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Article

Lisitsa, Alexei and Vernitski, Alexei (2024) Counting graphs induced by Gauss diagrams and families of mutant alternating knots. Examples and Counterexamples, 6. p. 100162. DOI https://doi.org/10.1016/j.exco.2024.100162

Lisitsa, Alexei and Salles, Mateo and Vernitski, Alexei (2024) Machine learning discovers invariants of braids and flat braids. Advances in Applied Clifford Algebras, 34 (5). DOI https://doi.org/10.1007/s00006-024-01349-4

Lisitsa, Alexei and Vernitski, Alexei (2024) Semigroups, keis and groups induced by knot diagrams: an experimental investigation with automated reasoning. Semigroup Forum, 109 (1). pp. 186-193. DOI https://doi.org/10.1007/s00233-024-10433-x

Lisitsa, Alexei and Lopatkin, Viktor and Vernitski, Alexei (2023) Describing realizable gauss diagrams using the concepts of parity or bipartite graphs. Journal of Knot Theory and Its Ramifications, 32 (10). DOI https://doi.org/10.1142/S0218216523500591

Vernitski, Alexei (2022) A blind spot in undergraduate mathematics: The circular definition of the length of the circle, and how it can be turned into an enlightening example. MSOR Connections, 20 (3). pp. 85-90. DOI https://doi.org/10.21100/msor.v20i3.1300

Higgins, Peter and Vernitski, Alexei (2022) Orientation-preserving and orientation-reversing mappings: a new description. Semigroup Forum, 104 (2). pp. 509-514. DOI https://doi.org/10.1007/s00233-022-10256-8

Daly, Ian and Bourgaize, Jake and Vernitski, Alexei (2019) Mathematical mindsets increase student motivation: Evidence from the EEG. Trends in Neuroscience and Education, 15. pp. 18-28. DOI https://doi.org/10.1016/j.tine.2019.02.005

Vernitski, Alexei and Tunsi, Laila and Ponchel, Colette and Lisitsa, Alexei (2018) Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links. Semigroup Forum, 97 (1). pp. 75-86. DOI https://doi.org/10.1007/s00233-018-9918-5

East, James and Vernitski, Alexei (2018) Ranks of ideals in inverse semigroups of difunctional binary relations. Semigroup Forum, 96 (1). pp. 21-30. DOI https://doi.org/10.1007/s00233-017-9846-9

Vernitski, Alexei (2017) Describing semigroups with defining relations of the form xy=yz xy and yx=zy and connections with knot theory. Semigroup Forum, 95 (1). pp. 66-82. DOI https://doi.org/10.1007/s00233-016-9808-7

Juhász, Zsófia and Vernitski, Alexei (2016) Semigroups with operation-compatible Green’s quasiorders. Semigroup Forum, 93 (2). pp. 387-402. DOI https://doi.org/10.1007/s00233-016-9792-y

Yang, Xinan and Vernitski, Alexei and Carrea, Laura (2016) An approximate dynamic programming approach for improving accuracy of lossy data compression by Bloom filters. European Journal of Operational Research, 252 (3). pp. 985-994. DOI https://doi.org/10.1016/j.ejor.2016.01.042

Pride, SJ and Vernitski, Alexei and Wong, KB and Wong, PC (2016) Conjugacy and Other Properties of One-Relator Groups. Communications in Algebra, 44 (4). pp. 1588-1598. DOI https://doi.org/10.1080/00927872.2015.1027368

Carrea, Laura and Vernitski, Alexei and Reed, MJ (2016) Yes-no Bloom filter: A way of representing sets with fewer false positives.

Carrea, Laura and Vernitski, Alexei and Reed, Martin (2014) Optimized hash for network path encoding with minimized false positives. Computer Networks, 58 (1). pp. 180-191. DOI https://doi.org/10.1016/j.comnet.2013.09.002

Vernitski, Alexei and Pyatkin, Artem (2012) Astral graphs (threshold graphs), scale-free graphs and related algorithmic questions. Journal of Discrete Algorithms, 12. pp. 24-28. DOI https://doi.org/10.1016/j.jda.2011.06.003

Juhasz, Z and Vernitski, Alexei (2011) Filters in (Quasiordered) Semigroups and Lattices of Filters. Communications in Algebra, 39 (11). pp. 4319-4335. DOI https://doi.org/10.1080/00927872.2010.523444

Juhász, Zsófia and Vernitski, Alexei (2011) Using filters to describe congruences and band congruences of semigroups. Semigroup Forum, 83 (2). pp. 320-334. DOI https://doi.org/10.1007/s00233-011-9330-x

Vernitski, Alexei (2009) One-side Nielsen transformations in free groups. International Journal of Algebra and Computation, 19 (07). pp. 855-871. DOI https://doi.org/10.1142/S0218196709005329

Vernitski, Alexei (2009) Inverse subsemigroups and classes of finite aperiodic semigroups. Semigroup Forum, 78 (3). pp. 486-497. DOI https://doi.org/10.1007/s00233-008-9121-1

Vernitski, Alexei (2008) Ordered and J-trivial semigroups as divisors of semigroups of languages. International Journal of Algebra and Computation, 18 (07). pp. 1223-1229. DOI https://doi.org/10.1142/s021819670800486x

Vernitski, Alexei (2008) On Using the Join Operation to Define Classes of Algebras. Communications in Algebra, 36 (3). pp. 1088-1096. DOI https://doi.org/10.1080/00927870701776896

Monograph

Kayaturan, Gokce Caylak and Vernitski, Alexei (2018) Encoding shortest paths in graphs assuming the code is queried using bit-wise comparison. Working Paper. Arxiv. (Unpublished)

Vernitski, Alexei (2015) An invariant of scale-free graphs. Working Paper. University of Essex. (Unpublished)

Vernitski, Alexei (2015) A simple technique for choosing and managing secure passwords: passwords with a random on-paper part. Working Paper. University of Essex, Department of Mathematical Sciences, Colchester. (Unpublished)

Conference or Workshop Item

Lisitsa, Alexei and Vernitski, Alexei (2024) On strong anti-learning of parity. In: OL2A 2023: International Conference on Optimization, Learning Algorithms and Applications 2023, 2023-09-27 - 2023-09-29, Ponta Delgada, Portugal. (In Press)

Armani, Federica and Daly, Ian and Vernitski, Alexei and Gillmeister, Helge and Scherer, Reinhold (2023) Maths Anxiety and cognitive state monitoring for neuroadaptive learning systems using electroencephalography. In: IEEE International Conference on Metrology for Extended Reality, Artificial Intelligence and Neural Engineering (MetroXRAINE), 2023-10-25 - 2023-10-27, Milano, Italy. (In Press)

Lisitsa, Alexei and Salles, Mateo and Vernitski, Alexei (2023) Supervised Learning for Untangling Braids. In: 15th International Conference on Agents and Artificial Intelligence (ICAART 2023), 2023-02-22 - 2023-02-24, Lisbon, Portugal. (In Press)

Khan, Abdullah and Vernitski, Alexei and Lisitsa, Alexei (2022) Untangling Braids with Multi-Agent Q-Learning. In: 2021 23rd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2021-12-07 - 2021-12-10, Timisoara, Romania.

Khan, Abdullah and Lisitsa, Alexei and Vernitski, Alexei (2022) Training AI to Recognize Realizable Gauss Diagrams: The Same Instances Confound AI and Human Mathematicians. In: 14th International Conference on Agents and Artificial Intelligence, 2022-02-03 - 2022-02-05.

Karapetyan, Daniel and Vernitski, Alexei (2017) Efficient adaptive implementation of the serial schedule generation scheme using preprocessing and bloom filters. In: International Conference on Learning and Intelligent Optimization: LION 2017, 2017-06-19 - 2017-06-21, Nizhny Novgorod, Russia.

Kayaturan, Gokce Caylak and Vernitski, Alexei (2016) Routing in hexagonal computer networks: How to present paths by Bloom filters without false positives. In: 2016 8th Computer Science and Electronic Engineering (CEEC), 2016-09-28 - 2016-09-30.

Kayaturan, Gökçe Çaylak and Vernitski, Alexei (2016) A Way of Eliminating Errors When Using Bloom Filters for Routing in Computer Networks. In: ICN 2016 : The Fifteenth International Conference on Networks, 2016-02-21 - 2016-02-25, Lisbon, Portugal.

Krol, Kat and Papanicolaou, Constantinos and Vernitski, Alexei and Sasse, M Angela (2015) “Too Taxing on the Mind!” Authentication Grids are not for Everyone. In: HAS 2015 International Conference on Human Aspects of Information Security, Privacy, and Trust, 2015-08-02 - 2015-08-07, Los Angeles, CA.

Vernitski, Alexei (2013) Authentication grid. In: Research seminar, ? - ?. (Unpublished)

Peng, Shuping and Nejabati, Reza and Escalona, Eduard and Simeonidou, Dimitra and Anastasopoulos, Markos and Georgakilas, Konstantinos and Tzanakaki, Anna and Vernitski, Alexei (2012) Performance modelling and analysis of dynamic virtual optical network composition. In: 2012 16th International Conference on Optical Networking Design and Modeling (ONDM), 2012-04-17 - 2012-04-20, Colchester.