We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of à is S for each à ∈ Q(A). Some properties of matrices with signed null-spaces are investigated.

This paper proposes a method to improve the shortest path problem on a NURBS (Non-uniform rational basis spline) surfaces. It comes from an application of the theory in classic differential geometry on surfaces and can improve the distance problem not only on surfaces but in the Euclidean 3-space R . Keywords—shortest paths, geodesic-like method, NURBS surfaces.

The hierarchy of the block bases of transfinite normalized averages of a normalized Schauder basic sequence is introduced and a criterion is given for a normalized weakly null sequence in C(K), the Ba-nach space of scalar valued functions continuous on the compact metric space K, to admit a block basis of normalized averages equivalent to the unit vector basis of c0, the Banach space of null sc...

At present situation travel becomes the biggest hassle for everyone. In this proposed research paper I have used GPS system to find out the shortest path to make your travel at ease. Through this navigation process it is clear-cut for us to find out right path. In this process, it is possible for an individual to analyse the exact shortest route from multiple paths. With the information from th...

We prove a null space property for the uniqueness of the sparse solution vectors recovered from a minimization in `q quasi-norm subject to multiple systems of linear equations, where q ∈ (0, 1]. Furthermore, we show that the null space property for the setting of the sparse solution vectors for multiple linear systems is equivalent to the null space property for the standard minimization in `q ...

An orthogonal basis for the null space of a rectangular m by n matrix, with m < n, is required in various contexts, and numerous well-known techniques, such as QR factorizations or singular value decompositions, are effective at obtaining numerical approximations to such a basis. However, validated bounds on the components of each of these null space basis vectors are sometimes required. In thi...

Algorithms to solve probabilistic planning problems can be classified in probabilistic planners and replanners. Probabilistic planners invest significant computational effort to generate a closed policy, i.e., a mapping function from every state to an action, and these solutions never “fail” if the problem correctly models the environment. Alternatively, replanners computes a partial policy, i....

We present the ‘Basic S*’ algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, G, which is constructed as a discrete representation of an underlying configuration space (a larger “continuous” space/manifold typically of dimension greater than one), we consider the Rips complex, R(G), associated with it. Such a complex, and hence shortes...

In this paper, we consider planning in stochastic shortest path (SSP) problems, a subclass of Markov Decision Problems (MDP). We focus on medium-size problems whose state space can be fully enumerated. This problem has numerous important applications, such as navigation and planning under uncertainty. We propose a new approach for constructing a multi-level hierarchy of progressively simpler ab...

Stochastic Shortest Path problems (SSPs) can be efficiently dealt with by the Real-Time Dynamic Programming algorithm (RTDP). Yet, RTDP requires that a goal state is always reachable. This paper presents an algorithm checking for goal reachability, especially in the complex case of an uncertain SSP where only a possible interval is known for each transition probability. This gives an analysis m...