Abstract: We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. ...

Consistency checking in the CSP ‖ B approach verifies that an individual controller process, defined using a sequential non-divergent subset of CSP, never calls a B operation outside its precondition. Previously this was done by preprocessing the CSP process to perform a weakest precondition semantics proof. An embedding of the CSP traces model already exists in the PVS theorem prover, which ma...

In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally, variants of the homological theorems are shown to hold in equal characteristic. This theory is then applied to Noetherian local rings in order to get: (i) over...

A theorem proved by Hrushovski for graphs and extended by Solecki and Vershik (independently from each other) to metric spaces leads to a stronger version of ultrahomogeneity of the infinite random graph R, the universal Urysohn metric space U, and other related objects. We propose a new proof of the result and show how it can be used to average out uniform and coarse embeddings of U (and its v...

This survey addresses sampling discretization and its connections with other areas of mathematics. The concentrates on norms elements finite-dimensional subspaces. We present here known results both integral the uniform norm beginning classical ending very recent achievements. also show how connects to spectral properties operator submatrices, embedding subspaces, moments marginals high-dimensi...

We prove a scaling limit result for random walk on certain planar maps with its natural time parametrization. In particular, we show that \(\gamma \in (0,2)\), the mated-CRT map parameter \) converges to \)-Liouville Brownian motion, quantum parametrization of motion gravity (LQG) surface. Our applies if is embedded into plane via embedding which comes from SLE/LQG theory or Tutte (a.k.a. harmo...

It is shown that some familiar properties of epimorphisms in the category of frames cary over to the category of uniform frames. This is achieved by suitably enriching certain frame homomorphisms to uniform frame homomorphisms. This note deals with the natural question, apparently never considered so far, whether certain familiar facts concerning epimorphisms, and specifically epi-extensions, o...

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of ass...

Motivated by a 40-year-old problem due to Peter Cameron on extending partial parallelisms, we provide necessary and sufficient conditions under which one can extend an r-factorization of a complete 3-uniform hypergraph on m vertices, K3 m, to an s-factorization of K3 n. This generalizes an existing result of Baranyai and Brouwer–where they proved it for the case r = s = 1.

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology pointwise convergence into Tychonoff product topological spaces, but applied function C(X,Y) all continuous from X uniform Y family subsets and (weak) set-open topology. We also investigated following question: how is related algebraic structures (such as groups, rings vector...