Cergy-Pontoise University (French: Université de Cergy-Pontoise) is a French university, in the Academy of Versailles. Cergy-Pontoise University is a public university and a leading centre of teaching and research, which welcomes 18,000 students and 1,500 international students interested in studying abroad. The university is located in the west of Paris (30 km from central Paris), in the Val-d'Oise department. The university also managed the Institut d'études politiques de Saint-Germain-en-Laye (in cooperation with the Versailles Saint-Quentin-en-Yvelines University).
This is an advanced introduction to the various types of normal random variables, with most of the needed preliminaries included. We first discuss the probability basics, standard central limits, and the theory of the usual, real normal variables, with examples, illustrations and numerous formulae. Then we go on a similar discussion regarding the complex normal variables, and the Rayleigh variables too. We then move to arbitrary dimensions, with a discussion regarding the Gaussian vectors, and related probability laws, featuring some functional analysis, and geometry and physics too. Finally, we provide an introduction to the quantum versions of the normal variables, and notably to those coming from free probability and random matrices.
IntroductionThe rheological behaviour of Self-Compacting Mortar (SCM) is very sensitive to the addition of various additives. This paper examines the impact of recycled Polyethylene Terephthalate (PET) fibres (obtained from plastic brooms) on the fresh and rheological properties of Self-Compacting Mortar (SCM). MethodsThe fibre SCM mix was prepared with four different volume fractions (0.5% to 2.0%) of wavy and linear PET fibres, both having the same length of 20 ± 2 mm. The workability was assessed using the slump-flow and V-funnel tests (LPF), and rheological properties were determined using an Anton Paar rotational rheometer. ResultsFlowability decreased as the fibre volume increased, with a maximum decrease of around 8% at 2% fibre volume. An increase in the V-funnel flow time of up to 1.5 seconds was observed, corresponding to an increased resistance to flow between the minimum and maximum fibre content. The rheometer results showed that all mortars followed the Bingham model. The fibres showed little influence on plastic viscosity and yield stress at low fibre dosages, but at high dosages (1.5% and above) the parameters were significantly increased. The wavy fibre showed lower viscosity and improved adaptability to the granular structure of the mortar than the linear fibre. DiscussionAccording to rheometer data, all mixtures complied with the Bingham model; low dosages showed that fibres had no effect on plastic viscosity or yield stress. However, beyond 1.5%, there were noticeable increases, and wavy fibres were shown to be less viscous and better able to adapt to the granular structure than linear fibres. ConclusionIn conclusion, the use of PET Fibre-reinforced Self-Compacting Mortar (PETF-SCM) exhibits satisfactory fresh workability, rheological properties, and good sustainability, making it a potential candidate for eco-efficient concrete.
We consider solutions to the initial boundary value problems for both heat and wave equations in two dimensions. In this paper, we aim to advance the development of high-order terms in the asymptotic expansions of current boundary perturbations caused by small perturbations of the shape of a C^2-boundary inhomogeneity. Our derivations are rigorously derived by the field expansion (FE) method (formal derivation) and proved by layer potential techniques. It extends those already derived for small-volume inhomogeneities to develop efficient algorithms for determining certain properties of the shape of an inhomogeneity based on boundary measurements.
We have studied the mean field dynamics of heterogenous quadratic integrate-and-fire neurons in presence of spike frequency adaptation (SFA) by considering the exact formulation in terms of the next generation neural mass models (NG-NMMs). In particular, we have examined the emergence of slow relaxation oscillations in purely excitatory and excitatory-inhibitory NG-NMMs with SFA acting only on the excitatory population. Relaxation oscillations (ROs) connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale (the lower is the adaptation strength) the higher is the complexity (number of peaks) displayed by the relaxation oscillations. The increase in the number of peaks is due to spike-adding sequences controlled by the SFA parameters. The increase in the adaptation time scale leads to a chaos-induced spike-adding mechanism where the spike-adding occurs via intermediate chaotic transition regions. Quite peculiarly these chaotic regimes can be of two different types: Population Spiking and Population Bursting Chaos. The emergence of ROs with an increasing number of peaks, controlled by the adaptation strength, occurs via a different spike-adding mechanism. The ROs with (n+1) peaks emerge through a saddle-node bifurcation, while coexisting, in a very narrow parameter region, with the solutions with n peaks, that looses stability via a sub-critical period doubling transition. In this case chaotic dynamics is not observable at the spike-adding bifurcations, but only in proximity of the population spiking-bursting transition. The considered NG-NMMs with SFA could be employed to interpret the results of neuro-physiological experiments on populations of neurons where the concentration of carbachol can be varied. Indeed, the increase (decrease) of carbachol can be interpreted as effectively reducing (increasing) the strength of SFA. As a matter of fact, the increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Furthermore, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength.
