small groups of finite morley rank with involutions by analogy with thompson s classification of nonsolvable finite n groups we classify groups of finite morley rank with solvable local subgroups of even and mixed type we also consider several aspects reminiscent of small groups of finite morley rank of odd type

importance sampling for estimating exact probabilities in permutational inference abstract this article discusses importance sampling as an alternative to conventional monte carlo sampling for estimating exact significance levels in a broad class of two sample tests including all of the linear rank tests with or without censoring homogeneity tests based on the chi squared hypergeometric and likelihood ratio statistics the mantel haenszel trend test and zelen s test for a common odds ratio in several 2 2 contingency tables inference is based on randomly selecting 2 k contingency tables from a reference set of all such tables with fixed marginals through a network algorithm the tables are selected in proportion to their importance for reducing the variance of the estimated monte carlo p value spectacular gains up to four orders of magnitude are achieved relative to conventional monte carlo sampling the technique is illustrated on four real data sets

rigorous inequalities between length and time scales in glassy systems glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order it is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length we prove rigorous bounds between length and time scales implying the growth of a properly defined length when the relaxation time increases our results are valid in a rather general setting which covers finite dimensional and mean field systems as an illustration we discuss the glauber heat bath dynamics of p spin glass models on random regular graphs we present the first proof that a model of this type undergoes a purely dynamical phase transition not accompanied by any thermodynamic singularity

exact nonparametric inference when doses are measured with random errors studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose if the doses are measured with error then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response if one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0 that is the dose errors are pure errors and not say systematic underreporting of exposure then the presence of zero dose controls is all that is needed to obtain exact distribution free confidence intervals and tests and consistent point estimates the method is simpler for matched pairs than for matched sets with two or more matched subjects and it is illustrated using two studies one of each kind with matched pairs as in this first example the method uses wilcoxon s signed rank test as the basis for inference when there are several zero dos

solvable groups of finite morley rank abstract we prove the following theorem the commutator subgroup of a solvable connected group of finite morley rank is nilpotent

on inverting permutation tests abstract polynomial time algorithms are presented for inverting permutation tests the one sample permutation test is inverted to make confidence statements about a location parameter and the two sample permutation test is inverted to make confidence statements concerning a shift in location or scale these algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time a computational method for the inversion of rank tests is also suggested the algorithms extend to stratified experiments

depletion potentials in highly size asymmetric binary hard sphere mixtures comparison of simulation results with theory we report a detailed study using state of the art simulation and theoretical methods of the effective depletion potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres the size disparity being measured by the ratio of diameters q ensuremath equiv ensuremath sigma s ensuremath sigma b small particles are treated grand canonically their influence being parameterized in terms of their packing fraction in the reservoir ensuremath eta s r two monte carlo simulation schemes the geometrical cluster algorithm and staged particle insertion are deployed to obtain accurate depletion potentials for a number of combinations of q ensuremath leqslant 0 1 and ensuremath eta s r after applying corrections for simulation finite size effects the depletion potentials are compared with the prediction of new density functional theory dft calculations based on the insertion trick using the rosenfeld functional and several subsequent modifications while agreement between the dft and simulation is generally good significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods namely ensuremath eta s r 0 35 these discrepancies are however small compared to those between simulation and the much poorer predictions of the derjaguin approximation at this ensuremath eta s r the recently proposed morphometric approximation performs better than derjaguin but is somewhat poorer than dft for the size ratios and small sphere packing fractions that we consider the effective potentials from simulation dft and the morphometric approximation were used to compute the second virial coefficient b 2 as a function of ensuremath eta s r comparison of the results enables an assessment of the extent to which dft can be expected to correctly predict the propensity toward fluid fluid phase separation in additive binary hard sphere mixtures with q ensuremath leqslant 0 1 in all the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size asymmetric mixtures

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

efficient monte carlo methods for conditional logistic regression abstract exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the remaining nuisance parameters despite the availability of fast numerical algorithms for the exact computations there are numerous instances where a data set is too large to be analyzed by the exact methods yet too sparse or unbalanced for the maximum likelihood approach to be reliable what is needed is a monte carlo alternative to the exact conditional approach which can bridge the gap between the exact and asymptotic methods of inference the problem is technically hard because conventional monte carlo methods lead to massive rejection of samples that do not satisfy the linear integer constraints of the conditional distribution we propose a network sampling approach to the monte carlo problem that eliminates rejection entirely its advantages over alternative saddlepoint

groupes de rang de morley fini de type pair avec un sous groupe faiblement inclus resume we show that a minimal counterexample to the cherlin zil ber conjecture of even type and with a weakly embedded subgroup is isomorphic to psl 2 k where k is an algebraically closed field of characteristic 2

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

exact logistic regression theory and examples we provide an alternative to the maximum likelihood method for making inferences about the parameters of the logistic regression model the method is based appropriate permutational distributions of sufficient statistics it is useful for analysing small or unbalanced binary data with covariates it also applies to small sample clustered binary data we illustrate the method by analysing several biomedical data sets

class of consistent fundamental measure free energies for hard sphere mixtures in fundamental measure theories the bulk excess free energy density of a hard sphere fluid mixture is assumed to depend on the partial number densities i only through the four scaled particle theory variables i e i by imposing consistency conditions it is proven here that such a dependence must necessarily have the form 0 ln 1 3 y 1 2 1 3 where y 2 2 12 1 1 3 is a scaled variable and y is an arbitrary dimensionless scaling function which can be determined from the free energy density of the one component system extension to the inhomogeneous case is achieved by standard replacements of the variables by the fundamental measure scalar vector and tensor weighted densities n r comparison with computer simulations shows the superiority of this bulk free energy over the white bear one

hard sphere fluids in contact with curved substrates the properties of a hard sphere fluid in contact with hard spherical and cylindrical walls are studied rosenfeld s density functional theory dft is applied to determine the density profile and surface tension gamma for wide ranges of radii of the curved walls and densities of the hard sphere fluid particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to gamma which is proportional to the logarithm of the radius of curvature moreover by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard sphere fluid close to arbitrary hard convex walls the agreement between the analytical expression and dft is good our results show no signs for the existence of a logarithmic term in the curvature dependence of gamma

permutation distributions via generating functions with applications to sensitivity analysis of discrete data abstract generating functions provide a simple and elegant way to describe probability or frequency distributions of discrete statistics and in particular permutation distributions they are also a computational tool many efficient algorithms including those described as fast fourier transform methods network methods and multiple shift methods are different implementations of the recursions needed to evaluate generating functions efficiently our goals here are twofold first we make the relationship between these efficient methods and generating functions explicit this establishes a language for looking at other questions in randomization exact inference and may help in finding more efficient implementations second we propose methods to examine the sensitivity of results of exact analysis of discrete data to small perturbations in the data specifically we consider two settings how the analysis would change if one outcome changed and how the analysis would change if one observation was adde

the classical involution theorem for groups of finite morley rank abstract this paper gives a partial answer to the cherlin zil ber conjecture which states that every infinite simple group of finite morley rank is isomorphic to an algebraic group over an algebraically closed field the classification of the generic case of tame groups of odd type follows from the main result of this work which is an analogue of aschbacher s classical involution theorem for finite simple groups

statistical mechanics of a fluid drop we obtain a statistical mechanical expression for the surface tension of a drop involving the direct correlation function by extending the work on the planar liquid vapour interface both from the fluctuation theory approach of triezenburg zwanzig phys rev lett 28 1183 1972 and from the method of wertheim j chem phys 65 2377 1976 based on a spectral analysis of the density density correlation function the result does not apply beyond the leading order difference from the planar limit

on obtaining permutation distributions in polynomial time abstract polynomial time algorithms are presented for finding the permutation distribution of any statistic that is a linear combination of some function of either the original observations or the ranks this class of statistics includes the original fisher two sample location statistic and such common nonparametric statistics as the wilcoxon ansari bradley savage and many others the algorithms are presented for the two sample problem and it is shown how to extend them to the multisample problem for example to find the distribution of the kruskal wallis and other extensions of the wilcoxon and to the single sample situation stratification ties and censored observations are also easily handled by the algorithms the algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time this savings is effected by first calculating and then inverting the characteristic function of the statistic

on solvable groups of finite morley rank we investigate solvable groups of finite morley rank we find conditions on g for g to split in g in particular if g is abelian and z g 1 we prove that g g t for some t and the ring z t anng is intepretable in g we exploit the methods used in proving these results to find more information about solvable groups

phase diagram of highly asymmetric binary hard sphere mixtures we study the phase behavior and structure of highly asymmetric binary hard sphere mixtures by first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective hamiltonian of the large spheres then using an explicit pairwise depletion potential approximation to this effective hamiltonian in computer simulations we determine fluid solid coexistence for size ratios q 0 033 0 05 0 1 0 2 and 1 0 the resulting two phase region becomes very broad in packing fractions of the large spheres as q becomes very small we find a stable isostructural solid solid transition for ql 0 05 and a fluid fluid transition for ql 0 10 however the latter remains metastable with respect to the fluid solid transition for all size ratios we investigate in the limit stackrel ensuremath rightarrow q 0 the phase diagram mimics that of the sticky sphere system as expected the radial distribution function g r and the structure factor s k of the effective one component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid solid boundary the value of s k at its first peak is much lower than the value given by the hansen verlet freezing criterion direct simulations of the true binary mixture of hard spheres were performed for qg 0 05 in order to test the predictions from the effective hamiltonian for those packing fractions of the small spheres where direct simulations are possible we find remarkably good agreement between the phase boundaries calculated from the two approaches even up to the symmetric limit q 1 and for very high packings of the large spheres where the solid solid transition occurs in both limits one might expect that an approximation which neglects higher body terms should fail but our results support the notion that the main features of the phase equilibria of asymmetric binary hard sphere mixtures are accounted for by the effective pairwise depletion potential description we also compare our results with those of other theoretical treatments and experiments on colloidal hard sphere mixtures

tame minimal simple groups of finite morley rank abstract we consider tame minimal simple groups of finite morley rank and of odd type we show that the prufer 2 rank of such a group is bounded by 2 we also find all potential nonalgebraic configurations there are essentially four of them and we delineate them with some precision

structure des groupes lineaires definissables dans un corps de rang de morley fini we generalize several properties of linear algebraic groups to the case of the linear groups which are defined in a field of finite morley rank we show three structure theorems and the conjugacy of the borels of the carter subgroups of the maximal tori in conclusion we generalize the results to fields of morley rank n without subgroups of finite rank in contrary to the case of finite morley rank there are known examples of such fields with definable non algebraic subgroups of gln k

signalizers and balance in groups of finite morley rank abstract there is a longstanding conjecture due to gregory cherlin and boris zilber that all simple groups of finite morley rank are simple algebraic groups the most successful approach to this conjecture has been borovik s program analyzing a minimal counterexample or simple k group we show that a simple k group of finite morley rank and odd type is either algebraic of else has prufer rank at most two this result signifies a switch from the general methods used to handle large groups to the specilized methods which must be used to identify psl 2 psl 3 psp 4 and g 2

many body correlations from integral geometry in a recent letter we presented a framework for predicting the concentrations of many particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest central to this framework was the morphometric approach a synthesis of integral geometry and liquid state theory which has traditionally been derived from fundamental measure theory we present the morphometric approach in a new context as a generalization of scaled particle theory and we derive several morphometric theories for hard spheres of fundamental and practical interest our central result is a new theory that is particularly suited to the treatment of many body correlation functions in the hard sphere liquid which we demonstrate by numerical tests against simulation

an algorithm for exact logistic regression abstract an efficient algorithm is given for the exact logistic analysis of a single parameter hypothesis tests and confidence intervals for a logistic regression parameter are obtained the method provides for the control of the effect of a stratification factor when making inferences concerning the regression parameter

allocation of effort in monte carlo simulation for power of permutation tests abstract consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample if the power of such a test is investigated by simulation the computer code must have two main loops in the outer loop which has o iterations data are generated under a specific alternative hypothesis for each outer iteration there are i inner iterations in each of which the data are permuted and the statistic calculated assume that the costs of inner and outer iterations are known and the total cost of the study is fixed so that i and o are constrained by o io for fixed this article considers what the optimal choice for i is in a mean squared sense a general expression is derived for the mean squared error of the distribution of p values if the alternative hypothesis is close to the null the optimal c

groups of mixed type the cherlin zil ber conjecture states that an infinite simple group of finite morley rank is an algebraic group over an algebraically closed field the proofs of the following three conjectures would provide a proof of the cherlin zil ber conjecture conjecture 1 there exist no nonsolvable connected groups of finite morley rank all of whose proper definable connected subgroups are nilpotent such groups are called bad groups 2 conjecture 2 there exists no structure k q a of finite morley rank where k is an algebraically closed field and a is an infinite proper definable subgroup of the multiplicative group of k such structures are called bad fields

on groups of finite morley rank with weakly embedded subgroups the present paper is a contribution to the classification of tame stable groups of finite morley rank a group of finite morley rank is called tame if it involves no bad groups and no bad fields in the sense of 1 see also 1 it is conjectured that an infinite simple tame group of finite morley rank is isomorphic to an algebraic group over an algebraically closed field it is known that a minimal counterexample is either of even type meaning that the sylow 2 subgroups are of bounded exponent or of odd type meaning that the sylow 2 subgroups are finite extensions of divisible abelian groups we deal here with tame simple groups of even type having a weakly embedded subgroup a notion related to the notion of strongly embedded subgroup in the finite case but having no exact analog in that case in 10 the classication of simple tame groups with a strongly embedded subgroup was derived in an inductive framework as follows

groupes de type mixte resume we show that a minimal counterexample to the cherlin zil ber conjecture tame or not cannot be of mixed type

theory of asymmetric nonadditive binary hard sphere mixtures it is shown that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard sphere mixture works equally well for nonadditive as it does for additive mixtures for highly asymmetric mixtures small size ratios the resulting effective hamiltonian of the one component fluid of big spheres which consists of an infinite number of many body interactions should be accurately approximated by truncating after the term describing the effective pair interaction using a density functional treatment developed originally for additive hard sphere mixtures the zero one and two body contribution to the effective hamiltonian are determined it is demonstrated that even small degrees of positive or negative nonadditivity have significant effect on the shape of the depletion potential the second virial coefficient b2 corresponding to the effective pair interaction between two big spheres is found to be a sensitive measure of the effects of nonadditivity the variation of b2 with the density of the small spheres shows significantly different behavior for additive slightly positive and slightly negative nonadditive mixtures possible repercussions of these results for the phase behavior of binary hard sphere mixtures are discussed and it is suggested that measurements of b2 might provide a means of determining the degree of nonadditivity in real colloidal mixtures

existence of a bending rigidity for a hard sphere liquid near a curved hard wall validity of the hadwiger theorem in the context of rosenfeld s fundamental measure theory we show that the bending rigidity is not equal to zero for a hard sphere fluid in contact with a curved hard wall the implication is that the hadwiger theorem does not hold in this case and the surface free energy is given by the helfrich expansion instead the value obtained for the bending rigidity i is an order of magnitude smaller than the bending constant associated with gaussian curvature ii changes sign as a function of the fluid volume fraction and iii is independent of the choice of the location of the hard wall

minimal connected simple groups of finite morley rank with strongly embedded subgroups let g be a simple k group of finite morley rank of odd type which is not algebraic then g has prufer 2 rank at most two this improves on an earlier result of the second and third authors for the tame case in the critical case g is minimal connected simple of odd type with a proper definable strongly embedded subgroup the bulk of the analysis relies on the first author s theory of 0 unipotence and the related 0 sylow subgroup theory as well as the so called bender method adapted to this context

a signalizer functor theorem for groups of finite morley rank there is a longstanding conjecture due to gregory cherlin and boris zilber that all simple groups of finite morley rank are simple algebraic groups towards this end the development of the theory of groups of finite morley rank has achieved a good theory of sylow 2 subgroups it is now common practice to divide the cherlin zilber conjecture into different cases depending on the nature of the connected component of the sylow 2 subgroup known as the sylow 2 subgroup we shall be working with groups whose sylow 2 subgroup is divisible or odd type groups to date the main theorem in the area of odd type groups is borovik s trichotomy theorem the trichotomy here is a case division of the minimal counterexamples within odd type more technically borovik s result represents a major success at transferring signalizer functors and their applications from finite group theory to the finite morley rank setting the major difference between the two settings is the absence of a solvable signalizer functor theorem this forced borovik to work only with nilpotent signalizer functors and the trichotomy theorem ends up depending on the assumption of tameness to assure that the necessary signalizer functors are nilpotent the present paper shows that one may obtain a connected nilpotent signalizer functor from any sufficiently non trivial solvable signalizer functor this result plugs seamlessly into borovik s work to eliminate the assumption of tameness from his trichotomy theorem in the meantime a new approach to the trichotomy theorem has been developed by borovik 7 based on the generic identification theorem of berkman and borovik 5 borovik uses his original signalizer functor arguments and incorporates the result of the present paper the paper is organized as follows the first section will develop a limited characteristic zero notion of unipotence to complement the usual p unipotence theory the section on centralizers and generation which follows will establish some background needed in the rest of the paper in section 4 we prove our main result on signalizer functors and in section 5 we discuss some applications with borovik s kind permission we include a proof of the nilpotent signalizer functor theorem as an appendix the results of section 3 are based in part on a section of an unpublished version of 3

bending rigidity and higher order curvature terms for the hard sphere fluid near a curved wall in this work i derive analytic expressions for the curvature dependent fluid substrate surface tension of a hard sphere fluid on a hard curved wall in the first step the curvature thermodynamic properties are found as truncated power series in the activity in terms of the exactly known second and third order cluster integrals of the hard sphere fluid near spherical and cylindrical walls these results are then expressed as packing fraction power series and transformed to different reference regions which is equivalent to considering different positions of the dividing surface based on the truncated series it is shown that the bending rigidity of the system is non null and that higher order terms in the curvature also exist in the second step approximate analytic expressions for the surface tension the tolman length the bending rigidity and the gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach it is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system further they are more accurate than any previously published expressions

computational tools for exact conditional logistic regression logistic regression analyses are often challenged by the inability of unconditional likelihood based approximations to yield consistent valid estimates and p values for model parameters this can be due to sparseness or separability in the data conditional logistic regression though useful in such situations can also be computationally unfeasible when the sample size or number of explanatory covariates is large we review recent developments that allow efficient approximate conditional inference including monte carlo sampling and saddlepoint approximations we demonstrate through real examples that these methods enable the analysis of significantly larger and more complex data sets we find in this investigation that for these moderately large data sets monte carlo seems a better alternative as it provides unbiased estimates of the exact results and can be executed in less cpu time than can the single saddlepoint approximation moreover the double saddlepoint approximation while computationally the easiest to obtain offers little practical advantage it produces unreliable results and cannot be computed when a maximum likelihood solution does not exist

non solvable groups of morley rank 3 abstract we prove the following theorem let g be a connected centerless non solvable group of morley rank 3 whose proper definable subgroups have rank 1 then g has no involutions and for all x g cg x is connected our method permits us to deduce that son r is not stable for n 3

efficient calculation of the permutation distribution of trimmed means abstract the permutation distribution of the trimmed mean in matched pairs designs is studied this statistic is important since it is robust to both outliers and distributional assumptions a polynomial time algorithm for this inherently exponential time problem is presented the characteristic function of the distribution provides both the basis for the algorithm and a vehicle for calculating the asymptotic permutation distribution