**W. Just** and **B. Stigler**;
*Efficiently Computing Groebner Bases of Ideals of Points*.

arXiv:0711.3475v1

*Abstract.*We present an algorithm for computing Groebner bases of vanishing ideals of points that is optimized for the case when the number of points in the associated variety is less than the number of indeterminates. The algorithm first identifies a set of essential variables, which reduces the time complexity with respect to the number of indeterminates, and then uses PLU decompositions to reduce the time complexity with respect to the number of points. This gives a theoretical upper bound for its time complexity that is an order of magnitude lower than the previously published one for the standard Buchberger-Moeller algorithm if the number of indeterminates is much larger than the number of points. Comparison of implementations of our algorithm and the standard Buchberger-Moeller algorithm in*Macaulay 2*confirm the theoretically predicted speedup. This work is motivated by recent applications of Groebner bases to the problem of network reconstruction in molecular biology.

**W. Just** and **M. Korb**;
*(In)consistency:
Some low-dimensional examples*.

*Abstract.*This note is a slightly revised version of an earlier note with the same title that was part of a larger research project of the Dynamical Systems Group at Ohio University. While the major findings of the project are described in the paper*Two classes of ODE models with switch-like behavior*by W. Just, M. Korb, B. Elbert, and T. R. Young, this note complements this paper as it contains a more extensive review of some basic low-dimensional examples of Boolean systems and their ODE counterparts and explores whether the ODE dynamics is consistent with the Boolean dynamics.

**W. Just** and **S. Ahn**;
*Lengths of attractors and transients in neuronal networks with random
connectivities*.

arXiv:1404.5536

*Abstract.*We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erdos-Renyi random graph and analytically derive scaling laws for the average lengths of the attractors and transients under certain restrictions on the intrinsic parameters of the neurons, that is, their refractory periods and firing thresholds. In contrast to earlier results that were reported in an earlier paper, here we focus on the connection probabilities near the phase transition where the most complex dynamics is expected to occur.

arXiv:1808.08789

*Abstract.*Studies of voluntary vaccination decisions by rational individuals predict that the population will reach a Nash equilibrium with vaccination coverage below the societal optimum. Human decision-making involves mechanisms in addition to rational calculations of self-interest, such as imitation of successful others. Previous research had shown that imitation alone cannot achieve better results. Under realistic choices of the parameters it may lead to equilibrium vaccination coverage even below the Nash equilibrium. However, these findings rely on the widely accepted use of Fermi functions for modeling the probabilities of switching to another strategy. We consider here a more general functional form of the switching probabilities. It is consistent with functions that give best fits for empirical data in a widely cited psychological experiment and involves one additional parameter alpha. This parameter can be loosely interpreted as a degree of open-mindedness. We found both by means of simulations and analytically that sufficiently high values of alpha will drive the equilibrium vaccination coverage arbitrarily close to the societal optimum.

**W. Just** and **Y. Xin**;
*Limsup is needed in the definitions of topological entropy via spanning or separation numbers.*
Dynamical Systems 35(3) (2020), 430-489.

*Abstract.*Studies of voluntary vaccination decisions by rational individuals predict that the population will reach a Nash equilibrium with vaccination coverage below the societal optimum. Human decision-making involves mechanisms in addition to rational calculations of self-interest, such as imitation of successful others. Previous research had shown that imitation alone cannot achieve better results. Under realistic choices of the parameters it may lead to equilibrium vaccination coverage even below the Nash equilibrium. However, these findings rely on the widely accepted use of Fermi functions for modeling the probabilities of switching to another strategy. We consider here a more general functional form of the switching probabilities. It is consistent with functions that give best fits for empirical data in a widely cited psychological experiment and involves one additional parameter alpha. This parameter can be loosely interpreted as a degree of open-mindedness. We found both by means of simulations and analytically that sufficiently high values of alpha will drive the equilibrium vaccination coverage arbitrarily close to the societal optimum.

**B. Oduro**, **M. Grijalva**, and **W. Just**;
*A model of insect control with imperfect treatment.*
Journal of Biological Dynamics 13(1) (2019).

**Y. Xin**, **C. K. Mudiyanselage**, and **W. Just**; *Development of epithelial tissues:
How are cleavage planes chosen?* PLoS ONE 13(11):e0205834 (2018).
https://doi.org/10.1371/journal.pone.0205834

*Abstract.*Epithelia are sheets of tightly adherent cells that line both internal and external surfaces in metazoans. Mathematically, a cell in an epithelial tissue can be modeled as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. A variety of mathematical models have been proposed to explain this phenomenon. Among the most parsimonious of such models are topological ones that take into account only the number of sides of a given cell and the neighborhood relation between cells. The model studied here is a refinement of a previously published such model (Patel et al., PLoS Comput. Biol., 2009). While using the same modeling framework as that paper, we introduce additional options for the choice of the endpoints of the cleavage plane in the simulated development of epithelial tissues. Some of these options appear to be more biologically realistic approximations of known mechanisms that influence the cleavage plane orientation. A comparative analysis of comprehensive simulations for relevant combinations of both previously studied and our newly designed options is reported here. We compared the outcomes with the empirical distributions of the same five organisms as in (Patel et al., 2009),*Drosophila, Hydra, Xenopus,*Cucumber, and*Anagallis.*We found that combinations of some of our new options consistently gave better fits with each of these data sets than combinations of previously studied options for choosing the cleavage plane.

**B. Oduro**, **M. Grijalva**, and **W. Just**;
*Models of disease vector control: When can aggressive initial intervention lower long-term cost?*

Bulletin of Mathematical Biology, 80(4) (2018), 788-824.

**W. Just** and **H. Callender Highlander**;
*Vaccination strategies for small worlds*.

In A. Wootton, V. Peterson, C. Lee, eds.,
*A Primer for Undergraduate Research: From Groups and Tiles to Frames and Vaccines.* Springer Verlag, 2018, 223-264.

**W. Just**, **J. Saldaña**, and **Y. Xin**;
*Oscillations in epidemic models with spread of awareness*.

Journal of Mathematical Biology, 76(4) (2018), 1027-1057.

Preliminary version available at arXiv:1606.08788

**W. Just** and **S. Ahn**;
*Lengths of attractors and transients in neuronal networks with random
connectivities*.

SIAM Journal on Discrete Mathematics 30(2) (2016) 912–933.

**W. Just**, **H. Callender**, **M. D. LaMar**, and **N. Toporikova**; *Transmission
of infectious diseases: Data, models, and simulations.*

In Raina Robeva (ed.), *Algebraic
and Discrete Mathematical Methods for Modern Biology.* Academic Press, 2015, 193-215.

**W. Just**, **H. Callender**, and **M. D. LaMar**;
*Disease transmission dynamics on
networks: Network structure vs. disease dynamics.*

In: Raina Robeva (ed.), *Algebraic
and Discrete Mathematical Methods for Modern Biology.* Academic Press, 2015, 217-235.

**W. Just** and **G. A. Enciso**;
*Ordered Dynamics in Biased and Cooperative Boolean Networks*.

Advances in Difference Equations 2013, 2013:313.

**W. Just, M. Korb, B. Elbert,** and **T. R. Young**;
*Two classes of ODE models with switch-like behavior*.

Physica D 264 (2013) 35-48.

**W. Just** and **M. Malicki**;
*Cooperative Boolean systems with generically long attractors II*.

Advances in Difference Equations 2013, 2013:268.

**W. Just** and **M. Malicki**;
*Cooperative Boolean systems with generically long attractors I*.

Journal of Difference Equations and Applications 19(5) (2013) 772-795.

**W. Just, S. Ahn,** and **D. Terman**;
*Neuronal Networks: A Discrete Model*.
In *Mathematical Concepts and Methods in Modern Biology*, R. Robeva and T. Hodge, eds., Academic Press, 2013, 179-211.

**S. Ahn** and **W. Just**;
*Digraphs vs. Dynamics in Discrete
Models of Neuronal Networks*.

Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
17(5) (2012) 1365-1381.

Journal of Difference Equations and Applications 18(2) (2012) 223-238.

*Abstract.*Discrete dynamical systems defined on the state space*{0,1,...,p-1}*have been used in multiple applications, most recently for the modeling of gene and protein networks. In this paper we study to what extent well-known theorems by Smale and Hirsch, which form part of the theory of (continuous) monotone dynamical systems, generalize or fail to do so in the discrete case. We show that that arbitrary^{n}*m*-dimensional systems cannot necessarily be embedded into*n*-dimensional cooperative systems for*n = m+1,*as in the Smale theorem for the continuous case, but we show that this is possible for*n = m+2*as long as*p*is sufficiently large. We also prove that a natural discrete analogue of strong cooperativity implies nontrivial bounds on the lengths of periodic orbits and imposes a condition akin to Lyapunov stability on all attractors. Finally, we explore several natural candidates for definitions of irreducibility of a discrete system. While some of these notions imply the strong cooperativity of a given cooperative system and impose even tighter bounds on the lengths of periodic orbits than strong cooperativity alone, other plausible definitions allow the existence of exponentially long periodic orbits.

**W. Just** and **G. A. Enciso**;
*Exponentially long orbits in Boolean networks with exclusively positive interactions*.

Nonlinear Dynamics and Systems Theory 11(3) (2011) 275-284.

**W. Just** and
**A. Nevai**;
*A Kolmogorov-type Competition Model with Finitely Supported Allocation Profiles and its
Applications to Plant Competition for Sunlight*.

Journal of Biological Dynamics 3(6) (2009) 599-619.

**W. Just, S. Ahn,** and
**D. Terman**;
*Minimal attractors in digraph system models of neuronal
networks*.

Physica D 237 (2008) 3186-3196.

**W. Just** and
**A. Nevai**;
*A Kolmogorov-type Competition Model with Multiple Coexistence States and its
Applications to Plant Competition for Sunlight*.

Journal of Mathematical Analysis and its Applications 348(2) (2008), 620-636.

**D. Terman,
S. Ahn, X. Wang,** and **W. Just**;
*Reducing neuronal networks to discrete dynamics*.

Physica D 237(3) (2008) 324-338.

**W. Just**; *Data requirements of reverse-engineering algorithms*.

Annals of the New York Academy of Sciences 1115 (2007) 142-153.

**W. Just**, **M.
R. Morris**, and **X. Sun**; *The evolution of aggressive losers*.

Behavioural Processes 74 (2007) 342-350.

*Abstract.*We examine the question of when aggressive behavior of likely losers should be part of an evolutionarily stable strategy. We modified an earlier model by the authors that found situations where likely losers initiate aggressive interactions more often than likely winners. The modifications allowed us to examine the robustness of the previous study by including an unusually high number of possible strategies (n = 81) and to examine a wide range of parameter settings. First, we show that restricting attention to only a few most plausible strategies may change the overall results. Second, within the space where escalation is predicted, for a large percentage of the parameter settings (85%), an ESS exists that leads to a somewhat counterintuitive situation where escalation is more often initiated by the likely loser than by the likely winner of the contest. In contrast, an ESS that favors escalation by likely winners was found only for about 3% of parameter settings. Furthermore, we use simulations of evolution in a finite population to verify for certain parameter settings that the analytically predicted ESSs could in fact evolve.

**W. Just**; *Reverse engineering discrete dynamical
systems from data sets with random input vectors*.
Journal of Computational Biology 13(8) (2006) 1435-1456.

**W. Just** and **G. Della Vedova**;
*Multiple Sequence Alignment
as a Facility Location Problem*.
INFORMS Journal on Computing 16(4) (2004) 430-440.

*Abstract.*This is a substantially expanded version of a workshop paper by the same authors. A connection is made between certain multiple sequence alignment problems and facility location problems, and the existence of a PTAS (polynomial time approximation scheme) for these problems is shown. Moreover, it is shown that multiple sequence alignment with SP-score and fixed gap penalties is MAX SNP-hard.

**W. Just** and **X. Sun**; *Is the Predicted ESS in the Sequential
Assessment Game Evolvable?* Proceedings of GECCO 2004 (Genetic and Evolutionary Computation Conference 2004), Kalyanmoy Deb et al. (eds.), Lecture Notes in Computer Science 3102, Springer Verlag: Berlin, 499-500.

**X. Sun** and **W. Just**; *Evolution of Strategies in Modified Sequential Assessment Games*.
Proceedings of CEC 2004
(2004 Congress on Evolutionary Computation), Garrison W. Greenwood (ed.),
IEEE Press, 388-394.

**W. Just** and **F. Zhu**;
*Individual-Based Simulations of the War of Attrition*.
Behavioural Processes 66(1) (2004) 53-62.

**W. Just** and **M. R. Morris**;
*The Napoleon Complex: Why Smaller Males Pick Fights.*
Evolutionary Ecology 17(5) (2003) 509-522.

**Y. Xiao** and **W. Just**;
*A Possible Mechanism of Repressing
Cheating Mutants in Myxobacteria*.
E. Cantú-Paz et al. (Eds.): Genetic and Evolutionary Computation Conference - GECCO 2003. LNCS 2723, Springer Verlag: Berlin, 154-155.

**W. Just** and **X. Sun**; *Simulating the Evolution of
Contest Escalation*.
Alwyn Barry (Ed.): Workshop Program for GECCO 2003 (Genetic and Evolutionary Computation Conference), 75-77.

**W. Just** and **F. Zhu**; *Effects of Genetic Architecture
on Simultaneous Evolution of Multiple Traits*.
Alwyn Barry (Ed.): Workshop Program for GECCO 2003 (Genetic and Evolutionary Computation Conference), 22-26.

**W. Just**; *Computational complexity of multiple
sequence alignment with SP-score.*
Journal of Computational Biology Vol 8, Number 6 (2001) 615-623.

**W. Just**; *$\clubsuit$-like principles under CH.*
Fundamenta Mathematicae 170 (2001) 247-256.

**J. Brendle**, **W. Just**, and **C. Laflamme**;
*On the refinement and countable refinement numbers*.
Questions and Answers in General Topology 18 (2000) 123-128.

**Z. T. Balogh**, **S. W. Davis**, **W. Just**,
**S. Shelah**, and **P. J. Szeptycki**;
*Strongly almost disjoint sets and weakly uniform bases*.
Transactions of the AMS 352 number 11 (2000) 4971-4987.

**W. Just** and **Gianluca Della Vedova**;
*Multiple Sequence Alignment as a Facility Location Problem*.
Proceedings of the Prague Stringology Club Workshop 2000,
Collaborative Report DC-2000-03, M. Balik and M. Simanek, eds.,
Department of Computer Science and Engineering, Czech Technical University,
60-70.

For a pdf-file of this paper, click here.

For a dvi-file of this paper, click here.

For a postscript file of this paper,
click here.

*Abstract.*A connection is made between certain multiple sequence alignment problems and facility location problems, and the existence of a PTAS (polynomial time approximation scheme) for these problems is shown. Moreover, it is shown that multiple sequence alignment with SP-score and fixed gap penalties is MAX SNP-hard.

For a Word file of the paper, click here.

*Abstract.*In some species of animals, fights for scarce resources tend to be initiated by the smaller contestant, who is also more likely to eventually lose the fight. An evolutionary algorithm is used to study under which conditions such a behavior would evolve. The simulations partially confirm predictions of an earlier mathematical model, but also show an unexpectedly complex evolutionary dynamic of the observed behavior patterns.

**A. V. Arhangel'skii**,
**W. Just**, **E. A. Reznichenko**, and
**P. J. Szeptycki**; *Sharp bases and weakly uniform bases versus
point-countable bases*.
Topology and its Applications 100 (2000) 39-46.

**W. Just**, **S. Shelah**, and **S. Thomas**;
*The Automorphism Tower Problem Revisited*.
Advances in Mathematics 148(2) (1999) 243-265.

**P. DeLaney** and **W. Just**;
*Two remarks on weaker connected topologies*.
Comment. Math. Univ. Carolinae 40,2 (1999) 327-329.

**S. Garcia-Ferreira** and **W. Just**;
*Some remarks on the $\gamma_p$-property*.
Questions and Answers in General Topology 17 (1999) 1-8.

**S. Garcia-Ferreira** and **W. Just**;
*Two examples of relatively pseudocompact spaces*.
Questions and Answers in General Topology 17 (1999) 35-45.

**W. Just** and **J. Tartir**;
*A $\kappa$-normal, not densely normal Tychonoff space*.
Proceedings of the AMS 127 Number 3 (1999) 901-905.

**W. Just** and
**P. Vojtas**; *On matrix rapid filters.*
Fundamenta Mathematicae 154 (1997) 177-182.

**W. Just** and
**A. Tanner**; *Splitting $\omega$-covers.*
Comment. Math. Univ. Carolinae 38,2 (1997) 375-378.

**W. Just**, **M. Scheepers**, **J. Steprans**, and
**P. J. Szeptycki**; *$G_\delta$-sets in topological spaces and
games.*
Fundamenta Mathematicae 153 (1997) 41-58.

**A. V. Arhangel'skii**,
**W. Just**, and **G. Plebanek**;
*Sequential continuity on dyadic compacta and topological groups.*
Comment. Math. Univ. Carolinae 37,4 (1996) 775-790.

**W. Just**, **A. W. Miller**, **M. Scheepers**, and
**P. J. Szeptycki**; *The combinatorics of open covers II.*
Topology and its Applications 73 (1996) 241-266.

**W. Just**;
*The sizes of relatively compact $T_1$-spaces.*
Comment. Math. Univ. Carolinae 37,2 (1996) 379-380.

**W. Just**,
**O. Sipacheva**, and **P. J. Szeptycki**;
*Nonnormal spaces $C_p(X)$ with countable extent.*
Proceedings of the AMS vol. 124(4) (1996) 1227-1235.

© Winfried Just.

Last modified September 14, 2020.