Structural properties of oracle classes

Denote by the class of oracles relative to which (collapsing oracles), and by the class of oracles relative to which (separating oracles). We present structural results on and . Using a diagonalization argument, we show that neither nor is closed under disjoint union, also known as join. We show that this implies that neither nor is closed under union, intersection, or symmetric difference. Consequently , the first level of the extended low hierarchy, is not closed under join.     

Methods for classification of two thyroid follicular tumour classes

The goal of the present paper is to show that certain cytometric (morphological, photometric and textural) features of isolated cell nuclei can be useful for discrimination and classification of two thyroid tumour classes, namely, follicular adenoma and follicular carcinoma which cannot in general be visually discriminated in cytological smears. Several linear classifiers both at cell and specimen levels are proposed, in order to estimate the true error rate of these classifiers, a ‘hold one specimen out’ scheme is employed.     

Optimal schedules for single facility with two job classes

A single facility scheduling problem with jobs divided into two mutually exclusive classes is considered when the setup time depends on the class of jobs immediately preceding the job being currently processed. The jobs in a given class need not be processed together. Based on a combinatorial analysis of the problem, an algorithm is developed to obtain an optimal schedule when the objective is to minimize mean flow time. The proposed algorithm is polynomially bounded in terms of the computational effort needed to solve the problem.     

Stabilizability and dead-beat controllers for two classes ofWiener-Hammerstein models

Two classes of block oriented models of the Wiener-Hammerstein type are considered. We prove that a generic condition is sufficient for a null controllable discrete-time system of this form to have a stabilizing minimum-time dead-beat controller. When the condition is violated, we show how to design a nonminimum time stabilizing (dynamic) dead-beat controller. The result is used to obtain stabilizability conditions for these systems     

The closure properties on real numbers under limits and computable operators

In effective analysis, various classes of real numbers are discussed. For example, the classes of computable, semi-computable, weakly computable, recursively approximable real numbers, etc. All these classes correspond to some kind of (weak) computability of the real numbers. In this paper we discuss mathematical closure properties of these classes under the limit, effective limit and computable function. Among others, we show that the class of weakly computable real numbers is not closed under effective limit and partial computable functions while the class of recursively approximable real numbers is closed under effective limit and partial computable functions.     

Relations between the stabilization properties of two classes of hereditary linear systems with commensurate delays

Two classes of hereditary linear systems each subjected to two alternative controller structures (one of a free delay dynamic nature while the other one includes delays under integral forms) are analysed from a stabilizability viewpoint. The first class of plants has pure commensurate delays in both state and input while the second has its time delayed contributions to the dynamics under integral form in the differential equations. Under certain weak conditions, the four closed-loop systems resulting from combining each open-loop plant structure with each controller structure can lead to identical state/output trajectories for appropriately related controller parametrizations. This allows the derivation of stabilizability results for any of the four closed-loop combinations of open-loop system plus controller by using results from the literature, each one being originally applicable to just one of the above combinations     

On structured perturbations for two classes of linear infinite-dimensional systems

This paper considers two classes of infinite-dimensional systems described by an abstract differential equationx (t) = (A + BC)x(t),x(0) =x ₀, on a Hilbert space, whereA, B, C are linear, possibly unbounded operators and is an unknown, linear, bounded perturbation. The two classes of systems are defined in terms of properties imposed on the triple (A, B, C). It is proved that for every the perturbed system (A + EF, B, C) inherits all the properties of the unperturbed system {A, B, C}) if (A, E, F) and {A, B, F} are in the same class.     

Linear discriminant analysis for two classes via removal ofclassification structure

A new method for two-class linear discriminant analysis, called “removal of classification structure”, is proposed. Its novelty lies in the transformation of the data along an identified discriminant direction into data without discriminant information and iteration to obtain the next discriminant direction. It is free to search for discriminant directions oblique to each other and ensures that the informative directions already found will not be chosen again at a later stage. The efficacy of the method is examined for two discriminant criteria. Studies with a wide spectrum of synthetic data sets and a real data set indicate that the discrimination quality of these criteria can be improved by the proposed method     

Connectivity properties of classes of linear systems

The number of pathwise-connected components of various classes of linear systems is determined. The proofs are based on the representation of these classes of systems in terms of balanced realizations. This provides a unified way of deriving well-known results as well as the new results presented here.     

Studying properties of classes of default logics

The study of different variants of default logic reveals not only differences but also properties they share. For example, there seems to be a close relationship between semi-monotonicity and the guaranteed existence of extensions. Likewise, formula-manipulating default logics tend to violate the property of cumulativity. The problem is that currently such properties must be established separately for each approach. This paper describes some steps towards the study of properties of classes of default logics by giving a rather general definition of what a default logic is. Essentially our approach is operational and restricts attention to purely formula-manipulating logics. We motivate our definition and demonstrate that it includes a variety of well-known default logics. Furthermore, we derive general results regarding the concepts of semi-monotonicity and cumulativity. As a benefit of the discussion we uncover that some design decisions of concrete default logics were not accidental as they may seem, but rather they were due to objective necessities.     

Modal controllability for systems of neutral type in classes of differential-difference controllers

We propose a solution for the modal controllability problem for linear autonomous differential systems of neutral type with commensurate delays in two classes of differentialdifference controllers.     

An efficiently computable metric for comparing polygonal shapes

A method for comparing polygons that is a metric, invariant under translation, rotation, and change of scale, reasonably easy to compute, and intuitive is presented. The method is based on the L₂ distance between the turning functions of the two polygons. It works for both convex and nonconvex polygons and runs in time O(mn log mn), where m is the number of vertices in one polygon and n is the number of vertices in the other. Some examples showing that the method produces answers that are intuitively reasonable are presented     

Anticipated rationing policy for two demand classes under service level constraints

This paper considers a periodic-review, infinite-horizon, backorder inventory model with two demand classes, where a base-stock policy controls replenishment. We propose an easy-to-use rationing policy, which reserves inventory for future high priority demands by taking the coming delivery of the next period into consideration, hence called anticipated rationing policy. By applying a multidimensional Markov chain approach, we are able to evaluate system performance exactly. We also derive structural results and find optimal solutions for both α-service level and γ-service level constraint problems. A numerical comparison study demonstrates the effectiveness of anticipated rationing policy, where the well-known constant level rationing policy serves as the benchmark.     

Stability properties of equilibria of classes of cooperativesystems

This note deals with the constant control problem for homogeneous cooperative and irreducible systems. These systems serve as models for positive systems. A necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known. Adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant. We prove that for every nontrivial nonnegative control vector a unique nontrivial equilibrium point is achieved which is globally asymptotically stable if the zero solution of the uncontrolled system is globally asymptotically stable. In addition a converse result is provided. Finally a stability result for a particular class of Kolmogorov systems is established. We compare our main results to those in the literature