fundamental limitations in passive time delay estimation part i narrow band systems time delay estimation of a noise like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar sonar applications a new method is presented to analyze the mean square error performance of delay estimation schemes based on a modified improved version of the ziv zakai lower bound zzlb this technique is shown to yield the tightest results on the attainable system performance for a wide range of signal to noise ratio snr conditions for delay estimation using narrow band ambiguity prone signals the fundamental result of this study is illustrated in fig 3 the entire domain of snr is divided into several disjoint segments indicating several distinct modes of operation if the available snr does not exceed snr 1 signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation as a result the attainable mean square error bar epsilon 2 is bounded only by the a priori parameter domain if snr 1 2 the modified zzlb coincides with the barankin bound in this regime differential delay observations are subject to ambiguities if snr snr 3 the modified zzlb coincides with the cramer rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved the transition from the ambiguity dominated mode of operation to the ambiguity free mode of operation starts at snr 2 and ends at snr 3 this is the threshold phenomenon in time delay estimation the various deflection points snr i and the various segments of the bound fig 3 are given as functions of such important system parameters as time bandwidth product wt signal bandwidth to center frequency ratio w 0 and the number of half wavelengths of the signal center frequency contained in the spacing between receivers with this information the composite bound illustrated in fig 3 provides the most complete characterization of the attainable system performance under any prespecified snr conditions

an accurate algebraic solution for moving source location using tdoa and fdoa measurements this paper proposes an algebraic solution for the position and velocity of a moving source using the time differences of arrival tdoas and frequency differences of arrival fdoas of a signal received at a number of receivers the method employs several weighted least squares minimizations only and does not require initial solution guesses to obtain a location estimate it does not have the initialization and local convergence problem as in the conventional linear iterative method the estimated accuracy of the source position and velocity is shown to achieve the crame spl acute r rao lower bound for gaussian tdoa and fdoa noise at moderate noise level before the thresholding effect occurs simulations are included to examine the algorithm s performance and compare it with the taylor series iterative method

aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

the cohomological dimension of a resultant variety in prime characteristicp 2 2 let f s t s x s q 2 x st q x t 1 f i f 3 be a collection of bii i0 i1 i2 nary quadratic forms with indeterminate coefficients over a field k and let w x r s k x the aim of this paper is to compute the cohomoi j 1f if 3 0 f jf 2 logical dimension of the ideal i r generated by the following sylvester resultants res f f res f f res f f and res f q f f 1 2 1 3 2 3 1 2 3 the closed points of the affine variety defined by i correspond to coefficients of the three forms having a common zero thus in the w x terminology of l1 i is a resultant system for f f and f compare 1 2 3 w x with theorem 1 b in l1 in general if f f are binary forms of 1 s degrees d g d g g d one can show that a resultant system is 1 2 s s w x generated by at least 1 q 1 q d elements theorem 1 in l1 and ts3 t one would like to know if this lower bound is sharp in our case where s s 3 and d s d s d s 2 the question is whether 1 2 3 4 i can be generated by three elements this would imply that h r s 0 i and this is the motivation behind the main result of this paper 4 it turns out that it is possible to show that h r s 0 working in the i subring of joint invariants of g s gl 2 k acting on r via change of variables in s t this calculation is based on some recent results by lyubeznik on f modules which include an algorithm for deciding whether local cohomology modules over regular rings of prime characteristic p vanish to the best of the author s knowledge theorem 9 in this paper is the first application of this algorithm yan has recently produced a 4 w x topological argument showing that h r vanishes in characteristic 0 y i

accurate localization of a rigid body using multiple sensors and landmarks this paper develops estimators for locating a rigid body using the time measurements and the doppler as well if it is moving between the sensors in the rigid body and a few landmarks outside the challenge of rigid body localization is that in addition to the position we are also interested in obtaining the rotation parameters of the rigid body that must belong to the special orthogonal group the proposed estimators are non iterative and have two steps preliminary and refinement the preliminary step provides a coarse estimate and the refinement step improves the first step estimate to yield an accurate solution when the rigid body is stationary we are able to locate the body with accuracy higher than the solutions of comparable complexity found in the literature when the rigid body is moving we develop an estimator that contains the additional unknowns of angular and translational velocities simulations show that the proposed estimators in both stationary and moving cases can approach the cramer rao lower bound performance under gaussian noise over the small error region

generators and defining relations for the ring of differential operators on a smooth affine algebraic variety in prime characteristic abstract for the ring of differential operators d o x on a smooth affine algebraic variety x over a perfect field of characteristic p 0 explicit algebra generators and defining relations are found a finite set of generators and a finite set of defining relations are given explicitly for the module der k o x of derivations on the algebra o x of regular functions on the variety x

finiteness properties of local cohomology modules an application of d modules to commutative algebra the main goal of this paper is to establish finiteness properties of local cohomology modules in characteristic 0 that would be analogous to those proven by c huneke and r sharp in characteristicp 0 our method based on the theory of algebraicd modules seems to be the first application ofd modules to commutative algebra

on invariants and endomorphism rings of certain local cohomology modules abstract let r m denote an n dimensional gorenstein ring for an ideal i r with grade i c we define new numerical invariants i j i as the socle dimensions of h m i h i n j r in case of a regular local ring containing a field these numbers coincide with the lyubeznik numbers i j r i we use d d i d dim r i to characterize the surjectivity of the natural homomorphism f r hom r h i r c r h i r c r as a technical tool we study several natural homomorphisms moreover we prove a few results on i j i

bias reduction for an explicit solution of source localization using tdoa this paper proposes two methods to reduce the bias of the well known algebraic explicit solution chan and ho a simple and efficient estimator for hyperbolic location ieee trans signal process vol 42 pp 1905 1915 aug 1994 for source localization using tdoa bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor bias also dominates performance when multiple times of independent measurements are available such as in uwb localization or in target tracking the paper starts by deriving the bias of the source location estimate from chan and ho the bias is found to be considerably larger than that of the maximum likelihood estimator two methods called biassub and biasred are developed to reduce the bias the biassub method subtracts the expected bias from the solution of chan and ho s work where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements the biasred method augments the equation error formulation and imposes a constraint to improve the source location estimate the biassub method requires the exact knowledge of the noise covariance matrix and biasred only needs the structure of it analysis shows that both methods reduce the bias considerably and achieve the crlb performance for distant source when the noise is gaussian and small the biassub method can nearly eliminate the bias and the biasred method is able to lower the bias to the same level as the maximum likelihood estimator the biasred method is extended for tdoa and fdoa positioning simulations corroborate the performance of the proposed methods

local cohomology modules of a smooth z algebra have finitely many associated primes let r be a commutative noetherian ring that is a smooth mathbb z algebra for each ideal mathfrak a of r and integer k we prove that the local cohomology module h k mathfrak a r has finitely many associated prime ideals this settles a crucial outstanding case of a conjecture of lyubeznik asserting this finiteness for local cohomology modules of all regular rings

delay and doppler estimation by time space partition of the array data an instrumentationally attractive technique for estimating the doppler time compression and its time derivatives is proposed and analyzed in this paper the basic scheme consists of m 1 generalized cross correlators gcc s in parallel where m is the number of sensors in the receiving array each of which is implemented successively to generate a sequence of differential delay measurements the resulting spatial temporal differential delay data are then compressed into the estimates of the doppler and its derivatives using a least squares ls filter it is shown that for signal to noise ratio snr conditions above the threshold level the indicated two step estimation procedure is very nearly optimal when operating near the threshold point however the proposed scheme is only distinctly suboptimal

cofiniteness of local cohomology modules for ideals of small dimension abstract let r be a commutative noetherian ring and let m be a non zero finitely generated r module let i be an ideal of r and t a non negative integer such that dim supp h i i m 1 for all i t it is shown that the r modules h i 0 m h i 1 m h i t 1 m are i cofinite and the r module hom r r i h i t m is finitely generated this immediately implies that if i has dimension one i e dim r i 1 then h i i m is i cofinite for all i 0 this is a generalization of the main results of delfino and marley d delfino t marley cofinite modules and local cohomology j pure appl algebra 121 1997 45 52 and yoshida k i yoshida cofiniteness of local cohomology modules for ideals of dimension one nagoya math j 147 1997 179 191 for an arbitrary noetherian ring r also we prove that if r is local and dim supp h i i m 2 for all i t then the r modules ext r j r i h i i m and hom r r i h i t m are weakly laskerian for all i t and all j 0 as a consequence it follows that the set of associated primes of h i i m is finite for all i 0 whenever dim r i 2

lyubeznik s invariants for cohomologically isolated singularities abstract in this note i give a description of lyubeznik s local cohomology invariants for a certain natural class of local rings namely the ones which have the same local cohomology vanishing as one expects from an isolated singularity this strengthens our results of manuel blickle raphael bondu local cohomology multiplicities in terms of etale cohomology ann inst fourier 55 7 2005 while at the same time somewhat simplifying the proofs through examples i further point out the bad behavior of these invariants under reduction mod p

associated primes of local cohomology of flat extensions with regular fibers and σ finite d modules abstract in this manuscript we study the following question raised by mel hochster let r m k be a local ring and s be a flat extension with regular closed fiber is v m s ass s h i i s finite for every ideal i s and i n we prove that the answer is positive when s is either a polynomial or a power series ring over r and dim r i r 1 in addition we analyze when this question can be reduced to the case where s is a power series ring over r an important tool for our proof is the use of finite d modules which are not necessarily finitely generated as d modules but whose associated primes are finite we give examples of this class of d modules and applications to local cohomology

uniform behaviour of the frobenius closures of ideals generated by regular sequences this paper is concerned with ideals in a commutative noetherian ring r of prime characteristic the main purpose is to show that the frobenius closures of certain ideals of r generated by regular sequences exhibit a desirable type of uniform behaviour the principal technical tool used is a result proved by r hartshorne and r speiser in the case where r is local and contains its residue field which is perfect and subsequently extended to all local rings of prime characteristic by g lyubeznik about a left module over the skew polynomial ring r x f associated to r and the frobenius homomorphism f in the indeterminate x that is both x torsion and artinian over r

some results on local cohomology of polynomial and formal power series rings the one dimensional case abstract in this paper we prove several results on the finiteness of local cohomology of polynomial and formal power series rings in particular we give a partial affirmative answer for a question of l nunez betancourt 2014 14

lyubeznik numbers of monomial ideals let r k x1 xn be the polynomial ring in n independent variables where k is a field in this work we will study bass numbers of local cohomology modules h r i r supported on a squarefree monomial ideal i r among them we are mainly interested in lyubeznik numbers we build a dictionary between the modules h r i r and the minimal free resolution of the alexander dual ideal i that allow us to interpret lyubeznik numbers as the obstruction to the acyclicity of the linear strands of i the methods we develop also help us to give a bound for the injective dimension of the local cohomology modules in terms of the dimension of the small support

computationally efficient angle estimation for signals with known waveforms this paper presents a large sample decoupled maximum likelihood deml angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise the deml estimator decouples the multidimensional problem of the exact ml estimator to a set of 1 d problems and hence is computationally efficient we shall derive the asymptotic statistical performance of the deml estimator and compare the performance with its cramer rao bound crb i e the best possible performance for the class of asymptotically unbiased estimators we will show that the deml estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms we will also show that for moderately correlated signals with known waveforms the deml estimator is no longer a large sample maximum likelihood ml estimator but the deml estimator may still be used for angle estimation and the performance degradation relative to the crb is small we shall show that the deml estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix finally several numerical examples showing the performance of the deml estimator are presented in this paper

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

on the support of local cohomology we examine the question of whether the support of an arbitrary local coho mology module of a finitely generated module over a noetherian ring with support in a given ideal must be closed in the zariski topology several results giving an armative answer to this question are given in particular we show that the support is closed when the given ideal has cohomological dimension at most two or the ambient ring is local of dimension at most four

graded annihilators of modules over the frobenius skew polynomial ring and tight closure this paper is concerned with the tight closure of an ideal a in a commutative noetherian local ring r of prime characteristic p several authors including r fedder k i watanabe k e smith n hara and f enescu have used the natural frobenius action on the top local cohomology module of such an r to good effect in the study of tight closure and this paper uses that device the main part of the paper develops a theory of what are here called special annihilator submodules of a left module over the frobenius skew polynomial ring associated to r this theory is then applied in the later sections of the paper to the top local cohomology module of r and used to show that if r is cohen macaulay then it must have a weak parameter test element even if it is not excellent

bass numbers of local cohomology modules let a be a regular local ring of positive characteristic this paper is concerned with the local cohomology modules of a itself but with respect to an arbitrary ideal of a the results include that all the bass numbers of all such local cohomology modules are finite that each such local cohomology module has finite set of associated prime ideals and that whenever such a local cohomology module is artinian then it must be injective this last result had been proved earlier by hartshorne and speiser under the additional assumptions that a is complete and contains its residue field which is perfect the paper ends with some low dimensional evidence related to questions about whether the analogous statements for regular local rings of characteristic 0 are true

cohomological dimension lyubeznik numbers and connectedness in mixed characteristic abstract we establish a second vanishing theorem for local cohomology modules over regular rings of unramified mixed characteristic which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology applying this and new results on the mixed characteristic lyubeznik numbers we further study connectedness properties of the spectra of a certain class of rings

d module structure of local cohomology modules of toric algebras let s be a toric algebra over a field k of characteristic 0 and let i be a monomial ideal of s we show that the local cohomology modules h i i s are of finite length over the ring of differential operators d s k generalizing the classical case of a polynomial algebra s as an application we compute the characteristic cycles of some local cohomology modules

a splitting theorem for local cohomology and its applications abstract let r be a commutative noetherian ring and m a finitely generated r module we show in this paper that for an integer t if the local cohomology module h a i m with respect to an ideal a is finitely generated for all i t then h a i m x m h a i m h a i 1 m for all a filter regular elements x contained in a enough large power of a and all i t 1 as consequences we obtain generalizations by very short proofs of the main results of m brodmann and a l faghani m brodmann a l faghani a finiteness result for associated primes of local cohomology modules proc amer math soc 128 2000 2851 2853 and of h l truong and the first author n t cuong h l truong asymptotic behavior of parameter ideals in generalized cohen macaulay module j algebra 320 2008 158 168

passive source localization using time differences of arrival and gain ratios of arrival a source signal will be subject to different amounts of time delay as well as attenuation when it reaches a number of spatially separated sensors both time delay and attenuation are dependent on the distance between the source and the receivers this paper performs a fundamental investigation of whether the gain ratios of arrival groas defined here as the ratio of the received signal amplitudes at the referenced sensor to the other sensors can be utilized in conjunction with the time differences of arrival tdoas to improve the source localization accuracy we begin with a gaussian random signal model and derive the cramer rao lower bound crlb of a source location estimate based on both groas and tdoas our conclusion is that the improvement from groas increases when the factor c omegao increases where c is the signal propagation speed and omegao is the signal bandwidth the paper proceeds to develop an algebraic closed form solution for the source location using groas and tdoas the algebraic solution is proved theoretically to reach the crlb accuracy under the gaussian data model numerical simulations are included to support and corroborate the theoretical developments

global parameter test ideals abstract this paper shows the existence of ideals whose localizations and completions at prime ideals are parameter test ideals of the localized and completed rings we do this for cohen macaulay localizations resp completions of non local rings for generalized cohen macaulay rings and for non local rings with isolated non cohen macaulay points each being an isolated non f rational point the tools used to prove these results are constructive in nature and as a consequence our results yield algorithms for the computation of these global parameter test ideals finally we illustrate the power of our methods by analyzing the hsl numbers of local cohomology modules with support at any prime ideal

mixture of subspaces image representation and compact coding for large scale image retrieval there are two major approaches to content based image retrieval using local image descriptors one is descriptor by descriptor matching and the other is based on comparison of global image representation that describes the set of local descriptors of each image in large scale problems the latter is preferred due to its smaller memory requirements however it tends to be inferior to the former in terms of retrieval accuracy to achieve both low memory cost and high accuracy we investigate an asymmetric approach in which the probability distribution of local descriptors is modeled for each individual database image while the local descriptors of a query are used as is we adopt a mixture model of probabilistic principal component analysis the model parameters constitute a global image representation to be stored in database then the likelihood function is employed to compute a matching score between each database image and a query we also propose an algorithm to encode our image representation into more compact codes experimental results demonstrate that our method can represent each database image in less than several hundred bytes achieving higher retrieval accuracy than the state of the art method using fisher vectors

on the discreteness and rationality of f jumping coefficients abstract we prove that the f jumping coefficients of a principal ideal of an excellent regular local ring of characteristic p 0 are all rational and form a discrete subset of r

associated primes of local cohomology modules and matlis duality abstract let r m be a commutative noetherian local ring of dimension d and i an ideal of r we show that the set of associated primes of the local cohomology module h i 2 r is finite whenever r is regular also it is shown that if x 1 x d is a system of parameters for r then d h x 1 x i i r has infinitely many associated prime ideals for all i d 1 where d hom r e denotes the matlis dual functor and e e r r m is the injective hull of the residue field r m finally we explore a counterexample of grothendieck s conjecture by showing that if d 3 then the r module hom r r i h i d 1 r is not finitely generated where i x 1 x 2 x d

discreteness and rationality of f jumping numbers on singular varieties we prove that the f jumping numbers of the test ideal tau x delta mathfrak a t are discrete and rational under the assumptions that x is a normal and f finite scheme over a field of positive characteristic p kx is mathbb q cartier of index not divisible p and either x is essentially of finite type over a field or the sheaf of ideals mathfrak a is locally principal this is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero

optimal source localization and tracking from passive array measurements if the signal of a moving source is observed at several spatially separated locations during a common time interval the received signals exhibit differential delays and doppler shifts which provide information about source location and velocity this paper deals with the optimal in the minimum mean square error sense source localization and tracking by utilizing differential delay and doppler observations at a linear array of receivers we shall be concerned with source ranges large compared with array baseline and with the distance traversed by the source during the observation interval it is shown that the optimal estimation procedure can be carried out in two sequential steps without any loss in performance in the first step source location is estimated from the differential delay group of measurements in the second step source velocity is estimated from the differential doppler group of measurements and the outcome of the first step furthermore by employing an intermediate track dependent parameter set the two step algorithm yields a closed form solution of the estimation problem

optimum discrete wavelet scaling and its application to delay and doppler estimation this paper studies the scaling of an arbitrary waveform from its samples the scaling problem is formulated as a mean square minimization and the resulting estimator consists of two parts noise filtering and sinc function scaling sinc function scaling is a time dependent process and requires o n sup 2 operations where n is the data length a fast algorithm based on the fft is proposed to reduce the complexity to o nlog sub 2 n this new algorithm is applied to wideband time delay and doppler estimation where the optimum wavelet is one of the received signal samples that has no analytic form the scaling method is found to be very effective in that the estimation accuracy achieves the cramer rao lower bound crlb

strong f regularity and generating morphisms of local cohomology modules abstract we establish a criterion for the strong f regularity of a non gorenstein cohen macaulay reduced complete local ring of dimension at least 2 and prime characteristic p we also describe an explicit generating morphism in the sense of lyubeznik for the top local cohomology module with support in certain ideals arising from an n n 1 matrix x of indeterminates for a perfect field k of characteristic p 5 these results led us to derive a simple new proof of the well known fact that the generic determinantal ring over k given by the maximal minors of x is strongly f regular

improved pseudolinear kalman filter algorithms for bearings only target tracking despite its stability and computational complexity advantages the pseudolinear kalman filter plkf suffers from severe bias problems in bearings only target tracking applications this paper develops new variants of the plkf with significant performance improvement first a detailed analysis of the plkf bias is provided for nearly constant velocity target dynamics this analysis uncovers the specific reasons of bias in state estimation and leads to a new bias compensated plkf bc plkf algorithm with the improved bias performance the bias arising from the correlation between the measurement vector and pseudolinear noise is tackled by a novel instrumental variable kalman filter ivkf while the method of instrumental variables has been successfully applied to batch pseudolinear estimation algorithms its extension to the plkf is new the ivkf embeds the method of recursive iv estimation into the bc plkf and employs the bc plkf to construct instrumental variable vectors with desired properties the ivkf is further improved by adopting the method of selective angle measurements sam which ensures that the performance of the ivkf is not degraded by a weak correlation between the instrumental variable vector and measurement vector in low signal to noise ratio snr situations comparative simulation examples are presented to demonstrate the performance improvement of the proposed recursive estimators the bc plkf ivkf and sam ivkf over the conventional plkf and the extended kalman filter the sam ivkf is observed to provide the best estimation performance among the proposed estimators by producing a negligible estimation bias and mean squared error close to the posterior cramer rao lower bound at moderate noise levels

galois extensions plus closure and maps on local cohomology abstract given a local domain r m of prime characteristic that is a homomorphic image of a gorenstein ring huneke and lyubeznik proved that there exists a module finite extension domain s such that the induced map on local cohomology modules h m i r h m i s is zero for each i dim r we prove that the extension s may be chosen to be generically galois and analyze the galois groups that arise

dimension reduction by local principal component analysis reducing or eliminating statistical redundancy between the components of high dimensional vector data enables a lower dimensional representation without significant loss of information recognizing the limitations of principal component analysis pca researchers in the statistics and neural network communities have developed nonlinear extensions of pca this article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute we exercise the algorithms on speech and image data and compare performance with pca and with neural network implementations of nonlinear pca we find that both nonlinear techniques can provide more accurate representations than pca and show that the local linear techniques outperform neural network implementations

on the uniform bound of frobenius test exponents abstract in this paper we prove the existence of a uniform bound for frobenius test exponents for parameter ideals of a local ring r m of prime characteristic in the following cases 1 r is generalized cohen macaulay our proof is much simpler than the original proof of huneke katzman sharp and yao 2 the frobenius actions on all lower local cohomologies h m i r i dim r are nilpotent

toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic let r k x 1 dots x n be a ring of polynomials over a field k of characteristic p 0 there is an algorithm due to lyubeznik for deciding the vanishing of local cohomology modules h i i r where i subset r is an ideal this algorithm has not been implemented because its complexity grows very rapidly with the growth of p which makes it impractical in this paper we produce a modification of this algorithm that consumes a modest amount of memory

on the structure of the endomorphism ring of a certain local cohomology module let r m denote an n dimensional gorenstein ring for an ideal i r of height c we are interested in the endomorphism ring b homr hic r hic r it turns out that b is a commutative ring in the case of r m a regular local ring containing a field b is a cohen macaulay ring its properties are related to the highest lyubeznik number l dimkextrd k hic r d dimr i in particular r b if and only if l 1 moreover we show that the natural homomorphism extrd k hic r k is non zero

product quantization for nearest neighbor search this paper introduces a product quantization based approach for approximate nearest neighbor search the idea is to decompose the space into a cartesian product of low dimensional subspaces and to quantize each subspace separately a vector is represented by a short code composed of its subspace quantization indices the euclidean distance between two vectors can be efficiently estimated from their codes an asymmetric version increases precision as it computes the approximate distance between a vector and a code experimental results show that our approach searches for nearest neighbors efficiently in particular in combination with an inverted file system results for sift and gist image descriptors show excellent search accuracy outperforming three state of the art approaches the scalability of our approach is validated on a data set of two billion vectors

cofiniteness and associated primes of local cohomology modules abstract let r be a d dimensional regular local ring i an ideal of r and m a finitely generated r module of dimension n we prove that the set of associated primes of ext r i r i h i j m is finite for all i and j in the following cases a dim m 3 b dim r 4 c dim m im 2 and m satisfies serre s condition s n 3 d dim m im 3 ann r m 0 r is unramified and m satisfies s n 3 in these cases we also prove that h i i m p is i p cofinite for all but finitely many primes p of r additionally we show that if dim r i 2 and spec r i m i is disconnected then h i d 1 r is not i cofinite generalizing a result due to huneke and koh

constructing arbitrary torsion elements for a local cohomology module local cohomology modules are in general not finitely generated over the ambient ring towards a better understanding of the structure of these modules huneke 1992 hu asked if they have finitely many associated prime ideals the answer is negative several authors have constructed a ring whose local cohomology module has infinitely many associated primes in certain situations one can prove that a local cohomology module has infinitely many associated primes by showing that z pz embeds into the local cohomology module for each prime integer p we show that in fact each finitely generated abelian group embeds into a local cohomology module

the d module structure of r f modules let r be a regular ring essentially of finite type over a perfect field k an r module m is called a unit r f module if it comes equipped with an isomorphism f e m m where f denotes the frobenius map on spec r and f e is the associated pullback functor it is well known that m then carries a natural d r module structure in this paper we investigate the relation between the unit r f structure and the induced d r structure on m in particular it is shown that if k is algebraically closed and m is a simple finitely generated unit r f module then it is also simple as a d r module an example showing the necessity of k being algebraically closed is also given

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

ideals in a perfect closure linear growth of primary decompositions and tight closure this paper is concerned with tight closure in a commutative noetherian ring r of prime characteristic p and is motivated by an argument of k e smith and i swanson that shows that if the sequence of frobenius powers of a proper ideal a of r has linear growth of primary decompositions then tight closure of a commutes with localization at the powers of a single element it is shown in this paper that provided r has a weak test element linear growth of primary decompositions for other sequences of ideals of r that approximate in a certain sense the sequence of frobenius powers of a would not only be just as good in this context but in the presence of a certain additional finiteness property would actually imply that tight closure of a commutes with localization at an arbitrary multiplicatively closed subset of r work of m katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the frobenius powers of a has only finitely many maximal members this paper develops through a careful analysis of the ideal theory of the perfect closure of r strategies for showing that tight closure of a specified ideal a of r commutes with localization at an arbitrary multiplicatively closed subset of r and for showing that the union of the associated primes of the tight closures of the frobenius powers of a is actually a finite set several applications of the strategies are presented in most of them it was already known that tight closure commutes with localization but the resulting affirmative answers to katzman s question in the various situations considered are believed to be new

cartier modules finiteness results on a locally noetherian scheme x over a field of positive characteristic p we study the category of coherent ox modules m equipped with a pe linear map i e an additive map c ox ox satisfying rc m c r p e m for all m a m r a ox the notion of nilpotence meaning that some power of the map c is zero is used to rigidify this cate gory the resulting quotient category called cartier crystals satisfies some strong finiteness conditions the main result in this paper states that if the frobenius morphism on x is a finite map i e if x is f finite then all cartier crystals have finite length we further show how this and related results can be used to recover and generalize other finiteness results of hartshorne speiser 19 lyubeznik 27 sharp 30 enescu hochster 14 and hochster 20 about the structure of modules with a left action of the frobenius for example we show that over any regular f finite scheme x lyubeznik s f finite modules 27 have finite length

iterative constrained weighted least squares source localization using tdoa and fdoa measurements this paper investigates the constrained weighted least squares cwls source localization problem by using time difference of arrival and frequency difference of arrival measurements the problem can be formulated as a quadratic programming with two indefinite quadratic equality constraints which is nonconvex and np hard moreover the weighting matrix is coupled with the unknown source position and velocity we propose an iterative cwls method that can efficiently solve this problem it iteratively performs a linearization procedure on the quadratic equality constraints to obtain an approximate programming with linear constraints which can be analytically solved and the weighting matrix is updated in each iteration theoretical analysis reveals that the proposed method if converges can lead to the global optimal solution of the formulated problem that reaches the crlb accuracy under mild assumptions on the measurement noises the monte carlo simulation results indicate that the percentage of convergence within mathbf 20 iterations is more than mathbf 96 and the localization accuracy is significantly improved over the previous methods with less computation time requirement moreover it is found from simulations that the iterative cwls method retains acceptable performance even under the ill conditioned situation when the sensor geometry is not desirable

improving bag of features for large scale image search this article improves recent methods for large scale image search we first analyze the bag of features approach in the framework of approximate nearest neighbor search this leads us to derive a more precise representation based on hamming embedding he and weak geometric consistency constraints wgc he provides binary signatures that refine the matching based on visual words wgc filters matching descriptors that are not consistent in terms of angle and scale he and wgc are integrated within an inverted file and are efficiently exploited for all images in the dataset we then introduce a graph structured quantizer which significantly speeds up the assignment of the descriptors to visual words a comparison with the state of the art shows the interest of our approach when high accuracy is needed experiments performed on three reference datasets and a dataset of one million of images show a significant improvement due to the binary signature and the weak geometric consistency constraints as well as their efficiency estimation of the full geometric transformation i e a re ranking step on a short list of images is shown to be complementary to our weak geometric consistency constraints our approach is shown to outperform the state of the art on the three datasets

a cohomological stability result for projective schemes over surfaces let x x0 be a projective morphism of schemes such that x0 is noetherian and essentially of finite type over a field k let i n0 let f be a coherent sheaf of modules and let l be an ample invertible sheaf over x we show that the set of associated points of the higher direct image sheaf ultimately becomes constant if n tends to provided x0 has dimensione 2 if this stability result need not hold any more to prove this we show that the set of associated primes of the n th graded component of the i th local cohomology module of a finitely generated graded module m over a homogeneous noetherian ring which is essentially of finite type over a field becomes ultimately constant in codimension 2 if n tends to

efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals we consider the problem of target localization by a network of passive sensors when an unknown target emits an acoustic or a radio signal its position can be localized with multiple sensors using the time difference of arrival tdoa information in this paper we consider the maximum likelihood formulation of this target localization problem and provide efficient convex relaxations for this nonconvex optimization problem we also propose a formulation for robust target localization in the presence of sensor location errors two cramer rao bounds are derived corresponding to situations with and without sensor node location errors simulation results confirm the efficiency and superior performance of the convex relaxation approach as compared to the existing least squares based approach when large sensor node location errors are present

bockstein homomorphisms in local cohomology let r be a polynomial ring in finitely many variables over the integers fix an ideal a of r we prove that for all but finitely prime integers p the bockstein homomorphisms on local cohomology h a r pr h k 1 a r pr are zero this vanishing of bockstein homomorphisms is predicted by lyubeznik s conjecture which states that when r is a regular ring the modules h a r have finitely many associated prime ideals we further show that when r is replaced by a hypersurface ring the vanishing of bockstein homomorphisms as well as the analogue of lyubeznik s conjecture need not hold bockstein homomorphisms have their origins in algebraic topology we establish a connection between algebraic and topological bockstein homomorphisms through stanley reisner theory

an excellent f pure ring of prime characteristic has a big tight closure test element in two recent papers the author has developed a theory of graded annihilators of left modules over the frobenius skew polynomial ring over a commutative noetherian ring r of prime characteristic p and has shown that this theory is relevant to the theory of test elements in tight closure theory one result of that work was that if r is local and the r module structure on the injective envelope e of the simple r module can be extended to a structure as a torsion free left module over the frobenius skew polynomial ring then r is f pure and has a tight closure test element one of the central results of this paper is the converse namely that if r is f pure then e has a structure as a torsion free left module over the frobenius skew polynomial ring a corollary is that every f pure local ring of prime characteristic even if it is not excellent has a tight closure test element these results are then used along with embedding theorems for modules over the frobenius skew polynomial ring to show that every excellent not necessarily local f pure ring of characteristic p must have a so called big test element

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

d module and f module length of local cohomology modules let r be a polynomial or power series ring over a field k we study the length of local cohomology modules hji r in the category of d modules and fmodules we show that the d module length of hji r is bounded by a polynomial in the degree of the generators of i in characteristic p 0 we obtain upper and lower bounds on the f module length in terms of the dimensions of frobenius stable parts and the number of special primes of local cohomology modules of r i the obtained upper bound is sharp if r i is an isolated singularity and the lower bound is sharp when r i is gorenstein and f pure we also give an example of a local cohomology module that has different d module and f module lengths

generic vanishing in characteristic p 0 and the characterization of ordinary abelian varieties we prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of kawamata s theorems a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the albanese map when the frobenius stable kodaira dimension is zero

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

localization of narrowband radio emitters based on doppler frequency shifts several techniques for emitter localization based on the doppler effect have been described in the literature one example is the differential doppler dd method in which the signal of a stationary emitter is intercepted by at least two moving receivers the frequency difference between the receivers is measured at several locations along their trajectories and the emitter s position is then estimated based on these measurements this two step approach is suboptimal since each frequency difference measurement is performed independently although all measurements correspond to a common emitter position instead a single step approach based on the maximum likelihood criterion is proposed here for both known and unknown waveforms the position is determined directly from all the observations by a search in the position space the method can only be used for narrowband signals that is under the assumption that the signal bandwidth must be small compared to the inverse of the propagation time between the receivers simulations show that the proposed method outperforms the dd method for weak signals while both methods converge to the cramer rao bound for strong known signals finally it is shown that in some cases of interest the proposed method inherently selects reliable observations while ignoring unreliable data

automatic estimation of multiple target positions and velocities using passive tdoa measurements of transients this paper considers the problem of the estimation of the motion parameters of multiple targets moving linearly in a three dimensional 3 d observation area contaminated by clutter the measurements are limited to time differences of arrival tdoas of short duration acoustic emissions or transients generated by the targets this problem can arise in situations where the level of continuous broadband target related noise is very low owing to the fact that transient emissions are nonstationary and can have low signal to noise ratio snr the corresponding tdoa measurement errors are usually non gaussian therefore gaussian mixture distributions are used to appropriately model these errors an iterative maximum likelihood optimization technique based on a modified deterministic annealing expectation maximization mdaem algorithm is applied to this problem in each iteration the algorithm uses a nonlinear least squares ls technique in computing the motion parameters for each target it generalizes the variance deflation method previously used for the initialization of target tracking algorithms and increases the possibility of attaining a globally optimal solution for random initial conditions simulation results are presented for several different numbers of targets clutter densities and probabilities of gross error of the target related measurements and are found to be comparable to the estimates obtained when the measurement to target assignments are exactly known

an asymptotically efficient estimator for tdoa and fdoa positioning of multiple disjoint sources in the presence of sensor location uncertainties this correspondence considers the problem of locating multiple disjoint sources using time differences of arrival tdoas and frequency differences of arrival fdoas in the presence of sensor position and velocity errors previous work applies to one source only with suboptimum performance for near source or requires joint estimation of the source and sensor locations that could be computation demanding through nonlinearly transforming the measurements and converting them with respect to the inaccurate sensor locations we have developed an algebraic solution to this problem the solution is shown analytically to achieve the cramer rao lower bound crlb performance over small noise region and does not require joint estimation with sensor locations

on the set of associated primes of a local cohomology module abstract assume r is a local cohen macaulay ring it is shown that ass r h l i r is finite for any ideal i and any integer l provided ass r h 2 x y r is finite for any x y r and ass r h 3 x 1 x 2 y r is finite for any y r and any regular sequence x 1 x 2 r furthermore it is shown that ass r h l i r is always finite if dim r 3 the same statement is even true for dim r 4 if r is almost factorial

multidimensional scaling analysis for passive moving target localization with tdoa and fdoa measurements a new framework for positioning a moving target is introduced by utilizing time differences of arrival tdoa and frequency differences of arrival fdoa measurements collected using an array of passive sensors it exploits the multidimensional scaling mds analysis which has been developed for data analysis in the field such as physics geography and biology particularly we present an accurate and closed form solution for the position and velocity of a moving target unlike most passive target localization methods focusing on minimizing a loss function with respect to the measurement vector the proposed method is based on the optimization of a cost function related to the scalar product matrix in the classical mds framework it is robust to the large measurement noise the bias and variance of the proposed estimator is also derived simulation results show that the proposed estimator achieves better performance than the spherical interpolation si method and the two step weighted least squares wls approach and it attains the cramer rao lower bound at a sufficiently high noise level before the threshold effect occurs moreover for the proposed estimator the threshold effect which is a result of the nonlinear nature of the localization problem occurs apparently later as the measurement noise increases for a near field target

big tight closure test elements for some non reduced excellent rings abstract this paper is concerned with existence of big tight closure test elements for a commutative noetherian ring r of prime characteristic p let r denote the complement in r of the union of the minimal prime ideals of r a big test element for r is an element of r which can be used in every tight closure membership test for every r module and not just the finitely generated ones the main results of the paper are that if r is excellent and satisfies condition r 0 and c r is such that r c is gorenstein and weakly f regular then some power of c is a big test element for r if i r is a homomorphic image of an excellent regular ring of characteristic p for which the frobenius homomorphism is intersection flat or ii r is f pure or iii r is local the gamma construction is not used

a simple and efficient estimator for hyperbolic location an effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed the approach is noniterative and gives an explicit solution it is an approximate realization of the maximum likelihood estimator and is shown to attain the cramer rao lower bound near the small error region comparisons of performance with existing techniques of beamformer spherical interpolation divide and conquer and iterative taylor series methods are made the proposed technique performs significantly better than spherical interpolation and has a higher noise threshold than divide and conquer before performance breaks away from the cramer rao lower bound it provides an explicit solution form that is not available in the beamforming and taylor series methods computational complexity is comparable to spherical interpolation but substantially less than the taylor series method

a motivic conjecture of milne let k be an algebraically closed field of characteristic p 0 let w k be the ring of witt vectors with coefficients ink we prove a motivic conjecture of milne that relates thecohomology with zp coefficients to the crystalline cohomology with integral coefficients in the wider context ofp divisible groups endowed with families of crystalline tensors over a finite discrete valuation ring extension of w k the result extends work of faltings as a main new tool we construct global deformations of p divisible groups endowed with crystalline tensors over certain regular formally smooth schemes over w k

f thresholds of hypersurfaces for every 0 that is f finite i e such that the frobenius morphism f r r is finite if a is an ideal in r and if is a nonnegative real number then the corresponding test ideal is denoted by a in this context we say that is an f jumping exponent or an f threshold if a 6 a for every the following is our main result about f jumping exponents in positive characteristic theorem 1 1 if r is an f finite regular ring and if a f is a principal ideal then the f jumping exponents of a are rational and they form a discrete set the discreteness and the rationality of f jumping numbers has been proved in bms for every ideal when the ring r is essentially of finite type over an f finite field we mention also that for r k x y with k a finite field the above result has been proved in ha using a completely different approach we stress that the difficulty in attacking this result does notcome from the fact that there is no available resolution of singularities in positive characteristic even

bernstein sato polynomials in positive characteristic abstract in characteristic zero the bernstein sato polynomial of a hypersurface can be described as the minimal polynomial of the action of an euler operator on a suitable d module we consider analogous d modules in positive characteristic and use them to define a sequence of bernstein sato polynomials corresponding to the fact that we need to consider also divided powers euler operators we show that the information contained in these polynomials is equivalent to that given by the f jumping exponents of the hypersurface in the sense of hara and yoshida n hara k i yoshida a generalization of tight closure and multiplier ideals trans amer math soc 355 2003 3143 3174