desingularization of quasi excellent schemes in characteristic zero grothendieck proved in ega iv that if any integral scheme of finite type over a locally noetherian scheme x admits a desingularization then x is quasi excellent and conjectured that the converse is probably true we prove this conjecture for noetherian schemes of characteristic zero namely starting with the resolution of singularities for algebraic varieties of characteristic zero we prove the resolution of singularities for noetherian quasi excellent q schemes

on the tropical torelli map abstract we construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties working in the category of what we call stacky fans we define the tropical torelli map between these two moduli spaces and we study the fibers tropical torelli theorem and the image of this map tropical schottky problem finally we determine the image of the planar tropical curves via the tropical torelli map and we use it to give a positive answer to a question raised by namikawa on the compactified classical torelli map

torelli theorem for graphs and tropical curves algebraic curves have a discrete analog in finite graphs pursuing this analogy we prove a torelli theorem for graphs namely we show that two graphs have the same albanese torus if and only if the graphs obtained from them by contracting all separating edges are 2 isomorphic in particular the strong torelli theorem holds for 3 connected graphs next using the correspondence between compact tropical curves and metric graphs we prove a tropical torelli theorem giving necessary and sufficient conditions for two tropical curves to have the same principally polarized tropical jacobian by contrast we prove that in a suitably defined sense the tropical torelli map has degree one finally we describe some natural posets associated to a graph and prove that they characterize its delaunay decomposition

vicious walks with long range interactions the asymptotic behavior of the survival or reunion probability of vicious walks with short range interactions is generally well studied in many realistic processes however walks interact with a long ranged potential that decays in d dimensions with distance r as r ensuremath d ensuremath ensuremath sigma we employ methods of renormalized field theory to study the effect of such long range interactions we calculate the exponents describing the decay of the survival probability for all values of parameters ensuremath sigma and d to first order in the double expansion in ensuremath epsilon 2 ensuremath d and ensuremath delta 2 ensuremath d ensuremath ensuremath sigma we show that there are several regions in the ensuremath sigma text ensuremath d plane corresponding to different scalings for survival and reunion probabilities furthermore we calculate the leading logarithmic corrections

tropicalization of the moduli space of stable maps let x be an algebraic variety and let s be a tropical variety associated to x we study the tropicalization map from the moduli space of stable maps into x to the moduli space of tropical curves in s we prove that it is a continuous map and that its image is compact and polyhedral loosely speaking when we deform algebraic curves in x the associated tropical curves in s deform continuously moreover the locus of realizable tropical curves inside the space of all tropical curves is compact and polyhedral our main tools are berkovich spaces formal models balancing conditions vanishing cycles and quantifier elimination for rigid subanalytic sets

kontsevich s formula and the wdvv equations in tropical geometry abstract using gromov witten theory the numbers of complex plane rational curves of degree d through 3 d 1 general given points can be computed recursively with kontsevich s formula that follows from the so called wdvv equations in this paper we establish the same results entirely in the language of tropical geometry in particular this shows how the concepts of moduli spaces of stable curves and maps evaluation and forgetful morphisms intersection multiplicities and their invariance under deformations can be carried over to the tropical world

exact results for vicious walker models of domain walls non intersecting or vicious random walker models in one dimension can be interpreted as models of domain walls in two dimensions three problems pertaining to vicious walker models are solved the first is the exact evaluation of the partition function for the random turns model of vicious walkers on a lattice in this model at each tick of the clock a randomly chosen walker must move one step to the left or one step to the right the second problem is the calculation of the mean spacing between walls in terms of the chemical potential for a brownian motion model of continuous domain walls in a strip while the final problem solved is the calculation of the correlation between defects which occur when two domain walls meet and end without crossing the whole system

exact fixed point for directed random walks the authors have shown that the renormalization group fixed point for mutually avoiding directed random walks in d 1 dimensions is exactly 2 pi in where in 2 d with no higher order terms in in since the whole calculation can be carried out to all orders exactly the model is also significant from a pedagogical point of view

loop mediated crossover in the three dimensional ising model the authors establish the existence of crossover from a three or any dimensional ising model to the anisotropic five vertex model by suppressing closed loops in the isomorphic dimer problem the crossover exponent is determined exactly using a renormalization group approach

sensitivity of spin glass order to temperature changes by a loop expansion around parisi s mean field theory for an ising spin glass it is shown that the overlap of the magnetization patterns belonging to two different temperatures t and t vanishes to any order si t si t 0 while the correlation overlap sisj t sisj t calculated to first loop order and for technical reasons for dimensions d 8 only is found to decay exponentially with a characteristic length approximately t t 1

form invariant linear filtering theory and applications the form invariant filters are by definition those shift variant filters such that their output for any given input turns out to be linearly scaled implying that its form does not change whenever the input is linearly scaled in this paper the most general classes of 1 d and 2 d linear form invariant filters are derived and their properties are discussed together with their implementation techniques two main implementation approaches are considered one based on the mellin transform the other on a combination of coordinate mappings and shift invariant filtering the paper also discusses the related works of other authors covering quite different fields such as optical pattern recognition image restoration and image reconstruction from projections radar signal processing etc it is shown that the mathematics of form invariant filtering provides a common framework if not a powerful unified approach to the many signal processing techniques spread in the above mentioned works and apparently different application areas the paper ends with a processing example showing the usefulness of form invariant filtering in a pattern recognition problem that is in the area where the most promising applications of such a filtering are foreseen

vanishing cycles for formal schemes let k be a non archimedean field and let x be a formal scheme locally finitely presented over the ring of integers k see 1 in this work we construct and study the vanishing cycles functor from the category of etale sheaves on the generic fibre x of x which is a k analytic space to the category of etale sheaves on the closed fibre xs of x which is a scheme over the residue field of k we prove that if x is the formal completion x of a scheme x finitely presented over k along the closed fibre then the vanishing cycles sheaves of x are canonically isomorphic to those of x as defined in sga7 exp xiii in particular the vanishing cycles sheaves of x depend only on x and any morphism x induces a homomorphism from the pullback of the vanishing cycles sheaves of x under s ys xs to those of y furthermore we prove that for each x one can find a nontrivial ideal of k such that if two morphisms x coincide modulo this ideal then the homomorphisms between the vanishing cycles sheaves induced by and coincide these facts were conjectured by p deligne in 1 we associate with a formal scheme x locally finitely presented over k a k analytic space x in the sense of ber1 and ber2 in 2 we find that the morphism y x which is induced by an etale morphism of formal schemes y x possesses a certain property morphisms of k analytic spaces with this property are called quasi etale and they give rise to a quasi etale site xqet of a k analytic space x there is a canonical morphism of sites xqet xet where xet is the etale site introduced in ber2 we show that the inverse image functor identifies the category of etale sheaves x et with a full subcategory of

image reconstruction from linograms implementation and evaluation the notion of a linogram corresponds to the notion of a sinogram in the conventional representation of projection data for image reconstruction in the sinogram points which correspond to rays through a fixed point in the cross section to be reconstructed all fall on a sinusoidal curve in the linogram however these points fall on a straight line the implementation of a novel image reconstruction method using this property is discussed the implementation is of order n sup 2 log n where n is proportional to the number of pixels on a side of the reconstruction region it is demonstrated that the performance of the algorithm is superior to that of the filter backprojection method in computational speed on realistic size problems and is equivalent to filtered backprojection in accuracy of reconstruction

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

reunion of vicious walkers results from epsilon expansion the anomalous exponent eta p for the decay of the reunion probability of p vicious walkers each of length n in d 2 epsilon dimensions is shown to come from the multiplicative renormalization constant of a p directed polymer partition function using renormalization group rg we evaluate eta p to o epsilon 2 the survival probability exponent is eta p 2 for p 2 our rg is exact and eta p stops at o epsilon for d 2 the log corrections are also determined the number of walkers that are sure to reunite is 2 and has no epsilon expansion

fast inversion of the radon transform using log polar coordinates and partial back projections in this paper a novel filtered back projection algorithm for inversion of a discretized radon transform is presented it makes use of invariance properties possessed by both the radon transform and its dual by switching to log polar coordinates both operators can be expressed in a displacement invariant manner explicit expressions for the corresponding transfer functions are calculated furthermore by dividing the back projection into several partial back projections inversion can be performed by means of finite convolutions and hence implemented by an fft algorithm in this way a fast and accurate reconstruction method is obtained

smooth p adic analytic spaces are locally contractible 0 introduction 293 1 piecewise rs linear spaces 298 2 r colored polysimplicial sets 308 3 r colored polysimplicial sets of length l 313 4 the skeleton of a nondegenerate pluri stable formal scheme 327 5 a colored polysimplicial set associated with a nondegenerate poly stable fibration 336 6 p adic analytic and piecewise linear spaces 346 7 strong local contractibility of smooth analytic spaces 355 8 cohomology with coefficients in the sheaf of constant functions 362

moments of vicious walkers and mobius graph expansions a system of brownian motions in one dimension all started from the origin and conditioned never to collide with each other in a given finite time interval 0 t is studied the spatial distribution of such vicious walkers can be described by using the repulsive eigenvalue statistics of random hermitian matrices and it was shown that the present vicious walker model exhibits a transition from the gaussian unitary ensemble gue statistics to the gaussian orthogonal ensemble goe statistics as the time t goes on from 0 to t in the present paper we characterize this gue to goe transition by presenting the graphical expansion formula for the moments of positions of vicious walkers in the gue limit stackrel ensuremath rightarrow t 0 only the ribbon graphs contribute and the problem is reduced to the classification of orientable surfaces by genus following the time evolution of the vicious walkers however the graphs with twisted ribbons called m obius graphs increase their contribution to our expansion formula and we have to deal with the topology of nonorientable surfaces application of the recent exact result of dynamical correlation functions yields closed expressions for the coefficients in the m obius expansion using the stirling numbers of the first kind

scaling of fluctuation for directed polymers with random interaction using a finite size scaling form for reunion probability we show numerically the existence of a binding unbinding transition for directed polymers with random interaction the cases studied are a1 two chains in 1 1 dimensions a2 two chains in 2 1 dimensions and b three chains in 1 1 dimensions a similar finite size scaling form for fluctuation establishes a disorder induced transition with identical exponents for cases a2 and b the length scale exponents in all the three cases are in agreement with previous exact renormalization group results

tropical geometry and correspondence theorems via toric stacks in this paper we generalize correspondence theorems of mikhalkin and nishinou siebert providing a correspondence between algebraic and parameterized tropical curves we also give a description of a canonical tropicalization procedure for algebraic curves motivated by berkovich s construction of skeletons of analytic curves under certain assumptions we construct a one to one correspondence between algebraic curves satisfying toric constraints and certain combinatorially defined objects called stacky tropical reductions that can be enumerated in terms of tropical curves satisfying linear constraints similarly we construct a one to one correspondence between elliptic curves with fixed j invariant satisfying toric constraints and stacky tropical reductions that can be enumerated in terms of tropical elliptic curves with fixed tropical j invariant satisfying linear constraints our theorems generalize previously published correspondence theorems in tropical geometry and our proofs are algebra geometric in particular the theorems hold in large positive characteristic

families of vicious walkers we consider a generalization of the vicious walker problem in which n random walkers in rd are grouped into p families using field theoretic renormalization group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t for d 2 this is constant but for d 2 it decays as a power t which we compute to e2 in an expansion in e 2 d the second order term depends on the ratios of the diffusivities of the different families in two dimensions we find a logarithmic decay ln t and compute exactly

trapping of a random walk by diffusing traps we present a systematic analytical approach to the trapping of a random walk by a finite density rho of diffusing traps in arbitrary dimension d we confirm the phenomenologically predicted e c d rho t d 2 time decay of the survival probability and compute the dimension dependent constant c d to leading order within an eps 2 d expansion

exactly solved model of self organized critical phenomena we define a variant of the model of bak tang and wiesenfeld of self organized critial behavior by introducing a preferred direction we characterize the critical state and by establishing equivalence to a voter model determine the critical exponents exactly in arbitrary dimension d the upper critical dimension for this model is three in two dimensions the model is equivalent to an earlier solved special case of directed percolation

a hankel transform approach to tomographic image reconstruction a relatively unexplored algorithm is developed for reconstructing a two dimensional image from a finite set of its sampled projections the algorithm referred to as the hankel transform reconstruction htr algorithm is polar coordinate based the algorithm expands the polar form fourier transform f r theta of an image into a fourier series in theta calculates the appropriately ordered hankel transform of the coefficients of this series giving the coefficients for the fourier series of the polar form image f p phi resolves this series giving a polar form reconstruction and interpolates this reconstruction to a rectilinear grid the htr algorithm is outlined and it is shown that its performance compares favorably to the popular convolution backprojection algorithm