We investigate a representation of the automorphism group connected graph X in unimodular matrices Uβ dimension β, where β is Betti number X. classify graphs for which does not embed into Uβ. It follows that if has no pendant vertices and simple cycle, then faithful AutX acts faithfully on H1(X,Z). The latter statement can be viewed as discrete analogue classical Hurwitz's theorem Riemann surfa...

Let G be a connected real Lie group. The universal representation kernel, Ko, oí G is defined as the intersection of all kernels of continuous finite dimensional representations of G. Evidently, Ko is a closed normal subgroup of G, and it is known from a theorem due to Goto (cf. [l, Theorem 7.1]) that G/Ko has a faithful continuous finite dimensional representation. Thus Kg is the smallest norm...

By applying the minimality principle for model selection, one should seek the model that describes the data by a code of minimal length. Learning is viewed as data compression that exploits the regularities or qualitative properties found in the data, in order to build a model containing the meaningful information. The theory of causal modeling can be interpreted by this approach. The regularit...

We prove a myriad of results related to the stabilizer in an algebraic group G generic vector representation V over algebraically closed field k. Our are on level schemes, which carries more information than considering both Lie algebra and G(k) k-points. For simple faithful irreducible, we existence general position, sometimes called principal orbit type. determine those for position is smooth...

Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the observed data. In this paper, we present a novel framework incorporating sparsity in different domains. We decompose the observed covariance matrix into a spars...

From results about digital convexity, we define a reversible polygon that faithfully represents the maximal convex and concave parts of a digital curve. Such a polygon always exists and is unique in the general case. It is computed from a given digital curve in linear-time using well-known routines: adding a point at the front of a digital straight segment and removing a point from the back of ...

On the linearization of the automorphism groups of algebraic domains. 1 Linearization Theorem and applications Let D be a domain in C n and G a topological group which acts effectively on D by holomorphic automorphisms. In this paper we are interested in projective linearizations of the action of G, i.e. a linear representation of G in some C N +1 and an equivariant imbedding of D into P N with...

Multiple discrete (non-spatial) and continuous (spatial) structures can be fitted to a proximity matrix to increase the information extracted about the relations among the row and column objects vis-à-vis a representation featuring only a single structure. However, using multiple discrete and continuous structures often leads to ambiguous results that make it difficult to determine the most fai...

In this paper, we present a quality point cloud normal estimation method via subspace segmentation based on guided least squares representation. A structure guided low-rank subspace segmentation model has been employed in normal estimation (LRRSGNE). In order to select a consistent sub-neighborhood for a point, the subspace segmentation model is adopted to analyze the underlying structure of it...