Publications
Enclosure Algorithm for the Fixed Points of OrderReversing Maps – Application to Polynomial Systems for Chemical Equilibrium  
Preprint  EnclosureAlgoFPOR.pdf 
Supplemental Slide Deck  EnclosureAlgoFPOR_suppl.pdf 
Software  EnclosureAlgoFPORChemEquil – 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 steadystate value independent of library size 
Journal  Chemometrics and Intelligent Laboratory Systems, Volume 125, 15 June 2013, Pages 6773 
DOI  10.1016/j.chemolab.2013.03.004 
Preprint  SampleBankMath.pdf 
Supplemental Article  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 18491852 
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 612622 
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 21582176 
DOI  10.1007/s1091001198953 
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 21372157 
DOI  10.1007/s1091001198962 
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 21172136 
DOI  10.1007/s1091001198944 
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 135141 
DOI  10.1016/j.mbs.2011.05.003 
Math Rev  2849209 
PubMed  21645524 
Preprint  CalcEquilRAB.pdf 
Overview  CalcEquilRAB.overview.pdf 
Effect of the Calcimimetic R568 on Correcting Inactivating Mutations in the Human CalciumSensing 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 775786 
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 394414 
DOI  10.1016/j.aam.2009.05.001 
Math Rev  2553547 
Preprint  Reversible_Binding_Reactions.pdf 
Fixed Points of OrderReversing Maps in R_{>0}^{n} and Chemical Equilibrium  
Journal  Mathematical Methods in the Applied Sciences, Volume 30, Issue 2, 25 January 2007, Pages 201211 
DOI  10.1002/mma.782 
Math Rev  2285121 
Preprint  FixedPoint.pdf 
Monotonicity of Interleukin1 ReceptorLigand 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 478488 
DOI  10.1016/j.jtbi.2006.07.023 
Math Rev  2293131 
PubMed  17011587 
Preprint  IL1_bump.pdf 
More Public Documents
Equilibria Exist in Compact Convex ForwardInvariant 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 
Older 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 395404 
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 3791 
PAS  fm16113 
Math Rev  1713200 
Phantom Maps in the Stable Module Category  
Journal  Journal of Algebra, Volume 201, Issue 2, 15 March 1998, Pages 686702 
DOI  10.1006/jabr.1997.7303 
Math Rev  1612359 
Phantom Maps and Purity over FiniteDimensional SelfInjective Algebras  
Ph.D. Thesis, University of Georgia, Athens, Georgia, USA, 1999  
Advisor  Prof. David J. Benson 
Math Rev  2699053 