Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems

Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of each agent can be defined as either (1) those agents whose opinions are in its "confidence range," or (2) those agents whose "influence range" contain the agent's opinion. The former definition is employed in Hegselmann and Krause's bounded confidence model, and the latter is novel here. As the confidence and influence ranges are distinct for each agent, the heterogeneous state-dependent interconnection topology leads to a poorly-understood complex dynamic behavior. In both models, we classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. Then, we define a positive invariant set centered at each equilibrium opinion vector. We show that if a trajectory enters one such set, then it converges to a steady state with constant interconnection topology. This result gives us a novel sufficient condition for both models to establish convergence, and is consistent with our conjecture that all trajectories of the bounded confidence and influence models eventually converge to a steady state under fixed topology.Comment: 22 pages, Submitted to SIAM Journal on Control and Optimization (SICON

The use of scaffolding-based software in developing pronunciation

This research looked at the use of a scaffolding-based software in helping learners to develop pronunciation and fluency modelled on standard American English. The study used Vygotsky’s zone of proximal development (ZPD) theory and Scaffolding Learning. Principles as a basis for observing how learners of English progressed through the learning process. Firstly, the research examined an accent-reduction software to find out how the software design supports scaffolding principles. To determine the effectiveness of the software on learners’ general pronunciation, pre-test and post-test were used. The data obtained from the pre-test and the post-test showed a significant improvement in learners’ general pronunciation after using the pronunciation learning software.Secondly, case studies were conducted to investigate Persian ESL learners’ progress in pronouncing English consonants that are absent from the phonemic inventory of Persian. The selected cases were recorded during class time, while they were working with the software. The obtained recordings were then analysed using PRAAT, a speech analysis programme. Later, two raters helped the researcher to determine the quality of the sounds produced by the learners. The results from the case study showed that with the appropriate scaffolds provided by the software, in the form of explicit instruction, native models and multimodal feedback, the learners were found to have the microgenesis improvements towards the native model and progressed within the ZPD to pronounce the consonants that were absent from the inventory system of their first language. Finally, learners’ perceptions of the software were asked in an interview session after the instructional programme. Based on their responses to the interview questions, it was found that the learners positively perceived the use of the scaffolding-based accent reduction software to improve their general pronunciation

Use Of Cryoprotectants In Enhancing Viability Of Probiotic Lactobacillus Strains During Freeze-Drying And Storage

In recent years, probiotics have been considered to be used as feed supplements to improve the health and growth performance of poultry in place of antibiotic growth promoters. This is due to concerns that the rampant use of antibiotic growth promoters in livestock, particularly poultry, may produce adverse effects on humans, such as the development of antibiotic resistant bacteria and production of antibiotic residues in animal products. Unlike probiotics for humans, which are usually kept refrigerated, probiotics for poultry are normally kept in the farm at room temperature, and this may reduce the viability of the micro-organisms used in the probiotics during storage. Cryoprotectants incorporated during freeze drying of the probiotic could enhance the shelf-life of the probiotic micro-organisms. Thus, in this investigation, the main objective was to determine the best combination of cryoprotectants to enhance the viability of Lactobacillus brevis I25 and L. reuteri C10 during freeze-drying by using the response surface methodology (RSM). A five-level, three-variable central composite rotatable design (CCRD) was used to evaluate the interactive effects of skim milk, sucrose and lactose as cryoprotectants, on the viability of L. brevis I25 and L. reuteri C10 during freeze drying. The inputs, log cfu/ml, were derived experimentally and tested by RSM. The models were found to describe adequately the experimental range studied. The optimum combination of cryoprotectants derived via RSM analysis were: 8% skim milk, 22% sucrose, 0.5% lactose for L. brevis I25 and 19.5% skim milk, 1% sucrose, 9% lactose for L. reuteri C10. The actual experimental results on the viability of L. brevis I25 and L. reuteri C10 after freeze-drying were 8.88 and 8.83 log cfu/ml, respectively, under optimum formulation. These values were highly comparable to the predicted values by RSM method of SAS/STAT which were 8.82 log cfu/ml for L. brevis I25 and 8.89 log cfu/ml for L. reuteri C10. The log cfu/ml values for controls (freeze-dried without cryoprotectants) were 7.65 and 7.2 for L. brevis I25 and L. reuteri C10, respectively. During the six month storage study at 4oC and 30oC, the optimum cryoprotectant combination for L. brevis I25 had a very high survival rate at 4oC but not at 30oC. On the other hand, the survival rate of the best combination for L. reuteri C10 was very high at both temperatures during storage. There was 0% residual viability for control culture after 16 weeks of storage for L. brevis I25 at 4oC and after 4 weeks at 30oC. For L. reuteri C10 after 12 and 8 weeks no bacterial growth were detected at 4oC and 30oC, respectively. The organic acids and amylase activity of bacterial cultures were also analysed during storage. The results showed that during storage at 4oC, the acetic acid concentration decreased from 144 mM to 100.25 mM for L. brevis I25 and from 153 mM to 115.6 mM for L. reuteri C10. In the case of lactic acid, the concentration decreased from 294 mM to 215 mM for L. brevis I25 and 205 mM to 124 mM for L. reuteri C10. The concentration of succinic acid also decreased from 2.9 mM to 1.2 mM for L. brevis I25 and from 17 mM to 9.4 mM for L. reuteri C10. There was also a reduction in amylase activity from 0.2 U to 0.11 U for L. brevis I25 and from 0.34 U to 0.18 U for L. reuteri C10. Acid production and amylase activity patterns for both Lactobacillus strains correspond to the survival rate of the bacteria during storage at 30oC

Secretions of Human Salivary Gland

The salivary glands play an important role in our body by the virtue of its ability to secrete saliva. Saliva has a role to play in maintaining the health of the oral cavity and for carrying out physiological functions like mastication, taste perception, speech etc. It also acts as a mirror to the systemic status of an individual owing to its ability to act as a diagnostic fluid for detecting a number of conditions and diseases. Saliva is a potential noninvasive diagnostic fluid for detection of a number of biomarkers of disease and health. Advancement in diagnostic methods has helped in identifying biomarkers of disease in saliva. In order to understand and diagnose pathological changes, a thorough understanding of the salivary gland anatomy, physiology and regulation of its secretion is warranted. This chapter aims to provide the basic understanding of the secretions of saliva