A Digital Signal Processing Short Summary

Modern digital signal processing makes use of a variety of mathematical techniques. These techniques are used to design and understand efficient filters for data processing and control. In an accelerator environment, these techniques often include statistics, one-dimensional and multidimensional transformations, and complex function theory. The basic mathematical concepts are presented in four sessions including a treatment of the harmonic oscillator, a topic that is necessary for the afternoon exercise sessions.

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Models of the Neuron
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This course discusses single neuron modeling, including molecular models of channels and channel gating, Hodgkin-Huxley style models of membrane currents, non-linear dynamics as a way of understanding membrane excitability, neural integration through cable theory, and network computation. The goals of the course are to understand how neurons work as biological computing elements and to give students experience with modeling techniques as applied to complex biological systems.

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Open #PhD #position in mathematical neuroscience in Berlin
Dear friends and colleagues,

we are looking for a PhD candidate in mathematical neuroscience on the topic "Dynamics and variability of structured spiking neural networks". Although the focus is on the theory side, the project also includes the analysis of neuronal population data and associated problems of data assimilation. Methods will be developed within the frameworks of stochastic processes, statistical physics and nonlinear dynamics.

The PhD position in my group will be part of the vibrant computational neuroscience community at the Bernstein Center for Computational Neuroscience Berlin and the Institute of Mathematics of TU Berlin.

The successful candidate should have a degree in mathematics or physics, keen interest in computational neuroscience, expertise in analytical calculations, programming skills (C++ or C, Python or Julia, LaTeX), and excellent command of the English language, and good communication skills.

Funding is provided for five years. Applications, including a letter of motivation, a CV, a current copy of academic trannoscripts, and a list of at least two potential referees should be sent by email to me:

schwalger@math.tu-berlin.de

The deadline for applications is October 15th 2021, however, later applications might also be considered. More information is available under:

https://tub.stellenticket.de/en/offers/106202/?locale=en

Kind regards,

Tilo Schwalger

The physics of higher-order interactions in complex systems

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.

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Recorded talks of Bernstein Conference 2021
All the recorded talks from Bernstein 2021 conference can be find in G-node repository.

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Visualizing the multi-scale complexity of the brain
The brain is complex over multiple length-scales, from many protein molecules forming intricate nano-machines in a synapse to many neurons forming interconnected networks across the brain. Unraveling this multi-scale complexity is fundamental to our understanding of brain function and disease. In this lecture, I will introduce advances in visualizing the complex, multi-scale structures in the brain...

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Introduction to Neural Computation

Course Denoscription:
This course introduces quantitative approaches to understanding brain and cognitive functions. Topics include mathematical denoscription of neurons, the response of neurons to sensory stimuli, simple neuronal networks, statistical inference and decision making. It also covers foundational quantitative tools of data analysis in neuroscience: correlation, convolution, spectral analysis, principal components analysis, and mathematical concepts including simple differential equations and linear algebra.
Instructors: Prof. Michale Fee | Daniel Zysman

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Anjan Chatterjee uses tools from evolutionary psychology and cognitive neuroscience to study one of nature's most captivating concepts: beauty. Learn more about the science behind why certain configurations of line, color and form excite us in this fascinating, deep look inside your brain.

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Manifolds in Neuroscience
This video explains in pretty intuitive terms how ideas from topology (or "rubber geometry") can be used in neuroscience, to help us understand the way information is embedded in high-dimensional representations inside neural circuits.

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Dynamical Systems with Applications using Python

Designed for a broad audience of students in applied mathematics, physics, and engineering
Represents dynamical systems with popular Python libraries like sympy, numpy, and matplotlib
Explores a variety of advanced topics in dynamical systems, like neural networks, fractals, and nonlinear optics, at an undergraduate level.

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A nice Interactive GUI for phase portraits based on its eigenvalues!

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Scientific Visualization – Python & Matplotlib
An open access book on scientific visualization using python and matplotlib to be released at the end of Summer 2021. Code will be available in this repository, the PDF book will be open-access and the printed book will cost 50$.
Author: Nicolas P. Rougier
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On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behavior. As the space of its applications grows, so does the diversity of meanings of the term “network model.” This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. Here we review the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along three primary dimensions: from data representations to first-principles theory, from biophysical realism to functional phenomenology, and from elementary denoscriptions to coarse-grained approximations..

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Two post-doctoral positions

1- Full-time postdoc: neural representations of syntactic structures.

Deadline: December 31st, 2021

2- Full-time postdoc: natural language processing and neuroscience.

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Interpreting encoding and decoding models
Highlights
• Decoding models can reveal whether particular information is present in a brain region in a format the decoder can exploit.

• Encoding models make comprehensive predictions about representational spaces and more strongly constrain computational theory.

• The weights of the fitted linear combinations used in encoding and decoding models are not straightforward to interpret.

• Interpretation of encoding and decoding models critically depends on the level of generalization achieved.

• Many models must be tested and inferentially compared for analyses to drive theoretical progress.

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