# Publications

Information of Absence Is Not Absence of Information: Can We Not Impute? | |

Research note | Can-We-Not-Impute.pdf |

Announcement | LinkedIn article |

Metrics of Binary Classifier Performance: Predictive vs. Retrodictive | |

Research note | Predictive-vs-Retrodictive.pdf predictive-vs-retrodictive.html |

Interactive | From retrodictive TPR and FPR to predictive pTPR and pFNR From retrodictive TPR and TNR to predictive PPV and NPV From predictive pTPR and pFNR to retrodictive TPR and FPR From predictive PPV and NPV to retrodictive TPR and TNR |

Announcement | LinkedIn article |

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 | |

Research note | 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 |