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• Creating a large scale predictive vision model incorporating feedback
• Analysis of network topologies emerging from spiking neural models and other simplified computational models
• Study of critical systems

• 2016 – Unsupervised Learning from Continuous Video in a Scalable Predictive Recurrent Network
• 2016 – Fundamental principles of cortical computation: unsupervised learning with prediction, compression and feedback
• 2010 – Persistent activation blobs in spiking neural networks with mexican hat connectivity – accepted to ICAISC 2010. Supplemental matlab script and movie 1, movie 2.
• 2010 – Spectra of the Spike Flow Graphs of Recurrent Neural Networks – presentation for the ICANN conference.
• 2010 – Theoretical model for mesoscopic-level scale-free self-organization of functional brain networks, preprint submitted to IEEE TNN (BiBTeX)
• 2009 – Spectra of the Spike Flow Graphs of Recurrent Neural Networks preprint submitted to ICANN(BiBTeX)
• 2009 – Robustness of Power Laws in Degree Distributions for Spiking Neural Networks preprint submitted to IJCNN 2009. BiBTeX
• 2008 – PhD thesis – defended on April 1st 2009 at Warsaw University.
• 2008 – Spontaneous Scale-free Structure of Spike Flow Graphs in Recurrent Neural Networks, preprint submitted to Neural Networks (BiBTeX)
• 2007 – Emergence of Scale-Free Graphs in Dynamical Spiking Neural Networks, a poster presented at 2007 International Joint Conference on Neural Networks, Orlando 2007 (BiBTeX)
• 2007 – Emergence of Scale-Free Graphs in Dynamical Spiking Neural Networks, 2007 International Joint Conference on Neural Networks, Orlando 2007 (BiBTeX)
• 2007 – Emergence of Scale-Free Spike Flow Graphs in Recurrent Neural Networks, 2007 IEEE Symposium on Foundations of Computational Intelligence, Honolulu Hawai 1-5 April 2007 (BiBTeX)
• 2006 – Mesoscopic Approach to Locally Hopfield Neural Networks in Presence of Correlated Patterns, 2006 International Joint Conference on Neural Networks, Vancouver, BC, Canada July 16-21, 2006, pp 5899 (BiBTeX)
• 2005 – Phase diagrams for locally Hopfield neural networks in presence of correlated patterns,Proceedings of International Joint Conference on Neural Networks, Montreal, Canada, July 31 – August 4, 2005, pp 776 (BiBTeX)
• 2004 – Visualizing and Analyzing Multidimensional Output from MLP Networks via Barycentric Projections, Springer-Verlag, Lecture Notes on Artificial Inteligence vol 3070 (BiBTeX)
• 2004 – Visual comparison of performance for different activation functions in MLP networks, Proceedings of Internartional Joint Conference on Neural Networks, Budapest, Hungary 2004, pp 2947-2953. (BiBTeX)
• Check my google scholar page for citations

• Sensory input processing apparatus in a spiking neural network Piekniewski, F., Izhikevich, E., Szatmary, B., & Petre, C. (2012). U.S. Patent Application 13/465,903.
• Spiking neural network object recognition apparatus and methods Piekniewski, F., Izhikevich, E., Szatmary, B., & Petre, C. (2012). U.S. Patent Application 13/465,918.
• Spiking neural network feedback apparatus and methods Piekniewski, F., Izhikevich, E., Szatmary, B., & Petre, C. (2012). U.S. Patent Application 13/465,924.
• ELEMENTARY NETWORK DESCRIPTION FOR EFFICIENT IMPLEMENTATION OF EVENT-TRIGGERED PLASTICITY RULES IN NEUROMORPHIC SYSTEMS Izhikevich, E. M., Szatmary, B., Petre, C., Piekniewski, F., & Nageswaran, J. M. (2013). U.S. Patent No. 20,130,073,492. Washington, DC: U.S. Patent and Trademark Office.
• ELEMENTARY NETWORK DESCRIPTION FOR EFFICIENT MEMORY MANAGEMENT IN NEUROMORPHIC SYSTEMS  Izhikevich, E. M., Szatmary, B., Petre, C., & Piekniewski, F. (2013). U.S. Patent No. 20,130,073,484. Washington, DC: U.S. Patent and Trademark Office.
• ELEMENTARY NETWORK DESCRIPTION FOR NEUROMORPHIC SYSTEMS Izhikevich, E. M., Szatmary, B., Petre, C., Nageswaran, J. M., & Piekniewski, F. (2013). U.S. Patent No. 20,130,073,495. Washington, DC: U.S. Patent and Trademark Office.
• ELEMENTARY NETWORK DESCRIPTION FOR EFFICIENT LINK BETWEEN NEURONAL MODELS AND NEUROMORPHIC SYSTEMS Izhikevich, E. M., Petre, C., Piekniewski, F., & Szatmary, B. (2013). U.S. Patent No. 20,130,073,498. Washington, DC: U.S. Patent and Trademark Office.
• APPARATUS AND METHOD FOR PARTIAL EVALUATION OF SYNAPTIC UPDATES BASED ON SYSTEM EVENTS Izhikevich, E. M., Piekniewski, F., & Nageswaran, J. M. (2013). U.S. Patent No. 20,130,073,499. Washington, DC: U.S. Patent and Trademark Office.
• APPARATUS AND METHODS FOR SYNAPTIC UPDATE IN A PULSE-CODED NETWORK Izhikevich, E. M., Piekniewski, F., & Nageswaran, J. M. (2013). U.S. Patent No. 20,130,073,491. Washington, DC: U.S. Patent and Trademark Office.
• APPARATUS AND METHODS FOR TEMPORALLY PROXIMATE OBJECT RECOGNITION Piekniewski, F. L., Petre, C., Sokol, S. H., Szatmary, B., Nageswaran, J. M., & Izhikevich, E. M. (2012). U.S. Patent No. 20,120,308,076. Washington, DC: U.S. Patent and Trademark Office.
• APPARATUS AND METHODS FOR TEMPORALLY PROXIMATE OBJECT RECOGNITION PIEKNIEWSKI, F., PETRE, C., SOKOL, S., SZATMARY, B., NAGESWARAN, J., & IZHIKEVICH, E. (2012). WIPO Patent No. 2012167164. Geneva, Switzerland: World Intellectual Property Organization.
• APPARATUS AND METHODS FOR SYNAPTIC UPDATE IN A PULSE-CODED NETWORK IZHIKEVICH, E., PIEKNIEWSKI, F., & NAGESWARAN, J. (2013). WIPO Patent No. 2013043903. Geneva, Switzerland: World Intellectual Property Organization.
• ELEMENTARY NETWORK DESCRIPTION FOR NEUROMORPHIC SYSTEMS IZHIKEVICH, E. M., SZATMARY, B., PETRE, C., NAGESWARAN, J. M., & PIEKNIEWSKI, F. (2013). WIPO Patent No. 2013043610. Geneva, Switzerland: World Intellectual Property Organization.
• More submitted, check my google scholar page

Spiking neural networks as a parallel computing paradigm June 2013, six lectures at Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń

• Lecture notes

Mathematical Foundations of Neuroscience – winter semester 2009/2010. Preliminary program. Any supplemental material will be published here.
Lecture presentations:

• Lecture 1 – Basic facts about the brain and its analysis, Sample questions
• Lecture 2 – Electrophysiology of neurons, Sample questions
• Lecture 3 – Electrophysiology of neurons (continued), Sample questions
• Lecture 4 – 1d systems, Sample questions
• Lecture 5 – 2d systems, Sample questions
• Lecture 6 – Bifurcations in 2d systems, Sample questions
• Lecture 7 – Bifurcations II, Sample questions
• Lecture 8 – Classes of excitability, Sample questions
• Lecture 9 – Simple models of neurons and synapses, Sample questions
• Lecture 10 – Bursting, Sample questions
• Lecture 11 – Bursting continued Sample questions
• Lecture 12 – Synchronization Sample questions
• Lecture 13 – Coupled Oscillators Sample questions
• Lecture 14 – Synchronization of neurons and synaptic plasticity Sample questions
• Lecture 15 – Building large models step by step Sample questions

Programs/scripts/animations:

• DTI tracking with Slicer 3d – a QuickTime animation
• Slicer3d program webpage – an opensource medical visualization software. Also check the tutorials which include the nescessary data files.
• Numerical stability demo – Matlab/Octave script
• Saddle node bifurcation of a 1d system – Matlab/Octave script
• Quadratic integrate and fire neuron – Matlab/Octave script
• Saddle-node bifurcation in 1d system – a QuickTime animation
• Saddle-node on invariant cicrle bifurcation in the Na-p-K model – a QuickTime animation
• Phase portrait plot – Matlab/Octave script and sample fields to plot: sample field (pdf image), sample field 2 (pdf image), sample field 3 (pdf image), sample field 4 (pdf image)
• Fold Cycle bifurcation in the canonical model – a QuickTime animation
• Saddle Homoclinic Orbit bifurcation in the Na-p-K model – a QuickTime animation
• Supercritical Andronov-Hopf bifurcation in the Na-p-K model – a QuickTime animation
• Subcritical Andronov-Hopf bifurcation in the Na-p-K model – a QuickTime animation
• Saddle node bifurcation in the Na-p-K model – a QuickTime animation
• Dynamic regimes near Bogdanov-Takens bifurcation – a QuickTime animation
• A script simulating an array of coupled neurons – good student project seed – Matlab/Octave script
• Lecture notes of Georgi Medvedev, useful supplementary material
• Publications of Eugene Izhikevich, useful supplementary material
• A script simulating a piece of an axon with the cable equation – good student project seed – Matlab/Octave script
• An animation of an action potential propagating spatialy along the fiber – a QuickTime animation
• Spiking Neuron Models Single Neurons, Populations, Plasticity a book by Wulfram Gerstner and Werner M. Kistler – useful supplementary material
• A script simulating a piece of an axon with the cable equation (FitzHugh-Nagumo) – good student project seed – Matlab/Octave script
• A spiking network with CUDA – A project by Jayram Moorkanikara Nageswaran et.al
• Hysteresis loop – a QuickTime animation
• Hysteresis loop – Matlab/Octave script
• INa-IK-IK(M) burster – Matlab/Octave script
• An animation of an action potential propagating spatialy along the fiber in a bursting model (fold/homoclinic bursting) – a QuickTime animation
• An animation of an action potential propagating spatialy along the fiber in a bursting model (circle/circle bursting) – a QuickTime animation
• INa-IK-IK(M) circle/circle burster spatial solution – Matlab/Octave script
• A mesh resembling a neuron in 3d – Blender file
• Another mesh resembling a neuron in 3d – Blender file
• INa-IK-IK(M) Fold/Homoclinic burster spatial solution – Matlab/Octave script
• Propagating Waves in Neocortical Slices Research results of JIAN-YOUNG WU, PH.D.
• Some more movies of Jian-Young Wu
• Okinawa computational neuroscience course – a very good summer school, I encourage my students to apply!
• Neuron – software for neuron simulations
• Web page of Bard Ermentrout an author of XPP and many publications on mathematical neuroscience
• Solution of a bursting neuron in 2d – note the artifacts related to the second order derrivative mask
• Solution of a bursting neuron in 2d (source) – Matlab/Octave script
• Rotating waves in a grid of coupled oscillators – a QuickTime animation
• Spiral waves in a grid of coupled oscillators – a QuickTime animation
• 2d grid of coupled oscillators (source) – Matlab/Octave script
• Computing PRC – Matlab/Octave script
• Poincare phase map – Matlab/Octave script

Selected student projects:

• Multi compartment neuron model Rafal Malkowski
• NiC (Neurons in CUDA) Michal Matuszak
• 3D Neuron Model Bartosz Paprzycki
• Persistent sodium and potassium neuron model Jaroslaw Piersa
• Neurotest Andrzej Rutkowski
• Neurons in flash Bartosz Zielinski
• The Hodgkin-Huxley model – action potential Marcin Duchinski

• Mixed photos from San Diego area, 2010,2011
• A movie related to Brain Corporation shown by PBS
• Milky Way time lapse movie taken on 14 Dec 2010 on Mt Laguna, some meteors are visible too, mov
• Mysterious e a presentation for high school, Swiecie 2009, polish pdf
• Scale-free networks a presentation on a seminar, polish pdf
• Digital Signal Processing a presentation for high school students, polish pdf
• Signal and image processing algorithms a presentation on a seminar, polish pdf
• Inside the Menger Sponge a ptviewer 360 panorama inside this exciting shape
• Scale free structures in recurrent neural networks a presentation on a seminar, polish pdf
• A Beamer theme with my Faculty colors and university logos
• Finding roots using binary or interpolation search a demonstration I made in Mathematica for Wolfram Demonstrations Project
• Cayley Trees in Mathematica a demonstration I made in Mathematica for Wolfram Demonstrations Project
• Map of Computer Science graphical representation of areas in computer science and relations between them, english pdf
• Expander graphs and their applications a presentation on a seminar, polish pdf
• A couple of pics of Torun in HSIR pictures with V (value) channel replaced by infrared image, nice effect
• Magia algorytmów obróbki obrazu a presentation for annual science and art festival about digital photography and image processing (polish, html)
• My faculty yard via PTviewer a 360 degree panorama of a yard at my faculty
• Fractals with Maple a set of Maple procedures used to plot a number of fractals
• My infrared photographs a couple of compositions done with Hoya R72 filter and olympus C7070
• 2d Lattice of Simplified Dynamical Neurons student project for OCNC 2006 (english, mov)
• Losowosc w informatyce a presentation for annual science and art festival in Torun (polish, pdf)
• WLAN safety – a presentation that I commited for the eduroam semminar in march 2006 (polish, pdf).
• Torun in my lens – a web gallery containing some photos of my hometown that I collected in recent years.
• Analiza stabilności i diagramów fazowych dla lokalnie hopfieldowskich sieci neuronowych w obecności wysoce skorelowanych wzorców okresowych – My masters thesis (Polish pdf)
• CS in Education 2005 Conference – Arythmetic routines in Pascal and C++ – materials for workshops (polish html)
• Samba and LDAP Howto – useful howto on ldap authorization in samba (Polish pdf)
• Real Video Streaming Howto – useful howto on real video streaming (Polish pdf)
• Fractals – Presentation for science festival about fractals (Polish HTML!!! <- NEW )
• Fractals – Presentation for science festival about fractals (Polish pdf)
• SIMP documentation – Technical aspects of the project that my team has written, and won departamets team programming contest ‘2004 (Polish pdf).
• Gamma tranformations – Short thesis about gamma transformations of digital images (Polish pdf).
• Java project – A small java applet for demonstration of Kohonen Self Organizing Map (neural network method).