Equivalence of two diagram representations of links in lens spaces and essential invariants

In this paper we study the relation between two diagrammatic representations of links in lens spaces: the disk diagram and the grid diagram and we find how to pass from one to the other. We also investigate whether the HOMFLY-PT invariant and the Link Floer Homology are essential invariants, that is, we try to understand if these invariants are able to distinguish links in $L(p,q)$ covered by the same link in $\mathbf{S}^3$. In order to do so, we generalize the combinatorial definition of Knot Floer Homology in lens spaces to the case of links and we analyze how both the invariants change when we switch the orientation of the link.Comment: 42 pages, 24 figure

Learning to predict target location with turbulent odor plumes

: Animal behavior and neural recordings show that the brain is able to measure both the intensity and the timing of odor encounters. However, whether intensity or timing of odor detections is more informative for olfactory-driven behavior is not understood. To tackle this question, we consider the problem of locating a target using the odor it releases. We ask whether the position of a target is best predicted by measures of timing vs intensity of its odor, sampled for a short period of time. To answer this question, we feed data from accurate numerical simulations of odor transport to machine learning algorithms that learn how to connect odor to target location. We find that both intensity and timing can separately predict target location even from a distance of several meters; however, their efficacy varies with the dilution of the odor in space. Thus, organisms that use olfaction from different ranges may have to switch among different modalities. This has implications on how the brain should represent odors as the target is approached. We demonstrate simple strategies to improve accuracy and robustness of the prediction by modifying odor sampling and appropriately combining distinct measures together. To test the predictions, animal behavior and odor representation should be monitored as the animal moves relative to the target, or in virtual conditions that mimic concentrated vs dilute environments

Progression of Left Ventricular Dysfunction and Remodelling under Optimal Medical Therapy in CHF Patients: Role of Individual Genetic Background

Background. Neurohormonal systems play an important role in chronic heart failure (CHF). Due to interindividual heterogeneity in the benefits of therapy, it may be hypothesized that polymorphisms of neurohormonal systems may affect left ventricular (LV) remodelling and systolic function. We aimed to assess whether genetic background of maximally treated CHF patients predicts variations in LV systolic function and volumes. Methods and Results. We prospectively studied 131 CHF outpatients on optimal treatment for at least six months. Echocardiographic evaluations were performed at baseline and after 12 months. Genotype analysis for ACE I/D, β1adrenergic receptor (AR) Arg389Gly, β2AR Arg16Gly, and β2AR Gln27Glu polymorphisms was performed. No differences in baseline characteristics were detected among subgroups. ACE II was a significant predictor of improvement of LV end-diastolic and end-systolic volume (P = .003 and P = .002, respectively) but not of LV ejection fraction (LVEF); β1AR389 GlyGly was related to improvement of LVEF (P = .02) and LV end-systolic volume (P = .01). The predictive value of polymorphisms remained after adjustment for other clinically significant predictors (P < .05 for all). Conclusions. ACE I/D and β1AR Arg389Gly polymorphisms are independent predictors of reverse remodeling and systolic function recovery in CHF patients under optimal treatment

Creation, Contingency, and Early Modern Science: The Impact of Voluntarist Theology on Seventeenth-Century Natural Philosophy

Could God have made it true that 2 + 2 = 5? Was he bound to make the best of all possible worlds? Is he able at this moment to alter the course of nature, either in whole or in part? Questions like these are often associated with medieval theology, not with early modern science. But science is done by people, and people have not always practiced the rigorous separation of science and theology that has come to characterize the modern world. Although many 17th century scientists sought validity for their work apart from revelation, divorcing science from religion was something they never intended. Indeed most natural philosophers of the scientific revolution assumed without question that the world and the human mind had been created by God. This was no small admission, for it meant that both the manner in which and the degree to which the world could be understood depended upon how God had acted in creating it and how he continued to act in sustaining it. Fifty years ago the late British philosopher M.B. Foster identified two different theologies of creation which differ profoundly in their implications for natural science. Rationalist theology, which assigns to God the activity of pure reason, involves both a rationalist X philosophy of nature and a rationalist theory of knowledge of nature. Voluntarist theology, which attributes to God an activity of will not wholly determined by reason, implies that the products of his creative activity are contingent and can be known only empirically. By a careful analysis of four natural philosophies of the early modern period--those of Galileo, Descartes, Boyle, and Newton--! intend to show that there was indeed a connection between theological voluntarism and empirical science in the 17th century

Extracellular Myocardial Volume in Patients With Aortic Stenosis

BACKGROUND: Myocardial fibrosis is a key mechanism of left ventricular decompensation in aortic stenosis and can be quantified using cardiovascular magnetic resonance (CMR) measures such as extracellular volume fraction (ECV%). Outcomes following aortic valve intervention may be linked to the presence and extent of myocardial fibrosis. OBJECTIVES: This study sought to determine associations between ECV% and markers of left ventricular decompensation and post-intervention clinical outcomes. METHODS: Patients with severe aortic stenosis underwent CMR, including ECV% quantification using modified Look-Locker inversion recovery-based T1 mapping and late gadolinium enhancement before aortic valve intervention. A central core laboratory quantified CMR parameters. RESULTS: Four-hundred forty patients (age 70 ± 10 years, 59% male) from 10 international centers underwent CMR a median of 15 days (IQR: 4 to 58 days) before aortic valve intervention. ECV% did not vary by scanner manufacturer, magnetic field strength, or T1 mapping sequence (all p > 0.20). ECV% correlated with markers of left ventricular decompensation including left ventricular mass, left atrial volume, New York Heart Association functional class III/IV, late gadolinium enhancement, and lower left ventricular ejection fraction (p < 0.05 for all), the latter 2 associations being independent of all other clinical variables (p = 0.035 and p < 0.001). After a median of 3.8 years (IQR: 2.8 to 4.6 years) of follow-up, 52 patients had died, 14 from adjudicated cardiovascular causes. A progressive increase in all-cause mortality was seen across tertiles of ECV% (17.3, 31.6, and 52.7 deaths per 1,000 patient-years; log-rank test; p = 0.009). Not only was ECV% associated with cardiovascular mortality (p = 0.003), but it was also independently associated with all-cause mortality following adjustment for age, sex, ejection fraction, and late gadolinium enhancement (hazard ratio per percent increase in ECV%: 1.10; 95% confidence interval [1.02 to 1.19]; p = 0.013). CONCLUSIONS: In patients with severe aortic stenosis scheduled for aortic valve intervention, an increased ECV% is a measure of left ventricular decompensation and a powerful independent predictor of mortality