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Learning algorithms for neural networks

This thesis deals mainly with the development of new learning algorithms and the study of the dynamics of neural networks. We develop a method for training feedback neural networks. Appropriate stability conditions are derived, and learning is performed by the gradient descent technique. We develop a new associative memory model using Hopfield's continuous feedback network. We demonstrate some of the storage limitations of the Hopfield network, and develop alternative architectures and an algorithm for designing the associative memory. We propose a new unsupervised learning method for neural networks. The method is based on applying repeatedly the gradient ascent technique on a defined criterion function. We study some of the dynamical aspects of Hopfield networks. New stability results are derived. Oscillations and synchronizations in several architectures are studied, and related to recent findings in biology. The problem of recording the outputs of real neural networks is considered

Computational design and experimental characterization of protein oligomers

Previous efforts in designing protein binding interfaces have focused on altering binding specificities. These methods fall short, however, when applied to the design of novel binding sites due to difficulties in accurately modeling protein backbones. The goal of this project is to create dimers from monomeric proteins. We developed a special docking algorithm that positions the member protein subunits to a plausible configuration with respect to each other using parameters determined from known complex structures. The docking procedure treats the proteins as rigid bodies and uses Fourier correlation theorem and fast Fourier transform to efficiently search for dimers with the highest interfacial surface complementarities. Using the docked structures as scaffolds for design and employing hydrophobic surface residues to drive dimer formation, we have demonstrated two successful designs, one heterodimer and one homodimer, using protein G and engrailed homeodomain respectively as the starting monomeric proteins. The designed dimers were characterized using circular dichroism, nuclear magnetic resonance, analytical ultracentrifugation, and X-ray crystallography methods. This is the first report of computationally designed de novo protein homodimers generated using a combination of protein docking and protein design tools. These results suggest that this strategy can be used to address the protein recognition problem, and is generally applicable to creating novel binding sites with compatible binding partners

Experiments on the upstream wake in magnetofluid dynamics

Measurements have been made of the perturbation magnetic field in front of a semi-infinite Rankine body moving parallel to a uniform impressed magnetic field in a conducting fluid. The purpose of these experiments was to investigate the so-called upstream wake effect which has been predicted by theory. It is believed that these are the first experiments in which the upstream wake was observed.

Bandwidth limitations and synthesis procedures for negative resistance and variable reactance amplifiers

The bandwidth limitation on the reflection coefficient of circuits containing a reactance limited negative conductance such as a tunnel diode is derived, and the insertion loss method of modern network theory is adapted to the synthesis of low pass ladder equivalents of amplifiers containing these elements. Amplifiers which have a considerable bandwidth advantage over simple single tuned circuits, and which approach the ultimate bandwidth limit as rapidly as possible as the number of passive components is increased, are demonstrated.

Cell polarity and morphogenesis: functions and mechanisms of cell divisions in vertebrate gastrulation

Gastrulation shapes a vertebrate embryo from an egg-shaped aggregate of cells. In many vertebrates, massive cell divisions occur during gastrulation. In this thesis, I investigate the pattern, function, and regulation of mitotic divisions in zebrafish gastrulation.

Ignition and combustion in a laminar mixing zone

The equations describing combustion in a flow field are modified for use in laminar flows where the so called boundary layer approximations may be employed. These equations are transformed into a corresponding incompressible flow with the Howarth transformation.

As an example of the use of boundary layer concepts this analysis considers the ignition and combustion in the laminar mixing zone between two parallel moving gas streams. One stream consists of a cool combustible mixture, the second is hot combustion products. The two streams come into contact at a given point and a laminar mixing process follows in which the velocity distribution is modified by viscosity, and the temperature and composition distributions by conduction, diffusion and chemical reaction. The decomposition of the combustible stream is assumed to follow first-order reaction kinetics with temperature dependence according to the Arrhenius law. For a given initial velocity, composition, and temperature distribution, the questions to be answered are: (1) Does the combustible material ignite and (2) How far downstream of the initial contact point does the flame appear and what is the detailed process of development?

Extending quantum error correction: new continuous measurement protocols and improved fault-tolerant overhead

Quantum mechanical applications range from quantum computers to quantum key distribution to teleportation. In these applications, quantum error correction is extremely important for protecting quantum states against decoherence. Here I present two main results regarding quantum error correction protocols.

The first main topic I address is the development of continuous-time quantum error correction protocols via combination with techniques from quantum control. These protocols rely on weak measurement and Hamiltonian feedback instead of the projective measurements and unitary gates usually assumed by canonical quantum error correction. I show that a subclass of these protocols can be understood as a quantum feedback protocol, and analytically analyze the general case using the stabilizer formalism; I show that in this case perfect feedback can perfectly protect a stabilizer subspace. I also show through numerical simulations that another subclass of these protocols does better than canonical quantum error correction when the time between corrections is limited.

Physiological and mechahototropinistic studies of pc Fe(II) oxidation in purple non-sulfur bacteria

Phototrophic Fe(II)-oxidizing bacteria use electrons from ferrous iron [Fe(II)] and energy from light to drive reductive CO2 fixation. This metabolism is thought to be ancient in origin, and plays an important role in environmental iron cycling. It has been implicated in the deposition of Banded Iron Formations, a class of ancient sedimentary iron deposits. Consistent with this hypothesis, we discovered that hydrogen gas, a thermodynamically favorable electron donor to Fe(II), in an Archean atmosphere would not have inhibited phototrophic Fe(II) oxidation. To understand this physiology and the connection to BIF formation at the molecular level, the mechanisms of phototrophic Fe(II) oxidation were examined in two purple non-sulfur bacteria, Rhodopseudomonas palustris TIE-1 and Rhodobacter sp. SW2.

Important advances were made in elucidating genes critical to phototrophic Fe(II) oxidation. In R. palustris TIE-1, the first genetically tractable phototrophic Fe(II) oxidizer isolated, transposon mutagenesis identified a putative integral membrane protein and a potential cobalamin (vitamin B12) biosynthesis protein involved in Fe(II) oxidation.

Experiments and analytical investigations of granular materials: shear flow and convective heat transfer

Granular materials flowing down an inclined chute were studied experimentally and analytically. Characteristics of convective heat transfer to granular flows were also investigated experimentally and numerically. Experiments on continuous, steady flows of granular materials in an inclined chute were conducted with the objectives of understanding the characteristics of chute flows and of acquiring information on the rheological behavior of granular material flow. Two neighboring fibre optic displacement probes were employed to measure mean velocity, one component of velocity fluctuations, and linear concentration at the wall and free surface boundaries. A shear gauge was also developed to make direct measurement of shear stress at the chute base. Measurements of solid fraction, velocity, shear rate, and velocity fluctuations were analyzed to understand the chute flow characteristics, and the rheological behavior of granular materials was studied with the present experimental data. The vertical profiles of mean velocity, velocity fluctuation, and solid fraction were also obtained at the sidewalls.

A model biochemical reaction

Asymptotic solutions are presented to the non-linear parabolic reaction-diffusion equations describing a model biochemical reaction proposed by I. Prigogine. There is a uniform steady state which, for certain values of the adjustable parameters, may be unstable. When the uniform solution is slightly unstable, the two-timing method is used to find the bifurcation of new solutions of small amplitude. These may be either non-uniform steady states or time-periodic solutions, depending on the ratio of the diffusion coefficients. In the limit that one of the diffusion coefficients is infinite, multiple steady states of finite amplitude are found. When one of the parameters is allowed to depend on space and the basic state is unstable, it is found that the non-uniform steady state which is approached may show localized spatial oscillations. The localization arises out of the presence of turning points in the linearized stability equations. When diffusion is absent it is shown how kinematic concentration waves arise. Detailed calculations using singular perturbation techniques are made of the basic oscillation giving rise to these waves, which is a relaxation oscillation. It is found that the equations in its asymptotic approximation are not obtained from the full equations as the result of a limit process.

Measuring stress in thin film - substrate systems featuring spatial nonuniformities of film thickness

It is very important to be able to accurately determine the film stress distribution in a thin film structure, since stress can lead directly to failure and as such is intimately related to reliability and process yield. The most common way of inferring film stress caused by a given process is by measuring system curvature before and after the process; the change in curvature is directly related to the stress caused by that process, usually through the Stoney formula. This formula was derived based on a number of restrictive assumptions. Two of these are the assumptions of a spatially uniform film thickness and a spatially uniform misfit strain; taken together, these assumptions imply constant curvature and film stress over the entire wafer. In practice, these conditions are rarely met, and yet the Stoney formula is still the film stress measurement standard.

Broadband waveform modeling over a dense seismic network

We developed a "two-way" calibration technique for studying clustered events, particularly their mechanisms and rupture directivities. First, we demonstrate that the magnitude 4 events with known source mechanisms can be used to calibrate the path effects on the short-period (0.5-2 sec) P waves, so that the corrected P waves can be modeled for determining focal mechanisms of the smaller events. The correction is formulated in terms of a station-specific "Amplitude Amplification Factor" (AAF), whose origin is mainly due to the site effect. Second, we show that the smaller events with radiation pattern corrections provide excellent empirical Green's functions (EGFs) for investigating the detailed rupture processes of the magnitude 4 events. In Chapter 2 of this thesis, we present the application of our methods to the 2003 Big Bear sequence.

Surface wave dispersion in layered anisotropic media

An analysis is made of the dispersive properties of layered anisotropic media, emphasis being placed on the geophysically important case of transverse isotropy. Period equations are derived for Rayleigh, Stoneley and Love type waves. A correspondence is established, in certain cases, with ray theoretical and plane stress solutions.

Constraining global carbon budget using vertically-integrated CO2 measurements

I demonstrate that high precision measurements of the vertical-average dry volumn-mixing-ratio of atmospheric carbon dioxide (CO2 ) can be obtained from ground-based solar spectra. Oxygen measurements from the same spectra can be used to calibrate CO2 retrievals across different instruments, enabling a global network of column CO2 observations to be constructed. I also illustrate that this new type of data, together with aircraft pro?le CO2 observations, provide new constraints on global carbon ?uxes.

Investigations of generalized conical flow fields

The conical transformation of variables of M.D. Haskind and S. V. Falkovich is applied to the steady-state problem of thin delta wings with subsonic leading edges in a supersonic flow.

Behavioral models of strategies in multi-armed bandit problems

In multi-armed bandit problems, agents must repeatedly choose among uncertain alternatives whose true values they can learn about only through experimentation. Information acquired from experimentation is valuable because it tells the agent whether to select a particular option again in the future. Economically significant applications include brand choice, natural resource exploration, research and development and, as special cases, job and price search.

The persistence of charm in the relentless decay of beauty

The results of calculations of semileptonic Bc meson exclusive decay channels using the quark potential model are presented. These results are compared with estimations made using the spectator model. The polarization of charmonia states resulting from b to c decay are also calculated, providing a more detailed experimental check of the model.

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Asymptotically optimal multistage hypothesis tests

This thesis investigates variable stage size multistage hypothesis testing in three different contexts, each building on the previous. We first consider the problem of sampling a random process in stages until it crosses a predetermined boundary at the end of a stage -- first for Brownian motion and later for a sum of i.i.d. random variables. A multistage sampling procedure is derived and its properties are shown to be not only sufficient but also necessary for asymptotic optimality as the distance to the boundary goes to infinity.

Superprotonic solid acids: structure, properties, and applications

In this work, the structure and properties of superprotonic MHnXO4-type solid acids (where M = monovalent cation, X = S, Se, P, As, and n = 1, 2) have been investigated and, for the first time, applied in fuel cell devices. Several MHnXO4-type solid acids are known to undergo a "superprotonic" solid-state phase transition upon heating, in which the proton conductivity increases by several orders of magnitude and takes on values of ~ 0.01 S/cm. The presence of superprotonic conductivity in fully hydrogen bonded solid acids, such as CsH2PO4, has long been disputed. In these investigations, through the use of pressure, the unequivocal identification of superprotonic behavior in both RbH2PO4 and CsH2PO4 has been demonstrated, whereas for chemically analogous compounds with smaller cations, such as KH2PO4 and NaH2PO4, superprotonic conductivity was notably absent.

Neural correlates of economic and moral decision-making

Our daily lives are shaped by a series of decision processes, ranging from very unimportant choices to life-changing judgments. The complexity of the decision processes increases tremendously when the decision-making takes place in a social context, i.e., when other human beings are directly involved in the decision. In such conditions the decision-maker not only tries to maximize his own utility, but also needs to take into account the interdependent nature of the situation. Information about others’ preferences, characteristics, and actions play an important role, and need to be thoroughly evaluated and predicted before making a decision. In this thesis we explore the neural correlates of two different types of social decision-making.

Biochemical, biophysical, and cellular investigations of the interactions of transferrin receptor with transferrin an

Hereditary hemochromatosis (HH) is a prevalent genetic disorder that results in the daily excess absorption of dietary iron. If untreated this disease leads to systemic organ failure and death. HH is caused by mutations to the gene coding for a protein called HFE, a type I transmembrane glycoprotein with a demonstrated role in regulating cellular iron homeostasis. HFE binds to the cell-surface receptor transferrin receptor (TfR), a dimeric type II transmembrane glycoprotein responsible for iron uptake into most mammalian cell types. TfR binds iron-loaded transferrin (Fe-Tf) from the blood and transports it to acidic recycling endosomes where iron is released from Fe-Tf in a TfR-facilitated process. Iron-free transferrin (apo-Tf) remains bound to TfR and is recycled to the cell surface, where apo-Tf rapidly dissociates from TfR upon exposure to the basic pH of blood. HFE and Fe-Tf can bind simultaneously to TfR to form a ternary complex, but HFE binding to TfR lowers the apparent affinity of the Fe-Tf/TfR interaction. This reduction could result from direct competition between HFE and Fe-Tf for receptor binding sites, from negative cooperativity, or both. We sought to understand the mechanism of HFE, Fe-Tf, and apo-Tf binding by TfR to help define HFE's role in iron homeostasis. We determined the binding constants for HFE, Fe-Tf, and apo-Tf to an extensive set of site-directed TfR mutants and discovered that HFE and Tf bind to an overlapping site on TfR, indicating the two proteins compete with each other for receptor binding. The mutagenesis results also identified differences in the contact points between TfR and the two forms of Tf, Fe-Tf and apo-Tf. By combining the mutations that are required for apo-Tf, but not Fe-Tf, binding we find that a highly conserved hydrophobic patch on the TfR surface is required for the receptor-mediated stimulation of iron release from Fe-Tf. From these data we propose a structure-based model for the mechanism of TfR-assisted iron release.

Hamilton-Pontryagin integrators on Lie groups

In this thesis structure-preserving time integrators for mechanical systems whose configuration space is a Lie group are derived from a Hamilton-Pontryagin (HP) variational principle. In addition to its attractive properties for degenerate mechanical systems, the HP viewpoint also affords a practical way to design discrete Lagrangians, which are the cornerstone of variational integration theory. The HP principle states that a mechanical system traverses a path that extremizes an HP action integral. The integrand of the HP action integral consists of two terms: the Lagrangian and a kinematic constraint paired with a Lagrange multiplier (the momentum). The kinematic constraint relates the velocity of the mechanical system to a curve on the tangent bundle. This form of the action integral makes it amenable to discretization.

Edgetones and acoustic resonances in a duct

Undesirable sound generation in the combustion chamber of segmented solid propellant rocket motors has been attributed to vortex shedding from obstructions that are uncovered as the propellant burns back. This phenomenon has been investigated experimentally and the mechanism explained.

Broadband modeling of earthquake source and mantle structures

Broadband seismic arrays have provided unprecedented data sets for seismologists to image the slips on faults and velocity structure beneath Earth's surface at all scales. In particular, plate boundary zones are the most complicated regions on the surface and full of complexities. Often that great earthquakes occur and rapid structural changes take place.

Metamorphism at the Contact of the Cable Stock, Montana

A study of metamorphic rocks is integrated with the areal geology in the vicinity of the Cable stock, a granodiorite intrusive surrounded by Paleozoic carbonate rocks. Detailed geology of the zones of most intense metamorphism at the intrusive contact is described.

Isochemical thermal metamorphism was followed by metasomatic addition of material and accompanied by various stages of alteration. Silicic magnesian limestones altered to diopside-grossularite marble by the introduction of iron. The addition of iron, little magnesia, and alumina altered the marble to a diopside-grandite tactite. Additional iron was deposited as magnetite and accompanied widespread dedolomitization and alteration. Rocks near the intrusive contact were replaced by epidote, mica, and scapolite.

Characterizing carbon-dioxide fluxes from oceans and terrestrial ecosystems

Understanding the processes that change the amount of carbon stored in the ocean and in the land biota, with their implications for future climate and ecology, is a fundamental goal of earth-system science. I have developed, refined, and applied several approaches that combine data analysis and modeling to better understand processes affecting carbon fluxes.

(1) Using a database of tree-ring widths from some 40,000 trees, I looked at the impact of large volcanic eruptions in the past millennium on tree growth globally. I found a decline in growth north of 45° N lasting for several years after eruptions, presumably due to eruption-associated cooling, and no significant impact at lower latitudes. This argues against the hypothesis that the increased diffuse-light fraction due to volcanic aerosols greatly increased plant carbon uptake after the 1991 Pinatubo eruption, suggesting that other explanations are needed for the slow increase in atmospheric CO2 levels in the early 1990s.

Earthquake source characterization using 3D numerical modeling

To understand the physics of earthquakes, it is important to know what happens during individual events. Dissembling the information about the source process from the recorded seismograms is a difficult and non-unique process, as there are severe trade-offs between many of the source parameters. In this thesis we attempt to add information from frequencies not used during the initial modeling of individual events to put more constraints on the source process, to learn about specific source parameters important to the physics of earthquakes. We model earthquakes using a spectral element method for wave-propagation that accurately accounts for the Earth's 3D elastic structure. We study the rupture speed of the 2001 Kunlun, China earthquake, the continuity of slip during the 1998 Balleny Islands event and the duration of slip during the 2004 Sumatra-Andaman, Indonesia earthquake. Finally, we explore the feasibility of using adjoint methods to learn about the earthquake source.

Dynamic compression of minerals in the MgO-FeO-SiO2 system

The first shock wave experiments performed on silicate materials were reported for quartz in 1962. The intervening forty years have allowed for extensive investigation of SiO2 by dynamic, static and theoretical means. Previous studies have concluded that quartz transforms completely to stishovite at ~40 GPa and melts at ~115 GPa along its Hugoniot. Recent discoveries that SiO2 transforms to phases slightly more dense than stishovite have led to a reexamination of the dynamic compression of SiO2 in this thesis. Based on comparing calculated Hugoniots to data for multiple initial SiO2 phases, it is proposed that, in addition to the stishovite and melt transitions, quartz is completely transformed to the CaCl2 structure at ~70 GPa. Coesite shows evidence of complete transformation to stishovite at ~ 50 GPa, and to the CaCl2 structure at ~65 GPa. Due to the higher temperature achieved in the quartz samples the slope of the stishovite-CaCl2 phase boundary is constrained to be ~180 K/GPa.

Shock-induced damage in rocks: application to impact cratering

Shock-induced damage beneath impact craters is studied in this work. Two representative terrestrial rocks, San Marcos granite and Bedford limestone, are chosen as test target. Impacts into the rock targets with different combinations of projectile material, size, impact angle, and impact velocity are carried out at cm scale in the laboratory.

Differential weathering effects and mechanisms

The physical and chemical characteristics of the two differential weathering effects, case hardening and core softening, are examined to determine their formation mechanisms by investigating several field areas exhibiting differential weathering effects. The terms differential weathering effects, factors, mechanisms, processes, morphologies and their cause and effect relationships are defined in the context of the overall problem.

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