Projects for Students
I am working on diverse problems (see for details of past and present projects in the CV and Research interest section). Below I have listed projects that interest me and I would like to recruit students to work with me on these projects. I also might 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 Math. Please read the project descriptions and suggestions at the end about the kind of students I think would feel comfortable with the project.
- Nonlinear differential equations and emergent biological properties
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 study self-organized systems. They have simple individuals with simple behavioral rules, but there is an interaction among the individuals and this leads 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 how this goes on. We are developing a model system, which uses simple positive feedbacks and is based on the principles of self-organization. The colony needs to allocate its worker force to cope with a series of tasks and also to 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 predict well the natural patterns and we can suggest new experiments for biologists based on the model predictions. This is for postdoc researchers and those with an MS degree.
- Agent-based modeling of insect societies
Over the last 10 years insect societies have became 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 net, to build up encyclopedias, and so on. Artificial life also gained a lot from the 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 research team, Istvan Karsai (theoretical biologist) and Abdul Jarrah (mathematician), propose to study basic science on the life of insect societies. The key approach is agent-based modeling. In this cellular automata like approach, the society consists of many agents where each agent has a local rule that changes its state. The state of a given agent at a given time is determined by its nearest neighbors’ states in the previous time step. 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 organization 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. For postdoc researcher and MS degree.
- Insect robots: Problem-solving 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 insects are distributed along a gradient. How are they distributed along the season? How do they detect patchy environment? How do their patterns match to another pattern (like to the plant coverage)? How community A (like ants) affect to the distribution of community B (like spiders)? A lot of interesting questions can be asked. After formulating the question you plan a sample technique. You sample the insects and you have a large number of creatures (dead generally in a jar) within 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 very useful, as well. 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 null-models 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
A 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 little very similar coral polyps and elaborated wasp nests are built up by 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, with work of Zeilberger representing the most serious attempt towards a solution. However, the somewhat different animals we consider lend themselves to analysis using a variety of tools such as generating function methodology; isoperimetric methods; and polyomino theory. 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 project a theoretical biologist (Istvan Karsai) and mathematician (Anant Godbole) will cooperate with students (MS degree) 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 activity patterns
This is a common project with Karl Joplin and Darrell Moore. If you are interested in the experiment talk with them, if you are interested in the analysis talk to me.
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.
Because we do not yet know exactly how the biological clock operates, we have to use a black box method to investigate its characteristics. We can experimentally change the input (for example we can provide different light/dark cycles, induce stress such as temperatures or administer pharmacological agents) and we can measure how the activity pattern changes.
Our studies consist of continuous monitoring of the loco motor activity patterns of insects under controlled laboratory conditions. In this project, our first aim is to find a tractable way to describe and understand these activity patterns. Our preliminary studies show that 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. One interesting line of research using this approach has been to compare the loco motor activity patterns of bees, which are highly social organisms, and flies, which have a solitary lifestyle. By varying the number of insects of the same species within an experimental enclosure (individual and social interactions), we can investigate whether the individual activities are temporally coupled under different conditions of density and, if so, how strongly. Initial observations suggest that social insects exhibit strong synchronization and drive the activity pattern into a more ordered state, while non-social insects affect each other in a less coupled way and generate a more chaotic activity pattern. For MS degree and undergraduate research.