Courses and Modules

Download full module catalogue (pdf)

Preparatory Courses

Mathematics Prep-Course

Course description:
This course is intended as a refreshment of mathematical tools of analysis, linear algebra and statistics which will be necessary for the CNS students in the first year. Students will acquire broadmathematical knowledge of functions in one resp. several real variables, in linear algebra, in differential equations, in probability theory and statistics, as needed for Computational Neuroscience. Basic mathematical skills for the analysis and approximation of functions, solutions of differential equations and signals, for solving linear systems and systems of ordinary differential equations will be refreshed. Participants will learn to apply mathematical foundations to the modeling and analysis of neural data and to use basic mathematical techniques to problems in Computational Neuroscience with guided assistance.

Lecturers:
Prof. Dr. Wilhelm Stannat, Torben Burow, Sebastian Zachrau

Course structure:
Time: Lecture 9:15 -12 AM, Tutorial 2-5 PM
Location: BCCN Berlin, Lecture Hall (lecture) and Seminar Room (tutorial) 

Target group:
This module is elective for students of the Master program Mathematics and Computational Neuroscience (generally for advanced Diploma students or master students). Please enroll per Email to graduateprograms@bccn-berlin.de

Requirements: 
Analysis, linear algebra, probability calculus and statistics, on a level comparable to mathematics courses for engineers (worth 24 credit points). Good command of the English language.

Course certificates:
Students who successfully passed the written exam, will be awarded 4 ECTS. Master students of Computational Neuroscience can recognize this course for their Individual Studies.

Links:
Link to the course content and schedule 2016
Link to the lecturer's website

Neurobiology Prep-Course

Course description:
This course is intended as bridge for students enrolled in Computational Neuroscience. The aim is to provide the basics in neurophysiology. The module provides an overview of the current state of brain research and a summary of the fundamental biological background necessary for the design and implementation of models. After completing the module, participants should understand the general architecture of the mammalian brain with its major components and areas including circuitry, the major cell types and their function and the basic physiological principles that govern brain function. Participating students will be given an introduction to state-of-the-art research approaches in various disciplines of neuroscience including behavioral neuroscience, electrophysiology and imaging techniques. The emphasis of the course is on imparting the absolutely necessary basics required for modeling biologically relevant information systems. The course covers basic neuroscience largely following the approach used in the textbook Bears, Connors & Paradiso. The course begins with a basic introduction to cells and neurons, the basic physiology of nerve cells and basic anatomy of the brain including the specific circuitry of major subregions such as the neocortex, hippocampus, limbic system, cerebellum and the basal ganglia. After this introduction, specific biologically based topics of interest to computational neuroscientist are treated including sensory transduction and different modalities, learning and memory, biological constraints on coding in the brain, large-scale approaches to understanding the brain, neuroscience in the laboratory and behavioural neuroscience. Time is given at the mid-point and end of the course for revision and discussions of relevant topics of interest to the students.

Lecturers:
Prof. Dr. Matthew Larkum, guest lecturers.

Course structure:
One week before the start of the winter semester, 30 hrs en block. The course is complemented by discussions and Q&A sessions based on reading materials provided during the lectures.

Target group:
This module is elective for students of the Master and Doctoral program Computational Neuroscience. Please enroll per Email to graduateprograms@bccn-berlin.de

Requirements:
Good command of the English language.

Course certificates
2 ECTS will be granted to students who successfully pass the final test. Master students of the Computational Neuroscience can take this course for the compulsory-elective module “Individual Studies”.

Links:
Link to the Moodle course page. The password will be given in the first lecture.
Link to the lecturer's website

 

Foundations (1st and 2nd semester)

Models of Neural Systems (1st semester)

Course description:
Participants should learn basic concepts, their theoretical foundation, and the most common models used in computational neuroscience. The module also provides the relevant basic neurobiological knowledge and the relevant theoretical approaches as well as the findings resulting form these approaches so far. After completing the module, participants should understand strengths and limitations of the different models. Participating students will learn to appropriately choose the theoretical methods for modeling neural systems. They will learn how to apply these methods while taking into account the neurobiological findings, and they should be able to critically evaluate results obtained. Participants should also be able to adapt models to new problems as well as to develop new models of neural systems.
Contents include:
Hodgkin-Huxley model, Channel models, Synapse models, Single-compartment neuron models, Models of dendrites and axons, Models of synaptic plasticity and learning, Network models, Phase-space analysis of neuron and network models (linear stability analysis, phase portraits, bifurcation theory).

Lecturers:
Prof. Dr. Richard Kempter, Prof. Dr. Benjamin Lindner

Course structure:
Theoretical lecture (2 ECTS)
Analytical tutorial (4 ECTS)
Programming tutorial (4 ECTS)
Experimental lecture (2 ECTS)

Target group:
This module is compulsory for students of the Master program Computational Neuroscience, compulsory elective or elective for the specialization Computational Neuroscience and Artificial Intelligence (generally for advanced Diploma students or master students).

Requirements:
Mathematical knowledge: Analysis, linear algebra, probability calculus and statistics, on a level comparable to mathematics courses for engineers (worth 24 credit points). Basic programming skills. Good command of the English language.

Course certificates:
Students who have successfully passed the analytical and programming tutorials are admitted to the oral exam. The duration of an individual oral examination is 30 minutes. After the oral exam, students will be granted 12 ECTS credit points.

For students not enrolled in the Master of Computational Neuroscience, additionally also varying combinations of the above components are possible. Please enquire details of the lecturer.

Links:
Link to the Moodle course page (the password will be given in the first lecture)
Link to the course homepage
Link to the lecturers' websites: Kempter, Lindner

Acquisition and Analysis of Neural Data (1st and 2nd semester)

Course description:
Students will gain knowledge about the most important methods for experimental acquisition of neural data and the respective analytical methods, they will learn about the different fields of application, the advantages and disadvantages of the different methods and will become familiar with the respective raw data. They will be enabled to choose the most appropriate analysis method and apply them to experimental data.
Contents include:
Acquisition of neural data (1st semester): large scale signals (fMRI, EEG, MEG etc) and cellular signals, hands-on experience with neural data acquisition techniques.
Analysis of neural data (2nd semester): firing rates, spike statistics, spike statistics and the neural code, neural encoding, neural decoding, discrimination and population decoding, information theory, statistical analysis of EEG) data, spatial filters, classification, adaptive classifiers.

Lecturers:
1st semester: Prof. Dr. John-Dylan Haynes, Prof. Dr. Michael Brecht, Prof. Dr. Gabriel Curio, and Dr. Vadim Nikulin
2nd semester: Prof. Dr. Richard Kempter, Prof. Dr. Benjamin Blankertz

Course structure:
Theoretical lecture (1st and 2nd semester, 2+2 ECTS)
Laboratory practical (1st semester, 3 ECTS)
Analytical tutorial (2nd semester, 5 ECTS)

Target group:
This module is compulsory for students of the Master program Computational Neuroscience, compulsory elective or elective for the specialization Computational Neuroscience, Artificial Intelligence, and Signal Processing (generally for advanced Diploma students or master students).

Requirements:
Sound knowledge in mathematics (Analysis, Linear Algebra, and Probability Theory / Statistics) and basic programming knowledge.

Course certificates:
Students who have successfully passed the lab sessions (1st semester) and the analytical tutorial (2nd semester) are admitted to the oral exam. The duration of an individual oral examination is 40 minutes (20 minutes for theory + 20 minutes for practice). After the oral exam, students will be granted 12 ECTS credit points.

For students not enrolled in the Master of Computational Neuroscience, additionally also following combinations of module components can be taken:

  1. 5 ECTS, just Winter Term
  2. 5 ECTS, just Summer Term without the projects
  3. 7 ECTS, just Summer Term incl. projects

 

Links:
Link to the Moodle course page (the password will be given in the first lecture)
Links to the lecturers' websites: Haynes, Brecht, Curio, Nikulin, Kempter, Blankertz

Machine Intelligence (1st and 2nd semester)

Course description:
Participants learn basic concepts, their theoretical foundation, and the most common algorithms used in machine learning and artificial intelligence. After completing the module, participants should understand strengths and limitations of the different paradigms, should be able to correctly and successfully apply methods and algorithms to real world problems, should be aware of performance criteria, and should be able to critically evaluate results obtained with those methods. Participants should also be able to modify algorithms to new tasks at hand as well as to develop new algorithms according to the paradigms presented in this course.
Contents include:
Artificial neural networks: Connectionist neurons, the multilayer perceptron, radial basis function networks, learning by empirical risk minimization, gradient-based optimization, overfitting and underfitting. Learning theories and support vector machines: statistical learning, learning by structural risk minimization.
Probabilistic methods: Bayesian inference and neural networks, generative models. Projections methods. Principal Component Analysis, Independent Component Analysis and blind source separation. Stochastic optimization. Clustering and embedding.

Lecturer:
Prof. Dr. Klaus Obermayer

Course structure:
Theoretical lecture (1st and 2nd semester, 2+2 ECTS)
Tutorial (1st and 2nd semester, 4+4 ECTS)

Target group:
This module is compulsory for students enrolled in the Master program Computational Neuroscience. Module components are compulsory elective or elective for students of other Master and Diploma programs of Berlin universities, who wish to specialize in Machine Learning and Artificial Intelligence, and who fulfill the prerequisites (see below).

Requirements:
Mathematical knowledge: Analysis, linear algebra, probability calculus and statistics, on a level comparable to mathematics courses for engineers (worth 24 credit points). Basic programming skills. Good command of the English language.

Course certificates:
At least 60% of all homework assignments have to be completed and an oral examination of up to one hour length has to be taken. The final grade is determined by the grade obtained in the oral examination. Students who successfully pass the oral exam will be awarded 12 ECTS credit points.

Links:
Link to the ISIS course page
Link to the lecturer's homepage

Models of Higher Brain Functions (2nd semester)

Course description:
Participants should learn the basic concepts and most important topics in the Cognitive Neurosciences. In addition, they should know the state-of-the-art models in these domains and their theoretical foundations. After completing the module, participants should understand strengths and limitations of the different modeling approaches (e.g. bottom-up versus top-down), should be able to understand the rationale behind models and their implementation, and should be aware of performance criteria and critical statistical tests. Participants should also be able to modify models of cognitive processes as well as to apply existing models to novel experimental paradigms, situations or data.
Contents include:
Auditory and visual system, natural image statistics and sensory processing, motor system, psychology and neuroscience of attention, memory systems, executive control, decision making, science of free will and consciousness. Data modeling and essential statistics, psychometric methods, signal detection theory, models of visual processing, models of visual attention, models of executive function. Signal processing, sensory and cognitive modeling using Python.

Lecturers:
Prof. Dr. John-Dylan Haynes (Cognitive Neuroscience), Prof. Dr. Henning Sprekeler

Course structure:
Seminar "Cognitive neuroscience" (2 ECTS, winter semester)
Theoretical lecture (2 ECTS)
Analytical tutorial (4 ECTS)
Programming tutorial (4 ECTS)

Target group:
This module is compulsory for students enrolled in the Master program Computational Neuroscience. Module components are compulsory elective or elective for students of other Master and Diploma programs of Berlin universities, who wish to specialize in cognitive neuroscience and who fulfill the prerequisites listed below.

Requirements:
Mathematical knowledge: Some acquaintance with analysis, linear algebra, probability calculus and statistics is desirable; in addition, basic knowledge about neurobiology and cognitive psychology is a prerequisite. Basic programming skills, preferably some knowledge of Python. Good command of the English language.

Course certificates:
About the contents of the theoretical lecture and Cognitive Neuroscience seminar an oral examination of up to 30 minutes (total duration) has to be taken. For the complete module as well as combinations involving the analytical and/or programming tutorial(s) the respective course certificates are a prerequisite for the admission to the oral examination. The final grade is determined by the oral examination only, however.
For students not enrolled in the Master of Computational Neuroscience, additionally also following combinations of module components can be taken:

    1. Seminar "Cognitive Neuroscience" (2 ECTS)

    2. Theoretical lecture + Analytical Tutorial + Programming Tutorial (10 ECTS)

    3. Theoretical lecture + Analytical Tutorial + seminar "Cognitive Neuroscience" (8 ECTS)

    4. Theoretical Cognitive Neuroscience: Theoretical lecture + Analytical Tutorial (6 ECTS)

Links:
Link to the Moodle course page
Link to the lecturer's homepage

Programming Course and Project (1st and 2nd semester)

Course description:
Students learn to write complex computerLink programs and to apply basic as well as advanced concepts of a modern programming language, such as imperative and object-oriented programming, and the basics of using design patterns. They learn to use tools for successful project management (such as version control tools, bug tracking, etc.) to develop a larger program in collaboration with other students including the necessary specifications, documentation and test. The course puts strong emphasis on the use of online resources and self-guided learning in order to teach the students how to acquire skills in a novel programming language using manuals and available resources.
At the end of the course students will be able:
- to write complex computer programs, and to apply basic as well as advanced concepts of a modern programming language, such as imperative and object oriented programming, and the basics of using design patterns;
- to use tools for successful project management, such as version control tools, bug tracking, etc.);
- to develop a larger program in collaboration with other students – including the necessary specifications, documentation and test.
The course puts strong emphasis on the use of online resources and self-guided learning in order to teach the students how to acquire skills in a novel programming language using manuals and available resources.

Lecturer:
David Higgins, PhD

Course structure:
Block seminar "Software Carpentry" (2 ECTS)
Programming tutorial (2 ECTS)
Computer project (2 ECTS)

Target group:
This module is compulsory for students enrolled in the Master program Computational Neuroscience.

Requirements:
Interest in programming, especially in Python. There are no special prerequisites.

Course certificates:
The module is ungraded. To pass it, participants need to fulfill the following requirements:
- at least 50% of all assignments have to be passed;
- the computer project has to be successfully completed and presented.
Students who pass the module will be granted 6 ECTS credit points.

Links:
Link to the Moodle course page (the password will be given in the first lecture)
Link to the lecturer's page

Individual Studies (upon consultation with mentor)

Course description:
Students shall acquire essential knowledge and skills, which are necessary to successfully attend the courses of the first year of study but which have not been covered during the studies leading to their first university degree. Students choose the topics upon consultation with their mentor. Depending on the subject of their first degree as well as on their individual background, students may for example choose to consolidate their mathematical knowledge in a specific area, acquire elementary computer skills, or study specific subjects in neurobiology. A two-week preparatory course in mathematics and/or a one-week preparatory course in neurobiology offered at the Bernstein Center can be recognized for this module.

Course structure:
Students can attend courses, but - alternatively - they may also receive a specific assignment by their mentor, e.g. reading recommended book chapters or solving specific homework assignments.

Target group:
This module is compulsory for students enrolled in the master program Computational Neuroscience.

Requirements:
The subject(s) of the individual studies must be approved by the mentor.

Course certificates:
The module is ungraded. Students will obtain a course certificate which contains the number of ECTS credit points and the grade "passed" or "not passed". Courses without proper course certificates cannot be recognized. In order to complete the module, students have to fill out the module recognition form and submit it to the coordination office.

Links:
Link to the list of recommended courses at Berlin universities (updated before and shortly after the semester begin). Hints to suitable courses are welcome. Please consult your mentor before you attend any courses.

 

Research-Oriented Phase (3rd and 4th semester)

Ethical Issues and Implications for Society

Course description:
In this module participants learn to reflect on the ethical and societal consequences of modern neuroscience. After completing the course the student should understand the principles of good scientific conduct and of data protection. Furthermore, the student should be able to critically discuss the ethics of animal experimentation, ethical implications and limits of clinical and biomedical research and the ethics of mental privacy. Of particular importance is that the student should be able to integrate the ethical aspects into their own ongoing and future research.
Contents include:
Philosophical theories of ethics, mental privacy, ethical aspects of animal experiments, ethical aspects of clinical neuroscience and patient research, good scientific practice, data protection and computer security, neurolaw, ethics committees.

Lecturers:
Prof. Dr. John-Dylan Haynes, invited lecturers

Course structure:
The course is offered as a winter school "Ethics and Neuroscience" during the first week after the end of the winter semester. Students are required to prepare for the course using the reading material provided. The course itself consists of a combination of lectures and group discussions. At the end of each section the lecturer will engage the students in a critical discussion of each topic. At the beginning of the course students will also be assigned to discussion groups where each group takes over one typical “ethical dilemma” faced everyday in neuroscientific research and in clinical practice. Over the week the students will learn to view their chosen topic from different angles and critically present their view on the topic in a group discussion in the last course section. The individual sections will be covered by experts in each field (stem cell research, animal experiments) and the data protection lecture will be provided by a computer security/data protection specialist.

Target group:
The course is compulsory for students of the Master Program in Computational Neuroscience.

Requirements:
Basic knowledge of neuroscientific research, good command of the English language.

Course certificates:
Students must participate in group discussions and give a presentation before the other students and the lecturers. The student’s performance is assessed according to the following criteria: participation in the group discussion, understanding of the topics, critical thinking, quality of the final presentation. The course is graded either “passed”, if achievements were at least fair, otherwise “not passed”.

Links:
Link to the lecturer's website: Haynes
Link to the course announcement and registration page
Link to the Moodle course page (password will be given after registration per Email to graduateprograms@bccn-berlin.de)

Courses on Advanced Topics (upon consultation with mentor)

Course description:
These courses shall complement the expertise in the topics selected for the lab rotations and shall provide the students the background knowledge in the subject area of the Master thesis. Students can choose from all courses offered within the "Hauptstudium" or Master programs of all Berlin universities upon consultation with their mentor. Subjects will typically be chosen from the areas brain sciences, mathematics, psychology and cognitive science, computer science and engineering.

Target group:
The course is compulsory-elective for students of the Master Program Computational Neuroscience.

Requirements:
The selection of courses as module components must be approved by the mentor and the Examination Board.

Course certificates:
Examination type and grading procedures for each module component are determined by the lecturer who is responsible for the corresponding course. At least 6 ECTS must be earned through graded courses. Up to 4 ECTS can consist of ungraded achievements. In order to pass the module, every module component must be passed individually. The final grade is then given by the numerical average of the grades of the graded components, weighted by the corresponding proportion of ECTS credit points earned. After having completed all module components, students must fill out the “Form for the recognition of Courses on Advanced Topics” and submit it along with the respective course certificates to the teaching coordination office. Courses without proper course certificates cannot be recognized.

Links:
Link to recommended courses (please consult your mentor before you choose any course)

Lab Rotations

Course description:
Students are trained in skills necessary for successfully doing independent research. Supervised by a hosting research group, students learn how to properly address a scientific problem and how to present research results in a rigorous scientific way. The abilities trained in this module include: literature survey, formulation of scientific hypotheses, project planning and design of experiments / computational studies, adequate documentation (lab book), critical evaluation and interpretation of results, report writing and oral presentation, and training of social competence in collaboration with the hosting research unit.

Course structure:
Every student will participate in research projects in three different laboratories affiliated with the Bernstein Center. Each of the three projects lasts for approximately two months (3 x 9 CP). The projects will be tailored to give intensive hands-on experience to the students. They will carry out individual research projects, and will be supervised by a senior researcher. The three projects include at least one theoretical and one experimental project. The research topic is usually chosen from the current research projects of the program’s teaching faculty. Topics must be in line with those covered by the Master Program in Computational Neuroscience.
It is allowed to complete one external lab rotation (in Germany or abroad). In this case students have to submit a short project proposal to the teaching coordination office, which has to be approved by the Examination Board. Further, students need to find a senior researcher from the BCCN who agrees to supervise the lab rotation and assess the final report and the presentation.
Students have to conduct a (guided) literature survey within the area the research problem has been chosen from, and have to read and understand one or two selected original publications. Students have to formulate a short (max. 2 page) project proposal, which is then to be discussed with members of the supervising research group. Students will then address the research problem independently in a rigorous scientific manner. Progress is monitored through regular meetings with members of the supervising research group. It is recommended to take the course as a block of seven consecutive weeks.

Target group:
The module is compulsory-elective for students of the Master Program in Computational Neuroscience.

Requirements:
Project-specific knowledge covered in the modules "Models of Neural Systems", "Models of Higher Brain Functions", "Analysis of Neural Data", or "Machine Intelligence". Please consult the hosting research group for further details. Depending on the concrete research problem, mathematical knowledge in analysis, linear algebra, and / or probability calculus and statistics, on a level comparable to mathematics courses for engineers, as well as basic programming skills may be required. Good command of the English language.

Course certificates:
Before starting a lab rotation, students are required to fill out and submit the lab rotation form to the teaching coordination office. For lab rotations done within the BCCN no project proposal is required.
At the end of the course, students have to compile a written report in the format of a short research paper (max. 8 pages) and have to present their findings to the hosting research group either through a poster or an oral presentation. It is possible to prepare a poster instead of one of three lab rotation reports, according to the prior agreement with the lab rotation supervisor. Students are welcome to present their posters at the annual lab rotations symposium for BCCN master students.The student’s performance is assessed according to the following criteria: understanding of the topic and the research problem, quality of the project proposal, scientific rigor during project work, independence and creativity during project work, quality of the documentation, quality of the written report (or poster), and quality of the final presentation. The course is graded either “passed”, if achievements were at least fair, otherwise “not passed”. Upon completion of the module, students have to submit all three lab rotation forms (signed on both pages) and the module recognition form to the teaching coordination office. Further, students are required to submit their lab rotation reports per email to the teaching coordination.

Master Thesis

Course description:
In the Master thesis, the candidate shall demonstrate that she/he is able to deal with a task in a selected study field independently and according to scientific methods within the stipulated period of time, and to present the results of such work appropriately in compliance with the standards of good scientific practice. The Master thesis is concluded by a public oral presentation (defense).

Course structure:
The Master Thesis of the Master Program Computational Neuroscience must be submitted as a written scientific report. Upon decision of the Examination Board, the Master Thesis can also be accomplished as a team-work. Accepted peer-reviewed journal papers are accepted as master theses, provided they are complemented by an appropriate general introduction. "Under review" journal papers are accepted as master theses, provided that they are complemented by an appropriate general introduction and that the first round of referee reports only requires minor changes before acceptance for publication.
The period for completion of the thesis is 4 (four) months. At the candidate’s request, upon hearing the supervisor, the Examination Board may, by way of exception, extend this period. The topic of the Master thesis can be returned only once and only within the first six weeks of the period granted for completion of the thesis.

Target group:
The module is compulsory for students of the Master Program Computational Neuroscience.

Requirements:
The candidate must have completed the modules “Models of Neural Systems”,”Models of Higher Brain Functions”, “Acquisition and Analysis of Neural Data”,”Machine Intelligence”, “Individual Studies” and “Ethical Issues and Implications for Society”. Further prerequisites are listed in this document (please read).

Course certificates:
The student applies to the Examination Board for approval of a Master thesis topic. In this context, the student can propose a supervisor and a topic; any examiner can be a supervisor. At the suggestion of the supervisor, upon consultation with the candidate, the Examination Board will allocate the topic and put the date of allocation on record.
The finished thesis shall be submitted, in due time, in triplicate to the Examination Office of the Technical University of Berlin, which will put the time of submission on record and forward the thesis for examination and assessment. The candidate shall defend the results of the final thesis in a university-public colloquium. The master thesis shall be assessed by at least two experts, among them the supervisor. Further details are available in this document (in English) and here (only in German).

 

Elective Courses

GRK Lecture Series "Machine Learning and Computational Neuroscience"

Course description:

Students will gain knowledge about current topics in machine learning and computational neuroscience. After completing the module, students should understand advanced concepts, algorithms and methods of machine learning and computational neuroscience and be able to implement them while solving related problems in their independent research work.
Contents include:
Perceptual decision making, spatial cognition, visual perception, analysis of spiking dynamics, statistical interference and many other.

Lecturers:
Principal investigators of the research training group "Sensory computation in neural systems". Each PI gives one lecture during the academic year.

Course structure:
Lectures take place on the first and third Wednesday of each month. Changes are possible. The course is managed via the learning management system "Moodle", for exact dates please see the schedule there (link below).
Time: 9.00 - 12.00
Location: BCCN Berlin, lecture hall
Each lecture includes a tutorial in the form of exercises, the homework has to be submitted via Moodle within two weeks.

Target group:
Advanced students of Computational Neuroscience Master Program, PhD students. Interested students of other programs who fulfill the prerequisites are welcome. For registration send an e-mail to graduateprograms@bccn-berlin.de

Requirements:
Mathematical knowledge: analysis/calculus, linear algebra, probability theory/statistics, on a level comparable to mathematical courses for engineers (worth 24 ECTS); advanced knowledge of biology and neuroscience; good command of the English language; basic programming skills.

Course certificates:
Students have to submit a home assignment after each lecture and have to achieve at least 50% on 75% of all assignments. A course certificate can be either ungraded ('pass/bestanden') or graded (according to the grades for the home assignments). Students who successfully pass the course will be awarded 6 ECTS credit points.

Links:
Link to the Moodle course page (the course key will be given during the first lecture)

Neural Noise and Neural Signals - Spontaneous activity and information transmission in models of single nerve cells

Course description:
Aspects of randomness in neural activity and information processing can be successfully analyzed in terms by stochastic models. This course gives an introduction to the models and measures of neural noise (or 'variability' as it is more often called) and should enable the student to follow the current literature on the subject on his/her own. To this end, some key concepts from nonlinear dynamics, stochastic processes, and information theory are outlined. Then a number of basic problems (see below) is addressed; here, the main emphasis is given to analytically tractable models, but simulation techniques are explained as well. As an outlook some more involved problems (ISI statistics under correlated ('colored') noise, with subthreshold oscillations, or with adaptation, stimulus-induced correlations) are sketched at the end of the course.
Contents include:
Key concepts from nonlinear dynamics (bifurcations, fixed points, manifolds, limit cycle), stochastic processes (Langevin and Fokker-Planck equations, Master equation, linear response theory), information theory (mutual information and its lower and upper bounds), point processes (Poisson process; renewal vs. nonrenewal point process).
Neural noise sources and how they enter different neuron models, the diffusion approximation of synaptic input or channel fluctuations by a Gaussian noise, measures of spike train and interval variability and their interrelation, Poisson spike train: entropy & information content, one-dimensional stochastic integrate-and-fire (IF) neurons: spontaneous activity, response to weak stimuli & information transfer, different forms of stochastic resonance in single neurons and neuronal populations, multidimensional IF models: subthreshold resonances, synaptic filtering & spike-frequency adaptation, effect of nonrenewal behavior of the spontaneous activity on the information transfer, outlook: stimulus-driven correlations; networks of stochastic neurons.

Lecturer:
Prof. Dr. Benjamin Lindner

Course structure:
The course takes place in the summer semester and consists of the following parts:
Theoretical lecture (every week, 2 ECTS)
Tutorial (every week, 4 ECTS)

Target group of the course:
This module is elective for students of the master program Computational Neuroscience (generally for advanced Diploma students or master students) and for PhD students of the research training group “Sensory Computation in Neural Systems”.

Requirements:
Mathematical knowledge: Analysis, linear algebra, probability calculus and statistics, on a level comparable to mathematics courses for engineers (worth 24 credit points). Good command of the English language.

Course certificates:
Students have to solve homework assignments which are given biweekly and must be usually solved within one or two weeks. At the end of the course an oral exam takes place. The certificate of successful participation in the tutorial is a prerequisite for the oral exam. Students who successfully pass the oral exam are awarded 6 ECTS.

Links:
Link to the lecturer's course page

Stochastic Processes in Neuroscience

Course description:
Participants should learn basic concepts, their theoretical foundation, and the most common models of stochastic processes used in computational neuroscience to model noisy neural systems. Participants will learn basic techniques to analyze the stochastic behavior of singles neurons and neural systems both qualitatively and quantitatively. Participants will also learn basic simulation techniques for stochastic neural systems and how to evaluate simulation output. Participants should also be able to adapt models to new problems as well as to develop new models of neural systems.
Contents include:
Brownian motion and stochastic calculus, stochastic models for single neurons (stochastic Hodgkin-Huxley model, stochastic integrate-andfire models, random oscillators), coupled neurons with noise, synchronization, stochastic stability, stochastic neural fields, travelling waves.

Lecturer:
Prof. Dr. Wilhelm Stannat

Course structure:
The course usually takes place in the winter semester at the TU Berlin, Institute for Mathematics. It comprises the following parts:
Theoretical lecture (6 ECTS)
Tutorial (4 ECTS)

Target group:
This module is elective for students of the Master program Mathematics and Computational Neuroscience (generally for advanced Diploma students or master students).

Requirements:
Mathematical knowledge: Analysis (worth 20 credit points), linear algebra (worth 10 credit points) and probability theory (worth 10 credit points) on a level comparable to courses for mathematicians. Basic programming skills. Good command of the English language.

Course certificates:
Students who have successfully completed the tutorial are admitted to the final oral exam. Students who pass it will be awarded 10 ECTS credit points.

Links:
Link to the lecturer's homepage

Stochastic Partial Differential Equations

Course description:
Participants should learn basic concepts, their theoretical foundation, and the most common models of stochastic evolution equations on Hilbert spaces with a view towards its applications to the modelling, analysis and numerical approximation of spatially extended neurons and neural systems subject to noise. Participants will learn basic techniques to analyze global properties of neural systems both qualitatively and quantitatively. Participants will also learn basic simulation techniques for stochastic neural systems and how to evaluate simulation output. Participants should also be able to adapt models to new problems as well as to develop new models of neural systems.
Contents include:
Gaussian measures on Hilbert spaces, stochastic integration on Hilbert spaces, semilinear stochastic evolution equations, stochastic reaction diffusion systems, continuum limits of neural networks.

Lecturer:
Prof. Dr. Wilhelm Stannat

Course structure:
The course usually takes place in the summer semester at the TU Berlin, Institute for Mathematics. It comprises the following parts:
Theoretical lecture (6 ECTS)
Tutorial (4 ECTS)

Target group:
This module is elective for students of the Master program Mathematics and Computational Neuroscience (generally for advanced Diploma students or master students).

Requirements:
Mathematical knowledge: Analysis (worth 20 credit points), linear algebra (worth 10 credit points) and probability theory (worth 10 credit points) on a level comparable to courses for mathematicians. Basic programming skills. Good command of the English language.

Course certificates:
Students who have successfully completed the tutorial are admitted to the final oral exam. Students who pass it will be awarded 10 ECTS credit points.

Links:
Link to the lecturer's homepage