Projects for Students
Note: My concrete research hypotheses and results are available in the Research and Publications section. This section is for students who are interested to find research projects.
I am working on diverse problems (see details of past and present projects in the CV and Research sections). Below, I have listed projects that interest me and that I would like to recruit students to work with me on. I might also be willing to help students who have their own projects. Some of my projects would benefit from collaborating with a postdoc researcher. Currently, I have no salary for a postdoc researcher, but in case of serious interest I am willing to submit proposals to cover the expenses. Master students are welcome to join my lab. In our Department there is a very good chance to receive a Graduate Assistantship (see details at http://www.etsu.edu/gradstud/gasch.htm). We also have a good system to support undergraduate research, and we are developing interesting undergraduate research cooperation with the Dept. of Mathematics and Statistics and the Dept. of Computer and Information Sciences. Please read the project descriptions and the suggestions at the end about the kind of students I think would feel comfortable with the project.
 Nonlinear processes and emergent biological systems
A lot of biological systems have emergent properties. The property is called emergent when we cannot derive the property from the unit itself. The unit needs interactions (like cooperation) to produce something “unexpected” in the higher level of organization. The life of social insects is one of the best tractable systems to the study selforganized systems. They have simple individuals with simple behavioral rules, but there are interactions among the individuals which lead to massive emergent properties. Examples are: bridge building of ants, exploratory patterns, bee swarms, and other highly organized spontaneous colony level patterns. Division of labor may also emerge in the same way. This means not all individuals do the same thing (although they can if they must), but they specialize. There are several ideas regarding how this occurs. We are developing a model system, which uses simple positive and negative feedbacks and is based on the principles of selforganization. The colony needs to allocate its worker force to cope with a series of tasks and also keep the system resilient to perturbations. Nonlinear differential equations will be used to describe the system. Experiments and published data will be used for parameter estimation. Our goal is to produce a model based on biological data that is mathematically tractable. We expect that our model will accurately predict natural patterns and that we can suggest new experiments for biologists based on the model predictions. This is for postdoc researchers and for graduate students.
 Agentbased modeling of insect societies
Over the last 10 years insect societies have become a model system to study and understand the way complex systems are functioning. Algorithms discovered in ant societies, for example, are used by artificial intelligence software to govern robots, to search on the Internet, to build up encyclopedias, and so on. Artificial life has also gained a lot from biological results. Hollywood, for example, uses the rule of swarming and other phenomenon in films where they need to move a large number of objects on the screen.
The key approach is agentbased modeling, where the society consists of many agents where each agent has only local perceptions and operates by simple rules. The state of a given agent at a given time is determined by its nearest neighbors’ states in the previous time step, by their interactions, and other variables. The agent can be a single insect or a group of insects that perform a specific task. The agents are interacting directly or indirectly (like through work) and they can solve colony level (a higher organizational level) problems. How is this possible? This is an interesting and important question. How can simple agents with simple rules solve complex tasks? This is an everyday question in insect societies. We will focus on some questions related to division of labor and nest construction. We will build models based on biological observations and experiments. We will use these models to predict patterns and then compare these predictions to the level of performance of insect societies. This project is suitable for postdoc researcher and for graduate students.
 Insect robots: Problemsolving algorithms both in silico and in physical environment
Today, for less than $200, you can buy a programmable board, motors and sensors, and, using Lego elements, you can build autonomous robots that can learn, explore and do a lot of things. You have a robot with a small set of rules, and it should solve a real life problem (for example escape from a labyrinth, cover a distance, explore an area, and collect objects and so on). We can measure these and study the efficiency of different rules (what we explicitly program into the robot). However, we cannot predict the efficiency from the rule itself because of the constraints of the environment. We also can compare these to the performance of real creatures like mice, frogs, and beetles. It is also easy to build simulations for this problem and compare model predictions to robot solutions. Models, for example, commonly neglect real problems like body size, or special technical issues, like radius of perception and the effect of environmental irregularities. It is a fun project with lot of potential; for MS degree, but it might be for serious undergraduate research.
 Insect community ecology
I started my work as community insect ecologist. This work involves questions like: How are insects are distributed along a gradient? How are they distributed along the season? How do they detect patchy environments? How do their patterns match to another pattern (like to plant coverage)? How does community A (like ants) affect the distribution of community B (like spiders)? A lot of interesting questions can be asked. After formulating the question you will plan a sample technique. You sample the insects and you have a large number of creatures (dead, generally, in a jar) in no time. Biologists determine the insects in a meaningful level like guild, family or species. The number of data can be very large. You have to evaluate the data using statistics and simple indices like Shannon, Wiener, and similarity ratios. Using multivariate analyses are also very useful. After the analyses you have to interpret the results biologically. For an extra challenge the student can generate simulations. For example, using the same number of data we can generate artificial insect communities in the computer and we can sample these. We can use these in silico ecology as nullmodels to interpret real data better. This project is for MS degree and undergraduate research. We also will try to recruit a math student to work with the biology student as a pair.
 Growing shapes by addition of modular units
lot of diversity we observe in nature stems from very simple processes, which use very simple and identical units. Snowflakes are each different, but they are built up by consecutive addition of tiny similar ice particles. Structures built by biological organisms commonly show similar characteristics. For example, different islands are built by very small coral polyps. Elaborated wasp nests are built up by wasps arranging similar hexagonal paper cells. Adding the same unit to an already existing structure can result in surprisingly diverse solutions. Geometrical constraints and simple additional rules may result in surprisingly regular and esthetic solutions (see Karsai, 1999).
Consider n square (or triangular, or hexagonal) cells that attach sequentially to each other in a “random fashion”, i.e., with each possible position being occupied at each stage with equal probability. We then get a variant of what combinatorialists call “random lattice animals”, with extensions to higher dimensions being quite natural. Even counting the possible number of animals is an open problem. Among the results already obtained are connections between random animal growth and graph theory (chromatic number, domination number, diameter); upper and lower bounds on the number of animals; and recurrence relations. In this interdisciplinary project I am cooperating with mathematicians and computer scientists. This project is suitable for postdoc researcher and for graduate students. We want to address the following questions:
 What is the shape distribution of random lattice animals?
 How does the shape depend on the geometry of the unit?
 How can biological facts on social behavior be incorporated gradually into mathematical models?
 How will changing the local constraints in the system affect to the global result?
 Chaos and order in patterns
There are many natural patterns that change in time. For example, in animals, the daily activity patterns, whether diurnal or nocturnal, appear to be very ordered phenomena. Creatures start their activity at a given time of a day, go through their routines, and then they retire. Although these patterns seem trivial and natural, they are far from simple. An internal clock, with many properties very different from a mechanistic clock, governs the daily rhythm of a living creature. The biological clock is affected by both internal physiological states and external influences, such as light/dark cycles, temperature cycles, and social or individual interactions. These influences can be reflected in the overt activity patterns, which can be reflected in the overt activity and can be very complex. Other patterns are governed by other mechanisms, but it seems that there is an underlying common theme of these rhythmic behaviors.
In general, these activity patterns have chaotic as well as ordered elements and properties. It is therefore appropriate to analyze these real time series data for system attractors and also to describe the system using Lyaponov exponents, entropy, BDS statistics, and so on. After establishing a basic description of the 'normal' system, we will compare the results to artificial systems generated using randomization, white noise, or very ordered systems such as a sine wave function. By varying the number of variables of the given system, we can investigate how these variables are influencing the given system. For example, whether the individual activities are temporally coupled under different conditions of density and, if so, how strongly. This project is suitable for graduate and undergraduate students who are interested in complexity research.

Computational or quantitative biology projects
I am willing to help to any student who has their own idea and research interest in the field of computational and quantitative biology, if I am able to promote the study into a meaningful publishable project. This project is suitable for graduate and undergraduate students and also for postdoc researchers.