Boundary Terms for Causal Sets

We propose a family of boundary terms for the action of a causal set with a spacelike boundary. We show that in the continuum limit one recovers the Gibbons-Hawking-York boundary term in the mean. We also calculate the continuum limit of the mean causal set action for an Alexandrov interval in flat spacetime. We find that it is equal to the volume of the codimension-2 intersection of the two light-cone boundaries of the interval

The Lie algebra of the lowest transitively differential group of degree three

We investigate the real Lie algebra of first-order differential operators with polynomial coefficients, which is subject to the following requirements. (1) The Lie algebra should admit a basis of differential operators with homogeneous polynomial coefficients of degree up to and including three. (2) The generator of the algebra must include the translation operators $\partial_k$ for all the variables $x_1$,...,$x_k$. (3) The Lie algebra is the smallest indecomposable Lie algebra satisfying (1) and (2). It turns out to be a 39-dimensional Lie algebra in six variables ($k=6$) and the construction of this algebra is also the simplest possible case in the general construction of the Lie algebras of the transitively differential groups introduced by Guillemin and Sternberg in 1964 involving the coefficients of degree 3. Those algebras and various subalgebras have similarities with algebras related to different applications in physics such as those of the Schr\"odinger, Conformal and Galilei transformation groups with and without central extension. The paper is devoted to the presentation of the structure and different decompositions of the Lie algebra under investigation. It is also devoted to the presentation of relevant Lie subalgebras and the construction of their Casimir invariants using different methods. We will rely, in particular, on differential operator realizations, symbolic computation packages, the Berezin bracket and virtual copies of the Lie algebras

Top ten risk factors for morbidity and mortality in patients with chronic systolic heart failure and elevated heart rate: the SHIFT risk model

Aims We identified easily obtained baseline characteristics associated with outcomes in patients with chronic heart failure (HF) and elevated heart rate (HR) receiving contemporary guideline-recommended therapy in the SHIFT trial, and used them to develop a prognostic model. Methods We selected the 10 best predictors for each of four outcomes (cardiovascular death or HF hospitalisation; all-cause mortality; cardiovascular mortality; and HF hospitalisation). All variables with p &#60; 0.05 for association were entered into a forward stepwise Cox regression model. Our initial analysis excluded baseline therapies, though randomisation to ivabradine or placebo was forced into the model for the composite endpoint and HF hospitalisation. Results Increased resting HR, low ejection fraction, raised creatinine, New York Heart Association class III/IV, longer duration of HF, history of left bundle branch block, low systolic blood pressure and, for three models, age were strong predictors of all outcomes. Additional predictors were low body mass index, male gender, ischaemic HF, low total cholesterol, no history of hyperlipidaemia or dyslipidaemia and presence of atrial fibrillation/flutter. The c-statistics for the four outcomes ranged from 67.6% to 69.5%. There was no evidence for lack of fit of the models with the exception of all-cause mortality (p = 0.017). Similar results were found including baseline therapies. Conclusion The SHIFT Risk Model includes simple, readily obtainable clinical characteristics to produce important prognostic information in patients with chronic HF, systolic dysfunction, and elevated HR. This may help better calibrate management to individual patient risk.</p

Visualisation of heterogeneous data with the generalised generative topographic mapping

Heterogeneous and incomplete datasets are common in many real-world visualisation applications. The probabilistic nature of the Generative Topographic Mapping (GTM), which was originally developed for complete continuous data, can be extended to model heterogeneous (i.e. containing both continuous and discrete values) and missing data. This paper describes and assesses the resulting model on both synthetic and real-world heterogeneous data with missing values

Effect of visit-to-visit variation of heart rate and systolic blood pressure on outcomes in chronic systolic heart failure: results from the Systolic Heart Failure Treatment With the If Inhibitor Ivabradine Trial (SHIFT) trial

Background: Elevated resting heart rate (HR) and low systolic blood pressure (SBP) are related to poor outcomes in heart failure (HF). The association between visit-to-visit variation in SBP and HR and risk in HF is unknown. Methods and Results: In Systolic Heart Failure Treatment with the If inhibitor ivabradine Trial (SHIFT) patients, we evaluated relationships between mean HR, mean SBP, and visit-to-visit variations (coefficient of variation [CV]=SD/mean×100%) in SBP and HR (SBP-CV and HR-CV, respectively) and primary composite endpoint (cardiovascular mortality or HF hospitalization), its components, all-cause mortality, and all-cause hospitalization. High HR and low SBP were closely associated with risk for primary endpoint, all-cause mortality, and HF hospitalization. The highest number of primary endpoint events occurred in the highest HR tertile (38.8% vs 16.4% lowest tertile; P&lt;0.001). For HR-CV, patients at highest risk were those in the lowest tertile. Patients in the lowest thirds of mean SBP and SBP-CV had the highest risk. The combination of high HR and low HR-CV had an additive deleterious effect on risk, as did that of low SBP and low SBP-CV. Ivabradine reduced mean HR and increased HR-CV, and increased SBP and SBP-CV slightly. Conclusions: Beyond high HR and low SBP, low HR-CV and low SBP-CV are predictors of cardiovascular outcomes with additive effects on risk in HF, but with an unknown effect size. Beyond HR reduction, ivabradine increases HR-CV. Low visit-to-visit variation of HR and SBP might signal risk of cardiovascular outcomes in systolic HF. Clinical Trial Registration: URL: http://www.isrctn.com/. Unique identifier: ISRCTN70429960

Efficacy profile of ivabradine in patients with heart failure plus angina pectoris

Objectives: In the Systolic Heart Failure Treatment with the If Inhibitor Ivabradine Trial (SHIFT), slowing of the heart rate with ivabradine reduced cardiovascular death or heart failure hospitalizations among patients with systolic chronic heart failure (CHF). Subsequently, in the Study Assessing the Morbidity-Mortality Benefits of the If Inhibitor Ivabradine in Patients with Coronary Artery Disease (SIGNIFY) slowing of the heart rate in patients without CHF provided no benefit for cardiovascular death or nonfatal myocardial infarction (primary composite end point), with secondary analyses suggesting possible harm in the angina subgroup. Therefore, we examined the impact of ivabradine in the patients with CHF plus angina in SHIFT. Methods: SHIFT enrolled adults with stable, symptomatic CHF, a left ventricular ejection fraction ≤35% and a sinus rhythm with a resting heart rate ≥70 bpm. Outcomes were the SHIFT and SIGNIFY primary composite end points and their components. Results: Of 6,505 patients in SHIFT, 2,220 (34%) reported angina at randomization. Ivabradine numerically, but not significantly, reduced the SIGNIFY primary composite end point by 8, 11 and 11% in the SHIFT angina subgroup, nonangina subgroup and overall population, respectively. Ivabradine also reduced the SHIFT primary composite end point in all 3 subgroups. Conclusions: In SHIFT, ivabradine showed consistent reduction of cardiovascular outcomes in patients with CHF; similar results were seen in the subgroup of SHIFT patients with angina

Kinetic modeling in the context of cerebral blood flow quantification by H215O positron emission tomography: The meaning of the permeability coefficient in Renkin–Crone׳s model revisited at capillary scale.

One the one hand, capillary permeability to water is a well-defined concept in microvascular physiology, and linearly relates the net convective or diffusive mass fluxes (by unit area) to the differences in pressure or concentration, respectively, that drive them through the vessel wall. On the other hand, the permeability coefficient is a central parameter introduced when modeling diffusible tracers transfer from blood vessels to tissue in the framework of compartmental models, in such a way that it is implicitly considered as being identical to the capillary permeability. Despite their simplifying assumptions, such models are at the basis of blood flow quantification by H215O Positron Emission Tomography. In the present paper, we use fluid dynamic modeling to compute the transfers of H215O between the blood and brain parenchyma at capillary scale. The analysis of the so-obtained kinetic data by the Renkin-Crone model, the archetypal compartmental model, demonstrates that, in this framework, the permeability coefficient is highly dependent on both flow rate and capillary radius, contrarily to the central hypothesis of the model which states that it is a physiological constant. Thus, the permeability coefficient in Renkin-Crone's model is not conceptually identical to the physiologic permeability as implicitly stated in the model. If a permeability coefficient is nevertheless arbitrarily chosen in the computed range, the flow rate determined by the Renkin-Crone model can take highly inaccurate quantitative values. The reasons for this failure of compartmental approaches in the framework of brain blood flow quantification are discussed, highlighting the need for a novel approach enabling to fully exploit the wealth of information available from PET data

Simulating seeded vacuum decay in a cold atom system

We propose to test the concept of seeded vacuum decay in cosmology using an analogue gravity Bose-Einstein condensate system. The role of the nucleation seed is played by a vortex within the condensate. We present two complementary theoretical analyses that demonstrate seeded decay is the dominant decay mechanism of the false vacuum. First, we adapt the standard instanton methods to the Gross-Pitaevskii equation. Second, we use the truncated Wigner method to study vacuum decay.Comment: 5 Pages, 4 figures, new intro in v

Visualisation of heterogeneous data with simultaneous feature saliency using Generalised Generative Topographic Mapping

Most machine-learning algorithms are designed for datasets with features of a single type whereas very little attention has been given to datasets with mixed-type features. We recently proposed a model to handle mixed types with a probabilistic latent variable formalism. This proposed model describes the data by type-specific distributions that are conditionally independent given the latent space and is called generalised generative topographic mapping (GGTM). It has often been observed that visualisations of high-dimensional datasets can be poor in the presence of noisy features. In this paper we therefore propose to extend the GGTM to estimate feature saliency values (GGTMFS) as an integrated part of the parameter learning process with an expectation-maximisation (EM) algorithm. The efficacy of the proposed GGTMFS model is demonstrated both for synthetic and real datasets