On Vague Computers

Vagueness is something everyone is familiar with. In fact, most people think that vagueness is closely related to language and exists only there. However, vagueness is a property of the physical world. Quantum computers harness superposition and entanglement to perform their computational tasks. Both superposition and entanglement are vague processes. Thus quantum computers, which process exact data without "exploiting" vagueness, are actually vague computers

Classical study of rotational excitation of a rigid rotor: Li+ plus H2

Classical trajectory study of rotationally inelastic scattering of hydrogen molecules by collisions with lithium ion

Growth rate for the expected value of a generalized random Fibonacci sequence

A random Fibonacci sequence is defined by the relation g_n = | g_{n-1} +/- g_{n-2} |, where the +/- sign is chosen by tossing a balanced coin for each n. We generalize these sequences to the case when the coin is unbalanced (denoting by p the probability of a +), and the recurrence relation is of the form g_n = |\lambda g_{n-1} +/- g_{n-2} |. When \lambda >=2 and 0 < p <= 1, we prove that the expected value of g_n grows exponentially fast. When \lambda = \lambda_k = 2 cos(\pi/k) for some fixed integer k>2, we show that the expected value of g_n grows exponentially fast for p>(2-\lambda_k)/4 and give an algebraic expression for the growth rate. The involved methods extend (and correct) those introduced in a previous paper by the second author

Construction of spherical cubature formulas using lattices

We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on the sphere of dimension n-1 for n=4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming

Repair of Aberrant Splicing in Growth Hormone Receptor by Antisense Oligonucleotides Targeting the Splice Sites of a Pseudoexon

Context: The GH receptor (GHR) pseudoexon 6 Psi defect is a frequent cause of GH insensitivity (GHI) resulting from a non-functioning GH receptor (GHR). It results in a broad range of phenotypes and may also be present in patients diagnosed as idiopathic short stature.Objective: Our objective was to correct aberrant GHR splicing and inclusion of 6 Psi using exon-skipping antisense oligonucleotides (ASOs).Design and Setting: Three ASOs binding the 5' (ASO-5), 3' (ASO-3), and branch site (ASO-Br) of 6 Psi were tested in an in vitro splicing assay and a cell transfection system. The wild-type (wt) and mutant (mt) DNA minigenes (wt- and mtL1-GHR6 Psi-L2, respectively) were created by inserting the GHR 6 Psi in a well-characterized splice reporter (Adml-par). For the in vitro splicing assay, the wt- and mtL1-GHR6 Psi-L2 were transcribed into pre-mRNA in the presence of [alpha P-32]GTP and incubated with ASOs in HeLa nuclear extracts. For the cell transfection studies, wt-and mtL1-GHR6 Psi-L2 cloned into pcDNA 3.1 were transfected with ASOs into HEK293 cells. After 48 h, RNA was extracted and radiolabeled RT-PCR products quantified.Results: ASO-3 induced an almost complete pseudoexon skipping in vitro and in HEK293 cells. This effect was dose dependent and maximal at 125-250 nM. ASO-5 produced modest pseudoexon skipping, whereas ASO-Br had no effect. Targeting of two splice elements simultaneously was less effective than targeting one. ASO-Br was tested on the wtL1-GHR6 Psi-L2 and did not act as an enhancer of 6 Psi inclusion.Conclusions: The exon-skipping ASO approach was effective in correcting aberrant GHR splicing and may be a promising therapeutic tool. (J Clin Endocrinol Metab 95: 3542-3546, 2010

Semantic variation operators for multidimensional genetic programming

Multidimensional genetic programming represents candidate solutions as sets of programs, and thereby provides an interesting framework for exploiting building block identification. Towards this goal, we investigate the use of machine learning as a way to bias which components of programs are promoted, and propose two semantic operators to choose where useful building blocks are placed during crossover. A forward stagewise crossover operator we propose leads to significant improvements on a set of regression problems, and produces state-of-the-art results in a large benchmark study. We discuss this architecture and others in terms of their propensity for allowing heuristic search to utilize information during the evolutionary process. Finally, we look at the collinearity and complexity of the data representations that result from these architectures, with a view towards disentangling factors of variation in application.Comment: 9 pages, 8 figures, GECCO 201

Optical properties of split ring resonator metamaterial structures on semiconductor substrates

Metamaterials based on single-layer metallic Split Ring Resonators (SRR) and Wires have been demonstrated to have a resonant response in the near infra-red wavelength range. The use of semiconductor substrates gives the potential for control of the resonant properties of split-ring resonator (SRR) structures by means of active changes in the carrier concentration obtained using either electrical injection or photo-excitation. We examine the influence of extended wires that are either parallel or perpendicular to the gap of the SRRs and report on an equivalent circuit model that provides an accurate method of determining the polarisation dependent resonant response for incident light perpendicular to the surface. Good agreement is obtained for the substantial shift observed in the position of the resonances when the planar metalisation is changed from gold to aluminium

An elementary approach to toy models for D. H. Lehmer's conjecture

In 1947, Lehmer conjectured that the Ramanujan's tau function $\tau (m)$ never vanishes for all positive integers $m$, where $\tau (m)$ is the $m$-th Fourier coefficient of the cusp form $\Delta_{24}$ of weight 12. The theory of spherical $t$-design is closely related to Lehmer's conjecture because it is shown, by Venkov, de la Harpe, and Pache, that $\tau (m)=0$ is equivalent to the fact that the shell of norm $2m$ of the $E_{8}$-lattice is a spherical 8-design. So, Lehmer's conjecture is reformulated in terms of spherical $t$-design. Lehmer's conjecture is difficult to prove, and still remains open. However, Bannai-Miezaki showed that none of the nonempty shells of the integer lattice \ZZ^2 in \RR^2 is a spherical 4-design, and that none of the nonempty shells of the hexagonal lattice $A_2$ is a spherical 6-design. Moreover, none of the nonempty shells of the integer lattices associated to the algebraic integers of imaginary quadratic fields whose class number is either 1 or 2, except for \QQ(\sqrt{-1}) and \QQ(\sqrt{-3}) is a spherical 2-design. In the proof, the theory of modular forms played an important role. Recently, Yudin found an elementary proof for the case of \ZZ^{2}-lattice which does not use the theory of modular forms but uses the recent results of Calcut. In this paper, we give the elementary (i.e., modular form free) proof and discuss the relation between Calcut's results and the theory of imaginary quadratic fields.Comment: 18 page