It is shown that there exist subsets A and B of the real line which are recursively constructible such that A has a nonrecursive Hausdorff dimension and B has a recursive Hausdorff dimension but has a finite, nonrecursive Hausdorff measure. It is also shown that there exists a polynomial-time computable curve on the two-dimensional plane that has a nonrecursive Hausdorff dimension between 1 and 2. Computability of Julia sets of computable functions on the real line is investigated. It is shown (...) that there exists a polynomial-time computable function f on the real line whose Julia set is not recurisvely approximable. (shrink)

Ko, K., On the computational complexity of integral equations, Annals of Pure and Applied Logic 58 201–228. The computational complexity of Volterra integral equations of the second kind and of the first kind is investigated. It is proved that if the kernel functions satisfy the Lipschitz condition, then the solutions of Volterra equations of the second kind are polynomial-space computable. If, one the other hand, the kernel functions only satisfy the local Lipschitz condition with the Lipschitz constants growing in an (...) exponential rate, then the solutions could be exponential-time hard. We identify a class of Volterra equations of the first kind that can be converted to Volterra equations of the second kind satisfying the local Lipschitz condition. The complexity of the solutions of these equations is also proved to be exponential-time hard. (shrink)

A theory of approximation to measurable sets and measurable functions based on the concepts of recursion theory and discrete complexity theory is developed. The approximation method uses a model of oracle Turing machines, and so the computational complexity may be defined in a natural way. This complexity measure may be viewed as a formulation of the average-case complexity of real functions—in contrast to the more restrictive worst-case complexity. The relationship between these two complexity measures is further studied and compared with (...) the notion of the distribution-free probabilistic computation. The computational complexity of the Lebesgue integral of polynomial-time approximable functions is studied and related to the question “FP = ♯P?”. (shrink)

The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...) bound for the domains of type , and has a #P lower bound for the domains of type. (shrink)

The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...) bound for the domains of type, and has a #P lower bound for the domains of type. (shrink)

Plagiarism and other transgressions of the norms of academic integrity appear to be a persistent problem among upper secondary students. Numerous surveys have revealed high levels of infringement of what appear to be clearly stated rules. Less attention has been given to students’ understanding of academic integrity, and to the potential misconceptions and false beliefs that may make it difficult for them to comply with existing rules and handle complex real-life situations.In this paper we report findings from a survey of (...) European upper secondary students’ views on issues relating to academic integrity. We relate these findings to the students’ training about academic integrity, self-reported level of questionable behavior and country of study.A total of 1654 students at 51 institutions located in 6 European countries participated in the study. The participants generally believed they had a good understanding of the rules applying to them and knew how to behave in compliance with norms of academic integrity. The results indicate, however, that often, in practice, this belief was mistaken. Many students had an inadequate understanding of core elements of academic integrity. They were uncertain about how to act, and they struggled in the handling of complex situations that require context-sensitive judgement. While some differences between countries were identified, they were modest and exhibited no clear pattern. Our results also suggest that reducing students’ level of uncertainty and, to a lesser degree, improving their level of knowledge could lead them to engage less in certain types of questionable behaviours. Surprisingly, the effect of academic training is modest and ambiguous. The study also confirms that perception of peer behaviour has the strongest association with student engagement in questionable behaviours. Thus, academic integrity at the upper secondary level cannot be explained simply in terms of individual ethics or knowledge. (shrink)

The notion of dynamical symmetry is discussed in the framework of the symplectic tomography scheme for the harmonic oscillator. The stationary states are shown to appear as solutions to eigenvalue equation for “classical” probabilities. All the probabilities describing the energy levels are constructed using dynamical-symmetry operators.

Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.

Anonymous didactic verse work, with paraphrase in Tamil and English; transcribed from a palm-leaf manuscript preserved in the Tanjore Maharaja Serfoji's Sarasvati Mahal Library.

Animal use in medical research is widely accepted on the basis that it may help to save human lives and improve their quality of life. Recently, however, objections have been made specifically to the use of animals in scientific investigation of human obesity. This paper discusses two arguments for the view that this form of animal use, unlike some other forms of animal-based medical research, cannot be defended. The first argument leans heavily on the notion that people themselves are responsible (...) for developing obesity and so-called ‘lifestyle’ diseases; the second involves the claim that animal studies of obesity's causes and therapies distract attention from preventive efforts. Drawing on both empirical data and moral reasoning, we argue that the relevant attributions of responsibility and claims about distraction are not plausible, and that, therefore, there is no reason to single out the use of animals in obesity research as especially problematic. (shrink)

The dynamical equations of quantum mechanics are rewritten in the form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated, and squeezed quadrature introduced in the so-called “symplectic tomography”. Then the possibility of a purely classical description of a quantum system as well as a reinterpretation of the quantum measurement theory is discussed and a comparison with the well-known quasi-probabilities approach is given. Furthermore, an analysis of the properties of this marginal distribution, which contains all the (...) quantum information, is performed in the framework of classical probability theory. Finally, examples of the harmonic oscillator's states dynamics are treated. (shrink)

Being follower of Buddhadasa Bhikkhu, a senior Thai Buddhist monk author narrates his experience and success in business by applying principles and teachings in setting his business ethics.

The notion of conditional entropy is extended to noncomposite systems. The \-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki–Lieb inequality is found for systems without subsystems.

Good academic practice is more than the avoidance of clear-cut cheating. It also involves navigation of the gray zones between cheating and good practice. The existing literature has left students’ understanding of gray zone practices largely unexplored. To begin filling in this gap, we present results from a questionnaire study involving N = 1639 undergraduate students from seven European countries representing all major disciplines. We show that large numbers of these students are unable to identify gray area issues and lack (...) sensitivity to the context dependence of these. We also show that a considerable proportion of students have a poor understanding of concepts like plagiarism and falsification, not only in gray zone scenarios, but also in cases of relatively clear-cut cheating. Our results are similar across the faculties and countries of study, and even for students who have attended academic integrity training. We discuss the implications of this for academic integrity training. (shrink)

Translated into Danish by Henrik Jøker Bjerre.