The critical threshold for Bargmann-Fock percolation

In this article, we study the excursions sets $\mathcal{D}\_p=f^{-1}([-p,+\infty[)$ where $f$ is a natural real-analytic planar Gaussian field called the Bargmann-Fock field. More precisely, $f$ is the centered Gaussian field on $\mathbb{R}^2$ with covariance $(x,y) \mapsto \exp(-\frac{1}{2}|x-y|^2)$. In [BG16], Beffara and Gayet prove that, if $p \leq 0$, then a.s. $\mathcal{D}\_p$ has no unbounded component. We show that conversely, if $p>0$, then a.s. $\mathcal{D}\_p$ has a unique unbounded component. As a result, the critical level of this percolation model is $0$. We also prove exponential decay of crossing probabilities under the critical level. To show these results, we develop several tools including a KKL-type result for biased Gaussian vectors (based on the analogous result for product Gaussian vectors by Keller, Mossel and Sen in [KMS12]) and a sprinkling inspired discretization procedure. These intermediate results hold for more general Gaussian fields, for which we prove a discrete version of our main result.Comment: 49 pages, 6 figures, minor changes introduce

Exceptional times for percolation under exclusion dynamics

We analyse in this paper a conservative analogue of the celebrated model of dynamical percolation introduced by H\"aggstr\"om, Peres and Steif in [HPS97]. It is simply defined as follows: start with an initial percolation configuration $\omega(t=0)$. Let this configuration evolve in time according to a simple exclusion process with symmetric kernel $K(x,y)$. We start with a general investigation (following [HPS97]) of this dynamical process $t \mapsto \omega_K(t)$ which we call $K$-exclusion dynamical percolation. We then proceed with a detailed analysis of the planar case at the critical point (both for the triangular grid and the square lattice $Z^2$) where we consider the power-law kernels $K^\alpha$ $$K^{\alpha}(x,y) \propto \frac 1 {\|x-y\|_2^{2+\alpha}} \, .$$ We prove that if $\alpha > 0$ is chosen small enough, there exist exceptional times $t$ for which an infinite cluster appears in $\omega_{K^{\alpha}}(t)$. (On the triangular grid, we prove that it holds for all $\alpha < \alpha_0 = \frac {217}{816}$.) The existence of such exceptional times for standard i.i.d. dynamical percolation (where sites evolve according to independent Poisson point processes) goes back to the work by Schramm-Steif in [SS10]. In order to handle such a $K$-exclusion dynamics, we push further the spectral analysis of exclusion noise sensitivity which had been initiated in [BGS13]. (The latter paper can be viewed as a conservative analogue of the seminal paper by Benjamini-Kalai-Schramm [BKS99] on i.i.d. noise sensitivity.) The case of a nearest-neighbour simple exclusion process, corresponding to the limiting case $\alpha = +\infty$, is left widely open.Comment: 50 pages, 6 figures, there was a problem with the compilation of the tex fil

Bargmann-Fock percolation is noise sensitive

We show that planar Bargmann-Fock percolation is noise sensitive under the Ornstein-Ulhenbeck process. The proof is based on the randomized algorithm approach introduced by Schramm and Steif and gives quantitative polynomial bounds on the noise sensitivity of crossing events for Bargmann-Fock. A rather counter-intuitive consequence is as follows. Let $F$ be a Bargmann-Fock Gaussian field in $\mathbb{R}^3$ and consider two horizontal planes $P_1,P_2$ at small distance $\varepsilon$ from each other. Even though $F$ is a.s. analytic, the above noise sensitivity statement implies that the full restriction of $F$ to $P_1$ (i.e. $F_{| P_1}$) gives almost no information on the percolation configuration induced by $F_{|P_2}$. As an application of this noise sensitivity analysis, we provide a Schramm-Steif based proof that the near-critical window of level line percolation around $\ell_c=0$ is polynomially small. This new approach extends earlier sharp threshold results to a larger family of planar Gaussian fields.Comment: 22 pages, 1 figure, minor changes introduced and two short appendices adde

Noise sensitivity of percolation via differential inequalities

Consider critical Bernoulli percolation in the plane. We give a new proof of the sharp noise sensitivity theorem shown by Garban, Pete and Schramm. Contrary to the previous approaches, we do not use any spectral tool. We rather study differential inequalities satisfied by a dynamical four-arm event, in the spirit of Kesten's proof of scaling relations. We also obtain new results in dynamical percolation. In particular, we prove that the Hausdorff dimension of the set of times with both primal and dual percolation equals $2/3$ a.s.Comment: 28 pages, 6 figure

FLIAT, an object-relational GIS tool for flood impact assessment in Flanders, Belgium

Floods can cause damage to transportation and energy infrastructure, disrupt the delivery of services, and take a toll on public health, sometimes even causing significant loss of life. Although scientists widely stress the compelling need for resilience against extreme events under a changing climate, tools for dealing with expected hazards lag behind. Not only does the socio-economic, ecologic and cultural impact of floods need to be considered, but the potential disruption of a society with regard to priority adaptation guidelines, measures, and policy recommendations need to be considered as well. The main downfall of current impact assessment tools is the raster approach that cannot effectively handle multiple metadata of vital infrastructures, crucial buildings, and vulnerable land use (among other challenges). We have developed a powerful cross-platform flood impact assessment tool (FLIAT) that uses a vector approach linked to a relational database using open source program languages, which can perform parallel computation. As a result, FLIAT can manage multiple detailed datasets, whereby there is no loss of geometrical information. This paper describes the development of FLIAT and the performance of this tool

Flood risk management in Flanders: past developments and future challenges

This paper presents the state of the art of flood risk management in Flanders, a low-lying region in the northern part of Belgium which is vulnerable to flooding. Possible flood hazard sources are not only the many rivers which pass through the Flemish inland, but also the North Sea, which is sensitive to the predicted sea level rise and which can affect large parts of the Flemish coastal area. Due to the expected increase in flood risks in the 21st century, the Flemish government has changed its flood management strategy from a flood control approach to a risk-based approach. Instead of focusing on protection against a certain water level, the objective now is to assure protection against the consequences of a flood, while considering its probability. In the first part, attention is given to the reasoning and functioning of the risk-based approach. Recent improvements to the approach are discussed, as well as the GIS-implementation of the entire model. The functioning of the approach is subsequently demonstrated in two case studies. The second part of the paper discusses future challenges for the flood risk management in Flanders. The driving force behind these challenges is the European Directive on the assessment and management of flood risks, which entered into force in 2007. The Flemish implementation of the directive is discussed and situated in the European landscape. Finally, attention is given to the communication of flood risks to the general public, since the "availability" of flood risk management plans is among the requirements of the EU Floods Directive

DETERMINATION OF INERTIA ELEMENTS FOR THE LOWER LIMBS

INTRODUCTION: For kinematic and dynamic studies of the lower limbs, using a three dimensional model is useful. Such models allow one to determine segment movements and forces acting on joints. Inverse Dynamic Analysis can be used to calculate the biomechanical loads applied (Elftman,1939). The reliability of the results depends on the degree of accuracy of the kinematic and anthropometric data (Kingma et al.,1996).The purpose of this paper is to explain a simple way to determine inertia elements of the lower limbs using anthropometric data available in the literature. METHODS: Body mass and stature are the only anthropometric parameters known for a subject. Body segment inertia parameters are obtained from cadavers and we use here de Leva (1996) segmental data for males to perform our calculations. We consider each segment of the lower limb (foot, shank and thigh) as rigid and independent. The model supposes a knowledge of the relative mass and the spatial coordinates of at least three points for each segment. A mathematical method is developed in order to obtain data which take into account the individual characteristics of the subjects. For each segment we have to determine three successive elements:- the localization of the center of mass,- a coordinate system assigned, - an inertia matrix assigned. RESULTS: The main difficulty is to place the markers properly on subjects. A simple test, allowing distance determination between markers, was proposed previously to further calculations. The mathematical model is developed in such a way as to be easily used. Conclusions: These simple-to-use methods presuppose a reducing hypothesis. We assume that for each joint a geometrical center exists. This point lies on the longitudinal axis of the segments and has a fixed three dimensional position relative to the segments forming the joint. The localization of the ‘joint center’ is not referenced to the sagittal and transversal axis. We use data reported by de Leva (1996). This supposes that the lower limb is a standard limb, reducing accuracy for subjects with some pathological segment orientation or for young, old and female subjects. As the error introduced by using inappropriate segment parameters could be substantial, the choice of the biomechanical model, as well as the optimal measurement method, is absolutely necessary to obtain for example a good evaluation of the forces acting on the different joints

SPINE MOVEMENT DURING HALF SQUAT EXERCISE

INTRODUCTION .Postural variations of the spine can be studied using radiological technique, but in order to minimize the ionizing radiation we suggested previously to use a non-invasive method. The aim of this study is to describe the movement of the different vertebral segments during half squat exercise. MATEFUAL AND METHOD As described previously external markers are glued to the projecting contours of the spinous processes on 20 voluntary subjects (10 males, 10 females). Markers were implanted on T7, T12, L1, L3, L5 and S1 vertebra levels. This technique was designed to locate angular displacement. Three positions were studied: neutral (vertical trunk, without additional charge), in charge (vertical trunk + 50 kg) and half squat with 50 kg on the shoulders. From the photos were measured, in the sagittal plane, the angular variations at each vertebral segment. RESULTS In standing position the barbell weight induces a general flexion on the cervical and thoracic levels. A verticalization of S1 with an extension of L5 is noticed. In squat position, the main displacement occurs in S1 according to the important movement of the coxo-femoral joint. L5 remains in a constant position. An important flexion is noticed in L3 and L1. T12 seems well fixed. T7 angulation is dependent of head position and of general trunk flexion. DISCUSSION In physical training session emphasis should be laid on the voluntary development of muscles surrounding pelvis, but also of muscles allowing the fixation of thoraco-lumbar joint

ELECTROSTIMULATION AND FORCE PRODUCTION

INTRODUCTION For muscular and sport exercise, the force production is one of the first important parameter to control. It is always possible to regulate force production via the intensity, but in order to minimize fatigue phenomenon it may be interesting to have a better control of parameters of stimulation. The aim of this work is to determine the interest of multi-electrodes with a new current type. METHOD The experiment was conducted on 8 healthy male volunteer subjects (P.E. students, 1.72111, 75kg, 29 years). The subjects were seated with the knee flexed at 60degr. Trunk and thigh angle was fixed at 1 lode. A force transducer linked to a computer is fixed on the ankle. Electrostimulation was provided by mean of a SG4 apparatus. A reference electrode was secured over the femoral nerve and the active electrodes were put in regards of the motor point of VL,VM, and Vl muscle. Left and right legs are stimulated alternately. A symmetrical square wave signal with a 2 ms rest between positive and negative phase (150 s) was applied at 80 Hz frequency. RESULTS After an initial ramp a nearly flat curve corresponding to tetanos was reached. The stimulation procedure allows to reach 90% and 100% of MVC on the left and right leg respectively. After training session (18 periods) we got a similar result and force induced on the right leg about 110% of the force considered as MVC. DISCUSSION For beginners as well as after electrical training sessions inducing performance increase, the new muscular stimulation procedures proposed allow to get maximal contraction with a relative comfort. Most of the studies report that ES can induce nearly 70 to 80% of MVC. With the proposed technique we can reached quite easily 100% of MVC. This will be a powerful tool to improve maximal force

Communicating flood risk to the public by cartography

Flood risk communication plays an important role in risk management, because it can strengthen people’s risk awareness and can motivate them to take precautionary actions. To inform the public about flood risks, the use of flood maps is encouraged by the recent EU Flood Directive (2007/60/EC). Mapping flood risks deals with the challenges of representing risks in a way people can understand and interpret them correctly. In this contribution, the use of flood maps is discussed within risk communication. Attention is further given to the cartographic principles of flood mapping and to the role of the Internet in communicating flood risks via web cartography. Eventually, the state of the flood risk mapping in Flanders (Belgium) is discussed, considering the theoretical aspects previously handled