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Granularity, Scale & CollectivittyGranularity, Scale & CollectivittyWhen size does and doesn’t matterWhen size does and doesn’t matter

Alan L Rector

BioHealth Information GroupDepartment of Computer Science

University of Manchester rector@cs.man.ac.uk

www.cs.man.ac.uk/migwww.co-ode.org

www.clinical-escience.org

O p en G A L E N

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Bridging Scale & GranularityBridging Scale & Granularity“A key challenge for Bioinformatics”“A key challenge for Bioinformatics”

• But what do we mean by “granularity” and “scale”?

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MotivationMotivationThe Problem of Representing Information on TissuesThe Problem of Representing Information on Tissues

Retain the inference that loosing a a finger is an ‘Injury’? Retain the inference that loosing a a finger is an ‘Injury’? Avoid the inference that normal cell turnover is an ‘injury’Avoid the inference that normal cell turnover is an ‘injury’((Loosing a hepatocyte is not an injury to the liver)Loosing a hepatocyte is not an injury to the liver)

Hepatocytes are normally evenly arranged – Hepatocytes are normally evenly arranged – cirrhosis disrupts organisationcirrhosis disrupts organisation

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MotivationMotivation

• Distinction arose in GALEN but was little used– Worked almost entirely at level of gross anatomy

– Defects/conditions/procedures were almost always effects on the whole• Special mechanism to distinguish defects of the “thing as a whole”

• Essential to understanding developmental anatomy and metabolism– Normal cell/organelle/… turnover must not be an injury

• Needed to manage annotation– In different kinds of drawings are annotations refer differently

• Some point at specific things and their relations – “the relations of the stomach are…”

• Others point to repeating patterns of things

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PlanPlan

• Distinguish collectivity & size

• Describe a representation of collectivity in OWL

– Including non-bio generalisations

• Return to the issue of tissues

– Provide a practical ontology schema in OWL

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Collectivity / GranularityCollectivity / GranularitySize doesn’t matterSize doesn’t matter

• Collectivity at many sizes– Galaxies are made up (in part) of collectives of stars

– Audiences are made up (in part) of collectives of people

– Livers are made up (in part) of collectives of hepatocytes

– Cells are made up (in part) of collectives of mitochondria

– Crystals are made up (in part) of collectives atoms

““Collectives: What you can’t see if you get too close”Collectives: What you can’t see if you get too close”

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Scale:Scale:Size MattersSize Matters

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Scaling up Scaling up Size MattersSize Matters

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CollectivityCollectivityEmergent Effects MatterEmergent Effects Matter

• The time for the hourglass is a feature of the collective of sand (and the glass)• Would you try to predict it from examing the

individual grains?

• The strength of the cable is a feature of the collective of the fibres and how the go together• We do know how to predict it;

• But would you want to travel on a bridge held up by cables that had not been tested?

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Collectivity:Collectivity:Patterns MatterPatterns Matter

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CollectivesCollectives

• “Collectives” are made up of “grains”

• “Collectives” are not mathematical sets

– Collectives’ identity does not depend on the identity of their grains• Collectives can gain or lose grains without changing their identity

• Being a collective (“collectivity”) is independent of size

– Information patterns about Collectives and grains are similar at all physical sizes from subatomic to cosmological• Although collectives are normally larger than their grains

– (Except for odd quantum effects)

• Not “granular partitions”

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Collectivity & SizeCollectivity & Size

• Collectivity– Grains vs Collectives

• Cell vs CellsSand vs BeachPerson vs Crowd

• Size range– Large vs Small

• Cosmological vs ‘everyday’– Relativistic vs Newtonian

• ‘Everyday’ vs microscopic– Gravity vs electrostatic

• Macroscopic vs quantum– Causality vs probability

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Collectivity is not…Collectivity is not…

• Level of detail– Information about either collectives or grains can be in either

greater or lesser detail

• Ontological density– How many closely related concepts are represented

• Level of specialisation/generalisation or depth of ontology– There can be information about entities at any level of

specialisation

• Connectivity– How many relations link the entities in the ontology

How dense the network

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DeterminateDeterminate & & GranularGranular Parts Parts

• “Determinate parts”

– Fingers, lobes of liver, eyes, bolts, pistons, handles,…• Determinate in number;

• Directly part of other determinate parts of the whole

• Removing one determinate part diminishes the whole– Cutting off my finger diminishes my hand

• “Granular parts”

– Cells of skin of finger, liver cells, cones of retina, fibers of cable, …• Indeterminate in number

• Part of the whole via being a grain of a collective that is a determinate part of the whole

• Removing one granular part does not diminish the whole– Rubbing cells off my finger does not diminish my hand

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ContentionsContentions

• Information about collectives is distinct from information about their individual grains– There are “emergent” characteristics and effects of collectives

• Information about granular parts is treated differently from information about determinate parts – Much information about determined parts is propagated transitively to

the whole

– Little information about about granular parts is propagated transitively to the whole

– A mechanism is required to control in which questions pertain to which situation

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Representation Representation

• A hierarchy of relations (properties)

– is_part_of Mereological parthood transitive, reflexive, antisymmetric

• is_determinate_part_of Determinate parthood transitive, reflexive,

antisymmetric

• is_grain_of Granular parthoodintransitive, irreflexive,

antisymmetric (antitransitive?)

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Basic SchemasBasic Schemas

• Collective_of_X Collective & has_grain ONLY Xs

• Determinate_part_of_Object_X Object & is_determinate_part_of SOME Object_X

• Granular_part_of_Object_X Grain_Y AND is_grain_of SOME (Collective AND is_determinate_part_of SOME Object_X AND has_grain ONLY Grain_Y)

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ExampleExample

• Lobe_of_Liver Lobe & is_determinate_part_of SOME Liver

• Hepatocyte Cell & is_grain_of SOME (Collective AND is_determinate_part_of SOME Liver AND has_grain ONLY Hepatocyte)

Doesn’t quite work…Doesn’t quite work…

Problem with relation between Collectives & LiverProblem with relation between Collectives & LiverThere is more information to expressThere is more information to express

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Mixtures, Patterns, & TissuesMixtures, Patterns, & Tissues

normal

cirrhotic

normalimage

abnormaldiagram

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Collectives can manifest patternsCollectives can manifest patterns

• Normal_hepatocyte_collective Collective AND has_grain ONLY Hepatocyte

AND has_pattern SOME Quasi_hexagonal

But…But…

There is more than just hepatocytesThere is more than just hepatocytes connective tissues, interstitial fluid, … connective tissues, interstitial fluid, …

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Digression to Blood & blood cellsDigression to Blood & blood cells

• To a limited level of detail…

– Blood is a mixture of plasma red and white blood cells …

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MixturesMixtures

• Schema – Amount_of_Mixture_X_and_Y

Amount_of_ Mixture AND has_ingredient SOME X AND has_ingredient SOME Y

– Amount_of_Normal_blood Amount_of_Mixture AND has_ingredient SOME Plasma has_ingredient SOME (Collective AND has_grain SOME_&_ONLY Red_Blood_cell ) has_ingredient SOME (Collective AND has_grain ONLY White_Blood_cell )

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Proportions – Proportions – “Reify” the relation “has_ingredient”“Reify” the relation “has_ingredient”

to “Proportion”to “Proportion”

• Schema– Amount_of_Mixture_of_X1_and_X2_and_…_and_Xn

Amount_of_Mixture AND has_proportion SOME (Proportion AND is_of_ingredient SOME X1 AND has_percentage VALUE p1) AND has_proportion SOME (Proportion AND is_of_ingredient SOME X2 AND has_percentage VALUE p2) AND …AND has_proportion SOME (Proportion AND is_of_ingredient SOME Xn AND has_percentage VALUE pn)

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ExampleExample

– Amount_of_Normal_Blood Amount_of_Mixture AND

has_proportion SOME (Proportion AND is_of_ingredient SOME Amount_of_Plasma AND has_percentage VALUE 59) AND has_proportion SOME (Proportion AND is_of_ingredient SOME (Collective AND has_grain ONLY Red_blood_cell) AND has_percentage VALUE 39) AND AND has_proportion SOME (Proportion AND is_of_ingredient SOME (Collection AND has_grain ONLY White_blood_cell) AND has_percentage VALUE 2)

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Simplification trickSimplification trick

• Use the property hierarchy

– has_ingredient (transitive)• has_proportion (non-transitive)• is_of_ingredient (non-transitive)

• Then

– X has_ingredient SOME I• X has_proportion SOME (P is_of_ingredient SOME I)

• Expressed in usual logic notationX has_proportion SOME (P is_of_ingredient SOME I)

X has_ingredient SOME I

• Therefore we shall ignore proportions for the remainder of paper

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Back to LiverBack to LiverSome bits from FMA (I hope)Some bits from FMA (I hope)

– Liver

“(right / left) Lobe of liver”• …

– “Parenchyma of (right/left) lobe of liver”

» Lamina of liver

“Hepatocyte”

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Material of the LiverMaterial of the Liver

• Amount_of_liver_material– Amount_of_mixture AND

has_ingredient SOME (Collection AND has_grain ONLY Hepatocyte) has_ingredient SOME Amount_of_interstitial_fluid …

• Liver_lamina – has_determinate_part SOME Amount_of_liver_material AND

has_determinate_part SOME Bile_canniculus

• Liver_parenchyma – Collection has_grain SOME_&_ONLY Liver_lamina

• Lobe_of_liver – Object AND is_constituted_by SOME Liver_parenchyma AND

…

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And for a GalaxyAnd for a Galaxy

• Galaxy_with_black_whole_core – Astronomical_object AND

is_constituted_by SOME Mixture AND has_ingredient SOME_&_ONLY Star has_ingredient SOME Amount_of_dust_ …has_determinate_part SOME Galactic_core_black_hole

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And TilesAnd Tiles

• Penrose_tiling – Collective AND

has_grain SOME_&_ONLY Tiles has_pattern SOME Penrose_tiling_pattern)

• Penrose_wall_tiling – Physical_object AND

is_constituted_of (Mixture AND has_ingredient SOME Penrose_tiling has_ingredient SOME Grout has_ingredient SOME Adhesive)

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Implementing itImplementing itAugmenting the Property HierarchyAugmenting the Property Hierarchy

NB: Gross_parts include ingredients

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Slightly Simplified View Implemented in OWLSlightly Simplified View Implemented in OWLBlood First (simpler)Blood First (simpler)

granular part only

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And the LiverAnd the Liver

granular part only

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Determinate CollectivesDeterminate Collectives

• Entities where there is information both about the individual grains and the collective

– the spine, fingers, etc.

• Requires allowing things to be both a determinate and granular parts

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Cognitivist vs Realist PerspectiveCognitivist vs Realist Perspective

• Lobe_of_liver – ???? SOME

Amount_of_liver_parenchyma_AND …

• What should the relation be?– Cognitivist: is_constituted_by (Guarino & Welty/DOLCE)

• There are two co-existing entities– “The statue and the clay of which the statue is made”

» The liver and the material of which the liver is made

– Realist: identity• There is just one entity

– The statue is identical to the clay of which it is made» The liver is the material of which it is made

• Whichever, information about collective effects must be conveyed

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What does it account for?What does it account for?

• Where to ascribe information on emergent – Chacteristics - e.g. patterns

• on Collective or Mixture

– Relations – e.g. concentrations• on Proportion

• When are part-whole relations transitive?– The loss (gain) of granular parts does not necessarily diminish

(augment) the whole

– The loss (gain) of determinate parts necessarily diminishes (augments) the whole

• Defects of determinate parts are defects of the whole;defects of granular parts are not– Cell turnover does not damage the liver/skin/…

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What is not accounted forWhat is not accounted for

• Detailed account of collectives themselves

– Interaction of determinate parts and collectives• The bile canniculus in the Liver lamina

• Leaves open the issue of “empty collectives”

– ONLY vs SOME_&_ONLY

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What is an artefact of Description What is an artefact of Description Logic/OWL?Logic/OWL?

• Extension beyond binary relational

– Little change – collectives and proportions would still need to be reified.

• Any two-valued logic

– ‘Vagueness’ of collectives would still be underspecified

• Higher order logic

– Proportions might, or might not, not need to be reified• Many things can be said about the Proportion other than its

concentration

• Extension to fuzziness or other multivalued logic

– Better characterisation of vagueness of “Collectives”

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What the notion of collective deniesWhat the notion of collective denies

• Distinct levels of collectivity– Can occur at any size

• Hair vs hairs and macroscopic• Cell vs cells is microscopic• Mitochondrion vs mitochondria is sub-microscopic• Stars vs galaxies is astronomical

– Transitions between individual and collective to not form neat boundaries• Although if we jump far enough in scale we are likely also

to change level of collectivity

• “Collectivity” is a neologism– Is there a better alternative?

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SummarySummary

• Objects often act as collectives

• There are emergent effects to be attributed to the collective rather than to its grains

• The transition from grain to collective is not transitive

• Collectives occur at all size scales

• A good approximation can be represented in OWL

• Future work

– Collectives needed for a language to represent information about what pathologists and others usually call “tissues”