Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

Influence of milk fat globule membrane and milk protein concentrate treated by ultrasound on the structural and emulsifying stability of mimicking human fat emulsions

The primary objective of the present study was to investigate the effectiveness of ultrasonic treatment time on the particle size, molecular weight, microstructure and solubility of milk fat globule membrane (rich in phospholipid, MPL) and milk protein concentrate (MPC). The mimicking human fat emulsions were prepared using modified proteins and compound vegetable oil and the structural, emulsifying properties and encapsulation efficiency of emulsions were evaluated. After ultrasonic treatment, the cavitation caused particle size decreased and structure change of both MPL and MPC, resulting in the enhancement of protein solubility. While, there was no significant change in molecular weight. Modified proteins by ultrasonic may cause a reduction in particle size and an improvement in emulsifying stability and encapsulation efficiency of emulsions. The optimal ultrasonic time to improve functional properties of MPL emulsion and MPC emulsion were 3 min and 6 min, respectively. The emulsifying stability of MPL emulsion was superior to MPC emulsion, which indicated that MPL is more suitable as membrane material to simulate human fat. Therefore, the obtained results can provide basis for quality control of infant formula.     

Comparison of oil-in-water emulsions prepared by ultrasound,high-pressure homogenization and high-speed homogenization

This study was designed to compare the properties of myofibrillar protein (MP) stabilized soybean oil-in-water emulsions fabricated by ultrasound-assisted emulsification (UAE), high-pressure homogenization (HPH) and high-speed homogenization (HSH). The emulsion properties, droplet characteristics, interfacial proteins, protein exposure extent, microrheological properties, multiple light scattering results, and 7 d storage stabilities of the three emulsions were specifically investigated. Our results indicate that UAE and HPH were better emulsification methods than HSH to obtain high-quality emulsions with higher emulsifying activity index (UAE 20.73 m²·g⁻¹, HPH 11.76 m²·g⁻¹ and HSH 6.80 m²·g⁻¹), whiteness (UAE 81.05, HPH 80.67 and HSH 74.09), viscosity coefficient (UAE 0.44 Pa·sⁿ, HPH 0.49 Pa·sⁿ and HSH 0.22 Pa·sⁿ), macroscopic viscosity index (UAE 2.31 nm⁻²·s, HPH 0.38 nm⁻²·s and HSH 0.34 nm⁻²·s), and storage stability, especially for the UAE. Furthermore, UAE was a more efficient emulsification method than HPH to prepare the fine MP-soybean oil emulsion. The protein-coated oil droplets were observed in the three emulsions. The emulsion droplet size of the UAE-fabricated emulsion was the lowest (0.15 μm) while the interfacial protein concentration (93.37%) and the protein exposure extent were the highest among the three emulsions. During the 7 d storage, no separation was observed for the UAE-fabricated emulsion, while the emulsions fabricated by HPH and HSH were separated after storage for 5 d and 2 h. Therefore, this work suggests that UAE could be a better method than HPH and HSH to fabricate MP-soybean oil emulsion.     

Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations

Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the m iterations on a coarse grid and correction once on a fine grid. A one-level Oseen iterative method on a fine mesh is further studied under a weak uniqueness condition. Moreover, the stability and error estimate are rigorously carried out, which prove that the proposed methods are stable and effective. Finally, some numerical examples corroborate the effectiveness of our theoretical analysis and the proposed methods.     

Synergic effects of ultrasound and ionic liquids on fluconazole emulsion

The aim of this work was to evaluate the influence of US on the properties of the fluconazole emulsions prepared using imidazolium-based ILs ([C_n C₁im]Br). The effects of the preparation method (mechanical stirring or US), US amplitude, alkyl chain length (of [C₁₂C₁im]Br or [C₁₆C₁im]Br), and IL concentration on the physicochemical properties were evaluated. Properties such as droplet size, span index, morphology, viscosity encapsulation efficiency, and drug release profile were determined. The results showed that US-prepared emulsions had a smaller droplet size and smaller polydispersity (Span) than those prepared by mechanical stirring. Additionally, the results showed that emulsions prepared with [C₁₆C₁im]Br and US had spherical shapes and increased stability compared to emulsions prepared by MS, and also depended on the IL concentration. The emulsion prepared by US at 40% amplitude had increased encapsulation efficiency. US provided a decrease in the viscosity of emulsions containing [C₁₂C₁im]Br; however, in general, all emulsions had viscosity close to that of water. Emulsions containing [C₁₆C₁im]Br had the lowest viscosities of all the emulsions. The emulsions containing the IL [C₁₆C₁im]Br had more controlled release and a lower cumulative percentage of drug release. The IL concentration required to prepare these emulsions was lower than the amount of conventional surfactant required, which highlights the potential synergic effects of ILs and US in preparing emulsions of hydrophobic drugs.     

Study on the emulsification and oxidative stability of ovalbumin-pectin-pumpkin seed oil emulsions using ovalbumin solution prepared by ultrasound

Pumpkin seed oil (PSO), which is a valuable compound with high nutritional value used for the prevention of various chronic diseases, is prone to oxidation. In this work, small and uniform (su) ovalbumin (OVA) and pectin (PEC) were used to stabilize PSO in the form of an emulsion. The results showed that suOVA-PEC-PSO emulsion with a droplet size of 9.82 ± 0.05 μm was successfully self-assembled from PSO, PEC, and suOVA solution (with a droplet size of 230.13 ± 14.10 nm) treated with 300 W ultrasound, owing to the formation of a more stable interfacial film on the surface of droplets. The interfacial, rheological, emulsifying, and antioxidant properties of the suOVA-PES-PSO emulsions were excellent, owing to the synergistic effects between PEC and suOVA solution. Moreover, the physical stability of the suOVA-PEC-PSO emulsions to salt stress, a freeze-thaw cycle, and heat treatment was also increased and the oxidation of linolenic acid was notably delayed. These results have extended the food-related applications of OVA and PSO, and provide a promising foundation for further exploration of the self-assembly of composite emulsions by small and uniform proteins.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

A Bootstrap Framework for Aggregating within and between Feature Selection Methods

In the past decade, big data has become increasingly prevalent in a large number of applications. As a result, datasets suffering from noise and redundancy issues have necessitated the use of feature selection across multiple domains. However, a common concern in feature selection is that different approaches can give very different results when applied to similar datasets. Aggregating the results of different selection methods helps to resolve this concern and control the diversity of selected feature subsets. In this work, we implemented a general framework for the ensemble of multiple feature selection methods. Based on diversified datasets generated from the original set of observations, we aggregated the importance scores generated by multiple feature selection techniques using two methods: the Within Aggregation Method (WAM), which refers to aggregating importance scores within a single feature selection; and the Between Aggregation Method (BAM), which refers to aggregating importance scores between multiple feature selection methods. We applied the proposed framework on 13 real datasets with diverse performances and characteristics. The experimental evaluation showed that WAM provides an effective tool for determining the best feature selection method for a given dataset. WAM has also shown greater stability than BAM in terms of identifying important features. The computational demands of the two methods appeared to be comparable. The results of this work suggest that by applying both WAM and BAM, practitioners can gain a deeper understanding of the feature selection process.