John Konvalina

Emergent decision-making in biological signal transduction networks

The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow simulation and dynamical analysis. Exposing the network to tens of thousands of random combinations of inputs and analyzing the combined dynamics of multiple outputs revealed a robust system capable of clustering widely varying input combinations into equivalence classes of biologically relevant cellular responses. This capability was nontrivial in that the network performed sharp, nonfuzzy classifications even in the face of added noise, a hallmark of real-world decision-making.

The number and probability of canalizing functions

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems, it is informative to know the number of canalizing functions with a given number of input variables. This is also important in the context of using the class of canalizing functions as a constraint during the inference of genetic networks from gene expression data. To this end, we derive an exact formula for the number of canalizing Boolean functions of n variables. We also derive a formula for the probability that a random Boolean function is canalizing for any given bias p of taking the value 1. In addition, we consider the number and probability of Boolean functions that are canalizing for exactly k variables. Finally, we provide an algorithm for randomly generating canalizing functions with a given bias p and any number of variables, which is needed for Monte Carlo simulations of Boolean networks.

Boolean modeling of biochemical networks

The use of modeling to observe and analyze the mechanisms of complex biochemical network function is be- coming an important methodological tool in the systems biology era. Number of different approaches to model these net- works have been utilized-- they range from analysis of static connection graphs to dynamical models based on kinetic in- teraction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of detail is generally not known, dynamic modeling requires simplifying assumptions in order to make it practical. In this review Boolean modeling will be discussed, a modeling method that depends on the simplifying assumption that all elements of a network exist only in one of two states.

Factors Influencing Success in Beginning Computer Science Courses.

AbstractEight factors were studied to determine their relationship to success in a beginning computer science course. Significant correlations were found between the final exam score and the following factors: reading comprehension, sequence completion, logical reasoning, and algorithmic execution. In addition, a stepwise multiple regression procedure was performed to determine the most important factors in predicting success in a beginning computer science course. When all eight factors were included, approximately 25% of the variability in the final exam scores was explained.

Identifying Factors Influencing Computer Science Aptitude and Achievement

AbstractThis paper considers the effect of eight factors on computer science aptitude and achievement. Aptitude is measured by a computer science aptitude test and achievement is measured by a final examination. High school performance was the first factor selected for both aptitude and achievement by a stepwise regression procedure. The high school mathematics background as well as any university mathematics background were the next two factors selected for computer science aptitude. Previous computer science education and the age of the student were selected on steps two and three, respectively, for computer science achievement.

On the converse of singer's theorem

Abstract A construction is given in which the nonzero elements of a planar difference set give rise to a totally symmetric quasi-group. Examples are provided which suggest that the quasi-group is essentially the additive group of the field. The evidence supports the conjecture that the converse of Singers theorem holds. The Multiplier Theorem is used to characterize when the totally symmetric quasi-groups are totally symmetric loops. The results extend to Abelian group difference sets (λ = 1).

The Use Of Computer Algebra Software in Teaching Intermediate and College Algebra

Two groups of students in an intermediate algebra course as well as two groups of students in acollege algebracourse were compared with respect tothe use/non-use of computer algebra software in the courses. In both courses, the students using the software outperformed the students not using the software on a common final exam. For the intermediate algebracourse, the experimental group (the one using the software) had a mean equal to 80.8, the control group had a mean equal to 76.1, and the p-value was 0.13. For the college algebra course, the experimental group had amean equal to 75.1, the control group had amean equal to 69.4, and the p-value was 0.22. Furthermore, the experimental groups expressed very positive feelings about the use of the software in the course. In addition, the instructors in the experimental groups received their best student evaluations ever when teaching algebra courses.

On the number of combinations without unit separation

Abstract Let f(n, k) denote the number of ways of selecting k objects from n objects arrayed in a line with no two selected having unit separation (i.e., having exactly one object between them). Then, if n ⩾ 2(k − 1), f(n,k)= ∑ i=0 κ ( n−k+I−2i k−2i ) (where κ = [ k 2 ] ). If n 3, g(n, k) = f(n − 2, k) + 2f(n − 5, k − 1) + 3f(n − 6, k − 2). In particular, if n ⩾ 2k + 1 then (n,k)=( n−k k )+( n−k−1 k−1 ) .

Bio-logic builder: a non-technical tool for building dynamical, qualitative models.

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.

A Generalization of Waring's Formula

Warings formula for expressing power sum symmetric functions in terms of elementary symmetric functions is generalized to monomial symmetric functions with equal exponents by applying the orthogonality property of Ramanujan sums together with the Mobius function over the set partition lattice.