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The purpose of this paper is to provide a characterization of solvable linear algebraic groups in terms of a geometric property of representations. Representations with a related property played an important role in the proof of the equivariant Riemann-Roch theorem [EG2]. In

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate

Let G be a complex reductive affine algebraic group. Let F, H be algebraic reductive subgroups. The homogeneous space G/F has a natural, transitive left action of G on it. We will consider the induced action of H on G/F. Hereafter a property of a space will be called generic if it occurs on a nonempty Zariski open set. Our main result is the following. The following theorem and its corollaries are true for both real and complex algebraic groups. Moreover, the results actually hold for real semi-algebraic groups by passing to finite index subgroups and finite covers of manifolds. We omit the details of the proofs for semi-algebraic groups. Theorem 1. Consider the induced action of H on G/F, then generic H-orbits are closed in G/F; that is, there is a nonempty Zariski open set of G/F such that the H-orbit of any point in this open set is closed. Corollary 2. Let G, H, F be as above. If H is normal in G, then all orbits of H are closed in G/F. Consequently, if G acts on V and the orbit Gv is closed, then Hv is also closed. Corollary 3. Let G be a reductive algebraic group. If H, F are generic reductive subgroups, then H ∩ F is also reductive. More precisely, take any two reductive subgroups H, F of G. Then H ∩ gFg −1 is reductive for generic g ∈ G.

representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function

definition of a classifier by domain experts) are a very good effectiveness, considerable savings in terms of expert labor power, and straightforward portability to different domains. This survey discusses the main approaches to text categorization that fall within the machine learning paradigm. We

path planners and solves problems for robots with many more degrees of freedom (DOFs). The power of the planner derives both from the "good " properties of the potential function and from the efficiency of the techniques used to escape the local minima of this function. The most powerful

The traditional SPM approach based on bag-of-features (BoF) requires nonlinear classifiers to achieve good image classification performance. This paper presents a simple but effective coding scheme called Locality-constrained Linear Coding (LLC) in place of the VQ coding in traditional SPM. LLC

approximating a value function and using that to compute a deterministic policy, we approximate a stochastic policy directly using an independent function approximator with its own parameters. For example, the policy might be represented by a neural network whose input is a representation of the state, whose

Abstract: When learners have to make sense of risky situations, they can use mathematical models and representations which facilitate successful risk assessment. Based on theoretical considerations on the benefits of specific models and specific representations in such contexts, we present