相关论文: The primal framework. II. Smoothness
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…
In this paper we generalize the higher-degree smoothness results in perturbation theory from the case that the stable maps have the fixed domain $S^2$ to the general genus zero case.
Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is…
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
In this paper, we study the problem of establishing the accountability and fairness of transparent machine learning models through monotonicity. Although there have been numerous studies on individual monotonicity, pairwise monotonicity is…
Robustness of neural networks has recently attracted a great amount of interest. The many investigations in this area lack a precise common foundation of robustness concepts. Therefore, in this paper, we propose a rigorous and flexible…
On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines---within fluctuations and behaviour very near the origin---smooth canonical matrices whose forms depend on the rank of…
We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models or existence of large cardinals). We prove (assuming a weak version of GCH…
The paper is devoted to metric properties of singularities. We investigate the relations among topology, metric properties and smoothness. In particular, we present some higher dimensional analogous of Mumford's theorem on smoothness of…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with…
We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a…
In \cite{tva}, Bertrand Toen and Michel Vaquie defined a scheme theory for a closed monoidal category $(C,\otimes,1)$. In this article, we define a notion of smoothness in this relative (and not necesarilly additive) context which…
We begin the investigation of the free factor complex of a free group of finite rank. For the case of rank 2 we axiomatize its theory and show that it is $\omega$-stable with prime model $AF_2$.
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
A core principle in statistical learning is that smoothness of target functions allows to break the curse of dimensionality. However, learning a smooth function seems to require enough samples close to one another to get meaningful estimate…
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
Debate about fairness in machine learning has largely centered around competing definitions of what fairness or nondiscrimination between groups requires. However, little attention has been paid to what precisely a group is. Many recent…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…