simple waves in quasilinear hyperbolic systems i theory of simple waves and simple states examples of applications this paper presents a new method of construction of solutions to nonlinear nonelliptic systems of partial differential equations and especially nonhomogeneous ones these equations have been considered from the point of view of integral elements in particular the connections between the structure of the set of integral elements and the possibility of a construction of special classes of solutions have been studied these classes consist of what is called simple waves and k waves for homogeneous systems and simple states in the case of nonhomogeneous systems they provide us with a possibility for a selection of simple integral elements from the set of all integral elements analyses have been performed using differential forms and cartan theory of system in involution the problem has been reduced to examining pfaff forms the cauchy problem for pfaff systems has been formulated and solved using the riemann function some remarks concerning the notion of backlund transformations for the case of k waves have been formulated it is shown that in contrast to simple wave the simple state has no gradient catastrophy the technique presented of constructing the solutions in form of simple states has been illustrated by the examples of korteweg and de vries and four dimensional klein gordon sine gordon and liouville equations it has been shown that the known soliton equations are closely connected with the elliptical functions and especially with the p weierstrass functions

on the integrability of 2 1 dimensional quasilinear systems a 2 1 dimensional quasilinear system is said to be integrable if it can be decoupled in infinitely many ways into a pair of compatible n component one dimensional systems in riemann invariants exact solutions described by these reductions known as nonlinear interactions of planar simple waves can be viewed as natural dispersionless analogues of n gap solutions it is demonstrated that the requirement of the existence of sufficiently many n component reductions provides the effective classification criterion as an example of this approach we classify integrable 2 1 dimensional systems of conservation laws possessing a convex quadratic entropy

confidence intervals for uncommon but dramatic responses to treatment a small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment the ranks used in these tests are very different from conventional ranks being relatively flat for low responses and then rising steeply and the associated tests are much more powerful than conventional rank tests when indeed only a small fraction of treated subjects exhibit dramatic responses because the tests are derived from considerations of local power they do not yield a plausible family of models for effect and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests there is a similarity between these tests and another family of tests originally motivated by different considerations involving peak performance in small subsets exploiting this similarity a method for obtaining confidence statements is proposed in the case of observational studies sensitivity to unobserved bias from nonrandom assignment of treatments is also examined two examples are used as illustrations i a study of smoking during pregnancy and its effects on birth weight in which smokers are matched to six controls and ii a matched pair study of damage to dna among workers at aluminum production plants

weighted m statistics with superior design sensitivity in matched observational studies with multiple controls in a nonrandomized or observational study a weak association between receipt of the treatment and an outcome may be explained not as effects caused by the treatment but rather by a small bias in the assignment of individuals to treatment or control however a strong association may be explained as noncausal only by a large bias the strength of the association between treatment and outcome is not uniform across the data from a study and this motivates giving greater weight where the association is stronger in an observational study with treated control matched pairs it is known that results are less sensitive to unmeasured biases if pairs with small absolute differences in outcomes are given little weight in the analysis more precisely such a test statistic has superior design sensitivity how should outcomes be weighted if an observational study is matched in sets with one treated subject and several controls an m statistic is the quantity equated to zero in defining huber s m estimates includin

cubulating graphs of free groups with cyclic edge groups we prove that if g is a group that splits as a finite graph of finitely generated free groups with cyclic edge groups and g has no non euclidean baumslag solitar subgroups then g is the fundamental group of a compact nonpositively curved cube complex in addition if g is also word hyperbolic i e if g contains no baumslag solitar subgroups of any type we show that g is linear in fact is a subgroup of sl n z

sensitivity analysis for multiple comparisons in matched observational studies through quadratically constrained linear programming abstracta sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding while sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest this stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant which in turn results in an overly pessimistic assessment of a study s sensitivity to unobserved biases by solving a quadratically constrained linear program we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatm

commensurability of groups quasi isometric to raags let g be a right angled artin group with defining graph gamma and let h be a finitely generated group quasi isometric to g we show if g satisfies that 1 its outer automorphism group is finite 2 gamma does not contain any induced 4 cycles 3 gamma is star rigid then h is commensurable to g we show condition 2 is sharp in the sense that if gamma contains an induced 4 cycle then there exists an h quasi isometric to g but not commensurable to g moreover one can drop condition 1 if h is a uniform lattice acting on the universal cover of the salvetti complex of g as a consequence we obtain a conjugation theorem for such uniform lattices the ingredients of the proof include a blow up building construction in huang and kleiner duke math j 167 3 537 602 2018 https doi org 10 1215 00127094 2017 0042 and a haglund wise style combination theorem for certain class of special cube complexes however in most of our cases relative hyperbolicity is absent so we need new ingredients for the combination theorem

discovering findings that replicate from a primary study of high dimension to a follow up study we consider the problem of identifying whether findings replicate from one study of high dimension to another when the primary study guides the selection of hypotheses to be examined in the follow up study as well as when there is no division of roles into the primary and the follow up study we show that existing meta analysis methods are not appropriate for this problem and suggest novel methods instead we prove that our multiple testing procedures control for appropriate error rates the suggested family wise error rate controlling procedure is valid for arbitrary dependence among the test statistics within each study a more powerful procedure is suggested for false discovery rate fdr control we prove that this procedure controls the fdr if the test statistics are independent within the primary study and independent or have positive dependence in the follow up study for arbitrary dependence within the primary study and either arbitrary dependence or positive dependence in the follow up study

stepwise confidence intervals without multiplicity adjustment for dose response and toxicity studies abstract not all simultaneous inferences need multiplicity adjustment if the sequence of individual inferences is predefined and failure to achieve the desired inference at any step renders subsequent inferences unnecessary then multiplicity adjustment is not needed this can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequence starting with the most restrictive one but what hypotheses are appropriate may not be obvious in some problems we give a fundamentally different confidence set based justification by partitioning the parameter space naturally and using the principle that exactly one member of the partition contains the true parameter in dose response studies designed to show superiority of treatments over a placebo negative control or a drug known to be efficacious active control the confidence set approach generates methods with meaningful guarantee against incorrect decision whereas previous applications of the closed testing app

a recycling framework for the construction of bonferroni based multiple tests in this paper we describe bonferroni based multiple testing procedures mtps as strategies to split and recycle test mass here test mass refers to parts of the nominal level alpha at which the family wise error rate is controlled briefly test mass is split between different null hypotheses and whenever a null hypothesis is rejected the part of alpha allocated to it may be recycled to the testing of other hypotheses these recycling mtps are closed testing procedures based on raw p values associated with testing the individual null hypotheses and the class of such mtps includes for example serial and parallel gatekeeping fallback and holm procedures graphical displays and a concise algebraic notation are provided for such mtps this recycling approach has pedagogical advantages and may facilitate the tailoring of mtps for different purposes

invariant solutions of hydrodynamic type equations conditions are established under which a system of hydrodynamic type equations with time dependent coefficients allows an infinite dimensional group of hydrodynamic type symmetries when this group exists it is used to linearize and solve the original system

a family of nonlinear klein gordon equations and their solutions various forms of the nonlinear klein gordon equation are seen to have exact solitonlike solutions when separation of variables is postulated the family for which these exact solutions are found includes the sine gordon equation as a special case an interesting conclusion obtained is that both the soliton antisoliton and breather solutions hitherto known for the sine gordon equations result from a broader class of klein gordon equations the method can be extended to other equations

the strong atiyah conjecture for virtually cocompact special groups we provide new conditions for the strong atiyah conjecture to lift to finite group extensions in particular we show that fundamental groups of compact special cube complexes satisfy these conditions so the conjecture holds for finite extensions of these groups

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

testing one hypothesis twice in observational studies in a matched observational study of treatment effects a sensitivity analysis asks about the magnitude of the departure from random assignment that would need to be present to alter the conclusions of an analysis that assumes that matching for measured covariates removes all bias the reported degree of sensitivity to unmeasured biases depends on both the process that generated the data and the chosen methods of analysis so a poor choice of method may lead to an exaggerated report of sensitivity to bias this suggests the possibility of performing more than one analysis with a correction for multiple inference say testing one null hypothesis using two or three different tests in theory and in an example it is shown that in large samples the gains from testing twice will often be large because testing twice has the larger of the two design sensitivities of the component tests and the losses due to correcting for two tests will often be small because two tests of one hypothesis will typically be highly correlated so a correction for multiple testing that takes this into account will be small an illustration uses data from the u s national health and nutrition examination survey concerning lead in the blood of cigarette smokers copyright 2012 oxford university press

residual finiteness growths of virtually special groups let g be a virtually special group then the residual finiteness growth of g is at most linear this result cannot be found by embedding g into a special linear group indeed the special linear group mathrm sl k mathbb z for k 2 has residual finiteness growth n k 1

the haantjes tensor and double waves for multi dimensional systems of hydrodynamic type a necessary condition for integrability an invariant differential geometric approach to the integrability of 2 1 dimensional systems of hydrodynamic type is developed we prove that the existence of special solutions known as double waves is equivalent to the diagonalizability of an arbitrary matrix of the two parameter familysince the diagonalizability can be effectively verified by calculating the haantjes tensor this provides a simple necessary condition for integrability

a general class of one sample nonparametric test statistics based on subsamples abstract a general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in subsamples of size m taken from n independent observations the test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m 1 and a modified wilcoxon signed rank test statistic for m 2 asymptotic normality of properly standardized versions of our statistics is established under general conditions small sample power simulations as well as pitman and bahadur efficiencies indicate that members of our class do well in comparison with already existing test statistics

a new u statistic with superior design sensitivity in matched observational studies summary in an observational or nonrandomized study of treatment effects a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naive analysis that presumes adjustments for observed covariates suffice to remove all bias the power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude in particular if this specified magnitude is no departure then this is the same as the power of a randomization test in a randomized experiment a new family of u statistics is proposed that includes wilcoxon s signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study wilcoxon s statistic has high power to detect small effects in large randomized experiments that is it often has good pitman efficiency but small effects are invariably sensitive to small unobserved biases members of this family of u statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis for example in one situation with 250 pair differences that are normal with expectation 1 2 and variance 1 the power of a sensitivity analysis that uses wilcoxon s statistic is 0 08 while the power of another member of the family of u statistics is 0 66 the topic is examined by performing a sensitivity analysis in three observational studies using an asymptotic measure called the design sensitivity and by simulating power in finite samples the three examples are drawn from epidemiology clinical medicine and genetic toxicology

bahadur efficiency of sensitivity analyses in observational studies an observational study draws inferences about treatment effects when treatments are not randomly assigned as they would be in a randomized experiment the naive analysis of an observational study assumes that adjustments for measured covariates suffice to remove bias from nonrandom treatment assignment a sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of the naive analysis say leading to the acceptance of a null hypothesis rejected in the naive analysis observational studies vary greatly in their sensitivity to unmeasured biases but a poor choice of test statistic can lead to an exaggerated report of sensitivity to bias the bahadur efficiency of a sensitivity analysis is introduced calculated and connected to established concepts such as the power of a sensitivity analysis and the design sensitivity the bahadur slope equals zero when the sensitivity parameter equ

limit groups are subgroup conjugacy separable abstract a group g is called subgroup conjugacy separable if for every pair of non conjugate finitely generated subgroups of g there exists a finite quotient of g where the images of these subgroups are not conjugate we prove that limit groups are subgroup conjugacy separable we also prove this property for one relator groups of the form r a 1 a n w n with n w the property is also proved for infinite virtual retracts equivalently for infinite quasiconvex subgroups of hyperbolic virtually special groups

the bianchi groups are separable on geometrically finite subgroups let d be a square free positive integer and od the ring of integers in q p id the main result of this paper is that the groups psl 2 od are

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

mixed 3 manifolds are virtually special letm be a compact oriented irreducible 3 manifold which is neither a graph manifold nor a hyperbolic manifold we prove that 1m is virtually special

the characterization of two component 2 1 dimensional integrable systems of hydrodynamic type we obtain the necessary and sufficient conditions for a two component 2 1 dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions these conditions are in involution implying that the systems in question are locally parametrized by 15 arbitrary constants it is proved that all such systems possess three conservation laws of hydrodynamic type and therefore are symmetrizable in godunov s sense moreover all such systems are proved to possess a scalar pseudopotential which plays the role of the dispersionless lax pair we demonstrate that the class of two component systems possessing a scalar pseudopotential is in fact identical with the class of systems possessing infinitely many hydrodynamic reductions thus establishing the equivalence of the two possible definitions of integrability explicit linearly degenerate examples are constructed

simple waves in quasilinear hyperbolic systems ii riemann invariants for the problem of simple wave interactions in this paper a generalization of the riemann invariant method to the case of a nonhomogeneous system of equations has been formulated we have discussed in detail the necessary and sufficient conditions for the existence of riemann invariants we perform the analysis using the apparatus of differential forms and cartan theory of systems in involution the problem has been reduced to examining pfaff forms we have considered the connections between the structure of the set of integral elements and the possibility of a construction of special classes of solutions depending on k arbitrary functions of one variable these solutions can be interpreted physically as the interactions between k simple waves on a simple state we have proven that in the case of interaction of many simple waves described by riemann invariants a conservation law for the type and quantity of waves holds it has been also shown that such a solution resulting from the interaction of many simple waves propagating on the simple state

coxeter groups are virtually special abstract in this paper we prove that every finitely generated coxeter group has a finite index subgroup that is the fundamental group of a special cube complex some consequences include every f g coxeter group is virtually a subgroup of a right angled coxeter group every word hyperbolic coxeter group has separable quasiconvex subgroups

amplification of sensitivity analysis in matched observational studies a sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed in matched observational studies of treatment effects a key assumption in some analyses is that subjects matched for observed covariates are comparable and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching what properties would such an unobserved covariate need to have to materially alter the inference about treatment effects for ease of calculation and reporting it is convenient that the sensitivity analysis be of low dimension perhaps indexed by a scalar sensitivity parameter but for interpretation in specific contexts a higher dimensional analysis may be of greater relevance an amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points perhaps a curve in a higher dimensional sensitivity analysis such that the possible inferences are

multi dimensional quasi simple waves in weakly dissipative flows abstract a multi dimensional simple wave formalism is employed to formulate a multi dimensional quasi simple wave for a weakly dissipative fluid this is a natural but nontrivial generalization of the so called unidirectional quasi simple wave the method is more close to multi orders analysis which is different from the standard perturbation method detailed solving up to the second order is presented for a 2d sound simple wave a new 2d burgers equation is derived for the wave phase it essentially differs from the known 2d generalizations of the burgers equation e g from the zabolotskaya khokhlov equation the derived equation is investigated in the framework of group analysis of differential equations multi parameter families of its exact solutions are constructed simplest solutions are chosen for analysis of their physical relevance in the initial variables

a combination theorem for special cube complexes we prove that certain compact cube complexes have special nite covers this means they have nite covers whose fundamental groups are quasiconvex subgroups of right angled artin groups as a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider our result applies in particular to a compact negatively curved cube complex whose hyperplanes do not self intersect for a cube complex with word hyperbolic fundamental group we show that it is virtually special if and only if its hyperplane stabilizers are separable in a nal application we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special

tits alternatives for graph products we discuss various types of tits alternative for subgroups of graph products of groups and prove that under some natural conditions a graph product of groups satisfies a given form of tits alternative if and only if each vertex group satisfies this alternative as a corollary we show that every finitely generated subgroup of a graph product of virtually solvable groups is either virtually solvable or large as another corollary we prove that every non abelian subgroup of a right angled artin group has an epimorphism onto the free group of rank 2 in the course of the paper we develop the theory of parabolic subgroups which allows to describe the structure of subgroups of graph products that contain no non abelian free subgroups we also obtain a number of results regarding the stability of some group properties under taking graph products

effect modification and design sensitivity in observational studies in an observational study of treatment effects subjects are not randomly assigned to treatment or control so differing outcomes in treated and control groups may reflect a bias from nonrandom assignment rather than a treatment effect after adjusting for measured pretreatment covariates perhaps by matching a sensitivity analysis determines the magnitude of bias from an unmeasured covariate that would need to be present to alter the conclusions of the naive analysis that presumes adjustments eliminated all bias other things being equal larger effects tend to be less sensitive to bias than smaller effects effect modification is an interaction between a treatment and a pretreatment covariate controlled by matching so that the treatment effect is larger at some values of the covariate than at others in the presence of effect modification it is possible that results are less sensitive to bias in subgroups experiencing larger effects two cases are considered i an a priori grouping into a few categ

cross screening in observational studies that test many hypotheses abstractwe discuss observational studies that test many causal hypotheses either hypotheses about many outcomes or many treatments to be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment in a sense that needs to be defined carefully hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing in the absence of bias it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases we propose a new strategy called cross screening different from but motivated by recent work of bogomolov and heller on replicability cross screening splits the data in half at random uses the first half to plan a study carried out on the second half then uses the second half to plan a study carried out on the first half and reports the more favorable conclusions of the tw