Related papers: Typical perturbation theory: conditions, accuracy …
The rupture of a medium under stress typifies breakdown phenomena. More generally, the latter encompass the dynamics of systems of many interacting elements governed by the interplay of a driving force with a pinning disorder, resulting in…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
We implement Lie transform perturbation theory to second order for the planar spin-orbit problem. The perturbation parameter is the asphericity of the body, with the orbital eccentricity entering as an additional parameter. We study first…
When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…
We consider problems in which a system receives external \emph{perturbations} from time to time. For instance, the system can be a train network in which particular lines are repeatedly disrupted without warning, having an effect on…
A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the…
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
In the absence of a fundamental theory that precisely predicts values for observable parameters, anthropic reasoning attempts to constrain probability distributions over those parameters in order to facilitate the extraction of testable…
The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…