Results 231 to 240 of about 5,846 (265)

Faithful Representations of Free Products

Journal of the London Mathematical Society, 1997
Let \((R_\alpha)_{\alpha\in\Lambda}\) be a family of domains of the same characteristic \(p\geq 0\). Let \((G_\alpha)_{\alpha\in\Lambda}\) be a family of matrix groups, \(G_\alpha\leq\text{GL}(n,R_\alpha)\), of the same degree \(n\geq 1\). The paper shows that the free product \(*_\alpha G_\alpha\) has a faithful representation of degree \(n+1\) over ...
openaire   +1 more source

Faithful Representations of Lie Algebras

The Annals of Mathematics, 1949
The object of this paper is to give a new proof of the theorem that every Lie algebra over a field K of characteristic zero, has a faithful representation. The first proof of this result, at least when K is algebraically closed, is due to Ado (1). Later Cartan (2) gave a simpler and entirely different proof for the case when K is the field of either ...
openaire   +2 more sources

Epistemic representation, informativeness and the aim of faithful representation

Synthese, 2012
In this paper, I take scientific models to be epistemic representations of their target systems. I define an epistemic representation to be a tool for gaining information about its target system and argue that a vehicle’s capacity to provide specific information about its target system—its informativeness—is an essential feature of this kind of ...
openaire   +1 more source

Faithful representation of nonmonotonic patterns of inference

Minds and Machines, 1992
Recently, John Bell has proposed that a specific conditional logic, C, be considered as a serious candidate for formally representing and faithfully capturing various (possibly all) formalized notions of nonmonotonic inference. The purpose of the present paper is to develop evaluative criteria for critically assessing such claims.
openaire   +1 more source

Representations of Rings with Faithful Monoform Modules

Journal of the London Mathematical Society, 1984
Cet article a la même motivation que celle d'un article précédent de l'A. [Commun. Algebra 9, 23-45 (1981; Zbl 0469.16004)], à savoir l'étude d'une classe d'anneaux caractérisés par un théorème de densité analogue au théorème de densité de Jacobson. Un anneau R est dit anneau m-dense de transformations linéaires si c'est un sous- anneau de l'anneau des
openaire   +2 more sources

Faithful Representation of Separable Distributions

Neural Computation, 1997
A geometric approach to data representation incorporating information theoretic ideas is presented. The task of finding a faithful representation, where the input distribution is evenly partitioned into regions of equal mass, is addressed. For input consisting of mixtures of statistically independent sources, we treat independent component analysis ...
Juan K. Lin, David G. Grier, Jack D. Cowan   +2 more
openaire   +1 more source

Faithful Representations of Polishable Ideals

Proceedings of the 12th Asian Logic Conference, 2013
Su Gao
exaly   +2 more sources

Towards Faithful and Meaningful Interpretable Representations.

CoRR, 2020
Interpretable representations are the backbone of many black-box explainers. They translate the low-level data representation necessary for good predictive performance into high-level human-intelligible concepts used to convey the explanation. Notably, the explanation type and its cognitive complexity are directly controlled by the interpretable ...
Kacper Sokol, Peter A. Flach
openaire   +1 more source

Faithful Representation of a Family of Sets by a Set of Intervals

SIAM Journal on Computing, 1975
Let $Q = \{ q_1 ,q_2 , \cdots ,q_m \} $ be a family of finite, nonempty sets, and $S = \cup_{q_i \in Q} \{ q_i \} $.
openaire   +3 more sources

Faithful Shape Representation for 2D Gaussian Mixtures

2007 IEEE International Conference on Image Processing, 2007
It has been recently discovered that a faithful representation for the shape of some simple distributions can be constructed using invariant statistics [1,2]. In this paper, we consider the more general case of a Gaussian mixture model. We show that the shape of generic Gaussian mixtures can be represented without any loss by the distribution of the ...
Mireille Boutin, Mary L. Comer
openaire   +1 more source