A framework for generalized group testing with inhibitors and its potential application in neuroscience

The main goal of group testing with inhibitors (GTI) is to identify a small number of defective items and inhibitor items in a large set of items. A test on a subset of items is positive if it satisfies some specific property. Inhibitor items cancel the effects of positive items, which often make the outcome of a test containing defective items negative. Different GTI models can be formulated by considering how specific properties have different cancellation effects. This work introduces generalized GTI (GGTI) in which a new type of items is added, i.e., hybrid items. A hybrid item plays the roles of both defectives items and inhibitor items. Since the number of GGTI models is large (at least 96), we introduce a framework for classifying all types of items non-adaptively, i.e., all tests are designed in advanced. We then explain how GGTI can be used to classify neurons in neuroscience. Finally, we optimize the construction of disjunct matrices, which are an important tool in GTI.

[1]  Hung-Lin Fu,et al.  Identification and Classification Problems on Pooling Designs for Inhibitor Models , 2010, J. Comput. Biol..

[2]  Peter Damaschke.  Threshold Group Testing , 2005, Electron. Notes Discret. Math..

[3]  Mayank Bakshi,et al.  GROTESQUE: Noisy Group Testing (Quick and Efficient) , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[4]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[5]  James G. King,et al.  Reconstruction and Simulation of Neocortical Microcircuitry , 2015, Cell.

[6]  Richard C. Singleton,et al.  Nonrandom binary superimposed codes , 1964, IEEE Trans. Inf. Theory.

[7]  M. Paradiso,et al.  Neuroscience: Exploring the Brain , 1996 .

[8]  Hung-Lin Fu,et al.  Threshold Group Testing on Inhibitor Model , 2013, J. Comput. Biol..

[9]  Michael G. Rabbat,et al.  Efficient Large-Scale Similarity Search Using Matrix Factorization , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[10]  Sampath Kannan,et al.  Group testing problems with sequences in experimental molecular biology , 1997, Proceedings. Compression and Complexity of SEQUENCES 1997 (Cat. No.97TB100171).

[11]  Arkadii G. D'yachkov,et al.  Cover-free codes and separating system codes , 2017, Des. Codes Cryptogr..

[12]  Li I. Zhang,et al.  Tone-evoked excitatory and inhibitory synaptic conductances of primary auditory cortex neurons. , 2004, Journal of neurophysiology.

[13]  Nikita Polyanskii,et al.  On multistage learning a hidden hypergraph , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[14]  Ding-Zhu Du,et al.  A survey on combinatorial group testing algorithms with applications to DNA Library Screening , 1999, Discrete Mathematical Problems with Medical Applications.

[15]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[16]  Nancy A. Lynch,et al.  Computational Tradeoffs in Biological Neural Networks: Self-Stabilizing Winner-Take-All Networks , 2016, ITCS.

[17]  A. Marty,et al.  Coexistence of Excitatory and Inhibitory GABA Synapses in the Cerebellar Interneuron Network , 2003, The Journal of Neuroscience.

[18]  Mahdi Cheraghchi.  Noise-resilient group testing: Limitations and constructions , 2013, Discret. Appl. Math..

[19]  Amin Karbasi,et al.  Graph-constrained group testing , 2010, ISIT.

[20]  Thach V. Bui,et al.  Efficiently Decodable Non-Adaptive Threshold Group Testing , 2019, IEEE Transactions on Information Theory.

[21]  D. Du,et al.  Combinatorial Group Testing and Its Applications , 1993 .

[22]  George Atia,et al.  Boolean Compressed Sensing and Noisy Group Testing , 2009, IEEE Transactions on Information Theory.

[23]  Sidharth Jaggi,et al.  Non-adaptive group testing with inhibitors , 2014, 2015 IEEE Information Theory Workshop (ITW).

[24]  Siu-Ming Yiu,et al.  Non-adaptive Complex Group Testing with Multiple Positive Sets , 2011, TAMC.

[25]  J. J. Hopfield,et al.  Pattern recognition computation using action potential timing for stimulus representation , 1995, Nature.

[26]  Thach V. Bui,et al.  Sublinear decoding schemes for non-adaptive group testing with inhibitors , 2019, TAMC.

[27]  Douglas R. Stinson,et al.  Generalized cover-free families , 2004, Discret. Math..

[28]  Arkadii G. D'yachkov,et al.  Families of Finite Sets in which No Intersection of Sets Is Covered by the Union of s Others , 2002, J. Comb. Theory, Ser. A.

[29]  David C. Torney,et al.  Sets pooling designs , 1999 .

[30]  Weili Wu,et al.  Group Testing with Multiple Inhibitor Sets and Error-Tolerant and Its Decoding Algorithms , 2016, J. Comput. Biol..

[31]  S. Herculano‐Houzel.  The Human Brain in Numbers: A Linearly Scaled-up Primate Brain , 2009, Front. Hum. Neurosci..

[32]  Thach V. Bui,et al.  Efficient (nonrandom) construction and decoding of non-adaptive group testing , 2019, J. Inf. Process..

[33]  Mahdi Cheraghchi.  Improved Constructions for Non-adaptive Threshold Group Testing , 2010, ICALP.

[34]  A. Sterrett.  On the Detection of Defective Members of Large Populations , 1957 .

[35]  Ely Porat,et al.  Search Methodologies , 2022 .

[36]  Naoshige Uchida,et al.  Bilingual neurons release glutamate and GABA , 2014, Nature Neuroscience.

[37]  Ramtin Pedarsani,et al.  Sub-linear Time Stochastic Threshold Group Testing via Sparse-Graph Codes , 2018, 2018 IEEE Information Theory Workshop (ITW).

[38]  Thach V. Bui,et al.  Improved encoding and decoding for non-adaptive threshold group testing , 2019, ArXiv.

[39]  Henry Markram,et al.  A computer-assisted multi-electrode patch-clamp system. , 2013, Journal of visualized experiments : JoVE.

[40]  Vladimir S. Lebedev.  Separating codes and a new combinatorial search model , 2010, Probl. Inf. Transm..

[41]  Mayank Bakshi,et al.  Stochastic threshold group testing , 2013, 2013 IEEE Information Theory Workshop (ITW).

[42]  Wulfram Gerstner,et al.  Spiking Neuron Models: Single Neurons, Populations, Plasticity , 2002 .

[43]  Tomasz Jurdzinski,et al.  Subquadratic Non-adaptive Threshold Group Testing , 2017, FCT.

[44]  Frank K. Hwang,et al.  Error-Tolerant Pooling Designs with Inhibitors , 2003, J. Comput. Biol..

[45]  Hung-Lin Fu,et al.  An upper bound of the number of tests in pooling designs for the error-tolerant complex model , 2008, Optim. Lett..

[46]  Henry Dale.  Pharmacology and Nerve Endings , 1935 .

[47]  Mayank Bakshi,et al.  Near-Optimal Stochastic Threshold Group Testing , 2013, ArXiv.

[48]  R. Dorfman.  The Detection of Defective Members of Large Populations , 1943 .

[49]  Dana Angluin,et al.  Learning a Hidden Hypergraph , 2005, J. Mach. Learn. Res..

[50]  Atri Rudra,et al.  Efficiently Decodable Error-Correcting List Disjunct Matrices and Applications - (Extended Abstract) , 2011, ICALP.

[51]  Annalisa De Bonis,et al.  Improved Algorithms for Group Testing with Inhibitors , 1998, Inf. Process. Lett..