A partition function algorithm for nucleic acid secondary structure including pseudoknots

Nucleic acid secondary structure models usually exclude pseudoknots due to the difficulty of treating these nonnested structures efficiently in structure prediction and partition function algorithms. Here, the standard secondary structure energy model is extended to include the most physically relevant pseudoknots. We describe an O(N(5)) dynamic programming algorithm, where N is the length of the strand, for computing the partition function and minimum energy structure over this class of secondary structures. Hence, it is possible to determine the probability of sampling the lowest energy structure, or any other structure of particular interest. This capability motivates the use of the partition function for the design of DNA or RNA molecules for bioengineering applications.     

Chapter 4:algebraic sets, polynomials, and other functions

Let T be a linear operator on the vector space V ofn×n matrices over a field F. We discuss two types of problems in this chapter. First, what can we say about T if we assume that T maps a given algebraic set such as the special linear group into itself? Second, let p(x) be a polynomial function (such as det) on V into F. What can we say about T if Tpreserves p(x), i.e. p(T(X)) = p(X) for all X in V?     

Comment on "Optical-fiber-based Mueller optical coherence tomography"

We comment on the recent Letter by Jiao et al. [Opt. Lett. 28, 1206 (2003)] in which a polarization-sensitive optical coherence tomography system was presented. Interrogating a sample with two orthogonal incident polarization states cannot always recover birefringence correctly. A previously presented fiber-based polarization-sensitive system was inaccurately characterized, and its method of eliminating the polarization distortion caused by single-mode optical fiber was presented earlier by Saxer et al. [Opt. Lett. 25, 1355 (2000)].     

Optic axis determination accuracy for fiber-based polarization-sensitive optical coherence tomography

We present a generalized analysis of fiber-based polarization-sensitive optical coherence tomography with an emphasis on determination of sample optic axis orientation. The polarization properties of a fiber-based system can cause an overall rotation in a Poincaré sphere representation such that the plane of possible measured sample optic axes for linear birefringence and diattenuation no longer lies in the QU-plane. The optic axis orientation can be recovered as an angle on this rotated plane, subject to an offset and overall indeterminacy in sign such that only the magnitude, but not the direction, of a change in orientation can be determined. We discuss the accuracy of optic axis determination due to a fundamental limit on the accuracy with which a polarization state can be determined as a function of signal-to-noise ratio.     

Congratulations to Akusticheskii Zhurnal on the occasion of its 50th anniversary. Vibrations of spherical inclusions in elastic solids

Variational principles are derived for the analysis of dynamical phenomena associated with spherical inclusions embedded in homogeneous isotropic elastic solids. The starting point is Hamilton’s principle, with the material properties assumed to vary only with the radial distance r from the origin. Attention is restricted to disturbances that are symmetric about the polar (z) axis, such that the nonzero displacement components in spherical coordinates, u _r and u_θ, are independent of the polar coordinate φ. The symmetry allows for a decoupling of the polar components, the nth of which is described by U _{r, n} (r, t)P _n (cosθ) and U_{θ, n}(r, t)dP _n /dθ. A variational principle is subsequently derived for the field quantities U _{r, n} and U_{θ, n}. Concepts analogous to those of the theory of matched asymptotic expansions are used to embellish the principle in order to allow for the damping associated with the outward radiation of elastic waves. Examples illustrating the use of the variational principle for formulating plausible lumped-parameter models are given for the cases of n = 0 and n = 1.     

Book Reviews

Linear Algebra and Analytic Geometry, by H. W. Brinkmann and E. A. Klotz. Addison-Wesley, Reading, Mass., 1971.

Metric Affine Geometry, by Ernst Snapper and Robert J. Troyer. Academic Press, New York, 1971. xx + 435 pp. ($13.50).

Metric Affine Geometry, by Ernst Snapper and Robert J. Troyer. Academic Press, New York, 1971. xx + 435 pp. ($13.50)

Studies in Pure Mathematics, papers presented to Richard Rado. Edited by L. Mirsky, Academic Press, 1971, vii + 276 pp. (£5.00)

Linear Algebra (2nd edition), by Hoffmann and Kunze.

Linear Algebra, by Georgi E. Shilov. Translated by Richard A. Silverman.

Linear Algebra, by Georgi E. Shilov. Translated by Richard A. Silverman.     

Application of inelastic proton scattering to the rapid determination of silicon in steels

A rapid, nondestructive method for the determination of silicon in steels has been developed based on the measurement of the 1.77-MeV γ-line emitted by the proton inelastic scattering reaction ²⁸Si(p,p')²⁸Si For some of the determinations the 0.84-MeV γ-line from the reaction ⁵⁶Fe(p,p')⁵⁶Fe was used as internal standard.     

Experience with the use of the nuclear microprobe for determining light element distributions

The components of the nuclear microprobe are considered briefly. Various techniques are summarized for the determination of the elements B, C, N, O, F and Si on a routine basis.     

Optimal impulsive control of compartment models,I: Qualitative aspects

Optimal impulsive control of systems arising from linear compartment models for drug distribution in the human body is considered. A system of linear, time-invariant, homogeneous differential equations is given along with a set of continuous constraints on state and control. The object is to develop a constructive algorithm for the computation of the optimal control relative to a convex cost functional. It is first shown that under suitable hypotheses, satisfying the continuous constraints is equivalent to satisfying the constraints at a finite set of abstractly definedcritical points. Once these critical points have been determined, the solution of the optimal control problem is found as the solution of a finite-dimensional convex programming problem. The set of critical points can often be determineda priori solely from the qualitative behavior of the solutions of the system. A class of such problems, generalizing the so-calledplateau effect, is considered in detail. It is shown that the solution achieving the plateau effect is indeed optimal in certain cases. In a subsequent paper, an iterative algorithm will be given for the solution of these problems when the critical points cannot all be determineda priori.This work was supported in part by the National Science Foundation under Grant No. GP-20130.