Negative regulators of a growth factor-mediated signaling pathway in the nematode Caenorhabditis elegans

Vulval differentiation in C. elegans is mediated by an Epidermal growth factor (EGF)- EGF receptor (EGFR) signaling pathway. I have cloned unc-101, a negative regulator of vulval differentiation of the nematode C. elegans. unc-101 encodes a homolog of AP47, the medium chain of the trans-Golgi clathrin-associated protein complex. This identity was confirmed by cloning and comparing sequence of a C. elegans homolog of AP50, the medium chain of the plasma membrane clathrin-associated protein complex. I provided the first genetic evidence that the trans-Golgi clathrin-coated vesicles are involved in regulation of an EGF signaling pathway. Most of the unc-101 alleles are deletions or nonsense mutations, suggesting that these alleles severely reduce the unc-101 activity. A hybrid gene that contains parts of unc-101 and mouse AP4 7 rescued at least two phenotypes of unc-101 mutations, the Unc and the suppression of vulvaless phenotype of let-23(sy1) mutation. Therefore, the functions of AP47 are conserved between nematodes and mammals.

unc-101 mutations can cause a greater than wild-type vulval differentiation in combination with certain mutations in sli-1, another negative regulator of the vulval induction pathway. A mutation in a new gene, rok-1, causes no defect by itself, but causes a greater than wild-type vulval differentiation in the presence of a sli-1 mutation. The unc-101; rok-1; sli-1 triple mutants display a greater extent of vulval differentiation than any double mutant combinations of unc-101, rok-1 and sli-1. Therefore, rok-1 locus defines another negative regulator of the vulval induction pathway.

I analyzed a second gene encoding an AP47 homolog in C. elegans. This gene, CEAP47, encodes a protein 72% identical to both unc-101 and mammalian AP47. A hybrid gene containing parts of unc-101 and CEAP47 sequences can rescue phenotypes of unc-101 mutants, indicating that UNC- 101 and CEAP47 proteins can be redundant if expressed in the same set of cells.

Diffraction-limited imaging on the 200-inch telescope

We have used the technique of non-redundant masking at the Palomar 200-inch telescope and radio VLBI imaging software to make optical aperture synthesis maps of two binary stars, β Corona Borealis and σ Herculis. The dynamic range of the map of β CrB, a binary star with a separation of 230 milliarcseconds is 50:1. For σ Her, we find a separation of 70 milliarcseconds and the dynamic range of our image is 30:1. These demonstrate the potential of the non-redundant masking technique for diffraction-limited imaging of astronomical objects with high dynamic range.

We find that the optimal integration time for measuring the closure phase is longer than that for measuring the fringe amplitude. There is not a close relationship between amplitude errors and phase errors, as is found in radio interferometry. Amplitude self calibration is less effective at optical wavelengths than at radio wavelengths. Primary beam sensitivity correction made in radio aperture synthesis is not necessary in optical aperture synthesis.

The effects of atmospheric disturbances on optical aperture synthesis have been studied by Monte Carlo simulations based on the Kolmogorov theory of refractive-index fluctuations. For the non-redundant masking with τ_c-sized apertures, the simulated fringe amplitude gives an upper bound of the observed fringe amplitude. A smooth transition is seen from the non-redundant masking regime to the speckle regime with increasing aperture size. The fractional reduction of the fringe amplitude according to the bandwidth is nearly independent of the aperture size. The limiting magnitude of optical aperture synthesis with τ_c-sized apertures and that with apertures larger than τ_c are derived.

Monte Carlo simulations are also made to study the sensitivity and resolution of the bispectral analysis of speckle interferometry. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of the heuristic interferometric view of image-forming process in the mid-spatial-frequency range. The signal-to- noise ratio of the bispectrum at arbitrary light levels is derived in the mid-spatial-frequency range.

The non-redundant masking technique is suitable for imaging bright objects with high resolution and high dynamic range, while the faintest limit will be better pursued by speckle imaging.

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.