We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when network consists single type also acts as an erasure code, we show it cannot be both locally sustain Motivated by this no-go theorem, desirability local contractibility...

We study contractibility and its approximation for two very general classes of soft global constraints. We introduce a general formulation of decomposition-based soft constraints and provide a sufficient condition for contractibility and an approach to approximation. For edit-based soft constraints, we establish that the tightest contractible approximation cannot be expressed in edit-based term...

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. key aspect of this approach it allows the user to approximate value integral without explicit knowledge an expression boundary surface. Instead, a tesselation node set utilized inform algorithm domai...

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV )), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP , APP , MA, AM ) in PV1 + dWPHP(PV ).

A generalized structure of complementary matrices involved in the input-state-output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and suffici...