We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together Cartan's and discrepancy estimates, we establish explicit bounds the large deviation theorem non-self-adjoint Toeplitz operators. As applications, obtain modulus continuity integrated density states pure point spectrum property analyti...

The generation effect refers to the finding that subjects who generate information (e.g., produce synonyms) remember the information better than they do material that they simply read. Meta-analytic techniques were used to summarize 445 effect sizes over 86 studies, thereby assessing the magnitude and 11 potential moderators of the generation effect. The size of the generation effect across the...

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field...

We apply the Basis Light-Front Quantization (BLFQ) approach to the Hamiltonian field theory of Quantum Electrodynamics (QED) in free space. We solve for the mass eigenstates corresponding to an electron interacting with a single photon in light-front gauge. Based on the resulting non-perturbative ground state light-front amplitude we evaluate the electron anomalous magnetic moment. The numerica...

We consider the optimal rate of approximation by single hidden feed-forward neural networks on the unit sphere. It is proved that there exists a neural network with n neurons, and an analytic, strictly increasing, sigmoidal activation function such that the deviation of a Sobolev class W²(2r)(S(d)) from the class of neural networks Φ(n)(ϕ), behaves asymptotically as n(-2r/d-1). Namely, we prove...

This paper proposes a multiplicative approach to solve defective issues in lexicographic goal programming of the analytic hierarchy process (LGPAHP). Although the LGPAHP can handle inconsistent interval comparison matrices, it generates different weights in the upper and lower triangular interval judgments. Instead of adopting additive constraints, the proposed method uses multiplicative constr...

The present paper provides a representation result for monetary risk measures (i.e., monotone translation invariant functionals) satisfying weak maxitivity property. This can be understood as functional analytic generalization of Gärtner-Ellis large deviations theorem. In contrast to the classical theorem, rate function is computed on an arbitrary set continuous real-valued functions rather tha...