geometry of free loci and factorization of noncommutative polynomials abstract the free singularity locus of a noncommutative polynomial f is defined to be the sequence of hypersurfaces z n f x m n k g det f x 0 the main theorem of this article shows that f is irreducible if and only if z n f is eventually irreducible a key step in the proof is an irreducibility result for linear pencils arising from this is a free singularity locus nullstellensatz for noncommutative polynomials apart from consequences to factorization in a free algebra the paper also discusses its applications to invariant subspaces in perturbation theory and linear matrix inequalities in real algebraic geometry

the lee yang and polya schur programs i linear operators preserving stability in 1952 lee and yang proposed the program of analyzing phase transitions in terms of zeros of partition functions linear operators preserving non vanishing properties are essential in this program and various contexts in complex analysis probability theory combinatorics and matrix theory we characterize all linear operators on finite or infinite dimensional spaces of multivariate polynomials preserving the property of being non vanishing whenever the variables are in prescribed open circular domains in particular this solves the higher dimensional counterpart of a long standing classification problem originating from classical works of hermite laguerre hurwitz and polya schur on univariate polynomials with such properties

the van der waerden conjecture for mixed discriminants we prove that the mixed discriminant of doubly stochastic n tuples of semidefinite hermitian n n matrices is bounded below by n nn and that this bound is uniquely attained at the n tuple 1ni 1ni this result settles a conjecture posed by r bapat in 1989 we consider various generalizations and applications of this result

comments on the cramer rao lower bounds for signals with constant amplitude and polynomial phase for original paper see ieee trans signal processing vol 39 p 749 52 march 1991 different expressions for the cramer rao lower bounds crlbs of constant amplitude polynomial phase signals embedded in white gaussian noise appear in the literature the present paper revisits the derivation of the bounds reported by peleg and porat 1991 and indicates that the resulting expressions depend on the interval over which the signal is defined the proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds

linear matrix inequality representation of sets this article concerns the question which subsets of m can be represented with linear matrix inequalities lmis this gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory also before having much hope of representing engineering problems as lmis by automatic methods one needs a good idea of which problems can and cannot be represented by lmis little is currently known about such problems in this article we give a necessary condition that we call rigid convexity which must hold for a set m in order for to have an lmi representation rigid convexity is proved to be necessary and sufficient when m 2 this settles a question formally stated by pablo parrilo and berndt sturmfels in 15 as shown by lewis parillo and ramana 11 our main result also establishes in the case of three variables a 1958 conjecture by peter lax on hyperbolic polynomials 2006 wiley periodicals inc

shift lifts preserving ramanujan property abstract in a breakthrough work marcus et al 1 recently showed that every d regular bipartite ramanujan graph has a 2 lift that is also d regular bipartite ramanujan as a consequence a straightforward iterative brute force search algorithm leads to the construction of a d regular bipartite ramanujan graph on n vertices in time 2 o d n shift k lifts studied in 2 lead to a natural approach for constructing ramanujan graphs more efficiently the number of possible shift k lifts of a d regular n vertex graph is k n d 2 suppose the following holds for k 2 n there exists a shift k lift that maintains the ramanujan property of d regular bipartite graphs on n vertices for all n then by performing a similar brute force algorithm one would be able to construct an n vertex bipartite ramanujan graph in time 2 o d log 2 n also if holds for all k 2 then one would obtain an algorithm that runs in poly n d time in this work we take a first step towards proving by showing the existence of shift k lifts that preserve the ramanujan property in d regular bipartite graphs for k 3 and for k 4

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

frames induced by the action of continuous powers of an operator abstract we investigate systems of the form a t g g g t 0 l where a b h is a normal operator in a separable hilbert space h g h is a countable set and l is a positive real number although the main goal of this work is to study the frame properties of a t g g g t 0 l as intermediate steps we explore the completeness and bessel properties of such systems from a theoretical perspective which are of interest by themselves beside the theoretical appeal of investigating such systems their connections to dynamical and mobile sampling make them fundamental for understanding and solving several major problems in engineering and science

approximation of the average of some random matrices abstract rudelson s theorem states that if for a set of unit vectors u i and positive weights c i we have that c i u i u i is the identity operator i on r d then the sum of a random sample of c d ln d of these diadic products is close to i the ln d term cannot be removed on the other hand the recent fundamental result of batson spielman and srivastava and its improvement by marcus spielman and srivastava show that the ln d term can be removed if one wants to show the existence of a good approximation of i as the average of a few diadic products it is known that essentially the same proof as rudelson s yields a more general statement about the average of positive semi definite matrices first we give an example of an average of positive semi definite matrices where there is no approximation of this average by cd elements thus the result of batson spielman and srivastava cannot be extended to this wider class of matrices next we present a stability version of rudelson s result on positive semi definite matrices and thus extend it to certain non symmetric matrices this yields applications to the study of the banach mazur distance of convex bodies finally we show that in some cases one needs to take a subset of the vectors of order d 2 to approximate the identity

mixed determinants and the kadison singer problem we adapt the arguments of marcus spielman and srivastava in their proof of the kadison singer problem to prove improved paving estimates working with anderson s paving formulation of kadison singer instead of weaver s vector balancing version we show that the machinery of interlacing polynomials due to marcus spielman and srivastava works in this setting as well the relevant expected characteristic polynomials turn out to be related to the so called mixed determinants that have been previously studied in a different context by borcea and branden this approach allows us to show that any projection with diagonal entries 1 2 can be 4 paved yielding improvements over the best known current estimates of 12 this approach also allows us to show that any projection with diagonal entries strictly less than 1 4 can be 2 paved matching recent results of bownik casazza marcus and speegle we also relate the problem of finding optimal paving estimates to bounding the root intervals of a natural one parameter deformation of the characteristic polynomial of a matrix that turns out to have several pleasing combinatorial properties

a non diagonalizable pure state we construct a pure state on the c algebra formula see text of all bounded linear operators on formula see text which is not diagonalizable i e it is not of the form formula see text for any orthonormal basis formula see text of formula see text and an ultrafilter u on n this constitutes a counterexample to anderson s conjecture without additional hypothesis and improves results of c akemann n weaver i farah and i smythe who constructed such states making additional set theoretic assumptions it follows from results of j anderson and the positive solution to the kadison singer problem due to a marcus d spielman and n srivastava that the restriction of our pure state to any atomic masa formula see text of diagonal operators with respect to an orthonormal basis formula see text is not multiplicative on formula see text

random reordering in sor type methods when iteratively solving linear systems by b by b with hermitian positive semi definite b and in particular when solving least squares problems for ax b ax b by reformulating them as aa y b aa y b it is often observed that sor type methods gau seidel kaczmarz perform suboptimally for the given equation ordering and that random reordering improves the situation on average this paper is an attempt to provide some additional theoretical support for this phenomenon we show error bounds for two randomized versions called shuffled and preshuffled sor that improve asymptotically upon the best known bounds for sor with cyclic ordering our results are based on studying the behavior of the triangular truncation of hermitian matrices with respect to their permutations

dilations of operator valued measures with bounded p variations and framings on banach spaces abstract the dilations for operator valued measures ovms and bounded linear maps indicate that the dilation theory is in general heavily dependent on the banach space nature of the dilation spaces this naturally led to many questions concerning special type of dilations in particular it is not known whether ultraweakly continuous normal maps can be dilated to ultraweakly continuous homomorphisms we answer this question affirmatively for the case when the domain algebra is an abelian von neumann algebra it is well known that completely bounded hilbert space operator valued measures correspond to the existence of orthogonal projection valued dilations in the sense of naimark and stinespring and ovms with bounded total variations are completely bounded but not the vice versa with the aim of classifying ovms from the dilation point of view we introduce the concept of total p variations for ovms we prove that any completely bounded ovm has finite 2 variation and any ovm with finite p variation can be dilated to a but usually non hilbertian projection valued measure of the same type with the help of framing induced ovms we prove that conventional minimal dilation space of a non trivial framing contains c 0 then does not have bounded p variation

hyperbolic polynomials interlacers and sums of squares hyperbolic polynomials are real polynomials whose real hypersurfaces are maximally nested ovaloids the innermost of which is convex these polynomials appear in many areas of mathematics including optimization combinatorics and differential equations here we investigate the special connection between a hyperbolic polynomial and the set of polynomials that interlace it this set of interlacers is a convex cone which we write as a linear slice of the cone of nonnegative polynomials in particular this allows us to realize any hyperbolicity cone as a slice of the cone of nonnegative polynomials using a sums of squares relaxation we then approximate a hyperbolicity cone by the projection of a spectrahedron a multiaffine example coming from the vamos matroid shows that this relaxation is not always exact using this theory we characterize the real stable multiaffine polynomials that have a definite determinantal representation and construct one when it exists

ramanujan coverings of graphs abstract let g be a finite connected graph and let be the spectral radius of its universal cover for example if g is k regular then 2 k 1 we show that for every r there is an r covering a k a an r lift of g where all the new eigenvalues are bounded from above by it follows that a bipartite ramanujan graph has a ramanujan r covering for every r this generalizes the r 2 case due to marcus spielman and srivastava 26 every r covering of g corresponds to a labeling of the edges of g by elements of the symmetric group s r we generalize this notion to labeling the edges by elements of various groups and present a broader scenario where ramanujan coverings are guaranteed to exist in particular this shows the existence of richer families of bipartite ramanujan graphs than was known before inspired by 26 a crucial component of our proof is the existence of interlacing families of polynomials for complex reflection groups the core argument of this component is taken from 27 another important ingredient of our proof is a new generalization of the matching polynomial of a graph we define the r th matching polynomial of g to be the average matching polynomial of all r coverings of g we show this polynomial shares many properties with the original matching polynomial for example it is real rooted with all its roots inside

four deviations suffice for rank 1 matrices abstract we prove a matrix discrepancy bound that strengthens the famous kadison singer result of marcus spielman and srivastava consider any independent scalar random variables 1 n with finite support e g 1 or 0 1 valued random variables or some combination thereof let u 1 u n m and 2 i 1 n var i u i u i 2 then there exists a choice of outcomes e 1 e n in the support of 1 n s t i 1 n e i u i u i i 1 n e i u i u i 4 a simple consequence of our result is an improvement of a lyapunov type theorem of akemann and weaver

a fast algorithm for estimating the parameters of a quadratic fm signal this paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated fm signal the proposed algorithm is fast in that it requires only one dimensional 1 d maximizations the optimal maximum likelihood method by contrast requires a three dimensional 3 d maximization which can only be realized with an exhaustive 3 d grid search asymptotic statistical results are derived for all the estimated parameters the amplitude estimate is seen to be optimal whereas the phase parameters are in general suboptimal of the four phase parameter estimates two approach optimality as the signal to noise ratio snr tends to infinity the other two have mean square errors that are within 50 of the theoretical lower bounds for high snr simulations are provided to support the theoretical results extensions to multiple components and higher order fm signals are also discussed

livsic type determinantal representations and hyperbolicity abstract hyperbolic homogeneous polynomials with real coefficients i e hyperbolic real projective hypersurfaces and their determinantal representations play a key role in the emerging field of convex algebraic geometry in this paper we consider a natural notion of hyperbolicity for a real subvariety x p d of an arbitrary codimension l with respect to a real l 1 dimensional linear subspace v p d and study its basic properties we also consider a class of determinantal representations that we call livsic type and a nice subclass of these that we call very reasonable much like in the case of hypersurfaces l 1 the existence of a definite hermitian very reasonable livsic type determinantal representation implies hyperbolicity we show that every curve admits a very reasonable livsic type determinantal representation our basic tools are cauchy kernels for line bundles and the notion of the bezoutian for two meromorphic functions on a compact riemann surface that we introduce we then proceed to show that every real curve in p d hyperbolic with respect to some real d 2 dimensional linear subspace admits a definite hermitian or even definite real symmetric very reasonable livsic type determinantal representation

the lee yang and polya schur programs ii theory of stable polynomials and applications in the first part of this series we characterized all linear operators on spaces of multivariate polynomials preserving the property of being nonvanishing in products of open circular domains for such sets this completes the multivariate generalization of the classification program initiated by polya and schur for univariate real polynomials we build on these classification theorems to develop here a theory of multivariate stable polynomials applications and examples show that this theory provides a natural framework for dealing in a uniform way with lee yang type problems in statistical mechanics combinatorics and geometric function theory in one or several variables in particular we answer a question of hinkkanen on multivariate apolarity

plurisubharmonic noncommutative rational functions abstract a noncommutative nc function in x 1 x g x 1 x g is called plurisubharmonic plush if its nc complex hessian takes only positive semidefinite values on an nc neighborhood of 0 the main result of this paper shows that an nc rational function is plush if and only if it is a composite of a convex rational function with an analytic no x j rational function the proof is entirely constructive further a simple computable necessary and sufficient condition for an nc rational function to be plush is given in terms of its minimal realization

the ising partition function zeros and deterministic approximation we study the problem of approximating the partition function of the ferromagnetic ising model with both pairwise as well as higher order interactions equivalently in graphs as well as hypergraphs our approach is based on the classical lee yang theory of phase transitions along with a new lee yang theorem for the ising model with higher order interactions and on an extension of ideas developed recently by barvinok and patel and regts that can be seen as an algorithmic realization of the lee yang theory our first result is a deterministic polynomial time approximation scheme an fptas for the partition function in bounded degree graphs that is valid over the entire range of parameters beta the interaction and lambda the external field except for the case left lambda right 1 the zero field case a polynomial time randomized approximation scheme fpras for all graphs and all beta lambda based on markov chain monte carlo simulation has long been known unlike most other deterministic approximation algorithms for problems in statistical physics and counting our algorithm does not rely on the decay of correlations property but as pointed out above on lee yang theory this approach extends to the more general setting of the ising model on hypergraphs of bounded degree and edge size where no previous algorithms even randomized were known for a wide range of parameters in order to achieve this latter extension we establish a tight version of the lee yang theorem for the ising model on hypergraphs improving a classical result of suzuki and fisher

polynomial convolutions in max plus algebra abstract recently in a work that grew out of their exploration of interlacing polynomials marcus spielman and srivastava 21 and marcus 20 studied certain combinatorial polynomial convolutions these convolutions preserve real rootedness and capture expectations of characteristic polynomials of unitarily invariant random matrices thus providing a link to free probability we explore analogues of these types of convolutions in the setting of max plus algebra in this setting the max permanent replaces the determinant the maximum is the analogue of the expected value and real rootedness is replaced by full canonical form our results resemble those of marcus et al however in contrast to the classical setting we obtain an exact and simple description of all roots of the convolution of p x and q x in terms of the roots of p x and q x

applications of stable polynomials to mixed determinants johnson s conjectures unimodality and symmetrized fischer products for n x n matrices a and b define eta a b sigma s det a s det b s where the summation is over all subsets of 1 n s is the complement of s and a s is the principal submatrix

characteristic polynomials of symmetric matrices over the univariate polynomial ring abstract viewing a bivariate polynomial f r x t as a family of univariate polynomials in t parametrized by real numbers x we call f real rooted if this family consists of monic polynomials with only real roots if f is the characteristic polynomial of a symmetric matrix with entries in r x it is obviously real rooted in this article the converse is established namely that every real rooted bivariate polynomial is the characteristic polynomial of a symmetric matrix over the univariate real polynomial ring as a byproduct we present a purely algebraic proof of the helton vinnikov theorem which solved the 60 year old lax conjecture on the existence of definite determinantal representation of ternary hyperbolic forms

iterative actions of normal operators abstract let a be a normal operator in a hilbert space h and let g h be a countable set of vectors we investigate the relations between a g and l that make the system of iterations a n g g g 0 n l g complete bessel a basis or a frame for h the problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis including frame theory and spectral theory it also has relations to topics in applied harmonic analysis including wavelet theory and time frequency analysis

design of higher order polynomial wigner ville distributions the polynomial wigner ville distribution pwvd is a time frequency signal analysis tool for representing polynomial frequency modulated fm signals we present an optimization procedure to design pwvds and discuss the need for higher order pwvds

on spectral cantor moran measures and a variant of bourgain s sum of sine problem abstract in this paper we show that if we have a sequence of hadamard triples n n b n l n with b n 0 1 n n 1 for n 1 2 except an extreme case then the associated cantor moran measure n n b n 1 n 1 b 1 1 n 1 n 2 b 2 1 n 1 n 2 n 3 b 3 n n with support inside 0 1 always admits an exponential orthonormal basis e e 2 i x for l 2 where is obtained from suitably modifying l n here n is the convolution of the first n dirac measures and n denotes the tail term we show that the completeness of e in general depends on the equi positivity of the sequence of the pull backed tail of the cantor moran measure n n n 1 n n 1 such equi positivity can be analyzed by the integral periodic zero set of the weak limit of n this result offers a new conceptual understanding of the completeness of exponential functions and it improves significantly many partial results studied by recent research whose focus has been specifically on b n 4 using the bourgain s example that a sum of sine can be asymptotically small we show that in the extreme case there exists some cantor moran measure such that the equi positive condition fails and the fourier transform of the associated n uniformly converges on some unbounded set

model subspaces techniques to study fourier expansions in l2 spaces associated to singular measures abstract let be a probability measure on t that is singular with respect to the haar measure in this paper we study fourier expansions in l 2 t using techniques from the theory of model subspaces of the hardy space since the sequence of monomials z n n n is effective in l 2 t it has a parseval frame associated via the kaczmarz algorithm our first main goal is to identify the aforementioned frame with boundary values of the frame p z n for the model subspace h h 2 h 2 where p is the orthogonal projection from the hardy space h 2 onto h the study of fourier expansions in l 2 t also leads to consider positive kernels in the hardy space our second main goal is to study the set of measures which reproduce a kernel contained in a model subspace we completely characterize this set when the kernel is the reproducing kernel of a model subspace and we study the consequences of this characterization

multivariate polya schur classification problems in the weyl algebra a multivariate polynomial is stable if it is nonvanishing whenever all variables have positive imaginary parts we classify all linear partial differential operators in the weyl algebra a n that preserve stability an important tool that we develop in the process is the higher dimensional generalization of polya schur s notion of multiplier sequence we characterize all multivariate multiplier sequences as well as those of finite order next we establish a multivariate extension of the cauchy poincare interlacing theorem and prove a natural analog of the lax conjecture for real stable polynomials in two variables using the latter we describe all operators in a 1 that preserve univariate hyperbolic polynomials by means of determinants and homogenized symbols our methods also yield homotopical properties for symbols of linear stability preservers and a duality theorem showing that an operator in a n preserves stability if and only if its fischer fock adjoint does these are powerful multivariate extensions of the classical hermite poulain jensen theorem polya s curve theorem and schur malo szegocomposition theorems examples and applications to strict stability preservers are also discussed

extracting a basis with fixed block inside a matrix abstract given u an n m matrix of rank n whose columns are denoted by u j j m several authors have already considered the problem of finding a subset 1 m such that u i i span r n and tr i u i u i t 1 is minimized in this paper we generalize this problem by selecting arbitrary rank matrices instead of rank 1 matrices another generalization is considering the same problem while allowing a part of the matrix to be fixed the methods of selection employed develop into algorithms

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

interlacing families ii mixed characteristic polynomials and the kadison singer problem we use the method of interlacing polynomials introduced in our previous article to prove two theorems known to imply a positive solution to the kadison singer problem the rst is weaver s conjecture ks 2 which is known to imply kadison singer via a projection paving conjecture of akemann and anderson the second is a formulation due to casazza et al of anderson s original paving conjecture s for which we are able to compute explicit paving bounds the proof involves an analysis of the largest roots of a family of polynomials that we call the mixed characteristic polynomials of a collection of matrices

mixed discriminants of positive semidefinite matrices abstract if ak akij k 1 2 n are n by n matrices then their mixed discriminant d a1 an is given by d a 1 a n 1 n s n a j ij where sn is the symmetric group of degree n and where denotes determinant we give certain alternative ways of defining the mixed discriminant and state some basic properties it is pointed out that a ryser type formula for the mixed discriminant exists in the literature and a simpler proof is given for it it is shown that the mixed discriminant can be expressed as an inner product a generalization of konig s theorem on 0 1 matrices is proved the following set d n which includes the set of n by n doubly stochastic matrices is defined and studied

twice ramanujan sparsifiers we prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices as linear sized spectral sparsifiers of complete graphs are expanders our sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs in particular we prove that for every d 1 and every undirected weighted graph g v e w on n vertices there exists a weighted graph h v f tilde w with at most lceil d n 1 rceil edges such that for every x in mathbb r v x t l g x leq x t l h x leq bigl frac d 1 2 sqrt d d 1 2 sqrt d bigr cdot x t l g x where l g and l h are the laplacian matrices of g and h respectively thus h approximates g spectrally at least as well as a ramanujan expander with dn 2 edges approximates the complete graph we give an elementary deterministic polynomial time algorithm for constructing h

a characterization of boundary representations of positive matrices in the hardy space via the abel product abstract spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure we consider in this paper the reverse for a positive matrix in the hardy space of the unit disc we consider which measures if any yield a boundary representation of the positive matrix we prove a characterization of those representing measures via a matrix identity by introducing a new operator product called the abel product

fisher zeros and correlation decay in the ising model we study the complex zeros of the partition function of the ising model viewed as a polynomial in the interaction parameter these are known as fisher zeros in light of their introduction by fisher in 1965 fisher m e the nature of critical points in lecture notes in theoretical physics edited by brittin w e university of colorado press 1965 vol 7c while the zeros of the partition function as a polynomial in the field parameter have been extensively studied since the classical work of lee and yang comparatively little is known about fisher zeros for general graphs our main result shows that the zero field ising model has no fisher zeros in a complex neighborhood of the entire region of parameters where the model exhibits correlation decay in addition to shedding light on fisher zeros themselves this result also establishes a formal connection between two distinct notions of phase transition for the ising model the absence of complex zeros analyticity of the free energy density or the normalized logarithm of the partition function and decay of correlations with distance we also discuss the consequences of our result for efficient deterministic approximation of the partition function our proof relies heavily on algorithmic techniques notably weitz s self avoiding walk tree and as such belongs to a growing body of work that uses algorithmic methods to resolve classical questions in statistical physics we study the complex zeros of the partition function of the ising model viewed as a polynomial in the interaction parameter these are known as fisher zeros in light of their introduction by fisher in 1965 fisher m e the nature of critical points in lecture notes in theoretical physics edited by brittin w e university of colorado press 1965 vol 7c while the zeros of the partition function as a polynomial in the field parameter have been extensively studied since the classical work of lee and yang comparatively little is known about fisher zeros for general graphs our main result shows that the zero field ising model has no fisher zeros in a complex neighborhood of the entire region of parameters where the model exhibits correlation decay in addition to shedding light on fisher zeros themselves this result also establishes a formal connection between two distinct notions of phase transition for the ising model the absence of complex zeros analyticity of the free energy density

the discretization problem for continuous frames abstract we characterize when a coherent state or continuous frame for a hilbert space may be sampled to obtain a frame which solves the discretization problem for continuous frames in particular we prove that every bounded continuous frame for a hilbert space may be sampled to obtain a frame we give multiple applications to different classes of frames such as scalable frames and gabor frames

a modification of the discrete polynomial transform the discrete polynomial transform dpt has been introduced as a computationally efficient algorithm for estimating the phase parameters of constant amplitude polynomial phase signals we present a modification of the dpt which improves the estimation accuracy we show by a perturbation analysis that the mean squared error of the estimates is reduced when the order of the polynomial is three or greater

aircraft flight parameter estimation based on passive acoustic techniques using the polynomial wigner ville distribution the acoustic signal from an overflying aircraft as heard by a stationary observer is used to estimate an aircraft s constant height ground speed range and acoustic frequency central to the success of this flight parameter estimation scheme is the need for an accurate estimate of the instantaneous frequency of the observed acoustic signal in this paper the polynomial wigner ville distribution is used in this application as the instantaneous frequency estimator its performance and the issue of the optimal time domain window length are addressed

random vectors in the isotropic position abstract letybe a random vector in r n satisfying e y y id letmbe a natural number and lety1 ymbe independent copies ofy we study the question of approximation of the identity operator by finite sums of the tensorsyi yi we prove that for some absolute constantc e 1 m i 1 m y i y i id c log n m e y log m 1 log m provided that the last expression is smaller than 1 we apply this estimate to improve a result of bourgain concerning the number of random points needed to bring a convex body into a nearly isotropic position

generalized high order phase function for parameter estimation of polynomial phase signal the high order phase function hpf has been introduced recently to estimate the parameters of a polynomial phase signal pps in this correspondence we generalize the standard hpf by introducing multiple time instants thus the standard hpf can be treated as a special example of the generalized hpf with identical time instants we propose a procedure for finding time instants minimizing the mean square error mse the proposed method achieves better performances than the high order ambiguity function haf and polynomial wigner ville distribution pwvd the theoretical analysis as well as the monte carlo simulations verify the advantages such as lower mse and lower snr threshold for the pps

improved bounds in weaver and feichtinger conjectures we sharpen the constant in the ks2 conjecture of weaver 28 which was validated by marcus spielman and srivastava 26 in their solution of the kadison singer problem we then apply this result to prove optimal asymptotic bounds on the size of partitions in the feichtinger conjecture

on subsemigroups of finitely presented semigroups the purpose of this paper is to investigate properties of subsemigroups of finitely presented semigroups particularly with respect to the property of being finitely presented more precisely we will consider various instances of the following main problem let s be a finitely presented semigroup i is every subsemigroup ideal one sided ideal of s finitely generated ii is every subsemigroup ideal one sided ideal of s which is finitely generated as a semigroup finitely presented iii is every subsemigroup ideal one sided ideal of finite index in s finitely presented for the definition of index see below for example if s is finite all these questions have an affirmative answer less trivially if s is a commutative semigroup then ii has an affirmative w x w x answer see 12 also in 2 it has been proved that a two sided ideal of finite index in a finitely presented semigroup is always finitely presented

bianalytic maps between free spectrahedra linear matrix inequalities lmis i d sum j 1 g a jx j sum j 1 g a j x j succeq 0 play a role in many areas of applications the set of solutions of an lmi is a spectrahedron lmis in dimension free matrix variables model most problems in linear systems engineering and their solution sets are called free spectrahedra free spectrahedra are exactly the free semialgebraic convex sets this paper studies free analytic maps between free spectrahedra and under certain generically valid irreducibility assumptions classifies all those that are bianalytic the foundation of such maps turns out to be a very small class of birational maps we call convexotonic the convexotonic maps in g variables sit in correspondence with g dimensional algebras if two bounded free spectrahedra mathcal d a and mathcal d b meeting our irreducibility assumptions are free bianalytic with map denoted p then p must after possibly an affine linear transform extend to a convexotonic map corresponding to a g dimensional algebra spanned by u i a 1 ldots u i a g for some unitary u furthermore b and ua are unitarily equivalent the article also establishes a positivstellensatz for free analytic functions whose real part is positive semidefinite on a free spectrahedron and proves a representation for a free analytic map from mathcal d a to mathcal d b not necessarily bianalytic another result shows that a function analytic on any radial expansion of a free spectrahedron is approximable by polynomials uniformly on the spectrahedron these theorems are needed for classifying free bianalytic maps

parseval p frames and the feichtinger conjecture abstract in this paper we give a precise characterization of parseval p frames by the known clarkson s inequality for l p as a direct application we show that every tight p frame g j j 1 for l p with frame bound b 0 and inf j g j c 0 can be decomposed into b c p standard q riesz basic sequences and we show that the estimate b c p is optimal moreover we prove the existence of a p frame which is not equivalent to any parsevel p frame for l p and a parseval p frame which is not a schauder frame sequence for the space or its dual space while we obtain that every p frame can become a pseudo framing with l q coefficients for the dual space

multivariate stable polynomials theory and applications univariate polynomials with only real roots while special do occur often enough that their properties can lead to interesting conclusions in diverse areas due mainly to the recent work of two young mathematicians julius borcea and petter branden a very successful multivariate generalization of this method has been developed the first part of this paper surveys some of the main results of this theory of multivariate stable polynomials the most central of these results is the characterization of linear transformations preserving stability of polynomials the second part presents various applications of this theory in complex analysis matrix theory probability and statistical mechanics and combinatorics

bianalytic free maps between spectrahedra and spectraballs abstract linear matrix inequalities lmis are ubiquitous in real algebraic geometry semidefinite programming control theory and signal processing lmis with dimension free matrix unknowns are central to the theories of completely positive maps and operator algebras operator systems and spaces and serve as the paradigm for matrix convex sets the matricial feasibility set of an lmi is called a free spectrahedron in this article the bianalytic maps between a very general class of ball like free spectrahedra examples of which include row or column contractions and tuples of contractions and arbitrary free spectrahedra are characterized and seen to have an elegant algebraic form they are all highly structured rational maps in the case that both the domain and codomain are ball like these bianalytic maps are explicitly determined and the article gives necessary and sufficient conditions for the existence of such a map with a specified value and derivative at a point in particular this result leads to a classification of automorphism groups of ball like free spectrahedra the proofs depend on a novel free nullstellensatz established only after new tools in free analysis are developed and applied to obtain fine detail geometric in nature locally and algebraic in nature globally about the boundary of ball like free spectrahedra

strong converse for identification via quantum channels we present a simple proof of the strong converse for identification via discrete memoryless quantum channels based on a novel covering lemma the new method is a generalization to quantum communication channels of ahlswede s 1979 1992 approach to classical channels it involves a development of explicit large deviation estimates to the case of random variables taking values in self adjoint operators on a hilbert space this theory is presented separately in an appendix and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems

quantum measurable cardinals abstract we investigate states on von neumann algebras which are not normal but enjoy various forms of infinite additivity and show that these exist on b h if and only if the cardinality of an orthonormal basis of h satisfies various large cardinal conditions for instance there is a singular countably additive pure state on b l 2 if and only if is ulam measurable and there is a singular additive pure state on b l 2 if and only if is measurable the proofs make use of farah and weaver s theory of quantum filters 12 we can generalize some of these characterizations to arbitrary von neumann algebras applications to ueda s peak set theorem for von neumann algebras are discussed in the final section