t trsrt tss strtrs - PowerPoint PPT Presentation

❖♥ t❤❡ tr❛♥s♣♦rt ♦❢ ✜♥✐t❡♥❡ss str✉❝t✉r❡s ▲✐♦♥❡❧ ❱❛✉①✱ ♠❛✐♥❧② ❜❛s❡❞ ♦♥ ❥♦✐♥t ✇♦r❦ ✇✐t❤ ❈❤r✐st✐♥❡ ❚❛ss♦♥ ■♥st✐t✉t ❞❡ ▼❛t❤é♠❛t✐q✉❡s ❞❡ ▲✉♠✐♥②✱ ▼❛rs❡✐❧❧❡✱ ❋r❛♥❝❡ ❚❆❈▲ ✷✵✶✶✱ ▼❛rs❡✐❧❧❡ ❏✉❧② ✷✻✲✸✵ ✷✵✶✶

❙❡ts ❛♥❞ r❡❧❛t✐♦♥s ❉❡✜♥✐t✐♦♥ ❚❤❡ ❝❛t❡❣♦r② Rel ♦❢ s❡ts ❛♥❞ r❡❧❛t✐♦♥s ❤❛s s❡ts ❛s ♦❜❥❡❝ts ❛♥❞ r❡❧❛t✐♦♥s ❛s ♠♦r♣❤✐s♠s✿ f ∈ Rel ( A, B ) ⇐ ⇒ f ⊆ A × B ✳ ❘❡❧❛t✐♦♥❛❧ ❝♦♠♣♦s✐t✐♦♥ ✐s ❣✐✈❡♥ ❜②✿ ( α, γ ) ∈ g ◦ f ⇐ ⇒ ∃ β, ( α, β ) ∈ f ∧ ( β, γ ) ∈ g. Rel ❛s ❛ ♠♦❞❡❧ ♦❢ ❧✐♥❡❛r ❧♦❣✐❝ ◮ ❝♦♠♣❛❝t ❝❧♦s❡❞✿ ⊗ = × ❛♥❞ f ⊥ = t f ❀ ◮ ❝❛rt❡s✐❛♥ ❛♥❞ ❝♦❝❛rt❡s✐❛♥✿ � ✐s ❛ ❜✐♣r♦❞✉❝t❀ ◮ ❡①♣♦♥❡♥t✐❛❧ str✉❝t✉r❡✿ ❣✐✈❡♥ ❜② t❤❡ ❝♦♠♦♥❛❞ ! = M f ✳

✐s ❝❛rt❡s✐❛♥ ❝❧♦s❡❞ ✇✐t❤ ♣r♦❞✉❝t ✳ ▼♦r❡♦✈❡r ✐t ✐s ❝♣♦✲❡♥r✐❝❤❡❞ ✭❢♦r s❡t ✐♥❝❧✉s✐♦♥✮✳ ❆ ❦❡② ✐♥t✉✐t✐♦♥ ▼♦r♣❤✐s♠s ✐♥ ❛r❡ t❤❡ s✉♣♣♦rt ♦❢ ♣♦✇❡r s❡r✐❡s✳ ❚❤❡ r❡❧❛t✐♦♥❛❧ ♠♦❞❡❧ ♦❢ t❤❡ λ ✲❝❛❧❝✉❧✉s ❆♣♣❧② t❤❡ ❝♦✲❑❧✐❡s❧✐ ❝♦♥str✉❝t✐♦♥ Rel ! ( A, B ) = Rel (! A, B ) ✇✐t❤ ❝♦♠♣♦s✐t✐♦♥ ❣✐✈❡♥ ❜②✿ �� n � � g ◦ ! f = � ; ∃ ([ β 1 , . . . , β n ] , γ ) ∈ g ∧ ∀ i, ( α i , β i ) ∈ f α i , γ i =1

❆ ❦❡② ✐♥t✉✐t✐♦♥ ▼♦r♣❤✐s♠s ✐♥ ❛r❡ t❤❡ s✉♣♣♦rt ♦❢ ♣♦✇❡r s❡r✐❡s✳ ❚❤❡ r❡❧❛t✐♦♥❛❧ ♠♦❞❡❧ ♦❢ t❤❡ λ ✲❝❛❧❝✉❧✉s ❆♣♣❧② t❤❡ ❝♦✲❑❧✐❡s❧✐ ❝♦♥str✉❝t✐♦♥ Rel ! ( A, B ) = Rel (! A, B ) ✇✐t❤ ❝♦♠♣♦s✐t✐♦♥ ❣✐✈❡♥ ❜②✿ �� n � � g ◦ ! f = � ; ∃ ([ β 1 , . . . , β n ] , γ ) ∈ g ∧ ∀ i, ( α i , β i ) ∈ f α i , γ i =1 Rel ! ✐s ❝❛rt❡s✐❛♥ ❝❧♦s❡❞ ✇✐t❤ ♣r♦❞✉❝t ⊎ ✳ ▼♦r❡♦✈❡r ✐t ✐s ❝♣♦✲❡♥r✐❝❤❡❞ ✭❢♦r s❡t ✐♥❝❧✉s✐♦♥✮✳

▼♦r♣❤✐s♠s ✐♥ ❛r❡ t❤❡ s✉♣♣♦rt ♦❢ ♣♦✇❡r s❡r✐❡s✳ ❚❤❡ r❡❧❛t✐♦♥❛❧ ♠♦❞❡❧ ♦❢ t❤❡ λ ✲❝❛❧❝✉❧✉s ❆♣♣❧② t❤❡ ❝♦✲❑❧✐❡s❧✐ ❝♦♥str✉❝t✐♦♥ Rel ! ( A, B ) = Rel (! A, B ) ✇✐t❤ ❝♦♠♣♦s✐t✐♦♥ ❣✐✈❡♥ ❜②✿ �� n � � g ◦ ! f = � ; ∃ ([ β 1 , . . . , β n ] , γ ) ∈ g ∧ ∀ i, ( α i , β i ) ∈ f α i , γ i =1 Rel ! ✐s ❝❛rt❡s✐❛♥ ❝❧♦s❡❞ ✇✐t❤ ♣r♦❞✉❝t ⊎ ✳ ▼♦r❡♦✈❡r ✐t ✐s ❝♣♦✲❡♥r✐❝❤❡❞ ✭❢♦r s❡t ✐♥❝❧✉s✐♦♥✮✳ ❆ ❦❡② ✐♥t✉✐t✐♦♥

❚❤❡ r❡❧❛t✐♦♥❛❧ ♠♦❞❡❧ ♦❢ t❤❡ λ ✲❝❛❧❝✉❧✉s ❆♣♣❧② t❤❡ ❝♦✲❑❧✐❡s❧✐ ❝♦♥str✉❝t✐♦♥ Rel ! ( A, B ) = Rel (! A, B ) ✇✐t❤ ❝♦♠♣♦s✐t✐♦♥ ❣✐✈❡♥ ❜②✿ �� n � � g ◦ ! f = � ; ∃ ([ β 1 , . . . , β n ] , γ ) ∈ g ∧ ∀ i, ( α i , β i ) ∈ f α i , γ i =1 Rel ! ✐s ❝❛rt❡s✐❛♥ ❝❧♦s❡❞ ✇✐t❤ ♣r♦❞✉❝t ⊎ ✳ ▼♦r❡♦✈❡r ✐t ✐s ❝♣♦✲❡♥r✐❝❤❡❞ ✭❢♦r s❡t ✐♥❝❧✉s✐♦♥✮✳ ❆ ❦❡② ✐♥t✉✐t✐♦♥ ▼♦r♣❤✐s♠s ✐♥ Rel ! ❛r❡ t❤❡ s✉♣♣♦rt ♦❢ ♣♦✇❡r s❡r✐❡s✳

❲❡ ♥❡❡❞ s♦♠❡ ♥♦t✐♦♥ ♦❢ ❝♦♥✈❡r❣❡♥❝❡✦ ❙✉❝❤ ✐♥t✉✐t✐♦♥s ✇❡r❡ ❛t t❤❡ ❝♦r❡ ♦❢ t❤❡ ✐♥✈❡♥t✐♦♥ ♦❢ ❧✐♥❡❛r ❧♦❣✐❝✳ ❋✐♥✐t❡♥❡ss s♣❛❝❡s ✭❊❤r❤❛r❞✱ ✷✵✵✵✬s✮ ■♥ ❛ t②♣❡❞ s❡tt✐♥❣✱ t❤❡ s✉♠ ✐s ❛❧✇❛②s ✜♥✐t❡✳ ▲❡❞ t♦ t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ t❤❡ ❞✐✛❡r❡♥t✐❛❧ ✲❝❛❧❝✉❧✉s ✭❊❤r❤❛r❞✕❘❡❣♥✐❡r✱ ✷✵✵✹✮✿ ❞✐✛❡r❡♥t✐❛t✐♦♥ ❛s ❛ ♥❛t✉r❛❧ tr❛♥s❢♦r♠❛t✐♦♥ ✳ ◗✉❛♥t✐t❛t✐✈❡ s❡♠❛♥t✐❝s ■❞❡❛ ✭●✐r❛r❞✱ ♣r❡✲▲▲✮ ■♥t❡r♣r❡t ❛ t❡r♠ s ❛s ❛ ❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥✿ � s � = � α ∈ � s � � s � α α s♦ t❤❛t ❛♣♣❧✐❝❛t✐♦♥ ✐s ❣✐✈❡♥ ❜②✿ � � s � ( α,β ) � t � α � s t � β = ( α,β ) ∈ � s � ✇❤❡r❡ � t � [ α 1 ,...,α k ] = � t � α 1 · · · � t � α k ✳

❙✉❝❤ ✐♥t✉✐t✐♦♥s ✇❡r❡ ❛t t❤❡ ❝♦r❡ ♦❢ t❤❡ ✐♥✈❡♥t✐♦♥ ♦❢ ❧✐♥❡❛r ❧♦❣✐❝✳ ❋✐♥✐t❡♥❡ss s♣❛❝❡s ✭❊❤r❤❛r❞✱ ✷✵✵✵✬s✮ ■♥ ❛ t②♣❡❞ s❡tt✐♥❣✱ t❤❡ s✉♠ ✐s ❛❧✇❛②s ✜♥✐t❡✳ ▲❡❞ t♦ t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ t❤❡ ❞✐✛❡r❡♥t✐❛❧ ✲❝❛❧❝✉❧✉s ✭❊❤r❤❛r❞✕❘❡❣♥✐❡r✱ ✷✵✵✹✮✿ ❞✐✛❡r❡♥t✐❛t✐♦♥ ❛s ❛ ♥❛t✉r❛❧ tr❛♥s❢♦r♠❛t✐♦♥ ✳ ◗✉❛♥t✐t❛t✐✈❡ s❡♠❛♥t✐❝s ■❞❡❛ ✭●✐r❛r❞✱ ♣r❡✲▲▲✮ ■♥t❡r♣r❡t ❛ t❡r♠ s ❛s ❛ ❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥✿ � s � = � α ∈ � s � � s � α α s♦ t❤❛t ❛♣♣❧✐❝❛t✐♦♥ ✐s ❣✐✈❡♥ ❜②✿ � � s � ( α,β ) � t � α � s t � β = ( α,β ) ∈ � s � ✇❤❡r❡ � t � [ α 1 ,...,α k ] = � t � α 1 · · · � t � α k ✳ ❲❡ ♥❡❡❞ s♦♠❡ ♥♦t✐♦♥ ♦❢ ❝♦♥✈❡r❣❡♥❝❡✦

t trsrt tss strtrs - PowerPoint PPT Presentation

t trsrt tss strtrs s t r t rst ss sttt

F air vie w Br idge R e plac e me nt and Str e e t Impr ove me nts (9 th Str e e t to 16 th

49.9 % $164.14 $81.84 28.5% 0.5% 28.9% Source: STR STR CALENDAR YEAR-TO-DATE September 2020

str t str t

Str e ss & Child obe sity: Die tar y pathways in the c onte xt of str e ss E le a no r T

Str e ss & Child obe sity: Die tar y pathways in the c onte xt of str e ss E le a no r T

YOUR TRUSTED PARTNER FOR HEALTH https://rafflesmedical.vn 167A Nam Ky Khoi Nghia Str., HCMC |Tel:

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with f-Strings Format Stings in Python Building up str values via concatenation can involve a

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BASE CHEMICALS INDIA CO. A H u b of I n d u str i a l Chem i ca ls ABOUT US W e appreciate your

9 floor s - ae r ial above inte r se c tion.jpg 9 floor s - str e e tvie w R ic hmond E

rrss rrt Pr

Hierarchies in inclusion logic Miika Hannula University of Helsinki 27.8.2014 Miika Hannula

Weighted Graphs weights on the edges of a graph represent distances, costs, etc. An

Fibrational View on Breadth-First Search Thorsten Wimann Informatik 8, Erlangen Oberseminar,

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t trsrt tss strtrs - PowerPoint PPT Presentation

t trsrt tss strtrs s t r t rst ss sttt

F air vie w Br idge R e plac e me nt and Str e e t Impr ove me nts (9 th Str e e t to 16 th

49.9 % $164.14 $81.84 28.5% 0.5% 28.9% Source: STR STR CALENDAR YEAR-TO-DATE September 2020

str t str t

Str e ss &amp; Child obe sity: Die tar y pathways in the c onte xt of str e ss E le a no r T

Str e ss &amp; Child obe sity: Die tar y pathways in the c onte xt of str e ss E le a no r T

YOUR TRUSTED PARTNER FOR HEALTH https://rafflesmedical.vn 167A Nam Ky Khoi Nghia Str., HCMC |Tel:

Analysis of kinship index y p distributions in Koreans using simulated autosomal STR profiles In

STR Regulatory Option Selection June 11 2019 Council Committee of the Whole STR Project Update

3D 3D- -Str Str Struct ucture re Pr Predict ction on of of th the 3D 3D Struct

What are the main data str u ct u res in P y thon ? P R AC TIC IN G C OD IN G IN TE R VIE W QU

Bar yon Resonanes and Str ong QCD Eb erhard Klempt Institut f ur Str ahlen{

with f-Strings Format Stings in Python Building up str values via concatenation can involve a

Str u ct u re &amp; optimal flo w C OU R SE C R E ATION AT DATAC AMP Da v id Campos Content De v

BASE CHEMICALS INDIA CO. A H u b of I n d u str i a l Chem i ca ls ABOUT US W e appreciate your

9 floor s - ae r ial above inte r se c tion.jpg 9 floor s - str e e tvie w R ic hmond E

rrss rrt Pr

Hierarchies in inclusion logic Miika Hannula University of Helsinki 27.8.2014 Miika Hannula

Weighted Graphs weights on the edges of a graph represent distances, costs, etc. An

Fibrational View on Breadth-First Search Thorsten Wimann Informatik 8, Erlangen Oberseminar,

(For Graduating Students) Chartered

Model checking and validity in propositional Jonni Virtema and modal inclusion logics

Larry Holder School of EECS Washington State University Artificial Intelligence 1 } Goal-based

Yangian symmetry of fishnet graphs Dmitry Chicherin JGU, Mainz, Germany IGST, 19 July 2017,

The classical integrable structure of AdS/CFT Beno t Vicedo DESY, Hamburg Cambridge, UK

Str e ss & Child obe sity: Die tar y pathways in the c onte xt of str e ss E le a no r T

Str e ss & Child obe sity: Die tar y pathways in the c onte xt of str e ss E le a no r T

Str u ct u re & optimal flo w C OU R SE C R E ATION AT DATAC AMP Da v id Campos Content De v