# Publications

An Invitation to Pharmacostatics | |

Journal | Bulletin of Mathematical Biology Volume 81, Issue 9, September 2019, Pages 3642–3654 |

DOI | 10.1007/s11538-017-0369-z |

PubMed | 29214428 |

Preprint | Pharmacostatics.pdf |

Enclosure Algorithm for the Fixed Points of Order-Reversing Maps – Application to Polynomial Systems for Chemical Equilibrium | |

Preprint | EnclosureAlgoFPOR.pdf |

Supplement | EnclosureAlgoFPOR_suppl.pdf |

Software | Enclosure-Algo-FPOR-Chem-Equil – a repository on GitHub |

A Mathematical Model for Projecting the Replenishment of Compounds in a Sample Bank | |

Authors | Gilles Gnacadja and Mark Gulbronson |

Highlights | ‣ Mathematical model of sample bank operations in high throughput screening ‣ Projection of replenishment needs as function of screening activity and copy count ‣ Replenishments projected to tend to steady-state value independent of library size |

Journal | Chemometrics and Intelligent Laboratory Systems, Volume 125, 15 June 2013, Pages 67-73 |

DOI | 10.1016/j.chemolab.2013.03.004 |

Preprint | SampleBankMath.pdf |

Supplement | Equidistribution3.pdf – An augmentation of the article below |

Asymptotic Equidistribution of Congruence Classes with respect to the Convolution Iterates of a Probability Vector | |

Journal | Statistics and Probability Letters, Volume 82, Issue 10, October 2012, Pages 1849-1852 |

DOI | 10.1016/j.spl.2012.05.025 |

Math Rev | 2956626 |

Preprint | Equidistribution.pdf |

Enhanced Postprint | Equidistribution2.pdf |

A Jacobian Criterion for the Simultaneous Injectivity on Positive Variables of Linearly Parameterized Polynomial Maps | |

Journal | Linear Algebra and its Applications, Volume 437, Issue 2, 15 July 2012, Pages 612-622 |

DOI | 10.1016/j.laa.2012.03.014 |

Math Rev | 2921721 |

Preprint | InjectivePolynomialMaps.pdf |

Reachability, Persistence, and Constructive Chemical Reaction Networks (Part III): A Mathematical Formalism for Binary Enzymatic Networks and Application to Persistence | |

Journal | Journal of Mathematical Chemistry, Volume 49, Number 10, November 2011, Pages 2158-2176 |

DOI | 10.1007/s10910-011-9895-3 |

Math Rev | 2846709 |

Preprint | Binary_Enzymatic_Networks.pdf |

Reachability, Persistence, and Constructive Chemical Reaction Networks (Part II): A Formalism for Species Composition in Chemical Reaction Network Theory and Application to Persistence | |

Journal | Journal of Mathematical Chemistry, Volume 49, Number 10, November 2011, Pages 2137-2157 |

DOI | 10.1007/s10910-011-9896-2 |

Math Rev | 2846708 |

Preprint | Species_Composition.pdf |

Reachability, Persistence, and Constructive Chemical Reaction Networks (Part I): Reachability Approach to the Persistence of Chemical Reaction Networks | |

Journal | Journal of Mathematical Chemistry, Volume 49, Number 10, November 2011, Pages 2117-2136 |

DOI | 10.1007/s10910-011-9894-4 |

Math Rev | 2846707 |

Preprint | Vacuous_Persistence.pdf |

Reachability, Persistence, and Constructive Chemical Reaction Networks | |

Article | ConstructiveCRNT.pdf |

Note | This article is the originally prepared version of the work that is now the content of the three articles above. |

A Method to Calculate Binding Equilibrium Concentrations in the Allosteric Ternary Complex Model that Supports Ligand Depletion | |

Highlights | ‣ Equilibrium concentrations are calculated without customary assumption that total receptor concentration is infinitesimal ‣ An implicit formula characterizes equilibrium receptor concentration and a simple convergent algorithm calculates it ‣ Two explicit formulas express equilibrium ligand concentrations in terms of equilibrium receptor concentration ‣ Customary method can give substantially incorrect results when total receptor concentration is not negligible |

Journal | Mathematical Biosciences, Volume 232, Issue 2, August 2011, Pages 135-141 |

DOI | 10.1016/j.mbs.2011.05.003 |

Math Rev | 2849209 |

PubMed | 21645524 |

Preprint | CalcEquilRAB.pdf |

Overview | CalcEquilRAB.overview.pdf |

Effect of the Calcimimetic R-568 on Correcting Inactivating Mutations in the Human Calcium-Sensing Receptor | |

Authors | Jenny Ying Lin Lu, Yuhua Yang, Gilles Gnacadja, Arthur Christopoulos and Jeff D. Reagan |

Journal | Journal of Pharmacology and Experimental Therapeutics, Volume 331, Number 3, December 2009, Pages 775-786 |

DOI | 10.1124/jpet.109.159228 |

PubMed | 19759318 |

Univalent Positive Polynomial Maps and the Equilibrium State of Chemical Networks of Reversible Binding Reactions | |

Journal | Advances in Applied Mathematics, Volume 43, Issue 4, October 2009, Pages 394-414 |

DOI | 10.1016/j.aam.2009.05.001 |

Math Rev | 2553547 |

Preprint | Reversible_Binding_Reactions.pdf |

Fixed Points of Order-Reversing Maps in R_{>0}^{n} and Chemical Equilibrium | |

Journal | Mathematical Methods in the Applied Sciences, Volume 30, Issue 2, 25 January 2007, Pages 201-211 |

DOI | 10.1002/mma.782 |

Math Rev | 2285121 |

Preprint | FixedPoint.pdf |

Monotonicity of Interleukin-1 Receptor-Ligand Binding with respect to Antagonist in the presence of Decoy Receptor | |

Authors | Gilles Gnacadja, Alex Shoshitaishvili, Michael J. Gresser, Brian Varnum, David Balaban, Mark Durst, Chris Vezina and Yu Li |

Journal | Journal of Theoretical Biology, Volume 244, Issue 3, 7 February 2007, Pages 478-488 |

DOI | 10.1016/j.jtbi.2006.07.023 |

Math Rev | 2293131 |

PubMed | 17011587 |

Preprint | IL-1_bump.pdf |

## More Public Documents | |

Equilibria Exist in Compact Convex Forward-Invariant Sets | |

Article | EquilExists.pdf |

Online | At MathOverflow |

Online | On my blog |

Question: Map Transformation to Force Convergence to Unique Fixed Point | |

Article | FixedPointAlgo_OPEN.pdf |

Online | At MathOverflow |

Online | On my blog |

Counting the Scaled +1/-1 Matrices that Satisfy the Restricted Isometry Property | |

Article | Scaled_P1M1_RIP_Matrices.pdf |

## Early-Academic Publications | |

Phantom Maps and Purity in Modular Representation Theory, II | |

Authors | D. J. Benson and G. Ph. Gnacadja |

Journal | Algebras and Representation Theory, Volume 4, Number 4, October 2001, Pages 395-404 |

DOI | 10.1023/A:1012475019810 |

Math Rev | 1863392 |

Phantom Maps and Purity in Modular Representation Theory, I | |

Authors | D. J. Benson and G. Ph. Gnacadja |

Journal | Fundamenta Mathematicae, Volume 161, 1999, Pages 37-91 |

DOI | 10.4064/fm-161-1-2-37-91 |

Math Rev | 1713200 |

Phantom Maps in the Stable Module Category | |

Journal | Journal of Algebra, Volume 201, Issue 2, 15 March 1998, Pages 686-702 |

DOI | 10.1006/jabr.1997.7303 |

Math Rev | 1612359 |

Phantom Maps and Purity over Finite-Dimensional Self-Injective Algebras | |

Ph.D. Thesis, University of Georgia, Athens, Georgia, USA, 1999 | |

Advisor | Prof. David J. Benson |

Math Rev | 2699053 |