complexity of graph self assembly in accretive systems and self destructible systems self assembly is a process in which small objects autonomously associate with each other to form larger complexes it is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nano scale structures recent years have seen convergent interest and efforts in studying self assembly from mathematicians computer scientists physicists chemists and biologists however most complexity theoretical studies of self assembly utilize mathematical models with two limitations 1 only attraction while no repulsion is studied 2 only assembled structures of two dimensional square grids are studied in this paper we study the complexity of the assemblies resulting from the cooperative effect of repulsion and attraction in a more general setting of graphs this allows for the study of a more general class of self assembled structures than the previous tiling model we define two novel assembly models namely the accretive graph assembly model and the self destructible graph assembly model and identify a fundamental problem in them the sequential construction of a given graph we refer to it as the accretive graph assembly problem agap and the self destructible graph assembly problem dgap in the respective models our main results are i agap is np complete even if the maximum degree of the graph is restricted to 4 or the graph is restricted to be planar with maximum degree 5 ii counting the number of sequential assembly orderings that result in a target graph agap is p complete and iii dgap is pspace complete even if the maximum degree of the graph is restricted to 6 this is the first pspace complete result in self assembly we also extend the accretive graph assembly model to a stochastic model and prove that determining the probability of a given assembly in this model is p complete

comment on identification in the linear errors in variables model on considere un modele etudie par kapteyn et wansbeek 1983 et on presente des conditions necessaires et suffisantes d identification

the anharmonic oscillator problem a new algebraic solution the second order one dimensional or radial differential schrodinger equation with the potential v r mu r2 nu r4 may be re interpreted as a difference equation of the fourth order indeed the hamiltonian is a pentadiagonal matrix in the standard harmonic oscillator basis mod n n 0 1 thus the authors construct its four independent general solutions by purely algebraic means via expansions in powers of n 1 14 next preserving the analogy between difference and differential equations the physical wavefunctions n mod psi and their energies are determined by the matching of the jost and regular solutions finally using the simplest matching conditions at the origin the resulting numerical algorithm is demonstrated to be both stable and quickly convergent

analytic treatment of the αx2 βx4 oscillator we carry out an investigation of the schrodinger equation with the x2 x4 interaction for 0 re x and exp i in the sectors 0 arg x 3 6 0 and 6 arg x 3 6 0 a subdominant solution is constructed essentially in terms of the laplace transform of a function f s 0 s which is expressible as a converging power series in s the solution y x thus obtained is compared and contrasted with the one valid in the usual case where re x 0 is included and it is argued that y x may not be accessible to perturbative approaches

proxies versus omitted variables in regression analysis when some variables to be used in a regression analysis contain measurement error the ols estimator will be inconsistent when these variables are left out ols will also be inconsistent in an appropriate metric the first type of inconsistency is smaller than the second type

linear constructions for dna codes in this paper we translate in terms of coding theory constraints that are used in designing dna codes for use in dna computing or as bar codes in chemical libraries we propose new constructions for dna codes satisfying either a reverse complement constraint a gc content constraint or both that are derived from additive and linear codes over four letter alphabets we focus in particular on codes over gf 4 and we construct new dna codes that are in many cases better sometimes far better than previously known codes we provide updated tables up to length 20 that include these codes as well as new codes constructed using a combination of lexicographic techniques and stochastic search

perturbative solution for the generalised anharmonic oscillators serious difficulties have been encountered in the past when attempting the straightforward application of the borel method to the summation of perturbation series in quantum mechanics and quantum field theory because of an analytic continuation of the borel transform series which is usually performed by means of conformal mapping techniques the author shows that this continuation may be accomplished by combining the borel method with the first confluent form of the epsilon algorithm of wynn 1960 1968 for the calculation of the ground state energy eigenvalue of the generalised anharmonic oscillators two different approaches are presented both of which lead to accurate results

potential r2 λr2 1 gr2 and the analytic continued fractions the author constructs the exact wavefunctions and an analytic continued fractional green function for the one and three dimensional schrodinger equation with the potential v r h r2 r2 lambda r2 1 gr2 h 1 4 lambda g 0 in the numerical application of the formulae the energy and norm of the boundary state psi may be approximated by both their lower and upper estimates

schrodinger equation as recurrences iii partitioning approach for pt ii see ibid vol 17 no 8 p 1603 10 1984 in the generalised lanczos basis the author partitions the hamiltonian to tridiagonal form and mutatis mutandis apply the ideas of i and ii it solves the schrodinger eigenvalue problem again the resulting method modifies and complements the formalism and simplifies its use and interpretation as an example of application the unique asymptotical effective hamiltonian is derived also for the anharmonic oscillators the convergence of its continued fractional definition is proved and the compact formula for the higher order asymptotic corrections is found

bounding the effects of measurement error in regressions involving dichotomous variables abstract in a multiple regression involving dichotomous independent variables the effects of measurement error in the dichotomous variables is analyzed unlike the case of classical i e white noise measurement error the measurement error in a dichotomous variable must be correlated with the true variable and any other variables correlated with the true variable nonetheless it is shown that the results for the classical errors in variables model can be used to analyze the implications of measurement error in dichotomous variables it is shown how the bounding procedure developed by klepper and leamer 1984 for the classical errors in variables model can be adapted to bound the coefficients when the regression contains mismeasured dichotomous variables the classical results are also used to analyze the inconsistency in least squares regression coefficient estimators computed from data on the mismeasured variables

comment on a solution of the bosonic and algebraic hamiltonians by using an aim we analyze a recently proposed variant of the asymptotic iteration method for bosonic hamiltonians koc et al 2010 j phys a math theor 43 395208 we show that the main equations proposed by the authors are inconsistent and only apply to trivial problems we conjecture how the authors obtained their results for nontrivial models

a solution of the bosonic and algebraic hamiltonians by using an aim we apply the notion of an asymptotic iteration method aim to determine the eigenvalues of the bosonic hamiltonians that include a wide class of quantum optical models we consider the solutions of the hamiltonians which are even the polynomials of the fourth order with respect to the boson operators we also demonstrate the applicability of the method for obtaining the eigenvalues of the simple lie algebraic structures the eigenvalues of the multi boson hamiltonians have been obtained by transforming them into the form of the single boson hamiltonian in the framework of the aim

chain models and their effective hamiltonians we develop a new formalism suitable for diagonalization of hamiltonians with 2t 1 nonzero diagonals chain models in a systematic perturbation like way we get the expansions of green and or wave functions they are generated by solution of a sequence of fixed point quadratic equations for t t dimensional matrices for t 1 and t 2 this solution is feasible by elementary means so that the respective tridiagonal and pentadiagonal chain models may be considered exactly solvable in this context in an alternative first order variational perturbation formulation the method may provide the simultaneous upper and lower energy bounds for any t

equidistant prototypes embedding for single sample based face recognition with generic learning and incremental learning abstract we develop a parameter free face recognition algorithm which is insensitive to large variations in lighting expression occlusion and age using a single gallery sample per subject we take advantage of the observation that equidistant prototypes embedding is an optimal embedding that maximizes the minimum one against the rest margin between the classes rather than preserving the global or the local structure of the training data our method called linear regression analysis lra applies a least square regression technique to map gallery samples to the equally distant locations regardless of the true structure of training data further a novel generic learning method which maps the intraclass facial differences of the generic faces to the zero vectors is incorporated to enhance the generalization capability of lra using this novel method learning based on only a handful of generic classes can largely improve the face recognition performance even when the generic data are collected from a different database and camera set up the incremental learning based on the greville algorithm makes the mapping matrix efficiently updated from the newly coming gallery classes training samples or generic variations although it is fairly simple and parameter free lra combined with commonly used local descriptors such as gabor representation and local binary patterns outperforms the state of the art methods for several standard experiments on the extended yale b cmu pie ar and feret databases

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

schrodinger equation as recurrences ii general solutions and their physical asymptotics for pt i see ibid vol 16 no 17 p 4001 11 1983 the general schrodinger equation is converted into equivalent 2t 1 term recurrences by the generalised lanczos construction of the basis then the exact bound states are given by the t parametric determinantal formula finally the values of the free parameters are shown to follow from the hill type normalisability requirement

complexities for generalized models of self assembly in this paper we study the complexity of self assembly under models that are natural generalizations of the tile self assembly model in particular we extend rothemund and winfree s study of the tile complexity of tile self assembly proceedings of the 32nd annual acm symposium on theory of computing portland or 2000 pp 459 468 they provided a lower bound of omega frac log n log log n on the tile complexity of assembling an n times n square for almost all n adleman et al proceedings of the 33rd annual acm symposium on theory of computing heraklion greece 2001 pp 740 748 gave a construction which achieves this bound we consider whether the tile complexity for self assembly can be reduced through several natural generalizations of the model one of our results is a tile set of size o sqrt log n which assembles an n times n square in a model which allows flexible glue strength between nonequal glues this result is matched for almost all n by a lower bound dictated by kolmogorov complexity for three other generalizations we show that the omega frac log n log log n lower bound applies to n times n squares at the same time we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets specifically for thin rectangles with length n and width k we provide a tighter lower bound of omega frac n 1 k k for the standard model yet we also give a construction which achieves o frac log n log log n complexity in a model in which the temperature of the tile system is adjusted during assembly we also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape we show that this problem is np hard for three of the generalized models

the rank of reduced dispersion matrices psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements psychometricians concentrate on cases in which low rank can be attained preferably rank one the spearman case econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one the frisch case in this paper we give an extensive historial discussion of both fields we prove the two key results in a more satisfactory and uniform way we point out various small errors and misunderstandings and we present a methodological comparison of factor analysis and regression on the basis of our results

reply to the comment on a solution of the bosonic and algebraic hamiltonians by using an aim we reply to the comment made by fernandez 2011 j phys a math theor 44 228001 on our recent paper koc et al 2010 j phys a math theor 43 395208 we have shown that the main equations are consistent and the results can be applied for solving a significant number of problems we admit that one or two steps missing in the original paper may lead to a different interpretation

minimum distance estimation of the errors in variables model using linear cumulant equations abstract we consider a multiple mismeasured regressor errors in variables model we develop closed form minimum distance estimators from any number of estimating equations which are linear in the third and higher cumulants of the observable variables using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions the estimators perform well in monte carlos calibrated to resemble the data from our applications although the cumulant estimators are asymptotically equivalent to the moment estimators from erickson and whited 2002 the finite sample performance of the cumulant estimators exceeds that of the moment estimators

dipole codes attractively encode glue functions dipole words are sequences of magnetic dipoles in which alike elements repel and opposite elements attract magnetic dipoles contrast with more general sets of bonding types called glues in which pairwise bonding strength is specified by a glue function we prove that every glue function g has a set of dipole words called a dipole code that attractively encodes g the pairwise attractions positive or non positive bond strength between the words are identical to those of g moreover we give such word sets of asymptotically optimal length similar results are obtained for a commonly used subclass of glue functions