Related papers: Tensorial generalization of characters
The hierarchy problem can be addressed by extending the four-dimensional space-time to include an extra compact spatial dimension with non-trivial "warped" metric, as first suggested by Randall and Sundrum. If the Randall-Sundrum framework…
We analyze the renormalization-group (RG) flows of two effective Lagrangians, one for measurement induced transitions of monitored quantum systems and one for entanglement transitions in random tensor networks. These Lagrangians, previously…
Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator,…
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce…
Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…
This paper builds on the theory of generalised functions begun in [1]. The Colombeau theory of generalised scalar fields on manifolds is extended to a nonlinear theory of generalised tensor fields which is diffeomorphism invariant and has…
Cet article se veut un survol des r\'eseaux de tenseurs et s'adresse aux d\'ebutants en la mati\`ere. Nous y mettons l'accent sur les outils n\'ecessaires \`a l'impl\'ementation concr\`ete d'algorithmes. Quatre op\'erations de base…
We consider a gauge-invariant, mass-independent prescription for renormalizing composite operators, regularized on the lattice, in the spirit of the coordinate space (X-space) renormalization scheme. The prescription involves only Green's…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
In this work, we apply the concept about operator connection to consider bivariate random tensor means. We first extend classical Markov and Chebyshev inequalities from a random variable to a random tensor by establishing Markov inequality…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
Extending the construction of the (intrinsically defined) full algebra of scalar valued Colombeau functions on a smooth manifold M (Grosser et al., Adv. Math. 166 (2002), 179-206) we present a suitable basic space for eventually obtaining…
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson…
Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and…
Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this…
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…
We propose a method to construct a tensor network representation of partition functions without singular value decompositions nor series expansions. The approach is demonstrated for one- and two-dimensional Ising models and we study the…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…