The research of GRC is currently developing in 3 main directions:

1. Time series pattern recognition and forecasting

2. Financial econometrics and risk management

3. Artificial intelligence and adaptive learning algorithms

A particular research emphasis is put on the development of methods and techniques from econophysics. Several thematic areas are used as an input to the GRC research and below follows a listing of 7 research categories, each including a number of interesting research papers. The listing is more subjective than complete and, rather than naming seminal monographs on the subject matter, it refers to ”hot” research papers, which illustrate the present state of the art or promising research directions.

Another particular characteristic of this listing is that a number of interesting papers could be simultaneously included in several or even most categories. For example, ideas from the information theory are used in physics papers, notions from economics form the basis of advanced learning algorithms. The lack of rigid boundaries indicates that many of these directions are likely to converge in a not so distant future. Let us hope that this emerging new science will enrich our understanding of natural and social processes at various levels of complexity.

1. Information and algorithms
2. Physics
3. Fractals
4. Machine learning and Artificial intelligence
5. Data mining, Pattern recognition and discovery.
6. Time series analysis and prediction  
7. Specific applications to finance and economics

Information and algorithms (up)
(information theory, algorithmic information theory, quantum information, Kolomogorov complexity, algorithmic probability, Levin search, etc)

• “Randomness”. Paul Vitanyi, math.PR/01100086, 2001
• “Meaningful Information”. Paul Vitanyi, cs.CC/0111053, 2001
• “The Generalized Universal Law of Generalization”, Nick Chater and Paul M.B. Vitanyi, cv/0101036, 2001
• “Algorithmic Statistics”. Peter Gacs, John Tromp, Pul Vitanyyi, math.PR/0006233, 2000
• “A Theory of Universal Artificial Intelligence based on Algorithmic Complexity”. Marcus Hutter, cs.AI/0004001, 2000
• “Minimum description Length Induction, Bayesianism, and Kolomogorov complexity”. Paul Vitanyi and Ming Li, cs.LG/99010144, 1999
• “Sequential prediction of individual sequences under general loss functions”. David Haussler and Jyrki Kivinen, UCSC-CRL-94-36, 1994
• “The Discovery of Algorithmic Probability”. Ray J. Solomonoff
• “A Century of Controversy over the Foundations of Mathematics”. G.J.Chaitin, chao-dyn/99909001, 1999
• “Regularities Unseen, Randomness Observed: Levels of Entropy convergence”. James P. Crutchfield and David P. Feldman, cond-mat/0102181, 2001
• “Applying MDL to Learning Best Model Granularity”. Qiong Gao, Ming Li, Paul M.B. Vitanyi, 1999
• “Model Selection and the Principle of Minimum Description Length”. Mark H. Hansen and Bin Yu , 1995
• “Shifting Inductive Bias with Success-Story Algorithm, Adaptive Levin Serach, and Incremental Self-Improvement“. Jurgen Schmidhuber, Machine Learning, 28, 105-132, 1997
• “Discovering Problem Solutions with Low Kolmogorov Complexity and High Generalization Capability”, Jurgen Schmidhuber, TR-FKI-194-94, 1994
• “Introduction to quantum information theory”. M.A.Nielsen, 2000
• “Quantum Information Theory”. Michael A. Nielsen, PhD dissertation, University of New Mexico, 1998
• “Quantum Computation”. Dorit Aharonov, in Annual Reviews of Computational Physics VI, World Scientific, 1998
• “Quantum Kolmogorov Complexity Based on Classical Descriptions”. Paul M.M. Vitanyi. IEEE Transactions on information theory, 1999

Physics (up)
(physics of information and information physics, quantum physics, statistical physics, discrete and finite dynamics, stochastics and chaos, theories of everything”)

• “Algorithmic Theory of Everything”. Jurgen Schmidhuber, quant-ph/0011122, 2000
• “A Computer Scientist’s View of Life, the Universe and Everything”. Jurgen Schmidhuber, In C. Freksa, ed., Foundations of Computer Science: Potential – Theory – Cognition. Lectures Notes in Computer Science, pp. 201-298, Springer, 1997
• “The Church-Turing thesis as a guiding principle for physics”. Karl Svozill, 1996
• “The Structure of the Multiverse” David Deutsch, 2001
• “Feynman Clocks, Casual Networks,and the Origin of Hierarchial’ Arrows of Time’ in Complex Systems. Part I. ‘Conjectures’ ”. Scott Hitchcock, MSUCL-1135, 2000
• “Quantum Foundations in the Light of Quantum Information”. Christopher A. Fuchs, quant-ph/0106166, 2001
• “Quantum Mechanics and Algorithmic Randomness”. Ulvi Yurtsever, quant-ph/9806059, 2000
• “Measurement of time in nonrelativistic quantum and classical mechanics”. Piret Kuusk and Madis Koiv. 2001
• “How to Measure a Beable”. J.Finkelstein. SJSU/TP-95-12, 1995
• “Event-Enhanced Formalizm of Quantum Theory or Columbus Solution to the Quantum Measurement Problem“. Ph. Blanchard and A.Jadczyk, HEP-TH-9408021, 1994
• “Varieties of Quantum Measurement”. W. G. Unruh, HEP-TH-9410168, 1994
• “Quantum mechanics of measurement”. N. J. Cerf and C. Adami, preprint MAP-198, 1997
• “Interpretations of quantum mechanics, and interpretations of violation of Bell’s inequality”. Willem. M. De Muynck, 1999
• “Path integral methods and applications”. R.MacKenzie. UdeM-GPP-TH-00-71, 2000
• “On Quantum Mechanics”. Carlo Rovelli, quant-ph/9609002, 1996
• “Quantum Mechanics”, A. Bohm, Berlin: Springer, 1986
• “Quantum Physics without Time” . F.Englert, Phys.Lett B, vol. 228, No 1, 111-114, 1989
• “Casual Quantum Mechanics Treating Position and Momentum Symmetrically”. S. M. Roy and Virendra Singh, CERN-TH.777481/94, 1994
• “Quantum Gravity as a Dissipative Deterministic System”. Gerard ‘t Hooft, hep-th/9903084, 1999
• “Strings from Logic”, Christof Shchmidhuber, CERN-TH/2000-316, 2000
• “On a Generalization in Quantum Theory: Is h Constant?”. Ronald J. Adler, 1999
• “Process physics: inertia, gravity and the quantum”. Reginald T. Cahill, 2001
• “A short introduction to Bit-String Physics”. H. P. Noyes, SLAC_PUB-7205, 1997
• “Noncommutativity and Discrete Physics”. Louis H. Kauffman, q-alg/9709012, 1997
• “Some remarks on discrete physics as an ultimate dynamical theory“. H. P. Noyes, SLAC-PUB-95-7017, 1995
• “Let’s call it Nonlocal Quantum Physics”. Manfred Requardt
• “The Quantum Theory of Ur-Objects as a Theory of Information”. H. Lyre. Int. Journ. of Th.Phys, Vol. 34, No. 8, p.1541-1552, 1995
• “Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena”. Andrei Khlebnikov, 2000
• “p-ADIC and ADELIC harmonic oscillator with time-dependent frequency”. Goran S. Djjoordjjevic and Branko Dragovich, 1998
• “On integrability and Chaos in discrete Systems”. Mark J. Ablowitz, Yasuhiro Ohta, A. David Trubatch, solv-int/9810020, 1998
• “Discrete physics and the Dirac equation”. Louis H. Kauffman and H. Pierre Noyes, SLAC-PUB-7115, 1996
• “On the Asymptotic Analysis of the Discrete Dirac Equation”. Ch. Gunn and M. Holschhhneider, Sfb 288 Prep. No 122, 1994
• “From quantum cellular automata to quantum lattice gases”. D.A.Meyer, quant-ph/9604003, 1996
• “Noncommutative Geometry”. A. Connes, Academic Press, 1994
• “Exploring Complexity”, G. Nicolis, I. Prigogine, San Francisco, W.H. Freeman, 1989
• “Quantum Chaos, Complex Spectral Representations and Time-Symmetry Breaking”, T.Petrosky, I. Prigogine, Chaos, Solitons and Fractals, 4, 311, 1994
• “Dynamical foundations of nonextensive statistical mechanics”. Christian Beck, cond-mat/01005374, 2001
• “Remark on the Second Principle of Thermodynamics”. Constantino Tsallis, cond-mat/0012371, 2000
• “On the definition of physical temperature and presure for nonextensive thermostatistics “. Raul Toral, cond-mat/01006060, 2001
• “Wher the Tsallis statistic is valid?”. L.Velllllazques and F.Guzman, cond-math/0105378, 2001
• “Probabilistic properties of nonextensive thermodynamic”. Frack Jedrzejewski, cond-mat/0103386, 2001

Fractals (up)

• “The Fractal. Geometry of Nature”, B. Mandelbrot, NY: W.H. Freeman, 1982
• “Unbiased estimation of multi-fractal dimensions of finite data sets”. A.J. Roberts and A. Cronin, chao-dyn/9601019, 1996
• “Multifractal Interpolation of Universal Multifractals”. V.G.Bar’yahtar, V.Yu.Gonchar, D.Schertzer, V.V.Yanovsky, chao-dyn/9711003, 1997
• “Fractal analysis for social systems”. C.M. Arizmendi, adap-org/9910001, 1999
• “Crossing of two mobile averages: A method for measuring the roughness exponent”. N. Vandewalle and M. Ausloss, Phys.Rev. E, vol.58, No 5, p 6832-6834, 1998
• “The use of generalized dimensions in measuring fractal dimension of time series“. Y. Ashkenazy, chao-dyn/9805001, 1998

• “A review of machine learning“. David M. Dutton and Gerald V. Conroy, The Knowledge Engineering Review, Vol 12:4, p 341-367, 1996
• “C4.5: Programs for Machine Learning”. J. R. Quinlan, San Mateo: Morgan Kaufmann, 1993
• “Separate-and-Conquer Rule Learning“. Johannes Furnkranz, TR-OEFAI-TR-96-25, 1996
• “Automatic Construction of Decision Trees from Data: A Multi-disciplinary survey”. Sreerama K. Murthy, 1997
• “Learning Domain theories using Abstract Background Knowledge”. Peter Clark and Stan Matwin, TR-92-95, Ottawa Machine Learning Group, 1992
• “Experiments with a New Boosting Algorithm”. Yoav Freud and Robert E. Schapire, Machine Learning: Proceedings of the Thirteenth International Conference, 1996
• “Naive Bayesian Classifier Committees”. Zijian Zheng, in Proceedings of ECML’98, Berlin; Springer Verlag, 196-207, 1998
• “A Survey of Evolution Strategies”. Thomas Back , Frank Hoffmeister, Hans-Paul Schwefel, 1992
• “The Cascade-Correlation Learning Architecture”. Scott E. Fahlman and Christian Lebiere, CMU-CS-90-100, 1991
• “Introduction to Radial Basis function Networks”. Mark J. L. Orr, 1996
• “Neural Networks”. Michael I. Jordan and Christofer M. Bishop, A.I. Memo No 1562, 1996
• “Independent Component Analysis by Minimization of Mututal Information”, Aapo Hyvarinen, 1997
• “Locally Connected Recurrent Networks”. Lai-Wan Chan and Evan Fung-Yu Young, CS-TR-95-10, 1995
• “A recurrent neural network with ever changing synapses”. M. Heerema and WA van Leeuwen, cond-mat/0002360, 2000
• “A Review of Machine Learning Methods”. M. Kubat, I. Bratko, R. Michalski
• “Machine Learning Research: Four Current directions.” T. G. Dietterich
• “Gene Expression Programming: a New Adaptive Algorithm for Solving Problems”. Candida Ferreira, Complex systems, 2001
• “The society of mind requires an economy of mind”. Ian Wright an dMichel Aube, 1996
• “Toward a Model of Intelligence as an Economy of Idiots“. Eric B. Baum, ICML’96, 1997
• “Evolving Non-Determinism: An Inventive and Efficient Tool for Optimization and Discovery of Strategies”. Hugues Juille, 1994

Data mining, Pattern recognition and discovery. (up)

• “Data Mining. The Search for Knowledge in Databases”. Marcel Holmmsheimer and Arno Siebs, Report CS-R9406, 1994
• “An indexing Scheme for Fast Similarity Search in Large Time Series Databases”. Eamonn J. Keogh and Michael J. Pazzani, 1998
• “Rule recovery from time series”. Gautam Das, King-Ip Lin, Heikki Mannila, Gopal Renganatham, Padhraic Smyth, 1997
• “Finding Similar Time Series”. Gautam Das, Dimitrios Gunopulos and Heikki Mannila. 1998
• “A Probabilistic Approach to Fast Pattern Matching in Time Series Databases”. Eamonn Keogh and Padhraic Smyth, 1995
• “Discovery of Frequent Patterns in Large Data Collections”. Hannu Toivonen, UHF Report A-1996-5, 1996
• “Pattern discovery and Computational Mechanics”. Cosma Rohilla Shalizi and James P. Crutchfield, cs.LG/0001027, 2000
• “Computational mechanics: Pattern and Prediction, Structure and simplicity”. Cosma Rohilla Shalizi and James P. Crutchfield, cond-mat/9907176, 2000

Time series analysis and prediction (up)

• “Time series forecasting: a nonlinear dynamics approach”. Stefano Sello, USG/180699, 1999
• “Nonlinear Time-Series Prediction with Missing and Noisy Data”. Volker Tresp and Reimar Hofmann, Neural Comp. 10, 731-747, 1998
• “Forecasting chaotic time series with genetic algorithms”. G.G.Szpiro, Phys.Rev. E, v.55, No 3, p.2557-2567, 1997
• “Statistical theory of self-similar time series as a nonextensive thermodynamic system”. Alexnder I. Olemskoi, cond-mat/015221, 2001
• “Noisy Time Series Prediction using Symbolic Representation and Recurrent Neural Network Grammatical Inference”. Steve Lawrence, Ah Chung Tsoi, C. Lee Giles, UMIACS-TR-96-27, 1996
• “Data analysis: generalizations of the local approximation method by singular spectrum analysis”. A. Loskutov, I. Istomin and O. Kotlyarov, nlin.CD/0109022, 2001
• “The Kalman-Levy filter”. Didier Sornette and Kayo Ide, cond-mat/0004369, 2000
• “Resummation Methods for Analysing Time Series”. S. Gluzman and V. I. Yukalov, cond-mat/9710290, 1998

Specific applications to finance and economics (up)

• “Quantum-like approach to financial risk: quantum anthropic principle”. E. W. Pitrowski and J. Sladkowski, quant-ph/011110046, 2001
• “Quantum Mechanics and Mathematical Economics are Isomorphic”. L. Lambertini, 2000
• “Pilot wave quantum model for the stock market”. Olga Choustova, 2001
• “Self-similar approach to market analysis”. V.I. Yukalov, cond-mat/0110285, 2001
• “fundamental Framework for Technical analysis”. J. V. Andersen, S. Gluzman and D. Sornette, cond-math/9910047, 1999
• “Statistical Mechanics of Nonlinear Nonequilibrium Finannncial Markets: Applications to Optimized Trading”. Lester Ingber
• “Some applications of statistical Mechanics of Financial Markets”. Lester Ingber
• “Finacial Market Dynamics”. Fredrick Michael and M.D. Johnson, cond-mat/01008017, 2001
• “Economic Forecasting: Challenges and Neural Network Solutions” John Moody, 1995
• “Forecasting price increments using an artificial Neural Network”. Filippo Castiglione, cond-math/0006486, 2000
• “Constructing Heterogeneous committees Using Input Feature Grouping: Application to Economic Forecasting”. Yuansong Liao and John Moody, OR 97291-1000, 1997
• “Market force, ecology, and evolution” J. Doyone Farmer, 1999
• “Evolutionary dynamics in finacial markets with many trader types”. William A. Brock and Cars H. Hommes, 2001
• “Application of multi-agent games to the prediction of finacial time-series”. Neil F. Johnson, David Lamper, Paul Jefferies, Michael L. Hart and Sam Howison, cond-mat/015303, 2001
• “Predictability of large future changes in a competitive evolving population”. D. Lamper, S. Howison and N.F. Johnson, cond-mat/0010005258, 2001
• “Theory of the evolutionary minority game”. T.S. Lo, P. M. Hui and N. F. Johnson, cond-math/0003379, 2000
• “Modeling Market Mechanism with Minority Game”. Damien Challet, Matteo Marili and Yi-Cheng Zang, cond-mat/9909265, 1999
• “A Model of Stock Market Participans”. Michael de la Maza and Deniz Yuret, 1995
• “Algorithmic complexity of Real Financial Markets”, R. Mansilla, 2000
• “Towards Understanding the Predictability of Stock Markets from the Prspective of Computational Complexity”. James Aspenes, David F. Fisher, Michael J. Fisher, Ming-Yang Kao and Alok Kumar, cs.CE/0010021, 2000
• “Genetic Algorithms with collective sharing for Robust Optimization in Financial Applications”. Oliver V. Pictet, michel M. Dacorogna, Rakhal D. Dave, Bastien Chopard, Roberto Schirru and Marco Tomassini, OVP-.1995-02-06, 1996
• “Patterns, Trends and Predictions in stock market indices and foreign currency exchange rates”. Marcel Ausloos and Kristinka Ivanova, cond-mat/0108013, 2001
• “Moving averages and markets inefficiency”. R. Baviera, M. Pasquini, J. Raboanary, M. Serva, cond-mat/00111337, 2000
• Markovian approximation in foreign exchange markets “ Robrto Baviera, Davide Vergini and Angelo Vulpiani, cond-mat/990331144, 1999