We study the representational power of a Boltzmann machine (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network...

For studying the difference effect on the Cosmic Microwave Background Radiation (CMB) anisotropy spectrum by scalar and tensor perturbation, we define another function Alm, which can reflect the effect of different magnetic quantum number m. For a given l, we find that the ratio relations of Alm is different for the scalar perturbation sources and tensor perturbation sources. This give a new wa...

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th ξ-symmetric tensor power of an operator and a matrix, when ξ is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tenso...

In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable p-minimal TTP of length ` (` ≥ 2) of exterior and divided power algebras is a tenso...

The norm of the mth derivative of the map that takes an operator to its kth antisymmetric tensor power is evaluated. The case m = 1 has been studied earlier by Bhatia and Friedland [R. Bhatia and S. Friedland. Variation of Grassman powers and spectra. Linear Algebra and its Applications, 40:1–18, 1981]. For this purpose a multilinear version of a theorem of Russo and Dye is proved: it is shown ...

The norm of the mth derivative of the map that takes an operator to its kth antisymmetric tensor power is evaluated. The case m = 1 has been studied earlier by Bhatia and Friedland [R. Bhatia and S. Friedland. Variation of Grassman powers and spectra. Linear Algebra and its Applications, 40:1–18, 1981]. For this purpose a multilinear version of a theorem of Russo and Dye is proved: it is shown ...

Let 9 be a connected complex domain and let G be a group of holomorphic transformations of 9. Let Hi (i = 1,2) be reproducing kernel Hilbert spaces of holomorphic functions from 9 to finite dimensional complex vector spaces Vi such that each Hi carries a unitary representation Vi of G. Then U1 @ Us is unitary in a reproducing kernel Hilbert space of holomorphic functions from 5-3 X 9 to Vi @ V,...