In the present study, a set of physics-informed and data-driven approaches are examined towards development an accurate reduced-order model for turbulent plane Couette flow. Based on utilisation proper orthogonal decomposition (POD), particular focus is given to where number POD modes not large enough cover full dynamics state, situation directly relevant modelling flows. Starting from conventi...

Matrix product states (MPS) and `dressed' ground of quadratic mean fields (e.g. Gutzwiller projected Slater Determinants) are both important classes variational wave-functions. This latter class has played roles in understanding superconductivity quantum spin-liquids. We present a novel method to obtain the finite infinite MPS (iMPS) representation state an arbitrary fermionic mean-field Hamilt...

Schwarz methods use a decomposition of the computational domain into subdomains and need to impose boundary conditions on subdomain boundaries. In truncation one restricts unbounded bounded must also put both fields there are vast bodies literature research is very active ongoing. It turns out be fruitful think in as onto subdomains. Seminal precursors this fundamental idea papers by Hagstrom, ...

Caspase-mediated truncation of tau is associated with aggregation. We examined the impact of manipulation of caspase activity on intracellular aggregation of a mutant form of tau (3PO) that forms spontaneous aggregates. Treatment with the caspase inhibitor Z-VAD-fmk reduced both N and C-terminal tau truncation but did not significantly reduce aggregation. Treatment with staurosporine, which act...

An Adaptive Block Truncation Coding Scheme and Its Data-Driven Parallel Implementation

We generalize the notion of Ekedahl-Oort strata to elements in the loop group of any connected reductive group, and call the resulting discrete invariant the truncation of level 1 of the element. We give conditions for the Newton points occurring among the elements of a given truncation of level 1 and especially for the generic Newton point in a given truncation stratum. We prove that truncatio...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...