foundations of network diagrams
play

Foundations of Network Diagrams: Dynamical Systems, Bayesian - PowerPoint PPT Presentation

Dec 26, 2023 •643 likes •942 views

Foundations of Network Diagrams: Dynamical Systems, Bayesian Networks and Quantum Processes Filippo Bonchi University of Pisa Quantum Teleportation Quantum Teleportation 1932: von Neumanns original formulation of quantum theory based on

  1. Foundations of Network Diagrams: Dynamical Systems, Bayesian Networks and Quantum Processes Filippo Bonchi University of Pisa

  2. Quantum Teleportation

  3. Quantum Teleportation 1932: von Neumann’s original formulation of quantum theory based on Hilbert spaces

  4. Quantum Teleportation 1932: von Neumann’s original formulation of quantum theory based on Hilbert spaces New York Times headline of May 4, 1935.

  5. Quantum Teleportation 1932: von Neumann’s original formulation of quantum theory based on Hilbert spaces 1935: EPR weirdness of non-locality: "spooky action at distance" New York Times headline of May 4, 1935.

  6. Quantum Teleportation 1932: von Neumann’s original formulation of quantum theory based on Hilbert spaces 1935: EPR weirdness of non-locality: "spooky action at distance" 1993: Bennet et al. conceived the feature of quantum teleportation. New York Times headline of May 4, 1935.

  7. Quantum Teleportation 1932: von Neumann’s original formulation of quantum theory based on Hilbert spaces 1935: EPR weirdness of non-locality: "spooky action at distance" 1993: Bennet et al. conceived the feature of quantum teleportation. New York Times headline of May 4, 1935. Why did it take so long?

  8. Quantum Pictorialism

  9. Quantum Pictorialism Reasoning about quantum systems via Hilbert spaces is rather incovenient, pretty much like programming a distributed application in Assembly

  10. Quantum Pictorialism Reasoning about quantum systems via Hilbert spaces is rather incovenient, pretty much like programming a distributed application in Assembly ¨ ˛ 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i ´ ´ ˚ ‹ π 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ´ i 1 ´ i ´ ´ 2 ˚ ‹ 1 ´ i 1 ´ i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ˚ ‹ vs. π ˚ ‹ 2 4 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ´ i 1 ´ i ´ ´ ˚ ‹ π 1 ´ i 1 ´ i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ ˚ ‹ 2 ˝ ‚ 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i ´ ´

  11. Quantum Pictorialism Reasoning about quantum systems via Hilbert spaces is rather incovenient, pretty much like programming a distributed application in Assembly ¨ ˛ 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i ´ ´ ˚ ‹ π 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ´ i 1 ´ i ´ ´ 2 ˚ ‹ 1 ´ i 1 ´ i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ˚ ‹ vs. π ˚ ‹ 2 4 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ´ i 1 ´ i ´ ´ ˚ ‹ π 1 ´ i 1 ´ i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ ˚ ‹ 2 ˝ ‚ 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i ´ ´ Developing an high level language for quantum system would boost the discovery of quantum features and the development of quantum technologies

  12. Quantum Pictorialism Reasoning about quantum systems via Hilbert spaces is rather incovenient, pretty much like programming a distributed application in Assembly ¨ ˛ 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i ´ ´ ˚ ‹ π 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ´ i 1 ´ i ´ ´ 2 ˚ ‹ 1 ´ i 1 ´ i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ˚ ‹ vs. π ˚ ‹ 2 4 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ´ i 1 ´ i ´ ´ ˚ ‹ π 1 ´ i 1 ´ i 1 ´ i 1 ´ i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ ˚ ‹ 2 ˝ ‚ 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i 1 ´ i 1 ´ i 1 ` i ´ ´ 1 ` i 1 ´ i 1 ´ i 1 ` i 1 ` i 1 ` i 1 ` i 1 ` i ´ ´ Developing an high level language for quantum system would boost the discovery of quantum features and the development of quantum technologies

  13. Network diagrams Electrical Circuits Bayesian Networks Quantum Processes Petri Nets Signal Flow Graphs x x x

  14. Network diagrams Signal Flow Graphs x x x

  15. Network diagrams Diagrammatic languages are not really made of syntax. Signal Flow Graphs x x x

  16. Network diagrams Diagrammatic languages are not really made of syntax. Signal Flow Graphs x x x We are able to describe the behaviour of the whole systems

  17. Network diagrams Diagrammatic languages are not really made of syntax. Signal Flow Graphs x x x We are able to describe the behaviour of the whole systems But not the behaviour of the single components

  18. Network diagrams Diagrammatic languages are not really made of syntax. Signal Flow Graphs x x x ? ? We are able to describe the behaviour of the whole systems But not the behaviour of the single components

  19. Network diagrams Diagrammatic languages are not really made of syntax. Signal Flow Graphs x x x ? ? We are able to describe the behaviour of the whole systems But not the behaviour of the single components The behaviour of the whole system should be "reducible" to the behaviour of its components

  20. Network diagrams Diagrammatic languages are not really made of syntax. Signal Flow Graphs x x x ? ? We are able to describe the behaviour of the whole systems But not the behaviour of the single components The behaviour of the whole system should be "reducible" to the behaviour of its components https://www.azimuthproject.org/azimuth/show/Network+theory

  21. Compositional Modelling There is an emerging, multi-disciplinary field aiming at studying different sorts of networks compositionally , inspired by the algebraic methods of programming language semantics. Diagrams are first-class citizens of the theory. The appropriate algebraic setting is monoidal (and not cartesian ) categories.

  22. https://www.forbes.com/sites/cognitiveworld/2019/07/29/the-future- Compositional Modelling will-be-formulated-using-category-theory/#71a09469625e There is an emerging, multi-disciplinary field aiming at studying different sorts of networks compositionally , inspired by the algebraic methods of programming language semantics. Diagrams are first-class citizens of the theory. The appropriate algebraic setting is monoidal (and not cartesian ) categories.

  23. Signal Flow Graphs Signal Flow Graphs are stream processing circuits widely adopted in Control Theory and Signal Processing k x Claude Shannon. The theory and design of linear differential equation machines (1942).

  24. Signal Flow Graphs Signal Flow Graphs are stream processing circuits widely adopted in Control Theory and Signal Processing c, d ::= k x k x c d c d Claude Shannon. The theory and design of linear differential equation machines (1942).

  25. Sound and Complete Axiomatisation for Signal Flow Graphs = = = = Bialgebra = = = = id0 ≤ ≤ ≤ ≤ ≤ ≤ id0 ≤ ≤

  26. Sound and Complete Axiomatisation for Signal Flow Graphs = = = = Bialgebra = = = = id0 ≤ ≤ ≤ ≤ ≤ ≤ id0 ≤ ≤ https://graphicallinearalgebra.net

  27. Sound and Complete Axiomatisation for Signal Flow Graphs These axioms = = are almost = = the same as Bialgebra those for = Quantum mechanics = = = id0 ≤ ≤ ≤ ≤ ≤ ≤ id0 ≤ ≤ https://graphicallinearalgebra.net

  28. Sound and Complete Axiomatisation for Signal Flow Graphs These axioms = = What is are almost = = the same as going on Bialgebra those for = ? Quantum mechanics = = = id0 ≤ ≤ ≤ ≤ ≤ ≤ id0 ≤ ≤ https://graphicallinearalgebra.net

  29. References Bonchi, Sobocinski, Zanasi - Full Abstraction for Signal Flow Graphs , • POPL, 2015. [see also Fabio Zanasi ph.D thesis - Interacting Hopf Algebras (ENS-Lyon, 2015)] Bonchi, Gadducci, Kissinger, Sobocinski, Zanasi - Rewriting modulo • symmetric monoidal structure - LICS 2016. Bonchi, Soboci ń ski, Zanasi - Interacting Hopf algebras. Journal of Pure • and Applied Algebra (2017). Bonchi, Holland, Piedeleu, Sobocinski, Zanasi - Diagrammatic Algebra: • From Linear to Concurrent Systems , POPL, 2019. [see also Robin Piedeleu Ph.D thesis - Picturing resources in concurrency (Oxford, 2019) ] Bonchi, Piedeleu, Sobocinski, Zanasi - Graphical Affine Algebra , LICS • 2019.

Recommend

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J CSCI 6268/TLEN 5831, Fall 2004 Introduction UC Davis PhD in 2000 Cryptography Interested in broader security as well

493 views • 12 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #25 Dec 1 st 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Remainder of the semester: Quiz #3 is Today 40 mins

414 views • 20 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #13 Oct 11 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Quiz #2 later today Allocate last 30 mins No Class

488 views • 30 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #3 Aug 30 st 2005 CSCI 6268/TLEN 5831, Fall 2005 Assignment #0 Please add yourself to the class mailing list Send mail

379 views • 35 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #22 Nov 11 th 2004 CSCI 6268/TLEN 5831, Fall 2004 Announcements Proj #2 Due week from today Following Thurs is

485 views • 25 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #12 Oct 6 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Project #0 assigned today Due Oct 18 th in class

718 views • 33 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #14 Oct 18 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Quiz #2 back today Well go over some points before we

686 views • 46 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #16 Oct 25 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Project #1 is assigned See web page for description and

799 views • 45 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #18 Oct 28 th 2004 CSCI 6268/TLEN 5831, Fall 2004 Announcements Quiz #3 Thurs, Nov 4 th A week from today How to

695 views • 50 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #15 Oct 20 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Reading: How to 0wn the Internet See schedule page

647 views • 49 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #24 Nov 29 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Remainder of the semester: Project #2 is due today (please

317 views • 29 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #13 Oct 7 th 2004 CSCI 6268/TLEN 5831, Fall 2004 Announcements Two new readings were assigned How to 0wn the Internet in

768 views • 39 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #6 Sep 8 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Quiz #1 later today Still some have not signed up for

799 views • 34 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #27 Dec 8 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Back from Tucson last night 7 below zero at DIA?!

402 views • 14 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #2 Aug 25 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Economist Survey Please read it Main points Security is a MUCH

600 views • 27 slides
Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn

Foundations of Network and Foundations of Network and Computer Security Computer Security J ohn Black J Lecture #9 Sep 22 nd 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Midterm #1, next class (Tues, Sept 27 th ) All lecture

739 views • 40 slides
Some Comments on the Some Comments on the Foundations of Network Analysis Foundations of Network

Some Comments on the Some Comments on the Foundations of Network Analysis Foundations of Network

Some Comments on the Some Comments on the Foundations of Network Analysis Foundations of Network Analysis Carter T. Butts Carter T. Butts Department of Sociology and Department of Sociology and Institute for Mathematical Behavioral Sciences

387 views • 11 slides
Visualizing Geometric Proofs 3D surface diagrams Lukas Heidemann Diagrams 0-diagrams 1

Visualizing Geometric Proofs 3D surface diagrams Lukas Heidemann Diagrams 0-diagrams 1

Visualizing Geometric Proofs 3D surface diagrams Lukas Heidemann Diagrams 0-diagrams 1 1-diagrams: bead diagrams 2 1-diagrams: bead diagrams 2 2-diagrams: string diagrams 3 2-diagrams: string diagrams 4 2-diagrams: string diagrams 5

696 views • 40 slides
Probabilistic Foundations of Statistical Network Analysis Chapter 3: Network sampling Harry Crane

Probabilistic Foundations of Statistical Network Analysis Chapter 3: Network sampling Harry Crane

Probabilistic Foundations of Statistical Network Analysis Chapter 3: Network sampling Harry Crane Based on Chapter 3 of Probabilistic Foundations of Statistical Network Analysis Book website: http://www.harrycrane.com/networks.html Harry Crane

375 views • 18 slides
Probabilistic Foundations of Statistical Network Analysis Chapter 5: Statistical modeling paradigm

Probabilistic Foundations of Statistical Network Analysis Chapter 5: Statistical modeling paradigm

Probabilistic Foundations of Statistical Network Analysis Chapter 5: Statistical modeling paradigm Harry Crane Based on Chapter 5 of Probabilistic Foundations of Statistical Network Analysis Book website: http://www.harrycrane.com/networks.html

443 views • 31 slides
What is network security? Friends and enemies: Alice, Bob, Trudy What is network security?

What is network security? Friends and enemies: Alice, Bob, Trudy What is network security?

Network security Network security Foundations: what is security? cryptography Network Security Network Security authentication message integrity key distribution and certification Security in practice: Srinidhi Varadarajan

334 views • 6 slides
Todays Lecture INF 111 / CSE 121: UML Software Tools and Methods Package Diagrams

Todays Lecture INF 111 / CSE 121: UML Software Tools and Methods Package Diagrams

Todays Lecture INF 111 / CSE 121: UML Software Tools and Methods Package Diagrams State Transition Diagrams Activity Diagrams y g Communication Diagrams Lecture Notes for Summer Quarter, 2008 Michele Rousseau Set 8

462 views • 7 slides
1 Class Diagrams and Entity Relationship Diagrams (ERD) Class diagrams and ERDs both model the

1 Class Diagrams and Entity Relationship Diagrams (ERD) Class diagrams and ERDs both model the

Tutorial W eek 7 - Class and Entity-Relationship Diagram s 1 Class Diagrams and Entity Relationship Diagrams (ERD) Class diagrams and ERDs both model the structure of a system. Class diagrams represent the dynamic aspects of a system: both

166 views • 14 slides
UML Class Diagrams Steven Zeil February 25, 2013 UML Class Diagrams Outline Class

UML Class Diagrams Steven Zeil February 25, 2013 UML Class Diagrams Outline Class

UML Class Diagrams UML Class Diagrams Steven Zeil February 25, 2013 UML Class Diagrams Outline Class Diagrams 1 A Class, in Isolation 2 Attributes Operations Generalization Relationships 3 Associations 4 Naming Your

948 views • 68 slides

More recommend