Related papers: The functional $f(R)$ approximation
We study asymptotic safety of models of the higher derivative quantum gravity with and without matter. The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found. It turns out…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
For any near-threshold asymptotic regime and for any Feynman diagram (involving loop and/or phase space integrals), a systematic prescription for explicitly constructing all-logs, all-powers (all-twists) expansions in perfectly factorized…
Linear second order differential equations of the form $d^{2}w/dz^{2}-\left \{ {u^{2}f\left( u,z\right) +g\left( z\right) }\right\} w=0$ are studied, where $\left| u\right| \rightarrow \infty $ and $z$ lies in a complex bounded or unbounded…
The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by…
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal}…
Spectral asymptotics of the Sturm-Liouville problem with a singular self-conformal weight measure is considered. A stronger version of the bounded distortion property is assumed for the conformal iterated function system corresponding to…
We construct a one-dimensional first-order theory for functionally graded elastic beams using the variational-asymptotic method. This approach ensures an asymptotically exact one-dimensional equations, allowing for the precise determination…
We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of…
In this paper we study scalar perturbations of the metric for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
We evaluate the influence functional for two dimensional models of dilaton gravity. This functional is exactly computed when the conformal invariance is preserved, and it can be written as the difference between the Liouville actions on…
We study the renormalization group flow of non-local form factors in four-dimensional quantum gravity within the proper-time formalism at quadratic order in the curvature expansion. We show that the flow equations can be integrated down to…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation…
There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultaneous approximation. In this paper, we develop a technique of…
Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist of an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating…
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
The concept of relativistic scaling is applied to describe the most recent data from inclusive electron-deuteron scattering at large momentum transfer. We calculate the asymptotic scaling function f(y) of the deuteron using its relationship…