iss small gain theorem for spatiotemporal delayed
play

ISS small-gain theorem for spatiotemporal delayed dynamics with - PowerPoint PPT Presentation

Mar 29, 2023 •180 likes •844 views

ISS small-gain theorem for spatiotemporal delayed dynamics with application to feedback attenuation of pathological brain oscillations A. Chaillet 1 , G. Detorakis 1 , S. Palfi 2 , S. Senova 2 1: L2S - Univ. Paris Sud - CentraleSup elec 1:

  1. ISS small-gain theorem for spatiotemporal delayed dynamics with application to feedback attenuation of pathological brain oscillations A. Chaillet 1 , G. Detorakis 1 , S. Palfi 2 , S. Senova 2 1: L2S - Univ. Paris Sud - CentraleSup´ elec 1: AP-HP, Hospital H. Mondor - INSERM, U955 Team 14 - Univ. Paris Est Seminar at CAS, Paris, 19/02/2016 A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 1 / 32

  2. Context and motivations 1 A spatiotemporal rate model for the STN-GPe pacemaker 2 ISS for delayed spatiotemporal dynamics 3 Stabilization of STN-GPe by proportional feedback 4 Conclusion and perspectives 5 A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 2 / 32

  3. Context and motivations 1 A spatiotemporal rate model for the STN-GPe pacemaker 2 ISS for delayed spatiotemporal dynamics 3 Stabilization of STN-GPe by proportional feedback 4 Conclusion and perspectives 5 A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 3 / 32

  4. Basal ganglia Basal ganglia (BG) are deep brain nuclei involved in motor, cognitive, associative and mnemonic functions ◮ Striatum (Str) ◮ External segment of globus pallidus (GPe) ◮ Internal segment of globus pallidus (GPi) ◮ Subthalamic nucleux (STN) ◮ Substantia nigra (SN) Interact with cortex, thalamus, brain stem and spinal cord, as well as other structures (superior colliculus (SC), reticular formation (RF), pedunculopontine nucleus (PPN), and [Bolam et al. 2009] lateral habenula (HBN)). A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 4 / 32

  5. Parkinson’s disease and BG activity Bursting activity of STN and GPe neurons: [Ammari et al. 2011] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 5 / 32

  6. Parkinson’s disease and BG activity Bursting activity of STN and GPe neurons: [Ammari et al. 2011] Local field potential (LFP) in PD STN and GPe show prominent 13 − 30 Hz ( β -band) oscillations: ◮ In parkinsonian patients: [Hammond et al. 2007] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 5 / 32

  7. Parkinson’s disease and BG activity Bursting activity of STN and GPe neurons: [Ammari et al. 2011] Local field potential (LFP) in PD STN and GPe show prominent 13 − 30 Hz ( β -band) oscillations: ◮ In parkinsonian patients: [Hammond et al. 2007] ◮ In MPTP monkeys: A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 5 / 32

  8. Parkinson’s disease and BG activity Reduction of β -band oscillations induces motor symptoms improvement [Hammond et al. 2007, Little et al. 2012] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 6 / 32

  9. Parkinson’s disease and BG activity Reduction of β -band oscillations induces motor symptoms improvement [Hammond et al. 2007, Little et al. 2012] β -oscillations may decrease during Deep Brain Stimulation [Eusebio et al. 2013] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 6 / 32

  10. Parkinson’s disease and BG activity Oscillations onset still debated Parkinsonian symptoms mechanisms are not fully understood either: Pacemaker effect of the STN-GPe loop ? Striatal endogenous oscillations ? Thalamo-cortical relay gating mechanism ? [Bolam et al. 2009] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 7 / 32

  11. Parkinson’s disease and BG activity Oscillations onset still debated Parkinsonian symptoms mechanisms are not fully understood either: Pacemaker effect of the STN-GPe loop ? Striatal endogenous oscillations ? Thalamo-cortical relay gating mechanism ? [Bolam et al. 2009] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 7 / 32

  12. Parkinson’s disease and BG activity Oscillations onset still debated Parkinsonian symptoms mechanisms are not fully understood either: Pacemaker effect of the STN-GPe loop ? Striatal endogenous oscillations ? Thalamo-cortical relay gating mechanism ? [Bolam et al. 2009] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 7 / 32

  13. Disrupting pathological oscillations Technological solutions to steer brain populations dynamics Deep Brain Stimulation [Benabid et al. 91] : A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 8 / 32

  14. Disrupting pathological oscillations Technological solutions to steer brain populations dynamics Deep Brain Stimulation [Benabid et al. 91] : Optogenetics [Boyden et al. 2005] : A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 8 / 32

  15. Disrupting pathological oscillations Technological solutions to steer brain populations dynamics Deep Brain Stimulation [Benabid et al. 91] : Acoustic neuromodulation [Eggermont & Tass 2015] Sonogenetics [Ibsen et al. 2015] Transcranial current stim. [Brittain et al. 2013] Transcranial magnetic stim. Optogenetics [Boyden et al. 2005] : [Strafella et al. 2004] Magnetothermal stim. [Chen et al. 2015] A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 8 / 32

  16. Some attempts towards closed-loop brain stimulation A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 9 / 32

  17. Modeling neuronal populations Rate models Firing rate: instantaneous number of spikes per time unit Mesoscopic models ◮ Focuses on populations rather than single neurons ◮ Allows analytical treatment ◮ Well-adapted to experimental constraints Relies on Wilson & Cowan model [Wilson & Cowan 1972] ◮ Interconnection of an inhibitory and an excitatory populations ◮ Too much synaptic strength generates instability Simulation analysis: [Gillies et al. 2002, Leblois et al. 2006] Analytical conditions for tremor onset [Nevado-Holgado et al. 2010, Pavlides et al. 2012, Pasillas-L´ epine 2013]. A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 10 / 32

  18. Modeling neuronal populations Rate models Firing rate: instantaneous number of spikes per time unit Mesoscopic models ◮ Focuses on populations rather than single neurons ◮ Allows analytical treatment ◮ Well-adapted to experimental constraints Relies on Wilson & Cowan model [Wilson & Cowan 1972] ◮ Interconnection of an inhibitory and an excitatory populations ◮ Too much synaptic strength generates instability Simulation analysis: [Gillies et al. 2002, Leblois et al. 2006] Analytical conditions for tremor onset [Nevado-Holgado et al. 2010, Pavlides et al. 2012, Pasillas-L´ epine 2013]. A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 10 / 32

  19. Modeling neuronal populations Rate models Firing rate: instantaneous number of spikes per time unit Mesoscopic models ◮ Focuses on populations rather than single neurons ◮ Allows analytical treatment ◮ Well-adapted to experimental constraints Relies on Wilson & Cowan model [Wilson & Cowan 1972] ◮ Interconnection of an inhibitory and an excitatory populations ◮ Too much synaptic strength generates instability Simulation analysis: [Gillies et al. 2002, Leblois et al. 2006] Analytical conditions for tremor onset [Nevado-Holgado et al. 2010, Pavlides et al. 2012, Pasillas-L´ epine 2013]. A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 10 / 32

  20. Modeling neuronal populations Limitations of existing works Spatial heterogeneity needs to be considered: ◮ Oscillations onset might be related to local neuronal organization [Schwab et al., 2013] ◮ Spatial correlation could play a role in PD symptoms [Cagnan et al., 2015] ◮ Possible exploitation of multi-plot electrodes. Techniques needed for analytical treatments of both: ◮ Nonlinearities ◮ Delays. A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 11 / 32

  21. Context and motivations 1 A spatiotemporal rate model for the STN-GPe pacemaker 2 ISS for delayed spatiotemporal dynamics 3 Stabilization of STN-GPe by proportional feedback 4 Conclusion and perspectives 5 A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 12 / 32

  22. Spatiotemporal model of STN-GPe dynamics Employed model: delayed neural fields   2 ∂ x 1 � w 1 j ( r , r ′ ) x j ( r ′ , t − d j ( r , r ′ )) dr ′ + α ( r ) u ( r , t ) � τ 1 ∂ t = − x 1 + S 1 (1a)   Ω j =1   2 ∂ x 2 � �  . τ 2 ∂ t = − x 2 + S 2 w 2 j ( r , r ′ ) x j ( r ′ , t − d j ( r , r ′ )) dr ′ (1b)  Ω j =1 1: STN population (directly controlled), 2: GPe population (no control) x i ( r , t ) rate of population i at time t and position r ∈ Ω τ i : decay rate w ij : synaptic weights distributions S i : activation functions d i : delay distributions α : impact of stimulation, u : control signal. A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 13 / 32

  23. Spatiotemporal model of STN-GPe dynamics Employed model: delayed neural fields   2 ∂ x 1 � w 1 j ( r , r ′ ) x j ( r ′ , t − d j ( r , r ′ )) dr ′ + α ( r ) u ( r , t ) � τ 1 ∂ t = − x 1 + S 1 (1a)   Ω j =1   2 ∂ x 2 � �  . τ 2 ∂ t = − x 2 + S 2 w 2 j ( r , r ′ ) x j ( r ′ , t − d j ( r , r ′ )) dr ′ (1b)  Ω j =1 1: STN population (directly controlled), 2: GPe population (no control) x i ( r , t ) rate of population i at time t and position r ∈ Ω τ i : decay rate w ij : synaptic weights distributions S i : activation functions d i : delay distributions α : impact of stimulation, u : control signal. A. Chaillet (L2S) Small-gain for spatiotemporal delayed dyn. CAS 13 / 32

Recommend

A Call For Action Daniel Ahmed Delayed, Delayed, Delayed Heroin Assisted Treatment Delays

A Call For Action Daniel Ahmed Delayed, Delayed, Delayed Heroin Assisted Treatment Delays

Heroin Assisted Treatment The Middlesbrough Story A Call For Action Daniel Ahmed Delayed, Delayed, Delayed Heroin Assisted Treatment Delays Require 3 licenses 1 = Diamorphine prescribing licenses 2 = Control drug licenses 3 =

306 views • 19 slides
Stabilization of interconnected switched control-affine systems via a Lyapunov-based small-gain

Stabilization of interconnected switched control-affine systems via a Lyapunov-based small-gain

Stabilization of interconnected switched control-affine systems via a Lyapunov-based small-gain approach Guosong Yang 1 Daniel Liberzon 1 Zhong-Ping Jiang 2 1 Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL

495 views • 20 slides
Comments on Delayed-Start Design, Doubly Randomized Delayed-Start & Matched-Control Design

Comments on Delayed-Start Design, Doubly Randomized Delayed-Start & Matched-Control Design

Comments on Delayed-Start Design, Doubly Randomized Delayed-Start & Matched-Control Design H.M. James Hung, Ph.D. Tristan Massie, Ph.D. Division of Biometrics I, OB/OTS/CDER, FDA Presented in ISCTM, Washington, DC, February 21, 2019 1

515 views • 13 slides
A spatiotemporal stochastic model for tropical precipitation and water vapor dynamics. Scott

A spatiotemporal stochastic model for tropical precipitation and water vapor dynamics. Scott

A spatiotemporal stochastic model for tropical precipitation and water vapor dynamics. Scott Hottovy and Sam Stechmann (UW) shottovy@math.wisc.edu University of Wisconsin ONR DURIP grant N00014-14-1-0251 S. Hottovy, UW Spatiotemporal

381 views • 16 slides
Planning for Winter Historical position of occupied bed days and delayed discharge Reasons

Planning for Winter Historical position of occupied bed days and delayed discharge Reasons

Delayed Discharge / Planning for Winter Historical position of occupied bed days and delayed discharge Reasons for delay Recommendations for the winter plan for 18/19 NHS Borders - Delayed Discharges Length of Delay at Census Point

381 views • 13 slides
A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits Nutan Limaye Compuer

A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits Nutan Limaye Compuer

A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits Nutan Limaye Compuer Science and Engineering Department, Indian Institute of Technology, Bombay, (IITB) India. Joint work with Suryajith Chillara, Christian Engels,

2.53k views • 191 slides
31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the

31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the

31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the divergence theorem is to Greens theorem, for the flux. Both are 3D generalisations of 2D theorems. Theorem 31.1 (Stokes Theorem) . Let C be any closed

406 views • 3 slides
29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a

29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a

29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a closed surface bounding a solid D , oriented outwards. Let F be a vector field with continuous partial derivatives. Then F d

471 views • 3 slides
Analysis on the spatiotemporal dis istribution of f OCO-2 2 XCO 2 over So South Korea Ga

Analysis on the spatiotemporal dis istribution of f OCO-2 2 XCO 2 over So South Korea Ga

Analysis on the spatiotemporal dis istribution of f OCO-2 2 XCO 2 over So South Korea Ga Gawon Kim im , Youngsuk Oh , Samuel Takele Kenea , Jaesang Rhee , Tae-Young Goo and Younghwa Byun NOAA GMD Annual Meeting 23-24, May, 2017 1.

601 views • 11 slides
Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over

Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over

Griffith University 3130CIT Theory of Computation (Based on slides by Harald Sndergaard of The University of Melbourne) Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over a finite

422 views • 17 slides
1 Spatiotemporal Query Service Design Goals of MobiQuery Allows a mobile user to periodically

1 Spatiotemporal Query Service Design Goals of MobiQuery Allows a mobile user to periodically

Mission-critical Applications Spatiotemporal Query for Wireless Sensor Networks Structural Health Fire Monitoring Real-time Tracking Monitoring Guoliang Xing ; Chenyang Lu, Octav Chipara Chien-Liang Fok, Sangeeta Bhattacharya Spatially

289 views • 4 slides
Spatiotemporal Regulation of ERK by Spatiotemporal Regulation of ERK by Dual- -specificity

Spatiotemporal Regulation of ERK by Spatiotemporal Regulation of ERK by Dual- -specificity

Spatiotemporal Regulation of ERK by Spatiotemporal Regulation of ERK by Dual- -specificity Phosphatases specificity Phosphatases Dual University of Bristol IN Cell 1000 University of Bristol IN Cell 1000 WT Equipment Grant WT Equipment

551 views • 20 slides
Conditional and Small Sample Probability August 6, 2019 August 6, 2019 1 / 63 Bayes Theorem

Conditional and Small Sample Probability August 6, 2019 August 6, 2019 1 / 63 Bayes Theorem

Conditional and Small Sample Probability August 6, 2019 August 6, 2019 1 / 63 Bayes Theorem Bayes Theorem will help us more easily calculate P (statement about variable 1 | statement about variable 2) when we have information about P

759 views • 63 slides
and Monitoring wit ith Streaming Spatiotemporal Data Nan Cao, Chaoguang Lin, Quihan Zhu, Yu-Ru

and Monitoring wit ith Streaming Spatiotemporal Data Nan Cao, Chaoguang Lin, Quihan Zhu, Yu-Ru

Voila: Vis isual Anomaly Detection and Monitoring wit ith Streaming Spatiotemporal Data Nan Cao, Chaoguang Lin, Quihan Zhu, Yu-Ru Lin, Xian Teng, Xidao Wen. IEEE Transactions on Visualization and Computer Graphics (Volume: PP, Issue: 99)

388 views • 13 slides
To gain an understanding of psychotropic medication and its purpose To gain an

To gain an understanding of psychotropic medication and its purpose To gain an

To gain an understanding of psychotropic medication and its purpose To gain an understanding of the roles that psychotropic medication may play in the assessment and intervention process To gain an understanding of how side effects

663 views • 38 slides
IMMORAL GAIN 9 Woe to him who gets evil gain for his house To put his nest on high, To be

IMMORAL GAIN 9 Woe to him who gets evil gain for his house To put his nest on high, To be

THE FOLLY OF IMMORAL GAIN 9 Woe to him who gets evil gain for his house To put his nest on high, To be delivered from the hand of calamity! THE FOLLY OF 10 You have devised a shameful thing for your house IMMORAL GAIN By cutting off many

532 views • 49 slides
PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks

PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks

PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks Theorem. Ingo Wegener, 2005 Computational Complexity, by Fu Yuxi PCP Theorem 1 / 119 S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof

1.53k views • 120 slides
Lecture 12- ECE 240a Threshold Mirror Loss Ver Chap. 8-9 Threshold Conditions Homogeneous

Lecture 12- ECE 240a Threshold Mirror Loss Ver Chap. 8-9 Threshold Conditions Homogeneous

Lecture 12- ECE 240a Review Small Signal Gain Resonant Frequencies Lasing Conditions Lasing Lecture 12- ECE 240a Threshold Mirror Loss Ver Chap. 8-9 Threshold Conditions Homogeneous Gain Media Gain Saturation 1 ECE 240a Lasers -

425 views • 40 slides
On Theorem Proving for Program Checking Historical perspective and recent developments Maria

On Theorem Proving for Program Checking Historical perspective and recent developments Maria

Outline Introduction Where is theorem proving in program checking Inside theorem proving Big and little engines together: a new theorem proving style Decision procedures with speculative inferences Current and future challenges On Theorem

944 views • 69 slides
1 Gain vs Vmesh 50000 y = 1.196305E-04e 3.300424E-02x y = 2.541469E-04e 2.812789E-02x Gain

1 Gain vs Vmesh 50000 y = 1.196305E-04e 3.300424E-02x y = 2.541469E-04e 2.812789E-02x Gain

1 Gain vs Vmesh 50000 y = 1.196305E-04e 3.300424E-02x y = 2.541469E-04e 2.812789E-02x Gain Ar:CO2 - 93:7 5000 Ar:CO2 - 80:20 500 450 500 550 600 650 700 Vmesh 2 Ar:CO2 80:20 3 Ar:CO2 - 80:20 (Mesh) for high n-rate Gain 2711

239 views • 21 slides
GAIN FFI GAIN Premix Facility Rizwan Yusufali Senior Associate March 2010 The GAIN Vision,

GAIN FFI GAIN Premix Facility Rizwan Yusufali Senior Associate March 2010 The GAIN Vision,

GAIN FFI GAIN Premix Facility Rizwan Yusufali Senior Associate March 2010 The GAIN Vision, Mission, Goal Driven by the vision of a world without malnutrition GAINs mission is to reduce global malnutrition through food

289 views • 15 slides
The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are

The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are

The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are finite subsets of V such that V = Span ( G ) , |G| = n , L is linearly independent, and |L| = m . Then m n and there is a set H G , such that

468 views • 36 slides
MINERAL CHELATION FACTS ON CHELATION IMPACT ON REPRODUCTION AND COMPOSITION OF GAIN JOEL F

MINERAL CHELATION FACTS ON CHELATION IMPACT ON REPRODUCTION AND COMPOSITION OF GAIN JOEL F

MINERAL CHELATION FACTS ON CHELATION IMPACT ON REPRODUCTION AND COMPOSITION OF GAIN JOEL F MANGALINDAN DVM Clinical Nutrition Practitioner www.agriaccess.com MINERALS - constitute very small fraction of body weight and diet - vital

973 views • 50 slides
Identification of Spatiotemporal Interdependencies and Complexity Evolution in a Multiple Aircraft

Identification of Spatiotemporal Interdependencies and Complexity Evolution in a Multiple Aircraft

Identification of Spatiotemporal Interdependencies and Complexity Evolution in a Multiple Aircraft Environment Marko Radanovic, Miquel Angel Piera, Thimjo Koca UAB Christian Verdonk, Francisco Javier Saez Cranfield University 7 th SESAR

413 views • 18 slides

More recommend