/(/spl omega/)) and the real part of dielectric function (/spl epsiv//sub 1/(/spl omega/)) are far from those of a metal. Instead, the optical spectra indicate that the charge carriers are localized with considerable oscillator strength within the gap. On the other hand, the optical spectra of PANI- CSA are characterized by distinct metal-like signatures arising from the combination of the Drude-like free carrier excitations in the far-IR and the existence of plasma resonance around 1.2 eV. These results indicate that the new processing of polyaniline with functionalized sulfonic acid (with surfactants as counterions) has greatly improved the homogeneity of the material and has resulted in a significant decrease in the extent of molecular scale disorder, thereby leading to the delocalization of the charge carriers in PANI-CSA. However, the deviation of /spl sigma/(/spl omega/) and /spl epsiv//sub 1/(/spl omega/) from the normal Drude metallic behaviors below 0.2 eV indicates that disorder induced localization still plays an important role in PANI-CSA. We present a quantitative analysis of /spl sigma/(/spl omega/) and /spl spl epsiv//sub 1/(/spl omega/) of PANI-CSA in terms of the localization modified Drude model, implying that PANI-CSA is a disordered metal on the metal-insulator boundary.

The relationship between weak convergence of channel probability measures, channel capacity, and error probability of block codes is examined for memoryless channels with general input and output alphabets. It is shown that channel capacity is a lower semi-continuous function and that every block code with maximal probability of error /spl delta/ for a nominal channel for any /spl epsiv/>0 can be modified such that the modification has a probability of error less than /spl delta/+/spl epsiv/ for all channels in a sufficiently small neighborhood of the nominal channel.

The probability distribution function of the FM clicks is derived for the case of a carrier impaired by Wiener-Levy phase noise and detected by a limiter-discriminator receiver with pre- and post-detection filtering. The analysis is performed accounting for the effects of predetection (RF) filtering on signal and phase noise and holds for /spl Delta//spl nu//B/spl Lt/1, /spl Delta//spl nu/ being the 3-dB linewidth of the unmodulated carrier and B the bandwidth of the RF filter. How small /spl Delta//spl nu//B is to be will depend on the kind of RF filter. For the raised cosine filter with small rolloff /spl epsiv/ considered here the analysis holds for /spl Delta//spl nu//B>

A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following edge-deletion problem; given a monotone property P and a graph G, compute the smallest number of edge deletions that are needed in order to turn G into a graph satisfying P. We denote this quantity by E/sub P/'(G). The first result of this paper states that the edge-deletion problem can be efficiently approximated for any monotone property. 1) For any /spl epsiv/ > 0 and any monotone property P, there is a deterministic algorithm, which given a graph G of size n, approximates E/sub P/'(G) in time O(n/sup 2/) to within an additive error of /spl epsiv/n/sup 2/. Given the above, a natural question is for which monotone properties one can obtain better additive approximations of E/sub P/'. Our second main result essentially resolves this problem by giving a precise characterization of the monotone graph properties for which such approximations exist; 1. If there is a bipartite graph that does not satisfy P, then there is a /spl delta/ > 0 for which it is possible to approximate E/sub P/' to within an additive error of n/sup 2-/spl delta// in polynomial time. 2) On the other hand, if all bipartite graphs satisfy P, then for any /spl delta/ > 0 it is NP-hard to approximate E/sub P/' to within an additive error of n/sup 2-/spl delta//. While the proof of (1) is simple, the proof of (2) requires several new ideas and involves tools from extremal graph theory together with spectral techniques. This approach may be useful for obtaining other hardness of approximation results. Interestingly, prior to this work it was not even known that computing E/sub P/' precisely for the properties in (2) is NP-hard. We thus answer (in a strong form) a question of Yannakakis [1981], who asked in 1981 if it is possible to find a large and natural family of graph properties for which computing E/sub P/' is NP-hard.

Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for /spl theta/-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its /spl phi//sub n/ nearest neighbors. A network is called /spl theta/-covered if every node, except those near the boundary, can find one of its /spl phi//sub n/ nearest neighbors in any sector of angle /spl theta/. For all /spl theta//spl isin/(0,2/spl pi/), if /spl phi//sub n/=(1+/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, it is shown that the probability of /spl theta/-coverage goes to one as n goes to infinity, for any /spl delta/>0; on the other hand, if /spl phi//sub n/=(1-/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, the probability of /spl theta/-coverage goes to zero. This sharp characterization of /spl theta/-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if /spl phi//sub n/=(1+/spl delta/)log/sub 2/n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.