Related papers: A general context for Goodwillie Calculus
We introduce the notion of $\mathcal{C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and…
We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial G-sets to symmetric G-spectra, where G is a finite group. We extend a notion of G-linearity suggested by Blumberg to define stably excisive and…
In this paper a Ward-Fonten\'e differential universal algebra is constructed. In this algebra it is possible to obtain a product $\psi$-rule and a general $\psi$-rule of Leibniz for any calculus on sequences. In particular, the simplicial…
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
This paper is intended as a reference for some basic theory for dg categories and their bar complexes. Our modest goal is to carefully record the most important envelope operations can one perform on dg categories (in which one adjoins…
We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categories of multivariable excisive functors from spectra to…
We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
Let $\mathscr{A}$ be an abelian category and let $\mathscr{C}$ and $\mathscr{D}$ be additive subcategories of $\mathscr{A}$. As a generalization of Gorenstein categories, we introduce one-sided $n$-$(\C,\D)$-Gorenstein categories with…
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
We present a new approach to the global fairness verification of tree-based classifiers. Given a tree-based classifier and a set of sensitive features potentially leading to discrimination, our analysis synthesizes sufficient conditions for…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
A pretorsion theory for the category of all categories is presented. The associated prekernels and precokernels are calculated for every functor.
Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent…