parametric imaging with bayesian priors a validation study with 11c altropane pet abstract it has been suggested that bayesian estimation methods may be used to improve the signal to noise ratio of parametric images however there is little experience with the method and some of the underlying assumptions and performance properties of bayesian estimation remain to be investigated we used a sample population of 54 subjects studied previously with 11 c altropane to empirically evaluate the assumptions performance and some practical issues in forming parametric images by using normality tests we showed that the underpinning normality assumptions of data and parametric distribution apply to more than 80 of voxels the standard deviation of the binding potential can be reduced 30 50 using bayesian estimation without introducing substantial bias the sample size required to form the a priori information was found to be modest as little as ten subjects may be sufficient and the choice of specific subjects has little effect on bayesian estimation a realistic simulation study showed that detection of localized differences in parametric images e g by statistical parametric mapping spm could be made more reliable and or conducted with smaller sample size using bayesian estimation in conclusion bayesian estimation can improve the snr of parametric images and better detect localized changes in cohorts of subjects

poisson homology in degree 0 for some rings of symplectic invariants abstract let g be a finite dimensional semi simple lie algebra h a cartan subalgebra of g and w its weyl group the group w acts diagonally on v h h as well as on c v the purpose of this article is to study the poisson homology of the algebra of invariants c v w endowed with the standard symplectic bracket to begin with we give general results about the poisson homology space in degree 0 denoted by hp 0 c v w in the case where g is of type b n c n or d n results which support alev s conjecture then we are focusing the interest on the particular cases of ranks 2 and 3 by computing the poisson homology space in degree 0 in the cases where g is of type b 2 so 5 d 2 so 4 then b 3 so 7 and d 3 a 3 so 6 sl 4 in order to do this we make use of a functional equation introduced by y berest p etingof and v ginzburg we recover by a different method the result established by j alev and l foissy according to which the dimension of hp 0 c v w equals 2 for b 2 then we calculate the dimension of this space and we show that it is equal to 1 for d 2 we also calculate it for the rank 3 cases we show that it is equal to 3 for b 3 c 3 and 1 for d 3 a 3

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

an evaluation of bayesian regression for estimating cerebral oxygen utilization with oxygen 15 and dynamic pet the use of bayesian regression for improving the estimation of cerebral oxygen utilization rate cmro was investigated based on plasma time activity curves of sup 15 o oxygen and sup 15 o water that were obtained previously in a normal subject realistic tissue time activity curves of sup 15 o radioactivity in gray and white matter as obtained in dynamic pet positron emission tomography sup 15 o oxygen studies were computer simulated for various noise conditions and blood flow variations bayesian regression and regular least square regressions were applied to estimate cmro from the kinetics the accuracy and precision of the estimates were evaluated the improvement in precision was as high as 50 for gray matter of 1 cm sup 3 size in a study of 0 5 million counts slice over 3 min similar improvement was achieved for white matter in 1 million count studies the amount of improvement is larger for higher noise cases

a general method of bayesian estimation for parametric imaging of the brain abstract we report a general method of bayesian estimation that uses prior measurements to improve the signal to noise ratio of parametric images computed from dynamic pet scanning in our method the ordinary weighted least squares cost function is augmented by a penalty term to yield k s min k c f k t c 1 c f k s k s 0 k k t k 1 k k where c is a pet concentration history and c is its variance f is the model of the concentration history k k 1 k 2 k m t is the parameter vector k is the vector of population means for the model parameters k is its covariance k k s 0 is the conventional weighted sum of squares s 0 is chosen to control the balance between the prior and new data data from a prior population of subjects are analyzed with standard methods to provide maps of the mean parameter values and their variances as an example of this approach we used the dynamic image data of 10 normal subjects who had previously been studied with 11 c raclopride to estimate the prior distribution the dynamic data were transformed to stereotactic coordinates and analyzed by standard methods the resulting parametric maps were used to compute the voxel wise sample statistics then the cohort of priors was analyzed as a function of s using nonlinear least squares estimation and the cost function shown above as s is increased the standard error in estimating bp in single subjects was substantially reduced allowing measurement in bp in thalamus cortex brain stem etc additional studies demonstrate that a range of s values exist for which the bias is not excessive even when parameter values differ markedly from the sample mean this method can be used with any kinetic model so long as it is possible to compute a map of a priori mean parameters and their variances

rayleigh benard convection with rotation at small prandtl numbers this paper reviews past results from and future prospects for experimental studies of rayleigh benard convection with rotation about a vertical axis at dimensionless rotation rates 0 20 and for prandtl numbers 1 kuppers lortz unstable patterns offered a unique opportunity to study spatio temporal chaos immediately above a supercritical bifurcation where weakly nonlinear theories in the form of ginzburg landau gl or swift hohenberg sh equations can be expected to be valid however the dependence of the time and length scales of the chaotic state on e t t c 1 was found to be different from the expected dependence based on the structure of gl equations for 70 and 0 7 5 patterns were found to be cellular near onset with local four fold coordination they differ from the theoretically expected kuppers lortz unstable state stable as well as intermittent defect free rotating square lattices exist in this parameter range

noetherian connected graded algebras of global dimension 3 abstract let a be a noetherian connected graded algebra of global dimension 3 we show that a is regular in the sense of artin and schelter if one of the following conditions holds 1 a is generated by two elements 2 the graded simple module has a standard resolution 3 the degrees of minimal relations are the same this includes the quadratic case some general properties of a are studied without assuming regularity

algebras associated to elliptic curves this paper completes the classification of artin schelter regular algebras of global dimension three for algebras generated by elements of degree one this has been achieved by artin schelter tate and van den bergh we are therefore concerned with algebras which are not generated in degree one we show that there exist some exceptional algebras each of which has geometric data consisting of an elliptic curve together with an automorphism just as in the case where the algebras are assumed to be generated in degree one in particular we study the elliptic algebras a a and a a where a p2 which were first defined in an earlier paper we omit a set s p2 consisting of 11 specified points where the algebras a a become too degenerate to be regular theorem let a represent a a or a a where a p2 s then a is an artin schelter regular algebra of global dimension three moreover a is a noetherian domain with the same hilbert series as the appropriately graded commutative polynomial ring in three variables this combined with our earlier results completes the classification

a non commutative homogeneous coordinate ring for the degree six del pezzo surface abstract let r be the free c algebra on x and y modulo the relations x 5 y x y and y 2 x y x endowed with the z grading deg x 1 and deg y 2 the ring r appears in somewhat hidden guise in a paper on quiver gauge theories let b 3 denote the blow up of cp 2 at three non colinear points the main result in this paper is that the category of quasi coherent o b 3 modules is equivalent to the quotient of the category of z graded r modules modulo the full subcategory of modules that are the sum of their finite dimensional submodules this reduces almost all representation theoretic questions about r to algebraic geometric questions about the del pezzo surface b 3 for example the generic simple r module has dimension six furthermore the main result combined with results of artin tate van den bergh and stephenson implies that r is a noetherian domain of global dimension three

the spatio temporal structure of spiral defect chaos abstract we present a study of the recently discovered spatially extended chaotic state known as spiral defect chaos which occurs in low prandtl number large aspect ratio rayleigh benard convection we employ the modulus squared of the space time fourier transform of time series of two dimensional shadowgraph images to construct the structure factor s k this analysis is used to characterize the average spatial and temporal scales of the chaotic state we find that the correlation length and time can be described by power law dependences on the reduced rayleigh number these power laws have as yet no theoretical explanation

characterization of the domain chaos convection state by the largest lyapunov exponent using numerical integrations of the boussinesq equations in rotating cylindrical domains with realistic boundary conditions we have computed the value of the largest lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths we study in particular the domain chaos state which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects we compare our results with those from egolf et al nature 404 733 2000 who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short lived spatially localized dislocation nucleation events we also show that the quantity lambda1 is not intensive for aspect ratios gamma over the range 20 gamma 40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

poisson co homology and isolated singularities abstract to each polynomial f x y z is associated a poisson structure on f 3 a surface and a poisson structure on this surface when is weight homogeneous with an isolated singularity we determine the poisson cohomology and homology of the two poisson varieties obtained

homologie des invariants d une algebre de weyl sous l action d un groupe fini resume soit g un sous groupe fini de sp 2 n c operant par automorphismes dans l algebre de weyl a n c nous calculons les groupes d homologie et de cohomologie de hochschild de l algebre d invariants a n c g let g be a finite subgroup of sp 2 n c acting by automorphisms in the weyl algebra a n c we compute the hochschild homology and cohomology groups of the invariant algebra a n c g

pattern selection in rotating convection with experimental boundary conditions present the results of weakly nonlinear calculations that enable us to compute accurately both the critical rotation rate beyond which rolls are kuppers lortz unstable as well as the angle with which the instability sets in these quantities are a sensitive function of the prandtl number and here the results differ considerably from those with more idealized boundary conditions the remainder of the paper is concerned with weakly nonlinear oscillatory convection the calculations are restricted to two spatial dimensions so that the nonlinear problem concerns only traveling and standing waves we determine the relative stability between these two patterns and show that either may be stable depending on the system parameters in this discussion we are careful to consider the impact of distant sidewalls in preventing the appearance of the mean flows that are associated with traveling patterns in unbounded systems as in the kiippers lortz calculation we consider stability only with respect to perturbations of the same wave number as the basic pattern although this procedure excludes a large class of potentially important perturbations prior experience suggests that the selected perturbations are the most dangerous in addition this restriction enables us to rely on results obtained from equivariant bifurcation theory this technique 6 allows us to classify the possible weakly nonlinear and spatially periodic states and establish their relative stability in addition it identifies precisely the computations that have to be carried out on the partial diiferential equations in order to discriminate among the possible scenarios the paper is organized as follows in the following section we summarize the relevant bifurcation theory results in sec iii we formulate the hydrodynamical equations and describe the technique we use to solve them in sec iv we solve the linear stability problem for the conduction solution and identify regions in parameter space where oscillatory and steady state convection takes place in sec v we restrict the region of stable smallamplitude rolls by computing the location of the onset of

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

noncommutative graded domains with quadratic growth letk be an algebraically closed field and letr be a finitely generated connected gradedk algebra which is a domain of gelfand kirillov dimension two write the graded quotient ringq r ofr asd z z 1 for some automorphism of the division ringd we prove thatd is a finitely generated field extension ofk of transcendence degree one moreover we describer in terms of geometric data ifr is generated in degree one then up to a finite dimensional vector space r is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curvey this implies in particular thatr is noetherian thatr is primitive when and thatr is a finite module over its centre when ifr is not generated in degree one thenr will still be noetherian and primitive if has infinite order butr need not be noetherian when has finite order

homological properties of graded noetherian pi rings abstract let r be a connected graded noetherian pi ring if injdim r n r is auslander gorenstein and cohen macaulay with gelfand kirillov dimension equal to n if gldim r n r is a domain finitely generated as a module over its centre and a maximal order in its quotient division ring similar results hold if r is assumed to be local rather than connected graded alternatively suppose that r is a noetherian pi ring with gldim r r m 1 hd r m 2 for any two maximal ideals m i in the same clique then r is a direct sum of prime rings is integral over its centre and is auslander gorenstein if r is a prime ring then the centre z r of r is a krull domain and r equals its trace ring tr moreover hd r m height m for every maximal ideal m of r