Professor Karl Schmidt

2023

• Escott-Price, V. and Schmidt, K. M. 2023. Pitfalls of predicting age related traits by polygenic risk scores. Annals of Human Genetics 87(5), pp. 203-209. (10.1111/ahg.12520)
• Schmidt, K. M. and Umeda, T. 2023. Continuum limits for discrete Dirac operators on 2D square lattices. Analysis and Mathematical Physics 13(46) (10.1007/s13324-023-00809-7)
• Simmonds, E. et al. 2023. What does heritability of Alzheimer’s disease represent?. PLoS ONE 18(4), article number: e0281440. (10.1371/journal.pone.0281440)
• Lettington, M. and Schmidt, K. 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658, pp. 62-85. (10.1016/j.laa.2022.10.024)

2021

• Brown, B. M., Schmidt, K. M., Shipman, S. P. and Wood, I. 2021. The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval. Mathematika 67(4), pp. 788-806. (10.1112/mtk.12105)
• Escott-Price, V. and Schmidt, K. M. 2021. Correction to: Probability of Alzheimer's disease based on common and rare genetic variants. Alzheimer's Research and Therapy 13(1), article number: 156. (10.1186/s13195-021-00898-1)
• Escott-Price, V. and Schmidt, K. M. 2021. Probability of Alzheimer’s disease based on common and rare genetic variants. Alzheimer's Research & Therapy 13, article number: 140. (10.1186/s13195-021-00884-7)
• Higham, N. J., Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622, pp. 250-267. (10.1016/j.laa.2021.03.028)
• Escott-Price, V. and Schmidt, K. M. 2021. Challenges of adjusting Single-Nucleotide Polymorphism effect sizes for linkage disequilibrium. Human Heredity 85(1), pp. 24-34. (10.1159/000513303)

2020

• Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20, article number: A61.
• Hill, S. L., Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)

2019

• Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78, pp. 178-199. (10.1007/s10998-018-00275-w)
• Phillips, T. R. L., Schmidt, K. M. and Zhigljavsky, A. 2019. Extension of the Schoenberg theorem to integrally conditionally positive definite functions. Journal of Mathematical Analysis and Applications 470(1), pp. 659-678. (10.1016/j.jmaa.2018.10.032)
• Vivian-Griffiths, T. et al. 2019. Predictive modeling of schizophrenia from genomic data: Comparison of polygenic risk score with kernel support vector machines approach. American Journal of Medical Genetics Part B: Neuropsychiatric Genetics 180(1), pp. 80-85. (10.1002/ajmg.b.32705)

2018

• Baker, E., Schmidt, K. M., Sims, R., O'Donovan, M. C., Williams, J., Holmans, P. and Escott-Price, V. 2018. POLARIS: polygenic LD-adjusted risk score approach for set-based analysis of GWAS data. Genetic Epidemiology 42(4), pp. 366-377. (10.1002/gepi.22117)
• Hill, S., Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34, pp. 170-190. (10.13001/1081-3810.3530)
• Phillips, T. and Schmidt, K. M. 2018. On unbounded positive definite functions. Mathematica Pannonica 26(2), pp. 33-51.

2017

• Lettington, M. C., Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66(8), pp. 1538-1563. (10.1080/03081087.2017.1363153)
• Vronskaya-Robl, M. and Schmidt, K. M. 2017. On perturbation stability of SSA and MSSA forecasts and the supportiveness of time series. Statistics and Its Interface 10(1), pp. 33-46.

2016

• Schmidt, K. M. 2016. On the asymptotics of the spectral density of radial Dirac operators with divergent potential. Integral Equations and Operator Theory 85, pp. 137-149. (10.1007/s00020-015-2276-8)

2015

• Schmidt, K. M. and Umeda, T. 2015. Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials. Letters in Mathematical Physics 105, pp. 1479-1497. (10.1007/s11005-015-0799-1)

2014

• Brunnock, R., Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459, pp. 175-207. (10.1016/j.laa.2014.06.054)
• Hughes, D. and Schmidt, K. M. 2014. Absolutely continuous spectrum of Dirac operators with square-integrable potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144(3), pp. 533-555. (10.1017/S0308210512001187)
• Escott-Price, V., Ghodsi, M. and Schmidt, K. M. 2014. How allele frequency and study design affect association test statistics with misrepresentation errors. Biostatistics 15(2), pp. 311-326. (10.1093/biostatistics/kxt048)
• Schmidt, K. M. and Umeda, T. 2014. Spectral properties of massless Dirac operators with real-valued potentials. Presented at: Spectral and scattering theory and related topics, Kyoto University, Japan, 14-16 December 2011RIMS Kôkyûroku Bessatsu B45: Spectral and Scattering Theory and Related Topics. Kyoto, Japan: pp. 25-30.

2013

• Schmidt, K. M. and Zhigljavsky, A. A. 2013. An extremal property of the generalized arcsine distribution. Metrika 76(3), pp. 347-355. (10.1007/s00184-012-0391-y)
• Kerfriden, P., Schmidt, K. M., Rabczuk, T. and Bordas, S. P. A. 2013. Statistical extraction of process zones and representative subspaces in fracture of random composites. International Journal for Multiscale Computational Engineering 11(3), pp. 253-287. (10.1615/IntJMultCompEng.2013005939)
• Brown, B. M., Eastham, M. S. P. and Schmidt, K. M. 2013. Periodic differential operators. Operator Theory: Advances and Applications Vol. 230. Basel: Birkhäuser.

2012

• Escott-Price, V., Schmidt, K. M., Vedernikov, A., Owen, M. J., Craddock, N. J., Holmans, P. A. and O'Donovan, M. C. 2012. Permutation-based approaches do not adequately allow for linkage disequilibrium in gene-wide multi-locus association analysis. European Journal of Human Genetics 20(8), pp. 890-896. (10.1038/ejhg.2012.8)
• Brown, B. M. and Schmidt, K. M. 2012. On the HELP Inequality for Hill Operators on Trees. In: Brown, B. M., Lang, J. and Wood, I. G. eds. Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends. Operator Theory: Advances and Applications Vol. 219. Basel: Springer, pp. 21-36., (10.1007/978-3-0348-0263-5_2)

2011

• Korotyaev, E. L. and Schmidt, K. M. 2011. On the resonances and eigenvalues for a 1D half-crystal with localised impurity. Journal für die reine und angewandte Mathematik (Crelles Journal) 2012(670), pp. 217-248. (10.1515/CRELLE.2011.153)

2010

• Schmidt, K. M. 2010. Spectral properties of rotationally symmetric massless dirac operators. Letters in Mathematical Physics 92(3), pp. 231-241. (10.1007/s11005-010-0393-5)

2009

• Brown, B. M., Christiansen, J. S. and Schmidt, K. M. 2009. Spectral properties of a q-Sturm–Liouville Operator. Communications in Mathematical Physics 287(1), pp. 259-274. (10.1007/s00220-008-0623-1)
• Evans, W. D. and Schmidt, K. M. 2009. A discrete Hardy-Laptev-Weidl type inequality and associated Schrödinger-type operators. Revista Matemática Complutense 22(1), pp. 75-90.
• Schmidt, K. M. and Zhigljavsky, A. A. 2009. A characterization of the arcsine distribution. Statistics & Probability Letters 79(24), pp. 2451-2455. (10.1016/j.spl.2009.08.018)

2008

• Escott-Price, V. and Schmidt, K. M. 2008. On multiple-testing correction in genome-wide association studies. Genetic Epidemiology 32(6), pp. 567-573. (10.1002/gepi.20331)
• Brown, B. M., Langer, M. and Schmidt, K. M. 2008. The HELP inequality on trees. Presented at: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8 January - 29 June 2007 Presented at Exner, P. et al. eds.Analysis on Graphs and Its Applications. Proceedings of Symposia in Pure Mathematics Vol. 77. Providence, RI: American Mathematical Society pp. 337-354.
• Aumann, S., Brown, B. M. and Schmidt, K. M. 2008. A Hardy-Littlewood-type inequality for the p-Laplacian. Bulletin of the London Mathematical Society 40(3), pp. 525-531. (10.1112/blms/bdn035)
• Eastham, M. S. P. and Schmidt, K. M. 2008. Asymptotics of the spectral density for radial dirac operators with divergent potentials. Publications of the Research Institute for Mathematical Sciences 44(1), pp. 107-129. (10.2977/prims/1207921078)

2007

• Monaquel, S. J. and Schmidt, K. M. 2007. On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems. Journal of Computational and Applied Mathematics 208(1), pp. 82-101. (10.1016/j.cam.2006.10.043)

2006

• Schmidt, K. M. 2006. Exceptional coupling constants for the Coulomb-Dirac operator with anomalous magnetic moment. Journal of Computational and Applied Mathematics 194(1), pp. 17-25. (10.1016/j.cam.2005.06.022)
• Escott-Price, V. and Schmidt, K. M. 2006. Susceptibility of Biallelic Haplotype and Genotype Frequencies to Genotyping Error. Biometrics 62(4), pp. 1116-1123. (10.1111/j.1541-0420.2006.00563.x)
• Escott-Price, V. and Schmidt, K. M. 2006. Individual SNP Allele Reconstruction from Informative Markers Selected by a Non-Linear Gauss-Type Algorithm. Human Heredity 62(2), pp. 97-106. (10.1159/000096097)

2005

• Eastham, M. S. P. and Schmidt, K. M. 2005. Absence of high-energy spectral concentration for Dirac systems with divergent potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135(4), pp. 689-702. (10.1017/S0308210500004078)
• Escott-Price, V., Holmans, P. A., Schmidt, K. M. and Craddock, N. J. 2005. Design of Case-controls Studies with Unscreened Controls. Annals of Human Genetics 69(5), pp. 566-576. (10.1111/j.1529-8817.2005.00175.x)

2004

• Kalf, H. and Schmidt, K. M. 2004. Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment. Journal of Differential Equations 205(2), pp. 408-423. (10.1016/j.jde.2004.04.009)
• Brown, B. M., Eastham, M. S. P., Hinz, A. M. and Schmidt, K. M. 2004. Distribution of eigenvalues in gaps of the essential spectrum of Sturm-Liouville operators - a numerical approach. Journal Of Computational Analysis And Applications 6(1), pp. 85-95.
• Schmidt, K. M. 2004. On the integrability of differential equations by quadratures according to Maximovič. Journal of Computational and Applied Mathematics 171(1-2), pp. 393-410. (10.1016/j.cam.2004.01.021)

2003

• Schmidt, K. M. 2003. Spectral properties of Dirac systems with coefficients infinite at infinity. RIMS Kokyuroku 1315, pp. 24-31.
• Escott-Price, V. and Schmidt, K. M. 2003. Approximate projectors in singular spectrum analysis. SIAM Journal on Matrix Analysis and Applications (SIMAX) 24(4), pp. 932-942. (10.1137/S0895479801398967)
• Schmidt, K. M. 2003. Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit. Proceedings Of The American Mathematical Society 131(4), pp. 1205-1214.

2002

• Schmidt, K. M. 2002. Eigenvalues in gaps of perturbed periodic Dirac operators: numerical evidence. Journal of Computational and Applied Mathematics 148(1), pp. 169-181. (10.1016/S0377-0427(02)00580-0)
• Schmidt, K. M. 2002. A short proof for Bargmann-type inequalities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 458(2027), pp. 2829-2832. (10.1098/rspa.2002.1021)

2001

• Schmidt, K. M. 2001. A remark on a paper by Evans and Harris on the point spectra of Dirac operators. Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics 131(A), pp. 1237-1243. (10.1017/S0308210500001360)
• Schmidt, K. M. 2001. An Application of Gesztesy–Simon–Teschl Oscillation Theory to a Problem in Differential Geometry. Journal of Mathematical Analysis and Applications 261(1), pp. 61-71. (10.1006/jmaa.2001.7471)

2000

• Schmidt, K. M. 2000. A Remark on The Essential Spectra of Dirac Systems. Bulletin of the London Mathematical Society 32(1), pp. 63-70. (10.1112/S0024609399006463)
• Schmidt, K. M. 2000. Relative Oscillation–Non-Oscillation Criteria for Perturbed Periodic Dirac Systems. Journal of Mathematical Analysis and Applications 246(2), pp. 591-607. (10.1006/jmaa.2000.6821)
• Schmidt, K. M. 2000. Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm-Liouville Operators. Communications in Mathematical Physics 211(2), pp. 465-485. (10.1007/s002200050822)

1999

• Schmidt, K. M. 1999. Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrodinger operators in the plane. Proceedings of the American Mathematical Society 127(8), pp. 2367-2374.

1998

• Schmidt, K. M. and Yamada, O. 1998. Spherically symmetric dirac operators with variable mass and potentials infinite at infinity. Publications Of The Research Institute For Mathematical Sciences 34(3), pp. 211-227.
• Brown, B. M., Eastham, M. S. P., Hinz, A. M., Kriecherbauer, T., McCormack, D. K. R. and Schmidt, K. M. 1998. Welsh Eigenvalues of radially periodic Schrödinger operators. Journal of Mathematical Analysis and Applications 225(1), pp. 347-357. (10.1006/jmaa.1998.6048)

1997

• Schmidt, K. M. 1997. Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity. Mathematical Proceedings of the Cambridge Philosophical Society 122(2), pp. 377-384.

1996

• Schmidt, K. M. 1996. Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 126(5), pp. 1087-1096. (10.1017/S0308210500023271)

1995

• Schmidt, K. M. 1995. A remark on boundary value problems for the Dirac operator. Quarterly Journal of Mathematics 46(184), pp. 509-516.
• Schmidt, K. M. 1995. Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators. Forum Mathematicum 7(7), pp. 459-475. (10.1515/form.1995.7.459)

1993

• Schmidt, K. M. 1993. On the essential spectrum of Dirac operators with spherically symmetric potentials. Mathematische Annalen 297(1), pp. 117-131. (10.1007/BF01459491)
• Schmidt, K. M. 1993. On the genericity of nonvanishing instability intervals in periodic Dirac systems. Annales De L'Institut Henri Poincare-Physique Theorique 59(3), pp. 315-326.