the approximability of constraint satisfaction problems we study optimization problems that may be expressed as boolean constraint satisfaction problems an instance of a boolean constraint satisfaction problem is given by m constraints applied to n boolean variables different computational problems arise from constraint satisfaction problems depending on the nature of the underlying constraints as well as on the goal of the optimization task here we consider four possible goals max csp min csp is the class of problems where the goal is to find an assignment maximizing the number of satisfied constraints minimizing the number of unsatisfied constraints max ones min ones is the class of optimization problems where the goal is to find an assignment satisfying all constraints with maximum minimum number of variables set to 1 each class consists of infinitely many problems and a problem within a class is specified by a finite collection of finite boolean functions that describe the possible constraints that may be used tight bounds on the approximability of every problem in max csp were obtained by creignou j comput system sci 51 1995 pp 511 522 in this work we determine tight bounds on the approximability i e the ratio to within which each problem may be approximated in polynomial time of every problem in max ones min csp and min ones combined with the result of creignou this completely classifies all optimization problems derived from boolean constraint satisfaction our results capture a diverse collection of optimization problems such as max 3 sat max cut max clique min cut nearest codeword etc our results unify recent results on the in approximability of these optimization problems and yield a compact presentation of most known results moreover these results provide a formal basis to many statements on the behavior of natural optimization problems that have so far been observed only empirically

approximation algorithms for node deletion problems on bipartite graphs with finite forbidden subgraph characterization in this paper we develop approximation algorithms for a few node deletion problems when the input is restricted to be a bipartite graph we look at node deletion problems for non trivial properties which can be characterized by forbidden structure which has a bounded intersection with both the bipartitions the approximation factors obtained directly depend upon the size of the largest such intersection special instances of this general problem include problems such as the minimum chain vertex deletion minimum dissociation vertex deletion minimum bipartite claw vertex deletion minimum bi complement vertex deletion and minimum bipartite threshold vertex deletion problems the algorithms are based upon the techniques of linear programming and iterative rounding we also use the node deletion algorithms to marginally improve the trivial approximation factor for complementary problem of determining the size of the maximum sized vertex induced subgraph lying in the given graph class and prove the apx completeness of all of these problems

a sensitivity tradeoff for plants with time delay in this paper we show that the sensitivity function of a scalar feedback system must satisfy an integral constraint when the open loop transfer function is strictly proper and contains a time delay the integral constraint is identical to the classical bode sensitivity integral which holds provided the open loop gain has greater than a one pole rolloff the design implications of the two constraints are somewhat different however and this difference is discussed the relation between open loop phase and a conflict between bandwidth and sensitivity properties is explored

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

enhanced multilevel linear sampling methods for inverse scattering problems we develop two enhanced techniques for the multilevel linear sampling method mlsm proposed in 32 for inverse scattering problems under some practical situations the mlsm suffers certain undesirable breakage cells problem we propose to avoid the curse of breakage cells by incorporating expanding and searching techniques the new techniques are shown to significantly improve the robustness of the mlsm and meanwhile they possess the same optimal computational complexity as the mlsm numerical experiments are presented to illustrate the promising features of the enhanced mlsms

iterative computational techniques in scattering based upon the integrated square error criterion an iterative technique is developed to rigorously compute the electromagnetic time and frequency domain scattering problems the method is based upon a wave function expansion technique this also includes the integral representation techniques in which the electromagnetic field equations and causality conditions are satisfied analytically while the boundary conditions or the constitutive relations have to be satisfied in a computational manner the latter is accomplished by an iterative minimization of the integrated square error for the solution of an integral equation it is shown how to obtain optimum convergence some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method

a comparison of two methods for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium abstract a comparison is made of two methods for solving the inverse scattering problem for acoustic waves in an inhomogeneous absorbing medium these methods were recently introduced by colton kirsch and monk and are based on considering a weighted average of the far field data instead of the far field data itself the comparison is based on numerical examples for the special case of spherically stratified media

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

shorter arithmetization of nondeterministic computations arithmetizing computation is a crucial component of many fundamental results in complexity theory including results that gave insight into the power of interactive proofs multi prover interactive proofs and probabilistically checkable proofs informally an arithmetization is a way to encode a machine s computation so that its correctness can be easily verified via few probabilistic algebraic checks we study the problem of arithmetizing nondeterministic computations for the purpose of constructing short probabilistically checkable proofs pcps with polylogarithmic query complexity in such a setting a pcp s proof length depends at least linearly on the length in bits of the encoded computation thus minimizing the number of bits in the encoding is crucial for minimizing pcp proof length in this paper we show how to arithmetize any t step computation on a nondeterministic turing machine by using a polynomial encoding of length o t log t 2 previously the best known length was t log t 4 for nondeterministic random access machines our length is o t log t 2 o 1 while prior work only achieved t log t 5 the polynomial encoding that we use is the reed solomon code when combined with the best pcps of proximity for this code our result yields quasilinear size pcps with polylogarithmic query complexity that are shorter by at least two logarithmic factors than in all prior work our arithmetization also enjoys additional properties first it is succinct i e the encoding of the computation can be probabilistically checked in log t o 1 time this property is necessary for constructing short pcps with a polylogarithmic time verifier furthermore our techniques extend in a certain well defined sense to the arithmetization of yet other nexp complete languages

approximation resistance from pairwise independent subgroups we show optimal up to a constant factor np hardness for a maximum constraint satisfaction problem with k variables per constraint max kcsp whenever k is larger than the domain size this follows from our main result concerning csps given by a predicate a csp is approximation resistant if its predicate contains a subgroup that is balanced pairwise independent our main result is analogous to austrin and mossel s bypassing their unique games conjecture assumption whenever the predicate is an abelian subgroup our main ingredient is a new gap amplification technique inspired by xor lemmas using this technique we also improve the np hardness of approximating independent set on bounded degree graphs almost coloring label cover and various other problems

on the complexity of approximating the independent set problem we show that for some positive constant c it is not feasible to approximate independent set for graphs of n nodes within a factor of n c provided maximum 2 satisfiability does not have a randomized polynomial time approximation scheme we also study reductions preserving the quality of approximations and exhibit complete problems

approximating the maximum weight clique using replicator dynamics given an undirected graph with weights on the vertices the maximum weight clique problem mwcp is to find a subset of mutually adjacent vertices a clique having the largest total weight this is a generalization of the problem of finding the maximum cardinality clique of an unweighted graph which is the special case of the mwcp when all vertex weights are equal the problem is np hard for arbitrary graphs and so is the problem of approximating it within a constant factor we present a parallel distributed heuristic for approximating the mwcp based on dynamics principles it centers around a continuous characterization of the mwcp a purely combinatorial problem and lets it be formulated in terms of continuous quadratic programming one drawback is the presence of spurious solutions and we present their characterizations to avoid them we introduce a regularized continuous formulation of the mwcp and show how it completely solves the problem the formulation naturally maps onto a parallel distributed computational network whose dynamical behavior is governed by the replicator equations these are dynamical systems introduced in evolutionary game theory and population genetics to model evolutionary processes on a macroscopic scale we present theoretical results which guarantee that the solutions provided by our clique finding replicator network are actually those sought experimental results confirm the effectiveness of the proposed approach

higher order nonlinear diffraction tomography inversion of the rytov series nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large possibly infinite number of terms in the rytov series the algorithms attain the form of a volterra series of nonlinear operators with the usual filtered backpropagation algorithm of diffraction tomography as the leading linear term a computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry

the finite element method contrast source inversion algorithm for 2d transverse electric vectorial problems the contrast source inversion algorithm is formulated using the finite element method for two dimensional transverse electric microwave imaging problems edge based triangular elements with vector basis functions are utilized to solve the te electromagnetic problem a single finite element method fem mesh is used to model both the electric field as well as the contrast source and contrast variables used in the inverse problem the electromagnetic field is modeled by taking the unknown values to be the tangential components of the transverse electric field along the edges of each triangular element the unknown contrast source and contrast variables are located at the centroids of every triangular element of the same fem mesh but only inside the imaging domain the adaptation of the fem contrast source inversion fem csi algorithm to 2d te problems on such an arbitrary mesh requires the implementation of special transformation operators which are presented herein the algorithm s capabilities are demonstrated by inverting the fresnel experimental te datasets as well as synthetically generated data

towards optimal lower bounds for clique and chromatic number it was previously known that neither max clique nor min chromatic number can be approximated in polynomial time within n1 e for any constant e 0 unless np zpp in this paper we extend the reductions used to prove these results and combine the extended reductions with a recent result of samorodnitsky and trevisan to show that unless np zptime 2o log n log log n 3 2 neither max clique nor min chromatic number can be approximated in polynomial time within n1 e n where e o log log n 1 2 since there exists polynomial time algorithms approximating both problems within n1 e n where e n log log n log n our result shows that the best possible ratio we can hope for is of the form n1 o 1 for some yet unknown value of o 1 between o log log n 1 2 and log log n log n

iterative forward and inverse algorithms based on domain integral equations for three dimensional electric and magnetic objects an iterative approach to full vector three dimensional inverse scattering problems where the unknown objects can have conductivity permittivity and permeability different from the known background medium is discussed since this problem involves a large number of unknowns it has to be solved effectively and efficiently so that the results can be obtained in timely manner the forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations and hence it is also of significant importance in the optimization process of the inverse problem the inverse scattering problem is attacked using the multiplicative regularized contrast source inversion method as known in the literature the complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type furthermore this inverse method has been armed with a weighted l2 norm regularizer which has been included as a multiplicative constraint some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms

locally testable codes and pcps of almost linear length we initiate a systematic study of locally testable codes that is error correcting codes that admit very efficient membership tests specifically these are codes accompanied with tests that make a constant number of random queries into any given word and reject non codewords with probability proportional to their distance from the code locally testable codes are believed to be the combinatorial core of pcps however the relation is less immediate than commonly believed nevertheless we show that certain pcp systems can be modified to yield locally testable codes on the other hand we adapt techniques that we develop for the construction of the latter to yield new pcps our main results are locally testable codes and pcps of almost linear length specifically we prove the existence of the following constructs locally testable binary linear codes in which k information bits are encoded by a codeword of length k exp o log k this improves over previous results that either yield codewords of exponential length or obtained almost quadratic length codewords for sufficiently large nonbinary alphabet pcp systems of almost linear length for sat the length of the proof is n exp o log n and verification in performed by a constant number i e 19 of queries as opposed to previous results that used proof length n 1 p o 1 q for verification by q queries the novel techniques in use include a random projection of certain codewords and pcp oracles that preserves local testability an adaptation of pcp constructions to obtain linear pcp oracles for proving conjunctions of linear conditions and design of pcps with some new soundness properties a direct construction of locally testable linear codes of subexponential length

a full vectorial contrast source inversion scheme for three dimensional acoustic imaging of both compressibility and density profiles imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields described via integral equations imaging is based on solving for the unknown medium parameters using known measured scattered wave fields and it is difficult to solve this ill posed inverse problem directly using a conjugate gradient inversion scheme here a contrast source inversion method is used in which the contrast sources defined via the product of changes in compressibility and density with the pressure and velocity wave fields respectively are computed iteratively after each update of the contrast sources an update of the medium parameters is obtained total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts the method successfully reconstructed three dimensional contrast profiles based on changes in both density and compressibility using synthetic data both with and without 50 white noise the results were compared with imaging based only on the pressure wave field where speed of sound profiles were solely based on changes in compressibility it was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density

interactive proofs and the hardness of approximating cliques the contribution of this paper is two fold first a connection is established between approximating the size of the largest clique in a graph and multi prover interactive proofs second an efficient multi prover interactive proof for np languages is constructed where the verifier uses very few random bits and communication bits last the connection between cliques and efficient multi prover interaction proofs is shown to yield hardness results on the complexity of approximating the size of the largest clique in a graph of independent interest is our proof of correctness for the multilinearity test of functions

a new integral equation method to solve highly nonlinear inverse scattering problems a family of new integral equations nie is proposed in this paper which are transformed from the original lippmann schwinger integral equation it can be shown that the nie can effectively reduce the nonlinearity of inverse scattering problems by reducing the global nonlinear effects introduced by the multiple scattering behaviors in estimating the contrast equipping the previously proposed twofold subspace based optimization method with such nie the new inversion method is able to solve inverse scattering problems with strong scatterers like with high contrast and or large dimensions in terms of wavelength ones furthermore such a family of nie could provide a convenient tool to appraise reconstructed results several representative numerical tests are carried out using both synthetic and experimental data to verify the efficacy of the new inversion method

on dinur s proof of the pcp theorem probabilistically checkable proofs are proofs that can checked probabilistically by reading very few bits of the proof in the early 1990 s it was shown that proofs could be transformed into probabilistically checkable ones with only a modest increase in their size the initial transformations though elementary were a little too complex a recent work due to irit dinur gives a dramatically simple and radically new construction of probabilistically checkable proofs this article explains the notion of a probabilistically checkable proof presents the formal definition and then introduces the reader to dinur s work along with some of the context

on testing monomials in multivariate polynomials this paper presents a summary of our initial work on developing a theory of testing monomials in multivariate polynomials the central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum product expansion the complexity aspects of this problem and its variants are investigated with two objectives one is to understand how this problem relates to critical problems in complexity and if so to what extent the other is to exploit possibilities of applying algebraic properties of polynomials to the study of those problems a series of results about email protected p and email protected polynomials is obtained in this paper laying a basis for further study along this line several randomized and deterministic algorithms are devised for testing multilinear monomials or p monomials in certain respective types of polynomials where p is prime

a modified gradient method for two dimensional problems in tomography abstract a method for reconstructing the complex index of refraction of a bounded two dimensional inhomogeneous object of known geometric configuration from measured scattered field data is presented this work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive over relaxation technique the relaxation parameter was chosen to minimize the residual error at each step convergence of this process was established for indices of refraction much larger than required for convergence of the born approximation for the inverse problem the same technique is applied except in this case both the index of refraction and the field are unknown iterative solutions for both unknowns are postulated with two relaxation parameters at each step they are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data this procedure retains the nonlinear relation between the two unknowns numerical results are presented for a number of representative two dimensional objects the algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent

a fast volume integral equation method for the direct inverse problem in elastic wave scattering phenomena a fast method for solving the volume integral equation is introduced for the solution of forward and inverse multiple scattering problems in an elastic 3 d full space for both forward and inverse scattering analysis the volume integral equation in the wavenumber domain is used by means of the discrete fourier transform the volume integral equation in the wavenumber domain can be dealt with as a fredholm equation of the 2nd kind with respect to a non hermitian operator on a finite dimensional vector space the bi cgstab method is employed to construct the krylov subspace in the wavenumber domain the current procedure establishes a fast and simplified method without requiring the derivation of a coefficient matrix several numerical results validate the accuracy and effectiveness of the current method for both forward and inverse scattering analysis according to the numerical results the reconstruction of inhomogeneities of the wave field is successful even for multiple scattering of several cubes

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

microwave imaging using the finite element method and a sensitivity analysis approach a method for reconstructing the constitutive parameters of two dimensional 2 d penetrable scatterers from scattered field measurements is presented this method is based on the differential formulation of the forward scattering problem which is solved by applying the finite element method fem given a set of scattered field measurements the objective is to minimize a cost function which consists of two terms the first is the standard error term which is related to the measurements and their estimates while the second term which is related to the tikhonov regularization is used to heal the ill posedness of the inverse problem the iterative polak ribiere nonlinear conjugate gradient algorithm is applied to the minimization of the cost function during each iteration of the algorithm the direction of correction is computed by using a sensitivity analysis approach which is carried out by an elaborate finite element scheme the adoption of the finite element method results in sparse systems of equations while the computational burden is further reduced by applying the adjoint state vector methodology finally a microwave medical imaging application which is related to the detection of proliferated bone marrow is examined while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated

iterative inverse scattering method employing gram schmidt orthogonalization abstract an inverse scattering method is tested which appears to work very well it is an iterative procedure based on the distorted wave born approximation the resulting fredholm equation of the first kind is solved by a projection method that requires the construction of an orthonormal set of basis functions from the set of kernel functions this can be done by the spectral expansion method which entails matrix diagonalization or by gram schmidt orthogonalization the method is tested on a simple one dimensional optical wave inverse scattering problem both orthonormalization methods lead to a rapidly convergent and stable iteration the spectral expansion method gives somewhat better results but the gram schmidt orthogonalization method which is the novel aspect of our approach is much less time consuming we show how the projection method can be generalized to the case of acoustic wave scattering where the target must be characterized by more than a single independent function of position

algebraic testing and weight distributions of codes we study the testing problem that is the problem of determining maybe probabilistically if a function to which one has oracle access satisfies a given property we propose a framework in which to formulate and carry out the analysis of several known tests this framework establishes a connection between testing and the theory of weight distributions of codes we illustrate this connection by giving a coding theoretic interpretation of several tests that fall under the label of low degree tests we also show how the connection naturally suggests a new way of testing for linearity over finite fields we derive from the macwilliams theorems a general result the duality testing lemma and use it to analyze the simpler tests that fall into our framework in contrast to other analyses of tests the ones we present elicit the fact that a test s probability of rejecting a fuction depends on how far away the function is from every function that satisfies the property of interest

reconstruction of two dimensional permittivity distribution using the distorted born iterative method the distorted born iterative method dbim is used to solve two dimensional inverse scattering problems thereby providing another general method to solve the two dimensional imaging problem when the born and the rytov approximations break down numerical simulations are performed using the dbim and the method proposed previously by the authors int j imaging syst technol vol 1 no 1 p 100 8 1989 called the born iterative method bim for several cases in which the conditions for the first order born approximation are not satisfied the results show that each method has its advantages the dbim shows faster convergence rate compared to the bim while the bim is more robust to noise contamination compared to the dbim

the complexity of counting in sparse regular and planar graphs we show that a number of graph theoretic counting problems remain cal np hard indeed cal p complete in very restricted classes of graphs in particular we prove that the problems of counting matchings vertex covers independent sets and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree we obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2 cnf formulae to achieve these results a new interpolation based reduction technique which preserves properties such as constant degree is introduced

the primal dual method for approximation algorithms in this survey we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to np hard problems in combinatorial optimization because of parallels with the primal dual method commonly used in combinatorial optimization we call it the primal dual method for approximation algorithms we show how this technique can be used to derive approximation algorithms for a number of different problems including network design problems feedback vertex set problems and facility location problems

wave field reciprocity and optimization in remote sensing a unified approach to local optimization techniques and wave field reciprocity as applied to constructing solutions to remote sensing imaging and inversion problems in acoustic elastic and electromagnetic wave theory is presented the starting point is a system of linear first order partial differential equations in space time of the class to which the indicated wave phenomena gives rise for this system three types of remote sensing problems the inverse source the inverse scattering and the inverse transducted wave field problems are formulated and the construction of their solutions via local optimization techniques is discussed emphasis is placed on iterative algorithms that are based on a guaranteed decrease in the mismatch between modelled and observed data at each update of the medium subsequently the wave field reciprocity theorems of the time convolution and the time correlation types are derived and their occurrence in the optimization procedures is discussed also attention is paid to approximate methods in particular to the rayleigh gans born approximation approximations of this sort provide the means to invoke the method of preconditioning in the process of inverting the operator equations exotic media for example chiral media in electromagnetics are included in the analysis

inverse obstacle scattering for homogeneous dielectric cylinders using a boundary finite element method a method for reconstructing the shape and the permittivity of a penetrable homogeneous cylinder is described it is the extension to penetrable cylinders of a previous work dealing with perfectly conducting cylinders a low frequency approximation is used to determine an initial guess then a rigorous boundary integral method permits us to reconstruct arbitrary shapes and complex permittivities it is based on an iterative conjugate gradient algorithm requiring the solving of two direct diffraction problems only a simple and original regularization scheme is presented which ensures the robustness of the algorithm numerical examples with lossy embedding media and additional random noise for both e spl par and h spl par polarizations are given

variational bayesian inversion of synthetic 3d controlled source electromagnetic geophysical data abstractinversion of controlled source electromagnetic data is dealt with for a geophysical application the goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave this constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations the inverse problem is solved in a bayesian framework in which prior information is introduced via a gauss markov potts model this model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions the posterior distribution of the unknowns is approached by means of the variational bayesian approximation as a separable distribution that minimizes the kullback leibler divergence with respect to the posterior law thus we get a parametric model for the distributions of the induced cu

constraints on sensitivity characteristics in linear multivariable discrete time control systems abstract this paper is concerned with the limitations on the sensitivity characteristics for linear multivariable discrete time control systems some integral type constraints and the lower bounds of the weighted h norm imposed by the unstable poles the unstable zeros and their directions of the open loop system or the given plant are developed by a factorization approach these constraints and bounds which are tighter than those in the previous work are also characterized by the state space representations the descriptions are closely related to a special type of the algebraic riccati equation and the relation between the sampling period and the sensitivity performance is discussed for digital control systems the constraints on the more general function mixed sensitivity function are investigated in a similar way

improving the performance guarantee for approximate graph coloring the performance guarantee of a graph coloring algorithm is the worst case ratio between the number of colors it uses on the input graph and the chromauc number of this graph the previous best known polynomial time algorithm had a performance guarantee o n logn for graphs on n vertices this result stood unchallenged for eight years this paper presents an efficient algorithm with performance guarantee of o n loglog n 2 logn 2

numerical solution of forward and backward problem for 2 d heat conduction equation for a two dimensional heat conduction problem we consider its initial boundary value problem and the related inverse problem of determining the initial temperature distribution from transient temperature measurements the conditional stability for this inverse problem and the error analysis for the tikhonov regularization are presented an implicit inversion method which is based on the regularization technique and the successive over relaxation sor iteration process is established due to the explicit difference scheme for a direct heat problem developed in this paper the inversion process is very efficient while the application of sor technique makes our inversion convergent rapidly numerical results illustrating our method are also given

conjugate gradient method applied to inverse scattering problem a new reconstruction algorithm for diffraction tomography is presented the algorithm is based on the minimization of a functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated object function by using the conjugate gradient method to minimize the functional one can derive an iterative formula for getting the object function numerical results for some two dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first order born approximation can not be applied in addition the number of iterations is reduced by using a priori information about the outer boundary of the objects furthermore the method is not so sensitive to the presence of noise in the scattered field data

algebraic methods for interactive proof systems a new algebraic technique for the construction of interactive proof systems is presented our technique is used to prove that every language in the polynomial time hierarchy has an interactive proof system this technique played a pivotal role in the recent proofs that ip pspace 28 and that mip nexp 4

numerical vector green s function for s parameter measurement with waveport excitation we present a numerical vector green s function that directly links the object material property within the electric field volume integral equation vie to the scattered s parameters this green s function is particularly useful for microwave inverse scattering applications in which s parameter measurements are used to reconstruct the dielectric properties of unknown objects in an inhomogeneous background where the green s function does not have an analytic form unlike the dyadic green s function in a standard vie which relates the fields in the object domain vector to the scattered fields vector this vector green s function kernel relates the object domain fields vector to the measured s parameters scalar also this new vector green s function uses a waveport source method which accurately accounts for the measured scattered s parameters between antenna feeds of arbitrary impedance and modes a detailed derivation is presented and simulated and experimental examples are provided to validate this vector green s function for the prediction of scattered s parameters

proof verification and the hardness of approximation problems we show that every language in np has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof if a string is in the language then there exists a proof such that the verifier accepts with probability 1 i e for every choice of its random string for strings not in the language the verifier rejects every provided proof with probability at least 1 2 our result builds upon and improves a recent result of arora and safra 1998 whose verifiers examine a nonconstant number of bits in the proof though this number is a very slowly growing function of the input length as a consequence we prove that no max snp hard problem has a polynomial time approximation scheme unless np p the class max snp was defined by papadimitriou and yannakakis 1991 and hard problems for this class include vertex cover maximum satisfiability maximum cut metric tsp steiner trees and shortest superstring we also improve upon the clique hardness results of feige et al 1996 and arora and safra 1998 and show that there exists a positive e such that approximating the maximum clique size in an n vertex graph to within a factor of n e is np hard

a comparison of material classification techniques for ultrasound inverse imaging the conjugate gradient method with edge preserving regularization cgep is applied to the ultrasound inverse scattering problem for the early detection of breast tumors to accelerate image reconstruction several different pattern classification schemes are introduced into the cgep algorithm these classification techniques are compared for a full sized two dimensional breast model one of these techniques uses two parameters the sound speed and attenuation simultaneously to perform classification based on a bayesian classifier and is called bivariate material classification bmc the other two techniques presented in earlier work are univariate material classification umc and neural network nn classification bmc is an extension of umc the latter using attenuation alone to perform classification and nn classification uses a neural network both noiseless and noisy cases are considered for the noiseless case numerical simulations show that the cgep bmc method requires 40 fewer iterations than the cgep method and the cgep nn method requires 55 fewer the cgep bmc and cgep nn methods yield more accurate reconstructions than the cgep method a quantitative comparison of the cgep bmc cgep nn and gn umc methods shows that the cgep bmc and cgep nn methods are more robust to noise than the gn umc method while all three are similar in computational complexity

on weighted vs unweighted versions of combinatorial optimization problems we investigate the approximability properties of several weighted problems by comparing them with the respective unweighted problems for an appropriate and very general definition of niceness we show that if a nice weighted problem is hard to approximate within r then its polynomially bounded weighted version is hard to approximate within r o 1 then we turn our attention to specific problems and we show that the unweighted versions of min vertex cover min sat max cut max dicut max 2sat and max exactksat are exactly as hard to approximate as their weighted versions we note in passing that min vertex cover is exactly as hard to approximate as min sat in order to prove the reductions for max 2sat max cut max dicut and max e3sat we introduce the new notion of mixing set and we give an explicit construction of such sets these reductions give new non approximability results for these problems

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

decentralized control of sequentially minimum phase systems fundamental limitations in decentralized control of systems with multivariable zeros are considered it is shown that arbitrary bandwidth can be obtained with a stable block diagonal controller if certain subsystems of the open loop system fail to have zeros in the right half plane and a high frequency condition holds implications on control structure design and sequential loop closuring methods are discussed

a simple deterministic reduction for the gap minimum distance of code problem we present a simple deterministic gap preserving reduction from sat to the minimum distance of code problem over f 2 we also show how to extend the reduction to work over any fixed finite field previously a randomized reduction was known due to dumer micciancio and sudan which was recently derandomized by cheng and wan these reductions rely on highly nontrivial coding theoretic constructions whereas our reduction is elementary as an additional feature our reduction gives hardness within a constant factor even for asymptotically good codes i e having constant positive rate and relative distance previously it was not known how to achieve a deterministic reduction for such codes

full wave three dimensional microwave imaging with a regularized gauss newton method theory and experiment a reconstruction algorithm is detailed for three dimensional full vectorial microwave imaging based on newton type optimization the goal is to reconstruct the three dimensional complex permittivity of a scatterer in a homogeneous background from a number of time harmonic scattered field measurements the algorithm combines a modified gauss newton optimization method with a computationally efficient forward solver based on the fast fourier transform method and the marching on in source position extrapolation procedure a regularized cost function is proposed by applying a multiplicative additive regularization to the least squares datafit this approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non linearity of the optimization problem it is furthermore shown that the modified gauss newton method converges much faster than the broyden fletcher goldfarb shanno quasi newton method promising quantitative reconstructions from both simulated and experimental data are presented the latter data are bi static polarimetric free space measurements provided by institut fresnel marseille france

testing reed muller codes a code is locally testable if there is a way to indicate with high probability that a vector is far enough from any codeword by accessing only a very small number of the vector s bits we show that the reed muller codes of constant order are locally testable specifically we describe an efficient randomized algorithm to test if a given vector of length n 2 sup m is a word in the rth order reed muller code r r m of length n 2 sup m for a given integer r spl ges 1 and real spl epsi 0 the algorithm queries the input vector spl upsi at o 1 spl epsi r2 sup 2r positions on the one hand if spl upsi is at distance at least spl epsi n from the closest codeword then the algorithm discovers it with probability at least 2 3 on the other hand if spl upsi is a codeword then it always passes the test our result is almost tight any algorithm for testing r r m must perform spl omega 1 spl epsi 2 sup r queries

logarithmic hardness of the undirected edge disjoint paths problem we show that there is no logf e m approximation for the undirected edge disjoint paths problem unless np zptime npolylog n where m is the size of the graph and e is any positive constant this hardness result also applies to the undirected all or nothing multicommodity flow problem and the undirected node disjoint paths problem

non signaling parallel repetition using de finetti reductions in the context of multiplayer games the parallel repetition problem can be phrased as follows given a game g with optimal winning probability 1 alpha and its repeated version g n in which n games are played together in parallel can the players use strategies that are substantially better than ones in which each game is played independently this question is relevant in physics for the study of correlations and plays an important role in computer science in the context of complexity and cryptography in this paper the case of multiplayer non signaling games is considered i e the only restriction on the players is that they are not allowed to communicate during the game for complete support games games where all possible combinations of questions have non zero probability to be asked with any number of players we prove a threshold theorem stating that the probability that non signaling players win more than a fraction 1 alpha beta of the n games is exponentially small in n beta 2 for every 0 leq beta leq alpha for games with incomplete support we derive a similar statement for a slightly modified form of repetition the result is proved using a new technique based on a recent de finetti theorem which allows us to avoid central technical difficulties that arise in standard proofs of parallel repetition theorems

integral constraints on sensitivity vectors for multivariable linear systems this paper develops integral constraints on sensitivity vectors for multivariable feedback systems due to either unstable poles or non minimum phase zeros of the plant the results presented cover the continuous rational or distributed case and are based on the use of directions corresponding to zeros or poles of the plant the integral constraints are in vector form and give new insights into the inherent trade offs in sensitivity reduction for multivariable systems and the cost of decoupling

profile inversion using the renormalized source type integral equation approach a novel and exact inversion equation is presented if approximations are to be made they will occur in the numerical methods used in the solution of this inversion equation this inversion approach is applicable to transverse electric te and extensible to transverse magnetic tm polarization with no explicit frequency limitation by prestoring the elements of the inversion operator the method does not require the solution to the full forward problem repeatedly it also allows in some cases the rigorous study of the degree of nonuniqueness involved in the inversion a point of great importance in the design problem

inapproximability results for equations over infinite groups an equation over a group g is an expression of form w 1 w k 1 g where each w i is either a variable an inverted variable or a group constant and 1 g denotes the identity element such an equation is satisfiable if there is a setting of the variables to values in g such that the equality is realized engebretsen et al 2002 10 in this paper we study the problem of simultaneously satisfying a family of equations over an infinite group g let eq g k denote the problem of determining the maximum number of simultaneously satisfiable equations in which each equation has occurrences of exactly k different variables when g is an infinite cyclic group we show that it is np hard to approximate eq 1 g 3 to within 48 47 e where eq 1 g 3 denotes the special case of eq g 3 in which a variable may only appear once in each equation it is np hard to approximate eq 1 g 2 to within 30 29 e it is np hard to approximate the maximum number of simultaneously satisfiable equations of degree at most d to within d e for any e for any k 4 it is np hard to approximate eq g k within any constant factor these results extend hastad s results hastad 2001 17 and results of engebretsen et al 2002 10 who established the inapproximability results for equations over finite abelian groups and any finite groups respectively

crossover frequency limitations in mimo nonminimum phase feedback systems this paper investigates limitations and design tradeoffs of the closed loop sensitivity performance of linear time invariant nonminimum phase uncertain multiple input multiple output plants with i inputs and m outputs where m spl les l it is shown that if rows i sub 1 i sub k of the plant transfer function form a k spl times l nonminimum phase transfer matrix and if the design is such that the sensitivity gain of k 1 rows among the rows i sub 1 i sub k of the closed loop transfer function is low then by necessity the sensitivity gain of the remaining row is high this sensitivity constraint is quantified with the help of the crossover frequency restriction of a specially constructed single input single output transfer function that includes the right half plane zeros and poles of the k spl times l transfer matrix

an adaptive weighting strategy for microwave imaging problems in the framework of microwave imaging applications an innovative strategy aimed at addressing the multiobjective inverse scattering problem is proposed starting from the spatial domain integral formulation the original multiobjective problem is recast into a single objective one by defining a suitable cost function as a linear combination of the data and state terms according to variable weighting parameters by iteratively tuning these parameters the optimization procedure is forced to solve an almost multiobjective problem avoiding the use of ad hoc multiple objective optimization methods and satisfying different objectives in a balanced way selected numerical results indicate that the use of such a strategy yields to accurate reconstructions with noise corrupted data as well by improving the performances of the adopted optimization procedure

parallel ga based approach for microwave imaging applications genetic algorithms gas are well known optimization strategies able to deal with nonlinear functions as those arising in inverse scattering problems however they are computationally expensive thus offering poor performances in terms of general efficiency when compared with inversion techniques based on deterministic optimization methods in this paper a parallel implementation of an inverse scattering procedure based on a suitable hybrid genetic algorithm is presented the proposed strategy is aimed at reducing the overall clock time in order to make the approach competitive with gradient based methods in terms of runtime but preserving the capabilities of escaping from local minima this result is achieved by exploiting the natural parallelism of evolutionary techniques and the searching capabilities of the hybrid approach the effectiveness of the proposed implementation is demonstrated by considering a selected numerical benchmark related to two dimensional scattering geometries

approximate graph coloring by semidefinite programming we consider the problem of coloring k colorable graphs with the fewest possible colors we present a randomized polynomial time algorithm that colors a 3 colorable graph on n vertices with min o 1 3 log 1 2 log n o n 1 4 log 1 2 n colors where is the maximum degree of any vertex besides giving the best known approximation ratio in terms of n this marks the first nontrivial approximation result as a function of the maximum degree this result can be generalized to k colorable graphs to obtain a coloring using min o 1 2 k log 1 2 log n o n 1 3 k 1 log 1 2 n colors our results are inspired by the recent work of goemans and williamson who used an algorithm for semidefinite optimization problems which generalize linear programs to obtain improved approximations for the max cut and max 2 sat problems an intriguing outcome of our work is a duality relationship established between the value of the optimum solution to our semidefinite program and the lovasz t function we show lower bounds on the gap between the optimum solution of our semidefinite program and the actual chromatic number by duality this also demonstrates interesting new facts about the t function

comparison of an enhanced distorted born iterative method and the multiplicative regularized contrast source inversion method for 2d transverse magnetic tm microwave inversion multiplicative regularized contrast source inversion mr csi and the distorted born iterative method dbim are compared the comparison is based on a computational resource analysis inversion of synthetic data and inversion of experimentally collected data from both the fresnel and upc barcelona data sets all inversion results are blind but appropriate physical values for the reconstructed contrast are maintained the data sets used to test the algorithms vary widely in terms of the background media antennas and far near field considerations to ensure that the comparison is replicable an automatic regularization parameter selection method is used for the additive regularization within the dbim which utilizes a fast implementation of the l curve method and the laplacian regularizer while not used in the classical dbim we introduce an mr term to the dbim in order to provide comparable results to mr csi the introduction of this mr term requires only slight modifications to the classical dbim algorithm and adds little computational complexity the results show that with the addition of the mr term in the dbim the two algorithms provide very similar inversion results but with the mr csi method providing advantages for both computational resources and ease of implementation

profile inversion in scattering theory the te case in this paper we discuss an inverse problem in which we try and determine the refractive index corresponding to the scattering of electromagnetic waves by an inhomogeneous medium from far field data in particular we shall extend the dual space method developed by colton and monk inverse problems 10 1994 87 for the tm case to the more complicated te case and consider the case of single frequency we shall emphasize on the influence of the wave number in the reconstructions several examples are presented which illustrate the algorithm

free bits pcps and nonapproximability towards tight results this paper continues the investigation of the connection between probabilistically checkable proofs pcps and the approximability of np optimization problems the emphasis is on proving tight nonapproximability results via consideration of measures such as the free bit complexity and the amortized free bit complexity of proof systems the first part of the paper presents a collection of new proof systems based on a new error correcting code called the long code we provide a proof system that has amortized free bit complexity of 2 epsilon implying that approximating maxclique within n frac13 e and approximating the chromatic number within n frac15 e are hard assuming np neq corp for any e 0 we also derive the first explicit and reasonable constant hardness factors for min vertex cover msat 2 and max cut and we improve the hardness factor for msat 3 we note that our nonapproximability factors for maxsnp problems are appreciably close to the values known to be achievable by polynomial time algorithms finally we note a general approach to the derivation of strong nonapproximability results under which the problem reduces to the construction of certain gadgets the increasing strength of nonapproximability results obtained via the pcp connection motivates us to ask how far this can go and whether pcps are inherent in any way the second part of the paper addresses this the main result is a reversal of the connection due to feige et al fglss connection j acm 43 1996 pp 268 292 where the latter had shown how to translate proof systems for np into np hardness of approximation results for maxclique we show how any np hardness of approximation result for maxclique yields a proof system for np roughly our result says that for any constant f if maxclique is np hard to approximate within n 1 1 f then np subseteq overline fpcp log f the latter being the class of languages possessing proofs of logarithmic randomness and amortized free bit complexity f this suggests that pcps are inherent to obtaining nonapproximability results furthermore the tight relation suggests that reducing the amortized free bit complexity is necessary for improving the nonapproximability results for maxclique the third part of our paper initiates a systematic investigation of the properties of pcp and fpcp free pcp as a function of the following various parameters randomness query complexity free bit complexity amortized free bit complexity proof size etc we are particularly interested in triviality results which indicate which classes are not powerful enough to capture np we also distill the role of randomized reductions in this area and provide a variety of useful transformations between proof checking complexity classes

the pcp theorem by gap amplification the pcp theorem arora and safra 1998 arora et al 1998 says that every language in np has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof the celebrated equivalence of this theorem and inapproximability of certain optimization problems due to feige et al 1996 has placed the pcp theorem at the heart of the area of inapproximability in this work we present a new proof of the pcp theorem that draws on this equivalence we give a combinatorial proof for the np hardness of approximating a certain constraint satisfaction problem which can then be reinterpreted to yield the pcp theorem our approach is to consider the unsat value of a constraint system which is the smallest fraction of unsatisfied constraints ranging over all possible assignments for the underlying variables we describe a new combinatorial amplification transformation that doubles the unsat value of a constraint system with only a linear blowup in the size of the system the amplification step causes an increase in alphabet size that is corrected by a standard pcp composition step iterative application of these two steps yields a proof for the pcp theorem the amplification lemma relies on a new notion of graph powering that can be applied to systems of binary constraints this powering amplifies the unsat value of a constraint system provided that the underlying graph structure is an expander we also extend our amplification lemma towards construction of assignment testers alternatively pcps of proximity which are slightly stronger objects than pcps we then construct pcps and locally testable codes whose length is linear up to a polylog factor and whose correctness can be probabilistically verified by making a constant number of queries namely we prove sat pcp 1 2 1 log2 n poly log n o 1

two query pcp with subconstant error we show that the np complete language 3sat has a pcp verifier that makes two queries to a proof of almost linear size and achieves subconstant probability of error eeo 1 the verifier performs only projection tests meaning that the answer to the first query determines at most one accepting answer to the second query the number of bits representing a symbol in the proof depends only on the error e previously by the parallel repetition theorem there were pcp theorems with two query projection tests but only arbitrarily small constant error and polynomial size there were also pcp theorems with subconstant error and almost linear size but a constant number of queries that is larger than 2 as a corollary we obtain a host of new results in particular our theorem improves many of the hardness of approximation results that are proved using the parallel repetition theorem a partial list includes the following 1 3sat cannot be efficiently approximated to within a factor of 7 8po 1 unless penp this holds even under almost linear reductions previously the best known np hardness factor was 7 8pe for any constant e 0 under polynomial reductions hastad 2 3lin cannot be efficiently approximated to within a factor of 1 2po 1 unless penp this holds even under almost linear reductions previously the best known np hardness factor was 1 2pe for any constant e 0 under polynomial reductions hastad 3 a pcp theorem with amortized query complexity 1 p o 1 and amortized free bit complexity o 1 previously the best known amortized query complexity and free bit complexity were 1pe and e respectively for any constant e 0 samorodnitsky and trevisan one of the new ideas that we use is a new technique for doing the composition step in the classical proof of the pcp theorem without increasing the number of queries to the proof we formalize this as a composition of new objects that we call locally decode reject codes ldrc the notion of ldrc was implicit in several previous works and we make it explicit in this work we believe that the formulation of ldrcs and their construction are of independent interest

blind shape reconstruction from experimental data a method for reconstructing the shape of a bounded impenetrable object from measured scattered field data is presented the reconstruction algorithm is in principle the same as that used before for reconstructing the conductivity of a penetrable object and uses the fact that for high conductivity the skin depth of the scatterer is small in which case the only meaningful information produced by the algorithm is the boundary of the scatterer a striking increase in efficiency is achieved by incorporating into the algorithm the fact that for large conductivity the contrast is dominated by a large positive imaginary part this fact together with the knowledge that the scatterer is constrained in some test domain constitute the only a priori information about the scatterer that is used there are no other implicit assumptions about the location connectivity convexity or boundary conditions the method is shown to successfully reconstruct the shape of an object from experimental scattered field data in a blind test

performance limitations of non minimum phase systems in the servomechanism problem abstract this paper studies the cheap regulator problem and the cheap servomechanism problem for systems which may be non minimum phase the study extends some well known properties of perfect regulation and the perfect tracking and disturbance rejection of minimum phase systems to non minimum phase systems it is shown that perfect rejection to disturbances applied to the plant input can be achieved no matter whether the system is minimum phase or non minimum phase whereas a fundamental limitation exists in the achievable transient performance of tracking and rejection to disturbances applied to the plant output for a non minimum phase system and that this limitation can be simply and completely characterized by the number and locations of those zeros of the system which lie in the right half of the complex plane furthermore this limitation provides a quantitative measure of the degree of difficulty which is inherent in the control of such non minimum phase systems

an algebraic solution method for nonlinear inverse scattering by using properly designed synthetic or virtual experiments and an original approximation of the contrast sources we are able to recast the inverse scattering problem in an algebraic form in a subset of points of the imaged domain and hence to solve it by means of closed form formulas the new approximation relies on the assumption that the contrast sources induced by the different virtual experiments are focused in given points belonging to the scatterer as such the method involves a preprocessing step in which the outcome of the original scattering experiments is recombined into the new virtual ones capable of enforcing the expected contrast sources behavior examples with numerical and experimental data are provided to assess the actual possibility of setting such a virtual experiments framework and show the effectiveness of the proposed method

overview and classification of some regularization techniques for the gauss newton inversion method applied to inverse scattering problems different regularization techniques used in conjunction with the gauss newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories the first category attempts to regularize the quadratic form of the nonlinear data misfit cost functional at different iterations of the gauss newton inversion method this can be accomplished by utilizing penalty methods or projection methods the second category tries to regularize the nonlinear data misfit cost functional before applying the gauss newton inversion method this type of regularization may be applied via additive multiplicative or additive multiplicative terms we show that these two regularization strategies can be viewed from a single consistent framework

ip pspace in this paper it is proven that when both randomization and interaction are allowed the proofs that can be verified in polynomial time are exactly those proofs that can be generated with polynomial space

combination can be hard approximability of the unique coverage problem we prove semilogarithmic inapproximability for a maximization problem called unique coverage given a collection of sets find a subcollection that maximizes the number of elements covered exactly once specifically assuming that mathrm np not subseteq operatorname bptime 2 n varepsilon for an arbitrary varepsilon 0 we prove o 1 log sigma n inapproximability for some constant sigma sigma varepsilon we also prove o 1 log 1 3 varepsilon n inapproximability for any varepsilon 0 assuming that refuting random instances of 3sat is hard on average and we prove o 1 log n inapproximability under a plausible hypothesis concerning the hardness of another problem balanced bipartite independent set we establish an omega 1 log n approximation algorithm even for a more general budgeted setting and obtain an omega 1 log b approximation algorithm when every set has at most b elements we also show that our inapproximability results extend to envy free pricing an important problem in computational economics we describe how the budgeted unique coverage problem motivated by real world applications has close connections to other theoretical problems including max cut maximum coverage and radio broadcasting

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

newton kantorovitch algorithm applied to an electromagnetic inverse problem an efficient algorithm is presented to compute the shape of perfectly conducting cylinders via knowledge of scattering cross sections this choice of scattering data avoids the difficulties linked with the phase measurements or reconstructions the mathematical analysis is performed in terms of operator and functions and the fundamental instability of the problem is demonstrated then the stability is restored by means of a tikhonov miller regularization the efficiency of the method is outlined by numerical examples references are given which show that the same algorithm applies to other electromagnetic inverse problems especially to gratings

robust multiplication based tests for reed muller codes we consider the following multiplication based tests to check if a given function f mathbb f q n to mathbb f q is a codeword of the reed muller code of dimension n and order d over the finite field mathbb f q for prime q i e f is the evaluation of a degree d polynomial over mathbb f q for q prime test e k pick p 1 ldots p k independent random degree e polynomials and accept if the function fp 1 cdots p k is the evaluation of a degree d ek polynomial i e is a codeword of the reed muller code of dimension n and order d ek we prove the robust soundness of the above mentioned tests for large values of e answering a question of dinur and guruswami previous soundness analyses of these tests were known only for the case when either e 1 or k 1 even for the case k 1 and e 1 earlier soundness analyses were not robust we also analyze a derandomized version of this test where for example the polynomials p 1 ldots p k can be the same random polynomial p this generalizes a result of guruswami et al one of the key ingredients that go into the proof of this robust soundness is an extension of the standard schwartz zippel lemma over general finite fields mathbb f q which may be of independent interest

microwave data inversions using the source receiver compression scheme we apply a source receiver compression approach to reduce the computational time and memory usage of the nonlinear inversion approaches for interpreting three dimensional microwave data by detecting and quantifying the extent of redundancy in the data we assemble a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers employed in the measurement setup because the number of these simultaneous sources and receivers can be significantly less than those of the physical sources and receivers the computational time and memory usage of any inversion method such as steepest descent nonlinear conjugate gradient contrast source inversion and quasi newton can be tremendously reduced the scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data compression is done through the elimination of eigenvectors corresponding to small eigenvalues consequently this will also suppress the effect of noise in the data as a concept demonstration we show that this approach has the potential of significantly reducing both computational time and memory usage of the gauss newton inversion method by few orders of magnitude

an improved lower bound for approximating minimum gcd multiplier in l norm gcdm in this paper we study the inapproximability of the following np complete number theoretic optimization problems introduced by rossner and seifert c rossner j p seifert the complexity of approximate optima for greatest common divisor computations in proceedings of the 2nd international algorithmic number theory symposium ants ii 1996 pp 307 322 given n numbers a 1 a n z find an minimum gcd multiplier for a 1 a n i e a vector x z n with minimum max 1 i n x i satisfying i 1 nx ia i gcd a 1 a n we show that assuming p np it is np hard to approximate the minimum gcd multiplier in norm gcdm within a factor n c l o g l o g n for some constant c 0 where n is the dimension of the given vector this improves on the best previous result the best result so far gave 2 l o g n 1 e factor hardness by rossner and seifert c rossner j p seifert the complexity of approximate optima for greatest common divisor computations in proceedings of the 2nd international algorithmic number theory symposium ants ii 1996 pp 307 322 where e 0 is an arbitrarily small constant

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

inapproximability results for the minimum integral solution problem with preprocessing over l norm the minimum integral solution problem with preprocessing has been introduced by alekhnovich khot kindler and vishnoi m alekhnovich s khot g kindler n vishnoi hardness of approximating the closest vector problem with preprocessing in proc 46th ieee symposium on focs 2005 pp 216 225 they studied the complexity of minimum integral solution problem with preprocessing over p norm email protected p 0 unless p np