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We present an approach to construct structure-preserving emulators for Hamiltonian flow maps and Poincaré maps based directly on orbit data. Intended applications are in moderate-dimensional systems, in particular, long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations. The method is based on multi-output Gaussian process (GP) regression on scattered training data. To obtain long-term stability, the symplectic property is enforced via the choice of the matrix-valued covariance function. Based on earlier work on spline interpolation, we observe derivatives of the generating function of a canonical transformation. A product kernel produces an accurate implicit method, whereas a sum kernel results in a fast explicit method from this approach. Both are related to symplectic Euler methods in terms of numerical integration but fulfill a complementary purpose. The developed methods are first tested on the pendulum and the Hénon-Heiles system and results compared to spectral regression of the flow map with orthogonal polynomials. Chaotic behavior is studied on the standard map. Finally, the application to magnetic field line tracing in a perturbed tokamak configuration is demonstrated. As an additional feature, in the limit of small mapping times, the Hamiltonian function can be identified with a part of the generating function and thereby learned from observed time-series data of the system's evolution. For implicit GP methods, we demonstrate regression performance comparable to spectral bases and artificial neural networks for symplectic flow maps, applicability to Poincaré maps, and correct representation of chaotic diffusion as well as a substantial increase in performance for learning the Hamiltonian function compared to existing approaches.
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Specialized Gaussian process regression is presented for data that are known to fulfill a given linear differential equation with vanishing or localized sources. The method allows estimation of system parameters as well as strength and location of point sources. It is applicable to a wide range of data from measurement and simulation. The underlying principle is the well-known invariance of the Gaussian probability distribution under linear operators, in particular differentiation. In contrast to approaches with a generic covariance function/kernel, we restrict the Gaussian process to generate only solutions of the homogeneous part of the differential equation. This requires specialized kernels with a direct correspondence of certain kernel hyperparameters to parameters in the underlying equation and leads to more reliable regression results with less training data. Inhomogeneous contributions from linear superposition of point sources are treated via a linear model over fundamental solutions. Maximum likelihood estimates for hyperparameters and source positions are obtained by nonlinear optimization. For differential equations representing laws of physics the present approach generates only physically possible solutions, and estimated hyperparameters represent physical properties. After a general derivation, modeling of source-free data and parameter estimation is demonstrated for Laplace's equation and the heat/diffusion equation. Finally, the Helmholtz equation with point sources is treated, representing scalar wave data such as acoustic pressure in the frequency domain.
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OBJECTIVE: Diagnoses are based on algorithms which count symptoms. The question is whether all or only sufficiently severe complaints of patients should qualify as diagnostic criteria and how prevalence rates of mental disorders change when all or only moderate or severe complaints are counted as symptoms in diagnostic algorithms. METHOD: One hundred thirty-nine general practice patients were diagnosed as suffering from major depression according to DSM-IV on the basis of the standardized clinical International Neuropsychiatric Diagnostic Interview (MINI). They additionally filled in the self-rating SCL-90, which allows patients to rate the intensity of each symptom on a five-point Likert scale. The diagnostic algorithm for major depression was modeled on the basis of the SCL-90 self-rating. MINI-diagnoses were compared with SCL-diagnoses when symptoms with different intensity were taken into account. RESULTS: The prevalence of "SCL-90-major depression" is 77.2% if all symptoms are counted, and 38.7% if only at least moderately severe symptoms, or 5.0% if only extremely severe symptoms are included in the diagnostic algorithm. Sensitivity rates vary from 10.8%, if only extremely severe symptoms are counted, to 94.2% if all complaints were included. Specificity rates vary from 37.4% for all complaints and 100% for extremely severe items. Accuracy is best when "a little bit" of complaint is omitted (78.1%) and lowest if only extremely severe symptoms are counted (58.9%). CONCLUSION: The data demonstrate the importance of the severity of single symptoms for the diagnosis of mental disorders. Symptom definition, recognition, and evaluation must find greater attention in research, clinical practice, and training of physicians.
Asunto(s)
Trastorno Depresivo Mayor/diagnóstico , Trastorno Depresivo Mayor/epidemiología , Evaluación de Síntomas , Alemania/epidemiología , Humanos , Prevalencia , Autoinforme , Sensibilidad y Especificidad , Índice de Severidad de la EnfermedadRESUMEN
Broiler farming is the fastest-growing animal production sector and broiler meat is the second most-consumed meat in the world. The intensification of broiler production often has a negative impact on the meat quality and carcass characteristics. Consumers, however, expect a quality product from animals reared extensively on farms providing good animal welfare, often intuitively associated with extensive farming practices. Therefore, this literature review investigates how the critical factors contributing to the degree of extensiveness of broiler production affect the quality of meat. We used the data from scientific articles published in the years 2012-2021 to analyze the effect of diet (n = 409), genetics (n = 86), enrichment (n = 25), and stocking density (n = 20) on meat quality and carcass characteristics. Minerals and microelements supplementation in the diet improved all the meat quality aspects: sensory, physical, and chemical in most studies. Minerals and enzymes in the diet had beneficial effects on carcass characteristics, unlike feed restriction and ingredient substitutions. The impact of outdoor access on meat quality and carcass characteristics was most frequently examined, in contrast to the use of perches or effects of litter quality. Overall, enrichment did not affect the meat's sensory or physical parameters, but outdoor access improved its lipid composition. Lower stocking density deteriorated intramuscular fat content, decreased tenderness and juiciness, yet lowered cooking and drip loss, and increased carcass and breast muscle yields. When it comes to genetics, in general, slow growing broiler strains have better meat quality parameters, especially regarding yellowness (b*), redness (a*), cooking and drip loss. Our review shows that the factors which contribute to extensiveness of broiler production systems and birds' welfare also affect meat quality and the carcass characteristics.