Membrangleichgewichte und Harmonien

Ohne Zusammenfassung     

An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem

This contribution is focused on an acceleration of branch and bound algorithms for the uncapacitated facility location problem. Our approach is based on the well-known Erlenkotters’ procedures and Körkels’ multi-ascent and multi-adjustment algorithms, which have proved to be the efficient tools for solving the large-sized instances of the uncapacitated facility location problem. These two original approaches were examined and a thorough analysis of their performance revealed how each particular procedure contributes to the computational time of the whole algorithms. These analyses helped us to focus our effort on the most frequent procedures. The unique contribution of this paper is a new dual ascent procedure. This procedure leads to considerable acceleration of the lower bound computation process and reduces the resulting computational time. To demonstrate more efficient performance of amended algorithms we present the results of extensive numerical experiments.     

Heat capacity measurements in carboxylic polyelectrolyte solutions

Apparent molal heat capacities as a function of the degree of neutralization have been determined for dilute aqueous solutions of poly(acrylic acid) (PAA), poly(methacrylic acid) (PMA), copoly(maleic acid-ethylene) (MAEt), and copoly(maleic acid-styrene) (MASt) using direct flow microcalorimetry. Apparent molal volumes were measured as well. Both molal heat capacity and molal volume decrease with increasing ionization of the polymer. The effect of the hydrophobic interactions of the methyl group or phenyl group was obtained from the difference in the molal quantities of PMA and PAA, or MASt and MAEt. No evidence of hydrophobic effects, as determined from the heat capacity, was found for the conformational transition of PMA, but the hydration of the phenyl groups in MASt was found to be changed significantly at a degree of neutralization of 0.4.     

Generalized solutions to free boundary problems for hyperbolic systems of functional partial differential equations

Summary Local a.e. solutions to a free boundary (Stefan) problem for a quasilinear hyperbolic system of functional PDE's of first order in two independent variables and diagonal form are investigated. The formulation includes retarded arguments and hereditary Volterra terms.     

Knowledge Discovery from Medical Data and Development of an Expert System in Immunology

Artificial intelligence is one of the fastest-developing areas of science that covers a remarkably wide range of problems to be solved. It has found practical application in many areas of human activity, also in medicine. One of the directions of cooperation between computer science and medicine is to assist in diagnosing and proposing treatment methods with the use of IT tools. This study is the result of collaboration with the Children’s Memorial Health Institute in Warsaw, from where a database containing information about patients suffering from Bruton’s disease was made available. This is a rare disorder, difficult to detect in the first months of life. It is estimated that one in 70,000 to 90,000 children will develop Bruton’s disease. But even these few cases need detailed attention from doctors. Based on the data contained in the database, data mining was performed. During this process, knowledge was discovered that was presented in a way that is understandable to the user, in the form of decision trees. The best models obtained were used for the implementation of expert systems. Based on the data introduced by the user, the system conducts expertise and determines the severity of the course of the disease or the severity of the mutation. The CLIPS language was used for developing the expert system. Then, using this language, software was developed producing six expert systems. In the next step, experimental verification was performed, which confirmed the correctness of the developed systems.     

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation.     

Random forests for functional covariates

We propose a form of random forests that is especially suited for functional covariates. The method is based on partitioning the functions' domain in intervals and using the functions' mean values across those intervals as predictors in regression or classification trees. This approach appears to be more intuitive to applied researchers than usual methods for functional data, while also performing very well in terms of prediction accuracy. The intervals are obtained from randomly drawn, exponentially distributed waiting times. We apply our method to data from Raman spectra on boar meat as well as near‐infrared absorption spectra. The predictive performance of the proposed functional random forests is compared with commonly used parametric and nonparametric functional methods and with a nonfunctional random forest using the single measurements of the curve as covariates. Further, we present a functional variable importance measure, yielding information about the relevance of the different parts of the predictor curves. Our variable importance curve is much smoother and hence easier to interpret than the one obtained from nonfunctional random forests.