Manuscripts

• 201017: Finally, after many years of research and after publication of several preliminary papers, in proceedings volumes and elsewhere, my findings were collected and published in "Entropy", cf. Paradigms of Cognition. The paper may be difficult to read for many as unfamiliar concepts and ways of thinking are introduced and also as the material is presented in its presently most general form. I hope to follow up with easier-to-read applications demonstrating the potential of the theory developed.
• 071015: A confession: In "Some bounds on the logarithmic function", see the entry 040604, it is understood that the material leads to a proof of Lamberts continued fraction expansion of the logarithmic function (equation (28) of the article). This does not seem to be so, as noted by some previous students and by professor Lawrence Paulson. So, on closer inspection, I have not been able to provide a proof of the expansion based on the rather elementary material discussed in the article. So now it is more of a challenge to the reader to find such a proof. To my mind that would be interesting as it will lead to the desired expansion in a more natural way than via the classical considerations going back to Gauss, based on properties of hypergeometric functions.
• 070912: "Beyond Shannon with examples from Geometry, Statistics and Information Theory". Slides from WITMSE 2012, to a great extent focusing on isotone regression and a surprising connection with a problem of universal coding, cf. my more formal manuscript here.
• 250412: Computation of universal objects for distributions over co-trees. To appear in IEEE Trans. Inform. Theory.
• 120811: I forgot to put this joint paper with Peter Harremoes on Zipf's law on my homepage. The published version from 2005 and the exact reference can be found here.
• 110811: "Cognition and inference in an abstract setting", slides presented at WITMSE 2011
• Memorial colloquium for Igor Vajda: see the program here. And slides from my own presentation, here.
• 070910: "Cognition and inference", internal lunch presentation, dealing with the philosophy of information in an abstract framework. Contains general Pythagorean theorem (related to MaxEnt and to I-projections), discussion of Tsallis entropy and connection to exponential families. I presented similar stuff at meetings during the summer, but found that the chosen slides are probably the most easily accessible. For homepages of the other meetings, see Leipzig conference, Tampare workshop, Prague Stochastics
• 100310:"From truth, belief and knowledge to Tsallis entropy", seminar at NBI, Copenhagen (similar to entry below).
• 061209: "Philosophy of information", talk at workshop in Paris, see link here
• 051009: "Towards operational interpretations of generalized entropies", contribution to the proceedings from a workshop in Kyoto, see second entry from 180709. Added note 160210: All publications from workshop here
• 020909: Slides from seminar "How to keep the expert honest or, how to prevent misinformation"
• 180709: Manuscript with Henrik D. Petersen "Computation of universal objects for distributions over co-trees", submitted for publication
• 180709: "Paradigms of cognition", talk at workshop in Kyoto see link here.
• 040509: Two manuscripts for presentation at ISIT2009: "Universal coding for distributions over co-trees", "On truth, belief and knowledge".
• 030409: "Interaction between Truth, Belief and Knowledge as the key to entropy measures of statistical physics", slides from talk at MECO34, Leipzig.
• 300908: In Danish: "Sandsynlighed og Information" (on information theory and probability). Published in "Matilde", Danish Math. Society.
• 100908: "On the generation of measures of entropy, divergence and complexity". Slides from talk in Lausanne. Part of this also presented 280808 at the workshop in Budapest, celebrating the 70 year birthday of Imre Csiszar.
• 210708:
  • A: "Interaction between Truth and Belief as the key to non-extensive statistical physics", slides from presentation at SigmaPhi2008, cf. this link to conference web-site.
  • B: Material above (in abridged form) was also presented at an informal poster session at ISIT2008.
  • C: The talk at SigmaPhi2008 was part of the mini-symposium "Fisher Information and Geometry", organised jointly with Jan Naudts and Peter Harremoes. The talks at the symposium will be made available at PH's homepage.
  • D: "Intrinsic Methods for Optimization Problems", slides from presentation at ISIT2008 cf. this link to to the conference web-site
• 290408: "Intrinsic methods for optimization problems", manuscript to appear in ISIT2008 proceedings
• 100408: Slides from a seminar on "Optimization inspired by Information Theory"
• 141207: I noted recently that many of my earlier papers are available electronically. I assume that the following three papers on more basic problems of topological measure theory are still of some interest: "Compactness in spaces of measures" and "Measure Spaces Connected by Correspondences" and "A unified approach to Riesz type representation theorems" (last ms. is joint work with David Pollard).
• 091207: "Power laws and other heavy-tailed distributions and associated codes related to Zipf's law", my presentation at "5th Trier Symposium on Quantitative Linguistics"
• 2910907: "Information and Games", my slides (except for two figures) for presentation at"Facets of Entropy", read more here.
• 291007: "Game Theoretical Optimization Techniques inspired by Information Theory", submitted to "Journal of Global Analysis".
• 210907: "Exponential Families and MaxEnt Calculations for Entropy Measures of Statistical Physics", to appear in an AIP-proceedings volume from conference CTnext in Catania. I will also post it soon on arXiv server (cond.mat).
• 210707: "Stability and Flexibility of natural languages (Zipf's law)", from a short talk and poster presentation at "Stat.Phys. Soc.Dyn.: Opinions, Semiotic Dyn. and Language, Erice 2007"
• 070707: Henrik Densing Petersen and FT: "Games, Entropy and Composability", presentation at CTnext2007, Catania
• 070707: Slides for poster presentation at ISIT2007, Nice and here link to ISIT2007
• 130607: Go to this page for rather extensive slides as used for plenary talk at NAOP2007, Isfahan
• 170507: Though intended for teaching purposes, this simple ms. on MaxEnt etc. may interest you
• 180307: Factorization and escorting in the game-theoretical approach to non-extensive entropy measures (appeared in Physica A, 365 (2006), 91-95).
• 180806: Combinatorics in relation to continued fractions, OH's for short communication at ICM 2006 Separately, click here for illuminating diagram (could not get separating lines right - to be adjusted later!
• 180806: Between truth and description, OH's for plenary talk at PragueStochastics 2006
• 180806: Non-stationary Markov chains related to continued fractions, pages for poster presentation at PragueStochastics 2006
• 090806: The Quantitative Theory of Information, joint ms with Peter Harremoes. To appear as a chapter in HPI: "Handbook on the Philosophy of Information", an ambitious project to make available for the first time in a coherent way views of several different disciplines on the concept of information. You should click on this link for more on the HPI-project, itself part of a larger project by Elsevier to publish a multi-volume "Handbook of the Philosophy of Science".
• 030606: Nash equilibrium in a game of calibration, joint ms with Glonti, Harremoes and Khechinashvili, to appear in Teor. Verejatnost...., click here for journal (translation of)
• 020606: Between truth and description, ms to be presented at PragueStochastics2006, look here
• 290306: Combinatorics of continued fractions, Slides used at a colloquium talk at DTU.
• 090805: The game-theoretical approach to non-extensive entropy measures, Slides for presentation at NEXT2005, Crete.
• 080904: Two general games of information, manuscript to be presented at ISITA2004.
• 180804: "Entropy and Index of Coincidence, lower bounds". Submitted for publication. NOTE: I think most use pdf-files and will not longer post also ps-files.
• 040604: "Some bounds for the logarithmic function", a "mini-essay", to appear in Inequal. Th. & Appl., Vol. 4, edited by Y.J. Cho, J.K. Kim and S.S. Dragomir. Posted on RGMIA Research Report Collection, 7(2), Article 6, 2004, accessible here.
• 220104: Manuscript which appeared in Physica A 340 (2004), 11-31 as one of the introductory papers, in special issue of Physica A devoted to Non Extensive Thermodynamics and Physical applications: "Entropy and Equilibrium via Games of Complexity" same, pdf
• Dec.3,2003: Manuscripts submitted to ISIT2004:
  • G. Kaniadakis and FT:"Entropy measures of physics via complexity" or same, pdf
  • B. Fuglede and FT: "Jensen-Shannon Divergence and Hilbert space embedding" or same, pdf
  • "Generalized notions of block symmetry for discrete memoryless channels" or same, pdf
• Two manuscripts from Bangalore proceedings (2002 IEEE Information Theory Workshop):
  • "Block Symmetry in Discrete Memoryless Channels" same, pdf
  • "Entropy, some new lower Bounds", same, pdf.
• 200303: Manuscript submitted for presentation at ITW2003 in Hong Kong (but event did not take place because of SARS):
  "Norm-based measures of Discrimination and Variation" (ps).
• 070303: Incomplete manuscript put here - click!. More final version to follow some other time!

• "Information Theory at the Service of Science" or same, pdf

  Accepted for publication in "Csiszar's Balatonlelle collection".
• Joint work with Peter Harremoes, published in the electronic journal "entropy" : MaximumEntropyFundamentals.ps or same.pdf
• ms. likewise published by "entropy" : Inf.Th.toolkit.ps or same.pdf
• Joint work with Boris Ryabko, now available electronically from homepage of Journal of Complexity in pdf-format:
  On Asymptotically Optimal Methods of Prediction and Adaptive Coding for Markov Sources
  but possibly simpler to download here: submitted ms.ps or submitted ms.pdf
• Paper, jointly with Peter Harremoes, IEEE Trans. Inform. Theory, vol. 47, november:
  Inf.Diagrams or same.pdf
• Jointly with Boris Ya. Ryabko (comment: By mistake of ISIT2001, this did NOT appear in conference proceedings volume): ISIT2001.Order or same.pdf
• Jointly with Peter Harremoes: ISIT2001.Diagrams or same.pdf
• ISIT2001.Trees or same.pdf
• Article from IEEE Trans. Information Theory vol. IT-46, pp. 1602 - 1609, July 2000, here possibly not final version: Ineq.Discrim.ps
• Publication from the electronic journal JIPAM, 2001, vol.2 no.2, article 25: Ent.Bds.ps or same.pdf
• Expository manuscript presented at a didactic colloquium in Eichstaett, Germany:
  Entropy and Codes.ps or same.pdf
  

The manuscripts ISIT2002xxx are not intended for publication as they are but have been submitted to ISIT2002. If approved they will be presented at ISIT2002 in Lausanne and printed in condensed form in the proceedings volume. The manuscripts may also form the basis of other publications.

• Joint work with Peter Harremoes:
  • Zipf's law, for proceedings (1 page, ps) or same, pdf
  • ISIT2002Zipf.ps or ISIT2002Zipf.pdf
• Joint work with Peter Harremoes: ISIT2002optimization.ps (delayed) or ISIT2002optimization.pdf
• Joint work with Jakob Bøje Pedersen: ISIT2002symmetry.ps or ISIT2002symmetry.pdf
• Submitted to IEEE Trans.Inform.Theory): (figures etc. still to be added) Pinskers.inequality.ps or same.pdf.
• Another ms approved for publication in IEEE Trans.Inform.Theory: MaxEnt+Applications to some classical Distributions or same.pdf.
• Short abstract to be presented at EMS2002: ps-format, same, pdf-format.
• Manuscript to be presented, if accepted, at Bangalore workshop. ps-format, same, ps-format,