tests for two separate regressions abstract several recently proposed tests for separate regressions in econometrics are re examined in the light of recommendations by cox 1961 this re examination points to simplified criteria and emphasizes the unity underlying the tests the exact distributions of some of the tests are developed under the tested hypothesis these are given a geometrical characterization which is helpful in exploring relations with the classical f test an orthogonal decomposition is proposed which provides a direct link between the f test and tests based upon artificial nesting

static and dynamic stability results for a class of three dimensional configurations of kirchhoff elastic rods we analyze the dynamical stability of a naturally straight inextensible and unshearable elastic rod under tension and controlled end rotation within the kirchhoff model in three dimensions the cases of clamped boundary conditions and isoperimetric constraints are treated separately we obtain explicit criteria for the static stability of arbitrary extrema of a general quadratic strain energy we exploit the equivalence between the total energy and a suitably defined norm to prove that local minimizers of the strain energy under explicit hypotheses are stable in the dynamic sense due to liapounov we also extend our analysis to damped systems to show that static equilibria are dynamically stable in the liapounov sense in the presence of a suitably defined local drag force

bootstrap j tests of nonnested linear regression models the j test for nonnested regression models often overrejects very severely as an asymptotic test we provide a theoretical analysis which explains why and when it performs badly this analysis implies that except in certain extreme cases the j test will perform very well when bootstrapped using several methods to speed up the simulations we obtain extremely accurate monte carlo results on the finite sample performance of the bootstrapped j test these results fully support the predictions of our theoretical analysis even in contexts where the analysis is not strictly applicable

a simple test for regression specification with non nested alternatives abstract in this paper i introduce a simple test for the presence of the data generating process among several non nested alternatives the test is an extension of the classical j test for non nested regression models i also provide a bootstrap version of the test that avoids possible size distortions inherited from the j test

comparison of local power of alternative tests of non nested regression models the paper derives and compares the local power of three different methods of testing non nested regression models that are available in the literature it shows that the asymptotic power of the orthodox f test against local alternatives is strictly less than that of cox s non nested test or the j test recently proposed by davidson and mackinnon 5 unless the number of non overlapping variables of the alternative hypothesis over the null hypothesis is unity in which case all three tests are shown to be asymptotically equivalent the final section of the paper gives results of monte carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the cox test and the orthodox test

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

on the comprehensive method of testing non nested regression models abstract the paper derives the specific form of the exponentially combined likelihood function of two competing multivariate non linear regression models and shows that the application of the comprehensive approach to testing non nested regression models will in general be indeterminate it establishes that in the univariate case there exists a large number of tests of non nested regression models which are consistent in addition to having the same asymptotic distribution under the null hypothesis the paper then derives a set of conditions under which all these consistent tests are asymptotically equivalent not only under the null hypothesis but also under local alternatives as an application of this latter result the paper establishes the asymptotic equivalence of the tests recently proposed by davidson and mackinnon and fisher and mcaleer under local alternatives and shows that within the class of tests considered in the paper these proposed tests possess maximum local power the latter test has this property only when the number of explanatory variables of the true model is not more than that of the false model

on the graph complement conjecture for minimum rank abstract the minimum rank of a graph has been an interesting and well studied parameter investigated by many researchers over the past decade or so one of the many unresolved questions on this topic is the so called graph complement conjecture which grew out of a workshop in 2006 this conjecture asks for an upper bound on the sum of the minimum rank of a graph and the minimum rank of its complement and may be classified as a nordhaus gaddum type problem involving the graph parameter minimum rank the conjectured bound is the order of the graph plus two other variants of the graph complement conjecture are introduced here for the minimum semidefinite rank and the colin de verdiere type parameter we show that if the graph complement conjecture is true for two graphs then it is true for the join of these graphs related results for the graph complement conjecture and the positive semidefinite version for joins of graphs are also established we also report on the use of recent results on partial k trees to establish the graph complement conjecture for graphs of low minimum rank

rcms right correction magnus series approach for oscillatory odes we consider rcms a method for integrating differential equations of the form y a a1 t y with highly oscillatory solution it is shown analytically and numerically that rcms can accurately integrate problems using stepsizes determined only by the characteristic scales of a1 t typically much larger than the solution wavelength in fact for a given t grid the error decays with or is independent of increasing solution oscillation rcms consists of two basic steps a transformation which we call the right correction and solution of the right correction equation using a magnus series with suitable methods of approximating the highly oscillatory integrals appearing therein rcms has high order of accuracy with little computational work moreover rcms respects evolution on a lie group we illustrate with application to the 1d schrodinger equation and to frenet serret equations the concept of right correction integral series schemes is suggested and right correction neumann schemes are discussed asymptotic analysis for a large class of odes is included which gives certain numerical integrators converging to exact asymptotic behaviour

alternative nonnested specification tests of time series investment models abstract this paper develops and compares non nested hypothesis tests for linear regression models with first order serially correlated errors it extends the non nested testing procedures of pesaran fisher and mcaleer and davidson and mackinnon and compares their performance on four conventional models of aggregate investment demand using quarterly u s investment data from 1951 i to 1983 iv the data and the non nested hypothesis tests initially indicate that none of the models are correctly specified the tests are also intransitive in their assessments before rejecting these conventional models of investment demand we investigate the small sample properties of these different non nested test procedures through a series of monte carlo studies we find that these non nested tests can have significant finite sample size and power biases

automatic classification of protein structure by using gauss integrals we introduce a method of looking at analyzing and comparing protein structures the topology of a protein is captured by 30 numbers inspired by vassiliev knot invariants to illustrate the simplicity and power of this topological approach we construct a measure scaled gauss metric sgm of similarity of protein shapes under this metric protein chains naturally separate into fold clusters we use sgm to construct an automatic classification procedure for the cath2 4 database the method is very fast because it requires neither alignment of the chains nor any chain chain comparison it also has only one adjustable parameter we assign 95 51 of the chains into the proper c class a architecture t topology and h homologous superfamily fold find all new folds and detect no false geometric positives using the sgm we display a map of the space of folds projected onto two dimensions show the relative locations of the major structural classes and zoom into the space of proteins to show architecture topology and fold clusters the existence of a simple measure of a protein fold computed from the chain path will have a major impact on automatic fold classification

some aspects of testing non nested hypotheses abstract this paper examines some aspects of testing non nested hypotheses an inequality between the cox and atkinson statistics is noted and the necessary and sufficient condition for the atkinson test to be consistent is derived a new test procedure is also outlined the rest of the paper illustrates the various test statistics their properties and relationships for competing linear regression models

a correction orthogonal representations and connectivity of graphs abstract this note corrects an error in the proof of the main result of the authors paper orthogonal representations and connectivity of graphs which appeared in linear algebra and its applications 114 115 1989 439 454

lower bounds in minimum rank problems abstract the minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the given graph the minimum semidefinite rank of a graph is the minimum rank among hermitian positive semidefinite matrices with the given graph we explore connections between os sets and a lower bound for minimum rank related to zero forcing sets as well as exhibit graphs for which the difference between the minimum semidefinite rank and these lower bounds can be arbitrarily large

monte carlo methodology and the finite sample properties of instrumental variables statistics for testing nested and non nested hypotheses using monte carlo methodology this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses simple numerical analytical formulae response surfaces are obtained which closely approximate the statistics unknown size and power functions for a dynamic simultaneous equations model the analysis illustrates the value and limitations of asymptotic theory in interpreting finite sample properties two practical results arise the f form and the wald statistic is favored over its chi squared form and large sigma and small effective sample size strongly affect the test of over identifying restrictions and the cox type test copyright 1991 by the econometric society

geometry of călugăreanu s theorem a central result in the space geometry of closed twisted ribbons is clugreanu s theorem also known as white s formula or the clugreanuwhitefuller theorem this enables the integer linking number

a comparison of nonnested tests for misspecified models using the method of approximate slopes abstract comparisons of the cox wald and j tests are conducted under a standard framework and in a misspecified setting the data generation process includes a regressor that is not in either model most power comparisons have been carried out for local alternatives but comparisons under a nonlocal alternatives framework using the method of approximate slopes developed by bahadur 1960 1967 are made in this paper monte carlo experiments are conducted and the cox test is shown to have the highest small sample power and approximate slope for most of the cases considered the results from response surface regressions provide strong evidence that the approximate slope is a good predictor of the small power of nonnested tests it is also useful for directly comparing the small sample power of one degree of freedom tests of nonnested hypotheses

maximum generic nullity of a graph abstract for a graph g of order n the maximum nullity of g is defined to be the largest possible nullity over all real symmetric n n matrices a whose i j th entry for i j is nonzero whenever i j is an edge in g and is zero otherwise maximum nullity and the related parameter minimum rank of the same set of matrices have been studied extensively a new parameter maximum generic nullity is introduced maximum generic nullity provides insight into the structure of the null space of a matrix realizing maximum nullity of a graph it is shown that maximum generic nullity is bounded above by edge connectivity and below by vertex connectivity results on random graphs are used to show that as n goes to infinity almost all graphs have equal maximum generic nullity vertex connectivity edge connectivity and minimum degree

linearly independent vertices and minimum semidefinite rank we study the minimum semidefinite rank of a graph using vector representations of the graph and of certain subgraphs we present a sufficient condition for when the vectors corresponding to a set of vertices of a graph must be linearly independent in any vector representation of that graph and conjecture that the resulting graph invariant is equal to minimum semidefinite rank rotation of vector representations by a unitary matrix allows us to find the minimum semidefinite rank of the join of two graphs we also improve upon previous results concerning the effect on minimum semidefinite rank of the removal of a vertex

entanglement distillation from greenberger horne zeilinger shares we study the problem of converting a product of greenberger horne zeilinger ghz states shared by subsets of several parties in an arbitrary way into ghz states shared by every party such a state can be described by a hypergraph on the parties as vertices and with each hyperedge corresponding to a ghz state shared among the parties incident with it our result is that if slocc transformations are allowed then the best asymptotic rate is the minimum of bipartite log ranks of the initial state which in turn equals the minimum cut of the hypergraph this generalizes a result by strassen on the asymptotic subrank of the matrix multiplication tensor

regularity conditions for cox s test of non nested hypotheses abstract in this article we provide for the first time general regularity conditions and a rigorous proof of the asymptotic normality of cox s statistic for testing separate families of hypotheses the cox test for choosing between competing linear regression models is discussed as an example

goodness of fit statistics for age specific reference intervals the age specific reference interval is a commonly used screening tool in medicine it involves estimation of extreme quantile curves such as the 5th and 95th centiles of a reference distribution of clinically normal individuals it is crucial that models used to estimate such intervals fit the data extremely well however few procedures to assess goodness of fit have been proposed in the literature and even fewer have been evaluated systematically here we consider procedures based on the distribution of the z scores standardized residuals from a model and on pearson chi 2 statistics for observed and expected counts in groups defined by age and the estimated reference centile curves two of the procedures q and grid tests are mainly inferential whereas the third permutation bands and b tests is essentially graphical we obtain approximations to the null distributions of several relevant test statistics and examine their size and power for a range of models based on real data sets we recommend q tests in all situations where z scores are available since they are general simple to calculate and usually have the highest power among the three classes of test considered for the cases considered the grid tests are always inferior to the q and b tests

statistical inference in non nested econometric models the purpose of this paper is to discuss some procedures that are available for testing non nested or separate hypotheses in the statistics and econometrics literature since many of these techniques may also be exploited in other disciplines it is hoped that an elaboration of the principal theoretical findings may make them more readily accessible to researchers in other disciplines several simple examples are used to illustrate the concepts of nested and non nested hypotheses and within the latter category global and partial non nested hypotheses two alternative methods of testing non nested hypotheses are discussed and contrasted the first of these is cox s modification of the likelihood ratio statistic and the second is atkinson s comprehensive model approach a major emphasis is placed on the role of the cox principle of hypothesis testing which enables a broad range of hypotheses to be tested within the same framework the problem associated with the application of the comprehensive model approach to composite non nested hypotheses is also highlighted roy s union intersection principle is presented as a viable method of dealing with this problem simulation results concerning the finite sample properties of various tests are discussed together with an analysis of some attempts to correct the poor size of the cox and related tests

a simulation approach to the problem of computing cox s statistic for testing nonnested models abstract this paper proposes a new procedure for computing the cox statistic for tests of nonnested hypotheses using the method of stochastic simulation the procedure is applicable to a wide class of probability distributions is relatively simple to implement and does not require an analytic derivation of the pseudo true estimators that enter the cox test statistic the paper also contains an application of the proposed method to the test of probit versus logistic formulations of the univariate binary choice models the empirical results show that the simulation method works reasonably well even for a moderate number of replications

frenet algorithm for simulations of fluctuating continuous elastic filaments we present an algorithm for generating the equilibrium configurations of fluctuating continuous elastic filaments based on a combination of statistical mechanics and differential geometry we use this to calculate the distribution function of the end to end distance of filaments with nonvanishing spontaneous curvature and show that for small twist and large bending rigidities there is an intermediate temperature range in which the filament becomes nearly completely stretched we show that volume interactions can be incorporated into our algorithm demonstrating this through the calculation of the effect of excluded volume on the end to end distance of the filament

fluctuating elastic rings statics and dynamics we study the effects of thermal fluctuations on elastic rings analytical expressions are derived for correlation functions of euler angles mean square distance between points on the ring contour radius of gyration and probability distribution of writhe fluctuations since fluctuation amplitudes diverge in the limit of vanishing twist rigidity twist elasticity is essential for the description of fluctuating rings we discover a crossover from a small scale regime in which the filament behaves as a straight rod to a large scale regime in which spontaneous curvature is important and twist rigidity affects the spatial configurations of the ring the fluctuation dissipation relation between correlation functions of euler angles and response functions is used to study the deformation of the ring by external forces the effects of inertia and dissipation on the relaxation of temporal correlations of writhe fluctuations are analyzed using langevin dynamics

supercoiling transitions of closed dna conformations of closed dna molecules are considered within a simple elastic model the interplay of elastic energies of bending and twisting can lead to supercoiling induced by variations of the linking difference these shape transformations are studied in the limit of a large length to thickness ratio of the molecule stationary shapes and energy diagrams are obtained by solving shape equations for closed rings four different families of stationary shapes can be distinguished i planar circles ii nonplanar rings iii self interacting rings and iv interwound configurations they all occur as shapes of minimal energy in the phase diagram of supercoiling the transitions between the different regions in this phase diagram can be either continuous or discontinuous the sequence of shape transitions turns out to be sensitive to the precise values of the elastic parameters the buckling instability of the circle changes within the range of physically accessible values from continuous to discontinuous behavior

exact permutation tests for non nested non linear regression models abstract this paper proposes exact distribution free permutation tests for the specification of a non linear regression model against one or more possibly non nested alternatives the new tests may be validly applied to a wide class of models including models with endogenous regressors and lag structures these tests build on the well known j test developed by davidson and mackinnon 1981 several tests for model specification in the presence of alternative hypotheses econometrica 49 781 793 and their exactness holds under broader assumptions than those underlying the conventional j test the j type test statistics are used with a randomization or monte carlo resampling technique which yields an exact and computationally inexpensive inference procedure a simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions the test procedure developed is illustrated by an application to inflation dynamics

elasticity of two dimensional filaments with constant spontaneous curvature we study the mechanical property of a two dimensional filament with constant spontaneous curvature and under uniaxial applied force we derive the equation that governs the stable shape of the filament and obtain analytical solutions for the equation we find that for a long filament with positive initial azimuth angle the azimuth angle is the angle between x axis and the tangent of the filament and under large stretching force the azimuth angle is a two valued function of the arclength decreases first and then increases with increasing arclength otherwise the azimuth angle is a monotonic function of arclength at finite temperature we derive the differential equation that governs the partition function and find exact solution of the partition function for a filament free of force we obtain closed form expressions on the force extension relation for a filament under low force and for a long filament under strong stretching force our results show that for a biopolymer with moderate length and not too small spontaneous curvature the effect of the spontaneous curvature cannot be replaced by a simple renormalization of the persistence length in the wormlike chain model

on comparing the writhe of a smooth curve to the writhe of an inscribed polygon we find bounds on the difference between the writhing numbers of a smooth curve and a polygonal curve inscribed within the proof is based on an extension of fuller s difference of writhe formula to the case of polygonal curves the results establish error bounds useful in the numerical computation of writhe in terms of bounds on the edge lengths of the polygon and the derivatives of the curve the bounds are adaptive in the sense that they improve when regions of the smooth curve with larger derivatives are approximated by shorter edges of the polygon

conformations of closed dna we examine the conformations of a model for a short segment of closed dna the molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number we obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of dna and a figure eight form that represents the onset of interwinding we are also able to generate knotted loops we suggest ways to use our approach to produce other configurations relevant to studies of dna structure the stability of the distorted configurations is assessed along with the effects of fluctuations on the free energy of the various configurations

tests of non nested regression models small sample adjustments and monte carlo evidence abstract it is known that the small sample significance levels of cox type tests of non nested regression models can be much greater than the nominal level adjustments designed to overcome this problem are discussed and two tests are proposed monte carlo evidence on the performance of the tests derived in this paper the davidson mackinnon j test and the fisher mcaleer test is presented the f test applied to the comprehensive model is also included in the simulation experiments

vector representations of graphs and distinguishing quantum product states with one way locc abstract distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory we introduce a graph theoretic approach based on the theory of vector representations of graphs to the core problem of distinguishing product states with one way locc we establish a number of results that show how distinguishing such states can be framed in terms of properties of the underlying graphs associated with a set of vector product states we also present a number of illustrative examples

on the asymmetric elasticity of twisted dsdna abstract we present an analytical based proof for the consistency of two asymmetric elastic models of the double stranded dna in the regime around the b form we derive the shape equations in terms of euler angles for a uniform ribbon with noncircular cross section and spontaneous torsion we study the conditions to form a helical ribbon for the model and find that the euler angle must be either 0 or 2 we find that the helix is always stable or at least metastable for the model and there is either a continuous or discontinuous transition of extension from a twisted straight ribbon to a helical ribbon an over collapse phenomena of extension is observed for the ribbon under twisting the stability of the helix and the intrinsic asymmetric elasticity under twisting are also studied

three connected graphs whose maximum nullity is at most three for a graph g v e with vertex set v 1 2 n let s g be the set of all n n real valued symmetric matrices a which represent g the maximum nullity of a graph g denoted by m g is the largest possible nullity of any matrix a s g fiedler showed that a graph g has m g 1 if and only if g is a path johnson et al gave a characterization of all graphs g with m g 2 independently hogben and van der holst gave a characterization of all 2 connected graphs with m g 2 in this paper we show that k connected graphs g have m g k that k connected partial k graphs g have m g k and that for 3 connected graphs g m g 3 if and only if g is a partial 3 path

the extended polar writhe a tool for open curves mechanics a measure of the writhing of a curve is introduced and is used to extend the c lug reanu decomposition for closed curves as well as the polar decomposition for curves bound between planes the new writhe measure is also shown to be able to assess changes in linking due to belt trick and knotting type deformations and further its utility is illustrated on examples taken from elastic rod parameter continuation studies finally c and mathematica codes are made available and shown to be faster than existing algorithms for the numerical computation of the writhe

testing nested or non nested hypotheses this paper presents a test procedure for nested or non nested hypotheses the test statistic is based on the difference between two estimators of the pseudo true value as defined for instance by sawa this statistic is similar to the usual wald statistic in the case of nested hypotheses and it can be replaced by an asymptotically equivalent one deduced from the score function

the encompassing principle and its application to testing nonnested hypotheses the encompassing principle is used to develop a testing framework which unifies the literature on non nested testing allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist as well as embracing nested hypothesis testing the concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative the analysis is illustrated by an application to two non nested linear regression models and it is shown that the conventional f test as well as all the one degree of freedom non nested tests has an encompassing interpretation and that the f test is a complete parametric encompassing test

encompassing tests when no model is encompassing this paper considers regression based tests for encompassing when none of the models under consideration encompasses all the other models for both in and out of sample applications i derive asymptotic distributions and propose feasible procedures to construct confidence intervals and test statistics procedures that are asymptotically valid under the null of encompassing e g davidson and mackinnon econometrica 49 1981 781 can have large asymptotic and finite sample distortions simulations indicate that the proposed procedures can work well in samples of size typically available though the divergence between actual and nominal confidence interval coverage sometimes is large

a robust test for non nested hypotheses we propose a robust version of cox type test statistics for the choice between two non nested hypotheses we first show that the influence of small amounts of contamination in the data on the test decision can be very large secondly we build a robust test statistic by using the results on robust parametric tests that are available in the literature and show that the level of the robust test is stable finally we show numerically not only the robustness of this new test statistic but also that its asymptotic distribution is a good approximation of its sample distribution unlike for the classical test statistic we apply our results to the choice between a pareto and an exponential distribution as well as between two competing regressors in the simple linear regression model without intercept

tests of non nested regression models some results on small sample behaviour and the bootstrap the most popular procedures for testing a regression model against a single non nested alternative can be substantially oversized in small samples also when a regression model is to be tested in the presence of several non nested alternatives the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes this approach leads to an implicit overall test with a significance level that is not known even asymptotically it is shown that the bootstrap can be used to control significance levels in both types of situation power estimates for various tests using bootstrap critical values are also obtained and compared

orthogonal representations and connectivity of graphs abstract it is proved that a graph on n nodes is k connected if and only if its nodes can be represented by real vectors in dimension n k such that a nonadjacent nodes are represented by orthogonal vectors and b any n k of them are linearly independent we show that the closure of the set of all representations with properties a and b is irreducible as an algebraic variety and study the question of irreducibility of the variety of all representations with property a

worm like polymer loops and fourier knots every smooth closed curve can be represented by a suitable fourier sum as a function of an arbitrary parameter we show that the ensemble of curves generated by randomly chosen fourier coefficients with amplitudes inversely proportional to spatial frequency with a smooth exponential cutoff can be accurately mapped on the physical ensemble of inextensible worm like polymer loops the s mapping of the curve parameter on the arc length s of the inextensible polymer is achieved at the expense of coupling all fourier harmonics in a non trivial fashion we characterize the obtained ensemble of conformations by looking at tangent tangent and position position correlations measures of correlation on the scale of the entire loop yield a larger persistence length than that calculated from the tangent tangent correlation function at small length scales the topological properties of the ensemble randomly generated worm like loops are shown to be similar to those of other polymer models

differential geometry of polymer models worm like chains ribbons and fourier knots we analyse several continuum models of polymers worm like chains ribbons and fourier knots we show that the torsion of worm like chains diverges and conclude that such chains cannot be described by the frenet serret fs equation of space curves while the same holds for ribbons as well their rate of twist is finite and therefore they can be described by the generalized fs equation of stripes finally fourier knots have finite curvature and torsion and therefore are sufficiently smooth to be described by the fs equation of space curves

comment on cyclic rotations contractibility and gauss bonnet it is shown that the proof of the hannay formula given by him is based on an improper argument an improved consideration is suggested

alternative procedures and associated tests of significance for non nested hypotheses this paper attempts to synthesize various procedures for testing non nested hypotheses within the framework of artificial nesting and establishes the result that different tests correspond to different treatments of its identification problem numerical and a priori identification methods are distinguished we derive two modified likelihood ratio tests that are asymptotically equivalent to the cox test and explain the relationship between them the tests are consistent this abstract was borrowed from another version of this item

conformations of linear dna we examine the conformations of a model for underwound and overwound dna the molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number we derive a fundamental relation between the euler angles that describe the curve and the topological linking number analytical expressions for the spatial configurations of the molecule in the infinite length limit are obtained a unique configuration minimizes the energy for a given set of physical conditions an elastic model incorporating thermal fluctuations provides excellent agreement with experimental results on the plectonemic transition

writhe formulas and antipodal points in plectonemic dna configurations the linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled dna defined as double integrals over the shape of the double helix these numbers are not always straightforward to compute though a simplified formula was established in a theorem by fuller proc natl acad sci u s a 75 3557 1978 we examine the range of applicability of this widely used simplified formula and show that it cannot be employed for plectonemic dna we show that inapplicability is due to a hypothesis of fuller theorem that is not met the hypothesis seems to have been overlooked in many works

the distributions of the j and cox non nested tests in regression models with weakly correlated regressors abstract this paper examines the asymptotic null distributions of the j and cox non nested tests in the framework of two linear regression models with nearly orthogonal non nested regressors the analysis is based on the concept of near population orthogonality npo according to which the non nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn new distributional results emerge under npo the j and cox tests tend to two different random variables asymptotically each of which is expressible as a function of a nuisance parameter c a n 0 1 variate and a 2 q variate where q is the number of non nested regressors in the alternative model the monte carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under npo by plugging consistent estimates of c into the relevant asymptotic expressions an empirical example illustrates the plug in procedure

expected values of parameters associated with the minimum rank of a graph abstract we investigate the expected value of various graph parameters associated with the minimum rank of a graph including minimum rank maximum nullity and related colin de verdiere type parameters let g v p denote the usual erd s renyi random graph on v vertices with edge probability p we obtain bounds for the expected value of the random variables mr g v p m g v p g v p and g v p which yield bounds on the average values of these parameters over all labeled graphs of order v

the minimum rank problem for circulants abstract the minimum rank problem is to determine for a graph g the smallest rank of a hermitian or real symmetric matrix whose off diagonal zero nonzero pattern is that of the adjacency matrix of g here g is taken to be a circulant graph and only circulant matrices are considered the resulting graph parameter is termed the minimum circulant rank of the graph this value is determined for every circulant graph in which a vertex neighborhood forms a consecutive set and in this case is shown to coincide with the usual minimum rank under the additional restriction to positive semidefinite matrices the resulting parameter is shown to be equal to the smallest number of dimensions in which the graph has an orthogonal representation with a certain symmetry property and also to the smallest number of terms appearing among a certain family of polynomials determined by the graph this value is then determined when the number of vertices is prime the analogous parameter over r is also investigated

sequence dependent effects on the properties of semiflexible biopolymers using a path integral technique we show exactly that for a semiflexible biopolymer in constant extension ensemble no matter how long the polymer and how large the external force the effects of short range correlations in the sequence dependent spontaneous curvatures and torsions can be incorporated into a model with well defined mean spontaneous curvature and torsion as well as a renormalized persistence length moreover for a long biopolymer with large mean persistence length the sequence dependent persistence lengths can be replaced by their mean however for a short biopolymer or for a biopolymer with small persistence lengths inhomogeneity in persistence lengths tends to make physical observables very sensitive to details and therefore less predictable

comparing non nested regression models a method for comparing the fits of two non nested models based on a suggestion of davidson and mackinnon 1981 is developed in the context of linear and nonlinear regression with normal errors each model is regarded as a special case of an artificial supermodel and is obtained by restricting the value of a mixing parameter gamma to 0 or 1 to enable estimation and hypothesis testing for gamma an approximate supermodel is used in which the fitted values from the individual models appear in place of the original parametrization in the case of nested linear models the proposed test essentially reproduces the standard f test the calculations required are for the most part straight forward basically linear regression through the origin the test is extended to cover situations in which serious bias in the maximum likelihood estimate of gamma occurs simple approximate bounds for the bias being given two real datasets are used illustratively throughout