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.

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)

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)

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.

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 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.

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)

Medication error is the most common and consistent type of error occurring in hospitals. This article attempts to explore the ethical issues relating to the nursing management of medication errors in clinical areas in Macau, China. A qualitative approach was adopted. Seven registered nurses who were involved in medication errors were recruited for in-depth interviews. The interviews were transcribed and analyzed using content analysis. Regarding the management of patients, the nurses acknowledged the mistakes but did not disclose the incidents to (...) patients and relatives. Concerning management of the nurses involved by senior staff, most participants experienced fairness, comfort and understanding during the process of reporting and investigation. The ethical issues relating to the incidents were discussed, particularly in the Chinese context. There is a need for further study relating to the disclosure of medication incidents to patients and some suggestions were made. (shrink)

Deep brain stimulation of the subthalamic nucleus is a clinically effective tool for treating medically refractory Parkinson’s disease, but its neural mechanisms remain debated. Previous work has demonstrated that STN DBS results in evoked potentials in the primary motor cortex, suggesting that modulation of cortical physiology may be involved in its therapeutic effects. Due to technical challenges presented by high-amplitude DBS artifacts, these EPs are often measured in response to low-frequency stimulation, which is generally ineffective at PD symptom management. This (...) study aims to characterize STN-to-cortex EPs seen during clinically relevant high-frequency STN DBS for PD. Intraoperatively, we applied STN DBS to 6 PD patients while recording electrocorticography from an electrode strip over the ipsilateral central sulcus. Using recently published techniques, we removed large stimulation artifacts to enable quantification of STN-to-cortex EPs. Two cortical EPs were observed – one synchronized with DBS onset and persisting during ongoing stimulation, and one immediately following DBS offset, here termed the “start” and the “end” EPs respectively. The start EP is, to our knowledge, the first long-latency cortical EP reported during ongoing high-frequency DBS. The start and end EPs differ in magnitude and latency, and the end, but not the start, EP magnitude has a significant relationship to ongoing high gamma power during the EP. These contrasts may suggest mechanistic or circuit differences in EP production during the two time periods. This represents a potential framework for relating DBS clinical efficacy to the effects of a variety of stimulation parameters on EPs. (shrink)