Related papers: Telescopic, Multiplicative, and Rational Extension…
We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the…
We generalize a terminating summation formula to a unilateral nonterminating, and further, a bilateral summation formula by a property of analytic functions. The unilateral one is proved to be a $q$-analogue of a $_4F_3$-summation formula.…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
The method of double extension, introduced by A.~Medina and Ph.~Revoy, is a procedure which decomposes a Lie algebra with an invariant symmetric form into elementary pieces. Such decompositions were developed for other algebras, for…
The availability of a vast array of research papers in any area of study, necessitates the need of automated summarisation systems that can present the key research conducted and their corresponding findings. Scientific paper summarisation…
We generalize regular subdivisions (polyhedral complexes resulting from the projection of the lower faces of a polyhedron) introducing the class of recursively-regular subdivisions. Informally speaking, a recursively-regular subdivision is…
We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can…
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
We show how to extrapolate an analytic function (or a smooth signal) by multiplying and dividing its values on geometric sequences that collapse to a point.
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…
This paper introduces some inverse sequences of different polyhedra all based on finite approximations of a compact metric space so they can be used to capture the shape type of the original space. It is shown that they are HPol-expansions,…
The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
Multimodal summarization requires models to jointly understand textual and visual inputs to generate concise, semantically coherent summaries. Existing methods often inject shallow visual features into deep language models, leading to…
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has…
In this paper, we introduce the super telescoping formula, a natural generalization of well-known telescoping formula. We explore various aspects of the formula including its origin and the telescoping cancellations emerging from symmetric…
The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables. In particular we characterize these expansions in terms of bounded derivatives and we develop tauberian…