State Dynamics of the Epileptic Brain

2013 ◽  
Author(s):  
Samuel P. Burns ◽  
Sabato Santaniello ◽  
William S. Anderson ◽  
Sridevi V. Sarma
Keyword(s):  
State Space ◽  
State Space Model ◽  
Network Connectivity ◽  
Seizure Onset ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Finite Set ◽  
Brain States ◽  
The Brain ◽  
Insight Into

Communication between specialized regions of the brain is a dynamic process allowing for different connections to accomplish different tasks. While the content of interregional communication is complex, the pattern of connectivity (i.e., which regions communicate) may lie in a lower dimensional state-space. In epilepsy, seizures elicit changes in connectivity, whose patterns shed insight into the nature of seizures and the seizure focus. We investigated connectivity in 3 patients by applying network-based analysis on multi-day subdural electrocorticographic recordings (ECoG). We found that (i) the network connectivity defines a finite set of brain states, (ii) seizures are characterized by a consistent progression of states, and (iii) the focus is isolated from surrounding regions at the seizure onset and becomes most connected in the network towards seizure termination. Our results suggest that a finite-dimensional state-space model may characterize the dynamics of the epileptic brain, and may ultimately be used to localize seizure foci.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

scholarly journals Unsupervised seizure localisation with attention-based graph neural networks

2020 ◽  
Author(s):  
Daniele Grattarola ◽  
Lorenzo Livi ◽  
Cesare Alippi ◽  
Richard Wennberg ◽  
Taufik Valiante
Keyword(s):  
Neural Networks ◽  
Brain Activity ◽  
Functional Networks ◽  
Seizure Onset ◽  
The Past ◽  
Seizure Onset Zone ◽  
Brain States ◽  
Graph Neural Networks ◽  
Intracranial Electroencephalography ◽  
The Brain

Abstract Graph neural networks (GNNs) and the attention mechanism are two of the most significant advances in artificial intelligence methods over the past few years. The former are neural networks able to process graph-structured data, while the latter learns to selectively focus on those parts of the input that are more relevant for the task at hand. In this paper, we propose a methodology for seizure localisation which combines the two approaches. Our method is composed of several blocks. First, we represent brain states in a compact way by computing functional networks from intracranial electroencephalography recordings, using metrics to quantify the coupling between the activity of different brain areas. Then, we train a GNN to correctly distinguish between functional networks associated with interictal and ictal phases. The GNN is equipped with an attention-based layer which automatically learns to identify those regions of the brain (associated with individual electrodes) that are most important for a correct classification. The localisation of these regions is fully unsupervised, meaning that it does not use any prior information regarding the seizure onset zone. We report results both for human patients and for simulators of brain activity. We show that the regions of interest identified by the GNN strongly correlate with the localisation of the seizure onset zone reported by electroencephalographers. We also show that our GNN exhibits uncertainty on those patients for which the clinical localisation was also unsuccessful, highlighting the robustness of the proposed approach.

Perturbation Theory for Weak Measurements in Quantum Mechanics, Systems with Finite-Dimensional State Space

2018 ◽  
Vol 20 (1) ◽  
pp. 299-335 ◽  
Author(s):  
Miguel Ballesteros ◽  
Nick Crawford ◽  
Martin Fraas ◽  
Jürg Fröhlich ◽  
Baptiste Schubnel
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
State Space ◽  
Weak Measurements ◽  
Finite Dimensional ◽  
Dimensional State Space

Finite Dimensional State-Space Models

2013 ◽  
pp. 17-44
Author(s):  
Brigitte d’Andréa-Novel ◽  
Michel De Lara
Keyword(s):  
State Space ◽  
State Space Models ◽  
Finite Dimensional ◽  
Dimensional State Space

scholarly journals Model building and verification for active control of microvibrations with probabilistic assessment of the effects of uncertainties

2004 ◽  
Vol 218 (4) ◽  
pp. 389-399 ◽  
Author(s):  
G S Aglietti ◽  
R S Langley ◽  
E Rogers ◽  
S B Gabriel
Keyword(s):  
Active Control ◽  
Model Building ◽  
Controller Design ◽  
Equations Of Motion ◽  
State Space Model ◽  
Experimental Studies ◽  
Model Approximation ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Low Amplitude

Microvibrations, generally defined as low-amplitude vibrations at frequencies up to 1 kHz, are of critical importance in a number of areas. It is now well known that, in general, the suppression of such microvibrations to acceptable levels requires the use of active control techniques which, in turn, require sufficiently accurate and tractable models of the underlying dynamics on which to base controller design and initial performance evaluation. Previous work has developed a systematic procedure for obtaining a finite-dimensional state-space model approximation of the underlying dynamics from the defining equations of motion, which has then been shown to be a suitable basis for robust controller design. In this paper, the experimental validation of this model prior to experimental studies is described in order to determine the effectiveness of the designed controllers. This includes details of the experimental rig and also the use of methods for assessing the safety of the resulting structure against uncertain parameters.

scholarly journals Quantum Aitchison geometry

2021 ◽  
Vol 24 (01) ◽  
pp. 2150001
Author(s):  
Attila Andai ◽  
Attila Lovas
Keyword(s):  
Hilbert Space ◽  
State Space ◽  
Scalar Product ◽  
Likelihood Function ◽  
Real Hilbert Space ◽  
Space Structure ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Probability Simplex ◽  
Log Ratio

Multiplying a likelihood function with a positive number makes no difference in Bayesian statistical inference, therefore after normalization the likelihood function in many cases can be considered as probability distribution. This idea led Aitchison to define a vector space structure on the probability simplex in 1986. Pawlowsky-Glahn and Egozcue gave a statistically relevant scalar product on this space in 2001, endowing the probability simplex with a Hilbert space structure. In this paper, we present the noncommutative counterpart of this geometry. We introduce a real Hilbert space structure on the quantum mechanical finite dimensional state space. We show that the scalar product in quantum setting respects the tensor product structure and can be expressed in terms of modular operators and Hamilton operators. Using the quantum analogue of the log-ratio transformation, it turns out that all the newly introduced operations emerge naturally in the language of Gibbs states. We show an orthonormal basis in the state space and study the introduced geometry on the space of qubits in details.

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