Pattern matching algorithms to find exact occurrences of a pattern S ∈ Σ in a text T ∈ Σ have been analyzed extensively with respect to asymptotic best, worst, and average case runtime. For more detailed analyses, the number of text character accesses X n performed by an algorithm A when searching a random text of length n for a fixed pattern S has been considered. Constructing a state space an...

‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...

We prove a converse to well-known results by E. Cartan and J. D. Moore. Let f:Mcn?Qc˜n+p be an isometric immersion of Riemannian manifold with constant sectional curvature c into space form c˜, free weak-umbilic points if c>c˜. show that the substantial codimension f is p=n?1 if, as shown Moore, first normal bundle possesses lowest possible rank n?1. These submanifolds are class has been extens...

Reinforcement learning (RL) deals with the problem of an agent that has to learn how to behave to maximize its utility by its interactions with an environment (Sutton & Barto, 1998; Kaelbling, Littman & Moore, 1996). Reinforcement learning problems are usually formalized as Markov Decision Processes (MDP), which consist of a finite set of states and a finite number of possible actions that the ...

Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H. In this paper we minimize the Schatten Cp-norm of suitable affine mappings from B(H) to Cp, using convex and differential analysis (Gâteaux derivative) as well as input from operator theory. The mappings considered generalize Penrose’s inequality which asserts that if A and B den...

Drs. Barrett and Myers are certainly well qualified to write such an ambitious book that spawns a multitude of subjects. It is a challenge to write a book that will satisfy the multidimensional needs of the practitioners of image science. This is a book for advanced students who have developed maturity in mathematical methods, physics, and systems analysis. The treatment of various subjects is ...

0.1. This paper presents an investigation of the following problem. Exhibit a class X of topological spaces which contains all peano spaces and which has the following properties: (1) a cyclic element theory exists in each space of the class, (2) the abstract set consisting of all cyclic element of any space X of the class can be topologized so as to be a member of the class X, and (3) the hype...

We use the idea of two-point stepsize gradient methods, developed to solve unconstrained minimization problems on R, for computing least-squares solutions of a given linear operator equation on Hilbert spaces. Among them we especially pay attention to corresponding modification of the scalar correction method. An application of this approach is presented related to computation of {1, 3} inverse...