Link Homology from Homological Mirror Symmetry

We explain how to calculate link homology for a Lie algebra $\mathfrak{g}$ using the Fukaya category associated to a 2d A-model. Links are represented as configurations of particular A-branes and link homology is given by Homs between these A-branes. In the case of $\mathfrak{g}=\mathfrak{su}_2$, we explain how to explicitly construct projective resolutions of the relevant A-branes in terms of thimbles, whose algebra is known. This gives an explicit algorithm for computing Khovanov homology. This algorithm can be extended to all Lie algebras.Comment: 16 pages, 15 figures, contribution to the proceedings of String Math 202

On the Quantization of Plane Gravitational Waves in Loop Quantum Gravity

Gravitational waves are oscillations in the geometry of spacetime caused by the movement of mass or energy. In loop quantum gravity, geometry is quantized so spatial quantities such as area and volume take on discrete values. We worked on quantizing plane gravitational waves, which propagate in one direction and have uniform wavefronts perpendicular to the direction of travel, using the method of canonical quantization on general relativity. For canonical quantization, a theory is expressed in terms of its canonical variables and constraints on those variables, then the variables and constraints are taken to quantum operators and the states of the quantum theory are those that satisfy the constraint operators. The canonical variables of general relativity are Ashtekar variables, which represent gravitational fields in a way that reveals their similarity to electromagnetic fields and other gauge fields. The symmetries of general relativity are formulated as constraints. We used vectors to visually represent the constraints on a spacetime diagram in a manner that is consistent with their actions and their algebra. We represented the constraints as either a Lorentz boost, a directional shift, or a propagation along a light cone. We verified the algebra of these constraints for gravitational waves. A correct quantum theory will have algebra that is consistent the classical constraint algebra. We found possible quantum operators for the unidirectional constraint, the constraint that ensures the plane wave moves only in one direction. We found quantum states satisfying the different versions of the operator and checked that these states were normalizable. We determined that two different versions of the operator had nontrivial normalizable solutions. These solutions could be used in conjunction with a consistent quantization of the other constraints as a quantum formulation of plane gravitational waves

Homological Link Invariants from Floer Theory

There is a generalization of Heegaard-Floer theory from ${\mathfrak{gl}}_{1|1}$ to other Lie (super)algebras $^L{\mathfrak{g}}$. The corresponding category of A-branes is solvable explicitly and categorifies quantum $U_q(^L{\mathfrak{g}})$ link invariants. The theory was discovered in \cite{A1,A2}, using homological mirror symmetry. It has novel features, including equivariance and, if $^L{\mathfrak{g}} \neq {\mathfrak{gl}}_{1|1}$, coefficients in categories. In this paper, we describe the theory and how it is solved in detail in the two simplest cases: the ${\mathfrak{gl}}_{1|1}$ theory itself, categorifying the Alexander polynomial, and the ${\mathfrak{su}}_{2}$ theory, categorifying the Jones polynomial. Our approach to solving the theory is new, even in the familiar ${\mathfrak{gl}}_{1|1}$ case.Comment: 146 page

Compliance with the current recommendations for prescribing antibiotics for paediatric community-acquired pneumonia is improving: data from a prospective study in a French network

International audienceBACKGROUND: Lower respiratory tract infection is a common cause of consultation and antibiotic prescription in paediatric practice. The misuse of antibiotics is a major cause of the emergence of multidrug-resistant bacteria. The aim of this study was to evaluate the frequency, changes over time, and determinants of non-compliance with antibiotic prescription recommendations for children admitted in paediatric emergency department (PED) with community-acquired pneumonia (CAP).METHODS: We conducted a prospective two-period study using data from the French pneumonia network that included all children with CAP, aged one month to 15 years old, admitted to one of the ten participating paediatric emergency departments. In the first period, data from children included in all ten centres were analysed. In the second period, we analysed children in three centers for which we collected additional data. Two experts assessed compliance with the current French recommendations. Independent determinants of non-compliance were evaluated using a logistic regression model. The frequency of non-compliance was compared between the two periods for the same centres in univariate analysis, after adjustment for confounding factors.RESULTS: A total of 3034 children were included during the first period (from May 2009 to May 2011) and 293 in the second period (from January to July 2012). Median ages were 3.0 years [1.4-5] in the first period and 3.6 years in the second period. The main reasons for non-compliance were the improper use of broad-spectrum antibiotics or combinations of antibiotics. Factors that were independently associated with non-compliance with recommendations were younger age, presence of risk factors for pneumococcal infection, and hospitalization. We also observed significant differences in compliance between the treatment centres during the first period. The frequency of non-compliance significantly decreased from 48 to 18.8 % between 2009 and 2012. The association between period and non-compliance remained statistically significant after adjustment for confounding factors. Amoxicillin was prescribed as the sole therapy significantly more frequently in the second period (71 % vs. 54.2 %, p < 0.001).CONCLUSIONS: We observed a significant increase in the compliance with recommendations, with a reduction in the prescription of broad-spectrum antibiotics, efforts to improve antibiotic prescriptions must continue

Second Nature: Hamilton College and the Natural Environment

The following histories explore the boundaries between the human and natural environment on Hamilton College’s campus. They were written for the Environmental Studies course “Interpreting the American Environment” and incorporated site visits and consultations of the historical record in order to better understand familiar places on Hamilton’s campus. Through this research, the contributors identified the human imprint on natural places and located nature in the built environment.https://digitalcommons.hamilton.edu/books/1012/thumbnail.jp

DE L'UTOPIE VERS L'ÉDEN : LE JOUEUR DE FLÛTE DE LOUIS HAMELIN

Dans Le Joueur de flûte (2001), Louis Hamelin suit les péripéties de son narrateur qui quitte son Québec natal pour se rendre sur une île de la côte ouest pour retrouver son père, écrivain disparu. En se fondant sur les catégories établies par le géographe Luc Bureau, cette réflexion s'attache à montrer comment l'île Mere est représentée comme un espace édénique qui reprend, en les parodiant, les stéréotypes couramment attachés à la côte Ouest. Il faut cependant prendre en compte la dimension paratextuelle de ce roman afin de rendre la complexité de son rapport à la spatialité – tant fictive que textuelle.Dans Le Joueur de flûte (2001), Louis Hamelin suit les péripéties de son narrateur qui quitte son Québec natal pour se rendre sur une île de la côte ouest pour retrouver son père, écrivain disparu. En se fondant sur les catégories établies par le géographe Luc Bureau, cette réflexion s'attache à montrer comment l'île Mere est représentée comme un espace édénique qui reprend, en les parodiant, les stéréotypes couramment attachés à la côte Ouest. Il faut cependant prendre en compte la dimension paratextuelle de ce roman afin de rendre la complexité de son rapport à la spatialité – tant fictive que textuelle

De la domestication : la maison - le corps - le livre dans la poésie de Pierre Morency et de Pierre Nepveu

Cet article propose une lecture des recueils de poèmes de Pierre Morency et Pierre Nepveu à la lumière de l'ouvrage Habit Habitat Habitus de Carole Simard-Laflamme paru aux éditions d'art Le Sabord. Habit Habitat Habitus rassemble des réflexions d'artistes ou de chercheurs issus de domaines très différents sur les analogies existantes entre espace corporel, espace référentiel et manière d'être, comportement du sujet. Néanmoins, le triptyque du titre semble masquer un quatrième aspect pourtant fondamental, évident du texte: celui de l'espace du livre. En effet, l'oeuvre de Simard-Laflamme s'apparente presque autant à un objet artistique qu'à un livre au sens traditionnel. Les pages compilent textes, photographies, images plus ou moins détournées, schémas, etc., et ce dans un jeu de couleurs et de formes qui ne laisse pas l'oeil indifférent. Par le biais de l'analogie, l'auteure fait apparaître des correspondances entre espace corporel et espace d'habitation, espace fictif et référentiel, celles-là même que développent les textes de Morency et de Nepveu