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To identify pattern components, let us examine 2D slices of 3D eigenarrays and elementary reconstructed components.
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The difference between the two vectors A (red) and B (blue) representing the two universal patterns (see Eqs. (4 - 5) in Section 2.4) is parallel to this component, let us denote it by m.
Therefore, taking the single component (let us denote it by (D_ell)) of (Bcap Omega) between (theta _{2ell }) and (theta _{2ell +1}), the tangent vector of its boundary changes angular direction from (theta _{2ell +1}-pi) to (theta _{2ell }) at (z_0).
At each time instant t and for each map, we compute the main connected component (let us call it (CC^{t}_{j}))—where j identifies one of the M views.
Let W = H . Applying Theorem 2.1 we get the existence of a connected component, let us say ϒ, of nontrivial T-pairs for (3.6) whose closure in [ 0, ∞ ) × C T ( R m × R s ) meets F − 1 ( 0 ) ∩ W and cannot be both bounded and contained in W. One sees immediately that Γ = H − 1 has the required properties. □.
Although we provide the analysis for two component carriers, let us note that it can be easily extended to other carrier aggregation schemes, where more component carriers are treated jointly.
Let D be the diagonal matrix such that its diagonal entries are components of x, let us check the tensor C = A ⋅ D ( 1 − m ) ⋅ D ⋅ … ⋅ D. It is clear that for i = 1, 2, …, n, ∑ i 2, …, i m = 1 n C i i 2 ⋯ i m = ( C e m − 1 ) i = ( A ⋅ D ( 1 − m ) ⋅ D ⋅ … ⋅ D ⏞ m − 1 e m − 1 ) i = τ ( A ). Hence B = C / τ ( A ) is the desired stochastic M-tensor.
As the results for the single-component case are promising, let us now evaluate the effectiveness of the proposed solution when the non-contiguous multicarrier transmission is applied for two adjacent component carriers.
Let us call the components with more sorting reversals "rich components," and the components with fewer sorting reversals "poor components".
However, a more efficient manner consists of performing a second SVD on the previously estimated set of positive and volume normalized PSFs, and retaining enough singular components for an excellent approximation (let us say, more than 60 80 dB).
In a more formal definition, let us consider a component α and a set F related to the components in which the variations of complex network measures will be computed.
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Justyna Jupowicz-Kozak
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