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.

Structure-function studies of serine hydrolases: synthesis of a gene for ∝-lytic protease and the purification and characterization of a mutant β-lactamase

The author has constructed a synthetic gene for ∝-lytic protease. Since the DNA sequence of the protein is not known, the gene was designed by using the reverse translation of ∝-lytic protease's amino acid sequence. Unique restriction sites are carefully sought in the degenerate DNA sequence to aid in future mutagenesis studies. The unique restriction sites are designed approximately 50 base pairs apart and their appropriate codons used in the DNA sequence. The codons used to construct the DNA sequence of ∝-lytic protease are preferred codons in E-coli or used in the production of β-lactamase. Codon usage is also distributed evenly to ensure that one particular codon is not heavily used. The gene is essentially constructed from the outside in. The gene is built in a stepwise fashion using plasmids as the vehicles for the ∝-lytic oligomers. The use of plasmids allows the replication and isolation of large quantities of the intermediates during gene synthesis. The ∝-lytic DNA is a double-stranded oligomer that has sufficient overhang and sticky ends to anneal correctly in the vector. After six steps of incorporating ∝-lytic DNA, the gene is completed and sequenced to ensure that the correct DNA sequence is present and that no mutations occurred in the structural gene.

β-lactamase is the other serine hydrolase studied in this thesis. The author used the class A RTEM-1 β- lactamase encoded on the plasmid pBR322 to investigate the roll of the conserved threonine residue at position 71. Cassette mutagenesis was previously used to generate all possible amino acid substitutions at position 71. The work presented here describes the purification and kinetic characterization of a T71H mutant previously constructed by S. Schultz. The mutated gene was transferred into plasmid pJN for expression and induced with IPTG. The enzyme is purified by column chromatography and FPLC to homogeneity. Kinetic studies reveal that the mutant has lower k_(cat) values on benzylpenicillin, cephalothin and 6-aminopenicillanic acid but no changes in k_m except for cephalothin which is approximately 4 times higher. The mutant did not change siginificantly in its pH profile compared to the wild-type enzyme. Also, the mutant is more sensitive to thermal denaturation as compared to the wild-type enzyme. However, experimental evidence indicates that the probable generation of a positive charge at position 71 thermally stabilized the mutant.

2,4-dimethylene-1,3-cyclobutanediyl and 2,4-dimethylenebicyclobutane. Synthesis, spectroscopy, and reactivity of a triplet biradical and its covalent isomer

The preparation and direct observation of triplet 2,4-dimethylene-1,3- cyclobutanediyl (1), the non-Kekule isomer of benzene, is described. The biradical was generated by photolysis of 5,6-dimethylene-2,3- diazabicyclo[2.1.1]hex-2-ene (2) (which was synthesized in several steps from benzvalene) under cryogenic, matrix-isolation conditions. Biradical 1 was characterized by EPR spectroscopy (‌‌‌‌‌│D/hc│ =0.0204 cm^(-1), │E/hc│ =0.0028 cm^(-1)) and found to have a triplet ground state. The Δm_s= 2 transition displays hyperfine splitting attributed to a 7.3-G coupling to the ring methine and a 5.9-G coupling to the exocyclic methylene protons. Several experiments, including application of the magnetophotoselection (mps) technique in the generation of biradical 1, have allowed a determination of the zero-field triplet sublevels as x = -0.0040, y = +0.0136, and z = -0.0096 cm^(-1), where x and y are respectively the long and short in-plane axes and z the out-of-plane axis of 1.

Triplet 1 is yellow-orange and displays highly structured absorption (λ_(max)= 506 nm) and fluorescence (λ_(max) = 510 nm) spectra, with vibronic spacings of 1520 and 620 cm^(-1) for absorption and 1570 and 620 cm^(-1) for emission. The spectra were unequivocally assigned to triplet 1 by the use of a novel technique that takes advantage of the biradical's photolability. The absorption є = 7200 M^(-1) cm^(-1) and f = 0.022, establishing that the transition is spin-allowed. Further use of the mps technique has demonstrated that the transition is x-polarized, and the excited state 1s therefore of B_(1g) symmetry, in accord with theoretical predictions.

Thermolysis or direct photolysis of diazene 2 in fluid solution produces 2,4- dimethylenebicyclo[l.l.0]butane (3), whose ^(l)H NMR spectrum (-80°C, CD_(2)Cl_(2)) consists of singlets at δ 4.22 and 3.18 in a 2:1 ratio. Compound 3 is thermally unstable and dimerizes with second-order kinetics between -80 and -25°C (∆H^(‡) = 6.8 kcal mol^(-1), (∆s^(‡) = -28 eu) by a mechanism involving direct combination of two molecules of 3 in the rate-determining step. This singlet-manifold reaction ultimately produces a mixture of two dimers, 3,8,9- trimethylenetricyclo[5.1.1.0^(2,5)]non-4-ene (75) and trans-3,10-dimethylenetricyclo[6.2.0.0^(2,5)]deca-4,8-diene (76t), with the former predominating. In contrast, triplet-sensitized photolysis of 2, which leads to triplet 1, provides, in addition to 75 and 76t, a substantial amount of trans-5,10- dimethylenetricyclo[6.2.0.0^(3,6)]deca-3,8-diene (77t) and small amounts of two unidentified dimers.

In addition, triplet biradical 1 ring-closes to 3 in rigid media both thermally (77-140 K) and photochemically. In solution 3 forms triplet 1 upon energy transfer from sensitizers having relatively low triplet energies. The implications of the thermal chemistry for the energy surfaces of the system are discussed.

Numerical solution of parabolic equations by the box scheme

The box scheme proposed by H. B. Keller is a numerical method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic equations. Von Neumann stability is shown to hold for the box scheme combined with the method of fractional steps to solve the two-dimensional heat equation. Computations were performed on Burgers' equation with three different initial conditions, and Richardson extrapolation is shown to be effective.

Macaque lateral intraparietal area and oculomotor behaviors

Neurons in the primate lateral intraparietal area (area LIP) carry visual, saccade-related and eye position activities. The visual and saccade activities are anchored in a retinotopic framework and the overall response magnitude is modulated by eye position. It was proposed that the modulation by eye position might be the basis of a distributed coding of target locations in a head-centered space. Other recording studies demonstrated that area LIP is involved in oculomotor planning. These results overall suggest that area LIP transforms sensory information for motor functions. In this thesis I further explore the role of area LIP in processing saccadic eye movements by observing the effects of reversible inactivation of this area. Macaque monkeys were trained to do visually guided and memory saccades and a double saccade task to examine the use of eye position signal. Finally, by intermixing visual saccades with trials in which two targets were presented at opposite sides of the fixation point, I examined the behavior of visual extinction.

In chapter 2, I will show that lesion of area LIP results in increased latency of contralesional visual and memory saccades. Contralesional memory saccades are also hypometric and slower in velocity. Moreover, the impairment of memory saccades does not vary with the duration of the delay period. This suggests that the oculomotor deficits observed after inactivation of area LIP is not due to the disruption of spatial memory.

In chapter 3, I will show that lesion of area LIP does not severely affect the processing of spontaneous eye movement. However, the monkeys made fewer contralesional saccades and tended to confine their gaze to the ipsilesional field after inactivation of area LIP. On the other hand, lesion of area LIP results in extinction of the contralesional stimulus. When the initial fixation position was varied so that the retinal and spatial locations of the targets could be dissociated, it was found that the extinction behavior could best be described in a head-centered coordinate.

In chapter 4, I will show that inactivation of area LIP disrupts the use of eye position signal to compute the second movement correctly in the double saccade task. If the first saccade steps into the contralesional field, the error rate and latency of the second saccade are both increased. Furthermore, the direction of the first eye movement largely does not have any effect on the impairment of the second saccade. I will argue that this study provides important evidence that the extraretinal signal used for saccadic localization is eye position rather than a displacement vector.

In chapter 5, I will demonstrate that in parietal monkeys the eye drifts toward the lesion side at the end of the memory saccade in darkness. This result suggests that the eye position activity in the posterior parietal cortex is active in nature and subserves gaze holding.

Overall, these results further support the view that area LIP neurons encode spatial locations in a craniotopic framework and is involved in processing voluntary eye movements.

Synthesis of (±)-7,8-epoxy-4-basmen-6-one by a transannular cyclization strategy

The first synthesis of the cembranoid natural product (±)-7,8-epoxy-4-basmen-6- one (1) is described. Key steps of the synthetic route include the cationic cyclization of the acid chloride from 15 to provide the macrocycle 16, and the photochemical transannular radical cyclization of the ester 41 to form the tricyclic product 50. Product 50 was transformed into 1 in ten steps. Transition-state molecular modeling studies were found to provide accurate predictions of the structural and stereochemical outcomes of cyclization reactions explored experimentally in the development of the synthetic route to 1. These investigations should prove valuable in the development of transannular cyclization as a strategy for synthetic simplification.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

The design and synthesis of a true, heterogeneous, asymmetric catalyst

This work describes the design and synthesis of a true, heterogeneous, asymmetric catalyst. The catalyst consists of a thin film that resides on a high-surface- area hydrophilic solid and is composed of a chiral, hydrophilic organometallic complex dissolved in ethylene glycol. Reactions of prochiral organic reactants take place predominantly at the ethylene glycol-bulk organic interface.

The synthesis of this new heterogeneous catalyst is accomplished in a series of designed steps. A novel, water-soluble, tetrasulfonated 2,2'-bis (diphenylphosphino)-1,1'-binaphthyl (BINAP-4S0_3Na) is synthesized by direct sulfonation of 2,2'-bis(diphenylphosphino)-1,1'-binaphthyl (BINAP). The rhodium (I) complex of BINAP-4SO_3Na is prepared and is shown to be the first homogeneous catalyst to perform asymmetric reductions of prochiral 2-acetamidoacrylic acids in neat water with enantioselectivities as high as those obtained in non-aqueous solvents. The ruthenium (II) complex, [Ru(BINAP-4SO_3Na)(benzene)Cl]Cl is also synthesized and exhibits a broader substrate specificity as well as higher enantioselectivities for the homogeneous asymmetric reduction of prochiral 2-acylamino acid precursors in water. Aquation of the ruthenium-chloro bond in water is found to be detrimental to the enantioselectivity with some substrates. Replacement of water by ethylene glycol results in the same high e.e's as those found in neat methanol. The ruthenium complex is impregnated onto a controlled pore-size glass CPG-240 by the incipient wetness technique. Anhydrous ethylene glycol is used as the immobilizing agent in this heterogeneous catalyst, and a non-polar 1:1 mixture of chloroform and cyclohexane is employed as the organic phase.

Asymmetric reduction of 2-(6'-methoxy-2'-naphthyl)acrylic acid to the non-steroidal anti-inflammatory agent, naproxen, is accomplished with this heterogeneous catalyst at a third of the rate observed in homogeneous solution with an e.e. of 96% at a reaction temperature of 3°C and 1,400 psig of hydrogen. No leaching of the ruthenium complex into the bulk organic phase is found at a detection limit of 32 ppb. Recycling of the catalyst is possible without any loss in enantioselectivity. Long-term stability of this new heterogeneous catalyst is proven by a self-assembly test. That is, under the reaction conditions, the individual components of the present catalytic system self-assemble into the supported-catalyst configuration.

The strategies outlined here for the design and synthesis of this new heterogeneous catalyst are general, and can hopefully be applied to the development of other heterogeneous, asymmetric catalysts.

Conformal geometry processing

This thesis introduces fundamental equations and numerical methods for manipulating surfaces in three dimensions via conformal transformations. Conformal transformations are valuable in applications because they naturally preserve the integrity of geometric data. To date, however, there has been no clearly stated and consistent theory of conformal transformations that can be used to develop general-purpose geometry processing algorithms: previous methods for computing conformal maps have been restricted to the flat two-dimensional plane, or other spaces of constant curvature. In contrast, our formulation can be used to produce---for the first time---general surface deformations that are perfectly conformal in the limit of refinement. It is for this reason that we commandeer the title Conformal Geometry Processing.

The main contribution of this thesis is analysis and discretization of a certain time-independent Dirac equation, which plays a central role in our theory. Given an immersed surface, we wish to construct new immersions that (i) induce a conformally equivalent metric and (ii) exhibit a prescribed change in extrinsic curvature. Curvature determines the potential in the Dirac equation; the solution of this equation determines the geometry of the new surface. We derive the precise conditions under which curvature is allowed to evolve, and develop efficient numerical algorithms for solving the Dirac equation on triangulated surfaces.

From a practical perspective, this theory has a variety of benefits: conformal maps are desirable in geometry processing because they do not exhibit shear, and therefore preserve textures as well as the quality of the mesh itself. Our discretization yields a sparse linear system that is simple to build and can be used to efficiently edit surfaces by manipulating curvature and boundary data, as demonstrated via several mesh processing applications. We also present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces.

A study of protein targeting reveals insights into mitigating protein aggregation

A unique chloroplast Signal Recognition Particle (SRP) in green plants is primarily dedicated to the post-translational targeting of light harvesting chlorophyll-a/b binding (LHC) proteins. Our study of the thermodynamics and kinetics of the GTPases of the system demonstrates that GTPase complex assembly and activation are highly coupled in the chloroplast GTPases, suggesting they may forego the GTPase activation step as a key regulatory point. This reflects adaptations of the chloroplast SRP to the delivery of their unique substrate protein. Devotion to one highly hydrophobic family of proteins also may have allowed the chloroplast SRP system to evolve an efficient chaperone in the cpSRP43 subunit. To understand the mechanism of disaggregation, we showed that LHC proteins form micellar, disc-shaped aggregates that present a recognition motif (L18) on the aggregate surface. Further molecular genetic and structure-activity analyses reveal that the action of cpSRP43 can be dissected into two steps: (i) initial recognition of L18 on the aggregate surface; and (ii) aggregate remodeling, during which highly adaptable binding interactions of cpSRP43 with hydrophobic transmembrane domains of the substrate protein compete with the packing interactions within the aggregate. We also tested the adaptability of cpSRP43 for alternative substrates, specifically in attempts to improve membrane protein expression and inhibition of amyloid beta fibrillization. These preliminary results attest to cpSRP43’s potential as a molecular chaperone and provides the impetus for further engineering endeavors to address problems that stem from protein aggregation.

Robust near-threshold QDI circuit analysis and design

The two most important digital-system design goals today are to reduce power consumption and to increase reliability. Reductions in power consumption improve battery life in the mobile space and reductions in energy lower operating costs in the datacenter. Increased robustness and reliability shorten down time, improve yield, and are invaluable in the context of safety-critical systems. While optimizing towards these two goals is important at all design levels, optimizations at the circuit level have the furthest reaching effects; they apply to all digital systems. This dissertation presents a study of robust minimum-energy digital circuit design and analysis. It introduces new device models, metrics, and methods of calculation—all necessary first steps towards building better systems—and demonstrates how to apply these techniques. It analyzes a fabricated chip (a full-custom QDI microcontroller designed at Caltech and taped-out in 40-nm silicon) by calculating the minimum energy operating point and quantifying the chip’s robustness in the face of both timing and functional failures.

Catalytic conversion of nitrogen to ammonia by an iron model complex

Threefold symmetric Fe phosphine complexes have been used to model the structural and functional aspects of biological N₂ fixation by nitrogenases. Low-valent bridging Fe-S-Fe complexes in the formal oxidation states Fe(II)Fe(II), Fe(II)/Fe(I), and Fe(I)/Fe(I) have been synthesized which display rich spectroscopic and magnetic behavior. A series of cationic tris-phosphine borane (TPB) ligated Fe complexes have been synthesized and been shown to bind a variety of nitrogenous ligands including N₂H₄, NH₃, and NH₂-. These complexes are all high spin S = 3/2 and display EPR and magnetic characteristics typical of this spin state. Furthermore, a sequential protonation and reduction sequence of a terminal amide results in loss of NH₃ and uptake of N₂. These stoichiometric transformations represent the final steps in potential N₂ fixation schemes.

Treatment of an anionic FeN₂ complex with excess acid also results in the formation of some NH₃, suggesting the possibility of a catalytic cycle for the conversion of N₂ to NH₃ mediated by Fe. Indeed, use of excess acid and reductant results in the formation of seven equivalents of NH₃ per Fe center, demonstrating Fe mediated catalytic N₂ fixation with acids and protons for the first time. Numerous control experiments indicate that this catalysis is likely being mediated by a molecular species.

A number of other phosphine ligated Fe complexes have also been tested for catalysis and suggest that a hemi-labile Fe-B interaction may be critical for catalysis. Additionally, various conditions for the catalysis have been investigated. These studies further support the assignment of a molecular species and delineate some of the conditions required for catalysis.

Finally, combined spectroscopic studies have been performed on a putative intermediate for catalysis. These studies converge on an assignment of this new species as a hydrazido(2-) complex. Such species have been known on group 6 metals for some time, but this represents the first characterization of this ligand on Fe. Further spectroscopic studies suggest that this species is present in catalytic mixtures, which suggests that the first steps of a distal mechanism for N₂ fixation are feasible in this system.

Pattern formation during Caenorhabditis Elegans vulval development

Pattern formation during animal development involves at least three processes: establishment of the competence of precursor cells to respond to intercellular signals, formation of a pattern of different cell fates adopted by precursor cells, and execution of the cell fate by generating a pattern of distinct descendants from precursor cells. I have analyzed the fundamental mechanisms of pattern formation by studying the development of Caenorhabditis elegans vulva.

In C. elegans, six multipotential vulval precursor cells (VPCs) are competent to respond to an inductive signal LIN-3 (EGF) mediated by LET- 23 (RTK) and a lateral signal via LIN-12 (Notch) to form a fixed pattern of 3°-3°-2°-1°-2°-3°. Results from expressing LIN-3 as a function of time in animals lacking endogenous LIN-3 indicate that both VPCs and VPC daughters are competent to respond to LIN-3. Although the daughters of VPCs specified to be 2° or 3° can be redirected to adopt the 1°fate, the decision to adopt the 1° fate is irreversible. Coupling of VPC competence to cell cycle progression reveals that VPC competence may be periodic during each cell cycle and involve LIN-39 (HOM-C). These mechanisms are essential to ensure a bias towards the 1° fate, while preventing an excessive response.

After adopting the 1° fate, the VPC executes its fate by dividing three rounds to form a fixed pattern of four inner vulF and four outer vulE descendants. These two types of descendants can be distinguished by a molecular marker zmp-1::GFP. A short-range signal from the anchor cell (AC), along with signaling between the inner and outer 1° VPC descendants and intrinsic polarity of 1° VPC daughters, patterns the 1° lineage. The Ras and the Wnt signaling pathways may be involved in these mechanisms.

The temporal expression pattern of egl-17::GFP, another marker ofthe 1° fate, correlates with three different steps of 1° fate execution: the commitment to the 1° fate, as well as later steps before and after establishment of the uterine-vulval connection. Six transcription factors, including LIN-1(ETS), LIN-39 (HOM-C), LIN-11(LIM), LIN-29 (zinc finger), COG-1 (homeobox) and EGL-38 (PAX2/5/8), are involved in different steps during 1° fate execution.

Seismic reflection experiments imaging the physical nature of crustal structures in southern California

Seismic reflection methods have been extensively used to probe the Earth's crust and suggest the nature of its formative processes. The analysis of multi-offset seismic reflection data extends the technique from a reconnaissance method to a powerful scientific tool that can be applied to test specific hypotheses. The treatment of reflections at multiple offsets becomes tractable if the assumptions of high-frequency rays are valid for the problem being considered. Their validity can be tested by applying the methods of analysis to full wave synthetics.

Three studies illustrate the application of these principles to investigations of the nature of the crust in southern California. A survey shot by the COCORP consortium in 1977 across the San Andreas fault near Parkfield revealed events in the record sections whose arrival time decreased with offset. The reflectors generating these events are imaged using a multi-offset three-dimensional Kirchhoff migration. Migrations of full wave acoustic synthetics having the same limitations in geometric coverage as the field survey demonstrate the utility of this back projection process for imaging. The migrated depth sections show the locations of the major physical boundaries of the San Andreas fault zone. The zone is bounded on the southwest by a near-vertical fault juxtaposing a Tertiary sedimentary section against uplifted crystalline rocks of the fault zone block. On the northeast, the fault zone is bounded by a fault dipping into the San Andreas, which includes slices of serpentinized ultramafics, intersecting it at 3 km depth. These interpretations can be made despite complications introduced by lateral heterogeneities.

In 1985 the Calcrust consortium designed a survey in the eastern Mojave desert to image structures in both the shallow and the deep crust. Preliminary field experiments showed that the major geophysical acquisition problem to be solved was the poor penetration of seismic energy through a low-velocity surface layer. Its effects could be mitigated through special acquisition and processing techniques. Data obtained from industry showed that quality data could be obtained from areas having a deeper, older sedimentary cover, causing a re-definition of the geologic objectives. Long offset stationary arrays were designed to provide reversed, wider angle coverage of the deep crust over parts of the survey. The preliminary field tests and constant monitoring of data quality and parameter adjustment allowed 108 km of excellent crustal data to be obtained.

This dataset, along with two others from the central and western Mojave, was used to constrain rock properties and the physical condition of the crust. The multi-offset analysis proceeded in two steps. First, an increase in reflection peak frequency with offset is indicative of a thinly layered reflector. The thickness and velocity contrast of the layering can be calculated from the spectral dispersion, to discriminate between structures resulting from broad scale or local effects. Second, the amplitude effects at different offsets of P-P scattering from weak elastic heterogeneities indicate whether the signs of the changes in density, rigidity, and Lame's parameter at the reflector agree or are opposed. The effects of reflection generation and propagation in a heterogeneous, anisotropic crust were contained by the design of the experiment and the simplicity of the observed amplitude and frequency trends. Multi-offset spectra and amplitude trend stacks of the three Mojave Desert datasets suggest that the most reflective structures in the middle crust are strong Poisson's ratio (σ) contrasts. Porous zones or the juxtaposition of units of mutually distant origin are indicated. Heterogeneities in σ increase towards the top of a basal crustal zone at ~22 km depth. The transition to the basal zone and to the mantle include increases in σ. The Moho itself includes ~400 m layering having a velocity higher than that of the uppermost mantle. The Moho maintains the same configuration across the Mojave despite 5 km of crustal thinning near the Colorado River. This indicates that Miocene extension there either thinned just the basal zone, or that the basal zone developed regionally after the extensional event.