decidable sentences of church rosser congruences abstract a decision procedure for a class of true sentences of congruences generated by finite monadic church rosser systems is developed using this decision procedure it is shown that if m t is the monoid presented by such a system t then i it is decidable given t whether m t is a group ii it is decidable given t and a finite set a whether the submonoid generated by a is a group or a left right two sided ideal and iii green s relations for m t are decidable

eeg extended source localization tensor based vs conventional methods the localization of brain sources based on eeg measurements is a topic that has attracted a lot of attention in the last decades and many different source localization algorithms have been proposed however their performance is limited in the case of several simultaneously active brain regions and low signal to noise ratios to overcome these problems tensor based preprocessing can be applied which consists in constructing a space time frequency stf or space time wave vector stwv tensor and decomposing it using the canonical polyadic cp decomposition in this paper we present a new algorithm for the accurate localization of extended sources based on the results of the tensor decomposition furthermore we conduct a detailed study of the tensor based preprocessing methods including an analysis of their theoretical foundation their computational complexity and their performance for realistic simulated data in comparison to conventional source localization algorithms such as sloreta cortical loreta cloreta and 4 exso music our objective consists on the one hand in demonstrating the gain in performance that can be achieved by tensor based preprocessing and on the other hand in pointing out the limits and drawbacks of this method finally we validate the stf and stwv techniques on real measurements to demonstrate their usefulness for practical applications

on language equations with invertible operations the paper studies language equations of the type x l r and l y r where l and r are given languages and is an invertible binary word language operation for most of the considered insertion and deletion operations the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular l and r in case l is a context free language and r is a regular one the existence of a solution is generally undecidable the results can be extended to more complex linear equations systems of linear equations as well as for equations of higher degree

church rosser controlled rewriting systems and equivalence problems for deterministic context free languages we use a description of deterministic context free languages dcfl by a special type of church rosser rewriting systems to extend several procedures testing the equality of two languages in a subfamilyfof dcfl to procedures testing the equality of two languages one of which is inf the other beeing a general dcfl

an efficient algorithm to decide whether a monoid presented by a regular church rosser thue system is a group abstract we give an o a 2 t algorithm that on the input of a regular church rosser thue system t on alphabet a decides whether or not the monoid m t presented by t is a group where a is the cardinality of a and t is the size of the thue system t in addition a problem is presented that is decidable for regular monadic church rosser thue systems but that is undecidable for finite non monadic church rosser thue systems

effective connectivity of fmri data using ancestral graph theory dealing with missing regions most of the current methods to assess effective connectivity from functional magnetic resonance imaging fmri rely on the assumption that all relevant brain regions are entered into the analysis if this assumption is untenable which we believe is most often the case then spurious connections between brain regions can appear in this paper we propose to use an ancestral graph to model connectivity which provides a way to avoid spurious connections the ancestral graph is determined from trial by trial variation and not from the time series a random effects model is defined for ancestral graphs which allows for individual differences in terms of graph parameters e g connection strength procedures for model selection model fit and hypothesis testing of ancestral graphs are proposed the hypothesis test can be used to find differences in connection strength between for example conditions monte carlo simulations show that the ancestral graph is appropriate to model connectivity from fmri condition specific trial data to assess the accuracy further the proposed method is applied to real fmri data to determine how brain regions interact during speech monitoring

cancellation in context free languages enrichment by reduction the following problem is shown to be decidable given a context free grammar g and a string w x does there exist a string u l g such that w is obtained from u by deleting all substrings ui that are elements of the symmetric dyck set d 1 the intersection of any two context free languages can be obtained from only one context free language by cancellation either with the smaller semi dyck set d 1 d 1 or with d 1 itself also the following is shown here for the first time if the set eq xnx n n n d 1 is used for this cancellation then each recursively enumerable set can be obtained from linear context free languages previous work has shown that cancellation of substrings from the semi dyck language d 1 or from any of the former languages d 1 or eq allows one to obtain the following from the context free languages any terminal petri net language 14 16 the intersections of any context free with a terminal petri net language and the nested iterated substitution thereof 15 we generalize this characterization by showing that linear context free languages suffice for generating terminal petri net languages in proving this we obtain a new closure property of the family of petri net languages which is not shared by the context free sets

when is a monoid a group the church rosser case is tractable abstract the following question is shown to be tractable given a finite monadic church rosser thue system t and a finite set a is the submonoid generated by a of the monoid presented by t a group

getting it right joint distribution tests of posterior simulators analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments this article develops simple tests of posterior simulators that detect both kinds of errors and uses them to detect and correct errors in two previously published articles the tests exploit the fact that a bayesian model specifies the joint distribution of observables data and unobservables parameters there are two joint distribution simulators the marginal conditional simulator draws unobservables from the prior and then observables conditional on unobservables the successive conditional simulator alternates between the posterior simulator and an observables simulator formal comparison of moment approximations of the two simulators reveals existing analytical or coding errors in the posterior simulator

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

detection and localization of multiple sources in noise with unknown covariance the authors present a novel technique for the detection and localization of multiple sources in the presence of noise with unknown and arbitrary covariance the technique is applicable to coherent and noncoherent signals and to arbitrary array geometry and is based on rissanen s minimum description length mdl principle 1989 for model selection its computational load is comparable to that of analogous techniques for white noise simulation results demonstrating the performance of this technique are included

the wald test and crame spl acute r rao bound for misspecified models in electromagnetic source analysis by using signal processing techniques an estimate of activity in the brain from the electro or magneto encephalogram eeg or meg can be obtained for a proper analysis a test is required to indicate whether the model for brain activity fits a problem in using such tests is that often not all assumptions are satisfied like the assumption of the number of shells in an eeg in such a case a test on the number of sources model order might still be of interest a detailed analysis is presented of the wald test for these cases one of the advantages of the wald test is that it can be used when not all assumptions are satisfied two different previously suggested wald tests in electromagnetic source analysis emsa are examined a test on source amplitudes and a test on the closeness of source pairs the wald test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis local alternatives it is shown that the wald test is asymptotically unbiased that it has the correct level and power which makes it appropriate to use in emsa an accurate estimate of the crame spl acute r rao bound crb is required for the use of the wald test when not all assumptions are satisfied the sandwich crb is used for this purpose it is defined for nonseparable least squares with constraints required for the wald test on amplitudes simulations with eeg show that when the sensor positions are incorrect or the number of shells is incorrect or the conductivity parameter is incorrect then the crb and wald test are still good with a moderate number of trials additionally the crb and wald test appear robust against an incorrect assumption on the noise covariance a combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude

monadic thue systems abstract certain infinite thue systems over a finite alphabet are studied in particular systems s e such that for each a e the set u u a s is a context freelanguage the syntactic structure of sets of ancestors and sets of descendants is considered as well as that of unions of congruence classes taken over infinite context free languages or regular sets the common descendant problem is shown to be tractable while the common ancestor problem is shown to be undecidable even for finite systems the word problem for confluent systems of this type is shown to be tractable the question of whether an infinite system of this type is confluent is shown to be undecidable as is the question of whether the congruence generated by such a system has a confluent presentation

bayesian reduced rank regression in econometrics abstract the reduced rank regression model arises repeatedly in theoretical and applied econometrics to date the only general treatment of this model have been frequentist this paper develops general methods for bayesian inference with noninformative reference priors in this model based on a markov chain sampling algorithm and procedures for obtaining predictive odds ratios for regression models with different ranks these methods are used to obtain evidence on the number of factors in a capital asset pricing model

wald statistic for model order selection in superposition models a consistent model selection algorithm is presented for superimposed signal models the proposed method is motivated by the wald statistic and reduces the computational complexity of procedures based on the minimum description length mdl principle the procedure is suggested when a noncyclostationary signal model or short data length prevents use of covariance rank test for maximum model order k the procedure provides o k computational savings over an mdl test additionally a proof establishes the consistency of a least squares estimator using overparametrized models finite sample performance of the proposed model selection method is studied via monte carlo simulations for estimating the multipath delays and amplitudes of a chirp signal

some undecidability results concerning the property of preserving regularity a finite string rewriting system r preserves regularity if and only if it preserves regularity where is the alphabet containing exactly those letters that have occurrences in the rules of r this proves a conjecture of gyenizse and vagvolgyi 1997 in addition some undecidability results are presented that generalize results of gilleron and tison 1995 from term rewriting systems to string rewriting systems it follows that the property of being regularity preserving is undecidable for term rewriting systems thus answering another question of gyenizse and vagvolgyi 1997 finally it is shown that it is undecidable in general whether a finite lengthreducing and confluent string rewriting system yields a regular set of normal forms for each regular language

infinite regular thue systems abstract the following new results are obtained about infinite regular thue systems s 1 if s is church rosser the word problem is solvable in linear time 2 if s is monadic church rosser it defines a nontrivial boolean algebra of dcfls 3 if s is monadic church rosser and so is another system t equivalence of s and t is decidable 4 if s is monadic it is decidable if s is church rosser 5 if s is not monadic it is undecidable if s is church rosser

corrigendum to bayesian reduced rank regression in econometrics j econometrics 75 1996 121 146 corrigendum to bayesian reduced rank regression in econometrics j econometrics 75 1996 121 146

anatomically informed basis functions for eeg source localization combining functional and anatomical constraints distributed linear solutions have frequently been used to solve the source localization problem in eeg here we introduce an approach based on the weighted minimum norm wmn method that imposes constraints using anatomical and physiological information derived from other imaging modalities the anatomical constraints are used to reduce the solution space a priori by modeling the spatial source distribution with a set of basis functions these spatial basis functions are chosen in a principled way using information theory the reduced problem is then solved with a classical wmn method further functional constraints can be introduced in the weighting of the solution using fmri brain responses to augment spatial priors we used simulated data to explore the behavior of the approach over a range of the model s hyperparameters to assess the construct validity of our method we compared it with two established approaches to the source localization problem a simple weighted minimum norm and a maximum smoothness loreta like solution this involved simulations using single and multiple sources that were analyzed under different levels of confidence in the priors

instrumental variable approach to array processing in spatially correlated noise fields high performance signal parameter estimation from sensor array data is a problem which has received much attention a number of so called eigenvector ev techniques such as music esprit wsf and mode have been proposed in the literature the ev techniques for array processing require knowledge of the spatial noise correlation matrix that constitutes a significant drawback a novel instrumental variable iv approach to the sensor array problem is proposed the iv technique relies on the same basic geometric properties as the ev methods to obtain parameter estimates however by exploiting the temporal correlation of the source signals no knowledge of the spatial noise covariance is required the asymptotic properties of the iv estimator are examined and an optimal iv method is derived computer simulations are presented to study the properties of the iv estimators in samples of practical length the proposed algorithm is also shown to perform better than music on a full scale passive sonar experiment

on regularity of context free languages this paper considers conditions under which a context free language is regular and conditions which imposed on productions of a rewriting system generating a context free language will guarantee that the generated language is regular in particular 1 1 necessary and sufficient conditions on productions of a unitary grammar are given that guarantee the generated language to be regular a unitary grammar is a semi thue system in which the left hand of each production is the empty word and 2 2 it is proved that commutativity of a linear language implies its regularity to obtain the former result we give a generalization of the myhill nerode characterization of the regular languages in terms of well quasi orders along with a generalization of higman s well quasi order result concerning the subsequence embedding relation on in obtaining the latter results we introduce the class of periodic languages and demonstrate how they can be used to characterize the commutative regular languages here we also utilize the theory of well quasi orders

a closure property of regular languages note given a semigroup homomorphism x p y where p y is the powerset of y we show that the inverse image k 1 of a regular set k y is regular too this theorem has several consequences generalizing previously known results

non parametric identification of viscoelastic materials from wave propagation experiments we investigate how the frequency dependent wave propagation coefficient and complex modulus for a linearly viscoelastic material can be estimated from wave propagation experiments the strains at different sections of a bar specimen are measured as functions of time the time series are transformed into the frequency domain where a non parametric identification is made a thorough analysis of the quality of the non parametric estimate is made in which approximate expressions for the covariance matrices of the wave propagation coefficient and the complex modulus are derived the validity of these expressions are confirmed by numerical studies and real experiments

some decision problems about controlled rewriting systems abstract a description of deterministic context free languages by some kind of finitely generated right congruences the sets of relations generating such right congruences are called controlled rewriting systems or c systems has been given previously in the first part of this paper we study several decision problems on c systems namely the confluence problem the equivalence problem the refinement problem the class equivalence problem and the class inclusion problem in the second part of the paper we deduce from the main theorem given previously a characterisation of dcfls by means of finitely generated congruences the sets of relations generating such congruences are now ordinary finite semi thue systems we study three decision problems on finite semi thue systems namely the class equivalence problem the word problem for the syntactic congruence of one class and the partial confluence problem all the problems are investigated in several classes of c systems or semi thue systems for every class we give an answer which may be yes the problem is decidable no the problem is undecidable or eq which means that the problem is recursively equivalent to the equivalence problem for dpda

back projection cortical potential imaging theory and results electroencephalography eeg is the single brain monitoring technique that is non invasive portable passive exhibits high temporal resolution and gives a directmeasurement of the scalp electrical potential amajor disadvantage of the eeg is its low spatial resolution which is the result of the low conductive skull that smears the currents coming from within the brain recording brain activity with both high temporal and spatial resolution is crucial for the localization of confined brain activations and the study of brainmechanismfunctionality whichis then followed by diagnosis of brain related diseases in this paper a new cortical potential imaging cpi method is presented the new method gives an estimation of the electrical activity on the cortex surface and thus removes the smearing effect caused by the skull the scalp potentials are back projected cpi bp cpi onto the cortex surface by building a well posed problem to the laplace equation that is solved by means of the finite elements method on a realistic head model a unique solution to the cpi problem is obtained by introducing a cortical normal current estimation technique the technique is based on the same mechanism used in the well known surface laplacian calculation followed by a scalp cortex back projection routine the bp cpi passed four stages of validation including validation on spherical and realistic head models probabilistic analysis monte carlo simulation and noise sensitivity tests in addition the bp cpi was compared with the minimum norm estimate cpi approach and found superior for multi source cortical potential distributions with very good estimation results cc 0 97 on a realistic head model in the regions of interest for two representative cases the bp cpi can be easily incorporated in different monitoring tools and help researchers by maintaining an accurate estimation for the cortical potential of ongoing or event related potentials in order to have better neurological inferences from the eeg

performance analysis of esprit and tam in determining the direction of arrival of plane waves in noise the authors evaluate two subspace based methods esprit and the toplitz approximation method tam for estimating the direction of arrival doa of plane waves in white noise in the case of linear equispaced sensor array it is shown that the least squares versions of esprit and tam result in the same estimate and are statistically equivalent it is also shown that asymptotically the estimates obtained using least squares esprit and total least squares esprit have the same mean squared error expressions for the asymptotic mean squared error in the estimates of the doa are derived for both methods simple closed form expressions are derived for the one and two source cases to get further insight computer simulation results are provided to substantiate the analysis

on the equivalence problem for regular thue systems abstract a decision procedure is presented for the equivalence problem for regular almost confluent thue systems on the other hand the equivalence problem for regular preperfect systems is shown to be undecidable

extended accuracy analysis of a covariance matching approach for identifying errors in variables systems a system identification method for errors in variables problems based on covariance matching was recently proposed in the first step a small amount of covariances of noisy input output data are computed and then a parametric model is fitted to these covariances in this paper the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances as an important byproduct an efficient algorithm is presented for computing the covariance matrix of the computed input output covariances

complexity results on the conjugacy problem for monoids abstract the complexity of the conjugacy problem cp m for monoids given by presentations of the form t is investigated here t denotes a possibly infinite thue system over the alphabet the following results are obtained 1 1 if t is finite and church rosser then cp m is in n time n if in addition t is special then cp m is in p 2 2 if t is infinite and church rosser but of the form i i d i r 1 where i is finite and each d i is in np then cp m is in np however if i is infinite then cp m can be undecidable even if t is recursive 3 3 if t is finite and almost confluent then cp m can be decidable with any degree in the grzegorczyk hierarchy or it can be undecidable with any recursively enumerable degree of unsolvability

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

a transform based covariance differencing approach for some classes of parameter estimation problems a method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance the proposed algorithm does not require multiple estimates of the signal covariance matrix instead it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner the noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible this is illustrated by applying the algorithm to the problems of bearing estimation resolution of overlapping echos and transient response analysis simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods

on a special monoid with a single defining relation abstract we show that no finite union of congruence classes w w being an arbitrary element of the free monoid a b with unit 1 is a context free language if the congruence is defined by the single pair abbaab 1 this congruence is neither confluent nor even preperfect the monoid formed by its congruence classes is a group which has infinitely many isomorphic proper subgroups

a combined order selection and parameter estimation algorithm for undamped exponentials we propose an approximate maximum likelihood parameter estimation algorithm combined with a model order estimator for superimposed undamped exponentials in noise the algorithm combines the robustness of fourier based estimators and the high resolution capabilities of parametric methods we use a combination of a wald 1945 statistic and a map test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders experiments using simulated data and synthetic radar data demonstrate improved performance over mdl map and aic in places of practical interest

undecidable questions related to church rosser thue systems abstract the following four properties are shown undecidable for finite thue systems s is s equivalent to a finite church rosser respectively almost confluent preperfect system does s generate a church rosser congruence

cisoid parameter estimation in the colored noise case asymptotic cramer rao bound maximum likelihood and nonlinear least squares the problem of estimating the parameters of complex valued sinusoidal signals cisoids for short from data corrupted by colored noise occurs in many signal processing applications we present a simple formula for the asymptotic large sample cramer rao bound crb matrix associated with this problem the maximum likelihood method mlm which estimates both the signal and noise parameters attains the performance corresponding to the asymptotic crb as the sample length increases more interestingly we show that a computationally much simpler nonlinear least squares method nlsm which estimates the signal parameters only achieves the same performance in large samples

a note on the efficiency of sandwich covariance matrix estimation the sandwich estimator also known as robust covariance matrix estimator heteroscedasticity consistent covariance matrix estimate or empirical covariance matrix estimator has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified surprisingly though there has been little discussion of properties of the sandwich method other than consistency we investigate the sandwich estimator in quasi likelihood models asymptotically and in the linear case analytically we show that under certain circumstances when the quasi likelihood model is correct the sandwich estimate is often far more variable than the usual parametric variance estimate the increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the p

source localization using recursively applied and projected rap music a new method for source localization is described that is based on a modification of the well known music algorithm in classical music the array manifold vector is projected onto an estimate of the signal subspace errors in the estimate of the signal subspace can make localization of multiple sources difficult recursively applied and projected rap music uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement the music projection to find the next source is then performed in this reduced subspace special assumptions about the array manifold structure such as vandermonde or shift invariance are not required using the metric of principal angles we describe a general form of the rap music algorithm for the case of diversely polarized sources through a uniform linear array simulation with two highly correlated sources we demonstrate the improved monte carlo error performance of rap music relative to music and two other sequential subspace methods s and ies music we then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography meg source localization simulation

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

a characterisation of deterministic context free languages by means of right congruences we study here a kind of rewriting systems called controlled rewriting systems c systems for short which generalise the notion of regular semi thue systems we show that the deterministic context free languages are exactly the sets of the form r s where r is a rational set and s is the right congruence generated by a c system of s of a restricted type s is basic and confluent

array processing in correlated noise fields based on instrumental variables and subspace fitting accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade a number of parametric estimation techniques have been proposed in the literature in general these methods require knowledge of the sensor to sensor correlation of the noise which constitutes a significant drawback this difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise in some applications the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise an instrumental variable iv approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise a computationally simple iv approach has recently been proposed by the authors herein a refined technique that can give significantly better performance is derived a statistical analysis of the parameter estimates is performed enabling optimal selection of certain user specified quantities a lower bound on the attainable error variance is also presented the proposed optimal iv method is shown to attain the bound if the signals have a quasideterministic character

mcnaughton families of languages in 1988 the church rosser languages were introduced by mcnaughton et al as those languages that are recognized by finite length reducing and confluent string rewriting systems using extra non terminal symbols here we generalize this concept by considering classes of languages that are obtained by other types of string rewriting systems to honour robert mcnaughton s original contribution we call the resulting families of languages mcnaughton families here it is shown that the concept of mcnaughton families is as powerful as the notion of turing machine or the notion of phrase structure grammar we investigate the relationships between the various mcnaughton families obtaining an extensive hierarchy of classes that includes many well known language and complexity classes as well as some new classes further we consider some closure and non closure properties for those mcnaughton families that are contained in the class of context free languages and we address the complexity of the fixed and the general membership problems for these families

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

large sample properties of separable nonlinear least squares estimators in this paper the large sample properties of the separable nonlinear least squares algorithm are investigated unlike the previous results in the literature the data are assumed to be complex valued and the whiteness assumption on the measurement noise sequence has been relaxed convergence properties of the parameter estimates are established asymptotic accuracy analysis has been carried out in which the assumptions used are relatively weaker than the assumptions in the previous related works it is shown under quite general conditions that the parameter estimates are asymptotically circular conditions for asymptotic complex normality are also established next a bound on the deviation of the asymptotic covariance matrix from the crame spl acute r rao bound crb is derived finally a sufficient condition for the nonlinear least squares estimate to achieve the crame spl acute r rao lower bound is established the results presented in this paper are general and can be applied to any specific application where separable nonlinear least squares is employed

groups presented by finite two monadic church rosser thue systems it is shown that a group g can be defined by a monoid presentation of the form 2 7 where t is a finite two monadic church rosser thue system over 2 if and only if g is isomorphic to the free product of a finitely generated free group with a finite number of finite groups

some undecidability results for non monadic church rosser thue systems abstract in this paper the computational power of finite church rosser thue systems that are non monadic is explored in particular it is shown that there exists a finite non monadic church rosser thue system t such that the set of linear sentences that are true under the interpretation given by t is undecidable this contrasts with the situation for finite church rosser thue systems that are monadic in addition some problems are presented that are decidable for finite monadic church rosser thue systems but that are undecidable in general for finite non monadic church rosser thue systems finally it is shown how degrees of complexity can be encoded in finite non monadic church rosser thue systems

elements of finite order for finite monadic church rosser thue systems a thue system t over z is said to allow nontrivial elements of finite order if there exist a word u e 2 and integers n 0 and k 1 such that u 9 tx

reductions in tree replacement systems abstract certain kinds of church rosser tree replacement systems reduction systems are studied most results presented here generalize results proved for string rewriting systems by book 1982 the concept of a tree rewriting system with a norm is introduced and studied a new tree reducing machine which reduces every input tree to an irreducible tree is defined as a consequence when the norm under consideration is the size of the tree the number of nodes the word problem for finite church rosser reduction systems is decidable in linear time in the size of the input tree church rosser monadic reduction systems generalizing the monadic thue systems of book 1982 and book et al 1982 are also studied it is shown that every congruence class and every finite union of congruence classes defined by such a system is accepted by a deterministic bottom up tree pushdown automation this new form of a tree automation is briefly studied

a polynomial algorithm testing partial confluence of basic semi thue systems we give a polynomial algorithm solving the problem is s partially confluent on the rational set r for finite basic noetherian semi thue systems the algorithm is obtained by a polynomial reduction of this problem to the equivalence problem for deterministic 2 tape finite automata which has been shown to be polynomially decidable in fri gre82

on the rational subset problem for groups we use language theory to study the rational subset problem for groups and monoids we show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups in particular it passes through free products amalgamated over finite subgroups and hnn extensions with finite associated subgroups we provide a simple proof of a result of grunschlag showing that the decidability of this problem is a virtual property we prove further that the problem is decidable for a direct product of a group g with a monoid m if and only if membership is uniformly decidable for g automaton subsets of m it follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership

testing for the church rosser property abstract it is shown that there is a polynomial time algorithm to determine whether a finite thue system is church rosser

electrical neuroimaging based on biophysical constraints this paper proposes and implements biophysical constraints to select a unique solution to the bioelectromagnetic inverse problem it first shows that the brain s electric fields and potentials are predominantly due to ohmic currents this serves to reformulate the inverse problem in terms of a restricted source model permitting noninvasive estimations of local field potentials lfps in depth from scalp recorded data uniqueness in the solution is achieved by a physically derived regularization strategy that imposes a spatial structure on the solution based upon the physical laws that describe electromagnetic fields in biological media the regularization strategy and the source model emulate the properties of brain activity s actual generators this added information is independent of both the recorded data and head model and suffices for obtaining a unique solution compatible with and aimed at analyzing experimental data the inverse solution s features are evaluated with event related potentials erps from a healthy subject performing a visuo motor task two aspects are addressed the concordance between available neurophysiological evidence and inverse solution results and the functional localization provided by fmri data from the same subject under identical experimental conditions the localization results are spatially and temporally concordant with experimental evidence and the areas detected as functionally activated in both imaging modalities are similar providing indices of localization accuracy we conclude that biophysically driven inverse solutions offer a novel and reliable possibility for studying brain function with the temporal resolution required to advance our understanding of the brain s functional networks