an arithmetic site for the rings of integers of algebraic number fields the study of extensions with prescribed ramification plays a central role in algebraic number theory it is a general hope to benefit from the analogy between number fields and function fields of trancendency degree 1 over finite fields because for the latter the situation is much better understood in this paper we introduce a new kind of restriction for the ramification of primes in extensions of algebraic number fields and we study the corresponding covering type over the ring of integers we will prove that the associated fundamental group has a description similar to that of the 6tale fundamental group of a smooth projective curve over a finite field let k be a number field p be a prime number and let s be a finite set of places of k containing all archimedian places and all places dividing p extensions of k which are unramified outside s correspond to ale covers of the open subscheme spec ox s of spec cx we denote the maximal pro p galois extension of k which is unramified outside s by ks p and we write

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

tests for high dimensional covariance matrices we propose tests for sphericity and identity of high dimensional covariance matrices the tests are nonparametric without assuming a specific parametric distribution for the data they can accommodate situations where the data dimension is much larger than the sample size namely the large p small n situations we demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes we applied the proposed test on a microarray dataset on yorkshire gilts and tested for the covariance structure for the expression levels for sets of genes

testing mutual independence in high dimension via distance covariance summary we introduce an l2 type test for testing mutual independence and banded dependence structure for high dimensional data the test is constructed on the basis of the pairwise distance covariance and it accounts for the non linear and non monotone dependences among the data which cannot be fully captured by the existing tests based on either pearson correlation or rank correlation our test can be conveniently implemented in practice as the limiting null distribution of the test statistic is shown to be standard normal it exhibits excellent finite sample performance in our simulation studies even when the sample size is small albeit the dimension is high and is shown to identify non linear dependence in empirical data analysis successfully on the theory side asymptotic normality of our test statistic is shown under quite mild moment assumptions and with little restriction on the growth rate of the dimension as a function of sample size as a demonstration of good power properties for our distance covariance based test we further show that an infeasible version of our test statistic has the rate optimality in the class of gaussian distributions with equal correlation

the almost equivalence of pairwise and mutual independence and the duality with exchangeability for a large collection of random variables in an ideal setting pairwise independence is shown to be almost equivalent to mutual independence an asymptotic interpretation of this fact shows the equivalence of asymptotic pairwise independence and asymptotic mutual independence for a triangular array or a sequence of random variables similar equivalence is also presented for uncorrelatedness and orthogonality as well as for the constancy of joint moment functions and exchangeability general unification of multiplicative properties for random variables are obtained the duality between independence and exchangeability is established through the random variables and sample functions in a process implications in other areas are also discussed which include a justification for the use of mutually independent random variables derived from sequential draws where the underlying population only satisfies a version of weak dependence macroscopic stability of some mass phenomena in economics is also characterized via almost mutual independence it is also pointed out that the unit interval can be used to index random variables in the ideal setting provided that it is endowed together with some sample space a suitable larger measure structure

distribution free tests of independence in high dimensions we consider the testing of mutual independence among all entries in a formula see text dimensional random vector based on formula see text independent observations we study two families of distribution free test statistics which include kendall s tau and spearman s rho as important examples we show that under the null hypothesis the test statistics of these two families converge weakly to gumbel distributions and we propose tests that control the type i error in the high dimensional setting where formula see text we further show that the two tests are rate optimal in terms of power against sparse alternatives and that they outperform competitors in simulations especially when formula see text is large

ein analogon zur fundamentalgruppe einer riemann schen flache im zahlkoperfall nach einem satz von grothendieck ist die struktur der maximalen zu f primen faktorgruppe der fundamentalgruppe einer glatten projektiven kurve 7 fiber einem algebraisch abgeschlossenen k6rer f der charakteristik e 0 explizit gegeben ffir die maximale pro p faktorgruppe fg p 4 f hat dies ergebnis zur folge dal3 ff eine demugkingruppe vom rang 2g ist wenn mit g das geschlecht von x bezeichnet wird genauer gibt es 2g erzeugende von mit der einzigen definierenden relation g

correlation tests and linear spectral statistics of the sample correlation matrix testing the independence of the entries of multidimensional gaussian observations is a very important problem in statistics with a number of applications in signal processing radar cognitive radio seismography and multiple other fields typically the problem is formulated as a binary hypothesis test whereby the presence of correlation is declared when the value of a certain statistic is higher than a certain predetermined threshold most of the statistics for correlation tests are constructed from the sample correlation matrix also known as sample coherence matrix in signal processing which is defined as a power normalized version of the sample covariance matrix in this paper correlation tests constructed from linear spectral statistics lss of the sample correlation matrix are analyzed under the asymptotic framework where both sample size and observation dimension become large but comparable in magnitude a central limit theorem clt is established on this class of statistics which is valid for generally correlated gaussian observations results show that lss asymptotically fluctuate as gaussian random variables under both the hypotheses with an asymptotic mean and variance that can be established for each particular test in particular this general clt can be used to establish the asymptotic behavior of two of the most important correlation test statistics namely the generalized likelihood ratio test and the frobenius norm test under both null and alternative hypotheses as a by product it is established that lss of sample covariance and sample correlation matrices have exactly the same first order behavior but quite different asymptotic fluctuations in the second order regime in both the cases the lss asymptotically behave as gaussian random variables although with quite different asymptotic means and variances

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

uber pro p fundamentalgruppen markierter arithmetischer kurven let k be a global field p an odd prime number dierent from char k and s t disjoint finite sets of primes of k let g t k p g k t p k be the galois group of the maximal p extension of k which is unramified outside s and completely split at t we prove the existence of a finite set of primes s0 which can be chosen disjoint from any given setm of dirichlet density zero such that the cohomology of g t s0 k p coincides with the etale cohomology of the associated marked arithmetic curve in particular cd g t s0 k p 2 furthermore we can choose s0 in such a way that k t s s0 p realizes the maximal p extension kp p of the local field kp for all p2 s s0 the cup product h 1 g t s0 k p fp h 1 g t s0 k p fp h 2 g t s0 k p fp is surjective and the decomposition groups of the primes in s establish a free product inside g t s0 k p this generalizes previous work of the author where similar results were shown in the case t under the restrictive assumption p cl k and p 2 k

dynamic across time measurement interpretation abstract incrementally maintaining a qualitative understanding of physical system behavior based on observations is crucial to tasks such as real time control monitoring and diagnosis this paper describes the datmi theory for interpretation tasks the key idea of datmi is to dynamically maintain a concise representation of the space of local and global interpretations across time that are consistent with the observations this representation has two key advantages first a set of possible interpretations is more useful than a single best candidate for many tasks such as conservative monitoring second this representation simplifies switching to alternative interpretations when data are faulty or incomplete domain specific knowledge about state and transition probabilities can be used to suggest the interpretation which is most likely domain specific knowledge about durations of states and paths of states can also be used to further constrain the interpretation space when no consistent interpretation exists faulty data hypotheses are generated and then tested by adjusting the interpretation space the datmi theory has been tested via implementation and we describe its performance on two examples

the kummerian property and maximal pro p galois groups abstract for a prime number p we give a new restriction on pro p groups g which are realizable as the maximal pro p galois group g f p for a field f containing a root of unity of order p this restriction arises from kummer theory and the structure of the maximal p radical extension of f we study it in the abstract context of pro p groups g with a continuous homomorphism g 1 p z p and characterize it cohomologically and in terms of 1 cocycles on g this is used to produce new examples of pro p groups which do not occur as maximal pro p galois groups of fields as above

higher massey products in the cohomology of mild pro p groups abstract translating results due to j labute into group cohomological language a schmidt proved that a finitely presented pro p group g is mild and hence of cohomological dimension cd g 2 if h 1 g f p u v as f p vector space and the cup product h 1 g f p h 1 g f p h 2 g f p maps u v surjectively onto h 2 g f p and is identically zero on v v this has led to important results in the study of p extensions of number fields with restricted ramification in particular in the case of tame ramification in this paper we extend labute s theory of mild pro p groups with respect to weighted zassenhaus filtrations and prove a generalization of the above result for higher massey products which allows to construct mild pro p groups with defining relations of arbitrary degree we apply these results to one relator pro p groups and obtain some new evidence of an open question due to serre

circular sets of prime numbers and p extensions of the rationals zusammenfassung sei p eine ungerade primzahl und s eine endliche menge von primzahlen kongruent 1 modulo p wir zeigen da die gruppe gs q p von kohomologischer dimension 2 ist wenn das verschlingungsdiagramm zu s und p einer gewissen technischen bedingung genaugt und wir zeigen da gs q p in diesen faallen eine dualitaatsgruppe ist au erdem untersuchen wir das zerlegungsverhalten von primstellen in der erweiterung qs p q und wir setzen die kohomologie von gs q p zur etalkohomolgie des schemas spec z is in beziehung schlie lich berechnen wir den dualisierenden modul abstract let p be an odd prime number and let s be a nite set of prime numbers congruent to 1 modulo p we prove that the group gs q p has cohomological dimension 2 if the linking diagram attached to s and p satis es a certain technical condition and we show that gs q p is a duality group in these cases furthermore we investigate the decomposition behaviour of primes in the extension qs p q and we relate the cohomology of gs q p to the etale cohomology of the scheme spec z i s finally we calculate the dualizing module

mild pro 2 groups and 2 extensions of q with restricted ramification abstract using the mixed lie algebras of lazard we extend the results of the first author on mild groups to the case p 2 in particular we show that for any finite set s 0 of odd rational primes we can find a finite set s of odd rational primes containing s 0 such that the galois group of the maximal 2 extension of q unramified outside s is mild we thus produce a projective system of such galois groups which converge to the maximal pro 2 quotient of the absolute galois group of q unramified at 2 and our results also allow results of alexander schmidt on pro p fundamental groups of marked arithmetic curves to be extended to the case p 2 over a global field which is either a function field of characteristic 2 or a totally imaginary number field