The Beilinson-Bernstein localization theorem for the affine Grassmannian

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages. 171-173).This thesis mainly deals with the study of the category of admissible modules for the affine Kac-Moody algebra at the critical level, and the study of its center.by Giorgia Fortuna.Ph.D

Local opers with two singularities: the case of sl(2)\mathfrak{sl}(2)

We study local opers with two singularities for the case of the Lie algebra sl(2), and discuss their connection with a two-variables extension of the affine Lie algebra. We prove an analogue of the Feigin-Frenkel theorem describing the centre at the critical level, and an analogue of a result by Frenkel and Gaitsgory that characterises the endomorphism rings of Weyl modules in terms of functions on the space of opers.Comment: 56 pages. Comments are very welcome

The semi-infinite cohomology of Weyl modules with two singular points

In their study of spherical representations of an affine Lie algebra at the critical level and of unramified opers, Frenkel and Gaitsgory introduced what they called the Weyl module $\mathbb{V}^{\lambda}$ corresponding to a dominant weight $\lambda$. This object plays an important role in the theory. In arXiv:2012.01858, we introduced a possible analogue $\mathbb{V}^{{\lambda},{\mu}}$ of the Weyl module in the setting of opers with two singular points, and in the case of sl(2) we proved that it has the "correct" endomorphism ring. In this paper, we compute the semi-infinite cohomology of $\mathbb{V}^{{\lambda},{\mu}}$ and we show that it does not share some of the properties of the semi-infinite cohomology of the Weyl module of Frenkel and Gaitsgory. For this reason, we introduce a new module $\tilde{\mathbb{V}}^{{\lambda},{\mu}}$ which, in the case of sl(2), enjoys all the expected properties of a Weyl module.Comment: 23 page

Infected pancreatic necrosis: outcomes and clinical predictors of mortality. A post hoc analysis of the MANCTRA-1 international study

: The identification of high-risk patients in the early stages of infected pancreatic necrosis (IPN) is critical, because it could help the clinicians to adopt more effective management strategies. We conducted a post hoc analysis of the MANCTRA-1 international study to assess the association between clinical risk factors and mortality among adult patients with IPN. Univariable and multivariable logistic regression models were used to identify prognostic factors of mortality. We identified 247 consecutive patients with IPN hospitalised between January 2019 and December 2020. History of uncontrolled arterial hypertension (p = 0.032; 95% CI 1.135-15.882; aOR 4.245), qSOFA (p = 0.005; 95% CI 1.359-5.879; aOR 2.828), renal failure (p = 0.022; 95% CI 1.138-5.442; aOR 2.489), and haemodynamic failure (p = 0.018; 95% CI 1.184-5.978; aOR 2.661), were identified as independent predictors of mortality in IPN patients. Cholangitis (p = 0.003; 95% CI 1.598-9.930; aOR 3.983), abdominal compartment syndrome (p = 0.032; 95% CI 1.090-6.967; aOR 2.735), and gastrointestinal/intra-abdominal bleeding (p = 0.009; 95% CI 1.286-5.712; aOR 2.710) were independently associated with the risk of mortality. Upfront open surgical necrosectomy was strongly associated with the risk of mortality (p < 0.001; 95% CI 1.912-7.442; aOR 3.772), whereas endoscopic drainage of pancreatic necrosis (p = 0.018; 95% CI 0.138-0.834; aOR 0.339) and enteral nutrition (p = 0.003; 95% CI 0.143-0.716; aOR 0.320) were found as protective factors. Organ failure, acute cholangitis, and upfront open surgical necrosectomy were the most significant predictors of mortality. Our study confirmed that, even in a subgroup of particularly ill patients such as those with IPN, upfront open surgery should be avoided as much as possible. Study protocol registered in ClinicalTrials.Gov (I.D. Number NCT04747990)

Photobehaviour of methyl-pyridinium and quinolinium iodide derivatives, free and complexed with DNA. A case of bisintercalation.

Excited state dynamics of four azinium salts were studied in buffered water and in the presence of salmon testes DNA. Complexation with DNA changes the photobehaviour of the free ligands lowering the photoreactivity and emission in favor of internal conversion. The interaction of these four dyes with DNA was studied with different techniques with the aim to establish the affinity and the type of binding between the ligands and DNA. The results from spectrophotometric and fluorimetric titrations provided evidence of a strong interaction between the azinium salts and the polynucleotide, with a binding constant of about 10(6) M(-1), making them interesting for therapeutical applications. Dichroic measurements allowed us to determine the possible modes of binding for each complex. Short living excited states of the free dyes were detected and characterized by ultrafast absorption spectroscopy. A further decrease of transient lifetimes was observed upon interaction with DNA. The bicationic pyridinium iodide was found to act as a bisintercalative agent, potentially increasing the cytotoxicity with low dose and less collateral effects

Spectroscopic Investigation of the Molecular Interaction of New Potential Anticancer Drugs with DNA and Non-Ionic Micelles

The interaction with DNA and with non-ionic micelles of new methyl-pyridinium and methyl-quinolinium derivatives, which showed good cytotoxicity in some cell lines, was investigated by UV-VIS spectroscopy and stationary fluorimetry. Also transient absorption spectroscopy with ns resolution, for detecting triplet and radicals formation, and with fs resolution, for ultrafast dynamics of singlet excited states, was performed. Spectrophotometric and fluorimetric titrations by adding salmon testes DNA provided evidence of a strong interaction between the quaternized azinium salts investigated and the polynucleotide, with binding constants of about 105÷106 M-1. Fluorimetric titrations showed a considerable enhancement of emission quantum yield, in agreement with a more rigid structure of the compounds involved in the binding with DNA. The predominant interaction mode, intercalation or groove binding, has been also investigated. Preliminary measurements by confocal fluorescence microscopy on cell lines in presence of the studied azinium salts will be performed with the aim to localize the compounds into cellular districts. Interaction between the azinium salts and some non-ionic surfactants was studied in order to find agents for drug solubilization and drug delivery. To check the ability of the micelles to encapsulate the studied salts into their hydrophobic core and to release them in presence of DNA, spectrophotometric and fluorimetric titrations were performed. Another proof of compounds encapsulation in micellar aggregates was obtained by ultrafast absorption spectroscopy, which demonstrated a slowdown of excited states dynamics in presence of surfactants, with respect to that of free compounds in aqueous medium. The obtained results suggested that the studied polar non-ionic micelles can act as promising drug delivery agents in order to minimize drug loss and degradation (preventing harmful side effects), to increase drug bioavailability and to release drugs into the cellular nuclei allowing their interaction with DNA

Photochemistry and DNA-affinity of some pyrimidine-substituted styryl-azinium iodides

The relaxation properties of the excited states of three iodides of trans-1,2-diarylethene analogues (where one aryl group is a methylpyridinium, methylquinolinium or dimethylimidazolium group and the other one is a phenyl ring para-substituted by a pyrimidine ring) have been investigated in buffered (pH = 7) aqueous solution. As found in previous works for several analogues, these quaternized salts undergo efficient trans\u2192cis photoisomerization while the yield of the radiative deactivation is very small at room temperature. The solvent effect on the spectral behaviour indicates the occurrence of intramolecular charge transfer which can induce interesting non-linear optical properties. The results of a study of the interactions of these salts with DNA, which might affect the cell metabolism, showed a relatively modest binding affinity for the pyridinium and imidazolium salts and a more substantial affinity for the quinolinium analogue. The formation of ligand-DNA complexes affects only slightly the radiative relaxation yield while leading to a relevant reduction of the isomerization yield. Measurements of the linear dichroism behaviour of the three compounds and comparison with three analogues bearing furan or thienyl groups, which have been found to display different affinity with DNA in previous works, gave interesting information on the nature of the ligand-DNA binding of these compounds

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic