Mathematical analysis of a model for a plant-herbivore system

The apple twig borer (Amphicerus bicaudatus) is an insect pest of the grape vine, causing considerable damage to the grape vine in early spring. A simple difference equation model is formulated and analysed for this plant-herbivore system based on two control strategies, cane removal and pesticide application. The system has two equilibria, one where the pest is present and one where the pest is absent. Regions are found in parameter space for global stability of the equilibria and in the absence of global stability it is shown that there exist periodic or quasiperiodic solutions.     

Mathematical model for adaptive evolution of populations based on a complex domain

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function.     

Mathematical elucidation of the Kaufmann effect based on the thermodynamic SSI model

The development rate of insects at hourly fluctuating temperatures is not infrequently different from that at constant temperatures even when the averages of these temperatures are the same. This temperature-dependent development phenomenon has been known as the Kaufmann effect. However, its theoretical analysis has not yet been successfully carried out owing to the insufficiency of mathematical insight especially into quantitative expressions. In insect development, the interrelationships among the three environmental temperatures, namely, the constant and alternating temperatures controlled in the laboratory and the hourly fluctuating temperatures in the natural environment, have not been clarified. Here, we completely succeeded in analyzing this phenomenon and in elucidating the interrelationships by introducing the components of the nonlinear SSI development model, the second derivative, the cosine-wave model of hourly fluctuating temperatures and their variance, and Taylor series. As a result, it has been possible to predict the development rate at fluctuating temperatures in the natural environment using prospective daily maximum, minimum and average temperatures and the development rate at constant temperatures without conducting experiments at alternating temperatures.     

A model for renal arterial branching based on graph theory

The kidney is one of the most complicated organs in terms of structure and physiology, in part because it is highly vascularized. The renal vascular development occurs through two mechanisms that sometimes overlap: vasculogenesis and angiogenesis. Here, we consider angiogenesis to model the renal arterial tree with the two processes of vascular angiogenesis: sprouting and splitting. We recognize the vessels are not tubes with ends that get glued but physiological factors are relevant into the vascular development. Our contribution integrates the graph theory and physiological information to derive a quantitative model for the vascular tree in the sense that the vertices and edges represent, respectively, a branching point and a vessel. From such a premise, development of the arterial vascular tree of the kidney is mathematically expressed, including physiological processes as the effect of the vascular endothelial growth factor (VEGF) on the vessel length. A definition of the graph is used to visualize the topology of vascular tree in kidney providing physiological information into the edges. Thus, renal arterial branching is modeled as a graph where edges are labeled and oriented.     

Development and use of a Mathematical model for an antarctic Lake

We describe the development and use of the first mathematical computer model for a polar lake. This dynamic model graphically illustrates seasonal and annual predictions of the changes in the biomass of plankton and attached primary producers, decomposers and consumers, changes in the quantities of potential nutrients and organic matter. The model consists of 100 submodels of which 79 are algebraic equations and 21 are differential equations. It has proven valuable as a means of identifying voids in our limnological program and probable errors in field measurements.Department of StatisticsDepartment of Biology     

Unsteady beam-plasma discharge: I. Mathematical model and linear theory

A mathematical model is constructed that describes the development of the beam-plasma instability in a traveling-wave tube amplifier in the presence of a neutral gas. Steady solutions are derived for conditions of microwave discharges in a magnetized plasma-filled traveling-wave tube amplifier, and their stability is investigated. It is shown that the steady-state amplification regime may become unstable and change to the self-modulation regime. The relationships between the amplifier parameters at the instability threshold are obtained, and the frequencies of the excited ion acoustic waves are determined. The results of numerical modeling are found to agree well with the analytical results.     

Minimal model for representing the central and peripheral pulse based on the pulse wave theory]

The present paper discusses an optimized model for describing central and peripheral pulse waves. On the basis of these computer-aided calculations, further haemodynamic data may be evaluated with the aim of improving the possibilities of clinically invasive diagnostic evaluation of cardiovascular diseases.     

New detection system for toxic agents based on continuous spectroscopic monitoring of living cells

In this study, we show the feasibility of a new type of cell based biosensor which uses spectroscopic in situ real time detection of biochemical changes in living cells exposed to toxic chemical agents. We used a high power 785 nm laser to measure the time dependent changes in the Raman spectrum of individual living human lung cells (A549 cell line) treated with a toxic agent (Triton X-100, 250 microM solution). Individual cells were monitored by Raman spectroscopy over a total time span of 420 min, with 30 min sampling intervals. During this period of time, the A549 cells were maintained in a purpose designed temperature controlled cell chamber, which allowed the cells to be maintained in physiological conditions. The time dependent changes in the Raman spectra were correlated with the sequences of events that occur during cell death. The molecular mechanisms involved in cell death are indicated by the decrease in the magnitude of Raman peaks corresponding to proteins (1322, 1342 and 1005 cm(-1)) and DNA (decrease by 80-90% in the 786 cm(-1) phosphodiester bonds C'5-O-P-O-C'3). To support these conclusions, viability tests and Western blotting analysis of PARP protein were carried out. This technique could overcome the limitations of other detection systems available, since the specific time dependent biochemical changes in the living cells can be used for the identification and quantification of a large range of toxic agents. This technique could also be used with cellular microarrays for high throughput in vitro toxicological testing of pharmaceuticals and in situ monitoring of the growth of engineered tissues.     

A theory for the membrane potential of living cells

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps. We demonstrate that the work done by the pumps equals the change in potential energy of the cell, plus the energy lost in downhill ionic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The model predicts the experimentally observed intracellular ionic concentration of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with experiment. We do not see any drift in the values of the concentrations in a long time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellular ionic concentrations. Received: 9 December 1998 / Revised version: 30 August 1999 / Accepted: 15 October 1999     

Domestication as a model system for niche construction theory

Niche Construction Theory (NCT) provides a powerful conceptual framework for understanding how and why humans and target species entered into domesticatory relationships that have transformed Earth’s biota, landforms, and atmosphere, and shaped the trajectory of human cultural development. NCT provides fresh perspective on how niche-constructing behaviors of humans and plants and animals promote co-evolutionary interactions that alter selection pressures and foster genetic responses in domesticates. It illuminates the role of niche-altering activities in bequeathing an ecological inheritance that perpetuates the co-evolutionary relationships leading to domestication, especially as it pertains to traditional ecological knowledge and the transmission of learned behaviors aimed at enhancing returns from local environments. NCT also provides insights into the contexts and mechanisms that promote cooperative interactions in both humans and target species needed to sustain niche-constructing activities, ensuring that these activities produce an ecological inheritance in which domesticates play an increasing role. A NCT perspective contributes to on-going debates in the social sciences over explanatory frameworks for domestication, in particular as they pertain to issues of reciprocal causation, co-evolution, and the role of human intentionality. Reciprocally, domestication provides a model system for evaluating on-going debates in evolutionary biology concerning the impact of niche construction, phenotypic plasticity, extra-genetic inheritance, and developmental bias in shaping the direction and tempo of evolutionary change.     

Biostructural theory of the living systems

Eugen Macovschi is among the few scientists who tried, and partly succeeded, to explain the differences between "dead" and "living" in biological sciences. He discovered and characterized the so-called biostructure of the living bodies and worked out a biostructural theory, which is the first supramolecular conception in biology. Nevertheless, complex biological systems are currently considered only from the molecular point of view, although they may be regarded as specific phenomena on highly structured bodies within the four-dimensional Universe. According to Macovschi, the biostructure provides organisms with life properties and controls their life processes and chemical changes. Nevertheless, plant cells or bacterial ones differ much from the animal or human cells. In fact, there are various biostructures which are related with cell properties. Hence, this theory creates confusions and cannot be easily used to explain all the properties of the biosystems. Consequently, it is our goal to highlight the principles, advantages, limitations, and applications of the biostructural theory, which might support new ideas and theories in modern life sciences.     

A planning framework based on system theory and GIS for urban emergency shelter system: A case of Guangzhou,China

The urban emergency shelter is of great significance to disaster prevention and mitigation. In China, the demand is enormous for emergency shelters while their construction generally lags behind the economic and social development, which has resulted in heavy casualties and economic losses. This article considers emergency shelters as a complete system from systemic perspective and also proposes a planning framework for emergency shelter system, including the function, hierarchy, type, scale, layout, standard, and supporting-service system of the shelters. Then, an empirical study applying the framework in GIS platform in the urban emergency shelter planning of Guangzhou city was conducted and highly valued by local experts and citizens as a feasible scheme to guide the construction of emergency shelters, indicating that the framework is an appropriate tool for urban emergency shelter planning.     

Performance of an automated system for capillary microinjection into living cells

An automated capillary microinjection system for nuclear and cytoplasmic injections into cells is described. The system has been tested with samples of DNA, RNA and proteins. Movements of the capillary with precise cell positioning and time of injections are controlled by a computer. This first automated microinjection system allows injection of more than 1500 cells per hour with a minimum of practical training, volumes injected are more reproducible and cells are less damaged when compared with the standard manual injection technique. Retrieval of the injected cells is accurate to within 1% without complicated and laborious produced orientation marks on the cell support. The number of successfully injected cells is easily determined with great accuracy and the error of the statistical evaluation of the results is reduced to a minimum. Standardized procedures for pulling, handling and storage of the injection capillaries were developed.