adaptive solution for blind identification equalization using deterministic maximum likelihood a deterministic maximum likelihood dml approach is presented for the blind channel estimation problem it is first proposed in a block version which consists of iterating two steps each one solving a least squares problem either in the channel or in the symbols in the noiseless case and under certain conditions this algorithm gives the exact channel and the exact symbol vector with a finite number of samples it is shown that even if the dml method has a single global minimum the proposed iterative procedure can converge to spurious local minima this problem can be detected under some channel diversity conditions by using a numerical test that is proposed in the paper based on these considerations we extend the maximum likelihood block algorithm mlba to recursive implementations maximum likelihood recursive algorithm mlra the mlra is able to track variations of the system by the introduction of an exponential forgetting factor in the dml criterion the link between the adaptive algorithm and a soft decision feedback equalizer sdfe is emphasized low complexity versions of the recursive and adaptive algorithm are presented

deterministic cca based algorithms for blind equalization of fir mimo channels in this paper a new deterministic technique for blind equalization of multiple input multiple output mimo channels is presented the proposed method relies on the channel order diversity of the finite impulse response mimo channel and it does not make any assumption about the spectra or the finite alphabet property of the sources assuming that the lengths of the single input multiple output channels are known or estimated a priori it is able to extract the sources up to a scale and rotation matrix ambiguity which only affects to those sources associated to single input multiple output simo channels with equal lengths unlike previously proposed techniques the method described in this paper obtains the equalizers and the best linear combination of their outputs in a single step and thus optimally the reformulation of the proposed method as a set of nested canonical correlation analysis problems is exploited to obtain efficient batch and adaptive equalization algorithms finally the performance of the proposed algorithms is evaluated by means of some simulation examples

joint order detection and blind channel estimation by least squares smoothing a joint order detection and blind estimation algorithm for single input multiple output channels is proposed by exploiting the isomorphic relation between the channel input and output subspaces it is shown that the channel order and channel impulse response are uniquely determined by finite least squares smoothing error sequences in the absence of noise the proposed subspace algorithm is shown to have marked improvement over existing algorithms in performance and robustness in simulations

variational problems with two phases and their free boundaries the problem of minimizing vu 2 q2 x 2 v dx in an appropriate class of functions v is considered here q x 0 and a2 t x2 if v 0 any minimizer u is harmonic in u 0 and vu 2 has a jump a2 x 22 across the free boundary u 0 regularity and various properties are established for the minimizer u and for the free boundary introduction in this paper we consider the problem of minimizing j v f vv 2 q2 x x2 v dx vgk where q2 x 0 a22 ifu 0 and x2 u is lower semicontinuous at v 0 it is assumed that a2 0 and a a2 a22 0 the class k consists of all functions v in l loc s2 with vu g l2 i2 such that v u on a given open subset s of 3i2 and s is a domain in r the analogous problem for functions in k v k v 0 a e was studied in 1 in that paper it was proved that any local minimizer of j v in k is lipschitz continuous and if n 2 the free boundary 8 w 0 is analytic if q x is analytic the present variational problem is motivated by applications to the now of two liquids in models of jets and cavities these applications will be studied in other forthcoming papers 5 6 the present work is aimed at extending results of 1 in particular we shall establish nondegeneracy theorems the lipschitz continuity of the solution and some properties of the free boundary for n 2 the free boundary is proved to be continuously differentiable a new and rather powerful tool introduced in this paper is the monotonicity formula lemma 5 1 asserting that for a minimizer u if u x0 0 then

adaptive blind channel estimation by least squares smoothing a least squares smoothing lss approach is presented for the blind estimation of single input multiple output simo finite impulse response systems by exploiting the isomorphic relation between the input and output subspaces this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output lss has the finite sample convergence property i e in the absence of noise the channel is estimated perfectly with only a finite number of data samples referred to as the adaptive least squares smoothing a lss algorithm the adaptive implementation has a high convergence rate and low computation cost with no matrix operations a lss is order recursive and is implemented in part using a lattice filter it has the advantage that when the channel order varies channel estimates can be obtained without structural change of the implementation for uncorrelated input sequence the proposed algorithm performs direct deconvolution as a by product

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

the number of maximal torsion cosets in subvarieties of tori we present sharp bounds on the number of maximal torsion cosets in a subvariety of the complex algebraic torus gm n our first main result gives a bound in terms of the degree of the defining polynomials a second result gives a bound in terms of the toric degree of the subvariety as a consequence we prove the conjectures of ruppert and of aliev and smyth on the number of isolated torsion points of a hypersurface these conjectures bound this number in terms of the multidegree and the volume of the newton polytope of a polynomial defining the hypersurface respectively

on permutations of hardy littlewood polya sequences let h q1 qr be a nite set of coprime integers and let n1 n2 denote the multiplicative semigroup generated by h and arranged in increasing order the distribution of such sequences has been studied intensively in number theory and they have remarkable probabilistic and ergodic properties for example the asymptotic properties of the sequence nkx are very similar to those of independent identically distributed random variables here denotes fractional part however the behavior of this sequence depends sensitively on the generating elements of nk and the combination of probabilistic and number theoretic e ects results in a unique highly interesting asymptotic behavior see e g 6 8 in particular the properties of nkx are not permutation invariant in contrast to i i d behavior the purpose of this paper is to show that nkx satis es a strong independence property interlaced mixing enabling one to determine the precise asymptotic behavior of permuted sums sn n k 1 f n k x as we will see the behavior of sn still follows that of sums of independent random variables but its growth speed depending on is given by the classical gal function of diophantine approximation theory some examples describing the class of possible growth functions are given ams 2000 subject classi cation 42a55 11k60 60f05 60f15

periodic subvarieties of semiabelian varieties and annihilators of irreducible representations abstract let g be a semiabelian variety defined over a field of characteristic 0 endowed with an endomorphism we prove there is no proper subvariety y g which intersects the orbit of each periodic point of g under the action of as an application we are able to give a topological characterization of the annihilator ideals of irreducible representations in certain skew polynomial algebras

steady filtration problems with seawater intrusion variational analysis on the basis of brezis kinderlehrer stampacchia variational approach a general steady filtration problem with seawater intrusion is formulated then qualitative properties are analyzed such as existence and uniqueness of solutions and free boundaries behavior

a stationary flow of fresh and salt groundwater in a coastal aquifer consider a horizontally situated homogeneous aquifer of constant thickness h in this aquifer fresh and salt water are present and separated by an abrupt interface let the flow be two dimensional in the vertical x z plane

on s unit equations in two unknowns j h evertse 1 k gy6ry 2 c l stewart 3 and r tijdeman 4 department of pure mathematics centre for mathematics and computer science kruislaan 413 nl 1098 sj amsterdam the netherlands 2 mathematical institute kossuth lajos university h 4010 debrecen hungary 3 department of pure mathematics university of waterloo waterloo ontario canada n2l 3gi 4 mathematical institute university of leiden nl 2333 ca leiden the netherlands

stable polynomials and crystalline measures explicit examples of positive crystalline measures and fourier quasicrystals are constructed using pairs of stable polynomials answering several open questions in the area

topology and geometry of cohomology jump loci we elucidate the key role played by formality in the theory of characteristic and resonance varieties we define relative characteristic and resonance varieties v k and r k related to twisted group cohomology with coefficients of arbitrary rank we show that the germs at the origin of v k and r k are analytically isomorphic if the group is 1 formal in particular the tangent cone to v k at 1 equals r k these new obstructions to 1 formality lead to a striking rationality property of the usual resonance varieties a detailed analysis of the irreducible components of the tangent cone at 1 to the first characteristic variety yields powerful obstructions to realizing a finitely presented group as the fundamental group of a smooth complex quasi projective algebraic variety this sheds new light on a classical problem of j p serre applications to arrangements configuration spaces coproducts of groups and artin groups are given

blind identification equalization using deterministic maximum likelihood and a partial prior on the input a semi deterministic maximum likelihood dml approach is presented to solve the joint blind channel identification and blind symbol estimation problem for single input multiple output systems a partial prior on the symbols is incorporated into the criterion which improves the estimation accuracy and brings robustness toward poor channel diversity conditions at the same time this method introduces fewer local minima than the use of a full prior statistical ml in the absence of noise the proposed batch algorithm estimates perfectly the channel and symbols with a finite number of samples based on these considerations an adaptive implementation of this algorithm is proposed it presents some desirable properties including low complexity robustness to channel overestimation and high convergence rate

quasi maximum likelihood multiuser detection using semi definite relaxation with application to synchronous cdma the maximum likelihood ml multiuser detector is well known to exhibit better bit error rate ber performance than many other multiuser detectors unfortunately ml detection mld is a nondeterministic polynomial time hard np hard problem for which there is no known algorithm that can find the optimal solution with polynomial time complexity in the number of users in this paper a polynomial time approximation method called semi definite sd relaxation is applied to the mld problem with antipodal data transmission sd relaxation is an accurate approximation method for certain np hard problems the sd relaxation ml sdr ml detector is efficient in that its complexity is of the order of k3 5 where k is the number of users we illustrate the potential of the sdr ml detector by showing that some existing detectors such as the decorrelator and the linear minimum mean square error detector can be interpreted as degenerate forms of the sdr ml detector simulation results indicate that the ber performance of the sdr ml detector is better than that of these existing detectors and is close to that of the true ml detector even when the cross correlations between users are strong or the near far effect is significant

the deligne mumford compactification of the real multiplication locus and teichmuller curves in genus 3 in the moduli space mathcal m g of genus g riemann surfaces consider the locus mathcal r mathcal m mathcal o of riemann surfaces whose jacobians have real multiplication by the order mathcal o in a totally real number field f of degree g if g 3 we compute the closure of mathcal r mathcal m mathcal o in the deligne mumford compactification of mathcal m g and the closure of the locus of eigenforms over mathcal r mathcal m mathcal o in the deligne mumford compactification of the moduli space of holomorphic 1 forms for higher genera we give strong necessary conditions for a stable curve to be in the boundary of mathcal r mathcal m mathcal o boundary strata of mathcal r mathcal m mathcal o are parameterized by configurations of elements of the field f satisfying a strong geometry of numbers type restriction

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

constrained maximum likelihood detection in cdma the detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a 0 1 constrained maximum likelihood ml problem a problem which is known to be np hard in contrast the unconstrained ml problem can be solved quite easily and is known as the decorrelating detector in this paper we consider the constrained ml problem where the solution vector is restricted to lie within a closed convex set ccs such a design criterion leads to detector structures which are ml under the constraint assumption a close relationship between a sphere constrained ml detector and the well known minimum mean square error detector is found and verified an iterative algorithm for solving a ccs constraint problem is derived based on results in linear variational inequality theory special cases of this algorithm subject to a box constraint are found to correspond to known nonlinear successive and parallel interference cancellation structures using a clipped soft decision for making tentative decisions while a weighted linear parallel interference canceler with signal dependent weights arises from the sphere constraint convergence issues are investigated and an efficient implementation is suggested the bit error rate performance is studied via computer simulations and the expected performance improvements over unconstrained ml are verified

the fields of real and complex numbers with a small multiplicative group we consider the model theory of the real and complex fields with a multiplicative group having the mann property among these groups are the finitely generated multiplicative groups in these fields as a by product we obtain some results on groups with the mann property in rings of witt vectors and in fields of positive characteristic k

o minimality and the andre oort conjecture for mathbb c n we give an unconditional proof of the andre oort conjecture for arbitrary products of modular curves we establish two generalizations the first includes the manin mumford conjecture for arbitrary products of elliptic curves defined over q as well as lang s conjecture for torsion points in powers of the multiplicative group the second includes the manin mumford conjecture for abelian varieties defined over q our approach uses the theory of o minimal structures a part of model theory and follows a strategy proposed by zannier and implemented in three recent papers a new proof of the manin mumford conjecture by pila zannier a proof of a special but new case of pink s relative manin mumford conjecture by masser zannier and new proofs of certain known results of andre oort manin mumford type by pila 2010 mathematics subject classification 11g18 03c64

linear equations over multiplicative groups recurrences and mixing i let u1 umu1 um be linear recurrences with values in a field kk of positive characteristic pp we show that the set of integer vectors k1 km k1 km such that u1 k1 um km 0u1 k1 um km 0 is pp normal in a natural sense generalizing that of the first author who proved the result for m 1m 1 furthermore the set is effectively computable if kk is we illustrate this with an example for m 4m 4 we also show that the corresponding set for zero characteristic is not decidable for m 557844m 557844 thus verifying a conjecture of cerlienco mignotte and piras

small points on subvarieties of a torus let v be a subvariety of a torus de ned over the algebraic numbers we give a qualitative and quantitative description of the set of points of v of height bounded by invariants associated to any variety containing v especially we determine whether such a set is or is not dense in v we then prove that these sets can always be written as the intersection of v with a nite union of translates of tori of which we control the sum of the degrees as a consequence we prove a conjecture by the rst author and david up to a logarithmic factor

linear equations in variables which lie in a multiplicative group let k be a field of characteristic 0 and let n be a natural number let r be a subgroup of the multiplicative group k n of finite rank r given a 1 a n e k write a a 1 a n for the number of solutions x x 1 x n of the equation a 1 x 1 a n x n 1 such that no proper subsum of a 1 x 1 a n x n vanishes we derive an explicit upper bound for a a 1 a n r which depends only on the dimension n and on the rank r

the number of solutions of decomposable form equations has only finitely many solutions the diophantine approximation techniques of thue and mahler and improvements by siegel dyson roth and bombieri made it possible to derive good explicit upper bounds for the number of solutions of 1 1 the best such upper bound to date due to bombieri 1 is 2 12r bombieri assumed that f is irreducible and r 6 which was not essential in his proof for t 0 i e f x y 1 in x y z bombieri and schmidt 2 derived the upper bound constant r which is best possible in terms of r

greatest common divisors and vojta s conjecture for blowups of algebraic tori we give results and inequalities bounding the greatest common divisor of multivariable polynomials evaluated at s unit arguments generalizing to an arbitrary number of variables results of bugeaud corvaja zannier hernandez luca and corvaja zannier in closely related results and in line with observations of silverman we prove special cases of vojta s conjecture for blowups of toric varieties as an application we classify when terms from simple linear recurrence sequences can have a large greatest common divisor in an appropriate sense the primary tool used in the proofs is schmidt s subspace theorem from diophantine approximation

on the dam problem this paper is concerned with the qualitative behavior of solutions of the dam problem for flow of an incompressible fluid through a two dimensional porous medium the cross section of the flow region is allowed to have a complicated boundary the flow domain is assumed to have a lipschitz boundary and minimal assumptions are made on the parts where various boundary conditions are to be satisfied the main contribution of the paper is to determine the corresponding properties of the solution after giving a concise proof of the known result that a solution exists the authors introduce the so called s 3 connected solutions s 3 is the impervious part of the boundary and prove several interesting results about them solutions which do not have these properties are such that there are pools of fluid not in contact with the outside reservoir and they prove that any solution can be written as a sum of an s 3 connected solution and pools also it is shown that s 3 connected solutions are unique for some boundaries it can be shown that only s 3 connected solutions exist so that uniqueness holds without qualification

multistep linear predictors based blind identification and equalization of multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider the estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers we extend the multistep linear prediction approach to mimo channels where the multichannel transfer function need not be column reduced moreover we allow infinite impulse response iir channels as well as the case where the subchannel transfer functions have common zeros in the past this approach has been confined to simo finite impulse response fir channels with no common subchannel zeros a related existing approach applicable to mimo channels is restricted to fir column reduced systems with equal length subchannels in our approach the knowledge of the nature of the underlying model fir or iir or the model order is not required our approach works when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data illustrative computer simulation examples are provided

arithmetic group symmetry and finiteness properties of torelli groups we examine groups whose resonance varieties characteristic varieties and sigma invariants have a natural arithmetic group symmetry and we explore implications on various niteness properties of subgroups we compute resonance varieties characteristic varieties and alexander polynomials of torelli groups and we show that all subgroups containing the johnson kernel have nite rst betti number when the genus is at least 4 we also prove that in this range the i adic completion of the alexander invariant is nite dimensional and the kahler property for the torelli group implies the nite generation of the johnson kernel

dynamical anomalous subvarieties structure and bounded height theorems abstract according to medvedev and scanlon 14 a polynomial f x q x of degree d 2 is called disintegrated if it is not conjugate to x d or to c d x where c d is the chebyshev polynomial of degree d let n n let f 1 f n q x be disintegrated polynomials of degrees at least 2 and let f 1 f n be the corresponding coordinate wise self map of p 1 n let x be an irreducible subvariety of p 1 n of dimension r defined over q we define the anomalous locus of x which is related to the periodic subvarieties of p 1 n we prove that the anomalous locus of x is zariski closed this is a dynamical analogue of a theorem of bombieri masser and zannier 4 we also prove that the points in the intersection of x with the union of all irreducible periodic subvarieties of p 1 n of codimension r have bounded height outside the anomalous locus of x this is a dynamical analogue of habegger s theorem 8 which was previously conjectured in 4 the slightly more general self maps f 1 f n where each f i q x is a disintegrated rational function are also treated at the end of the paper

a criterion for weak convergence on berkovich projective space we give a criterion for the weak convergence of unit borel measures on the n dimensional berkovich projective space bf p n k over a complete non archimedean field k as an application we give a sufficient condition for a certain type of equidistribution on bf p n k in terms of a weak zariski density property on the scheme theoretic projective space mathbb p n tilde k vphantom 0 over the residue field tilde k as a second application in the case of residue characteristic zero we give an ergodic theoretic equidistribution result for the powers of a point a in the n dimensional unit torus mathbb t n k over k this is a non archimedean analogue of a well known result of weyl over mathbb c and its proof makes essential use of a theorem of mordell lang type for mathbb g m n due to laurent

intersections of polynomial orbits and a dynamical mordell lang conjecture we prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection then the polynomials have a common iterate we also prove a special case of a conjectured dynamical analogue of the mordell lang conjecture

local systems on analytic germ complements abstract we prove that the cohomology jump loci of rank one local systems on the complement in a small ball of a germ of a complex analytic set are finite unions of torsion translates of subtori this is a generalization of the classical monodromy theorem stating that the eigenvalues of the monodromy on the cohomology of the milnor fiber of a germ of a holomorphic function are roots of unity