Nataliya Kraynyukova
@ieecr-bonn.de
U Bonn Medical Center
RESEARCH, TEACHING, or OTHER INTERESTS
Neuroscience, Computational Theory and Mathematics
Scopus Publications
Scopus Publications
Surbhit Wagle, Nataliya Kraynyukova, Anne-Sophie Hafner, and Tatjana Tchumatchenko
Elsevier BV
Pierre Ekelmans, Nataliya Kraynyukova, and Tatjana Tchumatchenko
Public Library of Science (PLoS)
Neural computations emerge from local recurrent neural circuits or computational units such as cortical columns that comprise hundreds to a few thousand neurons. Continuous progress in connectomics, electrophysiology, and calcium imaging require tractable spiking network models that can consistently incorporate new information about the network structure and reproduce the recorded neural activity features. However, for spiking networks, it is challenging to predict which connectivity configurations and neural properties can generate fundamental operational states and specific experimentally reported nonlinear cortical computations. Theoretical descriptions for the computational state of cortical spiking circuits are diverse, including the balanced state where excitatory and inhibitory inputs balance almost perfectly or the inhibition stabilized state (ISN) where the excitatory part of the circuit is unstable. It remains an open question whether these states can co-exist with experimentally reported nonlinear computations and whether they can be recovered in biologically realistic implementations of spiking networks. Here, we show how to identify spiking network connectivity patterns underlying diverse nonlinear computations such as XOR, bistability, inhibitory stabilization, supersaturation, and persistent activity. We establish a mapping between the stabilized supralinear network (SSN) and spiking activity which allows us to pinpoint the location in parameter space where these activity regimes occur. Notably, we find that biologically-sized spiking networks can have irregular asynchronous activity that does not require strong excitation-inhibition balance or large feedforward input and we show that the dynamic firing rate trajectories in spiking networks can be precisely targeted without error-driven training algorithms.
Nataliya Kraynyukova, Simon Renner, Gregory Born, Yannik Bauer, Martin A. Spacek, Georgi Tushev, Laura Busse, and Tatjana Tchumatchenko
Proceedings of the National Academy of Sciences
The brain’s connectome provides the scaffold for canonical neural computations. However, a comparison of connectivity studies in the mouse primary visual cortex (V1) reveals that the average number and strength of connections between specific neuron types can vary. Can variability in V1 connectivity measurements coexist with canonical neural computations? We developed a theory-driven approach to deduce V1 network connectivity from visual responses in mouse V1 and visual thalamus (dLGN). Our method revealed that the same recorded visual responses were captured by multiple connectivity configurations. Remarkably, the magnitude and selectivity of connectivity weights followed a specific order across most of the inferred connectivity configurations. We argue that this order stems from the specific shapes of the recorded contrast response functions and contrast invariance of orientation tuning. Remarkably, despite variability across connectivity studies, connectivity weights computed from individual published connectivity reports followed the order we identified with our method, suggesting that the relations between the weights, rather than their magnitudes, represent a connectivity motif supporting canonical V1 computations.
Laura Bernáez Timón, Pierre Ekelmans, Nataliya Kraynyukova, Tobias Rose, Laura Busse, and Tatjana Tchumatchenko
Wiley
AbstractDue to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large‐scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task‐oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance. image
Nataliya Kraynyukova, Anne-Sophie Hafner, and Tatjana Tchumatchenko
Springer Science and Business Media LLC
Yombe Fonkeu, Nataliya Kraynyukova, Anne-Sophie Hafner, Lisa Kochen, Fabio Sartori, Erin M. Schuman, and Tatjana Tchumatchenko
Elsevier BV
Nataliya Kraynyukova and Tatjana Tchumatchenko
Proceedings of the National Academy of Sciences
Significance Many fundamental neural computations from normalization to rhythm generation emerge from the same cortical hardware, but they often require dedicated models to explain each phenomenon. Recently, the stabilized supralinear network (SSN) model has been used to explain a variety of nonlinear integration phenomena such as normalization, surround suppression, and contrast invariance. However, cortical circuits are also capable of implementing working memory and oscillations which are often associated with distinct model classes. Here, we show that the SSN motif can serve as a universal circuit model that is sufficient to support not only stimulus integration phenomena but also persistent states, self-sustained network-wide oscillations along with two coexisting stable states that have been linked with working memory.
N. Kraynyukova, S. Nesenenko, P. Neff, and K. Chełmiński
Elsevier BV
Nataliya Kraynyukova and Sergiy Nesenenko
Cambridge University Press (CUP)
In this work we study the solvability of the initial boundary-value problems that model the quasi-static nonlinear behaviour of ferroelectric materials. Similar to the metal plasticity, the energy functional of a ferroelectric material can be additively decomposed into reversible and remanent parts. The remanent part associated with the remanent state of the material is assumed to be a convex non-quadratic function f of internal variables. In this work we introduce the notion of the measure-valued solutions for the ferroelectric models, and show their existence in the rate-dependent case, assuming the coercivity of the function f. Regularizing the energy functional by a quadratic positive-definite term, which can be viewed as hardening, we show the existence of measure-valued solutions for the rate-independent and rate-dependent problems, avoiding the coercivity assumption on f.
N. Kraynyukova and H.-D. Alber
Wiley
We consider a mathematical model, which describes piezoelectric material behavior. This model is similar to models of plasticity theory. However, piezoelectric models describe coupled mechanical and electrical material behavior. Therefore they contain additional nonlinearities in the piezoelectric tensor and in the enthalpy function, which is non quadratic. These nonlinearities cause difficulties in the proof of existence theorems. Under the assumption that the piezoelectric tensor is constant (i.e. independent of P), we show how the system of model equations can be reduced to a doubly nonlinear evolution equation of the form zt ∈ G(‐Mz‐Φ (z) + f), which contains a composition of two monotone operators. The monotone mapping G is a subdifferential of the indicator function of some convex set while the second monotone mapping Φ is the Nemyckii operator of a monotone function. We prove existence of strong solutions, if Φ is replaced by a regularization. If in addition Φ is Lipschitz continuous we can show that the solution is unique.
Nataliya Kraynyukova
Wiley
We present an existence result for an evolution equation with a nonlinear operator, which is a composition of two monotone mappings. The first monotone mapping is a subdifferential of the indicator function of some convex set while the other is constructed as the Nemyckii operator of a monotone function. Such equations arise from the mathematical models, which describe piezoelectric material behavior. Under some additional assumptions we prove the existence and uniqueness of the strong solution for the case, when the operator generated by the monotone function is a Lipschitz continuous mapping. In the case of a nonlinear growth of the monotone function we prove the existence of the strong solution (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)