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The disturbed data y δ as well as the noise δ = ∥ y − y δ ∥ are used as input data for the reconstruction process.
According to Equations (1) and (3), the disturbed data model is, y ̃ t = A θ + Δ A s t + n t (4).
(4.3) For disturbed data (f^{delta}(t)), we use the Tikhonov regularization method, which seeks a function (v^{delta}_{alpha} x,cdot)) from minimizing quadratic functional J_{alpha}bigl v^{delta}bigr):={biglVert Kv^{delta}-f^{delta}bigrVert }^{2}+{ alpha}^{2}{biglVert v^{delta}bigrVert }^{2}.
Physically, φ can only be measured with some measurement errors, and we would actually have a disturbed data function φ ϵ ( x, y ) = ∑ p, q = 1 ∞ φ p q ϵ sin p x sin q y ∈ L 2 , g ϵ ( x, y ) = ∑ p, q = 1 ∞ g p q ϵ sin p x sin q y ∈ L 2. for which ∥ φ ϵ − φ ∥ ≤ ϵ, ∥ g ϵ − g ∥ ≤ ϵ, where the constant ϵ > 0 represents a bound on the measurement error, ∥ ⋅ ∥ denotes the L 2 -norm.
In the physiopathological context of gonadal failure, DAP12 impairment and lymphocyte depletion do not act synergistically since bone mass reduction after ovariectomy is the same when either one or both of these factors are disturbed (Data S2).
Network inference with disturbed data was repeated 100 times, leading to a series of inferred models.
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In this study, as a solution for interpreting disturbed TRT data and to utilize additional information from the sequential plot method, we proposed an alternative method using a temporal superposition applied ILS model combined with the quasi-Newton optimization method.
The model process may generate incomplete cross-sections or geometries and cause Rhino to crash because they disturbed the data tree and initiated massive numbers of calculations instantly in Grasshopper.
A causal diagnosis solution relying on experts' knowledge concentrates on the different malfunctions that may disturb the data acquisition process and tells the engine test bench tuning engineer which malfunction has occurred or which malfunctions are most likely suspected.
Nevertheless, variable extract recovery rates and/or possible changes in the expression profiles during the several-hour separation procedure can disturb the data reproducibility.
Some literature suggests the role of the moderator during the FG interviews might disturb the data collection process; i.e. since the moderator determines the agenda of the FG interview, answers are more or less restricted to this agenda [ 39].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com