The political econmoy of state government debt : an analysis of constitutional limitations (1961-1990)

Over the past decade, scholarly interest concerning the use of limitations to constrain government spending and taxing has noticeably increased. The call for constitutional restrictions can be credited, in part, to Washington's apparent inability to legislate any significant reductions in government expenditures or in the size of the national debt. At the present time, the federal government is far from instituting any constitutional limitations on spending or borrowing; however, the states have incorporated many controls on revenues and expenditures, the oldest being strictures on full faith and credit borrowing. This dissertations examines the efficacy of these restrictions on borrowing across the states (excluding Alaska) for the period dating from 1961 to 1990 and also studies the limitations on taxing and spending synonymous with the Tax Revolt.

We include socio-economic information in our calculations to control for factors other than the institutional variables that affect state borrowing levels. Our results show that certain constitutional restrictions (in particular, the referendum requirement and the dollar debt limit) are more effective than others. The apparent ineffectiveness of other limitations, such as the flexible debt limit, seem related to the bindingness of the limitations in at least half of the cases. Other variables, such as crime rates, number of schoolage children, and state personal income do affect the levels of full faith and credit debt, but not as strongly as the limitations. While some degree of circumvention can be detected (the amount of full faith and credit debt does inversely affect the levels of nonguaranteed debt), it is so small when compared to the effectiveness of the constitutional restrictions that it is almost negligible. The examination of the tax revolt era limitations yielded quite similar conclusions, with the additional fact that constitutional restrictions appear more binding than statutory ones. Our research demonstrates that constitutional limitations on borrowing can be applied effectively to constrain excessive borrowing, but caution must be used. The efficacy of these restrictions decrease dramatically as the number of loopholes increase.

Binding site size limitations of imidazole-pyrrole polyamides for recognition in the minor groove of DNA

The discovery that the three ring polyamide Im-Py-Py-Dp containing imidazole (Im) and pyrrole (Py) carboxamides binds the DNA sequence 5'-(A,T)G(A,T)C(A,T)-3' as an antiparallel dimer offers a new model for the design of ligands for specific recognition of sequences in the minor groove containing both G,C and A,T base pairs. In Chapter 2, experiments are described in which the sequential addition of five N- methylpyrrolecarboxamides to the imidazole-pyrrole polyamide Im-Py-Py-Dp affords a series of six homologous polyamides, Im-(Py)_2-7-Dp, that differ in the size of their binding site, apparent first order binding affinity, and sequence specificity. These results demonstrate that DNA sequences up to nine base pairs in length can be specifically recognized by imidazole-pyrrole polyamides containing three to seven rings by 2:1 polyamide-DNA complex formation in the minor groove. Recognition of a nine base pair site defines the new lower limit of the binding site size that can be recognized by polyamides containing exclusively imidazole and pyrrolecarboxamides. The results of this study should provide useful guidelines for the design of new polyamides that bind longer DNA sites with enhanced affinity and specificity.

In Chapter 3 the design and synthesis of the hairpin polyamide Im-Py-Im-Py-γ-Im- Py-Im-Py-Dp is described. Quantitative DNase I footprint titration experiments reveal that Im-Py-Im-Py-γ-Im-Py-Im-Py-Dp binds six base pair 5'-(A,T)GCGC(A,T)-3' sequences with 30-fold higher affinity than the unlinked polyamide Im-Py-Im-Py-Dp. The hairpin polyamide does not discriminate between A•T and T•A at the first and sixth positions of the binding site as three sites 5'-TGCGCT-3', 5'-TGCGCA-3', and 5 'AGCGCT- 3' are bound with similar affinity. However, Im-Py-Im-Py-γ-Im-Py-Im-PyDp is specific for and discriminates between G•C and C•G base pairs in the 5'-GCGC-3' core as evidenced by lower affinities for the mismatched sites 5'-AACGCA-3', 5'- TGCGTT-3', 5'-TGCGGT-3', and 5'-ACCGCT-3'.

In Chapter 4, experiments are described in which a kinetically stable hexa-aza Schiff base La³⁺ complex is covalently attached to a Tat(49-72) peptide which has been shown to bind the HIV-1 TAR RNA sequence. Although these metallo-peptides cleave TAR site-specifically in the hexanucleotide loop to afford products consistent with hydrolysis, a series of control experiments suggests that the observed cleavage is not caused by a sequence-specifically bound Tat(49-72)-La(L)³⁺ peptide.

Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

I. Fundamental limitations in microelectronics. II. Power Schottky diode design and comparison with the junction diode. III. Permittivity of strontium titanate

Part I

The physical phenomena which will ultimately limit the packing density of planar bipolar and MOS integrated circuits are examined. The maximum packing density is obtained by minimizing the supply voltage and the size of the devices. The minimum size of a bipolar transistor is determined by junction breakdown, punch-through and doping fluctuations. The minimum size of a MOS transistor is determined by gate oxide breakdown and drain-source punch-through. The packing density of fully active bipolar or static non-complementary MOS circuits becomes limited by power dissipation. The packing density of circuits which are not fully active such as read-only memories, becomes limited by the area occupied by the devices, and the frequency is limited by the circuit time constants and by metal migration. The packing density of fully active dynamic or complementary MOS circuits is limited by the area occupied by the devices, and the frequency is limited by power dissipation and metal migration. It is concluded that read-only memories will reach approximately the same performance and packing density with MOS and bipolar technologies, while fully active circuits will reach the highest levels of integration with dynamic MOS or complementary MOS technologies.

Part II

Because the Schottky diode is a one-carrier device, it has both advantages and disadvantages with respect to the junction diode which is a two-carrier device. The advantage is that there are practically no excess minority carriers which must be swept out before the diode blocks current in the reverse direction, i.e. a much faster recovery time. The disadvantage of the Schottky diode is that for a high voltage device it is not possible to use conductivity modulation as in the p i n diode; since charge carriers are of one sign, no charge cancellation can occur and current becomes space charge limited. The Schottky diode design is developed in Section 2 and the characteristics of an optimally designed silicon Schottky diode are summarized in Fig. 9. Design criteria and quantitative comparison of junction and Schottky diodes is given in Table 1 and Fig. 10. Although somewhat approximate, the treatment allows a systematic quantitative comparison of the devices for any given application.

Part III

We interpret measurements of permittivity of perovskite strontium titanate as a function of orientation, temperature, electric field and frequency performed by Dr. Richard Neville. The free energy of the crystal is calculated as a function of polarization. The Curie-Weiss law and the LST relation are verified. A generalized LST relation is used to calculate the permittivity of strontium titanate from zero to optic frequencies. Two active optic modes are important. The lower frequency mode is attributed mainly to motion of the strontium ions with respect to the rest of the lattice, while the higher frequency active mode is attributed to motion of the titanium ions with respect to the oxygen lattice. An anomalous resonance which multi-domain strontium titanate crystals exhibit below 65°K is described and a plausible mechanism which explains the phenomenon is presented.