We refer to =-=[8]-=- for the proof of this theorem. This proof considers two cases separately: µ+1 ≤ µ2 and µ2 < µ + 1 . In the first case we use Foster’s criterion to design the stability condition and prove it. The pro......
ΔJ = J1 − J2andJ = J1 + J2for any two eigenstates withJ1, J2. Using the Nyquist-Shannon sampling theorem, the required temporal resolutionδtshould be\(\delta t\le \frac{1}{2{{\Delta }}\omega }\). The spatial resolutionδθandδϕcan be determined with...
sampling required by Nyquist–Shannon sampling theorem37for a certain resolution. This option enables a fast acquisition despite the frame-rate of current 2D array detectors being usually two to three orders slower than the acquisition rate of point detectors30,38,39. The dataset used for the p...
proof of concept implementation of our proposed techniques, we will only use IBM related tools (e.g., the IBM Rational Rhapsody Developer RulesComposer Add-On and the IBM Rational Rhapsody DiffMerge) to develop the different components of our proposed architectures as presented in Section 4 and ...
Proof The proof follows by observing that the state matrix F˜=A˜−G˜C˜ of Eq. (13.136) is AS, but the equation is driven by the unbounded dy which is the output of Eq. (13.134). The last equation is in series with the disturbance dynamics in Eq. (13.127). The state ...
We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear ...
Indeed, from the proof of Theorem 1 it is clear that, if P (0) → S−1 > 0 and P (T ) → H′S−1H ≥ 0, then the inequality (12) becomes an equality, which implies that optimality is reached in the limit sup w∈L2 ∞ z(t)′z(t) − γ2w(t)′w(t) dt →ξ0...
As a proof of concept, we also found that it is possible to apply our algorithm—without major modification—to classify SWS in rats. Moreover, consistent with the results in humans, analysis of EEG in rats also revealed a bimodal distribution of SWA (Fig. S6), suggesting that NREM sleep...
We present an algorithm that uses a referee to dynamically combine the policies of a contextual bandit and a multi-armed bandit. We capture the time-correlation of states through iteratively learning the action-reward transition model, allowing for efficient exploration of actions. Our setting is ...
sampling said current and voltage-related signals at predetermined times at a rate where is non-synchronous with the network frequency such that samples defining a cycle of each of the current and voltage related signals are taken over a plurality of cycles of the network waveforms and are not ...