Intrinsic uncertainty on the nature of dark energy

We argue that there is an intrinsic noise on measurements of the equation of state parameter $w=p/\rho$ from large-scale structure around us. The presence of the large-scale structure leads to an ambiguity in the definition of the background universe and thus there is a maximal precision with which we can determine the equation of state of dark energy. To study the uncertainty due to local structure, we model density perturbations stemming from a standard inflationary power spectrum by means of the exact Lema\^{i}tre-Tolman-Bondi solution of Einstein's equation, and show that the usual distribution of matter inhomogeneities in a $\Lambda$CDM cosmology causes a variation of $w$ -- as inferred from distance measures -- of several percent. As we observe only one universe, or equivalently because of the cosmic variance, this uncertainty is systematic in nature.Comment: 12 pages, 3 figures. Version as accepted for publication in Physics of the Dark Universe (Open Access

Tolerance analysis approach based on the classification of uncertainty (aleatory / epistemic)

Uncertainty is ubiquitous in tolerance analysis problem. This paper deals with tolerance analysis formulation, more particularly, with the uncertainty which is necessary to take into account into the foundation of this formulation. It presents: a brief view of the uncertainty classification: Aleatory uncertainty comes from the inherent uncertain nature and phenomena, and epistemic uncertainty comes from the lack of knowledge, a formulation of the tolerance analysis problem based on this classification, its development: Aleatory uncertainty is modeled by probability distributions while epistemic uncertainty is modeled by intervals; Monte Carlo simulation is employed for probabilistic analysis while nonlinear optimization is used for interval analysis.“AHTOLA” project (ANR-11- MONU-013

Schrodinger equation from an exact uncertainty principle

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. Thus there is an exact formulation of the uncertainty principle which precisely captures the essence of what is "quantum" about quantum mechanics.Comment: Latex, 18pp, nature of fluctuations & differences from stochastic mechanics clarifie

Bayesian Image Quality Transfer with CNNs: Exploring Uncertainty in dMRI Super-Resolution

In this work, we investigate the value of uncertainty modeling in 3D super-resolution with convolutional neural networks (CNNs). Deep learning has shown success in a plethora of medical image transformation problems, such as super-resolution (SR) and image synthesis. However, the highly ill-posed nature of such problems results in inevitable ambiguity in the learning of networks. We propose to account for intrinsic uncertainty through a per-patch heteroscedastic noise model and for parameter uncertainty through approximate Bayesian inference in the form of variational dropout. We show that the combined benefits of both lead to the state-of-the-art performance SR of diffusion MR brain images in terms of errors compared to ground truth. We further show that the reduced error scores produce tangible benefits in downstream tractography. In addition, the probabilistic nature of the methods naturally confers a mechanism to quantify uncertainty over the super-resolved output. We demonstrate through experiments on both healthy and pathological brains the potential utility of such an uncertainty measure in the risk assessment of the super-resolved images for subsequent clinical use.Comment: Accepted paper at MICCAI 201

Frequency domain criteria for lp-robust stability of systems with fuzzy parameters

The paper deals with the problem of determining stability margin of linear continuous-time system with fuzzy parametric uncertainty. Non-symmetric multivariate membership functions with lp -constraints describing the uncertainty of characteristic polynomial parameters are considered. An elegant solution, graphical in nature, based on generation of Tsypkin-Polyak plot is presented

Where do uncertainties reside within environmental risk assessments? Expert opinion on uncertainty distributions for pesticide risks to surface water organisms

A reliable characterisation of uncertainties can aid uncertainty identification during environmental risk assessments (ERAs). However, typologies can be implemented inconsistently, causing uncertainties to go unidentified. We present an approach based on nine structured elicitations, in which subject-matter experts, for pesticide risks to surface water organisms, validate and assess three dimensions of uncertainty: its level (the severity of uncertainty, ranging from determinism to ignorance); nature (whether the uncertainty is epistemic or aleatory); and location (the data source or area in which the uncertainty arises). Risk characterisation contains the highest median levels of uncertainty, associated with estimating, aggregating and evaluating the magnitude of risks. Regarding the locations in which uncertainty is manifest, data uncertainty is dominant in problem formulation, exposure assessment and effects assessment. The comprehensive description of uncertainty described will enable risk analysts to prioritise the required phases, groups of tasks, or individual tasks within a risk analysis according to the highest levels of uncertainty, the potential for uncertainty to be reduced or quantified, or the types of location-based uncertainty, thus aiding uncertainty prioritisation during environmental risk assessments. In turn, it is expected to inform investment in uncertainty reduction or targeted risk management action

The changing nature of risk and risk management: the challenge of borders, uncertainty and resilience

No abstract available

Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time

Over the last few years a certain class of dark-energy models decaying inversely proportional to the square of the horizon distance emerged on the basis either of Heisenberg uncertainty relations or of the uncertainty relation between the four-volume and the cosmological constant. The very nature of these dark energies is understood to be the same, namely it is the energy of background space/metric fluctuations. Putting together these uncertainty relations one finds that the model of random fluctuations of the background metric is favored over the holographic one.Comment: 3 page