Crystallization of Escherichia coli Catabolite Gene Activator Protein with its DNA Binding Site: The use of Modular DNA

To obtain crystals of the Escherichia coli catabolite gene activator protein (CAP) complexed with its DNA-binding site, we have searched for crystallization conditions with 26 different DNA segments ≥28 base-pairs in length that explore a variety of nucleotide sequences, lengths, and extended 5′ or 3′ termini. In addition to utilizing uninterrupted asymmetric lac site sequences, we devised a novel approach of synthesizing half-sites that allowed us to efficiently generate symmetric DNA segments with a wide variety of extended termini and lengths in the large size range (≥28 bp) required by this protein. We report three crystal forms that are suitable for X-ray analysis, one of which (crystal form III) gives measurable diffraction amplitudes to 3 Å resolution. Additives such as calcium, n-octyl-β-d-glucopyranoside and spermine produce modest improvements in the quality of diffraction from crystal form III. Adequate stabilization of crystal form III is unexpectedly complex, requiring a greater than tenfold reduction in the salt concentration followed by addition of 2-methyl-2,4-pentanediol and then an increase in the concentration of polyethylene glycol.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

Restructuring Justice: Moving Towards Gender-Responsive Programming and Alternatives to Incarceration for Non-Violent Female Offenders

The United States¿ Federal and State laws differentiate between acceptable (or, legal) and unacceptable (illegal) behavior by prescribing restrictive punishment to citizens and/or groups that violate these established rules. These regulations are written to treat every person equally and to fairly serve justice; furthermore, the sanctions placed on offenders seek to reform illegal behavior through limitations on freedoms and rehabilitative programs. Despite the effort to treat all offenders fairly regardless of social identity categories (e.g., sex, race, ethnicity, socioeconomic status, age, ability, and gender and sexual orientation) and to humanely eliminate illegal behavior, the American penal system perpetuates de facto discrimination against a multitude of peoples. Furthermore, soaring recidivism rates caused by unsuccessful re-entry of incarcerated offenders puts economic stress on Federal and State budgets. For these reasons, offenders, policy-makers, and law-abiding citizens should all have a vested interest in reforming the prison system. This thesis focuses on the failure of the United States corrections system to adequately address the gender-specific needs of non-violent female offenders. Several factors contribute to the gender-specific discrimination that women experience in the criminal justice system: 1) Trends in female criminality that skew women¿s crime towards drug-related crimes, prostitution, and property offenses; 2) Mandatory minimum sentences for drug crimes that are disproportionate to the crime committed; 3) So-called ¿gender-neutral¿ educational, vocational, substance abuse, and mental health programming that intends to equally rehabilitate men and women, but in fact favors men; and 4) The isolating nature of prison structures that inhibits smooth re-entry into society. I argue that a shift in the placement and treatment of non-violent female offenders is necessary for effective rehabilitation and for reducing recidivism rates. The first component of this shift is the design and implementation of gender- responsive treatment (GRT) rather than gender-neutral approaches in rehabilitative programming. The second shift is the utilization of alternatives to incarceration, which provide both more humane treatment of offenders and smoother reintegration to society. Drawing on recent scholarship, information from prison advocacy organizations, and research with men in an alternative program, I provide a critical analysis of current policies and alternative programs, and suggest several proposals for future gender- responsive programs in prisons and in place of incarceration. I argue that the expansion of gender-responsive programming and alternatives to incarceration respond to the marginalization of female offenders, address concerns about the financial sustainability of the United States criminal justice system, and tackle high recidivism rates.