Oxygen transport in soil and the vertical distribution of roots

An analytical solution for steady-state oxygen transport in soils including 2 sink terms, viz roots and microbes with the corresponding vertical distribution scaling lengths forming a ratio p, showed p governed the critical air-filled porosity, θ_c, needed by most plants. For low temperature and p, θ_c was <0.1 but at higher temperatures and p = 1, θ_c was >0.15 m³/m³. When root length density at the surface was 10⁴ m/m³ and p > 3, θ_c was 0.25 m³/m³, more than half the pore space. Few combinations of soil and climate regularly meet this condition. However, for sandy soils and seasonally warm, arid regions, the theory is consistent with observation, in that plants may have some deep roots. Critical θ_c values are used to formulate theoretical solutions in a forward mode, so different levels of oxygen uptake by roots may be compared to microbial activity. The proportion of respiration by plant roots increases rapidly with p up to p ≈2.

Transport of IgG across the blood-luminal barrier of the male reproductive tract of the rat and the effect of estradiol administration on reabsorption of fluid and IgG by the epididymal ducts

In rats immunized systemically with tetanus toxoid the concentration of specific anti-tetanus-toxoid-specific IgG in fluid from the rete testis and cauda epididymidis were respectively 0.6% and 1.4% the concentration in blood serum. The extratesticular duct system reabsorbed 97% of the IgG and 99% of the fluid leaving the rete, but estradiol administration affected the site of reabsorption. In untreated rats, the ductuli efferentes reabsorbed 94% of the IgG and 96% of the fluid leaving the rete, whereas estradiol-treated rats reabsorbed 83% of the IgG and 86% of the fluid, and the ductus epididymidis fully compensated for these different effects of estradiol on the ductuli efferentes. The concentrations of IgG in secretions of the seminal vesicles and prostate gland were lower (0.1% and 0.3% respectively of the titers in blood serum) than in fluids from the extratesticular ducts, and were not affected by the administration of estradiol. RT-PCR showed that Fcgrt (neonatal Fc receptor, also known as FcRn) is expressed in the reproductive ducts, where IgG is probably transported across epithelium, being particularly strong in the ductuli efferentes (where most IgG was reabsorbed) and distal caput epididymidis. It is concluded that IgG enters the rete testis and is concentrated only 2.5-fold along the extratesticular duct system, unlike spermatozoa, which are concentrated 95-fold. Further, the ductus epididymidis can recognize and compensate for changes in function of the ductuli efferentes.

A transport protocol for real-time applications in wireless networked control systems

A Networked Control System (NCS) is a feedback-driven control system wherein the control loops are closed through a real-time network. Control and feedback signals in an NCS are exchanged among the system’s components in the form of information packets via the network. Nowadays, wireless technologies such as IEEE802.11 are being introduced to modern NCSs as they offer better scalability, larger bandwidth and lower costs. However, this type of network is not designed for NCSs because it introduces a large amount of dropped data, and unpredictable and long transmission latencies due to the characteristics of wireless channels, which are not acceptable for real-time control systems. Real-time control is a class of time-critical application which requires lossless data transmission, small and deterministic delays and jitter. For a real-time control system, network-introduced problems may degrade the system’s performance significantly or even cause system instability. It is therefore important to develop solutions to satisfy real-time requirements in terms of delays, jitter and data losses, and guarantee high levels of performance for time-critical communications in Wireless Networked Control Systems (WNCSs). To improve or even guarantee real-time performance in wireless control systems, this thesis presents several network layout strategies and a new transport layer protocol. Firstly, real-time performances in regard to data transmission delays and reliability of IEEE 802.11b-based UDP/IP NCSs are evaluated through simulations. After analysis of the simulation results, some network layout strategies are presented to achieve relatively small and deterministic network-introduced latencies and reduce data loss rates. These are effective in providing better network performance without performance degradation of other services. After the investigation into the layout strategies, the thesis presents a new transport protocol which is more effcient than UDP and TCP for guaranteeing reliable and time-critical communications in WNCSs. From the networking perspective, introducing appropriate communication schemes, modifying existing network protocols and devising new protocols, have been the most effective and popular ways to improve or even guarantee real-time performance to a certain extent. Most previously proposed schemes and protocols were designed for real-time multimedia communication and they are not suitable for real-time control systems. Therefore, devising a new network protocol that is able to satisfy real-time requirements in WNCSs is the main objective of this research project. The Conditional Retransmission Enabled Transport Protocol (CRETP) is a new network protocol presented in this thesis. Retransmitting unacknowledged data packets is effective in compensating for data losses. However, every data packet in realtime control systems has a deadline and data is assumed invalid or even harmful when its deadline expires. CRETP performs data retransmission only in the case that data is still valid, which guarantees data timeliness and saves memory and network resources. A trade-off between delivery reliability, transmission latency and network resources can be achieved by the conditional retransmission mechanism. Evaluation of protocol performance was conducted through extensive simulations. Comparative studies between CRETP, UDP and TCP were also performed. These results showed that CRETP significantly: 1). improved reliability of communication, 2). guaranteed validity of received data, 3). reduced transmission latency to an acceptable value, and 4). made delays relatively deterministic and predictable. Furthermore, CRETP achieved the best overall performance in comparative studies which makes it the most suitable transport protocol among the three for real-time communications in a WNCS.

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.