Exact and approximation algorithms for a soft rectangle packing problem

We consider the problem of finding an arrangement of rectangles with given areas that minimizes the total length of all inner and outer border lines. We present a polynomial time approximation algorithm and derive an upper bound estimation on its approximation ratio. Furthermore, we give a formulation of the problem as mixed-integer nonlinear program and show that it can be approximatively reformulated as linear mixed-integer program. On a test set of problem instances, we compare our approximation algorithm with another one from the literature. Using a standard numerical mixed-integer linear solver, we show that adding the solutions from the approximation algorithm as advanced starter helps to reduce the overall solution time for proven global optimality, or gives better primal and dual bounds if a certain time-limit is reached before.     

Stabilized dynamic constraint aggregation for solving set partitioning problems

Dynamic constraint aggregation (DCA) and dual variable stabilization (DVS) are two methods that can reduce the negative impact of degeneracy when solving linear programs. The first uses a projection to reduce the primal space whereas the second acts in the dual space. In this paper, we develop a new method, called stabilized dynamic constraint aggregation (SDCA), that combines DCA and DVS for solving set partitioning problems. It allows to fight degeneracy from both primal and dual perspectives simultaneously. To assess the effectiveness of SDCA, we report computational results obtained for highly degenerate multi-depot vehicle scheduling problem instances solved by column generation. These results indicate that SDCA can reduce the average computational time of the master problem by a factor of up to 7 with respect to the best of the two combined methods. Furthermore, they show that its performance is robust with regard to increasing levels of degeneracy in test problems.     

Interactions of drugs and an oligonucleotide with charged membranes analyzed by immobilized liposome chromatography

We studied the effect of charged lipids or detergent on the retention of drugs and an oligonucleotide by immobilized liposome chromatography to characterize solute-membrane interactions. This is a novel approach in analysis of oligonucleotide-liposome interactions. The charged lipids (phosphatidylserine or distearoyltrimethylammoniumpropane) or detergent (sodium dodecylsulfate) interacted electrostatically in a concentration-dependent matter with the solutes. The oligonucleotide ions presumably bound to the liposomes by multipoint interactions, which was saturable. Sodium dodecylsulfate seemed to affect the drug-membrane interactions more strongly than phosphatidylserine did, probably due to different positioning in the bilayer.     

Hardy-Sobolev critical singular elliptic equations with mixed Dirichlet-Neumann boundary conditions

Three important inequalities (the Poincaré, Hardy and generalized Poincaré inequalities) on the mixed boundary conditions are firstly established by some analytical techniques. Then the existence and multiplicity of positive solutions are studied for a class of semilinear elliptic equations with mixed Dirichlet-Neumann boundary conditions involving Hardy terms and Hardy-Sobolev critical exponents by using the variational methods.     

Sorption of Bisphenol A as Model for Sorption Ability of Organoclays

The arrangement of bisphenol A molecules into organoclays and their interactions with the intercalated surfactant were studied. The organoclays were prepared via solid-state intercalation of four cationic surfactants, such as dodecyltrimethyl-, tetradecyltrimethyl-, hexadecyltrimethyl-, and didodecyldimethyl-ammonium, as bromide salts, at different loading levels into the interlayers of two natural clays. The natural clays, the prepared organoclays, and the spent organoclays were characterized by X-ray powder diffraction, infrared spectroscopy, and scanning electron microscopy. X-ray powder diffraction measurements showed successive interlayer expansions of the d₀₀₁ basal spacing due to the intercalation of the cationic surfactants and the bisphenol A sorption. The increased d₀₀₁ basal spacing of the organoclays after bisphenol A sorption indicates that the molecules are integrated between the alkyl chains of the surfactant in the organoclays interlayers. Infrared spectroscopy was employed to probe the intercalation of the cationic surfactants and the sorbed bisphenol A. New characteristic bands attributed to the bisphenol A phenol rings appear in the range 1518–1613 cm⁻¹ on the infrared spectra of the spent organoclays, proving the presence of bisphenol A in the hydrophobic interlayers. Scanning electron microscopy of the organoclays before and after BPA sorption shows that their morphology becomes fluffy and that the presence of the organic molecules expands the clay structure.     

Front Cover: Critical Assessment of pH-Dependent Lipophilicity Profiles of Small Molecules: Which One Should We Use and In Which Cases? (ChemPhysChem 24/2023)

Lipophilicity is a physicochemical property with wide relevance in drug design, computational biology, food, environmental and medicinal chemistry. Lipophilicity is commonly expressed as the partition coefficient for neutral molecules, whereas for molecules with ionizable groups, the distribution coefficient (D) at a given pH is used. The logD_pH is usually predicted using a pH correction over the logP_N using the pK_a of ionizable molecules, while often ignoring the apparent ion pair partitioning . In this work, we studied the impact of on the prediction of both the experimental lipophilicity of small molecules and experimental lipophilicity-based applications and metrics such as lipophilic efficiency (LipE), distribution of spiked drugs in milk products, and pH-dependent partition of water contaminants in synthetic passive samples such as silicones. Our findings show that better predictions are obtained by considering the apparent ion pair partitioning. In this context, we developed machine learning algorithms to determine the cases that should be considered. The results indicate that small, rigid, and unsaturated molecules with logP_N close to zero, which present a significant proportion of ionic species in the aqueous phase, were better modeled using the apparent ion pair partitioning . Finally, our findings can serve as guidance to the scientific community working in early-stage drug design, food, and environmental chemistry.