Download - fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Transcript
Page 1: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Identification of fast magnetic reconnection events in accretion disks under the action of MHD instabilitiesL U Í S H . S . K A D O WA K I

E L I S A B E T E M . D E G O U V E I A D A L P I N O

J A M E S M . S TO N E

O C TO B E R 1 7 , 2 0 1 7

M A G N E T I C F I E L D S I N T H E U N I V E R S E V I : F R O M L A B O R ATO R Y A N D S TA R S TO T H E P R I M O R D I A L S T R U C T U R E S

Page 2: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Outline

β€’ Magnetic reconnection in accretion disk systems

β€’ Numerical simulations with a shearing-box approach

β€’ MHD instabilities in accretion disks

β€’ Identification of fast magnetic reconnection events in the surroundings of accretion disks

β€’ Conclusions

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 2

Page 3: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Accretion disk systems

β€’ Accretion disks systems are believed to be very common structures in the Universe

β€’ These systems are associated to:β€’ Black Hole Binaries (BHBs)

β€’ Active Galactic Nuclei (AGNs)

β€’ Young Stellar Objects (YSOs) and so protoplanetary disks

β€’ The formation of a turbulent corona above and below accretion disks plays an important role in magnetic reconnection events

β€’ These events could explain the flare emissions in X-ray (YSOs) and in radio and gamma-ray (BHBs and AGNs)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 3

Page 4: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Turbulent magnetic reconnection in collisional flowsβ€’ Lazarian & Vishiniac (1999) model (Kowal’s talk):β€’ Reconnection triggered by tubulence

β€’ Several reconnection points (at all scales) due to the wandering magnetic field lines

β€’ β€œFast” reconnection

β€’ π‘‰π‘Ÿπ‘’π‘ ≃ 𝑉𝐴𝑀𝐴2

Numerical simulations (Kowal et al. 2009, 2012)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 4

Page 5: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

MHD numerical simulations of accretion disks and coronaMAGNETIC RECONNECTION UNDER THE ACTION OF MHD INSTABILITIES

Page 6: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Aims

β€’ The formation of a large scale poloidal magnetic field by the arising of loops due to the Parker-Rayleigh-Taylor instability

β€’ The role of Parker-Rayleigh-Taylor and magnetorotationalinstabilities in the formation of a turbulent magnetized corona around accretion disksβ€’ Where magnetic reconnection events could occur

β€’ The identification of fast magnetic reconnection events by the statistical analysis of the reconnection rate in the corona and disk

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 6

Page 7: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical method (shearing-box)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 7

Kadowaki (master’s thesis, 2011)

β€’ Shearing-Box (Hawley et al., 1995):β€’ A steady flow with a linear shearing velocity:

β€’ For a Keplerian disk:

Kadowaki et al. (2017, in prep.)

Page 8: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical method (shearing-box)β€’ MHD equations:

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 8

Page 9: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical method (shearing-box)β€’ Momentum equation:

Coriolis Force (Radial and Azimuthal components)

Centrifugal + Gravitational Forces (Radial component)

Gravity (Vertical component)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 9

Page 10: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical method (shearing-box)β€’ Boundary Conditions:β€’ Computational domain: 𝐿π‘₯, 𝐿𝑦e 𝐿𝑧

β€’ Strictly periodic in all the boundaries at 𝑑 = 0

β€’ The shearing is produced by the slipping of the boundaries in π‘₯ direction

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 10

Hawley et al. (1995)

Page 11: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

MHD instabilitiesMagnetorotational instability (MRI)

β€’ A weak magnetic field exerts an elastic force between two fluid elements

β€’ This force transfers angular momentum to the outer regionβ€’ Making possible the accretion in Keplerian

regimes

β€’ Linear regime: Amplification of the magnetic field (dynamo effect)

β€’ Non-linear regime: Saturation of the magnetic field and formation of turbulence

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 11

Page 12: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

MHD instabilitiesParker-Rayleigh-Taylor instability

β€’ Instability driven by strong magnetic fields:

β€’ 𝛽 =π‘ƒπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™

π‘ƒπ‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘= 1 (Magnetic buoyance)

β€’ Azimuthal magnetic field (βŠ₯ Ԧ𝑔)

β€’ Formation of magnetic loops β†’ Magnetic reconnection β†’ Release of energy in the coronal region

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 12

Kadowaki et al. (2017, in prep.)Parker (1966)

Page 13: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical results (Resolution: 2563)β€’ Athena code (Stone et al., 2008, 2010)

β€’ Model PMRIg_21H_oxyz12

β€’ Initial conditions: β€’ Isothermal system

β€’ Magnetostatic equilibrium

β€’ Azimuthal magnetic field (𝐡𝑦)

β€’ 𝛽 = 1.0

β€’ Initial Gaussian perturbation in the Keplerian velocity field

β€’ Boundaries conditions: β€’ π‘₯: Shearing-periodic

β€’ 𝑦: Periodic

β€’ 𝑧: Outflow

β€’ 12𝐻 Γ— 12𝐻 Γ— 12𝐻 (𝐻 = πΆπ‘†Ξ©βˆ’1)

β€’ 256𝐻 Γ— 256𝐻 Γ— 256𝐻 cells

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 13

Page 14: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical results (Resolution: 2563)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 14

Page 15: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical results (Resolution: 2563)

β€’ Transition between PRTI and MRI

β€’ Polarity inversions due to the action of the dynamo triggered by MRI

β€’ Zero net flux field ( 𝐡𝑧 β‰… 0)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 15

Page 16: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical results (Resolution: 2563)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 16

Page 17: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Numerical results (Comparison)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 17

Page 18: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Identification of fast magnetic reconnection events in accretion disksSTATISTICAL ANALYSIS OF THE MAGNETIC RECONNECTION RATE

Page 19: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

19Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 1st step: Sample of cells with 𝑗0 > πœ€ 𝛻 Γ— 𝐡

1 1 2 5 1

1 4 6 4 2

1 3 4 3 1

| 𝑗 | = 2.6

𝒙

π’š

In this work, we have used:πœ€ = 5

For Ξ΅ = 1

Page 20: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

20Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 2nd step: Sample of cells with local maxima π‘—π‘šπ‘Žπ‘₯ = 𝑀𝐴𝑋 𝑗 𝑛π‘₯×𝑛𝑦×𝑛𝑧

1 1 2 5 1

1 4 6 4 2

1 3 4 3 1

π‘—π‘šπ‘Žπ‘₯ = 6 =𝑀𝐴𝑋 𝑗 3Γ—3

𝒙

π’š

Page 21: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

21Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 3st step: Check if the local maxima is between opposite magnetic field polarity

π‘—π‘šπ‘Žπ‘₯Confirmed!

𝒙

π’š

𝑩𝒙

𝑩𝒙

π‘©π’šπ‘©π’š

Page 22: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

22Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 3st step: Check if the local maxima is between opposite magnetic field polarity

π‘—π‘šπ‘Žπ‘₯ Confirmed!

𝒙

π’š

𝑩𝒙

𝑩𝒙

π‘©π’šπ‘©π’š

Page 23: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

23Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 3st step: Check if the local maxima is between opposite magnetic field polarity

π‘—π‘šπ‘Žπ‘₯ Rejected!

𝒙

π’š

𝑩𝒙

𝑩𝒙

π‘©π’šπ‘©π’š

Page 24: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

24Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 4st step: Evaluate the eigenvectors of the Hessian matrix

𝐻 =

πœ•π‘₯π‘₯𝑗 πœ•π‘₯𝑦𝑗 πœ•π‘₯𝑧𝑗

πœ•π‘¦π‘₯𝑗 πœ•π‘¦π‘¦π‘— πœ•π‘¦π‘§π‘—

πœ•π‘§π‘₯𝑗 πœ•π‘§π‘¦π‘— πœ•π‘§π‘§π‘—

𝒙

π’š

π’†πŸ π’†πŸβ€’ π’†πŸ: Indicates the fastest decaying of 𝑗 (Thickness)

β€’ Projection of the magnetic and velocity fields along π’†πŸ, π’†πŸ and π’†πŸ‘ directions

Page 25: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Algorithm

25Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 5st step: Evaluate the magnetic reconnection rate

π’†πŸ

π’†πŸ

𝑉𝑖𝑛𝑉𝐴

=1

2ቀ

𝑉𝑒1𝑉𝐴 π‘™π‘œπ‘€π‘’π‘Ÿ

βˆ’ ቀ𝑉𝑒1𝑉𝐴 π‘’π‘π‘π‘’π‘Ÿ

𝑉𝐴 =𝐡𝑒1

2 + 𝐡𝑒22 + 𝐡𝑒3

2

πœŒπ‘™π‘œπ‘€π‘’π‘Ÿ

π‘’π‘π‘π‘’π‘Ÿ

𝑗 <1

2π‘—π‘šπ‘Žπ‘₯

𝑗 <1

2π‘—π‘šπ‘Žπ‘₯

𝑗 >1

2π‘—π‘šπ‘Žπ‘₯

Similar to Kowal et al. (2009)

Page 26: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Magnetic reconnection rate (Resolution: 2563)

26Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

Upper Corona

Confirmed!Rejected!

Page 27: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Magnetic reconnection rate (Resolution: 2563)

27Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

Upper Corona

Page 28: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Magnetic reconnection rate (Resolution: 2563)

28Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

Page 29: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Magnetic reconnection rate (Resolution: 2563)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 29

Page 30: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Magnetic reconnection rate (Resolution: 2563)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 31

Page 31: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Power spectrum (Resolution: 2563)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 32

t = 1 (Orbits) t = 2 (Orbits)

Page 32: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Power spectrum (Resolution: 2563)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 33

t = 4 (Orbits) t = 5 (Orbits)

Page 33: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Conclusions

β€’ Our simulations have revealed the arising of magnetic loops due to the PRTI followed by the development of turbulence due to PRTI and MRI

β€’ Even with an initial high magnetized regime, the disk evolves to a gas-pressure dominant regime with a magnetized coronaβ€’ Transport of magnetic field from the disk to the corona by buoyance process

β€’ We have evaluated the magnetic reconnection rates and detected the presence of fast magnetic reconnection events, as predicted by the theory of turbulence-induced fast reconnection (Lazarian & Vishiniac, 1999)

β€’ The algorithm applied to this work has demonstrated to be an efficient tool for the identification of magnetic reconnection sites in numerical simulations

Kadowaki, de Gouveia Dal Pino & Stone (2017, in prep.)

Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 34

Page 34: fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors of the Hessian matrix 𝐻= πœ• π‘—πœ• π‘—πœ• 𝑗 πœ• π‘—πœ• π‘—πœ•

Thank you!


Top Related

Two sample T 1) 1- 𝐻 0:𝜎12 =𝜎22 ... - fac.ksu.edu.safac.ksu.edu.sa/sites/default/files/excersices_2-328_stat_with_answers.pdf · t-Test: Paired Two Sample for Means method

Two sample T 1) 1- 𝐻 0:𝜎12 =𝜎22 ... - fac.ksu.edu.safac.ksu.edu.sa/sites/default/files/excersices_2-328_stat_with_answers.pdf · t-Test: Paired Two Sample for Means method

4st School of Engineering - SISTEMA AMBIENTEΒ Β· 2012. 11. 14.Β Β· - 1 - POLITECNICO DI TORINO 4st School of Engineering Master of Science in Management Engineering Graduation Thesis

4st School of Engineering - SISTEMA AMBIENTEΒ Β· 2012. 11. 14.Β Β· - 1 - POLITECNICO DI TORINO 4st School of Engineering Master of Science in Management Engineering Graduation Thesis

Geometry and measure - Higher Trigonometry Sine Curve ...Β Β· Trigonometry 𝑂 𝐻 𝐢 𝐴 𝐻 𝑂 𝐴 Example – finding a side: sin37=π‘₯ 5 x = 5 x sin 370 Example – finding

Geometry and measure - Higher Trigonometry Sine Curve ...Β Β· Trigonometry 𝑂 𝐻 𝐢 𝐴 𝐻 𝑂 𝐴 Example – finding a side: sin37=π‘₯ 5 x = 5 x sin 370 Example – finding

Holographic Entanglement of PurificationΒ Β· 2018-07-09Β Β· Strings 2018 (OIST) β€’Bekenstein-Hawking entropy 𝑆 𝐻= Area(π›Ύβ„Žπ‘–π‘§ Γ’ Γ‘) 4𝐺𝑁 β€’Holographic entanglement

Holographic Entanglement of PurificationΒ Β· 2018-07-09Β Β· Strings 2018 (OIST) β€’Bekenstein-Hawking entropy 𝑆 𝐻= Area(π›Ύβ„Žπ‘–π‘§ Γ’ Γ‘) 4𝐺𝑁 β€’Holographic entanglement

Grondement DRIVE V-BELTΒ Β· 2019. 11. 21.Β Β· gyro x(4st) gyro canopy(2st) gyro canopy(2st) gyro canopy(4st) γ‚Έγƒ₯γƒͺγ‚ͺ50（julio ... td01 td01 td01 td02 ta02 ta02 ta03 af52 af24

Grondement DRIVE V-BELTΒ Β· 2019. 11. 21.Β Β· gyro x(4st) gyro canopy(2st) gyro canopy(2st) gyro canopy(4st) γ‚Έγƒ₯γƒͺγ‚ͺ50（julio ... td01 td01 td01 td02 ta02 ta02 ta03 af52 af24

Automatic highlighting Contextual entity searchxye/papers_and_ppts/ppts/entities...Microsoft Research 116 𝐻 … I spent a lot of time finding music that was motivating and that

Automatic highlighting Contextual entity searchxye/papers_and_ppts/ppts/entities...Microsoft Research 116 𝐻 … I spent a lot of time finding music that was motivating and that

Lecture 22 - Princeton University Computer Science(t) = (1- Ξ³) wi(t) 𝐾wj(t) 𝑗=1 + Ξ³. 1 𝐾, i = 1,…,K β€’ Balancing exploration and exploitation in Exp3 –The distribution

Lecture 22 - Princeton University Computer Science(t) = (1- Ξ³) wi(t) 𝐾wj(t) 𝑗=1 + Ξ³. 1 𝐾, i = 1,…,K β€’ Balancing exploration and exploitation in Exp3 –The distribution

Calit.rala St.3tpc Lib:yrs Foundation Money Not 4st For ...

Calit.rala St.3tpc Lib:yrs Foundation Money Not 4st For ...

Languages
Pages
Legal

Copyright Β© 2022 FDOCUMENTS