Search results for: H. Brouwer

Authors: Philippe Bich, Yu Lu

Abstract:

We provide n-dimensional fixed-point theorems for possibly discontinuous functions which extend Brouwer’s fixed-point theorem and encompass interesting cases of Tarski’s fixed-point theorem. The main idea is to require that at any discontinuity point where the graph of the function “crosses the diagonal”, the function satisfies a specific assumption (similar to upward jumps). For this purpose, we classify some types of discontinuities, and use them to prove our new fixed-point theorems, with some applications in game theory.

Keywords: fixed-point, Brouwer's fixed-point theorem, Tarski's fixed-point theorem, discontinuity, Nash equilibrium, supermodular game

Procedia PDF Downloads 3

Authors: Skezeer John B. Paz, Ederlina G. Nocon

Abstract:

Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

Procedia PDF Downloads 722

Authors: Bello Gonzalez, Setten Van M., Brouwer M.

Abstract:

The chicken small intestine represents a dynamic and complex organ in which the enzymatic digestion and absorption of nutrients take place. The development of an in vitro fermentation chicken small intestinal model could be used as an alternative to explore the interaction between the microbiota and nutrient metabolism and to enhance the efficacy of targeting interventions to improve animal health. In the present study we have developed an in vitro fermentation chicken ileum microbiota model for unrevealing the complex interaction of ileum microbial community under physiological conditions. A two-vessel continuous fermentation process simulating in real-time the physiological conditions of the ileum content (pH, temperature, microaerophilic/anoxic conditions, and peristaltic movements) has been standardized as a proof of concept. As inoculum, we use a pool of ileum microbial community obtained from chicken broilers at the age of day 14. The development and validation of the model provide insight into the initial characterization of the ileum microbial community and its dynamics over time-related to nutrient assimilation and fermentation. Samples can be collected at different time points and can be used to determine the microbial compositional structure, dynamics, and diversity over time. The results of studies using this in vitro model will serve as the foundation for the development of a whole small intestine in vitro fermentation chicken gastrointestinal model to complement our already established in vitro fermentation chicken caeca model. The insight gained from this model could provide us with some information about the nutritional strategies to restore and maintain chicken gut homeostasis. Moreover, the in vitro fermentation model will also allow us to study relationships between gut microbiota composition and its dynamics over time associated with nutrients, antimicrobial compounds, and disease modelling.

Keywords: broilers, in vitro model, ileum microbiota, fermentation

Procedia PDF Downloads 10

Authors: Bello Gonzalez T. D. J., Setten Van M., Essen Van A., Brouwer M., Veldman K. T.

Abstract:

Resistance to fluoroquinolones (FQ) has evolved increasingly over the years, posing a significant challenge for the treatment of human infections, particularly gastrointestinal tract infections caused by zoonotic bacteria transmitted through the food chain and environment. In broiler chickens, a relatively high proportion of FQ resistance has been observed in Escherichia coli indicator, Salmonella and Campylobacter isolates. We hypothesize that flumequine (Flu), used as a secondary choice for the treatment of poultry infections, could potentially be associated with a high proportion of FQ resistance. To evaluate this hypothesis, we used an in vitro fermentation chicken caeca model. Two continuous single-stage fermenters were used to simulate in real time the physiological conditions of the chicken caeca microbial content (temperature, pH, caecal content mixing, and anoxic environment). A pool of chicken caecal content containing FQ-resistant E. coli obtained from chickens at slaughter age was used as inoculum along with a spiked FQ-susceptible Campylobacter jejuni strain isolated from broilers. Flu was added to one of the fermenters (Flu-fermenter) every 24 hours for two days to evaluate the selection and maintenance of FQ resistance over time, while the other served as a control (C-Fermenter). The experiment duration was 5 days. Samples were collected at three different time points: before, during and after Flu administration. Serial dilutions were plated on Butzler culture media with and without Flu (8mg/L) and enrofloxacin (4mg/L) and on MacConkey culture media with and without Flu (4mg/L) and enrofloxacin (1mg/L) to determine the proportion of resistant strains over time. Positive cultures were identified by mass spectrometry and matrix-assisted laser desorption/ionization (MALDI). A subset of the obtained isolates were used for Whole Genome Sequencing analysis. Over time, E. coli exhibited positive growth in both fermenters, while C. jejuni growth was detected up to day 3. The proportion of Flu-resistant E. coli strains recovered remained consistent over time after antibiotic selective pressure, while in the C-fermenter, a decrease was observed at day 5; a similar pattern was observed in the enrofloxacin-resistant E. coli strains. This suggests that Flu might play a role in the selection and persistence of enrofloxacin resistance, compared to C-fermenter, where enrofloxacin-resistant E. coli strains appear at a later time. Furthermore, positive growth was detected from both fermenters only on Butzler plates without antibiotics. A subset of C. jejuni strains from the Flu-fermenter revealed that those strains were susceptible to ciprofloxacin (MIC < 0.12 μg/mL). A selection of E. coli strains from both fermenters revealed the presence of plasmid-mediated quinolone resistance (PMQR) (qnr-B19) in only one strain from the C-fermenter belonging to sequence type (ST) 48, and in all from Flu-fermenter belonged to ST189. Our results showed that Flu selective impact on PMQR-positive E. coli strains, while no effect was observed in C. jejuni. Maintenance of Flu-resistance was correlated with antibiotic selective pressure. Further studies into antibiotic resistance gene transfer among commensal and zoonotic bacteria in the chicken caeca content may help to elucidate the resistance spread mechanisms.

Keywords: fluoroquinolone-resistance, escherichia coli, campylobacter jejuni, in vitro model

Procedia PDF Downloads 28