Eigenvalue Coincidences and Multiplicity Free Spherical Pairs

In recent work, we related the structure of subvarieties of $n\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\mathbb{C})$-orbits on the flag variety of $\mathfrak{gl}(n,\mathbb{C})$. In the first part of this paper, we extend these results to the complex orthogonal Lie algebra $\mathfrak{g}=\mathfrak{so}(n,\mathbb{C})$. In the second part of the paper, we use these results to study the geometry and invariant theory of the $K$-action on $\mathfrak{g}$, in the cases where $(\mathfrak{g}, K)$ is $(\mathfrak{gl}(n,\mathbb{C}), GL(n-1,\mathbb{C}))$ or $(\mathfrak{so}(n,\mathbb{C}), SO(n-1,\mathbb{C}))$. We study the geometric quotient $\mathfrak{g}\to \mathfrak{g}//K$ and describe the closed $K$-orbits on $\mathfrak{g}$ and the structure of the zero fibre. We also prove that for $x\in \mathfrak{g}$, the $K$-orbit $Ad(K)\cdot x$ has maximal dimension if and only if the algebraically independent generators of the invariant ring $\mathbb{C}[\mathfrak{g}]^{K}$ are linearly independent at $x$, which extends a theorem of Kostant. We give applications of our results to the Gelfand-Zeitlin system.Comment: 38 page

Adaptive Management for Impacts to Eelgrass Habitat in Gloucester Harbor

The Massachusetts Office of Coastal Zone Management and the Massachusetts Institute of Technology Sea Grant College Program, along with partners, led an effort to create an eelgrass bank, raise awareness of the value of eelgrass habitat, and facilitate transplanting efforts to Boston Harbor in the summer and fall of 2006. A planned impact to eelgrass habitat in Gloucester Harbor warranted efforts to try to save this valuable and declining resource. This unfortunate circumstance was used to educate interested citizens, students and teachers from regional schools, and government employees. Methods to transplant and store eelgrass were researched and tested in attempt to facilitate restoration of the impact area. Two community events were organized at Pavilion Beach to harvest eelgrass from the impact area. These events were attended by a variety of government (city, state, and federal) and non-government employees, along with students and teachers, and attracted much attention of the citizens of Gloucester. Eelgrass was successfully transplanted to Boston Harbor by the Massachusetts Division of Marine Fisheries. Harvested eelgrass was also maintained in a hydroponic raft system for three months (October-December) and used to set-up an interpretative display in a flow-through tank at the Gloucester Maritime Heritage Center. While the harvested eelgrass was ultimately not transplanted back to the impact corridor, experience in storing eelgrass within hydroponic and tank systems could assist future restoration efforts. By teaming up to save the eelgrass at Pavilion Beach in Gloucester Harbor, project partners demonstrated the advantage of creative, adaptive, and cooperative efforts to manage coastal resources. The project was a learning experience in adaptive management for eelgrass habitat and a success in outreach

Out of Jail... But Still Not Free to Litigate - Using Congressional Intent to Interpret 28 U.S.C. Sec. 1915(b)\u27s Application to Released Prisoners

This Comment argues that, based on the Prison Litigation Reform Act (PLRA)’s purpose and legislative history, prisoners who fulfilled the statute’s payment obligations while incarcerated should be entitled to apply for traditional in forma pauperis (IFP) status under § 1915(a)(1) upon release. Part I traces the historical development of prisoners’ right of access to the courts and its ties to the IFP doctrine. It then examines the PLRA’s many amendments to the federal IFP statute. Part II explains the divergent readings that circuit courts currently apply to § 1915(b). After analyzing the statute’s plain language and legislative history, Part III concludes that Congress sought to impose the filing fee requirement on prisoners because they encounter fewer financial and logistical obstacles throughout the litigation process, a justification that cannot extend to released inmates. Finally, Part IV recommends that courts decide the continuing application of the PLRA on a case-by-case basis that first takes into account a released prisoner’s prior compliance with the payment formula, a solution that upholds both the prisoner’s constitutional right of access and the countervailing government interests

Genetic and process engineering for the production of protein therapeutics for the treatment of CNS disorders

Neurological disorders constitute the major cause of disability adjusted-life years (DALYs). Alzheimer’s disease and other dementias are included in the group of the most prevalent disorders in this field (Feigin et al., 2017). Nevertheless, the urgency of the treatment of these pathologies is not met by efficacious drug development, as indicated by a recent statistical analysis measuring the likelihood of approval of new drugs by disease area (Hay et al., 2014). In neurology only 8.4% of the candidate drugs have been approved in the 2006 – 2015 decade and the drugs categorized as “Large Molecules” were characterized by 13.2% rate of success (Hay et al., 2014). This statistical analysis would suggest that only those molecules proving robust Proof of Mechanism (PoM) and Proof of Principle (PoP) during their early development deserve the risk for further development. On the other hand, proteins used in protein replacement therapies (PRTs) constitute an exception in this scenario as the iter for their approval is generally more straightforward (Gorzelany and De Souza, 2013). In this case the main hurdles involving the drug development directly coincide with the production, the purification and the stable formulation of the final product rather than the assessment of its efficacy or toxicity (Saccardo, Corchero and Ferrer-Miralles, 2016). In the present document we describe the approaches followed in the implementation of biotechnological processes for the production of two different proteins with potential applications in the treatment of central nervous system (CNS) disorders. In the first chapter we present the establishment of a simple and efficient pipeline for the E. coli recombinant expression and purification of the bacterial toxin named CNF1. This 114 kDa protein is involved in a series of infectious diseases (Ho et al., 2018), but it has also been demonstrated to be promising in the treatment of severe neurological pathologies like Alzheimer’s disease, Parkinson disease, Rett syndrome and epilepsy (Maroccia et al., 2018). Nevertheless, during the development of the project we decided not to pursue any further attempt in the clinical development of CNF1 as a drug because of the lack of robust, clear and completely demonstrated PoM and PoP. However, the proposed procedure for the purification and final formulation of the product outperforms the others reported in the literature in terms of yield, purity and stability and it can be easily employed in the future for further structural and functional analyses in toxicological and immunological perspectives. The reproducibility of the entire pipeline has been demonstrated repeating the production and purification protocols dozens of times at intervals of several months. Moreover, the stability of the final product was routinely ascertained using SDS-PAGE, size-exclusion chromatography, DLS and activity assays. In the second chapter of this thesis we describe the employment of Pseudoalteromonas haloplanktis TAC125 in the production of a human protein to be used in a PRT. Although the quality of the product achievable in this host seemed better than the one previously obtained with other expression systems, the overall yields remained low. Slight improvements in this sense were achieved by the genetic engineering of the coding sequence of the target protein and by the implementation of alternative expression plasmids. Nevertheless, further studies demonstrated that the whole expression platform – the host and the plasmids – are affected by imperfections and bottlenecks whose correction is pivotal for a satisfying recombinant production. This kind of issues is typical of unconventional and less explored recombinant bacteria, but there are several examples in the literature about how they can be systematically overcome. Hence, a series of measures to be taken for the improvement of this microbial factory are proposed