precision of incidence predictions based on poisson distributed observations disease incidence predictions are useful for a number of administrative and scientific purposes the simplest ones are made using trend extrapolation on either an arithmetic or a logarithmic scale this paper shows how approximate confidence prediction intervals can be calculated for such predictions both for the total number of cases and for the age adjusted incidence rates by assuming poisson distribution of the age and period specific numbers of incident cases generalizations for prediction models for example using power families and extra poisson variation are also presented cancer incidence predictions for the stockholm gotland oncological region in sweden are used as an example

a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

homology and closure properties of autostackable groups abstract autostackability for finitely presented groups is a topological property of the cayley graph combined with formal language theoretic restrictions that implies solvability of the word problem the class of autostackable groups is known to include all asynchronously automatic groups with respect to a prefix closed normal form set and all groups admitting finite complete rewriting systems although groups in the latter two classes all satisfy the homological finiteness condition f p we show that the class of autostackable groups includes a group that is not of type f p 3 we also show that the class of autostackable groups is closed under graph products and extensions

estimating cancer incidence using a bayesian back calculation approach we propose a bayesian hierarchical model for the calculation of incidence counts from mortality data by a convolution equation that expresses mortality through its relationship with incidence and the survival probability density the basic idea is to use mortality data together with an estimate of the survival distribution from cancer incidence to cancer mortality to reconstruct the numbers of individuals who constitute previously incident cases that give rise to the observed pattern of cancer mortality this model is novel because it takes into account the uncertainty from the survival distribution thus a bayesian mixture cure model for survival is introduced furthermore projections are obtained starting from a bayesian age period cohort model the main advantage of the proposed approach is its consideration of the three components of the model the convolution equation the survival mixture cure model and the age period cohort projection within a directed acyclic graph model furthermore the estimation are obtained through the gibbs sampler we applied the model to cases of women with stomach cancer using six age classes 15 45 45 55 55 65 65 75 75 85 and 85 95 and validated it by using data from the tuscany cancer registry the model proposed and the program implemented are convenient because they allow different cancer disease to be analysed because the survival time is modelled by flexible distributions that are able to describe different trends

schur complements of selfadjoint krein space operators abstract given a bounded selfadjoint operator w on a krein space h and a closed subspace s of h the schur complement of w to s is defined under the hypothesis of weak complementability a variational characterization of the schur complement is given and the set of selfadjoint operators w admitting a schur complement with these variational properties is shown to coincide with the set of s weakly complementable selfadjoint operators

non commutative graded algebras and their hilbert series abstract this paper begins to develop a theory of non commutative graded algebras and their hilbert series which parallels the extensive already existing theory on commutative graded algebras we begin with a discussion of order ideals of monomials which give us vector space bases for these algebras we develop next the concept of weak summand which is a special relationship a subalgebra may have to an algebra and the concept of strongly free sets strongly free sets have many properties which are analogous to the properties of regular sequences in commutative algebras we discuss combinatorially free sets which are useful for constructing examples of many of the preceding ideas we conclude with an application of our results to algebraic topology by showing that there is a finite cw complex with only nine positive dimensional cells whose loop space has an irrational poincare series

a simple non linear model in incidence prediction a simple model is proposed for incidence prediction the model is non linear in parameters but linear in time following models in environmental cancer epidemiology assuming a poisson distribution for the age and period specific numbers of incident cases approximate confidence and prediction intervals are calculated the major advantage of this model over current models is that age specific predictions can be made with greater accuracy the model also preserves in the period of prediction the age pattern of incidence rates existing in the data it may be fitted with any package which includes an iteratively reweighted least squares algorithm for example glim cancer incidence predictions for the stockholm gotland oncological region in sweden are presented as an example

discrete morse theory and classifying spaces abstract the aim of this paper is to develop a refinement of forman s discrete morse theory to an acyclic partial matching on a finite regular cw complex x forman introduced a discrete analogue of gradient flows although forman s gradient flow has been proved to be useful in practical computations of homology groups it is not sufficient to recover the homotopy type of x forman also proved the existence of a cw complex which is homotopy equivalent to x and whose cells are in one to one correspondence with the critical cells of but the construction is ad hoc and does not have a combinatorial description by relaxing the definition of forman s gradient flows we introduce the notion of flow paths which contains enough information to reconstruct the homotopy type of x while retaining a combinatorial description the critical difference from forman s gradient flows is the existence of a partial order on the set of flow paths from which a 2 category c is constructed it is shown that the classifying space of c is homotopy equivalent to x by using homotopy theory of 2 categories this result can be also regarded as a discrete analogue of the unpublished work of cohen jones and segal on morse theory in early 90 s

the alternating syzygy behavior of monomial algebras abstract in this paper we present a minimal projective resolution of a monomial algebra over its enveloping algebra the syzygies for this resolution exhibit an alternating behavior which is explained by the construction of a special sequence of paths from the quiver of

initial ideals veronese subrings and rates of algebras abstract let s be a polynomial ring over an infinite field and let i be a homogeneous ideal of s let t d be a polynomial ring whose variables correspond to the monomials of degree d in s we study the initial ideals of the ideals v d i t d that define the veronese subrings of s i in suitable orders they are easily deduced from the initial ideal of i we show that in v d i is generated in degree max reg i d 2 where reg i is the regularity of the ideal i in other words the d th veronese subrings of any commutative graded ring s i has a grobner basis of degree max i d 2 we also give bounds on the regularity of i in terms of the degrees of the generators of in i and some combinatorial data this implies a version of backelin s theorem that high veronese subrings of any ring are homogeneous koszul algebras in the sense of priddy trans amer math soc 152 1970 39 60 we also give a general obstruction for a homogeneous ideal i s to have an initial ideal in i that is generated by quadrics beyond the obvious requirement that i itself should be generated by quadrics and the stronger statement that s i is koszul we use the obstruction to show that in certain dimensions a generic complete intersection of quadrics cannot have an initial ideal that is generated by quadrics for the application to backelin s theorem we require a result of backelin whose proof has never appeared we give a simple proof of a sharpened version bounding the rate of growth of the degrees of generators for syzygies of any multihomogenous module over a polynomial ring modulo an ideal generated by monomials following a method of bruns and herzog

shorting parallel addition and form sums of nonnegative selfadjoint linear relations abstract we extend the operations of shorting and parallel addition from the cone of bounded nonnegative selfadjoint operators in a hilbert space to the set of all nonnegative selfadjoint linear relations new properties of these operations and connections with the cayley transforms are established it is shown that for a pair of nonnegative selfadjoint linear relations there exist in general two arithmetic harmonic means applications of the arithmetic harmonic and arithmetic harmonic means to the theory of nonnegative selfadjoint extensions of nonnegative symmetric linear relations are given

convergent presentations and polygraphic resolutions of associative algebras several constructive homological methods based on noncommutative grobner bases are known to compute free resolutions of associative algebras in particular these methods relate the koszul property for an associative algebra to the existence of a quadratic grobner basis of its ideal of relations in this article using a higher dimensional rewriting theory approach we give several improvements of these methods we define polygraphs for associative algebras as higher dimensional linear rewriting systems that generalise the notion of noncommutative grobner bases and allow more possibilities of termination orders than those associated to monomial orders we introduce polygraphic resolutions of associative algebras giving a categorical description of higher dimensional syzygies for presentations of algebras we show how to compute polygraphic resolutions starting from a convergent presentation and how these resolutions can be linked with the koszul property

pruned cellular free resolutions of monomial ideals abstract using discrete morse theory we give an algorithm that prunes the excess of information in the taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal the pruned resolution is not simplicial in general but we can slightly modify our algorithm in order to obtain a simplicial resolution we also show that the lyubeznik resolution fits into our pruning strategy the pruned resolution is not always minimal but it is a lot closer to the minimal resolution than the taylor and the lyubeznik resolutions as we will see in some examples we finally use our methods to give a different approach to the theory of splitting of monomial ideals we deduce from this splitting strategy that the pruned resolution is always minimal in the case of edge ideals of paths and cycles

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

a combinatorial approach to the set theoretic solutions of the yang baxter equation a bijective map r x2 x2 where x x1 xn is a finite set is called a set theoretic solution of the yang baxter equation ybe if the braid relation r12r23r12 r23r12r23 holds in x3 a nondegenerate involutive solution x r satisfying r xx xx for all x x is called square free solution there exist close relations between the square free set theoretic solutions of ybe the semigroups of i type the semigroups of skew polynomial type and the bieberbach groups as it was first shown in a joint paper with michel van den bergh in this paper we continue the study of square free solutions x r and the associated yang baxter algebraic structures the semigroup s x r the group g x r and the k algebra a k x r over a field k generated by x and with quadratic defining relations naturally arising and uniquely determined by r we study the properties of the associated yang baxter structures and prove a conjecture of the present author that the three notions a square free solution of set theoretic ybe

on the golod property of stanley reisner rings abstract recently in m jollenbeck on the multigraded hilbert and poincare series of monomial rings j pure appl algebra 207 2 2006 261 298 the second author made a conjecture about the structure of ext a k k as an n n n graded vector space where a is a monomial ring over a field k that is the quotient of a polynomial ring p k x 1 x n by a monomial ideal and he verified this conjecture for several classes of such rings using the results of a berglund poincare series and homotopy lie algebras of monomial rings licentiate thesis stockholm university http www math su se reports 2005 6 2005 by the first author we are able to prove this conjecture in general in particular we get a new explicit formula for the multigraded hilbert series of ext a k k a surprising consequence of our results is that a monomial ring a is golod if and only if the product on tor p a k is trivial for stanley reisner rings of flag complexes we get a complete combinatorial characterization of golodness we introduce the concept of minimally non golod complexes and show that boundary complexes of stacked polytopes are minimally non golod finally we discuss the relation between minimal non golodness and the gorenstein property for simplicial complexes

bilateral shorted operators and parallel sums in this paper we study shorted operators relative to two different subspaces for bounded operators on infinite dimensional hilbert spaces we define two notions of complementability in the sense of ando for operators and study the properties of the shorted operators when they can be defined we use these facts in order to define and study the notions of parallel sum and substraction in this hilbertian context

derivations of leavitt path algebras abstract in this paper we describe the k module h h 1 l k of outer derivations of the leavitt path algebra l k of a row finite graph with coefficients in an associative commutative ring k with unit we explicitly describe a set of generators of h h 1 l k and relations among them we also describe a lie algebra structure of outer derivation algebra of the toeplitz algebra we prove that every derivation of a leavitt path algebra can be extended to a derivation of the corresponding c algebra

quadratic algebras yang baxter equation and artin schelter regularity abstract we study two classes of quadratic algebras over a field k the class c n of all n generated pbw algebras with polynomial growth and finite global dimension and the class of quantum binomial algebras we show that a pbw algebra a is in c n iff its hilbert series is h a z 1 1 z n furthermore the class c n contains a unique up to isomorphism monomial algebra a k x 1 x n x j x i 1 i j n a surprising amount can be said when a is a quantum binomial algebra that is its defining relations are nondegenerate square free binomials x y c x y z t c x y k our main result shows that for an n generated quantum binomial algebra a the following conditions are equivalent i a is an artin schelter regular pbw algebra ii a is a yang baxter algebra that is the set of relations defines canonically a solution of the yang baxter equation iii a is a binomial skew polynomial ring with respect to an enumeration of x iv the koszul dual a is a quantum grassmann algebra

on monomial algebras of finite global dimension let g be an associative monomial k algebra if g is assumed to be finitely presented then either g contains a free subalgebra on two monomials or else g has polynomial growth if instead g is assumed to have finite global dimension then either g contains a free subalgebra or else g has a finite presentation and polynomial growth also a graded hopf algebra with generators in degree one and relations in degree two contains a free hopf subalgebra if the number of relations is small enough

monotone convergence theorems for semi bounded operators and forms with applications let hn be a monotone sequence of non negative self adjoint operators or relations in a hilbert space then there exists a self adjoint relation h such that hn converges to h in the strong resolvent sense this result and related limit results are explored in detail and new simple proofs are presented the corresponding statements for monotone sequences of semi bounded closed forms are established as immediate consequences applications and examples illustrating the general results include sequences of multiplication operators sturm liouville operators with increasing

generalized resolvents and the boundary value problems for hermitian operators with gaps a hermitian operator a with gaps j j 1 j m is studied the self adjoint extensions which put exactly kj eigenvalues into each gap j j in particular for kj 0 1 j m the extensions preserving the gaps are described in terms of boundary conditions the generalized resolvents of the extensions with the indicated properties are described also a solvability criterion and description of all the solutions of the hamburger moment problem with supports in r j 1m j j are obtained in terms of the nevanlinna matrix

plactic monoids a braided approach abstract young tableaux carry an associative product described by the schensted algorithm they thus form a monoid pl called plactic it is central in numerous combinatorial and algebraic applications in this paper the tableaux product is shown to be completely determined by an idempotent braiding on the much simpler set of columns col here a braiding is a set theoretic solution to the yang baxter equation as an application we identify the hochschild cohomology of pl which resists classical approaches with the more accessible braided cohomology of col the cohomological dimension of pl is obtained as a corollary also the braiding is proved to commute with the classical crystal reflection operators s i

regularity of trace rings of generic matrices is called the ring of m generic n x n matrices g n the f subalgebra of m em generated by g and tr g is the ring of m generic n x n matrices and is denoted by t n these trace rings appear naturally in the study of finite dimensional representations of free algebras and in the invariant theory of n x n matrices 7 unlike rings of generic matrices t n shares some properties with commutative polynomial rings e g they are maximal orders and even unique factorization rings in the sense of chatters and jordan however their homological properties are far from being understood the main aim of this paper is to prove the following result

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

boundary relations and their weyl families the concepts of boundary relations and the corresponding weyl families are introduced let s be a closed symmetric linear operator or more generally a closed symmetric relation in a hilbert space h let h be an auxiliary hilbert space let graphics and let jh be defined analogously a unitary relation g from the krein space h 2 j h to the kre in space h 2 j h is called a boundary relation for the adjoint s if ker gamma s the corresponding weyl family m lambda is de ned as the family of images of the defect subspaces n over cap lambda lambda is an element of c r under gamma here gamma need not be surjective and is even allowed to be multi valued while this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex hilbert space h and the class of unitary relations gamma h 2 j h h 2 j h it also generalizes the notion of so called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems moreover these new notions yield for instance the following realization theorem every h valued maximal dissipative for lambda is an element of c holomorphic family of linear relations is the weyl family of a boundary relation which is unique up to unitary equivalence if certain minimality conditions are satisfied further connections between analytic and spectral theoretical properties of weyl families and geometric properties of boundary relations are investigated and some applications are given

co homology of lie algebras via algebraic morse theory abstract the fundamental theorem of cancellation amt 4 and 11 which is the algebraic generalization of discrete morse theory 2 for simplicial complexes and smooth morse theory 10 for differentiable manifolds is discussed in the context of general chain complexes of free modules the chevalley co homology table of a lie algebra is often a tremendous beast using amt we compute the homology of the lie algebra of all triangular matrices sol n over q or z p for large enough primes p we determine the column and row in the table of h k sol n z where the p torsion first appears module h k sol n z p is expressed by the homology of a chain subcomplex for the lie algebra of all strictly triangular matrices nil n using the kunneth formula all conclusions are accompanied by computer experiments then we generalize some results to lie algebras of strictly triangular matrices gl n and gl n with respect to any partial ordering on n we determine the multiplicative structure of h gl n w r t the cup product over fields of zero or sufficiently large characteristic the result being the exterior algebra matchings used here can be analogously defined for other lie algebra families and in other co homology theories we collectively call them normalization matchings they are useful for theoretical as well as computational purposes

discrete morse theory for manifolds with boundary we introduce a version of discrete morse theory specific for manifolds with boundary the idea is to consider morse functions for which all boundary cells are critical we obtain relative morse inequalities relating the homology of the manifold to the number of interior critical cells we also derive a ball theorem in analogy to forman s sphere theorem the main corollaries of our work are 1 for each d 3 and for each k 0 there is a pl d sphere on which any discrete morse function has more than k critical d 1 cells this solves a problem by chari 2 for fixed d and k there are exponentially many combinatorial types of simplicial d manifolds counted with respect to the number of facets that admit discrete morse functions with at most k critical interior d 1 cells this connects discrete morse theory to enumerative combinatorics discrete quantum gravity 3 the barycentric subdivision of any simplicial constructible d ball is collapsible this almost solves a problem by hachimori 4 every constructible ball collapses onto its boundary minus a facet this improves a result by the author and ziegler 5 any 3 ball with a knotted spanning edge cannot collapse onto its boundary minus a facet this strengthens a classical result by bing and a recent result by the author and ziegler

a spatiotemporal back calculation approach to estimate cancer incidence measures incidence rates are an important population level disease risk measure cancer incidence data in the united states which are collected by disease registries have been spatiotemporally sparse back calculation methods can yield incidence estimates for a spatial domain by solving a convolution equation that relates mortality to incidence through survival estimates we propose a novel back calculation approach that uses spatiotemporal age period cohort apc modeling to estimate incidence for spatial units within a region the method is applied to state specific lung cancer data in the united states for males ages 30 to 84 in years 1975 2004 seer data are used to model cancer progression from incidence to mortality along three timescales apc and across four regions using mortality data from national vital statistics system incidence is back calculated for unique birth cohorts in 49 states a conditionally autoregressive model with cubic splines for temporal effects is used to smooth back calculated estimates bayesian estimates of model parameters are obtained using integrated nested laplace approximation results show varying time trends in lung cancer risk across states which may quantify effects of state policies

on the homology of associative algebras we present a new free resolution for k as an g module where g is an associative augmented algebra over a field k the resolution reflects the combinatorial properties of g introduction let k be a field and let g be an associative augmented k algebra for many purposes one wishes to have a projective resolution of k as a g module the bar resolution is always easy to define but it is often too large to use in practice at the other extreme minimal resolutions may exist but they are often hard to write down in a way that is amenable to calculations the main theorem of this paper presents a compromise resolution though rarely minimal it is small enough to offer some bounds but explicit enough to facilitate calculations as it relies heavily upon combinatorial constructions it is best suited for analyzing otherwise tricky algebras given via generators and relations since several results we get as consequences of the main theorem have been obtained before through other means this paper may be viewed as generalizing and unifying several seemingly unrelated ideas in particular we are generalizing priddy s results on koszul algebras 12 extending homology computations by govorov 9 and backelin 3 and complementing bergman s methods regarding the diamond lemma 6 three results may be of interest the homology of the mod p steenrod algebra is given in terms of the homology of a new chain complex smaller than the a algebra in theorem 3 5 formula 16 offers an efficient algorithm for the determination of hilbert series and theorem 4 2 asserts the existence of new bounds on the torsion groups of commutative graded rings 1 definitions and the main theorem throughout this paper k denotes any field and g is an associative k algebra with unity the field k embeds in g via 77 k g and we suppose that g has an augmentation i e a k algebra map s g k for which 77 is a right inverse s denotes a set of generators for g as a k algebra and k s is the free associative k algebra with unity on s there is a canonical surjection f k s g once s is chosen and the augmentation e is determined once we know s x for each x e s in particular this means that k s may be augmented such that f becomes a map of augmented algebras to s we associate a function e s z called a grading in the absence of a more compelling choice we often take e to be grading by length i e e x 1 for received by the editors may 23 1983 and in revised form february 22 1984 this paper was the subject of an invited one hour address in boulder colorado during the week long ams summer program on combinatorics and algebra june 1983 1980 mathematics subject classification 1985 revision primary 16a62 secondary 13d03 55s10 1986 american mathematical society 0002 9947 86 1 00 25 per page

lebesgue type decompositions for nonnegative forms a nonnegative form t on a complex linear space is decomposed with respect to another nonnegative form tu it has a lebesgue decomposition into an almost dominated form and a singular form the part which is almost dominated is the largest form majorized by t which is almost dominated by w the construction of the lebesgue decomposition only involves notions from the complex linear space an important ingredient in the construction is the new concept of the parallel sum of forms by means of hilbert space techniques the almost dominated and the singular parts are identified with the regular and a singular parts of the form this decomposition addresses a problem posed by b simon the lebesgue decomposition of a pair of finite measures corresponds to the present decomposition of the forms which are induced by the measures t ando s decomposition of a nonnegative bounded linear operator in a hilbert space with respect to another nonnegative bounded linear operator is a consequence it is shown that the decomposition of positive definite kernels involving families of forms also belongs to the present context the lebesgue decomposition is an example of a lebesgue type decomposition i e any decomposition into an almost dominated and a singular part there is a necessary and sufficient condition for a lebesgue type decomposition to be unique this condition is inspired by the work of ando concerning uniqueness questions c 2009 elsevier inc all rights reserved

uncertainty of aids incubation time and its effects on back calculation estimates incubation time is the period from the onset of hiv infection to aids the distribution of the incubation time is one of the main parameters of the back calculation method for the estimation of incidence of hiv infection because of the long and variable incubation time the assessment of its distribution is uncertain and this uncertainty spreads through the back calculation method and affects the estimation of the precision of incidence of hiv infection we propose a method to investigate the sensitivity of the estimates to variations of the incubation times with particular regard to the covariate age in the modelling of the incubation period making use of the parametric bootstrap an application to the hiv epidemic in italy is presented the amplification of the uncertainty of the hiv incidence estimates resulting from the implementation of our proposed method tends to concentrate around the earlier periods of the epidemic corresponding to the right tail of the incubation time distribution which is very sensitive to small perturbations

free products cyclic homology and the gauss manin connection abstract we use the techniques of cuntz and quillen to present a new approach to periodic cyclic homology our construction is based on a t d t i a noncommutative equivariant de rham complex of an associative algebra a here d is the karoubi de rham differential and i is an operation analogous to contraction with a vector field as a byproduct we give a simple explicit construction of the gauss manin connection introduced earlier by e getzler on the relative periodic cyclic homology of a flat family of associative algebras over a central base ring we introduce and study free product deformations of an associative algebra a new type of deformation over a not necessarily commutative base ring natural examples of free product deformations arise from preprojective algebras and group algebras for compact surface groups

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

morse theory from an algebraic viewpoint forman s discrete morse theory is studied from an algebraic viewpoint and we show how this theory can be extended to chain complexes of modules over arbitrary rings as applications we compute the homologies of a certain family of nilpotent lie algebras and show how the algebraic morse theory can be used to derive the classical anick resolution as well as a new two sided anick resolution

a hierarchical bayesian approach to age specific back calculation of cancer incidence rates we propose a bayesian hierarchical model to estimate age specific cancer incidence per year from age specific cancer mortality the model is based upon the empirical bayesian approach of liao and brookmeyer 1995 and extends that model by consideration of the dependence on age the incident cases per year are considered as observations from a discrete time stochastic process following an autoregressive structure within a poisson regression model the model assumes that the survival probability among those with cancer is known we have investigated the sensitivity of the model to the choice of this distribution and have found that this is the most sensitive part of the model by comparison the predictions of the model are relatively robust to changes in other key areas such as the number of years an incident case contributes before death assumptions about parameter equality for identification and the initial prior distributions the proposed methodology has been investigated using lung cancer mortality data from scotland parameter estimates were obtained through markov chain monte carlo methods implemented using bugs