Knot Invariants for Intersecting Loops

We generalize the braid algebra to the case of loops with intersections. We introduce the Reidemeister moves for 4 and 6-valent vertices to have a theory of rigid vertex equivalence. By considering representations of the extended braid algebra, we derive skein relations for link polynomials, which allow us to generalize any link Polynomial to the intersecting case. We perturbatively show that the HOMFLY Polynomials for intersecting links correspond to the vacuum expectation value of the Wilson line operator of the Chern Simon's Theory. We make contact with quantum gravity by showing that these polynomials are simply related with some solutions of the complete set of constraints with cosmological constantComment: 22 page

How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity

Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existance of a deep connection between quantum gravity and knot theory at a dynamical level.Comment: 7p

Towards a loop representation for quantum canonical supergravity

We study several aspects of the canonical quantization of supergravity in terms of the Asthekar variables. We cast the theory in terms of a $GSU(2)$ connection and we introduce a loop representation. The solution space is similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the $GSU(2)$ Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which coincides exactly with the Dubrovnik version of the Kauffman Polynomial. This provides for the first time the possibility of finding explicit analytic expressions for the coefficients of that knot polynomial.Comment: 12 pages Revtex, figures with epsf. An important revision was made of section four. We were able to identify the exact quantum state of all the constraints of supergravity as the Dubrovnik version of the Kauffman polynomial. This provides the first known link of that polynomial to quantum field theor

Jones Polynomials for Intersecting Knots as Physical States of Quantum Gravity

We find a consistent formulation of the constraints of Quantum Gravity with a cosmological constant in terms of the Ashtekar new variables in the connection representation, including the existence of a state that is a solution to all the constraints. This state is related to the Chern-Simons form constructed from the Ashtekar connection and has an associated metric in spacetime that is everywhere nondegenerate. We then transform this state to the loop representation and find solutions to all the constraint equations for intersecting loops. These states are given by suitable generalizations of the Jones knot polynomial for the case of intersecting knots. These are the first physical states of Quantum Gravity for which an explicit form is known both in the connection and loop representations. Implications of this result are also discussed.Comment: 23p

On the sodium overabundance of giants in open clusters: The case of the Hyades

Sodium abundances have been determined in a large number of giants of open clusters but conflicting results, ranging from solar values to overabundances of up to five orders of magnitude, have been found. The reasons for this disagreement are not well-understood. As these Na overabundances can be the result of deep mixing, their proper understanding has consequences for models of stellar evolution. As discussed in the literature, part of this disagreement comes from the adoption of different corrections for non-LTE effects and from the use of different atomic data for the same set of lines. However, a clear picture of the Na behaviour in giants is still missing. To contribute in this direction, this work presents a careful redetermination of the Na abundances of the Hyades giants, motivated by the recent measurement of their angular diameters. An average of [Na/Fe] = +0.30, in NLTE, has been found. This overabundance can be explained by hydrodynamical models with high initial rotation velocities. This result, and a trend of increasing Na with increasing stellar mass found in a previous work, suggests that there is no strong evidence of Na overabundances in red giants beyond those values expected by evolutionary models of stars with more than ~ 2 Msun.Comment: MNRAS accepted, 11 Page

Quantum Einstein-Maxwell Fields: A Unified Viewpoint from the Loop Representation

We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wavefunctions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simons form and the Jones Polynomial play a role in the model.Comment: 13pp. no figures, Revtex, UU-HEP-92/9, IFFI 92-1

The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.Comment: The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.0

Impulse control disorders and use of dopamine agonists in early onset Parkinson’s disease

IntroductionImpulse control disorders (ICDs) are defined as excessive and repetitive behaviors that may affect Parkinson’s disease (PD) patients exposed to dopamine agonists. Current data on ICDs in patients with early-onset Parkinson’s disease (EOPD) is lacking. In this study we aim to assess the frequency of use of dopamine agonists, the prevalence of ICDs, and to explore potential factors associated with their development in patients with EOPD.MethodsWe used the Mayo Clinic Data Explorer system to investigate a population-based cohort of EOPD patients between 1990 and 2022 at Mayo Clinic, Rochester, MN. We used ICD coding for parkinsonism; then, we reviewed all the clinical records and included only those patients with a clinical diagnosis of PD with symptoms onset at or before the age of 50, and who developed ICDs after using therapeutic doses of dopamine agonists.ResultsA total of 831 (513 males and 318 females) patients with EOPD were included with a median age at symptom onset of 42 years of age (CI: 37–46). Dopamine agonists were used in 49.7% of all patients; of these, only 14.5% developed symptoms of one or more ICDs. Hypersexuality was the most commonly observed ICD (38.3%), and the only one having a statistically significant male predominance (p = 0.011).ConclusionICDs are common in EOPD, particularly when associated with the use of dopamine agonists

The London Dialect of the Late Fourteenth Century. a Transformational Analysis in Historical Linguistics.

Ph.D.LinguisticsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/156900/1/6614537.pd