Additive Approximation for Edge-Deletion Problems

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.

Summary form only given. The single-particle theory of electron multipactor is now well understood. The multipactor parameter space is spanned by the normalized magnetic and electric field parameters. In particular, for given normalized magnetic field /spl Omega/ multipactor can errupt within a certain range of electric field amplitudes /spl epsi//sub 1/</spl epsi/</spl epsi//sub 2/; to each value /spl epsi/ corresponds a different locked-phase /spl phi/. Once a multipactor has been launched, it is very important to know the saturation level; the latter determines the cavity power losses when the multipactor is a parasitic side effect, or the saturated current when a multipactor is deliberately triggered for the production of short period high current pulsed beams. The collective space charge effects must be included to address multipactor saturation. One proposed approach employs a single charge sheet and yields saturation when the secondary emission coefficient /spl delta/ equals one. Setting /spl delta/=1 fixes the impact parameters and therefore the value of the driving electric field /spl epsi/; the external RF field adjusts to that value through the nonlinear effect of the induced multipactor current on the cavity LC circuit. A limitation of the method is that one must start near the appropriate /spl epsi/ since the range of the voltage self-adjustment is usually small. A most general approach introduced here is based on multilayered space charge cloud involving electrons emitted at slightly different times. There is a continuous distribution of impact energies and interaction phases between the leading and the trailing edge of the bunch.

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. >

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.

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/.

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>

Minimal reducible bounds for induced-hereditary properties

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 minimum distance of some families of expander codes is studied, as well as some related families of codes defined on bipartite graphs. The weight spectrum and the minimum distance of a random ensemble of such codes are computed and it is shown that it sometimes meets the Gilbert-Varshamov (GV) bound. A lower bound on the minimum distances of constructive families of expander codes is derived. The relative minimum distance of the expander code is shown to exceed the product bound, i.e., the quantity /spl delta//sub 0//spl delta//sub 1/ where /spl delta//sub 0/ and /spl delta//sub 1/ are the minimum relative distances of the constituent codes. As a consequence of this, a polynomially constructible family of expander codes is obtained whose relative distance exceeds the Zyablov bound on the distance of serial concatenations.

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 high-Q hemispherical open resonator is connected to an automatic network analyzer to enable precise and fast determination of the permittivity and loss tangent of low-loss dielectric materials at 100 GHz. Both scalar theory and vector theory with a frequency variation method are used to determine the dielectric properties of low-loss materials which are used in quasioptical components, for example in fusion reactor windows and tenses for millimeter-wave receivers. The uncertainty of the measurement is 0.02% to 0.04% for /spl epsi//sub r/(/spl epsiv//sub r//spl ges/2) and 6-40/spl times/10/sup -6/ for tan /spl delta/(10/sup -4//spl les/tan /spl delta//spl les/10/sup -3/).

We provide some evidence that unique k-SAT is as hard to solve as general k-SAT, where k-SAT denotes the satisfiability problem for k-CNFs and unique k-SAT is the promise version where the given formula has 0 or 1 solutions. Namely, defining for each k/spl ges/1, s/sub k/=inf{/spl delta//spl ges/0|/spl exist/aO(2/sup /spl delta/n/)-time randomized algorithm for k-SAT} and, similarly, /spl sigma//sub k/=inf{/spl delta//spl ges/0|/spl exist/aO(2/sup /spl delta/n/)-time randomized algorithm for Unique k-SAT}, we show that lim/sub k/spl rarr//spl infin//s/sub k/=lim/sub k/spl rarr//spl infin///spl sigma//sub k/. As a corollary, we prove that, if Unique 3-SAT can be solved in time 2/sup /spl epsi/n/ for every /spl epsi/>0, then so can k-SAT for k/spl ges/3. Our main technical result is an isolation lemma for k-CNFs, which shows that a given satisfiable k-CNF can be efficiently probabilistically reduced to a uniquely satisfiable k-CNF, with nontrivial, albeit exponentially small, success probability.

The cause for the changes in polarization state of microwave signals is searched after physical properties of the channel of propagation and their variations in accordance with atmospheric state. The characteristics of the air, as propagation medium, are determined by the content, concentration and physical properties of the suspended particulates; especially it is noticeable in the surface layer over the areas with high levels of aerosol concentration and humidity (urban, semi-arid, highways, etc.). The interaction between aerial water and solid particulates leads to the appearance of increased amounts of enlarged grains with changed dielectric permittivity /spl epsiv//spl tilde//sub g/, which value depends on the water fraction in the grain, particularly in the centimeter wave range. The formation of less or more dense volumes with various /spl epsiv//spl tilde//sub g/ entails displacement of the transmitted signal, while wind exerts control over the distribution of such irregularities in the air. Fairly high correlation (with coefficients |/spl rho/|>0.45) between temperature, humidity, concentration of suspended particles and winds, and the power P/sub r/ and cross-polarization discrimination (XPD) characteristics (XPD and /spl delta/) of microwave signals was observed under moderate weather conditions. During a quiet 24-h cycle the mean level of P/sub r/ and XPD changes in /spl sim/ 10% and 30%, correspondently; fastest variations in depolarization degree are obtained close to sunset and after sunrise, when the large gradients of meteorological parameters and maximum instability of air streams take place. Seasonal fluctuations of P/sub r/ and XPD are registered, too.

Let G=(V, E) be a connected graph and let /spl phi/ be a permutation of V. The total relative displacement of the permutation /spl phi/ of G is /spl delta//sub /spl phi//(G)=/spl Sigma//sub {x,y}/spl sub/V/|d(x,y)-d(/spl phi/(x), /spl phi/(y))|, where d(x, y) means the distance between x and y in G. The maximum value of /spl delta//sub /spl phi//(G) among all permutations in a graph G is called the chaotic number of G and the permutation which attains to the chaotic number is called a chaotic mapping of G. In this paper, we study the chaotic number of bipartite and tripartite graphs and find the closed form formulas for the bipartite graphs and an algorithm running in O(n/sub 3//sup 4/) time to find the chaotic numbers of tripartite graphs where n/sub 3/ is the number of vertices in the biggest partite set. We emphasize that it partially improves an algorithm proposed in (H. L. Fu et al, J. of Combin. Optimization, vol.110, no.3, p.545-556, 2001).