p sufficient statistics for pac learning k term dnf formulas through enumeration working in the framework of pac learning theory we present special statistics for accomplishing in polynomial time proper learning of dnf boolean formulas having a fixed number of monomials our statistics turn out to be near sufficient for a large family of distribution laws that we call butterfly distributions we develop a theory of most powerful learning for analyzing the performance of learning algorithms with particular reference to trade offs between power and computational costs focusing attention on sample and time complexity we prove that our algorithm works as efficiently as the best algorithms existing in the literature while the latter only take care of subclasses of our family of distributions

compatibility of local and global langlands correspondences we prove the compatibility of local and global langlands correspondences for gln which was proved up to semisimplification in ht more precisely for the ndimensional l adic representation rl of the galois group of an imaginary cm field l attached to a conjugate self dual regular algebraic cuspidal automorphic representation of gln al which is square integrable at some finite place we show that frobenius semisimplification of the restriction of rl to the decomposition group of a place v of l not dividing l corresponds to v by the local langlands correspondence if v is square integrable for some finite place v 6 l we deduce that rl is irreducible we also obtain conditional results in the case v l

l espace symetrique de drinfeld et correspondance de langlands locale ii we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

learnability with respect to fixed distributions consider a first order typed language with semantics s for expressions and types adding subtyping means that a partial order on types is defined and that the typing rules are extended to the effect that expression e has type t whenever e has type s and s t we show how to adapt the semantics s in a simple set theoretic way obtaining a semantics s that satisfies in addition to some obvious requirements also the property that s s is included in s t whenever s t

weight monodromy conjecture for p adically uniformized varieties the aim of this paper is to prove the weight monodromy conjecture deligne s conjecture on the purity of monodromy filtration for varieties p adically uniformized by the drinfeld upper half spaces of any dimension the ingredients of the proof are to prove a special case of the hodge standard conjecture and apply a positivity argument of steenbrink m saito to the weight spectral sequence of rapoport zink as an application by combining our results with the results of schneider stuhler we compute the local zeta functions of p adically uniformized varieties in terms of representation theoretic invariants we also consider a p adic analogue by using the weight spectral sequence of mokrane

effects of domain characteristics on instance based learning algorithms this paper presents average case analyses of instance based learning algorithms the algorithms analyzed employ a variant of k nearest neighbor classifier k nn our analysis deals with a monotone m of n target concept with irrelevant attributes and handles three types of noise relevant attribute noise irrelevant attribute noise and class noise we formally represent the expected classification accuracy of k nn as a function of domain characteristics including the number of training instances the number of relevant and irrelevant attributes the threshold number in the target concept the probability of each attribute the noise rate for each type of noise and k we also explore the behavioral implications of the analyses by presenting the effects of domain characteristics on the expected accuracy of k nn and on the optimal value of k for artificial domains

characterizations of monotonic and dual monotonic language learning the present paper deals with monotonic and dual monotonic language learning from positive as well as from positive and negative examples the three notions of monotonicity reflect different formalizations of the requirement that the learner has to produce better and better generalizations when fed more and more data on the concept to be learned the three versions of dual monotonicity describe the concept that the inference device has to produce specializations that fit better and better to the target language we characterize strong monotonic monotonic weak monotonic dual strong monotonic dual monotonic and monotonic dual monotonic as well as finite language learning from positive data in terms of recursively generable finite sets these characterizations provide a unifying framework for learning from positive data under the various monotonicity constraints moreover they yield additional insight into the problem of what a natural learning algorithm should look like

curvature estimation along noisy digital contours by approximate global optimization in this paper we introduce a new curvature estimator along digital contours which we called global min curvature gmc estimator as opposed to previous curvature estimators it considers all the possible shapes that are digitized as this contour and selects the most probable one with a global optimization approach the gmc estimator exploits the geometric properties of digital contours by using local bounds on tangent directions defined by the maximal digital straight segments the estimator is then adapted to noisy contours by replacing maximal segments with maximal blurred digital straight segments experiments on perfect and damaged digital contours are performed and in both cases comparisons with other existing methods are presented

on learning read k satisfy j dnf we study the learnability of read k satisfy j rksj dnf formulas these are boolean formulas in disjunctive normal form dnf in which the maximum number of occurrences of a variable is bounded by k and the number of terms satisfied by any assignment is at most j after motivating the investigation of this class of dnf formulas we present an algorithm that for any unknown rksj dnf formula to be learned with high probability finds a logically equivalent dnf formula using the well studied protocol of equivalence and membership queries the algorithm runs in polynomial time for k cdot j o log n over log log n where n is the number of input variables

logical analysis of binary data with missing bits we model a given pair of sets of positive and negative examples each of which may contain missing components as a partially defined boolean function with missing bits pbmb t f where email protected 0 1 n and email protected 0 1 n and stands for a missing bit then we consider the problem of establishing a boolean function an extension f 0 1 n 0 1 belonging to a given function class c such that f is true respectively false for every vector in t respectively in f this is a fundamental problem encountered in many areas such as learning theory pattern recognition example based knowledge bases logical analysis of data knowledge discovery and data mining in this paper depending upon how to deal with missing bits we formulate three types of extensions called robust consistent and most robust extensions for various classes of boolean functions such as general positive horn threshold decomposable and k dnf the complexity of the associated problems are then clarified some of them are solvable in polynomial time while the others are np hard

identification criteria and lower bounds for perceptron like learning rules perceptron like learning rules are known to require exponentially many correction steps in order to identify boolean threshold functions exactly we introduce criteria that are weaker than exact identification and investigate whether learning becomes significantly faster if exact identification is replaced by one of these criteria probably approximately correct pac identification order identification and sign identification pac identification is based on the learning paradigm introduced by valiant 1984 and is known to be easier than exact identification order identification uses the fact that each threshold function induces an ordering relation on the input variables that can be represented by weights of linear size sign identification is based on a property of threshold functions known as unateness and requires only weights of constant size we show that perceptron like learning rules cannot satisfy these criteria when the number of correction steps is to be bounded by a polynomial we also pre

how to construct random functions a constructive theory of randomness for functions based on computational complexity is developed and a pseudorandom function generator is presented this generator is a deterministic polynomial time algorithm that transforms pairs g r where g is any one way function and r is a random k bit string to polynomial time computable functions r 1 2 k 1 2 k these r s cannot be distinguished from random functions by any probabilistic polynomial time algorithm that asks and receives the value of a function at arguments of its choice the result has applications in cryptography random constructions and complexity theory

parameterized learnability of juntas we study the parameterized complexity of learning k juntas and some variations of juntas we show the hardness of learning k juntas and subclasses of k juntas in the pac model by reductions from a w 2 complete problem on the other hand as a consequence of a more general result we show that k juntas are exactly learnable with improper equivalence queries and access to a w p oracle

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

interpolation and approximation of sparse multivariate polynomials over gf 2 a function f 0 1 n to 0 1 is called t sparse if the n variable polynomial representation of f over gf 2 contains at most t monomials such functions are uniquely determined by their values at the so called critical set of all binary n tuples of hamming weight geqq n lfloor log 2 t rfloor 1 an algorithm is presented for interpolating any t sparse function f given the values of f at the critical set the time complexity of the proposed algorithm is proportional to n t and the size of the critical set then the more general problem of approximating 1 sparse functions is considered in which case the approximating function may differ from f at a fraction varepsilon of the space 0 1 n it is shown that o t varepsilon cdot n evaluation points are sufficient for the deterministic varepsilon approximation of any t sparse function and that an order t varepsilon alpha t varepsilon cdot log n points are necessary for this purpose wh

complexity of learning in artificial neural networks some basic issues in the statistical mechanics of learning from examples are reviewed the approach of statistical physics is contrasted with the analysis of learning within the framework of mathematical statistics and the question of the algorithmic complexity of explicit learning prescriptions is addressed even in very simple learning scenarios the typical properties of which can be analyzed in great quantitative detail by methods from statistical mechanics the determination of a suitable hypothesis approximating the target rule may be an np complete problem some special learning setups are suggested as model systems for the comparison between the approaches of statistical mechanics and computer science to the theory of computationally hard problems

inductive inference of approximations in this paper we investigate inductive inference identification criteria which permit infinitely many errors in explanations but which require that the density of these errors be no more than a certain prespectified amount we introduce three hierarchies of such criteria each of which has the same order type as the real unit interval these three hierarchies are progressively more strict in the way they measure density of errors of explanations the strictest of the three turns out to have all of its members save one incomparable to the identification criterion which permits finitely many errors in explanations

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

error free and best fit extensions of partially defined boolean functions abstract in this paper we address a fundamental problem related to the induction of boolean logic given a set of data represented as a set of binary truen vectors or positive examples and a set of falsen vectors or negative examples we establish a boolean function or an extension f so thatfis true resp false in every given true resp false vector we shall further require that such an extension belongs to a certain specified class of functions e g class of positive functions class of horn functions and so on the class of functions represents our a priori knowledge or hypothesis about the extensionf which may be obtained from experience or from the analysis of mechanisms that may or may not cause the phenomena under consideration the real world data may contain errors e g measurement and classification errors might come in when obtaining data or there may be some other influential factors not represented as variables in the vectors in such situations we have to give up the goal of establishing an extension that is perfectly consistent with the given data and we are satisfied with an extensionfhaving the minimum number of misclassifications both problems i e the problem of finding an extension within a specified class of boolean functions and the problem of finding a minimum error extension in that class will be extensively studied in this paper for certain classes we shall provide polynomial algorithms and for other cases we prove their np hardness

on the power of probabilistic strategies in inductive inference abstract inductive inference of programs of recursive functions from input output examples by probabilistic strategies with an a priori bound n n of changes of hypotheses is investigated advantages of probabilistic strategies over deterministic ones are shown concerning their power in principle for every n 2 with probability arbitrarily close to 1 inference of function classes which cannot be inferred by any deterministic strategy with n changes of hypotheses as well as their computational complexity linear speed up of the number of changes of hypotheses necessary for inference by deterministic strategies

theorie de lubin tate non abelienne ell entiere resume for two primes 6 p we investigate the z cohomology of the lubin tate towers of a p adic field we prove that it realizes some version of langlands and jacquet langlands correspondences for flat families of irreducible supercuspidal representations parametrized by a z algebra r in a way compatible with extension of scalars applied to r f this gives a cohomological realization of the langlands vigneras correspondence for supercuspidals and a new proof of its existence applied to complete local algebras this provides bijections between deformations of matching f representations besides we also get a virtual realization of both the semi simple langlands vigneras correspondence and the modular langlands jacquet transfer for all representations by using the cohomology complex and working in a suitable grothendieck group

knot segmentation in 3d ct images of wet wood this paper proposes a fully automatic method to segment wood knots from images obtained by an x ray computed tomography scanner wood knot segmentation is known to be a difficult problem in the presence of sapwood because of the quite similar density of knots and wet sapwood classical segmentation techniques produce unsatisfactory results due to the very weak distinction between these two intensities to overcome this limitation caused by physical characteristics we propose to exploit the geometric properties of both the knot shapes and knot sapwood interface based on previous work related to automatic knot detection a new segmentation algorithm is proposed that uses a robust curvature estimation of 2d digital contours the segmentation process is fast easily parallelizable and produces better segmentation results than other state of the art algorithms it may be reproduced from the precise description given here or from source code available online

learning curves of the clipped hebb rule for networks with binary weights networks with binary weights are very important from both the theoretical and practical points of view in this paper we investigate the clipped hebb rule for learning different networks of non overlapping binary perceptrons under uniform distribution we calculate exactly its learning curves in the limit of a large number of inputs where the average behaviour becomes the typical behaviour this calculation is performed using only very simple counting arguments and the central limit theorem the results indicate that the clipped hebb rule does indeed learn this class of networks in particular the generalization rates converge extremely rapidly often exponentially to perfect generalization these results are very encouraging given the simplicity of the learning rule the analytic expression of the learning curves are in excellent agreement with the numerical simulations

power watershed a unifying graph based optimization framework in this work we extend a common framework for graph based image segmentation that includes the graph cuts random walker and shortest path optimization algorithms viewing an image as a weighted graph these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework we then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm which we term the power watershed in particular when q 2 the power watershed leads to a multilabel scale and contrast invariant unique global optimum obtained in practice in quasi linear time placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation

comparison of identification criteria for machine inductive inference abstract a natural pl 1 hierarchy of successively more general criteria of success for inductive inference machines is described based on the size of sets of anomalies in programs synthesized by such machines these criteria are compared to others in the literature some of our results are interpreted as tradeoff results or as showing the inherent relative computational complexity of certain processes and others are interpreted from a positivistic mechanistic philosophical stance as theorems in philosophy of science the techniques of recursive function theory are employed including ordinary and infinitary recursion theorems

on learning perceptrons with binary weights we present an algorithm that pac learns any perceptron with binary weights and arbitrary threshold under the family of product distributions the sample complexity of this algorithm is of o n e 4 ln n and its running time increases only linearly with the number of training examples the algorithm does not try to find an hypothesis that agrees with all of the training examples rather it constructs a binary perceptron based on various probabilistic estimates obtained from the training examples we show that under the restricted case of the uniform distribution and zero threshold the algorithm reduces to the well known clipped hebb rule we calculate exactly the average generalization rate i e the learning curve of the algorithm under the uniform distribution in the limit of an infinite number of dimensions we find that the error rate decreases exponentially as a function of the number of training examples hence the average case analysis gives a sample complexity of o n ln 1 e a large improvement over the pac learning analysis the analytical expression of the learning curve is in excellent agreement with the extensive numerical simulations in addition the algorithm is very robust with respect to classification noise

fast identification of geometric objects with membership queries we investigate the number of membership queries that are needed to identify polygons i e intersections of halfplanes over a two dimensional grid 0 n 1 2 we exhibit a learning algorithm that learns 100 correctly while requiring no random examples and not more membership queries than previous algorithms needed in addition to their random examples for probably almost correctly learning even for moderate values of furthermore the learning algorithm in this paper uses only grid points for its membership queries this appears to be appropriate in situations where the probing device has only a limited resolution and for applications to the set of pixels on a two dimensional screen the learning algorithm that is described in this paper overcomes a fundamental obstacle related to the zigzag borderline that is generated by a halfplane over a discrete grid this obstacle had thwarted previous attempts to show that in angluin s model for on line learning with equivalence and membership queries one can learn in an efficient manner even those classes of geometric objects which cannot be learnt fast by equivalence queries alone such as rectangles in general position

cohomology of sheaves on the building and r representations this article contains four parts the subject of the first one is to compare open compact subgroups of a reductive connected group g over a local non archimedean field associated to certain natural concave functions by the theory of bruhat tits bt1 we compare the groups which appear in the theory of unrefined minimal types by moy and prasad mp1 mp2 with those which appear in the theory of complex sheaves on the building x by schneider and stuhler ss schneider and stuhler give to special vertices a predominant role hiding in this way some symetry that we restaure we need all vertices in particular we describe how the groups vary along a geodesic starting from any point in a discussion with kutzko and with schneider it appeared that there are in the literature two different definitions for an iwahori subgroup the connected and the non connected as i was not aware of this and as there are may be other definitions i include here the unique decomposition property for the possible iwahori subgroups this part is entirely geometric and is certainly trivial for someone who is familiar with the theory of bruhat and tits

a physicist s approach to number partitioning the statistical physics approach to the number partioning problem a classical np hard problem is both simple and rewarding very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase boundary that separates the easy to solve from the hard to solve phase of the npp as well as for the probability distributions of the optimal and sub optimal solutions in addition it can be shown that solving a number portioning problem of size n to some extent corresponds to locating the minimum in an unsorted list of o 2n numbers considering this correspondence it is not surprising that known heuristics for the partitioning problem are not signi4cantly better than simple random search

equivalence of models for polynomial learnability abstract in this paper we consider several variants of valiant s learnability model that have appeared in the literature we give conditions under which these models are equivalent in terms of the polynomially learnable concept classes they define these equivalences allow comparisons of most of the existing theorems in valiant style learnability and show that several simplifying assumptions on polynomial learning algorithms can be made without loss of generality we also give a useful reduction of learning problems to the problem of finding consistent hypotheses and give comparisons and equivalences between valiant s model and the prediction learning models of haussler littlestone and warmuth in 29th annual ieee symposium on foundations of computer science 1988

measuring teachability using variants of the teaching dimension in a typical algorithmic learning model a learner has to identify a target object from partial information conversely in a teaching model a teacher has to give information that allows the learners to identify a target object we devise two variants of the classical teaching model for boolean concept classes based on the teaching dimension and describe them by teaching dimension like combinatorial parameters in the first model the learners choose consistent hypotheses with least complexity we show that 1 decision lists are the harder to teach the longer they are and that 2 term dnfs are the harder to teach the more terms they have this contrasts with the teachability results for these classes in the teaching dimension model in our second model the learners choose consistent hypotheses based on the assumption that the teacher is optimal we show that monomials can be taught with a linear number of examples whereas some 1 decision lists need exponentially many

training a single sigmoidal neuron is hard we first present a brief survey of hardness results for training feedforward neural networks these results are then completed by the proof that the simplest architecture containing only a single neuron that applies a sigmoidal activation function r satisfying certain natural axioms e g the standard logistic sigmoid or saturated linear function to the weighted sum of n inputs is hard to train in particular the problem of finding the weights of such a unit that minimize the quadratic training error within 2 or its average over a training set within 5 2 12n of its infimum proves to be np hard hence the well known backpropagation learning algorithm appears not to be efficient even for one neuron which has negative consequences in constructive learning

watershed cuts minimum spanning forests and the drop of water principle we study the watersheds in edge weighted graphs we define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface we first establish the consistency of these watersheds they can be equivalently defined by their catchment basinsrdquo through a steepest descent property or by the dividing linesrdquo separating these catchment basins through the drop of water principle then we prove through an equivalence theorem their optimality in terms of minimum spanning forests afterward we introduce a linear time algorithm to compute them to the best of our knowledge similar properties are not verified in other frameworks and the proposed algorithm is the most efficient existing algorithm both in theory and in practice finally the defined concepts are illustrated in image segmentation leading to the conclusion that the proposed approach improves on the tested images the quality of watershed based segmentations

theorie de lubin tate non abelienne et representations elliptiques non abelian lubin tate theory studies the cohomology of some moduli spaces for p divisible groups the broadest definition of which is due to rapoport zink aiming both at providing explicit realizations of local langlands functoriality and at studying bad reduction of shimura varieties in this paper we consider the most famous examples the so called drinfeld and lubin tate towers in the lubin tate case harris and taylor proved that the supercuspidal part of the cohomology realizes both the local langlands and jacquet langlands correspondences as conjectured by carayol recently boyer computed the remaining part of the cohomology and exhibited two defects first the representations of gl d which appear are of a very particular and restrictive form second the langlands correspondence is not realized anymore in this paper we study the cohomology complex in a suitable equivariant derived category and show how it encodes langlands correspondence for elliptic representations then we transfer this result to the drinfeld tower via an enhancement of a theorem of faltings due to fargues we deduce that deligne s weight monodromy conjecture is true for varieties uniformized by drinfeld s coverings of his symmetric spaces this completes the computation of local l factors of some unitary shimura varieties

on the complexity of learning strings and sequences abstract it is shown that strings sequences cannot be learned by strings sequences in valiant s distribution free pac learning model assuming rp np

geometric approach to the local jacquet langlands correspondence in this paper we give a purely geometric approach to the local jacquet langlands correspondence for rm gl n over a p adic field under the assumption that the invariant of the division algebra is 1 n we use the ell adic etale cohomology of the drinfeld tower to construct the correspondence at the level of the grothendieck groups with rational coefficients moreover assuming that n is prime we prove that this correspondence preserves irreducible representations this gives a purely local proof of the local jacquet langlands correspondence in this case we need neither a global automorphic technique nor detailed classification of supercuspidal representations of rm gl n

version spaces and the consistency problem a version space is a collection of concepts consistent with a given set of positive and negative examples mitchell artificial intelligence 18 1982 203 226 proposed representing a version space by its boundary sets the maximally general g and maximally specific consistent concepts s for many simple concept classes the size of g and s is known to grow exponentially in the number of positive and negative examples this paper argues that previous work on alternative representations of version spaces has disguised the real question underlying version space reasoning we instead show that tractable reasoning with version spaces turns out to depend on the consistency problem i e determining if there is any concept consistent with a set of positive and negative examples indeed we show that tractable version space reasoning is possible if and only if there is an efficient algorithm for the consistency problem our observations give rise to new concept classes for which tractable version space reasoning is now possible e g 1 decision lists monotone depth two formulas and halfspaces

l espace symetrique de drinfeld et correspondance de langlands locale i we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

computational limitations on learning from examples the computational complexity of learning boolean concepts from examples is investigated it is shown for various classes of concept representations that these cannot be learned feasibly in a distribution free sense unless r np these classes include a disjunctions of two monomials b boolean threshold functions and c boolean formulas in which each variable occurs at most once relationships between learning of heuristics and finding approximate solutions to np hard optimization problems are given

on the cohomology of rapoport zink spaces of el type in this article we are interested in determining the l adic cohomology of rapoport zink spaces associated to rm gl n over an unramified extension of bbb q p called unramified el type in connection with the local langlands correspondence for rm gl n in fact we compute the alternating sum of certain representation theoretic functors defined in terms of their cohomology on the level of grothendieck groups in case rapoport zink spaces parametrize p divisible groups of dimension one the above alternating sum is determined by harris and taylor without the unramifiedness assumption for p divisible groups of rm dim 1 fargues has obtained an answer for the supercuspidal part when the p divisible groups are basic i e their associated newton polygons are straight lines our main result is an identity among the cohomology of rapoport zink spaces that appear in the newton stratification of the same unitary shimura variety our result implies a theorem of fargues providing a second proof and reveals new information about the cohomology of rapoport zink spaces for non basic p divisible groups we propose an inductive procedure to completely determine the above alternating sum assuming a strengthening of our main result along with a conjecture of harris