Indicateur de dispersion | EPFL Graph Search

En statistique, un indicateur de dispersion mesure la variabilité des valeurs d’une série statistique. Il est toujours positif et d’autant plus grand que les valeurs de la série sont étalées. Les plus courants sont la variance, l'écart-type et l'écart interquartile. Ces indicateurs complètent l’information apportée par les indicateurs de position ou de tendance centrale, mesurés par la moyenne ou la médiane. Dans la pratique, c'est-à-dire dans l'industrie, les laboratoires ou en métrologie, où s'effectuent des mesurages, cette dispersion est estimée par l'écart type. Étendue Létendue est la différence entre la valeur maximale et la valeur minimale du caractère statistique : x – x. Exemple : soit une série de mesures {8, 1, 2, 3, 7, 10, 9} ; la valeur maximale x est 10 et la valeur minimale x est 1. L'étendue de cette série statistique vaut donc . Écart interquartile Écart interquartile L'écart interquartile est la différence entre le troisième et le premier

Towards patient-tailored interventions for stroke recovery: graph theoretical approaches and modeling of non-invasive brain stimulation

Giorgia Giulia Evangelista

Stroke is a disease that causes the death of precious brain cells that will never grow back and which will affect one in four humans at some point in their life. While therapies and treatments for this debilitating condition are fairly standard, their outcomes are highly heterogeneous, with deficits all too often leading to permanent disability. These unsatisfactory outcomes point to the need for a paradigm shift towards precision medicine, where therapies and treatments are tailored to individual patients. This in turn requires a better understanding of the mechanisms underlying post-stroke impairment and recovery. Recent technological innovations provide an unprecedented opportunity to acquire a detailed picture of the anatomy and electrophysiology of the human brain non-invasively. Therefore, we apply multimodal methodologies to investigate the inner workings of the stroke-affected brain with a view to establishing biomarkers and creating stratifications that maximize the effectiveness of stroke therapy by making it personalized.In the first part of this thesis, network-theoretic models of the brain known as connectomes are created, under the assumption that these provide sufficiently detailed information about the individual patient to inform personalized recommendations. In particular, we leverage existing knowledge about how brain networks are organized into specialized modules connected by a "rich-club" of hubs. In a novel contribution to the field of connectomics, we combine these connectomes with detailed images of the lesion to obtain a network-theoretic lesion profile and a map of the non-lesioned part of the network, which we expect to be a better reflection of true brain connectivity. Using this methodology, we establish that the rich-club, in addition to being a source of network robustness, is also a source of vulnerability in that attacks against it lead to poor behavioral outcomes disproportionate to the size of the attacks.The creation of in-silico simulation of individual patients presents a great opportunity to quickly experiment with treatments, making it a potential game-changer in medical research. However, current technology is not able to faithfully capture the complexity of a whole human brain. The complex brain abnormalities inherent to stroke only add to the difficulty of the challenge. Any models one might wish to create must strike a balance between technological feasibility and sensitivity to inter-patient variability across a large parameter space. In the second part of this thesis, we investigate whether one major source of inter-patient variability, namely the size and location of the lesion, induces substantial variability in the effects of non-invasive brain stimulation to be included as factors in the design of stimulation protocols. Based on our modeling of the stimulation, personalizing stimulation protocols by taking the lesion into account produces little added value, except possibly when one is targeting brain areas close to the lesion and the lesion is significantly large.The proposed studies represent a step of the march towards precision medicine, by examining sources of variability in stroke patients and by associating them with variability in some outcomes of interest. Each step of this march brings stroke therapy farther from the status quo of homogeneous treatments and heterogeneous outcomes and closer to the ideal of heterogeneous treatments and homogeneously positive outcomes.

EPFL2022

Monitoring and adaptation of existing buildings to a hydraulic network Impact of the retrofit of buildings and heat distribution systems on the system performance

Nicole Calame, Matthias Dubuis, Luc Girardin, François Maréchal

Based on the audits realised on buildings by the UNIGE-CUEPE in 2007 [2], [3], the present work studies the conditions of the integration of the energy conversion system and of the building refurbishment options to fit with the GLN network and to prepare the data for integration using the tools developped in the frame of GE WP1.1. The method developed for designing and optimising the large scale integration through low temperature networks of district area is based on the data generated using the method described in [1]. When existing buildings are considered, the data obtained by extrapolation of statistical measures may be replaced by the data measured in the building. In order to maximise the efficiency of the building integratiojn, it is important to realise the study of the integration of existing buildings, considering on the one hand the results of the measurement done in the building and on the other hand the possible options related to the building refurbishment and the reuse of existing equipment. This report explains the approach developed to study the audited buildings inorder to generate the data needed to apply the so called DESD(OP)2 program (``District Energy System Design and OPeration Optimisation'') which has been developped in the frame of the WP1.1. The measured information from the audits carried out by the UNIGE-CUEPE are needed to set the problem with the different building signatures, annual energy quantities and the corresponding temperature levels. The climatisation distribution loops only have been audited, no data was available from these reports regarding heating and sanitary hot water values and therefore for these data the statistical values will be used.

2009

Vehicle-to-Grid for Reliable Frequency Regulation

Dirk Lauinger

Future low-carbon societies will need to store vast amounts of electricity to stabilize electricity grids and to power electric vehicles. Vehicle-to-grid allows vehicle owners and grid operators to share the costs of electricity storage by making the batteries of electric vehicles available to the grid. In practice, vehicle owners decide when to reserve their cars for driving and when to make them available for grid services. Vehicle aggregators then decide how to commit the vehicles to grid services. For vehicle-to-grid to succeed, both vehicle owners and grid operators must be able to trust aggregators, i.e., vehicles should be available for driving and for grid services when the aggregators promise they will be. In this thesis, we solve a decision-making problem that ensures reliable commitments by vehicle aggregators for a particular grid service known as primary frequency regulation, considered one of the most profitable applications of vehicle-to-grid. Mathematically, we first formulate a robust optimization problem with functional uncertainties that maximizes the expected profit from selling primary frequency regulation to grid operators and guarantees that vehicle owners can meet their market commitments for all frequency deviation trajectories in an uncertainty set that encodes applicable European Union regulations. Functional uncertainties ensure that vehicle owners and grid operators can trust the decisions of aggregators at all times. Faithfully modeling the energy conversion losses during battery charging and discharging renders the optimization problem nonconvex. By exploiting a total unimodularity property of the proposed uncertainty sets and an exact linear decision rule reformulation, we prove that the nonconvex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Somewhat counterintuitively, the underlying deterministic problem for a known frequency deviation trajectory does not reduce to a linear program but results in a large-scale mixed-integer linear program, even if time is discretized. We believe that we have thus discovered the first practically interesting class of optimization problems that become dramatically easier through robustification. Through extensive numerical experiments using real-world data, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. In particular, we find that the prevailing penalties for non-delivery of promised regulation power are too low to incentivize aggregators to honor their promises toward grid operators. For general electricity storage devices, we then solve a simplified version of the decision-making problem analytically to understand how the optimal frequency regulation commitments depend on the roundtrip efficiency of the storage device, the dispersion of the frequency deviations, and the EU delivery guarantee. We show how the marginal cost of frequency regulation decreases with roundtrip efficiency and increases with frequency deviation dispersion. For energy-constrained storage devices, we find that the profits from frequency regulation are inversely proportional to the length of time for which storage operators commit regulation power. Establishing an intra-day market for frequency regulation would thus make electricity storage devices more competitive with other regulation providers, such as thermal power plants.

EPFL2022