Gilles Gnacadja

math.gillesgnacadja.info

Publications



An Invitation to Pharmacostatics
Preprint Pharmacostatics.pdf

Enclosure Algorithm for the Fixed Points of Order-Reversing Maps – Application to Polynomial Systems for Chemical Equilibrium
Preprint EnclosureAlgoFPOR.pdf
Supplemental Slide Deck 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
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 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>0n 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




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 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
PAS fm16113
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