Related papers: Urgent problems at small x

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory…

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…

We present a simple representation for arbitrary-order rogue wave solution and study on the trajectories of them explicitly. We find that the global trajectories on temporal-spatial distribution all look like "X" shape for rogue waves.…

Adaptive retrieval-augmented generation (ARAG) aims to dynamically determine the necessity of retrieval for queries instead of retrieving indiscriminately to enhance the efficiency and relevance of the sourced information. However, previous…

We study several approaches for constructing a minimal model of Universe evolution by matching different stages of scale factor laws. We discuss the continuity in the transitions among the stages and the time variables involved. We develop…

It has recently been argued that the symmetric orbifold theory of T4 is dual to string theory on AdS3 x S3 x T4 at the tensionless point. At this point in moduli space, the theory possesses a very large symmetry algebra that includes, in…

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave…

Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…

Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…

We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low…

In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these…

We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\r3$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the…

We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are…

The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid…

Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…

A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional…

This paper aims to address the challenge of data generation beyond the training data and proposes a framework for Structural Extrapolated Data GEneration (SEDGE) based on suitable assumptions on the underlying data-generating process. We…

We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…

Deep generative models (DGMs) are data-eager because learning a complex model on limited data suffers from a large variance and easily overfits. Inspired by the classical perspective of the bias-variance tradeoff, we propose regularized…