interpreting perspective images a fundamental problem in computer vision is how to determine the 3 d spatial orientation of curves and surfaces appearing in an image the problem is generally underconstrained and is complicated by the fact that metric properties such as orientation and length are not invariant under projection under perspective projection the correct model for most real images the transform is nonlinear and therefore hard to invert two constructive methods are presented the first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines the second determines the orientation of planes by backprojection of two intrinsic properties of contours angle magnitude and curvature

regularity of the invariant measure and of the density of states in the one dimensional anderson model abstract let h 1 2 v on l2 z where v x x z are i i d r v s with common probability distribution let h t e itvd v let n e be the integrated density of states and let e be the invariant measure at energy e it is proven 1 1 let h be d times differentiable on 0 with bounded derivatives such that h j t 0 as t for j 0 1 d then i n e is a cd function ii if d 3 e is absolutely continuous for all e r and d e dx is of class c d 1 2 1 jointly in e and x 2 2 let h be differentiable on 0 with h j t o e b t for j 0 1 and some b 0 then d e dx is jointly analytic in e and x

on the homology of the hilbert scheme of points in the plane geir ellingsrud 1 and stein arild stromme 2 i matematisk institutt universitetet i oslo blindern n oslo 3 norway 2 matematisk institutt universitetet i bergen n 5014 bergen norway although several authors have been interested in the hilbert scheme hilba ip z parametrizing finite subschemes of length d in the projective plane i1 i2 f 1 f2 br among others not much is known about the topological properties of this space the picard group has been calculated i f2 and the homology groups of hilb3 ip 2 have been computed hi in this paper we give a precise description of the additive structure of the homology of hilba ip2 applying the results of birula bialynicki b1 b2 on the cellular decompositions de fined by a torus action to the natural action of a maximal torus of sl 3 on hilbe ipz a rather easy consequence of the fact that this action has finitely many fixpoints is that the cycle maps between the chow groups and the homology groups are isomorphisms in particular there is no odd homology and the homology groups are all free the main objective of this work is to compute their ranks the betti numbers of hilba ipz as a byproduct of our method we get similar results on the homology of the punctual hilbert scheme and of the hilbert scheme of points in the affine plane it seems natural to generalize our results to any toric smooth surface however we give the results only for the rational ruled surfaces if with an indication of the necessary changes in the proofs for simplicity we work over the field of complex numbers but with an appropriate interpretation of the word homology our results remain valid over any base field

some irreducible hilbert schemes number thus h a parametrizes subschemes of if r consisting of finitely many points there are some examples of irreducible hilbert schemes of curves of low genus and degree cp 5 but the only classes of irreducible hilbert schemes which are mentioned in the literature seem to be those of plane curves embedded in some p and of hypersurfaces cp 1 thm 1 4 and 7 prop 3 the aim of the paper is to find a class of examples which in some sense is a mixture of these two classes in order to state the result we have to recall a theorem of f s macaulay according to which the hilbert scheme h e is non empty if and only if

random lie group actions on compact manifolds a perturbative analysis a random lie group action on a compact manifold generates a discrete time markov process the main object of this paper is the evaluation of associated birkhoff sums in a regime of weak but sufficiently effective coupling of the randomness this effectiveness is expressed in terms of random lie algebra elements and replaces the transience or furstenberg s irreducibility hypothesis in related problems the birkhoff sum of any given smooth function then turns out to be equal to its integral w r t a unique smooth measure on the manifold up to errors of the order of the coupling constant applications to the theory of products of random matrices and a model of a disordered quantum wire are presented

a grouping principle and four applications wertheimer s theory suggests a general perception law according to which objects having a quality in common get perceptually grouped the helmholtz principle is a quantitative version of this general grouping law it states that a grouping is perceptually meaningful if its number of occurrences would be very small in a random situation geometric structures are then characterized as large deviations from randomness in two previous works we have applied this principle to the detection of orientation alignments and boundaries in a digital image in this paper we show that the method is fully general and can be extended to a grouping by any quality we treat as an illustration the alignments of objects their grouping by color and by size and the vicinity gestalt clusters collaboration of the gestalt grouping laws and their pyramidal structure are illustrated in a case study

sklyanin algebras and hilbert schemes of points we construct projective moduli spaces for torsion free sheaves on noncommutative projective planes these moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual commutative projective plane p2 the generic noncommutative plane corresponds to the sklyanin algebra s skl e constructed from an automorphism of infinite order on an elliptic curve e p2 in this case the fine moduli space of line bundles over s with first chern class zero and euler characteristic 1 n provides a symplectic variety that is a deformation of the hilbert scheme of n points on p2 e

exact generalized lyapounov exponents for one dimensional disordered tight binding models a conceptually simple procedure is given for computing the moments of the distribution of states of one dimensional disordered tight binding models from which generalized lyapounov exponents are defined

hilbert series of modules of gk dimension two over elliptic algebras abstract we characterize the hilbert functions and minimal resolutions of critical cohen macaulay graded right modules of gelfand kirillov dimension two over generic quadratic and cubic three dimensional artin schelter regular algebras see also y berest g wilson ideal classes of the weyl algebra and noncommutative projective geometry with an appendix by michel van den bergh int math res not 2002 26 2002 1347 1396 l le bruyn moduli spaces for right ideals of the weyl algebra j algebra 172 1995 32 48 t a nevins j t stafford sklyanin algebras and hilbert schemes of points math ag 0310045 2003 8 14 15

standard bases of perfect homogeneous polynomial ideals of height 2 this paper concerns minimal systems of homogeneous generators i e standard bases of homogeneous ideals z in a commutative polynomial ring k with coefficients in a field k a basic numerical question about a standard basis b of z is to determine its cardinality or more generally the number of the elements in b of degree t for each t 0 this number depends only on z and not on the choice of b and will be denoted by v z in this paper we obtain a sharp estimate for the numbers v p when p is a perfect homogeneous ideal of height 2 in k precisely in 2 1 we provide upper and lower bounds for v p in terms of the hilbert function h h k p of k p and of an integer i which ranges in an interval defined by h then in 3 3 we show the sharpness of these bounds in fact we prove a more general result by exhibiting examples of ideals p with given h and i having for each degree t one of the possible values v p expected from 2 1 finally in 4 1 we modify the preceding examples and obtain under certain hypotheses radical ideals with the same properties the preceding results offer refined versions of well known theorems in fact from 2 1 we obtain cf 2 3 a more complete form of dubreil s inequalities cf 2 11 moreover 3 3 and 4 1 improve in the particular hypotheses under consideration a classic result of macaulay cf lo 143 and its reduced version cf 6 11 131 finally particular cases of our estimates in 2 1 can be found in 7 8 5 121 for points in generic position in the projective plane in 1 for hilbert function completeintersections and in 4 for monomial ideals of height 2

contribution to the determination of vanishing points using hough transform we propose a method to locate three vanishing points on an image corresponding to three orthogonal directions of the scene this method is based on two cascaded hough transforms we show that even in the case of synthetic images of high quality a naive approach may fail essentially because of the errors due to the limitation of the image size we take into account these errors as well as errors due to detection inaccuracy of the image segments and provide a method efficient even in the case of real complex scenes

the general hyperplane section of a curve in this paper we discuss some necessary and sufficient conditions for a curve to be arithmetically cohen macaulay in terms of its general hyperplane section we obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non arithmetically cohen macaulay curve of p 3 we prove that almost all the degree matrices with positive subdiagonal that occur for the general plane section of a non arithmetically cohen macaulay curve of p 3 arise also as degree matrices of some smooth integral non arithmetically cohen macaulay curve and we characterize the exceptions we give a necessary condition on the graded betti numbers of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay curve in p for curves in p 3 we show that any set of betti numbers that satisfies that condition can be realized as the betti numbers of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay curve we also show that the matrices that arise as a degree matrix of the general plane section of an arithmetically buchsbaum integral smooth non arithmetically cohen macaulay space curve are exactly those that arise as a degree matrix of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay space curve and have positive subdiagonal we also prove some bounds on the dimension of the deficiency module of an arithmetically buchsbaum space curve in terms of the degree matrix of the general plane section of the curve and we prove that they are sharp

parametrizations of ideals in k x y and k x y z abstract we parametrize the affine space of artinian affine ideals of k x y which have a given initial ideal with respect to the degree reverse lexicographic term order the fact that the term order is degree compatible allows us to extend the parametrization to the projective case namely zero dimensional subschemes of p 2 with some extra assumption and to determine the betti strata of these grobner cells this allows us to prove a formula due to a iarrobino for the codimension of the betti strata of codimension two punctual schemes in p 2

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

positive lyapunov exponents for a class of deterministic potentials letv be a smooth non constant function on the torus and lett be a hyperbolic toral automorphism consider a discrete one dimensional schrodinger operatorh whose potential at sitej is given bygv j gv t j we prove that wheng 0 is small andg 1 2 e 2 g 1 2 the lyapunov exponent for the cocycle generated byh e is proportional tog 2 the proof relies on a formula of pastur and figotin and on symbolic dynamics

non commutative mori contractions and p1 bundles abstract we give a method for constructing maps from a non commutative scheme to a commutative projective curve with the aid of artin zhang s abstract hilbert schemes this is used to construct analogues of the extremal contraction of a k negative curve with self intersection zero on a smooth projective surface this result will hopefully be useful in studying artin s conjecture on the birational classification of non commutative surfaces as a non trivial example of the theory developed we look at non commutative ruled surfaces and more generally at non commutative p 1 bundles we show in particular that non commutative p 1 bundles are smooth have well behaved hilbert schemes and we compute its serre functor we then show that non commutative ruled surfaces give examples of the aforementioned non commutative mori contractions

dequantizing image orientation we address the problem of computing a local orientation map in a digital image we show that standard image gray level quantization causes a strong bias in the repartition of orientations hindering any accurate geometric analysis of the image in continuation a simple dequantization algorithm is proposed which maintains all of the image information and transforms the quantization noise in a nearby gaussian white noise we actually prove that only gaussian noise can maintain isotropy of orientations mathematical arguments are used to show that this results in the restoration of a high quality image isotropy in contrast with other classical methods it turns out that this property can be obtained without smoothing the image or increasing the signal to noise ratio snr as an application it is shown in the experimental section that thanks to this dequantization of orientations such geometric algorithms as the detection of nonlocal alignments can be performed efficiently we also point out similar improvements of orientation quality when our dequantization method is applied to aliased images

linear equations over noncommutative graded rings abstract we call a graded connected algebra r effectively coherent if for every linear equation over r with homogeneous coefficients of degrees at most d the degrees of generators of its module of solutions are bounded by some function d d for commutative polynomial rings this property has been established by hermann in 1926 we establish the same property for several classes of noncommutative algebras including the most common class of rings in noncommutative projective geometry that is strongly noetherian rings which includes noetherian pi algebras and sklyanin algebras we extensively study so called universally coherent algebras that is such that the function d d is bounded by 2d for d 0 for example finitely presented monomial algebras belong to this class as well as many algebras with finite groebner basis of relations

betti strata of height two ideals abstract let r k x y denote the polynomial ring in two variables over an infinite field k we study the betti strata of the family g h parametrizing graded artinian quotients of r k x y having given hilbert function h the betti stratum g h parametrizes all quotients a of having the graded betti numbers determined by h and the minimal relation degrees with i dim k tor 1 r i k i we recover that the betti strata are irreducible and we calculate their codimension in the family g h theorem the codimension of g h in g h satisfies letting i generators of degree i and i relations of degree i cod g h i i i here min i h i i 1 the initial degree of the ideals when k is algebraically closed we also show that the closure of a betti stratum is the union of more special strata and is cohen macaulay theorem 2 18 our method is to identify g h as a product of determinantal varieties ours is a more direct argument than that of a iarrobino v kanev power sums gorenstein algebras and determinantal loci lecture notes in math vol 1721 springer heidelberg 1999 345 xxvii pp theorem 5 63 which obtains the codimension of betti substrata of a postulation stratum for punctual subschemes of p 2 there we relied on a result of m boij determining the codimension of betti strata of height three gorenstein algebras m boij betti number strata of the space of codimension three gorenstein artin algebras preprint 2001 key tools throughout include properties of an invariant v the number of generators of the ancestor ideal v r and previous results concerning the projective variety g h in a iarrobino punctual hilbert schemes mem amer math soc 10 188 1977 we adapt a method of m boij that reduces the calculation of the codimension of the betti strata to showing that the most special stratum has the right codimension as applications we determine which hilbert functions are possible for artinian quotients of r given the socle type theorem 3 2 and we also determine the hilbert function of the intersection of t general enough level ideals in r each having a specified hilbert function theorem 3 6

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

delocalization in random polymer models a random polymer model is a one dimensional jacobi matrix randomly composed of two finite building blocks if the two associated transfer matrices commute the corresponding energy is called critical such critical energies appear in physical models an example being the widely studied random dimer model it is proven that the lyapunov exponent vanishes quadratically at a generic critical energy and that the density of states is positive there large deviation estimates around these asymptotics allow to prove optimal lower bounds on quantum transport showing that it is almost surely overdiffusive even though the models are known to have pure point spectrum with exponentially localized eigenstates for almost every configuration of the polymers furthermore the level spacing is shown to be regular at the critical energy

weak disorder expansion for the anderson model on a tree we show how certain properties of the anderson model of a tree are related to the solutions of a nonlinear integral equation whether the wave function is extended or localized for example corresponds to whether or not the equation has a complex solution we show how the equation can be solved in a weakdisorder expansion we find that for small disorder strength there is an energyec above which the density of states and the conducting properties vanish to all orders in perturbation theory we compute pertubatively the position of the lineec which begins in the limit of zero disorder at the band edge of the pure system inside the band of the pure system the density of states and conducting properties can be computed perturbatively this expansion breaks down nearec because of small denominators we show how it can be resummed by choosing the appropriate scaling of the energy for energies greater thanec we show that nonperturbative effects contribute to the density of states but we have been unable to tell whether they also contribute to the conducting properties

ideals of cubic algebras and an invariant ring of the weyl algebra hasselt univ dept wni b 3590 diepenbeek belgium univ antwerp dept wiskunde informat b 2020 antwerp belgium de naeghel k hasselt univ dept wni agoralaan gebouw d b 3590 diepenbeek belgium koendenaeghel hotmail com nicolas marconnet ua ac be

the gotzmann coefficients of hilbert functions abstract in this paper we investigate some algebraic and geometric consequences which arise from an extremal bound on the hilbert function of the general hyperplane section of a variety green s hyperplane restriction theorem these geometric consequences improve some results in this direction first given by green and extend others by bigatti geramita and migliore other applications of our detailed investigation of how the hilbert polynomial is written as a sum of binomials are to conditions that must be satisfied by a polynomial if it is to be the hilbert polynomial of a non degenerate integral subscheme of p n a problem posed by r p stanley we also give some new restrictions on the hilbert function of a zero dimensional reduced scheme with the uniform position property

maximal meaningful events and applications to image analysis we discuss the mathematical properties of a recently introduced method for computing geometric structures in a digital image without any a priori information this method is based on a basic principle of perception which we call the helmholtz principle according to this principle an observed geometric structure is perceptually meaningful if the expectation of its number of occurrences in other words its number of false alarms nf is very small in a random image it is maximal meaningful if its nf is minimal among the meaningful structures of the same kind which it contains or is contained in this definition meets the gestalt theory requirement that parts of a whole are not perceived we explain by large deviation estimates why this definition leads to an a priori knowledge free method compatible with phenomenology we state a principle according to which maximal structures do not meet we prove this principle in the large deviations framework in the case of alignments in a digital image we show why these results make maximal meaningful structures computable and display several applications

on incidence between strata of the hilbert scheme of points on p 2 the hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated hilbert series in general the precise inclusion relation between the closures of the strata is still unknown guerimand ph d thesis universite de nice 2002 studied this problem for strata whose hilbert series are as close as possible preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata in this paper we present a new approach based on deformation theory to guerimand s result this allows us to show that the technical condition is not necessary

families of artinian and one dimensional algebras abstract the purpose of this paper is to study families of artinian or one dimensional quotients of a polynomial ring r with a special look to level algebras let gradalg h r be the scheme parametrizing graded quotients of r with hilbert function h let b a be any graded surjection of quotients of r with hilbert function h b 1 h 1 h j and h a respectively if dim a 0 respectively dim a depth a 1 and a is a truncation of b in the sense that h a 1 h 1 h j 1 0 0 respectively h a 1 h 1 h j 1 for some h j then we show there is a close relationship between gradalg h a r and gradalg h b r concerning e g smoothness and dimension at the points a and b respectively provided b is a complete intersection or provided the castelnuovo mumford regularity of a is at least 3 sometimes 2 larger than the regularity of b in the complete intersection case we generalize this relationship to non truncated artinian algebras a which are compressed or close to being compressed for more general artinian algebras we describe the dual of the tangent and obstruction space of graded deformations in a manageable form which we make rather explicit for level algebras of cohen macaulay type 2 this description and a linkage theorem for families allow us to prove a conjecture of iarrobino on the existence of at least two irreducible components of gradalg h r h 1 3 6 10 14 10 6 2 whose general elements are artinian level algebras of type 2

homography based visual servo control with imperfect camera calibration in this technical note a robust adaptive uncalibrated visual servo controller is proposed to asymptotically regulate a robot end effector to a desired pose a homography based visual servo control approach is used to address the six degrees of freedom regulation problem a high gain robust controller is developed to asymptotically stabilize the rotation error and an adaptive controller is developed to stabilize the translation error while compensating for the unknown depth information and intrinsic camera calibration parameters a lyapunov based analysis is used to examine the stability of the developed controller

instability of the anomalies in the one dimensional anderson model at weak disorder we study the asymptotic behavior of the invariant measure the lyapunov exponent and the density of states in the weak disorder limit in the case where the single site potential distribution is not centered and for the special energiese cos p q we also prove that in general the above quantities can be continuously extended to zero disorder as continuous functions in the disorder parameter for all energiese 1 1

positivity of mixed multiplicities let r u v n2r u v be a standard bigraded algebra over an artinian local ring k r 0 0 standard means r is generated over k by a finite number of elements of degree 1 0 and 0 1 since the length r u v of r u v is finite we can consider r u v as a function in two variables u and v this function was first studied by van der waerden w and bhattacharya b who proved that there is a polynomial pr u v of total degree dimr 2 such that r u v pr u v for u and v large enough katz mandal andverma kmv found out that the degree of pr u v is equal to rdimr 2 where rdimr is the relevant dimension of r defined as follows let r denote the ideal generated by the homogeneous elements of degree u v with u 1 v 1 let projr be the set of all homogeneous prime ideals r of r then rdimr max dimr projr if projr and rdimr can be any negative integer if projr if we write

single view metrology we describe how 3d affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image this minimal information is typically the vanishing line of a reference plane and a vanishing point for a direction not parallel to the plane it is shown that affine scene structure may then be determined from the image without knowledge of the camera s internal calibration e g focal length nor of the explicit relation between camera and world pose in particular we show how to i compute the distance between planes parallel to the reference plane up to a common scale factor s ii compute area and length ratios on any plane parallel to the reference planes iii determine the camera s location simple geometric derivations are given for these results we also develop an algebraic representation which unifies the three types of measurement and amongst other advantages permits a first order error propagation analysis to be performed associating an uncertainty with each measurement we demonstrate the technique for a variety of applications including height measurements in forensic images and 3d graphical modelling from single images

vanishing point detection without any a priori information even though vanishing points in digital images result from parallel lines in the 3d scene most of the proposed detection algorithms are forced to rely heavily either on additional properties like orthogonality or coplanarity and equal distance of the underlying 3d lines or on knowledge of the camera calibration parameters in order to avoid spurious responses in this work we develop a new detection algorithm that relies on the helmoltz principle recently proposed for computer vision by desolneux et al 2001 2003 both at the line detection and line grouping stages this leads to a vanishing point detector with a low false alarms rate and a high precision level which does not rely on any a priori information on the image or calibration parameters and does not require any parameter tuning

ideal classes of three dimensional artin schelter regular algebras abstract we determine the possible hilbert functions of graded rank one torsion free modules over three dimensional artin schelter regular algebras it turns out that as in the commutative case they are related to castelnuovo functions from this we obtain an intrinsic proof that the space of torsion free rank one modules on a non commutative p 2 is connected a different proof of this fact based on deformation theoretic methods and the known commutative case has recently been given by nevins and stafford sklyanin algebras and hilbert schemes of points math ag 0310045 for the weyl algebra it was proved by wilson invent math 133 1 1998 1 41

a stratification of the hilbert scheme of points in the projective plane this result is analogous to a theorem of iarrobino and brian on on the stratification of the punctual hilbert scheme where a different hilbert function defined by initial forms instead is used however cp i l thm 2 9 p 26 the proof essentially makes use of the smoothness of h a cp f p 517 and a general result of bialynicki birula on the action of the multiplicative group on a smooth projective scheme as already was done in a study of the homology of h a by ellingsrud and stromme this method is applied here to a study of h a around points which are invariant under the borel group in the appendix a method for computing the dimension of h is represented which rests on iarrobino s description of the tangent space to certain points of h a and the theorem of bialynicki birula finally i would like to mention that hirschowitz has outlined a general program for studying stratifications including those defined by hilbert functions cp h p 175 but the result obtained here can at best be regarded only as the most simple perhaps non trivial example

the hilbert function of generic plane sections of curves of ℙ3 a characteristic condition is given on a zero dimensional differentiable 0 sequenceh hi i 0 h1 3 in order to be the hilbert function of a generic plane section of a reduced irreducible curve of 3 hence of points of 2 with the uniform position property in this way an answer is given to some question stated by harris in ha2

a supersymmetric transfer matrix and differentiability of the density of states in the one dimensional anderson model let h v on 2 z where v x 9 xez are d r v s with common probability distribution v let h t e itvdv v and let k e be the integrated density of states it is proven i if h is n times differentiable with h j t 0 l t for some 0 7 0 l n then k e is a cn function in particular if v has compact support and h t 0 l h 1 with 0 then k e is c this allows v to be singular continuous ii lfh t 0 e a tl for some 0 then k e is analytic in a strip about the real axis the proof uses the supersymmetric replica trick to rewrite the averaged green s function as a two point function of a one dimensional supersymmetric field theory which is studied by the transfer matrix method

the non lefschetz locus abstract we study the weak lefschetz property of artinian gorenstein algebras and in particular of artinian complete intersections in codimension four and higher it is an open problem whether all complete intersections have the weak lefschetz property for a given artinian gorenstein algebra a we ask what linear forms are lefschetz elements for this particular algebra i e which linear forms l give maximal rank for all the multiplication maps l a i a i 1 this is a zariski open set and its complement is the non lefschetz locus for monomial complete intersections we completely describe the non lefschetz locus for general complete intersections of codimension three and four we prove that the non lefschetz locus has the expected codimension which in particular means that it is empty in a large family of examples for general gorenstein algebras of codimension three with a given hilbert function we prove that the non lefschetz locus has the expected codimension if the first difference of the hilbert function is of decreasing type for completeness we also give a full description of the non lefschetz locus for artinian algebras of codimension two

subspaces of non commutative spaces this paper concerns the closed points closed subspaces open subspaces weakly closed and weakly open subspaces and effective divisors on a non commutative space

an a contrario decision framework for region based motion detection the aim of motion detection is to decide whether a given part of an image belongs to a moving object or to the static background this paper proposes an automatic decision rule for the detection of moving regions the proposed framework is derived from a perceptual grouping principle namely the helmholtz principle this principle basically states that perceptually relevant events are perceived because they deviate from a model of complete randomness detections are then said to be performed a contrario moving regions appear as low probability events in a model corresponding to the absence of moving objects in the scene a careful design of the events considered under the hypothesis of absence of moving objects results in a general and robust motion detection algorithm no posterior parameter tuning is necessary furthermore a confidence level is attached to each detected region

weak disorder expansions for the anderson model on a one dimensional strip at the center of the band we study the asymptotic behavior of the averaged diagonal matrix elements of the greens kernel for the anderson model on a one dimensional strip and for a set of special energies close to the center of the band

performance evaluation and analysis of vanishing point detection techniques vanishing point detection algorithms based on a gaussian sphere representation have been employed in a variety of computer vision systems for extracting 3d line orientations as a first step towards object detection typically these algorithms have been applied to imagery with strong perspective effects and with little noise or texture resulting in good solutions for line orientations however these algorithms can fail if perspective effects are weak or if texture edges are predominant they also fail to take advantage of knowledge about the objects to be detected in this paper two new techniques for robust vanishing point detection on the gaussian sphere are presented primitive based vanishing point analysis and interpretation plane error modeling the performance of these methods along with two other existing methods from the literature are quantitatively evaluated and compared for the task of building detection in complex aerial imagery

uniform position properties and hilbert functions for points on a smooth quadric abstract if x is a set of points of p3 with the uniform position property we study the structure of the hilbert function of x with special care in the case when x lies on a smooth quadric q in this particular situation we also investigate the behaviour of the hilbert matrix of x when the uniform position property is enlarged to the divisors of q

anomalies in the one dimensional anderson model at weak disorder we show that at the special energiese 2cos p q the invariant measure the lyapunov exponent and the density of states can be extended to zero disorder as c functions in the disorder parameter in particular we obtain asymptotic series in the disorder parameter this gives a rigorous proof of the existence of the anomalies originally discovered by kappus and wegner and studied by derrida and gardner and by bovier and klein

an a contrario decision method for shape element recognition shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database up to a certain invariance most shape recognition methods simply sort shapes from the database along some dis similarity measure to the query shape their main weakness is the decision stage which should aim at giving a clear cut answer to the question do these two shapes look alike in this article the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes ensuring that the obtained matches are not likely to occur by chance as an application one can decide with a parameterless method whether any two digital images share some shapes or not

a study of one dimensional correlated disordered systems using the invariant measure method the behaviour of electronic states of one dimensional correlated disordered systems which are modelled by a tight binding hamiltonian is studied analytically using the invariant measure method the approach of bovier is generalized to include the possibility of different site energies and nearest neighbour hopping integrals inside the correlated sites or the cluster the process is further elaborated by applying to the symmetric random trimer model which contains in it many hitherto known models of this category an alternative mathematical definition of the exceptional energy from the invariant measure density along with physical arguments substantiating it is presented furthermore the procedure for obtaining exceptional energies is outlined and applied to the symmetric random trimer model to derive conditions for obtaining doubly degenerate exceptional energies the lyapunov exponent or the inverse localization length of states around the exceptional energy is found to vary as in the leading order n denotes the degeneracy of the exceptional energy the density of states at the exceptional energies are calculated we further propose that one dimensional correlated disordered systems can be mapped to a lloyd model in which the width of the distribution of site energies is determined by the reflection coefficient of the cluster embedded in the lattice of the other constituent the importance of our results is discussed

ideal classes of three dimensional sklyanin algebras abstract in this paper we classify graded reflexive ideals up to isomorphism and shift in certain three dimensional artin schelter regular algebras this classification is similar to the classification of right ideals in the first weyl algebra a problem that was completely settled recently the situation we consider is substantially more complicated however