Related papers: Around general neron desingularization
This paper focuses on the domain generalization task where domain knowledge is unavailable, and even worse, only samples from a single domain can be utilized during training. Our motivation originates from the recent progresses in deep…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
This article will summarise the status of current and future long baseline neutrino oscillation experiments.
The proliferation of deep neural networks in various domains has seen an increased need for interpretability of these models. Preliminary work done along this line and papers that surveyed such, are focused on high-level representation…
A new homological symmetry condition is exhibited that extends and unifies several recently defined and widely used concepts. Applications include general constructions of tilting modules and derived equivalences, and characterisations of…
A short review of form factors, parton distribution functions and generalized parton distributions is given. A possible application of generalized parton distributions in the weak sector is discussed.
In this work, we formulate NEWRON: a generalization of the McCulloch-Pitts neuron structure. This new framework aims to explore additional desirable properties of artificial neurons. We show that some specializations of NEWRON allow the…
In this paper we propose the concept of formal desingularizations as a substitute for the resolution of algebraic varieties. Though a usual resolution of algebraic varieties provides more information on the structure of singularities there…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use…
We study d-minimal expansions of ordered fields, and dense pairs thereof. We also consider other generalizations of o-minimality.
A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
Isoparametric hypersurfaces and their application to special geometries
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…
Work in progress concerning alternative formalizations of arithmetic.