New directions in sparse sampling and estimation for underdetermined systems

A central objective in signal processing is to infer meaningful information from a set of measurements or data. While most signal models have an overdetermined structure (the number of unknowns less than the number of equations), traditionally very few statistical estimation problems have considered a data model which is underdetermined (number of unknowns more than the number of equations). However, in recent times, an explosion of theoretical and computational methods have been developed primarily to study underdetermined systems by imposing sparsity on the unknown variables. This is motivated by the observation that inspite of the huge volume of data that arises in sensor networks, genomics, imaging, particle physics, web search etc., their information content is often much smaller compared to the number of raw measurements. This has given rise to the possibility of reducing the number of measurements by down sampling the data, which automatically gives rise to underdetermined systems.

In this thesis, we provide new directions for estimation in an underdetermined system, both for a class of parameter estimation problems and also for the problem of sparse recovery in compressive sensing. There are two main contributions of the thesis: design of new sampling and statistical estimation algorithms for array processing, and development of improved guarantees for sparse reconstruction by introducing a statistical framework to the recovery problem.

We consider underdetermined observation models in array processing where the number of unknown sources simultaneously received by the array can be considerably larger than the number of physical sensors. We study new sparse spatial sampling schemes (array geometries) as well as propose new recovery algorithms that can exploit priors on the unknown signals and unambiguously identify all the sources. The proposed sampling structure is generic enough to be extended to multiple dimensions as well as to exploit different kinds of priors in the model such as correlation, higher order moments, etc.

Recognizing the role of correlation priors and suitable sampling schemes for underdetermined estimation in array processing, we introduce a correlation aware framework for recovering sparse support in compressive sensing. We show that it is possible to strictly increase the size of the recoverable sparse support using this framework provided the measurement matrix is suitably designed. The proposed nested and coprime arrays are shown to be appropriate candidates in this regard. We also provide new guarantees for convex and greedy formulations of the support recovery problem and demonstrate that it is possible to strictly improve upon existing guarantees.

This new paradigm of underdetermined estimation that explicitly establishes the fundamental interplay between sampling, statistical priors and the underlying sparsity, leads to exciting future research directions in a variety of application areas, and also gives rise to new questions that can lead to stand-alone theoretical results in their own right.

Engineering multi-step electron tunneling systems in proteins

Multi-step electron tunneling, or “hopping,” has become a fast-developing research field with studies ranging from theoretical modeling systems, inorganic complexes, to biological systems. In particular, the field is exploring hopping mechanisms in new proteins and protein complexes, as well as further understanding the classical biological hopping systems such as ribonuclease reductase, DNA photolyases, and photosystem II. Despite the plethora of natural systems, only a few biologically engineered systems exist. Engineered hopping systems can provide valuable information on key structural and electronic features, just like other kinds of biological model systems. Also, engineered systems can harness common biologic processes and utilize them for alternative reactions. In this thesis, two new hopping systems are engineered and characterized.

The protein Pseudomonas aeruginosa azurin is used as a building block to create the two new hopping systems. Besides being well studied and amenable to mutation, azurin already has been used to successfully engineer a hopping system. The two hopping systems presented in this thesis have a histidine-attached high potential rhenium 4,7-dimethyl-1,10-phenanthroline tricarbonyl [Re(dmp)(CO)3] + label which, when excited, acts as the initial electron acceptor. The metal donor is the type I copper of the azurin protein. The hopping intermediates are all tryptophan, an amino acid mutated into the azurin at select sites between the photoactive metal label and the protein metal site. One system exhibits an inter-molecular hopping through a protein dimer interface; the other system undergoes intra-molecular multi-hopping utilizing a tryptophan “wire.” The electron transfer reactions are triggered by excitation of the rhenium label and monitored by UV-Visible transient absorption, luminescence decays measurements, and time-resolved Infrared spectroscopy (TRIR). Both systems were structurally characterized by protein X-ray crystallography.

Theoretical studies of novel organic systems : biradicals, polyradicals, and conducting polymers

Chapter 1

Cyclobutanediyl has been studied in both its singlet and triplet states by ab initio electronic structure theory. The triplet, which is the ground state of the molecule, exists in both C_(2h) and C_(2v) forms, which interconvert via a C_s transition state. For the singlet, only a C_(2h) form is found. It passes, via a C_s transition state, onto the C_(2v) surface on which bicyclobutane is the only minimum. The ring-flipping (inversion) process in bicyclobutane includes the singlet biradical as an intermediate, and involves a novel, nonleast motion pathway. Semiclassical periodic orbit theory indicates that the various minima on both the singlet and triplet surfaces can interconvert via quantum mechanical tunneling.

Chapter 2

The dimethylenepolycyclobutadienes (n) are the non-Kekulé analogues of the classical acenes. Application of a variety of theoretical methods reveals several novel features of such structures. Most interesting is the emergence of a parity rule. When n is even, n is predicted to be a singlet, with n disjoint NBMOs. When n is odd, theory predicts a triplet ground state with (n+1) NBMOs that are not fully disjoint.

Chapter 3

Bi(cyclobutadienyl) (2), the cyclobutadiene analogue of biphenyl, and its homologues tri- (3) and tetra(cyclobutadienyl) (4) have been studied using electronic structure theory. Ab initio calculations on 2 reveal that the central bond is a true double bond, and that the structure is best thought of as two allyl radicals plus an ethylene. The singlet and triplet states are essentially degenerate. Trimer 3 is two allyls plus a dimethylenecyclobutanediyl, while 4 is two coplanar bi(cyclobutadienyl) units connected by a single bond. For both 3 and 4, the quintet, triplet, and singlet states are essentially degenerate, indicating that they are tetraradicals. The infinite polymer, polycyclobutadiene, has been studied by HMO, EHCO, and VEH methods. Several geometries based on the structures of 3 and 4 have been studied, and the band structures are quite intriguing. A novel crossing between the valence and conduction bands produces a small band gap and a high density of states at the Fermi level.

Chapter 4

At the level of Hückel theory, polyfulvene has a HOCO-LUCO degeneracy much like that seen in polyacetylene. Higher levels of theory remove the degeneracy, but the band gap (E_g) is predicted to be significantly smaller than analogous structures such as polythiophene and polypyrrole at the fulvenoid geometry. An alternative geometry, which we have termed quinoid, is also conceivable for polyfulvene, and it is predicted to have a much larger E_g. The effects of benzannelation to produce analogues of polyisothianaphthene have been evaluated. We propose a new model for such structures based on conventional orbital mixing arguments. Several of the proposed structures have quite interesting properties, which suggest that they are excellent candidates for conducting polymers.

Chapter 5

Theoretical studies of polydimethylenecyclobutene and polydiisopropylidene- cyclobutene reveal that, because of steric crowding, they cannot achieve a planar, fully conjugated structure in either their undoped or doped states. Rather, the structure consists of essentially orthogonal hexatriene units. Such a structure is incompatible with conventional conduction mechanisms involving polarons and bipolarons.

Analysis-aware design of embedded systems software

In the past many different methodologies have been devised to support software development and different sets of methodologies have been developed to support the analysis of software artefacts. We have identified this mismatch as one of the causes of the poor reliability of embedded systems software. The issue with software development styles is that they are ``analysis-agnostic.'' They do not try to structure the code in a way that lends itself to analysis. The analysis is usually applied post-mortem after the software was developed and it requires a large amount of effort. The issue with software analysis methodologies is that they do not exploit available information about the system being analyzed.

In this thesis we address the above issues by developing a new methodology, called "analysis-aware" design, that links software development styles with the capabilities of analysis tools. This methodology forms the basis of a framework for interactive software development. The framework consists of an executable specification language and a set of analysis tools based on static analysis, testing, and model checking. The language enforces an analysis-friendly code structure and offers primitives that allow users to implement their own testers and model checkers directly in the language. We introduce a new approach to static analysis that takes advantage of the capabilities of a rule-based engine. We have applied the analysis-aware methodology to the development of a smart home application.

Electron energy-loss spectroscopy study of polyatomic molecular systems under pyrolytic conditions

The technique of variable-angle, electron energy-loss spectroscopy has been used to study the electronic spectroscopy of the diketene molecule. The experiment was performed using incident electron beam energies of 25 eV and 50 eV, and at scattering angles between 10° and 90°. The energy-loss region from 2 eV to 11 eV was examined. One spin-forbidden transition has been observed at 4.36 eV and three others that are spin-allowed have been located at 5.89 eV, 6.88 eV and 7.84 eV. Based on the intensity variation of these transitions with impact energy and scattering angle, and through analogy with simpler molecules, the first three transitions are tentatively assigned to an n → π* transition, a π - σ* (3s) Rydberg transition and a π → π* transition.

Thermal decomposition of chlorodifluoromethane, chloroform, dichloromethane and chloromethane under flash-vacuum pyrolysis conditions (900-1100°C) was investigated by the technique of electron energy-loss spectroscopy, using the impact energy of 50 eV and a scattering angle of 10°. The pyrolytic reaction follows a hydrogen-chloride α-elimination pathway. The difluoromethylene radical was produced from chlorodifluoromethane pyrolysis at 900°C and identified by its X^1 A_1 → A^1B_1 band at 5.04 eV.

Finally, a number of exploratory studies have been performed. The thermal decomposition of diketene was studied under flash vacuum pressures (1-10 mTorr) and temperatures ranging from 500°C to 1000°C. The complete decomposition of the diketene molecule into two ketene molecules was achieved at 900°C. The pyrolysis of trifluoromethyl iodide molecule at 1000°C produced an electron energy-loss spectrum with several iodine-atom, sharp peaks and only a small shoulder at 8.37 eV as a possible trifluoromethyl radical feature. The electron energy-loss spectrum of trichlorobromomethane at 900°C mainly showed features from bromine atom, chlorine molecule and tetrachloroethylene. Hexachloroacetone decomposed partially at 900°C, but showed well-defined features from chlorine, carbon monoxide and tetrachloroethylene molecules. Bromodichloromethane molecule was investigated at 1000°C and produced a congested, electron energy-loss spectrum with bromine-atom, hydrogen-bromide, hydrogen-chloride and tetrachloroethylene features.

Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice

In the first part I perform Hartree-Fock calculations to show that quantum dots (i.e., two-dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. I tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wave function and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, I also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states and suggest an experimental method to detect Wigner crystals.

The second part of the thesis investigates infinite nuclear matter on a cubic lattice. The exact thermal formalism describes nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin-exchange and isospin-exchange interaction. Using auxiliary field Monte Carlo methods, I show that energy and basic saturation properties of nuclear matter can be reproduced. A first order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. The structure of the clusters is investigated with the help two-body correlations. I compare symmetry energy and first sound velocities with literature and find reasonable agreement. I also calculate the energy of pure neutron matter and search for a similar phase transition, but the survey is restricted by the infamous Monte Carlo sign problem. Also, a regularization scheme to extract potential parameters from scattering lengths and effective ranges is investigated.

Engineering enzyme systems by recombination

Homologous recombination is a source of diversity in both natural and directed evolution. Standing genetic variation that has passed the test of natural selection is combined in new ways, generating functional and sometimes unexpected changes. In this work we evaluate the utility of homologous recombination as a protein engineering tool, both in comparison with and combined with other protein engineering techniques, and apply it to an industrially important enzyme: Hypocrea jecorina Cel5a.

Chapter 1 reviews work over the last five years on protein engineering by recombination. Chapter 2 describes the recombination of Hypocrea jecorina Cel5a endoglucanase with homologous enzymes in order to improve its activity at high temperatures. A chimeric Cel5a that is 10.1 °C more stable than wild-type and hydrolyzes 25% more cellulose at elevated temperatures is reported. Chapter 3 describes an investigation into the synergy of thermostable cellulases that have been engineered by recombination and other methods. An engineered endoglucanase and two engineered cellobiohydrolases synergistically hydrolyzed cellulose at high temperatures, releasing over 200% more reducing sugars over 60 h at their optimal mixture relative to the best mixture of wild-type enzymes. These results provide a framework for engineering cellulolytic enzyme mixtures for the industrial conditions of high temperatures and long incubation times.

In addition to this work on recombination, we explored three other problems in protein engineering. Chapter 4 describes an investigation into replacing enzymes with complex cofactors with simple cofactors, using an E. coli enolase as a model system. Chapter 5 describes engineering broad-spectrum aldehyde resistance in Saccharomyces cerevisiae by evolving an alcohol dehydrogenase simultaneously for activity and promiscuity. Chapter 6 describes an attempt to engineer gene-targeted hypermutagenesis into E. coli to facilitate continuous in vivo selection systems.

Cooperative properties of lipid bilayers : collective director fluctuations and the effects of hydrophobic mismatch in protein/lipid membrane systems

Cooperative director fluctuations in lipid bilayers have been postulated for many years. ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements have been used identify these motions and to determine the origin of increased slow bilayer motion upon addition of unlike lipids or proteins to a pure lipid bilayer.

The contribution of cooperative director fluctuations to NMR relaxation in lipid bilayers has been expressed mathematically using the approach of Doane et al.^1 and Pace and Chan.^2 The T_2^(-1)’s of pure dimyristoyllecithin (DML) bilayers deuterated at the 2, 9 and 10, and all positions on both lipid hydrocarbon chains have been measured. Several characteristics of these measurements indicate the presence of cooperative director fluctuations. First of all, T_2^(-1) exhibits a linear dependence on S2/CD. Secondly, T_2^(-1) varies across the ^2H-NMR powder pattern as sin^2 (2, β), where , β is the angle between the average bilayer director and the external magnetic field. Furthermore, these fluctuations are restricted near the lecithin head group suggesting that the head group does not participate in these motions but, rather, anchors the hydrocarbon chains in the bilayer.

T_2^(-1)has been measured for selectively deuterated liquid crystalline DML hilayers to which a host of other lipids and proteins have been added. The T_2^(-1) of the DML bilayer is found to increase drastically when chlorophyll a (chl a) and Gramicidin A' (GA') are added to the bilayer. Both these molecules interfere with the lecithin head group spacing in the bilayer. Molecules such as myristic acid, distearoyllecithin (DSL), phytol, and cholesterol, whose hydrocarbon regions are quite different from DML but which have small,neutral polar head groups, leave cooperative fluctuations in the DML bilayer unchanged.

The effect of chl a on cooperative fluctuations in the DML bilayer has been examined in detail using ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements. Cooperative fluctuations have been modelled using the continuum theory of the nematic state of liquid crystals. Chl a is found to decrease both the correlation length and the elastic constants in the DML bilayer.

A mismatch between the hydrophobic length of a lipid bilayer and that of an added protein has also been found to change the cooperative properties of the lecithin bilayer. Hydrophobic mismatch has been studied in a series GA' / lecithin bilayers. The dependence of 2H-NMR order parameters and relaxation rates on GA' concentration has been measured in selectively deuterated DML, dipalmitoyllecithin (DPL), and DSL systems. Order parameters, cooperative lengths, and elastic constants of the DML bilayer are most disrupted by GA', while the DSL bilayer is the least perturbed by GA'. Thus, it is concluded that the hydrophobic length of GA' best matches that of the DSL bilayer. Preliminary Raman spectroscopy and Differential Scanning Calorimetry experiments of GA' /lecithin systems support this conclusion. Accommodation of hydrophobic mismatch is used to rationalize the absence of H_(II) phase formation in GA' /DML systems and the observation of H_(II) phase in GA' /DPL and GA' /DSL systems.

1. J. W. Doane and D. L. Johnson, Chem. Phy3. Lett., 6, 291-295 (1970). 2. R. J. Pace and S. I. Chan, J. Chem. Phy3., 16, 4217-4227 (1982).

Nonlinear dynamic transfer functions for certain retinal neuronal systems

The applicability of the white-noise method to the identification of a nonlinear system is investigated. Subsequently, the method is applied to certain vertebrate retinal neuronal systems and nonlinear, dynamic transfer functions are derived which describe quantitatively the information transformations starting with the light-pattern stimulus and culminating in the ganglion response which constitutes the visually-derived input to the brain. The retina of the catfish, Ictalurus punctatus, is used for the experiments.

The Wiener formulation of the white-noise theory is shown to be impractical and difficult to apply to a physical system. A different formulation based on crosscorrelation techniques is shown to be applicable to a wide range of physical systems provided certain considerations are taken into account. These considerations include the time-invariancy of the system, an optimum choice of the white-noise input bandwidth, nonlinearities that allow a representation in terms of a small number of characterizing kernels, the memory of the system and the temporal length of the characterizing experiment. Error analysis of the kernel estimates is made taking into account various sources of error such as noise at the input and output, bandwidth of white-noise input and the truncation of the gaussian by the apparatus.

Nonlinear transfer functions are obtained, as sets of kernels, for several neuronal systems: Light → Receptors, Light → Horizontal, Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derived models can predict, with reasonable accuracy, the system response to any input. Comparison of model and physical system performance showed close agreement for a great number of tests, the most stringent of which is comparison of their responses to a white-noise input. Other tests include step and sine responses and power spectra.

Many functional traits are revealed by these models. Some are: (a) the receptor and horizontal cell systems are nearly linear (small signal) with certain "small" nonlinearities, and become faster (latency-wise and frequency-response-wise) at higher intensity levels, (b) all ganglion systems are nonlinear (half-wave rectification), (c) the receptive field center to ganglion system is slower (latency-wise and frequency-response-wise) than the periphery to ganglion system, (d) the lateral (eccentric) ganglion systems are just as fast (latency and frequency response) as the concentric ones, (e) (bipolar response) = (input from receptors) - (input from horizontal cell), (f) receptive field center and periphery exert an antagonistic influence on the ganglion response, (g) implications about the origin of ERG, and many others.

An analytical solution is obtained for the spatial distribution of potential in the S-space, which fits very well experimental data. Different synaptic mechanisms of excitation for the external and internal horizontal cells are implied.

Variable-angle electron spectroscopic studies of various polyatomic molecular systems

The complementary techniques of low-energy, variable-angle electron-impact spectroscopy and ultraviolet variable-angle photoelectron spectroscopy have been used to study the electronic spectroscopy and structure of several series of molecules. Electron-impact studies were performed at incident beam energies between 25 eV and 100 eV and at scattering angles ranging from 0° to 90°. The energy-loss regions from 0 eV to greater than 15 eV were studied. Photoelectron spectroscopic studies were conducted using a HeI radiation source and spectra were measured at scattering angles from 45° to 90°. The molecules studied were chosen because of their spectroscopic, chemical, and structural interest. The operation of a new electron-impact spectrometer with multiple-mode target source capability is described. This spectrometer has been used to investigate the spin-forbidden transitions in a number of molecular systems.

The electron-impact spectroscopy of the six chloro-substituted ethylenes has been studied over the energy-loss region from 0-15 eV. Spin-forbidden excitations corresponding to the π → π*, N → T transition have been observed at excitation energies ranging from 4.13 eV in vinyl chloride to 3.54 eV in tetrachloroethylene. Symmetry-forbidden transitions of the type π → np have been oberved in trans-dichloroethyene and tetrachlor oethylene. In addition, transitions to many states lying above the first ionization potential were observed for the first time. Many of these bands have been assigned to Rydberg series converging to higher ionization potentials. The trends observed in the measured transition energies for the π → π*, N → T, and N → V as well as the π → 3s excitation are discussed and compared to those observed in the methyl- and fluoro- substituted ethylenes.

The electron energy-loss spectra of the group VIb transition metal hexacarbonyls have been studied in the 0 eV to 15 eV region. The differential cross sections were obtained for several features in the 3-7 eV energy-loss region. The symmetry-forbidden nature of the ¹A_1g → ¹A_1g, 2t_2g(π) → 3t_2g(π*) transition in these compounds was confirmed by the high-energy, low-angle behavior of their relative intensities. Several low lying transitions have been assigned to ligand field transitions on the basis of the energy and angular behavior of the differential cross sections for these transitions. No transitions which could clearly be assigned to singlet → triplet excitations involving metal orbitals were located. A number of states lying above the first ionization potential have been observed for the first time. A number of features in the 6-14 eV energy-loss region of the spectra of these compounds correspond quite well to those observed in free CO.

A number of exploratory studies have been performed. The π → π*, N → T, singlet → triplet excitation has been located in vinyl bromide at 4.05 eV. We have also observed this transition at approximately 3.8 eV in a cis-/trans- mixture of the 1,2-dibromoethylenes. The low-angle spectrum of iron pentacarbonyl was measured over the energy-loss region extending from 2-12 eV. A number of transitions of 8 eV or greater excitation energy were observed for the first time. Cyclopropane was also studied at both high and low angles but no clear evidence for any spin- forbidden transitions was found. The electron-impact spectrum of the methyl radical resulting from the pyrolysis of tetramethyl tin was obtained at 100 eV incident energy and at 0° scattering angle. Transitions observed at 5.70 eV and 8.30 eV agree well with the previous optical results. In addition, a number of bands were observed in the 8-14 eV region which are most likely due to Rydberg transitions converging to the higher ionization potentials of this molecule. This is the first reported electron-impact spectrum of a polyatomic free radical.

Variable-angle photoelectron spectroscopic studies were performed on a series of three-membered-ring heterocyclic compounds. These compounds are of great interest due to their highly unusual structure. Photoelectron angular distributions using HeI radiation have been measured for the first time for ethylene oxide and ethyleneimine. The measured anisotropy parameters, β, along with those measured for cyclopropane were used to confirm the orbital correlations and photoelectron band assignments. No high values of β similar to those expected for alkene π orbitals were observed for the Walsh or Forster-Coulson-Moffit type orbitals.

Control of dynamical systems with temporal logic specifications

This thesis is motivated by safety-critical applications involving autonomous air, ground, and space vehicles carrying out complex tasks in uncertain and adversarial environments. We use temporal logic as a language to formally specify complex tasks and system properties. Temporal logic specifications generalize the classical notions of stability and reachability that are studied in the control and hybrid systems communities. Given a system model and a formal task specification, the goal is to automatically synthesize a control policy for the system that ensures that the system satisfies the specification. This thesis presents novel control policy synthesis algorithms for optimal and robust control of dynamical systems with temporal logic specifications. Furthermore, it introduces algorithms that are efficient and extend to high-dimensional dynamical systems.

The first contribution of this thesis is the generalization of a classical linear temporal logic (LTL) control synthesis approach to optimal and robust control. We show how we can extend automata-based synthesis techniques for discrete abstractions of dynamical systems to create optimal and robust controllers that are guaranteed to satisfy an LTL specification. Such optimal and robust controllers can be computed at little extra computational cost compared to computing a feasible controller.

The second contribution of this thesis addresses the scalability of control synthesis with LTL specifications. A major limitation of the standard automaton-based approach for control with LTL specifications is that the automaton might be doubly-exponential in the size of the LTL specification. We introduce a fragment of LTL for which one can compute feasible control policies in time polynomial in the size of the system and specification. Additionally, we show how to compute optimal control policies for a variety of cost functions, and identify interesting cases when this can be done in polynomial time. These techniques are particularly relevant for online control, as one can guarantee that a feasible solution can be found quickly, and then iteratively improve on the quality as time permits.

The final contribution of this thesis is a set of algorithms for computing feasible trajectories for high-dimensional, nonlinear systems with LTL specifications. These algorithms avoid a potentially computationally-expensive process of computing a discrete abstraction, and instead compute directly on the system's continuous state space. The first method uses an automaton representing the specification to directly encode a series of constrained-reachability subproblems, which can be solved in a modular fashion by using standard techniques. The second method encodes an LTL formula as mixed-integer linear programming constraints on the dynamical system. We demonstrate these approaches with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

Gene enrichment using antibodies to DNA/RNA hybrids : mapping the ribosomal DNA of slime mold and rat

A novel method for gene enrichment has been developed and applied to mapping the rRNA genes of two eucaryotic organisms. The method makes use of antibodies to DNA/RNA hybrids prepared by injecting rabbits with the synthetic hybrid poly(rA)•poly(dT). Antibodies which cross-react with non-hybrid nucleic acids were removed from the purified IgG fraction by adsorption on columns of DNA-Sepharose, oligo(dT)-cellulose, and poly(rA)-Sepharose. Subsequent purification of the specific DNA/RNA hybrid antibody was carried out on a column of oligo(dT)-cellulose to which poly(rA) was hybridized. Attachment of these antibodies to CNBr-activated Sepharose produced an affinity resin which specifically binds DNA/RNA hybrids.

In order to map the rDNA of the slime mold Dictyostelium discoideum, R-loops were formed using unsheared nuclear DNA and the 178 and 268 rRNAs of this organism. This mixture was passed through a column containing the affinity resin, and bound molecules containing R- loops were eluted by high salt. This purified rDN A was observed directly in the electron microscope. Evidence was obtained that there is a physical end to Dictyostelium rDN A molecules approximately 10 kilobase pairs (kbp) from the region which codes for the 268 rRNA. This finding is consistent with reports of other investigators that the rRNA genes exist as inverse repeats on extra-chromosomal molecules of DNA unattached to the remainder of the nuclear DNA in this organism.

The same general procedure was used to map the rRNA genes of the rat. Molecules of DNA which contained R-loops formed with the 188 and 288 rRNAs were enriched approximately 150- fold from total genomal rat DNA by two cycles of purification on the affinity column. Electron microscopic measurements of these molecules enabled the construction of an R-loop map of rat rDNA. Eleven of the observed molecules contained three or four R-loops or else two R-loops separated by a long spacer. These observations indicated that the rat rRNA genes are arranged as tandem repeats. The mean length of the repeating units was 37.2 kbp with a standard deviation of 1.3 kbp. These eleven molecules may represent repeating units of exactly the same length within the errors of the measurements, although a certain degree of length heterogeneity cannot be ruled out. If significantly shorter or longer repeating units exist, they are probably much less common than the 37.2 kbp unit.

The last section of the thesis describes the production of antibodies to non-histone chromosomal proteins which have been exposed to the ionic detergent sodium dodecyl sulfate (SDS). The presence of low concentrations of SDS did not seem to affect either production of antibodies or their general specificity. Also, a technique is described for the in situ immunofluorescent detection of protein antigens in polyacrylamide gels.

Synthetic, kinetic and mechanistic studies in early transition metal systems. I. α- and β-hydrogen elimination reactions in derivatives of permethyltitanocene, -zirconocene, and -hafnocene. II. The reactions of aluminum alkyls with derivatives of permethylniobocene

The thermal decomposition of Cp*Ti(CH_3)_2 (Cp*≡ ƞ^5-C_5Me_5) toluene solution follows cleanly first-order kinetics and produces a single titanium product Cp*(C_5Me_4CH_2)Ti(CH_3) concurrent with the evolution of one equivalent of methane. Labeling studies using Cp*_2Ti- (CD_3)_2 and (Cp*-d_(15))_2Ti(CH_3)_2 show the decomposition to be intramolecular and the methane to be produced by the coupling of a methyl group with a hydrogen from the other TiCH_3 group. Activation parameters, ΔH^‡ and ΔS^‡, and kinetic deuterium isotope effects have been measured. The alternative decomposition pathways of α-hydrogen abstraction and a-hydrogen elimination, both leading to a titanium-methylidene intermediate, are discussed.

The insertion of unactivated acetylenes into the metal-hydride bonds of Cp*_2MH_2 (M = Zr, Hf) proceeds rapidly at low temperature to form monoand/ or bisinsertion products, dependent upon the steric bulk of the acetylene substituents. Cp*_2M(H)(C(Me)=CHMe), Cp*_2M(H)(CH=CHCMe_3), Cp*_2M(H)-(CH=CHPh), Cp*_2M(CH=CHPh)_2, Cp*_2M(CH=CHCH_3)_2 and Cp*_2Zr- (CH=CHCH_2CH_3)_2 have been isolated and characterized. To extend the study of unsaturated-carbon ligands, Cp*_2M(C≡CCH_3)_2 have been prepared by treating Cp*_2MCl_2 with LiC≡CCH_3. The reactivity of many of these complexes with carbon monoxide and dihydrogen is surveyed. The mono(2- butenyl) complexes Cp*_2M(H)(C(Me)=CHMe) rearrange at room temperature, forming the crotyl-hydride species Cp*_2M(H)(ƞ^3-C_4H_7). The bis(propenyl) and bis(l-butenyl) zirconium complexes Cp*_2Zr(CH=CHR)_2 (R = CH_3, CH_2CH_3) also rearrange, forming zirconacyclopentenes. Labeling studies, reaction chemistry, and kinetic measurements, including deuterium isotope effects, demonstrate that the unusual 6-hydrogen elimination from an sp^2-hybridized carbon is the first step in these latter rearrangements but is not observed in the former. Details of these mechanisms and the differences in reactivity of the zirconium and hafnium complexes are discussed.

The reactions of hydride- and alkyl-carbonyl derivatives of permethylniobocene with equimolar amounts of trialkylaluminum reagents occur rapidly producing the carbonyl adducts Cp*_2Nb(R)(COAlR'_3) (R = H, CH_3, CH_2CH_3, CH_2CH_2Ph, C(Me)=CHMe; R' = Me, Et). The hydride adduct Cp*_2NbH_3•AlEt_3 has also been formed. In solution, each of these compounds exists in equilibrium with the uncomplexed species. The formation constants for Cp*_2Nb(H)(COA1R'_R) have been measured. They indicate the steric bulk of the Cp* ligands plays a deciding factor in the isolation of the first example of an aluminum Lewis acid bound to a carbonyl-oxygen in preference to a metalhydride. Reactions of Cp*_2Nb(H)CO with other Lewis acids and of the one:one adducts with H_2, CO and C_2H_4 are also discussed.

Cp*_2Nb(H)(C_2H_4) also reacts with equimolar amounts of trialkylaluminum reagents, forming a one:one complex that ^1H NMR spectroscopy indicates contains a Nb-CH_2CH_2-Al bridge. This adduct also exists in equilibrium with the uncomplexed species in solution. The formation constant for Cp*_2N+/b(H)(CH_2CH_2ĀlEt_3) has been measured. Reactions of Cp*_2Nb(H)(C_2H_4) with other Lewis acids and the reactions of Cp*_2N+b(H)- (CH_2CH_2ĀlEt_3) with CO and C_2H_4 are described, as are the reactions of Cp_*2Nb(H)(CH_2=CHR) (R = Me, Ph), Cp*_2Nb(H)(CH_3C≡CCH_3) and Cp*_2Ti-(C_2H_4) with AlEt_3.

The steady-state response of multidegree-of-freedom systems with a spatially localized nonlinearity

This thesis is concerned with the dynamic response of a General multidegree-of-freedom linear system with a one dimensional nonlinear constraint attached between two points. The nonlinear constraint is assumed to consist of rate-independent conservative and hysteretic nonlinearities and may contain a viscous dissipation element. The dynamic equations for general spatial and temporal load distributions are derived for both continuous and discrete systems. The method of equivalent linearization is used to develop equations which govern the approximate steady-state response to generally distributed loads with harmonic time dependence.

The qualitative response behavior of a class of undamped chainlike structures with a nonlinear terminal constraint is investigated. It is shown that the hardening or softening behavior of every resonance curve is similar and is determined by the properties of the constraint. Also examined are the number and location of resonance curves, the boundedness of the forced response, the loci of response extrema, and other characteristics of the response. Particular consideration is given to the dependence of the response characteristics on the properties of the linear system, the nonlinear constraint, and the load distribution.

Numerical examples of the approximate steady-state response of three structural systems are presented. These examples illustrate the application of the formulation and qualitative theory. It is shown that disconnected response curves and response curves which cross are obtained for base excitation of a uniform shear beam with a cubic spring foundation. Disconnected response curves are also obtained for the steady-state response to a concentrated load of a chainlike structure with a hardening hysteretic constraint. The accuracy of the approximate response curves is investigated.

A probabilistic treatment of uncertainty in nonlinear dynamical systems

In this work, computationally efficient approximate methods are developed for analyzing uncertain dynamical systems. Uncertainties in both the excitation and the modeling are considered and examples are presented illustrating the accuracy of the proposed approximations.

For nonlinear systems under uncertain excitation, methods are developed to approximate the stationary probability density function and statistical quantities of interest. The methods are based on approximating solutions to the Fokker-Planck equation for the system and differ from traditional methods in which approximate solutions to stochastic differential equations are found. The new methods require little computational effort and examples are presented for which the accuracy of the proposed approximations compare favorably to results obtained by existing methods. The most significant improvements are made in approximating quantities related to the extreme values of the response, such as expected outcrossing rates, which are crucial for evaluating the reliability of the system.

Laplace's method of asymptotic approximation is applied to approximate the probability integrals which arise when analyzing systems with modeling uncertainty. The asymptotic approximation reduces the problem of evaluating a multidimensional integral to solving a minimization problem and the results become asymptotically exact as the uncertainty in the modeling goes to zero. The method is found to provide good approximations for the moments and outcrossing rates for systems with uncertain parameters under stochastic excitation, even when there is a large amount of uncertainty in the parameters. The method is also applied to classical reliability integrals, providing approximations in both the transformed (independently, normally distributed) variables and the original variables. In the transformed variables, the asymptotic approximation yields a very simple formula for approximating the value of SORM integrals. In many cases, it may be computationally expensive to transform the variables, and an approximation is also developed in the original variables. Examples are presented illustrating the accuracy of the approximations and results are compared with existing approximations.