Nonnegative solutions of algebraic Riccati equations

AbstractNonnegative Hermitian solutions of various types of continuous and discrete algebraic Riccati equations are studied. The Hamiltonian is considered with respect to two different indefinite scalar products. For the set of nonnegative solutions the order structure and the topology of the set and the stability of solutions is treated. For general Hermitian solutions a method to compute the inertia is given. Although most attention is payed to the classical types arising from LQ optimal control theory, the case where the quadratic term has an indefinite coefficient is studied as well

Fermions on one or fewer Kinks

We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we find some of the low lying bound states explicitly.Comment: 7 pages, 4 figure

Impact of foods with health logo on ssaturated fat, sodium and sugar intake of young Dutch adults

Objective Health logos are introduced to distinguish foods with ‘healthier’ nutrient composition from regular foods. In the present study, we evaluated the effects of changed food compositions according to health logo criteria on the intake of saturated fat, sugar and sodium in a Dutch population of young adults. Design Foods in the Dutch food composition table were evaluated against nutrient criteria for logo eligibility. Three replacement scenarios were compared with the nutrient intake ‘as measured’ in the Dutch consumption survey. The foods not complying with health logo criteria were replaced either by ‘virtual’ foods exactly complying with the health logo criteria, with real 2007 market shares (scenario I) and 100 % market shares (scenario II), or by existing similar foods with a composition that already complied with the health logo criteria (scenario III). Results The percentage reduction in nutrient intake with the current 2007 market shares of ‘health logo foods’ was -2·5 % for SFA, 0 % for sodium and -1 % for sugar. With a 100 % market share these reductions would be -10 % for SFA, -4 % for sodium and -6 % for sugar. This may lead to a reduction of -40 % for SFA, -23 % for sodium and -36 % for sugar in the most optimal replacement scenario. Conclusions With ‘health logo foods’, available in 2007 and current consumption patterns, small reductions can be achieved for SFA and sugar. For additional reductions, lowering the fat/sodium content of meat (products) towards health logo criteria and drinks without sugar towards limits far below health logo criteria would be the most effective reformulation strategy

A Quantum-Quantum Metropolis Algorithm

Recently, the idea of classical Metropolis sampling through Markov chains has been generalized for quantum Hamiltonians. However, the underlying Markov chain of this algorithm is still classical in nature. Due to Szegedy's method, the Markov chains of classical Hamiltonians can achieve a quadratic quantum speedup in the eigenvalue gap of the corresponding transition matrix. A natural question to ask is whether Szegedy's quantum speedup is merely a consequence of employing classical Hamiltonians, where the eigenstates simply coincide with the computational basis, making cloning of the classical information possible. We solve this problem by introducing a quantum version of the method of Markov-chain quantization combined with the quantum simulated annealing (QSA) procedure, and describe explicitly a novel quantum Metropolis algorithm, which exhibits a quadratic quantum speedup in the eigenvalue gap of the corresponding Metropolis Markov chain for any quantum Hamiltonian. This result provides a complete generalization of the classical Metropolis method to the quantum domain.Comment: 7 page

Reproducibility and validity of a diet quality index for children assessed using a FFQ

The diet quality index (DQI) for preschool children is a new index developed to reflect compliance with four main food-based dietary guidelines for preschool children in Flanders. The present study investigates: (1) the validity of this index by comparing DQI scores for preschool children with nutrient intakes, both of which were derived from 3d estimated diet records; (2) the reproducibility of the DQI for preschoolers based on a parentally reported forty-seven-item FFQ DQI, which was repeated after 5 weeks; (3) the relative validity of the FFQ DQI with 3d record DQI scores as reference. The study sample included 510 and 58 preschoolers (2-5-6.5 years) for validity and reproducibility analyses, respectively. Increasing 3d record DQI scores were associated with decreasing consumption of added sugars, and increasing intakes of fibre, water, Ca and many micronutrients. Mean FFQ DQI test-retest scores were not significantly different: 72 (so 11) v. 71 (Si) 10) (P-=0-218) out of a maximum of 100. Mean 3d record DQI score (66 (so 10)) was significantly lower than mean FFQ DQI (71 (so 10);

The χ2\chi^2 - divergence and Mixing times of quantum Markov processes

We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in [1-3] for classical Markov chains is taken to bound the trace-distance from the steady state of a quantum processes. A strict spectral bound to the convergence rate can be given for time-discrete as well as for time-continuous quantum Markov processes. Furthermore the contractive behavior of the $\chi^2$-divergence under the action of a completely positive map is investigated and contrasted to the contraction of the trace norm. In this context we analyse different versions of quantum detailed balance and, finally, give a geometric conductance bound to the convergence rate for unital quantum Markov processes

Quantum Chi-Squared and Goodness of Fit Testing

The density matrix in quantum mechanics parameterizes the statistical properties of the system under observation, just like a classical probability distribution does for classical systems. The expectation value of observables cannot be measured directly, it can only be approximated by applying classical statistical methods to the frequencies by which certain measurement outcomes (clicks) are obtained. In this paper, we make a detailed study of the statistical fluctuations obtained during an experiment in which a hypothesis is tested, i.e. the hypothesis that a certain setup produces a given quantum state. Although the classical and quantum problem are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. Just as in the case of classical hypothesis testing, the confidence in quantum hypothesis testing scales exponentially in the number of copies. In this paper, we will argue 1) that the physically relevant data of quantum experiments is only contained in the frequencies of the measurement outcomes, and that the statistical fluctuations of the experiment are essential, so that the correct formulation of the conclusions of a quantum experiment should be given in terms of hypothesis tests, 2) that the (classical) $\chi^2$ test for distinguishing two quantum states gives rise to the quantum $\chi^2$ divergence when optimized over the measurement basis, 3) present a max-min characterization for the optimal measurement basis for quantum goodness of fit testing, find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiency, and determine the associated divergence rates.Comment: 22 Pages, with a new section on parameter estimatio