Related papers: Urgent problems at small x
We briefly review past applications of Regge calculus in classical numerical relativity, and then outline a programme for the future development of the field. We briefly describe the success of lattice gravity in constructing initial data…
Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training,…
This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable…
This paper describes an efficient algorithm REx for generating symbolic rules from artificial neural network (ANN). Classification rules are sought in many areas from automatic knowledge acquisition to data mining and ANN rule extraction.…
The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…
We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology…
Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…
It is shown that the idea of ``minimal'' coupling to gauge fields can be conveniently implemented in the proper time formalism by identifying the equivalent of a ``covariant derivative''. This captures some of the geometric notion of the…
Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.
These Lecture notes give an introduction to Regge calculus as a discrete model of General Relativity.
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to studying the convergence of the finite element lifting of a…
We review the current status of small x resummation of evolution of parton distributions and of deep-inelastic coefficient functions. We show that the resummed perturbative expansion is stable, robust upon different treatments of subleading…
The so-called "principle of maximal conformality" is ineffective and does nothing to resolve the renormalization-scheme-dependence problem. Some essential facts about that problem are summarized. It is stressed that RG invariance is a…
Despite notable advancements in Retrieval-Augmented Generation (RAG) systems that expand large language model (LLM) capabilities through external retrieval, these systems often struggle to meet the complex and diverse needs of real-world…
Explicit expressions for the non-singlet and singlet structure functions g_1 in the small-x region are obtained. They include the total resummation of the double- and single- logarithms of x and account for the running QCD coupling effects.…
Retrieval-Augmented Generation (RAG) has become the dominant approach for answering questions over large corpora. However, current datasets and methods are highly focused on cases where only a small part of the corpus (usually a few…
We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most…
Knowledge graph embedding (KGE) models represent each entity and relation of a knowledge graph (KG) with low-dimensional embedding vectors. These methods have recently been applied to KG link prediction and question answering over…
We examine the behavior of the leading Regge trajectory of the open bosonic string in a uniform electromagnetic background and present a consistent set of Fierz-Pauli conditions for these symmetric tensors that generalizes the Argyres-Nappi…