On solving variational inequalities defined on fixed point sets of multivalued mappings in Banach spaces

We are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive mapping in a reflexive Banach space. Both implicit and explicit approaches are studied. Strong convergence of the implicit method is proved if the space satisfies Opial’s condition and has a duality map weakly continuous at zero, and the strong convergence of the explicit method is proved if the space has a weakly continuous duality map. An essential assumption on the multivalued nonexpansive mapping is that the mapping be single valued on its nonempty set of fixed points.

The Consciousness Unit (CU) Model

The present paper attempts to handle the question how an unconscious mental state (MS) is transformed into a conscious-MS, by developing an outline of a new model, the conscious unit (CU) model. The essential assumption of this model is as follows. In the cognitive system there is an inborn, special linking-mechanism that links to a MS a CU, i.e., a unit of consciousness (or a stream of such units when the represented by the MS is complex). As a result, the individual becomes aware (conscious) of the represented by the MS. This model was applied successfully to certain empirical observations and to several problems, which were directed toward the higher-order (HO) theories of consciousness [especially the higher-order thought (HOT) theory].

Why Experimentum Crucis is Possible in Psychology of Perception

Summary This paper examines the experimentum crucis under the light of the Duhem’s holistic thesis. This methodological instrument is not usable in physics, because physical theories are always logically connected to many assumptions. On the contrary, it is usable in psychological research oriented to perceptual laws, when these laws are, without any hypothetical term, isolated systems. An application of experimentum crucis in Experimental Phenomenology of perception is presented. In conclusion, the role of perceptual knowledge as an essential assumption in other scientific disciplines that have a high degree of theoricity is also underlined.

The new enlightenment hypothesis: All learners are rational

The proposal to recruit available formal structures to build an algorithmic model of all learning falters on close examination of its essential assumption: that the input and output of the model are propositional in structure. After giving three framework considerations, I describe three possibly fatal problems with this assumption, concluding each with a question that needs answering to avoid fatality.

A test of the hypothesis of partial common principal components

A test of the equality of the first h eigenvectors of covariance matrices of several populations is constructed without the assumption that the sampled distributions are Gaussian. It is proved that the test statistic is asymptotically chi-square distributed. In this general setting, an explicit formula for column space of the asymptotic covariance matrix of the sample eigenvectors is derived and the rank of this matrix is computed. An essential assumption in deriving the asymptotic distribution of the presented test statistic is the existence of the finite fourth moments and the simplicity of the h largest eigenvalues of population covariance matrices, which makes possible to use the formulas for derivatives of eigenvectors of symmetric matrices.

Actuator Fault Diagnosis with Robustness to Sensor Distortion

Actuator fault diagnosis is often studied under strong assumptions on available sensors. Typically, it is assumed that the sensors are either fault free or sufficiently redundant. The purpose of this paper is to present a new method foractuatorfault diagnosis which is robust tosensordistortion. It does not require sensor redundancy to compensate sensor distortion. The essential assumption is that sensor distortions are strictly monotonous. Despite the nonlinear and unknown nature of distortions, such sensors still provide useful information for fault diagnosis. The robustness of the presented diagnosis method is analyzed, as well as its ability to detect actuator faults. A numerical example is provided to illustrate its efficiency.

PHILOSOPHICAL PROBLEMS IN COST–BENEFIT ANALYSIS

Cost–benefit analysis (CBA) is much more philosophically interesting than has in general been recognized. Since it is the only well-developed form of applied consequentialism, it is a testing-ground for consequentialism and for the counterfactual analysis that it requires. Ten classes of philosophical problems that affect the practical performance of cost–benefit analysis are investigated: topic selection, dependence on the decision perspective, dangers of super synopticism and undue centralization, prediction problems, the indeterminateness of our control over future decisions, the need to exclude certain consequences for moral reasons, bias in the delimitation of consequences, incommensurability of consequences, difficulties in defending the essential requirement of transferability across contexts, and the normatively questionable but equally essential assumption of interpersonal compensability.

Quantum algorithm for measuring the energy of n qubits with unknown pair-interactions

The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown n-qubit pair-interaction Hamiltonian into a conditional one such that standard phase estimation can be applied to measure the energy. Our essential assumption is that the considered system can be brought into interaction with a quantum computer. For large n the algorithm could still be applicable for estimating the density of energy states and might therefore be useful for finding energy gaps in solid states.

A Measurement Model of Disease Severity in Absence of a Gold Standard

In the absence of a gold standard, we propose the use of confirmatory factor analysis for the quantification of agreement between diagnostic measurements and the true disease severity. The essential assumption is conditional independence of diagnostic measurements adjusted for the severity of the disease. However, depending on the number of measurements available, the method works even if some of them are conditionally dependent. We illustrate the method using an example related to glaucoma eye disease.