algebraic invariants for right angled artin groups a finite simplicial graph determines a right angled artin group g with generators corresponding to the vertices of and with a relation w w for each pair of adjacent vertices we compute the lower central series quotients the chen quotients and the first resonance variety of g directly from the graph

on the imaging of reflectors in the earth in this paper i present a modification of the beylkin inversion operator this modification accounts for the band limited nature of the data and makes the role of discontinuities in the sound speed more precise the inversion presented here partially dispenses with the small parameter constraint of the born approximation this is shown by applying the proposed inversion operator to upward scattered data represented by the kirchhoff approximation using the angularly dependent geometrical optics reflection coefficient a fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these kirchhoff approximate data for the forward problem the inversion of these data involves integration over the source receiver surface the reflecting surface and frequency the spatial integrals are computed by the method of stationary phase the output is asymptotically a scaled singular function of the reflecting surface the singular function of a

velocity inversion using a stratified reference we present an inversion algorithm for backscattered stacked seismic data which will reconstruct the velocity profile in realistic earth conditions the basic approach follows that of the original constant reference speed cohen and bleistein paper 1979a in that hig hfrequency asymptotics and perturbation methods are used however we use a reference speed which may vary with depth and this greatly enhances the validity of the perturbation assumption and hence the inversion results the new algorithm enjoys the same economies and stability properties of the original algorithm making it very competitive with current migration schemes four major assumptions are made 1 the acoustic wave equation is an adequate model 2 stacked data have amplitude information worth preserving fairly accurately 3 the actual reflectivity coefficients can be adequately modeled as perturbations from a continuous reference velocity which depends only on the depth variable and 4 the subsurface can be adequately

hyperchaotic encryption based on multi scroll piecewise linear systems a hyperchaotic multi scroll piecewise linear system in r4 is binarized to generate a pseudo random sequence which encrypt a grayscale image via symmetric key algorithm the sequence is analyzed throughout statistical tests according to the national institute of standards and technology nist specifications the scrolls of the system are the result of a switching law that changes between the saddle hyperbolic equilibria of piecewise linear systems with eigenvalues as follows two negative real and one pair of complex conjugate eigenvalues with positive real part thus the encryption quality is evaluated depending on the variation of the number of scrolls

a secret sharing scheme based on cellular automata a new secret sharing scheme based on a particular type of discrete delay dynamical systems memory cellular automata is proposed specifically such scheme consists of a k n threshold scheme where the text to be shared is considered as one of the k initial conditions of the memory cellular automata and the n shares to be distributed are n consecutive configurations of the evolution of such cellular automata it is also proved to be perfect and ideal

alexander invariants of complex hyperplane arrangements leta be an arrangement of n complex hyperplanes the funda mental group of the complement of a is determined by a braid monodromy homomorphism fi fs pn using the gassner representation of the pure braid group we flnd an explicit presentation for the alexander invariant ofa from this presentation we obtain combinatorial lower bounds for the ranks of the chen groups ofa we also provide a combinatorial criterion for when these lower bounds are attained

lower central series and free resolutions of hyperplane arrangements if m is the complement of a hyperplane arrangement and a h m k is the cohomology ring of m over a field of characteristic 0 then the ranks k of the lower central series quotients of 1 m can be computed from the betti numbers bii dimtor a k k i of the linear strand in a minimal free resolution of k over a we use the cartan eilenberg change of rings spectral sequence to relate these numbers to the graded betti numbers b dimtor e a k j of a minimal resolution of a over the exterior algebra e from this analysis we recover a formula of falk for 3 and obtain a new formula for 4 the exact sequence of low degree terms in the spectral sequence allows us to answer a question of falk on graphic arrangements and also shows that for these arrangements the algebra a is koszul if and only if the arrangement is supersolvable we also give combinatorial lower bounds on the betti numbers b 1 of the linear strand of the free resolution of a over e if the lower bound is attained for i 2 then it is attained for all i 2 for such arrangements we compute the entire linear strand of the resolution and we prove that all components of the first resonance variety of a are local for graphic arrangements which do not attain the lower bound unless they have no braid sub arrangements we show that b 1 is determined by the number of triangles and k4 subgraphs in the graph

a t n multi secret sharing scheme in the t n multi secret sharing scheme there are n participants in the system at least t or more participants can easily pool their secrets shadows and reconstruct p secrets at the same time chien et al ieice trans fundamentals e83 a 2000 2762 used n p t 1 public values 2 n p t x n p storages and solved n p t simultaneous equations to share p secrets in this article we shall propose an alternative t n multi secret sharing based on shamir s secret sharing we shall use n p t 1 or n 1 public values 2 t 1 or 2 p 1 storages and employ the lagrange interpolation polynomial to share p secrets our scheme will have exactly the same power as chien et al s scheme

hyperplane arrangement cohomology and monomials in the exterior algebra we show that if x is the complement of a complex hyperplane arrangement then the homology of x has linear free resolution as a module over the exterior algebra on the first cohomology of x we study invariants of x that can be deduced from this resolution a key ingredient is a result of aramova avramov and herzog 2000 on resolutions of monomial ideals in the exterior algebra we give a new conceptual proof of this result

a computer implementation of 2 5 d common shot inversion the computer implementation of a two and one half dimensional 2 5 d constant density prestack inversion formalism with laterally and depth dependent background propagation speed is a kirchhoff type inversion summing data from a line of receivers over traveltime curves in the depth dependent background medium with weights determined from born kirchhoff inversion theory this theory predicts that the output will be a reflector map with peak amplitudes on each reflector being in known proportion to the angularly dependent geometrical optics reflection coefficient the 2 5 d feature provides for out of plane spreading correction consistent with the prescribed background medium the method is applied to a synthetic data set and to a physically modeled data set generated at the seismic acoustic laboratory the graphical output demonstrates the validity of the formalism as a kirchhoff migration parameter estimation for the synthetic data confirmed the theory parameter estimation for the experimental data wa

three dimensional born inversion with an arbitrary reference recent work of g beylkin helped set the stage for very general seismic inversions we have combined these broad concepts for inversion with classical high frequency asymptotics and perturbation methods to bring them closer to practically implementable algorithms applications include inversion schemes for both stacked and unstacked seismic data basic assumptions are that the data have relative true amplitude and that a reasonably accurate background velocity c x y z is available the perturbation from this background is then sought since high frequency approximations are used throughout the resulting algorithms essentially locate discontinuities in velocity an expression for a full 3 d velocity inversion can be derived for a general data surface in this degree of generality the formula does not represent a computationally feasible algorithm primarily because a key jacobian determinant is not expressed in practical terms in several important cases however this shortcoming can be overcome and

theory and applications of cellular automata in cryptography this paper deals with the theory and application of cellular automata ca for a class of block ciphers and stream ciphers based on ca state transitions certain fundamental transformations are defined which are block ciphering functions of the proposed enciphering scheme these fundamental transformations are found to generate the simple alternating group of even permutations which in turn is a subgroup of the permutation group these functions are implemented with a class of programmable cellular automata pca built around rules 51 153 and 195 further high quality pseudorandom pattern generators built around rule 90 and 150 programmable cellular automata with a rule selector i e combining function has been proposed as running key generators in stream ciphers both the schemes provide better security against different types of attacks with a simple regular modular and cascadable structure of ca hardware implementation of such schemes idealy suit vlsi implementation

permutation and sampling with maximum length ca or pseudorandom number generation abstract in this paper we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata ca dynamic permutation and sampling have not been explored in previous ca work and a suitable implementation is shown using a two ca model three different schemes that incorporate these two operations are suggested weighted permutation vector sampling with controlled multiplexing weighted permutation vector sampling with irregular decimation and permutation programmed ca sampling the experiment results show that the resulting sequences have varying degrees of improvement in diehard results and linear complexity compared to the ca

prestack kirchhoff inversion of common offset data in trying to resolve complex geologic structures the pitfalls in employing the cdp method become evident additionally stacking multioffset traces corrupts the amplitudes necessary for stratigraphic analysis in order to preserve whatever structural and amplitude information is in the data prestack processing should be performed given common offset data and the velocity above a reflector prestack acoustic kirchhoff inversion resolves the location of the interface when amplitude information has been preserved in the data the method additionally calculates the reflection coefficient at each interface point for band limited seismic data the inversion operator produces a sinc like picture of the reflector with the peak amplitude of this band limited singular function equal to the angularly dependent reflection coefficient the inversion development is based upon high frequency kirchhoff data which are inserted into a general 3 d inversion operator asymptotically evaluating the four resulting integrals by the method of four dimensional stationary phase permits an inversion amplitude function to be chosen so that the inversion operator produces a singular function of support on the reflector weighted by the reflection coefficient specializing the three dimensional inversion operator to two and one half dimensions allows for processing of single lines of common offset data synthetic examples illustrate the accuracy of the method for constant velocity kirchhoff data as well as the problems in applying constant velocity data to multivelocity models

sheaf cohomology and free resolutions over exterior algebras in this paper we derive an explicit version of the bernstein gel fand gel fand bgg correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite free reso lutions over its koszul dual exterior algebra among the facts about the bgg correspondence that we derive is that taking homology of a complex of sheaves corresponds to taking the linear part of a resolution over the exterior algebra we explore the structure of free resolutions over an exterior algebra for example we show that such resolutions are eventually dominated by their linear parts in the sense that erasing all terms of degree 1 in the complex yields a new complex which is eventually exact as applications we give a construction of the beilinson monad which expresses a sheaf on projective space in terms of its cohomology by using sheaves of differential forms the explicitness of our version allows us to to prove two conjectures about the morphisms in the monad and we get an efficient method for machine computation of the cohomology ofsheaves we also construct all the monads for a sheaf that can be built from sums of line bundles and show that they are often characterized by numerical data let v be a finite dimensional vector space over a field k and let w v be the dual space in this paper we will study complexes and resolutions over the exterior algebra e v and their relation to modules over s sym w and sheaves on projective space p w in this paper we study the bernstein gel fand gel fand bgg correspondence 1978 usually stated as an equivalence between the derived category of bounded complexes of coherent sheaves on p w and the stable category of finitely generated graded modules over e its essential content is a functor r from complexes of graded s modules to complexes of graded e modules and its adjoint l for example if m imi is a graded s module regarded as a complex with just one term then the first and third authors are grateful to the nsf for partial support during the preparation of this paper the third author wishes to thank msri for its hospitality

resonance linear syzygies chen groups and the bernstein gelfand gelfand correspondence if a is a complex hyperplane arrangement with complement x we show that the chen ranks of g 1 x are equal to the graded betti numbers of the linear strand in a minimal free resolution of the cohomology ring a h x k viewed as a module over the exterior algebra e on a k g dim k tor e k 1 a k k for k 2 where k is a field of characteristic 0 the chen ranks conjecture asserts that for k sufficiently large k g k 1 r 1 r k 1 k where h r is the number of r dimensional components of the projective resonance variety r 1 a our earlier work on the resolution of a over e and the above equality yield a proof of the conjecture for graphic arrangements using results on the geometry of r 1 a and a localization argument we establish the inequality k g k 1 r 1 hr r k 1 k for k 0 for arbitrary a finally we show that there is a polynomial p t of degree equal to the dimension of r 1 a such that k g p k for all k 0

two and one half dimensional born inversion with an arbitrary reference multidimensional inversion algorithms are presented for both prestack and poststack data gathered on a single line these algorithms both image the subsurface i e give a migrated section and given relative true amplitude data estimate reflection strength or impedance on each reflector the algorithms are two and one half dimensional 2 5 d in that they incorporate three dimensional 3 d wave propagation in a medium which varies in only two dimensions the use of 3 d sources does not entail any computational penalty and it avoids the serious degradation of amplitude incurred by using the 2 d wave equation our methods are based on the linearized inversion theory associated with the born inversion thus we assume that the sound speed profile is well approximated by a given background velocity plus a perturbation it is this perturbation that we seek to reconstruct we are able to treat the case of an arbitrary continuous background profile however the cost of implementation increases as one

on the generation of high quality random numbers by two dimensional cellular automata finding good random number generators rngs is a hard problem that is of crucial import in several fields ranging from large scale statistical physics simulations to hardware self test in this paper we employ the cellular programming evolutionary algorithm to automatically generate two dimensional cellular automata ca rngs applying an extensive suite of randomness tests to the evolved cas we demonstrate that they rapidly produce high quality random number sequences moreover based on observations of the evolved cas we are able to handcraft even better rngs which not only outperform previously demonstrated high quality rngs but can be potentially tailored to satisfy given hardware constraints

chen ranks and resonance abstract the chen groups of a group g are the lower central series quotients of the maximal metabelian quotient of g under certain conditions we relate the ranks of the chen groups to the first resonance variety of g a jump locus for the cohomology of g in the case where g is the fundamental group of the complement of a complex hyperplane arrangement our results positively resolve suciu s chen ranks conjecture we obtain explicit formulas for the chen ranks of a number of groups of broad interest including pure artin groups associated to coxeter groups and the group of basis conjugating automorphisms of a finitely generated free group