Studying conscious and unconscious vision with functional Magnetic Resonance Imaging : the BOLD promise

Waking up from a dreamless sleep, I open my eyes, recognize my wife’s face and am filled with joy. In this thesis, I used functional Magnetic Resonance Imaging (fMRI) to gain insights into the mechanisms involved in this seemingly simple daily occurrence, which poses at least three great challenges to neuroscience: how does conscious experience arise from the activity of the brain? How does the brain process visual input to the point of recognizing individual faces? How does the brain store semantic knowledge about people that we know? To start tackling the first question, I studied the neural correlates of unconscious processing of invisible faces. I was unable to image significant activations related to the processing of completely invisible faces, despite existing reports in the literature. I thus moved on to the next question and studied how recognition of a familiar person was achieved in the brain; I focused on finding invariant representations of person identity – representations that would be activated any time we think of a familiar person, read their name, see their picture, hear them talk, etc. There again, I could not find significant evidence for such representations with fMRI, even in regions where they had previously been found with single unit recordings in human patients (the Jennifer Aniston neurons). Faced with these null outcomes, the scope of my investigations eventually turned back towards the technique that I had been using, fMRI, and the recently praised analytical tools that I had been trusting, Multivariate Pattern Analysis. After a mostly disappointing attempt at replicating a strong single unit finding of a categorical response to animals in the right human amygdala with fMRI, I put fMRI decoding to an ultimate test with a unique dataset acquired in the macaque monkey. There I showed a dissociation between the ability of fMRI to pick up face viewpoint information and its inability to pick up face identity information, which I mostly traced back to the poor clustering of identity selective units. Though fMRI decoding is a powerful new analytical tool, it does not rid fMRI of its inherent limitations as a hemodynamics-based measure.

The intramolecular Buchner reaction of α-diazo-β-ketonitriles : development and application to the total synthesis of (+)-Salvileucalin B

Since its discovery in 1896, the Buchner reaction has fascinated chemists for more than a century. The highly reactive nature of the carbene intermediates allows for facile dearomatization of stable aromatic rings, and provides access to a diverse array of cyclopropane and seven-membered ring architectures. The power inherent in this transformation has been exploited in the context of a natural product total synthesis and methodology studies.

The total synthesis work details efforts employed in the enantioselective total synthesis of (+)-salvileucalin B. The fully-substituted cyclopropane within the core of the molecule arises from an unprecedented intramolecular Buchner reaction involving a highly functionalized arene and an α-diazo-β-ketonitrile. An unusual retro-Claisen rearrangement of a complex late-stage intermediate was discovered on route to the natural product.

The unique reactivity of α-diazo-β-ketonitriles toward arene cyclopropanation was then investigated in a broader methodological study. This specific di-substituted diazo moiety possesses hitherto unreported selectivity in intramolecular Buchner reactions. This technology was enables the preparation of highly functionalized norcaradienes and cyclopropanes, which themselves undergo various ring opening transformations to afford complex polycyclic structures.

Finally, an enantioselective variant of the intramolecular Buchner reaction is described. Various chiral copper and dirhodium catalysts afforded moderate stereoinduction in the cyclization event.

A report on increasing the thrust of a turbojet engine by combustion of fuel in the tail pipe

The purpose of this work was to develop a means of increasing the thrust of a turbojet engine by burning kerosene in the tail pipe.

A combustion system was developed which gave the following results:
(l) Maximum thrust increase using a G.E. I-14 engine was 64 per cent over straight tail pipe thrust corresponding to 42 per cent increase over the normal engine thrust. This increase was accomplished at an engine rpm of 12,000.
(2) Increase of maximum thrust obtained was 51 per cent over the straight tail pipe thrust corresponding to 23 per cent over the normal engine thrust. This increase was accomplished at an engine rpm of l6,000.
(3) For the thrust increases mentioned in (1) and (2) above, increases of Specific Fuel Consumption were 66 per cent and 76 per cent respectively over normal engine SFC.

Mechanism and applications of the photochemistry of Bis(η^5-cyclopentadienyl)titanacyclobutanes

The photochemically induced reductive elimination of cyclopropanes from bis(η⁵-cyclopentadienyl)titanacyclobutanes has been examined. Stereochemical labelling studies indicate that the cyclopropane is initially formed in a 6±1:1, ratio favoring retention of stereochemistry. The starting titanacyclobutane is isomerized during the course of the reaction. The isomerization of the starting material results from metal-carbon bond homolysis to yield a 1,4-biradical, which can either close to give the starting material or generate cyclopropane. The 1,4-biradical can be observed through a cyclopropyl carbinyl rearrangement employing 2-bis(η⁵- cyclopentadienyl)titana-5,5-dimethylbicyclo[2.1.0]pentane, to give the titanium alkylidene, 1-bis(η⁵-cyclopentadienyl)titana-3,3-dimethyl-1,4- pentadiene, which can be observed directly by NMR at low temperature.

The oxidation of titanacyclobutanes by chemical and electrochemical methods also yields cyclopropanes. Reduction of the metal center does not yield cyclopropanes. Depending on the oxidant, stereochemically labelled titanacyclobutanes yield cyclopropanes that are between 7:1 and 100:1 retention:isomerization. The fragmentation reaction resembles the photochemically induced reductive elimination. Both result from formal oxidation of a metal-carbon bond, which then results in very rapid formation of cyclopropane.

The titanocene generated photochemically reacts with a variety of substrates even at low temperature. Titanocene can be generated in a glass at 77 K. The titanocene can be trapped in noncoordinating solvents in high yield with bulky internal acetylenes to give monoacetylene adducts of titanocene. Less bulky acetylenes give the titanacyclopentadienes. The titanocene can be trapped with olefins to give less stable adducts, which appear by NMR analysis to be intermediate in structure between a titanacyclopropane and an η² olefin adduct of titanocene. Reaction of titanocene with butadiene gives a stable product, which appears to be the s-trans butadiene adduct of titanocene. It does not isomerize on heating. Titanocene reacts with epoxides to give titanocene-µ-oxo polymer and olefin. Stereochemically labelled epoxides and episulfides yield isomerized olefin upon deoxygenation by titanocene. The observations are rationalized as a result of a 1,4-biradical formed by stepwise insertion of titanocene into a carbon-oxygen bond.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Water conservation in the city of Pasadena

The object of this report will be to make a complete study of the water that is wasted in the storm drains of Pasadena and determine if there is any practical way of conserving this water.

The pyrolysis of n-butane

A study of the pyrolysis of n-butane was carried out using an all-gold tubular reactor. The initial rate of decomposition of the n-butane was of 1.50-order with respect to the partial pressure of the n-butane. A free radical mechanism, similar to that originally proposed by Rice, accounted satisfactorily for the distribution of products. Oxygen was rigorously excluded from the pyrolysis gases. The surfaces of the gold reactor had been acid-treated to remove oxide impurities. Some preliminary experiments were performed in the partial oxidation of n-butane.

On the Cesari fixed point method in a Banach space

In a paper published in 1961, L. Cesari [1] introduces a method which extends certain earlier existence theorems of Cesari and Hale ([2] to [6]) for perturbation problems to strictly nonlinear problems. Various authors ([1], [7] to [15]) have now applied this method to nonlinear ordinary and partial differential equations. The basic idea of the method is to use the contraction principle to reduce an infinite-dimensional fixed point problem to a finite-dimensional problem which may be attacked using the methods of fixed point indexes.

The following is my formulation of the Cesari fixed point method:

Let B be a Banach space and let S be a finite-dimensional linear subspace of B. Let P be a projection of B onto S and suppose Г≤B such that pГ is compact and such that for every x in PГ, P^-1x∩Г is closed. Let W be a continuous mapping from Г into B. The Cesari method gives sufficient conditions for the existence of a fixed point of W in Г.

Let I denote the identity mapping in B. Clearly y = Wy for some y in Г if and only if both of the following conditions hold:

(i) Py = PWy.

(ii) y = (P + (I - P)W)y.

Definition. The Cesari fixed paint method applies to (Г, W, P) if and only if the following three conditions are satisfied:

(1) For each x in PГ, P + (I - P)W is a contraction from P^-1x∩Г into itself. Let y(x) be that element (uniqueness follows from the contraction principle) of P^-1x∩Г which satisfies the equation y(x) = Py(x) + (I-P)Wy(x).

(2) The function y just defined is continuous from PГ into B.

(3) There are no fixed points of PWy on the boundary of PГ, so that the (finite- dimensional) fixed point index i(PWy, int PГ) is defined.

Definition. If the Cesari fixed point method applies to (Г, W, P) then define i(Г, W, P) to be the index i(PWy, int PГ).

The three theorems of this thesis can now be easily stated.

Theorem 1 (Cesari). If i(Г, W, P) is defined and i(Г, W, P) ≠0, then there is a fixed point of W in Г.

Theorem 2. Let the Cesari fixed point method apply to both (Г, W, P₁) and (Г, W, P₂). Assume that P₂P₁=P₁P₂=P₁ and assume that either of the following two conditions holds:

(1) For every b in B and every z in the range of P₂, we have that ‖b=P₂b‖ ≤ ‖b-z‖

(2)P₂Г is convex.

Then i(Г, W, P₁) = i(Г, W, P₂).

Theorem 3. If Ω is a bounded open set and W is a compact operator defined on Ω so that the (infinite-dimensional) Leray-Schauder index i_LS(W, Ω) is defined, and if the Cesari fixed point method applies to (Ω, W, P), then i(Ω, W, P) = i_LS(W, Ω).

Theorems 2 and 3 are proved using mainly a homotopy theorem and a reduction theorem for the finite-dimensional and the Leray-Schauder indexes. These and other properties of indexes will be listed before the theorem in which they are used.

Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.