some downwards transfer properties for n2 construction d un modele de zermelo fraenkel axiome du choix zfc hypothese du continu generalise ou le cardinal aleph 2 possede des proprietes de transfert descendant

on the weak reflection principle the weak reflection principle for 2 or wrp 2 is the statement that every stationary subset of p 1 2 reflects to an uncountable ordinal in 2 the reflection principle for 2 or rp 2 is the statement that every stationary subset of p 1 2 reflects to an ordinal in 2 with cofinality 1 let be a supercompact cardinal and assume 2 then there exists a forcing poset p which collapses to become 2 and p wrp 2 rp 2 in this paper we will be concerned with reflection of stationary subsets of p 1 2 recall that for an uncountable ordinal a set s p 1 x x 1 is stationary if for any function f there is a set b in s which is closed under f let s p 1 2 be a stationary set we say that s reflects to where is an uncountable ordinal in 2 if s p 1 is stationary in p 1 the weak reflection principle for 2 or wrp 2 is the statement that for every stationary set s p 1 2 there is an uncountable ordinal in 2 such that s reflects to this principle is a special case of the stronger weak reflection principle introduced in 1 the statement wrp 2 has a number of interesting combinatorial consequences including 2 2 4 6 2 7 and every stationary subset of 2 cof reflects to an ordinal in 2 with cofinality 1 a related principle is the reflection principle for 2 or rp 2 which asserts that every stationary subset of p 1 2 reflects to an ordinal in 2 with cofinality 1 the standard models for obtaining wrp 2 for example by levy collapsing a large cardinal to become 2 all satisfy rp 2 also it tends to be easier to work with rp 2 than with wrp 2 thus it is a natural question and one which has been open for some time whether wrp 2 implies rp 2 a standard argument shows that if a holds for every stationary set a 2 cof then for any stationary set s p 1 2 there is a stationary set t s which does not reflect to any uncountable ordinal in 2 with cofinality so assuming the existence of such diamonds wrp 2 implies rp 2 classically the existence of such diamonds were known to follow from gch more recently shelah 5 has proven they are a consequence of 21 2 thus assuming 21 2 wrp 2 implies rp 2 originally this result was proven in 2 by a different argument the weak reflection principle for 2 is equiconsistent with a weakly compact cardinal however sakai 3 has shown that a kind of local reflection is consistent from zfc specifically assuming gch and 1 there is a generic extension in which there exists a stationary set s p 1 2 such that every stationary subset of s reflects to an uncountable ordinal in 2 with cofinality date february 2010 2000 mathematics subject classification primary 03e35 secondary 03e05

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

asymptotically minimum variance second order estimation for noncircular signals with application to doa estimation this paper addresses asymptotically minimum variance amv algorithms within the class of algorithms based on second order statistics for estimating direction of arrival doa parameters of possibly spatially correlated even coherent narrowband noncircular sources impinging on arbitrary array structures to reduce the computational complexity due to the nonlinear minimization required by the matching approach the covariance matching estimation technique comet is included in the algorithm numerical examples illustrate the performance of the amv algorithm

efficient modularity density heuristics for large graphs abstract modularity density maximization is a community detection optimization problem which improves the resolution limit degeneracy of modularity maximization this paper presents seven scalable heuristics for modularity density and compares them with literature results from exact mixed integer linear programming and gaod imeme net hain and bmd heuristics the results are also compared with cnm and louvain which are scalable heuristics for modularity maximization the results suggest that our seven heuristics are faster than gaod imeme net hain and bmd modularity density heuristics our experiments also show that some of our heuristics surpassed the objective function value reported by imeme net hain and bmd for some real graphs our seven heuristics were tested with real graphs from the stanford large network dataset collection and the experiments show that they are scalable this feature was confirmed by an amortized complexity analysis which reveals average linear time for three of our heuristics hypothesis tests suggest that four proposed heuristics are state of the art since they are scalable for hundreds of thousands of nodes for the modularity density problem and they find the high objective value partitions for the largest instances ground truth experiments in artificial random graphs were performed and suggest that our heuristics lead to better cluster detection than both cnm and louvain

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

performance limits of alphabet diversities for fir siso channel identification finite impulse responses fir of single input single output siso channels can be blindly identified from second order statistics of transformed data for instance when the channel is excited by binary phase shift keying bpsk minimum shift keying msk or quadrature phase shift keying qpsk inputs identifiability conditions are derived by considering that noncircularity induces diversity theoretical performance issues are addressed to evaluate the robustness of standard subspace based estimators with respect to these identifiability conditions then benchmarks such as asymptotically minimum variance amv bounds based on various statistics are presented some illustrative examples are eventually given where monte carlo experiments are compared to theoretical performances these comparisons allow to quantify limits to the use of the alphabet diversities for the identification of fir siso channels and to demonstrate the robustness of algorithms based on high order statistics

age related changes in modular organization of human brain functional networks graph theory allows us to quantify any complex system e g in social sciences biology or technology that can be abstractly described as a set of nodes and links here we derived human brain functional networks from fmri measurements of endogenous low frequency correlated oscillations in 90 cortical and subcortical regions for two groups of healthy young and older participants we investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks newman s modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra and inter modular connectivity both young and older brain networks demonstrated significantly non random modularity the young brain network was decomposed into 3 major modules central and posterior modules which comprised mainly nodes with few inter modular connections and a dorsal fronto cingulo parietal module which comprised mainly nodes with extensive inter modular connections the mean network in the older group also included posterior superior central and dorsal fronto striato thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced whereas the number of connector nodes in posterior and central modules was increased

community detection in networks with positive and negative links detecting communities in complex networks accurately is a prime challenge preceding further analyses of network characteristics and dynamics until now community detection took into account only positively valued links while many actual networks also feature negative links we extend an existing potts model to incorporate negative links as well resulting in a method similar to the clustering of signed graphs as dealt with in social balance theory but more general to illustrate our method we applied it to a network of international alliances and disputes using data from 1993 2001 it turns out that the world can be divided into six power blocs similar to huntington s civilizations with some notable exceptions

fluctuations between high and low modularity topology in time resolved functional connectivity modularity is an important topological attribute for functional brain networks recent human fmri studies have reported that modularity of functional networks varies not only across individuals being related to demographics and cognitive performance but also within individuals co occurring with fluctuations in network properties of functional connectivity estimated over short time intervals however characteristics of these time resolved functional networks during periods of high and low modularity have remained largely unexplored in this study we investigate basic spatiotemporal properties of time resolved networks in the high and low modularity periods during rest with a particular focus on their spatial connectivity patterns temporal homogeneity and test retest reliability we show that spatial connectivity patterns of time resolved networks in the high and low modularity periods are represented by increased and decreased dissociation of the default mode network module from task positive network modules respectively we also find that the instances of time resolved functional connectivity sampled from within the high respectively low modularity period are relatively homogeneous respectively heterogeneous over time indicating that during the low modularity period the default mode network interacts with other networks in a variable manner we confirmed that the occurrence of the high and low modularity periods varies across individuals with moderate inter session test retest reliability and that it is correlated with previously reported individual differences in the modularity of functional connectivity estimated over longer timescales our findings illustrate how time resolved functional networks are spatiotemporally organized during periods of high and low modularity allowing one to trace individual differences in long timescale modularity to the variable occurrence of network configurations at shorter timescales

martin s maximum saturated ideals and non regular ultrafilters part ii we prove assuming the existence of a huge cardinal the consistency of fully non regular ultrafilters on the successor of any regular cardinal we also construct ultrafilters with ultraproducts of small cardinality part ii is logically independent of part i

effects of lesions on synchrony and metastability in cortical networks at the macroscopic scale the human brain can be described as a complex network of white matter tracts integrating grey matter assemblies the human connectome the structure of the connectome which is often described using graph theoretic approaches can be used to model macroscopic brain function at low computational cost here we use the kuramoto model of coupled oscillators with time delays calibrated with respect to empirical functional mri data to study the relation between the structure of the connectome and two aspects of functional brain dynamics synchrony a measure of general coherence and metastability a measure of dynamical flexibility specifically we investigate the relationship between the local structure of the connectome quantified using graph theory and the synchrony and metastability of the model s dynamics by removing individual nodes and all of their connections from the model we study the effect of lesions on both global and local dynamics of the nine nodal graph theoretical properties tested two were able to predict effects of node lesion on the global dynamics the removal of nodes with high eigenvector centrality leads to decreases in global synchrony and increases in global metastability as does the removal of hub nodes joining topologically segregated network modules at the level of local dynamics in the neighbourhood of the lesioned node structural properties of the lesioned nodes hold more predictive power as five nodal graph theoretical measures are related to changes in local dynamics following node lesions we discuss these results in the context of empirical studies of stroke and functional brain dynamics

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

tolerating the community detection resolution limit with edge weighting communities of vertices within a giant network such as the world wide web are likely to be vastly smaller than the network itself however fortunato and barthelemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than l 2 edges where l is the number of edges in the entire network this resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks fortunato and barthelemy s argument can be extended to networks with weighted edges as well and we derive this corollary argument we conclude that weighted modularity algorithms may fail to resolve communities with less than we 2 total edge weight where w is the total edge weight in the network and e is the maximum weight of an intercommunity edge if e is small then small communities can be resolved given a weighted or unweighted network we describe how to derive new edge weights in order to achieve a low e we modify the clauset newman and moore cnm community detection algorithm to maximize weighted modularity and we show that the resulting algorithm has greatly improved accuracy in experiments with an emerging community standard benchmark we find that our simple cnm variant is competitive with the most accurate community detection methods yet proposed

weight conserving characterization of complex functional brain networks complex functional brain networks are large networks of brain regions and functional brain connections statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures important functional network measures include measures of modularity measures of the goodness with which a network is optimally partitioned into functional subgroups and measures of centrality measures of the functional influence of individual brain regions characterizations of functional networks are increasing in popularity but are associated with several important methodological problems these problems include the inability to characterize densely connected and weighted functional networks the neglect of degenerate topologically distinct high modularity partitions of these networks and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties in this study we describe a set of methods to overcome these problems specifically we generalize measures of modularity and centrality to fully connected and weighted complex networks describe the detection of degenerate high modularity partitions of these networks and introduce a weighted connectivity null model of these networks we illustrate our methods by demonstrating degenerate high modularity partitions and strong correlations between two complementary measures of centrality in resting state functional magnetic resonance imaging mri networks from the 1000 functional connectomes project an open access repository of resting state functional mri datasets our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects

smoke and mirrors combinatorial properties of small cardinals equiconsistent with huge cardinals abstract since the work of godel and cohen many questions in infinite combinatorics have been shown to be independent of the usual axioms for mathematics zermelo frankel set theory with the axiom of choice zfc attempts to strengthen the axioms to settle these problems have converged on a system of principles collectively known as large cardinal axioms these principles are linearly ordered in terms of consistency strength as far as is currently known all natural independent combinatorial statements are equiconsistent with some large cardinal axiom the standard techniques for showing this use forcing in one direction and inner model theory in the other direction the conspicuous open problems that remain are suspected to involve combinatorial principles much stronger than the large cardinals for which there is a current fine structural inner model theory for the main results in this paper show that many standard constructions give objects with combinatorial properties that are in turn strong enough to show the existence of models with large cardinals are larger than any cardinal for which there is a standard inner model theory

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

modularity from fluctuations in random graphs and complex networks the mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection we show that finding the modularity of a network is analogous to finding the ground state energy of a spin system moreover we demonstrate that due to fluctuations stochastic network models give rise to modular networks specifically we show both numerically and analytically that random graphs and scale free networks have modularity we argue that this fact must be taken into consideration to define statistically significant modularity in complex networks

mazur intersection property for asplund spaces abstract the main result of the present note states that it is consistent with the zfc axioms of set theory relying on martin s maximum mm axiom that every asplund space of density character 1 has a renorming with the mazur intersection property combined with the previous result of jimenez and moreno based upon the work of kunen under the continuum hypothesis we obtain that the mip renormability of asplund spaces of density 1 is undecidable in zfc

two consequences of determinacy consistent with choice we begin with a ground model satisfying zf ad acr and from it construct a generic extension satisfying zfc 6 c2 the nonstationary ideal on coi is co2 saturated 0 introduction the axiom of determinacy henceforth ad implies many interesting propositions about small cardinal numbers for example c and o2 it is natural to ask whether these propositions are true or more realistically can be true in the full universe v of sets our working hypothesis is that in v the axiom of choice is true and all definable games are determined so the question becomes whether these propositions are consistent with zfc together with definable determinacy we shall be vague about definable when we can afford to in this paper we shall consider two such consequences of ad the first being that 2i w2 and the second that the nonstationary ideal on xl is o2 saturated we shall show that the theory consisting of zfc adl r together with these two propositions is consistent adl r is the assertion that all games in l r a large class of definable games are deterniined in consonance with our working hypothesis we would like to prove our result assuming only the consistency of zfc adl r or equivalently that of zf ad dc cf 1 at present we cannot do this we instead assume the consistency of zf ad acr where acr is the axiom of choice for families indexed by the reals consistency wise zf ad acr is one of the strongest theories known to man we show in 1 that it proves the consistency of zf ad dc the only upper bound we know on the consistency strength of zf ad acr is that of zf adr 0 is regular we offer some partial justification for our use of such a strong hypothesis at the end of the paper our consistency proof is by forcing we start with a ground model m satisfying zf ac acr by a two step iteration we construct a generic extension m g onto so that 3h h 2 rm the forcing will add no new reals and preserve co2 i e rm rm g and m 1m g we then pass to the inner model n l rm h and show it has the desired properties the paper is organized as follows in 1 we give some preliminaries and background information in particular we set forth those consequences of ad whose received by the editors february 18 1980 1980 mathematics subject classification primary 03e35 secondary 03e60 1 982 american mathematical society 0002 9947 8 1 001000 05 75

statistical parametric network analysis of functional connectivity dynamics during a working memory task abstract network analysis has become a tool of choice for the study of functional and structural magnetic resonance imaging mri data little research however has investigated connectivity dynamics in relation to varying cognitive load in fmri correlations among slow

extension of the matrix bartlett s formula to the third and fourth order and to noisy linear models with application to parameter estimation this paper focuses on the extension of the asymptotic covariance of the sample covariance denoted bartlett s formula of linear processes to thirdand fourth order sample cumulant and to noisy linear processes closed form expressions of the asymptotic covariance and cross covariance of the sample second third and fourth order cumulants are derived in a relatively straightforward manner thanks to a matrix polyspectral representation and a symbolic calculus akin to a high level language as an application of these extended formulae we underscore the sensitivity of the asymptotic performance of estimated arma parameters by an arbitrary third or fourth order based algorithm with respect to the signal to noise ratio the spectra of the linear process and the colored additive noise

new results on fir system identification using higher order statistics the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is considered the system is driven by an i i d independent and identically distributed non gaussian sequence that is not observed the noise is additive and may be colored and non gaussian re parametrization of an existing linear method and a modification to it are discussed simulation results show a distinct improvement in the numerical conditioning of both the reparametrized algorithm and its modification for the noisefree case for the case of i i d noise the reparametrized algorithm shows a marked degradation in performance whereas its modification degrades far more gracefully

a study of analysis parameters that influence the sensitivity of event related fmri analyses to assess the effect of various analysis parameters on the sensitivity of event related fmri analyses 36 analyses were performed on a single fmri data set varying parameters along four axes 1 resampled voxel size 2 spatial smoothing 3 temporal smoothing and 4 the set of basis functions used to model event related responses sensitivity i e the probability of detecting an activation given it exists was assessed in terms of z scores and by a metric for corrected p values the negative log of the expected euler characteristic sixteen brain regions distributed across cortical and subcortical areas were included in the meta analysis main effects on sensitivity were found for resampled voxel size spatial smoothing temporal smoothing and the set of basis functions chosen the analysis parameters that generally produced the most sensitive analyses were a 2 mm 3 resampled voxel size 10 mm spatial smoothing 4 s temporal smoothing and a basis set comprising a hemodynamic response function and its temporal derivative r 2000 academic press

forcing axioms and the continuum hypothesis woodin has demonstrated that in the presence of large cardinals there is a single model of zfc which is maximal for 2 sentences over the structure h 2 ns 1 in the sense that its h 2 ns 1 satisfies every 2 sentence for which h 2 ns 1 can be forced by set forcing in this paper we answer a question of woodin by showing that there are two 2 sentences over the structure h 2 1 which can each be forced to hold along with the continuum hypothesis but whose conjunction implies 2 aleph 0 2 aleph 1 in the process we establish that there are two preservation theorems for not introducing new real numbers by a countable support iterated forcing which cannot be subsumed into a single preservation theorem

modular structure of functional networks in olfactory memory graph theory enables the study of systems by describing those systems as a set of nodes and edges graph theory has been widely applied to characterize the overall structure of data sets in the social technological and biological sciences including neuroscience modular structure decomposition enables the definition of sub networks whose components are gathered in the same module and work together closely while working weakly with components from other modules this processing is of interest for studying memory a cognitive process that is widely distributed we propose a new method to identify modular structure in task related functional magnetic resonance imaging fmri networks the modular structure was obtained directly from correlation coefficients and thus retained information about both signs and weights the method was applied to functional data acquired during a yes no odor recognition memory task performed by young and elderly adults four response categories were explored correct hit and incorrect false alarm fa recognition and correct and incorrect rejection we extracted time series data for 36 areas as a function of response categories and age groups and calculated condition based weighted correlation matrices overall condition based modular partitions were more homogeneous in young than elderly subjects using partition similarity based statistics and a posteriori statistical analyses we demonstrated that several areas including the hippocampus caudate nucleus and anterior cingulate gyrus belonged to the same module more frequently during hit than during all other conditions modularity values were negatively correlated with memory scores in the hit condition and positively correlated with bias scores liberal conservative attitude in the hit and fa conditions we further demonstrated that the proportion of positive and negative links between areas of different modules i e the proportion of correlated and anti correlated areas accounted for most of the observed differences in signed modularity taken together our results provided some evidence that the neural networks involved in odor recognition memory are organized into modules and that these modular partitions are linked to behavioral performance and individual strategies

fir system identification using higher order statistics alone this paper focuses on fir system identification in gaussian arma noise using higher order cumulants alone two new types of cumulant based normal equations are established and two algorithms are proposed for ma parameter estimation simulations verify the high performance of the new developments

perfect set properties inl r u abstract we study perfect set properties in the modell r u whenl r is elementarily equivalent to a solovay model anduis a selective ultrafilter on the integers generic overl r

forcing axioms and stationary sets is stationary in general if x is any class of posets the forcing axioms xfa and xfa are obtained by replacing semi proper ly by 9 e x in the above definitions sometimes we denote these axioms by fa x and fa x thus for example fa ccc is the familiar martin s axiom man the notion of semi proper as an extension of a previous notion of proper was defined and extensively studied by shelah in shl j these forcing notions generalize ccc and countably closed forcing and can be iterated without collapsing n spfa is implicit in shl as an obvious strengthening of the proper forcing axiom pfa previously formulated and proved consistent by baumgartner see bal del pfa had settled many combinatorial questions on the uncountable and spfa was not

topological applications of generic huge embeddings in the foreman laver model obtained by huge cardinal collapse for many p ni implies ofi there are a variety of set theoretic and topo logical applications in particular to paracompactness the key tools are generic huge embeddings and preservation via k centred forcing we also formulate potent axioms a la foreman which enable us to transfer from n to all car dinals one such axiom implies that all n collectionwise normal moore spaces are metrizable it also implies as does martin s maximum that a first count able generalized ordered space is hereditarily paracompact iff every subspace of size ki is paracompact assuming the consistency of a huge cardinal foreman and laver fl con struct a model of zfc gch in which as they put it n2 possesses some downwards transfer properties for example in their model every graph of size and chromatic number n2 has a vertex induced subgraph of size and chro matic number ki and groups of size n2 are the union of ni free subgroups if all their subgroups of size ni are free we shall establish in their model a variety of such transfer propositions in a topological context actually we think of taking properties holding at ni and transferring them to n2 the method of proof is to use an elementary embedding with strong closure properties de finable in an ni centred k2 closed forcing extension of the model to perform the transfer and then argue that the forcing could not have accomplished the transfer unless it already held it is natural to generalize this idea to trans fer from n to other cardinals it is not known at present how to accomplish this from the usual large cardinals so we proceed axiomatically in the style of fo3 our results impinge on a number of areas of set theoretic topology but the most interesting ones deal with paracompactness e g the one mentioned in the abstract the techniques however are widely applicable as can be seen not only from our results on trees and ideals but from those of foreman and laver quoted above the paper is organized as follows we state the basic features of the foreman laver model and use them to go from ni to n2 next we present a variety of counterexamples to show our results do not hold in zfc we then introduce axioms that enable us to transfer from ni to arbitrary cardinals we finish with some results proved from supercompact cardinals and then a list of problems