We show that even on purely numerical-valued data the results of text classification on the derived text-like representation outperforms the more naive numbers-as-tokens representation and, more importantly, is competitive with mature numerical classification methods such as C4.5, Ripper, and SVM.
If we take the strict form of the Wilson models (where all nodes, all excitatory couplings, and all inhibitory couplings are identical) and we assume that the associated differential equations are highly idealized rate models (as Wilson does), then the derived patterns in the monkey-text experiment are always unstable.
Coding was based on the themes derived from text as well as those related to aspects of context, process and actor involvement.
As a corollary of Lemma 10.4, we have the triangulated category of derived coalgebras ({text {DCoalg}}(C_cdot ({text {Ab}}),Q)) of Definition 10.2, with the conservative forgetful functor (e:{text {DCoalg}}(C_cdot ({text {Ab}}),Q) rightarrow {mathcal {D}}({text {Ab}})) to the derived category ({mathcal {D}}({text {Ab}}) cong {text {Ho}}(C_cdot ({text {Ab}}))) of the category of abelian groups.
For triangulated categories, the statement is wrong, and moreover, one cannot recover the derived category ({mathcal {D}}({text {Sec}}(mathcal {C}))) from the family of the derived categories ({mathcal {D}}(mathcal {C}_i)), (i in I).
The corresponding triangulated category is the derived category ({mathcal {D}}_c(X)) of complexes with coherent homology, and it is in fact equivalent to the derived category ({mathcal {D}}({text {Coh}}(X))).
For the sake of clarity, the derived correction factors ( C_{f}^{text{CUR}} ) and ( C_{f}^{text{CUP}} ) together with the corrections factors reported in the literature are listed in Table 2.
Passing to the homotopy categories, we obtain the (ordinary) homology functor begin{aligned} H mathsf{StHom}rightarrow {text {Ho}}(C_cdot ({text {Ab}})) = {mathcal {D}}({text {Ab}}) end{aligned} (10.8 from (mathsf{StHom}) to the derived category ({mathcal {D}}({text {Ab}})) of the category of abelian groups.
In the interests of full disclosure, we should mention that it is probably equivalent to the derived category ({mathcal {D}}({text {Rec}}(I,{text {QCoh}}(X(i)))) of the abelian category ({text {Rec}}(I,{text {QCoh}}(X(i)))), although we did not check this.
Is the conclusion reached and the lesson derived from the text the most relevant and meaningful message?
He derived the text of the litany from two medieval Sarum rite litanies and a German Litany by Martin Luther.
