相关论文: On the predictive power of Local Scale Invariance

The relativistic theory of structure formation in cosmology is based mainly on linear perturbations about a homogeneous background. But we are now driven to understand the theory of higher-order perturbations in full detail, both from…

In order to check on a recent suggestion that local scale invariance [M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function…

In four dimensional unitary scale invariant theories, arguments based on the proof of the a-theorem suggest that the trace of the energy-momentum tensor T vanishes when the momentum is light-like, p^2=0. We show that there exists a local…

Despite the wide use of explainability techniques to attempt to understand the behavior of Artificial Intelligence (AI), the generated explanations may not always be reliable. An explanation can appear plausible to humans but fail to…

The \textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically…

Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

Conformal invariance powerfully constrains the critical behavior of two-dimensional classical systems with short-range interactions and the critical theories in two-dimensions are parametrized by a dimensional number, termed central charge…

Analogical reasoning relies on conceptual abstractions, but it is unclear whether Large Language Models (LLMs) harbor such internal representations. We explore distilled representations from LLM activations and find that function vectors…

Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this…

Inhomogeneities in real-world data, e.g., due to changes in the observation noise level or variations in the structural complexity of the source function, pose a unique set of challenges for statistical inference. Accounting for them can…

Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…

In the context of integrated correlators in $\mathcal{N}=4$ SYM, we study the 2-point functions of local operators with a superconformal line defect. Starting from the mass-deformed $\mathcal{N}=2^*$ theory in presence of a…

We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for…

The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local…

With the advancement of technology for artificial intelligence (AI) based solutions and analytics compute engines, machine learning (ML) models are getting more complex day by day. Most of these models are generally used as a black box…

Extending the concept of multi-selfsimilar random field we study multi-scale invariant (MSI) fields which have component-wise discrete scale invariant property. Assuming scale parameters as $\lambda_i>1$, $i=1,\ldots,d$ and the parameter…

The local scale invariance has been investigated in the nonequilibrium kinetic Ising model exhibiting absorbing phase transition of PC type in 1+1 dimension. Numerical evidence has been found for the satisfaction of this symmetry and…

A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…

This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known…