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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1440-1443 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper extends recent results by the author [J. Math. Phys. 31, 1898 (1990), J. Math. Phys. 32, 57 (1991)] that show a scaling parameter sequence h yields an orthonormal wavelet basis for L2(R) if and only if an associated operator Sh has eigenvalue 1 with multiplicity 1. The operator transforms a sequence a by Sh(a)(k)=2Σm,n∼(h(m))h(n)a(2k+m−n). A correspondence is derived between Sh and Galerkin projection operators related to the multiresolution analysis defined by the orthonormal wavelet basis. The spectrum of Sh is characterized in terms of the Fourier modulus of the (unique) scaling function φ that satisfies φ(x)=2Σnh(n)φ(2x−n). This characterization yields several results including a direct, alternate proof that the eigenvalue 1 of Sh has multiplicity 1.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1898-1901 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by Daubechies [Commun. Pure Appl. Math. 41, 909 (1988)]. For each integer N≥1, a family of wavelet functions ψ having support [0,2N−1] is constructed such that {ψjk(x)=2j/2ψ(2jx−k) kj,k∈Z} is a tight frame of L2(R), i.e., for every f∈L2(R), f=c∑jk 〈ψjk||f〉ψjk for some c〉0. This family is parametrized by an algebraic subset VN of R4N. Furthermore, for N≥2, a proper algebraic subset WN of VN is specified such that all points in VN outside of WN yield orthonormal bases. The relationship between these tight frames and the theory of group representations and coherent states is discussed.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 57-61 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper proves a previous conjecture of the author characterizing sequences h∈l2(Z) that yield orthonormal wavelet bases of L2(R) in terms of the multiplicity of the eigenvalue 1 of an operator associated to h. The proof utilizes a result of Cohen characterizing these sequences in terms of the real zeros of their Fourier transforms. The mapping from sequences to wavelets is shown to define a continuous mapping from a subset of l2(Z) into L2(R). Related conjectures are discussed.
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  • 4
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 51 (1987), S. 403-405 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We have calculated the response of a nonlinear directional coupler fabricated in an AlGaAs/GaAs structure using a realistic model for the optical nonlinearities. The model takes into account carrier-density-dependent index of refraction and absorption, and lateral carrier diffusion in each of the two coupled channel waveguides. Our results differ considerably from those obtained using a Kerr model for the optical nonlinearities.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 3297-3301 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Measurements on commercially available fused silica fibers and fiber tapers have shown that Nd:glass laser pulses of irradiance 〉3.5 GW cm−2 can be transmitted without bulk or surface damage. Optical energy at the fiber output can be used for efficient acceleration of thin metal foils. For 0.025-mm-thick aluminum coupled to a 0.2-mm-diam fiber, target foil velocities up to 2.3 km s−1 have been achieved with very modest laser energies (〈25 mJ).
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  • 6
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 77 (2000), S. 3797-3799 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We calculate the self-capacitance and charging energy of a spherical nanoparticle in the Thomas–Fermi approximation. The result is CTF=C0[1−p−1 tanh p]/[1−(1−cursive-epsilon−1)p−1 tanh p], with CTF≥C0. Here C0=4πcursive-epsilon0R is the classical geometrical value, p=R/l is the ratio of the particle radius R to the Thomas–Fermi screening length l, and cursive-epsilon is the material dielectric constant. The addition of surface localized states drives C toward C0. These results should be relevant to tunneling spectroscopy studies of giant carbon onions and "large" semiconductor nanocrystals that do not require a full quantum treatment. © 2000 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 65 (1994), S. 2542-2544 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Optically controlled planar orientation of liquid crystal molecules with polarized light is used to make phase gratings in liquid crystal media. The electro-optical properties of liquid crystal linear and chirped gratings are discussed. © 1994 American Institute of Physics.
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  • 8
    Publication Date: 2014-04-14
    Description: The mechanistic basis of regulatory variation and the prevailing evolutionary forces shaping that variation are known to differ between sexes and between chromosomes. Regulatory variation of gene expression can be due to functional changes within a gene itself ( cis ) or in other genes elsewhere in the genome ( trans ). The evolutionary properties of cis mutations are expected to differ from mutations affecting gene expression in trans . We analyze allele-specific expression across a set of X substitution lines in intact adult Drosophila simulans to evaluate whether regulatory variation differs for cis and trans , for males and females, and for X-linked and autosomal genes. Regulatory variation is common (56% of genes), and patterns of variation within D. simulans are consistent with previous observations in Drosophila that there is more cis than trans variation within species (47% vs. 25%, respectively). The relationship between sex-bias and sex-limited variation is remarkably consistent across sexes. However, there are differences between cis and trans effects: cis variants show evidence of purifying selection in the sex toward which expression is biased, while trans variants do not. For female-biased genes, the X is depleted for trans variation in a manner consistent with a female-dominated selection regime on the X. Surprisingly, there is no evidence for depletion of trans variation for male-biased genes on X. This is evidence for regulatory feminization of the X, trans -acting factors controlling male-biased genes are more likely to be found on the autosomes than those controlling female-biased genes.
    Electronic ISSN: 1759-6653
    Topics: Biology
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  • 9
    Publication Date: 2013-01-06
    Description: We explore the evolutionary origins of dosage compensation (DC) in sex chromosomes in the context of metabolic control theory. We consider first the cost of gene loss (hemizygosity) per se in reducing flux, and examine two relationships between flux and fitness (linear and Gaussian) to calculate a fitness cost of hemizygosity. Recognizing that new sex chromosomes are derived from autosomes, we also calculate the cost of unmasking deleterious mutations segregating on the nascent sex chromosomes as loci become hemizygous. The importance of deleterious mutations to the fitness cost of hemizygosity depends on their frequency, and on the relative costs of halving gene dose for wild-type alleles. We then consider the evolution of DC in response to gene loss, and include a cost of overexpression (i.e., DC such that expression exceeds the wild-type homozygote). Even with costs to excess flux, hypomorphic mutations can cause the optimal level of DC to be higher than 2-fold when the absolute cost of hemizygosity is small. Finally, we propose a three-step model of DC evolution: 1) once recombination ceases and the Y begins to deteriorate, genes from longer metabolic pathways should be lost first, as halving these genes does not drastically reduce flux or, thereby, fitness; 2) both the cost of hemizygosity and the presence of hypomorphic mutations will drive an increase in expression, that is, DC; 3) existing DC will now permit loss of genes in short pathways.
    Electronic ISSN: 1759-6653
    Topics: Biology
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  • 10
    Publication Date: 2016-10-08
    Description: Sigma virus (DMelSV) is ubiquitous in natural populations of Drosophila melanogaster. Host-mediated, selective RNA editing of adenosines to inosines (ADAR) may contribute to control of viral infection by preventing transcripts from being transported into the cytoplasm or being translated accurately; or by increasing the viral genomic mutation rate. Previous PCR-based studies showed that ADAR mutations occur in DMelSV at low frequency. Here we use SOLiD TM deep sequencing of flies from a single host population from Athens, GA, USA to comprehensively evaluate patterns of sequence variation in DMelSV with respect to ADAR. GA dinucleotides, which are weak targets of ADAR, are strongly overrepresented in the positive strand of the virus, consistent with selection to generate ADAR resistance on this complement of the transient, double-stranded RNA intermediate in replication and transcription. Potential ADAR sites in a worldwide sample of viruses are more likely to be "resistant" if the sites do not vary among samples. Either variable sites are less constrained and hence are subject to weaker selection than conserved sites, or the variation is driven by ADAR. We also find evidence of mutations segregating within hosts, hereafter referred to as hypervariable sites. Some of these sites were variable only in one or two flies (i.e., rare); others were shared by four or even all five of the flies (i.e., common). Rare and common hypervariable sites were indistinguishable with respect to susceptibility to ADAR; however, polymorphism in rare sites were more likely to be consistent with the action of ADAR than in common ones, again suggesting that ADAR is deleterious to the virus. Thus, in DMelSV, host mutagenesis is constraining viral evolution both within and between hosts.
    Electronic ISSN: 1759-6653
    Topics: Biology
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