# Professor Alexander Balinsky

Professor of Mathematical Physics

- balinskya@cardiff.ac.uk
- +44 (0)29 2087 5528
- Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG

## Overview

### Administrative duties

- WIMCS Research Chair in Mathematical Physics

## Publications

### 2021

- 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), article number: 275. (10.3390/axioms10040275)
- Blackmore, D.et al. 2021. Entropy and ergodicity of Boole-type transformations. Entropy 23(11), article number: 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), article number: 979. (10.3390/sym13060979)
- Balinsky, A. A.et al. 2021. On the dynamics of matrix models for immune clonal networks. Nonlinear Oscillations 23(4), pp. 439-456., article number: 1322.

### 2020

- Balinsky, A. A.et al. 2020. Geometric aspects of the isentropic liquid dynamics and vorticity invariants. Entropy 22(11), article number: 1241. (10.3390/e22111241)
- 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)
- 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. 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

- Spasic, I.et al. 2019. Cohort selection for clinical trials from longitudinal patient records: text mining approach. JMIR Medical Informatics 7(4), article number: e15980. (10.2196/15980)
- 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)
- 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)

### 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), article number: 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 2018DocEng '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 2014Proceedings of the 2014 ACM Symposium on Document Engineering. Association for Computing Machinery pp. 73-80., (10.1145/2644866.2644874)

### 2013

- 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.
- Balinsky, A., Balinsky, H. and Simske, S. J. 2013. Keyword determination based on a weight of meaningfulness. 8375022 [Patent].

### 2012

- 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 Presented at Stoica, A. et al. eds.Proceedings: EST 2012: Third International Conference on Emerging Security Technologies. Los Alamitos, CA: IEEE pp. 99-102., (10.1109/EST.2012.11)
- 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 Presented at 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)

### 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 2011Proceedings of the 11th ACM symposium on Document engineering. New York, NY: Association for Computing Machinery pp. 175-184., (10.1145/2034691.2034731)
- 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)
- 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 Presented at 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)

### 2010

- Balinsky, H., Balinsky, A. and Simske, S. 2010. On the Helmholtz Principle for data mining. Hewlett Packard Development Company. (HPL-2010-133)
- Balinsky, A. and Evans, W. D. 2010. Spectral Analysis of Relativistic Operators. London: Imperial College Press.
- 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., 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 Presented at 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 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 Presented at 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)

### 2009

- 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)
- 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 2009IEEE 2009 Workshop on Applications of Computer Vision WACV 2009, Dec. 7-8 2009, Snowbird Utah. IEEE Computer Society pp. 1-6.
- 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 2009Proceedings 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)

### 2008

- 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), article number: 43514. (10.1063/1.2912229)
- 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.

### 2007

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

### 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 Zero Modes of Weyl-Dirac Operators and their Multiplicity. Bulletin of the London Mathematical Society 34(2), pp. 236-242. (10.1112/S0024609301008736)
- 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)

### 2001

- 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. 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. 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. Stability of One-Electron Molecules in the Brown-Ravenhall Model. Communications in Mathematical Physics 202(2), pp. 481-500. (10.1007/s002200050592)
- 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)

### 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. 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)
- 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)

### 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)

## Teaching

I teach the following modules:

- MA3700 Mathematical Methods for Data Mining
- MA4009 Mathematics of Image Processing

I am a member of the Mathematical Analysis Research Group.