Integer Sparse Distributed Memory and Modular Composite Representation

Challenging AI applications, such as cognitive architectures, natural language understanding, and visual object recognition share some basic operations including pattern recognition, sequence learning, clustering, and association of related data. Both the representations used and the structure of a system significantly influence which tasks and problems are most readily supported. A memory model and a representation that facilitate these basic tasks would greatly improve the performance of these challenging AI applications.Sparse Distributed Memory (SDM), based on large binary vectors, has several desirable properties: auto-associativity, content addressability, distributed storage, robustness over noisy inputs that would facilitate the implementation of challenging AI applications. Here I introduce two variations on the original SDM, the Extended SDM and the Integer SDM, that significantly improve these desirable properties, as well as a new form of reduced description representation named MCR.Extended SDM, which uses word vectors of larger size than address vectors, enhances its hetero-associativity, improving the storage of sequences of vectors, as well as of other data structures. A novel sequence learning mechanism is introduced, and several experiments demonstrate the capacity and sequence learning capability of this memory.Integer SDM uses modular integer vectors rather than binary vectors, improving the representation capabilities of the memory and its noise robustness. Several experiments show its capacity and noise robustness. Theoretical analyses of its capacity and fidelity are also presented.A reduced description represents a whole hierarchy using a single high-dimensional vector, which can recover individual items and directly be used for complex calculations and procedures, such as making analogies. Furthermore, the hierarchy can be reconstructed from the single vector. Modular Composite Representation (MCR), a new reduced description model for the representation used in challenging AI applications, provides an attractive tradeoff between expressiveness and simplicity of operations. A theoretical analysis of its noise robustness, several experiments, and comparisons with similar models are presented.My implementations of these memories include an object oriented version using a RAM cache, a version for distributed and multi-threading execution, and a GPU version for fast vector processing

Collected Papers (on Neutrosophic Theory and Its Applications in Algebra), Volume IX

This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang

Dna Sequences Generated By ℤ4-linear Codes

One of the puzzling problems in mathematical biology is to show the existence of any form of error-correcting code in the DNA structure. Here we propose a model for the biological coding system similar to that of a digital communication system. This model consists of an encoder (a mapper and a BCH code over ℤ4) and a modulator (genetic code). Here we show that DNA sequences including proteins and targeting sequences from different species with 63, 255, and 1023 nucleotides long were identified as codewords of ℤ4-linear codes. © 2010 IEEE.13201324Schneider, T.D., Information content of individual genetic sequences (1997) Journal of Theoretical Biology, 189, pp. 427-441Liebovitch, L.S., Tao, Y., Todorov, A.T., Levine, L., Is there an error correcting code in the base sequence in DNA? (1996) Biophysical Journal, 71, pp. 1539-1544Rosen, G.L., Examining coding structure and redundancy in DNA (2006) IEEE Engineering in Medicine and Biology, 25, pp. 62-68May, E., Vouk, M., Bitzer, D., Rosnick, D., An error-correcting code framework for genetic sequence analysis (2004) Journal of the Franklin Institute, 34, pp. 89-109Battail, G., Information theory and error correcting codes in genetics and biological evolution (2006) Introduction to Biosemiotics, , Springer: New York, USAYockey, H., (1992) Information Theory and Molecular Biology, , Cambridge University Press: CambridgeDawy, Z., Hanus, P., Weindl, J., Dingel, J., Morcos, F., On genomic coding theory (2007) European Transactions on Telecommunications, 18, pp. 873-879Loeliger, H.A., Signal sets matched to groups (1991) IEEE Trans. Inform. Theory, IT-37, pp. 1675-1682Forney, G.D., Geometrically uniform codes (1991) IEEE Trans. Inform. Theory, IT-37, pp. 1241-1260Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Sole, P., The Z4-linearity of kerdock, preparata, goethals, and related codes (1994) IEEE Trans. Inform. Theory, IT-40, pp. 301-319Gerônimo, J.R., Palazzo Jr., R., Interlando, J.C., Alves, M.M.S., Costa, S.I.R., The symmetry group of ℤq N in the Lee space and the ℤq N-linear codes (1997) Lecture Notes in Computer Science, 1255, pp. 66-77Alves, M.M.S., Araújo, M.C., Palazzo Jr., R., Costa, S.I.R., Interlando, J.C., Relating propelinear and G-linear codes (2001) Discrete Mathematics, 243 (1-3), pp. 187-194Nordstrom, A.W., Robinson, J.P., An optimum nonlinear code (1967) Info. and Control, 11, pp. 613-616Preparata, F.P., A class of optimum nonlinear double-error correcting codes (1968) Info. and Control, 13, pp. 378-400McWillians, F.J., Sloane, N.J.A., (1977) The Theory of Error Correcting Codes, , North-Holland Publishing CompanyPeterson, W.W., Weldon Jr., E.J., (1972) Error-Correcting Codes, , 2nd edition, MIT PressInterlando, J.C., Palazzo Jr., R., Elia, M., On the decoding of BCH and Reed-Solomon codes over integer residues rings (1997) IEEE Trans. Inform. Theory, IT-43 (3), pp. 1013-1021Andrade, A.A., Palazzo Jr., R., Construction and decoding of BCH codes over finite commutative rings (1999) Linear Algebra and its Applications, 286, pp. 69-85Elia, M., Interlando, J.C., Palazzo Jr., R., Computing the reciprocal of units in finite Galois rings (2000) Journal of Discrete Mathematical Sciences and Cryptography, 3 (1-3), pp. 41-55Andrade, A.A., Palazzo Jr., R., Alternant and BCH codes over certain local finite rings (2003) Computational and Applied Mathematics, 22 (2), pp. 233-247Shankar, P., On BCH codes over arbitrary integer rings (1979) IEEE Transactions on Information Theory, IT-25 (4), pp. 480-48