Academics

3 posts

Physics diploma thesis

Physics Diploma Thesis: Exploration of different confinement and hyperfine interactions in a constituent quark model for baryons

Reinhold Kainhofer, January 2003

Abstract

In this work we investigate the spectra of light and strange baryons for different effective interactions between constituent quarks. In particular we examine the influence of an additional Coulomb term on top of a linear confinement and variants of the hyperfine interactions derived from Goldstone-boson-exchange (GBE) dynamics; the latter include specifically pseudoscalar, vector and scalar exchanges. We present our own parametrization of an extended GBE constituent quark model (CQM) with all but spin-orbit forces included. The resulting spectra produce most states to a high accuracy, and the correct level orderings in the nucleon, $\Lambda$ and $\Sigma$ spectra can be obtained.

The only remaining problems are the states N(1680) and N(1675), which cannot be described in accordance with their almost degeneracy observed in experiment, and the Lambda(1405), which is obviously much influenced by the nearby KN threshold and can probably not be explained by a constituent quark model relying on {QQQ} configurations only.

The version of the extended GBE CQM constructed here is mainly intended to serve as a basis for the inclusion of the missing spin-orbit terms of the meson-exchange potentials, which is the central subject matter in a parallel diploma work.

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Download the whole work as a PDF file (950 kB).

PhD Thesis (Dissertation in Technical Mathematics, Graz University of Technology)

R. Kainhofer: Quasi-Monte Carlo Algorithms with Applications in Numerical Analysis and Finance

Abstract

This thesis is devoted to the development and application of various Quasi-Monte Carlo methods for numerical integration and also for the solution of differential equations. In contrast to Monte Carlo schemes, they employ deterministic sequences with good distribution properties. This has the effect that explicit error bounds can be shown, and the numerical error usually is improved compared to Monte Carlo methods.

First, a dividend barrier model from risk theory is investigated, where the dividend payments and the survival probability can be described by integro-differential equations. Several different schemes for their solution are presented and compared.

Second, a Quasi-Monte Carlo algorithm for the solution of retarded differential equations is developed. While for slowly changing equations conventional methods perform better, for heavily oscillating equations Quasi-Monte Carlo schemes become competitive and might even be applied in unstable regions where conventional schemes fail.

Finally, the problem of numerical integration of singular functions with respect to a given density is explored. A convergence theorem is proved, and an adapted construction schemes for non-uniformly distributed low-discrepancy sequences is presented. As a numerical example from finance the valuation of an Asian option is investigated. Several different scheme for the singular non-uniform integration are compared, and again the Quasi-Monte Carlo approach turns out to be the most beneficial.

Download: PDF (1.5MB)

Zusammenfassung

Diese Dissertation widmet sich der Entwicklung diverser Quasi-Monte Carlo (QMC) Verfahren zur numerischen Integration sowie zur Lösung von Differentialgleichungen. Im Gegensatz zu Monte Carlo Verfahren basieren diese auf deterministischen Folgen mit guten Verteilungseigenschaften. Dadurch können explizite Fehlerschranken angegeben und numerische Fehler deutlich verbessert werden.

Der erste Teil beschätigt sich mit einem Modell einer Dividendenschranke in der Risikotheorie, wobei die Dividenden und die Überlebenswahrscheinlichkeit durch Integro-Differentialgleichungen beschrieben werden. Verschiedene Schemata zu deren Lösung werden präsentiert und verglichen.

Im zweiten Teil wird ein QMC Algorithmus für retardierte Differentialgleichungen entworfen. Während für sich langsam ändernde Gleichungen konventionelle Runge-Kutta Verfahren bessere Ergebnisse liefern, können Quasi-Monte Carlo Methoden bei schnell oszillierenden Gleichungen teilweise sogar in Bereichen angewendet werden, wo konventionelle Verfahren versagen.

Im dritten Teil wird das Problem der numerischen Integration von singulären Funktionen bezüglich beliebiger Dichten behandelt. Neben einem Konvergenzbeweis wird eine Folgenkonstruktion von Hlawka and Mück adaptiert. Als Beispiel aus der Finanzwissenschaft dient die Bewertung asiatischer Optionen, wobei mehrere Methoden zur Auswertung des singulären Integrals verglichen werden. Auch hier zeigt sich, dass der QMC Zugang am vorteilhaftesten ist.

Mathematical Research (during my University career)

My main research areas were:

  • Quasi-Monte Carlo methods and other numerical methods
  • Actuarial mathematics

Scientific Publications

Nr.Title of the paperFieldDownload
1)B. Aichernig and R. Kainhofer: Modeling and validating hybrid systems using VDM and Mathematica.
In C.Michael Holloway, editor, Lfm2000, Fifth NASA Langley Formal Methods Workshop, Williamsburg, Virginia, June 2000, number CP-2000-210100, pages 35-46. NASA, June 2000.		CSpdf
2)H. Albrecher and R. Kainhofer: Risk theory with a non-linear dividend barrier, Computing 68 (2002), No.4, 289-311.Mathpdf
3)H. Albrecher, R. Kainhofer and R.F. Tichy: Simulation methods in ruin models with non-linear dividend barriers, Math. Comput. Simulation 62 (2003), 277-287.MathAbstract: pdf
Paper: pdf
4)H. Albrecher, R. Kainhofer and R.F. Tichy: Efficient simulation techniques for a generalized ruin model, Grazer Math. Ber., Nr. 345 (2002), 79-110.Mathpdf
5)R. Kainhofer: QMC Methods for the solution of delay differential equations, J. Comp. Appl. Math., vol. 155/2 (2003), 239-252.Mathpdf
6)R. Kainhofer and R.F. Tichy: QMC Methods for the solution of differential equations with multiple delayed arguments, Grazer Math. Ber., Nr. 345 (2002), 111-129.Mathpdf
7)R. Kainhofer and R.F. Tichy: QMC Methods for the solution of delay differential equations, Proc. Appl. Math. Mech. (PAMM), Proceedings of the GAMM 2002 meeting, 2 (2003), 503-504.Mathpdf
8)J. Hartinger, R. Kainhofer and R. Tichy: Quasi-Monte Carlo algorithms for unbounded, weighted integration problems, Journal of Complexity, 20/5 (2004), 654-668.Mathpdf
9)R. Kainhofer: The CSSSave package: Extending the built-in HTMLSave function with style sheets, 2003, Proceedings of PrimMath[2003].CSpdf
10)R. Kainhofer and R. Simonovits: M@th Desktop and MD Tools: Mathematics and Mathematica Made Easy for Students, 2003, Proceedings of PrimMath[2003].CS, Didact.pdf
11)K. Glantschnig, R. Kainhofer, W. Plessas, B. Sengl, R.F. Wagenbrunn: Extended Goldstone-Boson-Exchange Constituent Quark Model, 2004, European Physical Journal A, accepted.Phys.ArXiv
12)J. Hartinger and R. Kainhofer: Non-uniform low-discrepancy sequence generation and integration of singular integrands, In: H. Niederreiter, D. Talay (Eds.): Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, 2006.Mathpdf
13)J. Hartinger, R. Kainhofer, and V. Ziegler: On the corner avoidance properties of various low-discrepancy sequences, 2005, in press.MathPDF
14)R. Kainhofer, M. Predota, and U. Schmock: The New Austrian Annuity Valuation Table AVÖ 2005R, Mitteilungen der Aktuarvereinigung Österreichs, Heft 13, Seiten 55-135, 2006.MathPDF
15)R. Kainhofer, M. Predota, and U. Schmock: Die neue österreichische Rententafel AVÖ 2005R, Versicherungswirtschaft, 10/2006, volume 61, 847-851, 2006.MathPDF
16)P. Grandits, R. Kainhofer, and G. Temnov: On the impact of hidden trends for a compound Poisson model with Pareto-type claims, International Journal of Theoretical and Applied Finance, accepted, 2010.Math 
17)R. Kainhofer: A MusicXML Test Suite and a Discussion of Issues in MusicXML 2.0, Proceedings of the LAC 2010 Conference, Utrecht, 2010.CS, MusicPDF
18)R. Kainhofer: OrchestralLily: A Package for Professional Music Publishing with LilyPond and LaTeX, Proceedings of the LAC 2010 Conference, Utrecht, 2010.CS, MusicPDF
19)R. Kainhofer: An extensive MusicXML 2.0 test suite, Proceedings of the 7th International Symposion on Computer Music Modelling and Retrieval (CMMR) 2010, Malaga, 2010.CS, MusicPDF

The following is not one of my publications, but about my RK Fonts:

  • Michael H. Zach: Varia Meroitica II, Kommentar zu den Fonts RK Meroitic, Göttinger Miszellen 173 (1999), 197-202

Scientific Talks and Presentations

Nr.Title of the talk 
0)R. Kainhofer, M. Lacher, T. Triffterer, A. Soucek: Beyond the horizon: The history of satellites. Presentation held at the 5th Int. EURISY youth forum 1996 in Bristol / UK.Text: html
1)Goldstone Bosonen Austausch (GBE) chirales Konstituentenquark-Modell. Talk held at the 32. Summer school for high energy physics, Maria Laach, Germany. September 2000.Abstract: ps
2)Quasi-Monte Carlo Runge Kutta methods for delay differential equations. Presentation held at GAMM 2002, Augsburg, Germany. March 26, 2002.Abstract: pdf
Slides: pdf
3)Quasi-randomized schemes for the solution of retarded differential equations. Talk held at the Dagstuhl Seminar 2401 “Algorithms and Complexity for Continuous Problems”, Schloss Dagstuhl, Wadern, Germany. Sept. 29 – Oct. 4, 2002.Abstract: pdf
Slides: pdf
4)Hlawka-Mück techniques for option pricing – Quasi-Monte Carlo methods with NIG distribution. Talk given at MCQMC 2002, Singapore. November 25, 2002.Abstract: pdf
Slides: pdf (ppower4)
5)Numerical solution of delayed differential equations using QMC methods. Quasi-randomized schemes for heavily varying equations. Talk given at the FSP workshop, Linz, Austria. February 28, 2003.Slides: pdf (ppower4)
6)Quasi-Monte Carlo Algorithms with Applications in Numerical Analysis and Finance. Rigorosumsvortrag, Inst. f. Mathematik, TU Graz, Austria. May 16, 2003.Slides: pdf (ppower4)
7)Transformation methods for the creation of non-uniformly distributed low-discrepancy sequences. MCM2003, Berlin. September 2003.Abstract: pdf, Slides: pdf (ppower4)
8)The CSSSave` Package for Mathematica – Extending the built-in HTMLSave function with (cascading) style sheets. PrimMath[2003], Zagreb. September 2003.Abstract: pdf
Slides: pdf
9)M@th Desktop and MD Tools – Mathematics and Mathematica Made Easy for Students. PrimMath[2003], Zagreb. September 2003.Abstract: pdf
Slides: pdf
10)Entwicklung sublinearer Dividendenmodelle und deren numerische Behandlung. FAM, TU Wien. November 2003.Slides: pdf
11)QMC integration of improper integrals. An overview with non-uniform sequences in mind. MC2QMC 2004, Juan-les-Pins, France. June 2004.Abstract: pdf
Slides: pdf (ppower4)
12)Zur Erstellung der neuen Österreichischen Rententafeln AVÖ 2005R – Vorläufiger Stand der Arbeitsgruppe. FAM, Vienna University of Technology. February 17, 2005.Slides: pdf
13)Rohentwurf der neuen Österreichischen Rententafel AVÖ 2005R – Vorläufiger Stand der Arbeitsgruppe. Aktuarvereinigung Österreichs (Actuarial Association of Austria), Vienna. March 3, 2005.Slides: pdf
14)Die neue Österreichische Rententafel AVÖ 2005R – Endresultat der Arbeitsgruppe der AVÖ. Versicherungsverband Österreichs (Austrian Association of Insurance Companies), Vienna, Austria, April 26, 2005.Slides: pdf
15)Die Rentenversicherungssterbetafel AVÖ 2005R. General Assembly of the Actuarial Association of Austria, Vienna. May 12, 2005.Slides: pdf
Additional slides: pdf
16)Quasi-Monte Carlo Methoden – Am Schnittpunkt von numerischer Analysis, Zahlentheorie und Finanzmathematik. Lecture Series “Wissenswertes aus der Mathematik”, Vienna University of Technology, Austria. June 20, 2005.Slides: pdf
17)Die Rentenversicherungssterbetafel AVÖ 2005R. Financial Market Authority (FMA) of Austria, Vienna. April 10, 2006.Slides: pdf
Additional slides: pdf
18)Corner avoidance properties of various low discrepancy sequences. MCQMC 2006, Ulm, Germany. August 18, 2006.Slides: pdf
19)Erstellung einer offiziellen österreichischen Rententafel und deren Anwendung auf ein stochastisches Lebensversicherungsmodell. Workshop for young mathematicians, Deutsche Aktuarsakademie (DAA), Reisensburg, Günzburg, Germany. September 22, 2007.Slides: pdf
20)Die Erstellung von Rechnungsgrundlagen – Ausflug eines Mathematikers in die Praxis. Kolloquim “Finanz- und Versicherungsmathematik in Theorie und Praxis”, Graz University of Technology, Graz, Austria. January 11, 2008.Slides: pdf
21)Stochastische Simulation in der Lebensversicherung – Monte-Carlo Methoden und deren Anwendung in Versicherungen, ÖFdV-Seminar “Stochastische Simulation”, Vienna, Austria, December 10, 2009.Slides: pdf
22)OrchestralLily: A Package for Professional Music Publishing with LilyPond and LaTeX, LAC 2010, Utrecht, Netherlands, May 3, 2010.Slides: pdf, Handout: pdf
23)A MusicXML Test Suite and a Discussion of Issues in MusicXML 2.0, LAC 2010, Utrecht, Netherlands, May 4, 2010.Slides: pdf, Handout: pdf
24)An extensive MusicXML 2.0 Test Suite, 7th International Symposion on Computer Music Modelling and Retrieval (CMMR) 2010, Poster-Presentation, Málaga, Spain, June 22, 2010.Poster (A4): pdf, Presentation: pdf

 Academic Theses

Nr.TitleField 
1)R. Kainhofer: Mit HERA und ZEUS durch die Götterwelt der Teilchenphysik: Moderne Beschleuniger- und Detektortechnik am Beispiel des Deutschen Elektronen-Synchrotrons, Fachbereichsarbeit von Reinhold Kainhofer, Borromäum, Salzburg, February 1996Physics
2)R. Kainhofer: Die numerische Simulation von Transportgleichungen mittels Quasi-Monte Carlo Methoden, Diplomarbeit aus Technischer Mathematik, Technische Universität Graz, August 2000.MathematicsPDF
3)R. Kainhofer: Exploration of different confinement and hyperfine interactions in a constituent quark model for baryons, Diploma thesis in theoretical physics, Karl-Franzens-University Graz, January 2003PhysicsAbstract: html
Download: PDF (950 kB)
4)R. Kainhofer: Quasi-Monte Carlo Algorithms with Appplications in Numerical Analysis and Finance, PhD thesis in Technical Mathematics, Graz University of Technology, April 2003MathematicsAbstract: html
Download: PDF (1.5 MB)

Technical Reviews

Nr.Technical Review 
1)R. Kainhofer: IETF Review of the RFC 2446bis-07 draft: iCalendar Transport-Independent Interoperability Protocol (iTIP). September 8, 2008.PDF
2)R. Kainhofer: IETF Review of the RFC 2447bis-05 draft: iCalendar Message-Based Interoperability Protocol (iMIP). October 1, 2008.PDF

Significant contributions and involvement in the creation of the following technical standards:

Nr.Technical Standard 
1)B. Desruisseaux (Ed.): Internet Calendaring and Scheduling Core Object Specification (iCalendar). RFC 5545. September 2009.Text
2)C. Daboo (Ed.): iCalendar Transport-Independent Interoperability Protocol (iTIP). RFC 5546. December 2009.Text
3)A. Melnikov (Ed.): iCalendar Message-Based Interoperability Protocol (iMIP). Draft RFC 6047. December 2010.Text