- Mar 2023
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rieoei.org rieoei.org
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AMBIENTES DE APRENDIZAJE LÚDICOS
Incluir la lúdica en los ambientes educativos, permite promover la construcción de identidad, pertenencia cognitiva, aumenta la confianza del sujeto en sí mismo e incentiva la motivación en diversos aspectos. Debe comprenderse que los ambientes lúdicos no solo generan diversión, por ello se hace vital mencionar que el juego permite ver más allá de lo convergente, da la posibilidad de aludir la realidad de forma temporal, dando la oportunidad de habitar otros mundos posibles y donde predomine lo fantástico, promoviendo de esta manera el desarrollo de la creatividad y la imaginación de los individuos.
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- Jul 2017
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he canonical divergence D induces the metric g and the connections∇and∇∗. The same holds for the mean canonical divergence D∇mcd
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if∇is integrable, then it is notgenerally true that X(q,p) =−gradqD∇mcd(p‖·)
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mean canonical divergenceD∇mcd(p‖q):=12(D(p‖q) +D∗(q‖p))(64)which obviously satisfiesD(∇∗)mcd(p‖q) =D∇mcd(q‖p)
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he energy of the geodesicγp,qas the symmetrized version of the canonical divergence:12(D(p‖q) +D(q‖p))=12∫10∥∥ ̇γp,q(t)∥∥2dt
Fazendo a mudança de variável $$ s \mapsto t(s) = 1- s $$ e usando o fato de que \( \gamma_{q,p}(s) = \gamma_{p,q}(1 - s) \), temos: $$ \begin{aligned} D(q||p) & := \int0^1 s ||\dot{\gamma}{q,p}(s)||^2 ds \ & = - \int1^0 (1 - t) ||\dot{\gamma}{p,q}(t)||^2 dt \ & = \int0^1 ||\dot{\gamma}{q,p}(t)||^2 dt - D(p||q) \end{aligned} $$
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D(p‖q) =∫10t∥∥ ̇γp,q(t)∥∥2dt(61)whereγp,qdenotes the geodesic from p to q.
Até o momento, a conexão dual parece não desempenhar nenhum papel.
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D(p‖q) =∫10(1−t)∥∥ ̇γq,p(t)∥∥2dt
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n-dimensional dual manifold(M,g,∇,∇∗). Consider a∇-geodesicγq,p:[0, 1]→Mconnectingqandp. We define a tangent vector fieldXt(p,q)along this geodesic:Xt(q,p):=X(γq,p(t),p)(52)Obviously,X0=X(q,p)(53)X1(q,p) =0(54)Definition 3.A canonical divergence from p to q is defined by the path integralD(p‖q) =∫10〈Xt(q,p), ̇γq,p(t)〉dt
Qual o papel da conexão dual?
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∫10〈X(γ(t),p), ̇γ(t)〉dt=−∫10〈gradγ(t)Dp, ̇γ(t)〉dt=−∫10(dγ(t)Dp)( ̇γ(t))dt=−∫10d Dp◦γd t(t)dt=Dp(γ(0))−Dp(γ(1))=Dp(q)−Dp(p) =Dp(q) =D(p‖q)(13)In particular, we can apply this derivation to the geodesic connectingqandpeven when theintegrability ofXis not guaranteed and obtain the definition of a general canonical divergence
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functionsDpsatisfying the condition of Equation (12) then they are uniqueup to a constant that can vary withp, and we can therefore assumeDp(p) =0
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manifold is dually flat, a canonical divergence was introduced by Amari and Nagaoka [2], which isa Bregman divergence
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a divergence exists for any such manifold. However, it isnot unique and there are infinitely many divergences that give the same geometrical structure
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When a coordinate systemξ:p7→ξp= (ξ1p, . . . ,ξnp)∈Rnis given inM, we pose one condition that, for two nearby pointsξpandξq=ξp+∆ξ,Dis expanded asD(p‖q) =12Dgij(p)∆ξi∆ξj+O(‖∆ξ‖3)(2)and(Dgij(p))ijis a positive definite matrix.
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A divergence functionD(p‖q)is a differentiable real-valued function of two pointspandqin amanifoldM. It satisfies the non-negativity conditionD(p‖q)≥0(1)with equality if and only ifp=q.
A saturação (rigidez) da desigualdade é uma espécie de não-degenerescência da divergência.
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