Professor Alexander Balinsky

2025

• Balinsky, A. and Balinsky, A. D. 2025. When can we reuse a calibration set for multiple conformal predictions?. Proceedings of Machine Learning Research 266 , pp.34-42.

2024

• Balinsky, A. A. and Balinsky, A. D. 2024. Enhancing conformal prediction using E-test statistics. Presented at: 13th Symposium on Conformal and Probabilistic Prediction with Applications Milan, Italy 9-11 September 2024.
• Balinsky, A. A. , Bovdi, V. A. and Prykarpatski, A. K. 2024. On the quantum deformations of associative Sato Grassmannian algebras and the related matrix problems. Symmetry 16 (1) 54. (10.3390/sym16010054)
• Prykarpatski, A. K. and Balinsky, A. A. 2024. The two-dimensional boole-type transform and its ergodicity. Journal of Mathematical Sciences 278 , pp.1055–1076. (10.1007/s10958-024-06977-6)

2023

• Balinsky, A. A. et al. 2023. On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold P2(C). Ukrainskyi Matematychnyi Zhurnal 75 (1)(10.37863/umzh.v75i1.7320)
• Hentosh, O. E. et al., 2023. Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type hamiltonian systems. II. Ukrainian Mathematical Journal (10.1007/s11253-023-02140-7)
• Hentosh, O. E. et al., 2023. Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I. Ukrainian Mathematical Journal (10.1007/s11253-023-02129-2)
• Prykarpatski, A. K. and Balinsky, A. A. 2023. Special issue editorial "symmetry of Hamiltonian systems: classical and quantum aspects". Symmetry 15 (1) 96. (10.3390/sym15010096)

2022

• Balinsky, A. A. et al. 2022. On the dynamics of matrix models for immune clonal networks. Journal of Mathematical Sciences 263 , pp.198-214. (10.1007/s10958-022-05920-x)

2021

• Balinsky, A. A. et al. 2021. On the dynamics of matrix models for immune clonal networks. Nonlinear Oscillations 23 (4), pp.439-456. 1322.
• Balinsky, A. A. and Prykarpatski, A. K. 2021. On the finite dimensionality of closed subspaces in Lp(M, dμ) ∩ Lq(M, dν). Axioms 10 (4) 275. (10.3390/axioms10040275)
• Blackmore, D. et al., 2021. Entropy and ergodicity of Boole-type transformations. Entropy 23 (11) 1405. (10.3390/e23111405)
• Prykarpatski, A. K. and Balinsky, A. A. 2021. On symmetry properties of frobenius manifolds and related lie-algebraic structures. Symmetry 13 (6) 979. (10.3390/sym13060979)

2020

• Balinsky, A. A. et al. 2020. Geometric aspects of the isentropic liquid dynamics and vorticity invariants. Entropy 22 (11) 1241. (10.3390/e22111241)
• Byszewski, L. et al., 2020. Solvability, completeness and computational analysis of a perturbed control problem with delays. Mathematics and Statistics 8 (2), pp.187-202. (10.13189/ms.2020.080215)
• Hentosh, O. Y. , Balinsky, A. A. and Prykarpatski, A. K. 2020. The generalized centrally extended Lie algebraic structures and related integrable heavenly type equations. Carpathian Mathematical Publications 12 (1), pp.242-265. (10.15330/cmp.12.1.242-264)
• Hentosh, O. E. , Balinsky, A. A. and Prykarpatski, A. K. 2020. Poisson structures on (non)associative noncommutative algebras and integrable Kontsevich type Hamiltonian systems. Annals of Mathematics and Physics 3 (1), pp.001-006. (10.17352/amp.000010)
• Nouretdinov, I. , Balinsky, A. and Gammerman, A. 2020. Conformal anomaly detection for visual reconstruction using gestalt principles. Presented at: 9th Symposium on Conformal and Probabilistic Prediction with Applications (COPA 2020) Verona, Italy 9-11 September 2020. Vol. 128., pp.1-20.

2019

• Artemovych, O. , Balinsky, A. and Prykarpatski, A. 2019. The quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras. Annals of Mathematics and Physics 2 (1), pp.026-037. (10.17352/amp.000007)
• Hentosh, O. et al., 2019. The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure. Annals of Mathematics and Physics 2 (1), pp.011-025. (10.17352/amp.000006)
• Prykarpatski, A. , Balinsky, A. and Artemovych, O. 2019. Hamiltonian operators and related differential-algebraic Balinsky-Novikov, Riemann and Leibniz type structures on nonassociative noncommutative algebras. Proceedings of the International Geometry Center 12 (4)(10.15673/tmgc.v12i4.1554)
• Spasic, I. et al. 2019. Cohort selection for clinical trials from longitudinal patient records: text mining approach. JMIR Medical Informatics 7 (4) e15980. (10.2196/15980)

2018

• Artemovych, O. D. et al., 2018. Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators. Symmetry 10 (11) 601. (10.3390/sym10110601)
• Krzeminski, D. , Balinsky, H. and Balinsky, A. 2018. Helmholtz principle on word embeddings for automatic document segmentation. Presented at: DocEng 18: 18th ACM Symposium on Document Engineering Halifax, Nova Scotia, Canada 28-31 August 2018. DocEng '18: Proceedings of the ACM Symposium on Document Engineering 2018. New York, NY: ACM. (10.1145/3209280.3229103)
• Percy, I. et al. 2018. Text mining and recommender systems for predictive policing. Presented at: DocEng 18: 18th ACM Symposium on Document Engineering Halifax, Nova Scotia, Canada 28-31 August 2018.

2017

• Balinsky, A. , Balinsky, H. and Simske, S. 2017. On the Helmholtz Principle for data mining. In: Kreinovich, V. ed. Uncertainty Modeling. Vol. 683, Studies in Computational Intelligence Springer. , pp.15-35.

2016

• Balinsky, A. , Balinsky, H. and Simske, S. 2016. Detecting unusual behaviour and mining unstructured data. In: Aston, P. J. , Mulholland, A. J. and Tant, K. M. M. eds. UK Success Stories in Industrial Mathematics. Springer. , pp.181-187. (10.1007/978-3-319-25454-8_23)

2015

• Balinsky, A. , Evans, W. D. and Roger, L. 2015. The analysis and geometry of Hardy's Inequality. Springer.

2014

• Dadachev, B. , Balinsky, A. and Balinsky, H. 2014. On automatic text segmentation. Presented at: DocEng 14: 2014 ACM Symposium on Document Engineering Denver, CO, USA 16-19 September 2014. Proceedings of the 2014 ACM Symposium on Document Engineering. Association for Computing Machinery. , pp.73-80. (10.1145/2644866.2644874)

2013

• Balinsky, A. , Balinsky, H. and Simske, S. J. 2013. Keyword determination based on a weight of meaningfulness. 8375022[Patent]
• Dadachev, B. et al. 2013. Automatic text and data stream segmentation using weighted feature extraction. Presented at: 3rd IMA Conference on Mathematics in Defence Tom Elliott Conference Centre, QinetiQ, Malvern, UK 24 October 2013.

2012

• Balinsky, A. , Evans, W. D. and Lewis, R. T. 2012. Hardy's inequality and curvature. Journal of Functional Analysis 262 (2), pp.648-666. (10.1016/j.jfa.2011.10.001)
• Balinsky, H. , Balinsky, A. and Simske, S. J. 2012. Text documents as social networks. Presented at: SPIE Conference on Imaging and Printing in a Web 2.0 World III Burlingame, CA, USA 25-26 January 2012. Published in: Lin, Q. , Allebach, J. P. and Fan, Z. eds. Imaging and Printing in a Web 2.0 World III. Proceedings of the SPIE Vol. 8302. Bellingham, WA: SPIE. , pp.830207. (10.1117/12.909110)
• Dadachev, B. et al. 2012. On the Helmholtz Principle for Data Mining. Presented at: 2012 Third International Conference on Emerging Security Technologies (EST) Lisbon, Portugal 5-7 September 2012. Published in: Stoica, A. et al., Proceedings: EST 2012: Third International Conference on Emerging Security Technologies. Los Alamitos, CA: IEEE. , pp.99-102. (10.1109/EST.2012.11)

2011

• Balinsky, A. , Balinsky, H. and Simske, S. 2011. Rapid change detection and text mining. Presented at: 2nd IMA Conference on Mathematics in Defence Defence Academy of the United Kingdom, Swindon 20 October 2011.
• Balinsky, A. , Evans, W. D. and Umeda, T. 2011. The Dirac-Hardy and Dirac-Sobolev inequalities in L1. Publications of the Research Institute for Mathematical Sciences 47 (3), pp.791-801. (10.2977/PRIMS/51)
• Balinsky, A. and Mohammad, N. 2011. Non-linear filter response distributions of natural images and applications in image processing. Applied Mathematics and Information Sciences 5 (3), pp.367-389.
• Balinsky, H. , Balinsky, A. and Simske, S. 2011. Automatic text summarization and small-world networks. Presented at: 11th ACM symposium on Document engineering Mountain View, CA, USA 19-22 September 2011. Proceedings of the 11th ACM symposium on Document engineering. New York, NY: Association for Computing Machinery. , pp.175-184. (10.1145/2034691.2034731)
• Balinsky, H. , Balinsky, A. and Simske, S. 2011. Document sentences as a small world. Presented at: 2011 IEEE International Conference on Systems, Man, and Cybernetics (SMC) Anchorage, AK, USA 9-12 October 2011. Published in: Tunstel, E. and Nahavandi, S. eds. Proceedings of the 2011 IEEE International Conference on Systems, Man, and Cybernetics (SMC). Los Alamitos, CA: IEEE. , pp.2583-2588. (10.1109/ICSMC.2011.6084065)
• Kovalerchuk, B. and Balinsky, A. 2011. Visual Data Mining and Discovery in Multivariate Data Using Monotone n-D Structure. Lecture Notes in Computer Science 6581 , pp.297-313. (10.1007/978-3-642-22140-8_20)

2010

• Balinsky, A. , Balinsky, H. Y. and Simske, S. J. 2010. On helmholtz's principle for documents processing. Presented at: 10th ACM Symposium on Document Engineering (DocEng2010) Manchester, UK 21-24 September 2010. Published in: Antonacopoulos, A. , Grmish, M. and Ingold, R. eds. Proceedings of the 10th ACM symposium on Document engineering. New York: ACM Press. , pp.283-286. (10.1145/1860559.1860624)
• Balinsky, A. and Evans, W. D. 2010. Some recent results on Hardy-type inequalities. Applied Mathematics and Information Sciences 4 (2), pp.191-208.
• Balinsky, A. and Evans, W. D. 2010. Spectral Analysis of Relativistic Operators. London: Imperial College Press.
• Balinsky, A. and Mohammad, N. 2010. Sparse natural image statistics and their applications to colorization and compression. Presented at: 17th IEEE International Conference on Image Processing (ICIP) Hong Kong, China 26-29 September 2010. Published in: Siu, W. ed. 2010 17th IEEE International Conference on Image Processing (ICIP), Hong Kong, 26-29 Sept. 2010. Los Alamitos, CA: IEEE. , pp.1661-1664. (10.1109/ICIP.2010.5652168)
• Balinsky, H. , Balinsky, A. and Simske, S. 2010. On the Helmholtz Principle for data mining. Hewlett Packard Development Company(HPL-2010-133)

2009

• Balinsky, A. and Balinsky, H. 2009. On semi-supervised learning and sparsity. Presented at: IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA 11-14 October 2009. Proceedings 2009 International Conference on Systems, Man and Cybernetics October 11-14, 2009 : San Antonio, Texas, USA. Los Alamitos, CA: IEEE. , pp.3083-3087. (10.1109/ICSMC.2009.5345946)
• Balinsky, A. and Mohammad, N. 2009. Colorization of natural images via L1 optimization. Presented at: IEEE Workshop on Applications of Computer Vision Snowbird, UT, USA 7-8 December 2009. IEEE 2009 Workshop on Applications of Computer Vision WACV 2009, Dec. 7-8 2009, Snowbird Utah. IEEE Computer Society. , pp.1-6.
• Balinsky, A. and Mohammad, N. 2009. Non-linear filter response distributions of natural colour images. Lecture Notes on Computer Science 5646 , pp.101-108. (10.1007/978-3-642-03265-3_11)

2008

• Balinsky, A. , Evans, W. and Hundertmark, D. 2008. On inequalities of Hardy-Sobolev type. Banach Journal of Mathematical Analysis (BJMA) 2 (2), pp.94-106.
• Balinsky, A. , Evans, W. D. and Saito, Y. 2008. Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators. Journal of Mathematical Physics 49 (4) 043514. (10.1063/1.2912229)

2007

• Balinsky, A. and Ryan, J. 2007. Some Sharp L2 Inequalities for Dirac Type Operators. Symmetry, Integrability and Geometry: Methods and Applications 3 114. (10.3842/SIGMA.2007.114)
• Balinsky, H. and Balinsky, A. 2007. Affine invariant total variation models. Technical Report.

2006

• Tyukov, A. E. and Balinsky, A. 2006. On localization of pseudo-relativistic energy. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462 (2067), pp.897-912. (10.1098/rspa.2005.1606)

2004

• Balinsky, A. , Laptev, A. and Sobolev, A. V. 2004. Generalized Hardy inequality for the magnetic Dirichlet forms. Journal of Statistical Physics 116 (1-4), pp.507-521. (10.1023/B:JOSS.0000037228.35518.ca)

2003

• Balinsky, A. 2003. Hardy type inequalities for Aharonov-Bohm magnetic potential with multiple singularities. Mathematical Research Letters 10 (2), pp.169-176.

2002

• Balinsky, A. and Evans, W. D. 2002. On the spectral properties of the Brown-Ravenhall operator. Journal of Computational and Applied Mathematics 148 (1), pp.239-255. (10.1016/S0377-0427(02)00583-6)
• Balinsky, A. and Evans, W. D. 2002. On the Zero Modes of Weyl-Dirac Operators and their Multiplicity. Bulletin of the London Mathematical Society 34 (2), pp.236-242. (10.1112/S0024609301008736)

2001

• Balinsky, A. and Evans, W. D. 2001. On the zero modes of Pauli operators. Journal of Functional Analysis 179 (1), pp.120-135. (10.1006/jfan.2000.3670)
• Balinsky, A. , Evans, W. D. and Lewis, R. T. 2001. On the number of negative eigenvalues of Schrödinger operators with an Aharanov-Bohm magnetic field. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences 457 (2014), pp.2481-2489. (10.1098/rspa.2001.0851)
• Balinsky, A. , Evans, W. D. and Lewis, R. T. 2001. Sobolev, Hardy and CLR inequalities associated with Pauli operators in R3 [Letter]. Journal of Physics A: Mathematical and General 34 (5), pp.L19-L23. (10.1088/0305-4470/34/5/101)

1999

• Balinsky, A. and Evans, W. D. 1999. On the stability of relativistic one-electron molecules [Letter]. Journal of Physics A: Mathematical and General 32 (11), pp.L129-L132. (10.1088/0305-4470/32/11/001)
• Balinsky, A. and Evans, W. D. 1999. Stability of One-Electron Molecules in the Brown-Ravenhall Model. Communications in Mathematical Physics 202 (2), pp.481-500. (10.1007/s002200050592)

1998

• Balinsky, A. and Evans, W. D. 1998. On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded Eigenvalues. Letters in Mathematical Physics 44 (3), pp.233-248. (10.1023/A:1007425400991)

1996

• Balinsky, A. and Burman, Y. 1996. Quadratic Poisson brackets and the Drinfeld theory for associative algebras [Letter]. Letters in Mathematical Physics 38 (1), pp.63-75. (10.1007/BF00398299)

1994

• Balinsky, A. 1994. Generalized quantization scheme for central extensions of Lie algebras [Letter]. Journal of Physics A: Mathematical and General 27 (3), pp.L87-L90. (10.1088/0305-4470/27/3/005)
• Balinsky, A. and Burman, Y. M. 1994. Quadratic Poisson brackets compatible with an algebra structure [Letter]. Journal of Physics A: Mathematical and General 27 (18), pp.L693-L696. (10.1088/0305-4470/27/18/008)

1993

• Balinsky, A. and Balinsky, A. I. 1993. On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type [Letter]. Journal of Physics A: Mathematical and General 26 (7), pp.L361-L364. (10.1088/0305-4470/26/7/002)