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Xholon
------
Title: Applied Category Theory - NIST workshop
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My Notes
--------
April 24, 2018
Notes on NIST workshop on applied category theory, held March 15th & 16th

References
----------
(1) http://www.appliedcategorytheory.org/?p=*
    Applied Category Theory
    Thanks again to all of the participants at the NIST workshop on applied category theory, held March 15th & 16th.
    Below are links to the slides and videos for most of the talks from the meeting.

(2) https://johncarlosbaez.wordpress.com/2018/04/18/applied-category-theory-at-nist-part-2/
    Here are links to the slides and videos for most of the talks from this workshop:
    • Applied Category Theory: Bridging Theory & Practice, March 15–16, 2018, NIST, Gaithersburg, Maryland, USA. Organized by Spencer Breiner and Eswaran Subrahmanian.

(3) https://golem.ph.utexas.edu/category/2018/02/applied_category_theory_at_nis.html
    Applied Category Theory at NIST
    My former student Blake Pollard is working at the National Institute of Standards and Technology on applications of category theory to electrical engineering. He’s working with Spencer Breiner… and now Breiner is running a workshop on this stuff:
    • Applied Category Theory: Bridging Theory & Practice, March 15–16, 2018, NIST, Gaithersburg, Maryland, USA.

(4) https://www.youtube.com/playlist?list=PLjBkYfAO7i9Ai0G4C8YybJOuersb32IrU
    playlist

(5) https://www.darpa.mil/program/complex-adaptive-system-composition-and-design-environment
    KSW - mentioned in Applied Category Theory workshop; mentioned in John Baez talk
    Complex Adaptive System Composition And Design Environment (CASCADE)
    Dr. John S. Paschkewitz
    System-of-Systems (SoS) architectures are increasingly central in managing defense, national security and urban infrastructure applications.
    However, it is difficult to model and currently impossible to systematically design such complex systems using existing tools, which has led to inferior performance, unexpected problems and weak resilience.
    The DARPA Complex Adaptive System Composition And Design Environment (CASCADE) program seeks to address these shortcomings and fundamentally change how systems are designed for real-time resilient response
    to dynamic, unexpected contingencies.
    The goal of CASCADE is to provide a unified view of system behavior, allowing understanding and exploitation of these complex interactions and a formal language for complex adaptive system composition and design.
    This unified view of system behavior, enabled by appropriate mathematical foundations, may also enable adaptation to unanticipated environments using arbitrary system components by providing a framework
    to dynamically identify and correct deficient system capabilities.

(6) http://catinf.com/
    March 2018
    - CI announces the completion of its research program, with million rows per minute pullbacks and pushouts, at the NIST Applied Category Theory Conference.
    February 2018
    - CI is named as a sub-contractor for PROTEUS, and delivers a milestone for BRASS.

(7) https://www.darpa.mil/program/prototype-resilient-operations-testbed-for-expeditionary-urban-operations
    PROTEUS
    Prototype Resilient Operations Testbed for Expeditionary Urban Operations (PROTEUS)
    Dr. John S. Paschkewitz
    As nation-state and non-state adversaries adapt and apply commercially available state-of-the-art technology in urban conflict,
    expeditionary U.S. forces face a shrinking operational advantage in potential future military conflicts,
    which are most likely to be fought in littoral and coastal cities.
    The goal of the Prototype Resilient Operations Testbed for Expeditionary Urban Operations (PROTEUS) program is to create and
    demonstrate tools to develop and test agile expeditionary urban operations concepts based on dynamically composable force packages.
    The program seeks to:
    - Develop software for simultaneous and dynamic real-time task organization, force package (i.e. platforms & weapons) combination and configuration, and tactics planning suitable for implementation in devices available to Marines in the 2030-2040 timeframe;
    - Develop a purpose-built virtual test environment to exercise and demonstrate this capability with an appropriately detailed virtual representation of combined arms operations in a complex urban battlespace; and
    - Exercise both capabilities in a series of benchmarking tests involving a participant cohort for both friendly and opposing forces drawn from active duty Marines. These tests will demonstrate that the ability to dynamically compose small unit organization, capabilities and tactics enables superior performance in the battlespace quantified using metrics such as lethality/(area-cost), resilience, and cost imposition.
    - If successful, the software tools and concepts developed in the PROTEUS program will enable assessment and exploration of new approaches to combined arms operations involving coordination of effects in multiple domains.

(8) https://www.darpa.mil/program/building-resource-adaptive-software-systems
    BRASS
    Building Resource Adaptive Software Systems (BRASS)
    Dr. Sandeep Neema
    The goal of the Building Resource Adaptive Software Systems program (BRASS) is to realize foundational advances in the design and implementation of
    long-lived, survivable and complex software systems that are robust to changes in the physical and logical resources provided by their ecosystem.
    These advances will necessitate integration of new resource-aware program abstractions and analyses, in addition to novel compiler and systems designs to trigger adaptive transformations and validate their effectiveness.

(9) https://www.youtube.com/watch?v=bL3lTMvpKHE&index=5&list=PLjBkYfAO7i9Ai0G4C8YybJOuersb32IrU
  ) http://www.appliedcategorytheory.org/wp-content/uploads/2018/03/John-Baez-Compositional-Design-and-Tasking-of-Networks-Part-1.pdf
    John Baez talk
    John Baez Compositional Design and Tasking of Networks Part 1

    Three ways of composing networks, of sticking things together:
    1. series
       Categories and operates are uniquely suited to describing that works and ways of composing them.
       Networks can be connected end-to-end in series.

    2. parallel
       networks can also be set side-by-side, in parallel
    Mathematicians now understand these forms of composition very well using categories with extra structure:
     - monoidal categories, dagger-compact categories, hypergraph categories... all these are algebras of various operads.
    In the complex adaptive system composition and design environment project,
    I am working with Metron scientific solutions to build networks using another form of composition -
    overlaying.
    The hope is that new ideas from category Theory can give new ways to design complex systems.

    3. overlaying
       Sometimes we can overlay two networks with the same vertices.
       There are many kinds of Networks, and many possible rules for overlaying them.
       - Simple graphs
       - Multigraphs
       - Directed multigraphs
       - Directed multigraphs with colored edges and nodes
       - Hypergraphs
       - huge numbeer of other possible networks

    We should handle all these kinds of networks in a unified way.

    Define a network model to be a symmetric lax monoidal functor
     F: S(C) -> Mon
    where S(C) is the free symmetric monoidal category on some
    set C of vertex colors, and Mon is the category of monoids.
    Mon is a set of networks with those specific nodes.
    It's a monooid because you cn multiply two networks; you can overlay them.
    The overlay operation is the operation in this monoid.

    For any network model F there is an operad Of whose
    operations are ways to assemble networks of type F.
    These operations include overlaying networks, setting networks side-by-side,
    and thus also attaching networks end-to-end.

    The operad OF will have many algebras. These describe
    different kinds of systems that can be modeled using networks of type F.

]]></Notes>

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	<Notes><![CDATA[
	Xholon
	------
	Title: Applied Category Theory - NIST workshop
	Description:
	Url: http://www.primordion.com/Xholon/gwt/
	InternalName: 3f888eeb48d36ff94c6dce9b6ec520f4
	Keywords:

	My Notes
	--------
	April 24, 2018
	Notes on NIST workshop on applied category theory, held March 15th & 16th

	References
	----------
	(1) http://www.appliedcategorytheory.org/?p=*
	Applied Category Theory
	Thanks again to all of the participants at the NIST workshop on applied category theory, held March 15th & 16th.
	Below are links to the slides and videos for most of the talks from the meeting.

	(2) https://johncarlosbaez.wordpress.com/2018/04/18/applied-category-theory-at-nist-part-2/
	Here are links to the slides and videos for most of the talks from this workshop:
	• Applied Category Theory: Bridging Theory & Practice, March 15–16, 2018, NIST, Gaithersburg, Maryland, USA. Organized by Spencer Breiner and Eswaran Subrahmanian.

	(3) https://golem.ph.utexas.edu/category/2018/02/applied_category_theory_at_nis.html
	Applied Category Theory at NIST
	My former student Blake Pollard is working at the National Institute of Standards and Technology on applications of category theory to electrical engineering. He’s working with Spencer Breiner… and now Breiner is running a workshop on this stuff:
	• Applied Category Theory: Bridging Theory & Practice, March 15–16, 2018, NIST, Gaithersburg, Maryland, USA.

	(4) https://www.youtube.com/playlist?list=PLjBkYfAO7i9Ai0G4C8YybJOuersb32IrU
	playlist

	(5) https://www.darpa.mil/program/complex-adaptive-system-composition-and-design-environment
	KSW - mentioned in Applied Category Theory workshop; mentioned in John Baez talk
	Complex Adaptive System Composition And Design Environment (CASCADE)
	Dr. John S. Paschkewitz
	System-of-Systems (SoS) architectures are increasingly central in managing defense, national security and urban infrastructure applications.
	However, it is difficult to model and currently impossible to systematically design such complex systems using existing tools, which has led to inferior performance, unexpected problems and weak resilience.
	The DARPA Complex Adaptive System Composition And Design Environment (CASCADE) program seeks to address these shortcomings and fundamentally change how systems are designed for real-time resilient response
	to dynamic, unexpected contingencies.
	The goal of CASCADE is to provide a unified view of system behavior, allowing understanding and exploitation of these complex interactions and a formal language for complex adaptive system composition and design.
	This unified view of system behavior, enabled by appropriate mathematical foundations, may also enable adaptation to unanticipated environments using arbitrary system components by providing a framework
	to dynamically identify and correct deficient system capabilities.

	(6) http://catinf.com/
	March 2018
	- CI announces the completion of its research program, with million rows per minute pullbacks and pushouts, at the NIST Applied Category Theory Conference.
	February 2018
	- CI is named as a sub-contractor for PROTEUS, and delivers a milestone for BRASS.

	(7) https://www.darpa.mil/program/prototype-resilient-operations-testbed-for-expeditionary-urban-operations
	PROTEUS
	Prototype Resilient Operations Testbed for Expeditionary Urban Operations (PROTEUS)
	Dr. John S. Paschkewitz
	As nation-state and non-state adversaries adapt and apply commercially available state-of-the-art technology in urban conflict,
	expeditionary U.S. forces face a shrinking operational advantage in potential future military conflicts,
	which are most likely to be fought in littoral and coastal cities.
	The goal of the Prototype Resilient Operations Testbed for Expeditionary Urban Operations (PROTEUS) program is to create and
	demonstrate tools to develop and test agile expeditionary urban operations concepts based on dynamically composable force packages.
	The program seeks to:
	- Develop software for simultaneous and dynamic real-time task organization, force package (i.e. platforms & weapons) combination and configuration, and tactics planning suitable for implementation in devices available to Marines in the 2030-2040 timeframe;
	- Develop a purpose-built virtual test environment to exercise and demonstrate this capability with an appropriately detailed virtual representation of combined arms operations in a complex urban battlespace; and
	- Exercise both capabilities in a series of benchmarking tests involving a participant cohort for both friendly and opposing forces drawn from active duty Marines. These tests will demonstrate that the ability to dynamically compose small unit organization, capabilities and tactics enables superior performance in the battlespace quantified using metrics such as lethality/(area-cost), resilience, and cost imposition.
	- If successful, the software tools and concepts developed in the PROTEUS program will enable assessment and exploration of new approaches to combined arms operations involving coordination of effects in multiple domains.

	(8) https://www.darpa.mil/program/building-resource-adaptive-software-systems
	BRASS
	Building Resource Adaptive Software Systems (BRASS)
	Dr. Sandeep Neema
	The goal of the Building Resource Adaptive Software Systems program (BRASS) is to realize foundational advances in the design and implementation of
	long-lived, survivable and complex software systems that are robust to changes in the physical and logical resources provided by their ecosystem.
	These advances will necessitate integration of new resource-aware program abstractions and analyses, in addition to novel compiler and systems designs to trigger adaptive transformations and validate their effectiveness.

	(9) https://www.youtube.com/watch?v=bL3lTMvpKHE&index=5&list=PLjBkYfAO7i9Ai0G4C8YybJOuersb32IrU
	) http://www.appliedcategorytheory.org/wp-content/uploads/2018/03/John-Baez-Compositional-Design-and-Tasking-of-Networks-Part-1.pdf
	John Baez talk
	John Baez Compositional Design and Tasking of Networks Part 1

	Three ways of composing networks, of sticking things together:
	1. series
	Categories and operates are uniquely suited to describing that works and ways of composing them.
	Networks can be connected end-to-end in series.

	2. parallel
	networks can also be set side-by-side, in parallel
	Mathematicians now understand these forms of composition very well using categories with extra structure:
	- monoidal categories, dagger-compact categories, hypergraph categories... all these are algebras of various operads.
	In the complex adaptive system composition and design environment project,
	I am working with Metron scientific solutions to build networks using another form of composition -
	overlaying.
	The hope is that new ideas from category Theory can give new ways to design complex systems.

	3. overlaying
	Sometimes we can overlay two networks with the same vertices.
	There are many kinds of Networks, and many possible rules for overlaying them.
	- Simple graphs
	- Multigraphs
	- Directed multigraphs
	- Directed multigraphs with colored edges and nodes
	- Hypergraphs
	- huge numbeer of other possible networks

	We should handle all these kinds of networks in a unified way.

	Define a network model to be a symmetric lax monoidal functor
	F: S(C) -> Mon
	where S(C) is the free symmetric monoidal category on some
	set C of vertex colors, and Mon is the category of monoids.
	Mon is a set of networks with those specific nodes.
	It's a monooid because you cn multiply two networks; you can overlay them.
	The overlay operation is the operation in this monoid.

	For any network model F there is an operad Of whose
	operations are ways to assemble networks of type F.
	These operations include overlaying networks, setting networks side-by-side,
	and thus also attaching networks end-to-end.

	The operad OF will have many algebras. These describe
	different kinds of systems that can be modeled using networks of type F.

	]]></Notes>

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