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Pr♦❜❛❜✐❧✐st✐❝ ❆✐r❝r❛❢t ❈♦♥✢✐❝t ❉❡t❡❝t✐♦♥ ❛♥❞ ❘❡s♦❧✉t✐♦♥ ❈♦♥s✐❞❡r✐♥❣ ❲✐♥❞ ❯♥❝❡rt❛✐♥t②

❊✉❧❛❧✐❛ ❍❡r♥á♥❞❡③✲❘♦♠❡r♦✱ ❆❧❢♦♥s♦ ❱❛❧❡♥③✉❡❧❛✱ ❛♥❞ ❉❛♠✐á♥ ❘✐✈❛s

❊s❝✉❡❧❛ ❚é❝♥✐❝❛ ❙✉♣❡r✐♦r ❞❡ ■♥❣❡♥✐❡rí❛✱ ❯♥✐✈❡rs✐❞❛❞ ❞❡ ❙❡✈✐❧❧❛✱ ❙♣❛✐♥

✼t❤ ❙❊❙❆❘ ■♥♥♦✈❛t✐♦♥ ❉❛②s ❈♦♥❢❡r❡♥❝❡ ❙■❉✬ ✶✼✱ ❇❡❧❣r❛❞❡✱ ❙❡r❜✐❛ ✷✽✲✸✵ ◆♦✈❡♠❜❡r ✷✵✶✼

✶ ✴ ✶✾

❖✉t❧✐♥❡

■♥tr♦❞✉❝t✐♦♥ ❈♦♥✢✐❝t ❝❤❛r❛❝t❡r✐③❛t✐♦♥ Pr♦❜❛❜✐❧✐st✐❝ ❈❉❘ ❆♣♣❧✐❝❛t✐♦♥ ✲ ❘❡s✉❧ts ❙✉♠♠❛r② ✲ ❋✐♥❛❧ r❡♠❛r❦s

✷ ✴ ✶✾

▼♦t✐✈❛t✐♦♥

❯♥❞❡rst❛♥❞✐♥❣✴ ♠❛♥❛❣✐♥❣ ✉♥❝❡rt❛✐♥t② ✐s ❦❡② t♦ ♣r♦✈✐❞❡ ❜❡tt❡r ❞❡❝✐s✐♦♥ s✉♣♣♦rt✳ Pr♦❝❡❞✉r❡s t♦ ✐♥t❡❣r❛t❡ ✉♥❝❡rt❛✐♥t② ✐♥❢♦r♠❛t✐♦♥ ✐♥t♦ t❤❡ ❆❚▼ ♣❧❛♥♥✐♥❣ ♣r♦❝❡ss ♠✉st ❜❡ ❞❡✈❡❧♦♣❡❞✳ ■♥ ♣❛rt✐❝✉❧❛r✱ ✇❡❛t❤❡r ♣r❡❞✐❝t✐♦♥ ✉♥❝❡rt❛✐♥t②✳ ■t ✐s ❡①♣❡❝t❡❞ t❤❛t ❜② ❝♦♥s✐❞❡r✐♥❣ t❤❡ ✇❡❛t❤❡r ♣r❡❞✐❝t✐♦♥ ✉♥❝❡rt❛✐♥t②✱ t❤❡ s❛❢❡t② ❛♥❞ ❡✣❝✐❡♥❝② ♦❢ t❤❡ ❛✐r tr❛✣❝ ♠❛② ❜❡ ✐♠♣r♦✈❡❞✳ Pr♦❥❡❝t ❚❇❖✲▼❡t ✭❍✷✵✷✵ ❘❡❢✳ ✻✾✾✷✾✹✮ ▼❡t❡♦r♦❧♦❣✐❝❛❧ ❯♥❝❡rt❛✐♥t② ▼❛♥❛❣❡♠❡♥t ❢♦r ❚r❛❥❡❝t♦r② ❇❛s❡❞ ❖♣❡r❛t✐♦♥s✳ ❙❊❙❆❘ ✷✵✷✵ ❊①♣❧♦r❛t♦r② ❘❡s❡❛r❝❤❀ ❚♦♣✐❝✿ ▼❡t❡♦r♦❧♦❣②✳

✸ ✴ ✶✾

❈❛s❡ st✉❞②

Pr♦❜❧❡♠✿ Pr♦❜❛❜✐❧✐st✐❝ ❈♦♥✢✐❝t ❉❡t❡❝t✐♦♥ ❛♥❞ ❘❡s♦❧✉t✐♦♥ ❯♥❝❡rt❛✐♥t② s♦✉r❝❡✿ ❲✐♥❞ ❖❜❥❡❝t✐✈❡✿ ❘❡s♦❧✈❡ t❤❡ ❝♦♥✢✐❝t ✐♥ s✉❝❤ ❛ ✇❛② t❤❛t ✐ts ♣r♦❜❛❜✐❧✐t② ❜❡ s♠❛❧❧❡r t❤❛♥ ❛ ❣✐✈❡♥ t❤r❡s❤♦❧❞ ✭✐♥ t❤✐s ✇♦r❦ Pcon ≤ ✵.✶✪✮

✹ ✴ ✶✾

❘❡s✉❧ts ♣r❡✈✐❡✇

◆♦♠✐♥❛❧ s❝❡♥❛r✐♦ Pcon = ✼✵.✹✪ ❉❡❝♦♥✢✐❝t❡❞ s❝❡♥❛r✐♦ Pcon = ✵.✶✪

✺ ✴ ✶✾

❊♥s❡♠❜❧❡ ✇❡❛t❤❡r ❢♦r❡❝❛st✐♥❣

❲❡❛t❤❡r ✉♥❝❡rt❛✐♥t② ✐s ❞❡✜♥❡❞ ❜② ❊♥s❡♠❜❧❡ ❲❡❛t❤❡r ❋♦r❡❝❛sts ✭❊❲❋✬s✮✳ ❆♥ ❊❲❋ ✐s ♦❜t❛✐♥❡❞ ❜② s❧✐❣❤t❧② ❛❧t❡r✐♥❣ t❤❡ ✐♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s ❛♥❞✴♦r ♣❤②s✐❝❛❧ ♣❛r❛♠❡t❡rs✱ ❛♥❞✴♦r ❝♦♥s✐❞❡r✐♥❣ t✐♠❡✲❧❛❣❣❡❞ ♦r ♠✉❧t✐✲♠♦❞❡❧ ❛♣♣r♦❛❝❤❡s✳ ❆♥ ❊❲❋ ❝♦♥st✐t✉t❡s ❛ r❡♣r❡s❡♥t❛t✐✈❡ s❛♠♣❧❡ ♦❢ t❤❡ ♣♦ss✐❜❧❡ r❡❛❧✐③❛t✐♦♥s ♦❢ t❤❡ ♣♦t❡♥t✐❛❧ ✇❡❛t❤❡r ♦✉t❝♦♠❡✳ ❚❤❡ ✉♥❝❡rt❛✐♥t② ✐♥❢♦r♠❛t✐♦♥ ✐s ✐♥ t❤❡ s♣r❡❛❞ ♦❢ t❤❡ ✈❛r✐♦✉s ❢♦r❡❝❛sts ♦❢ t❤❡ ❡♥s❡♠❜❧❡✳

✻ ✴ ✶✾

❈♦♥✢✐❝t ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ✭✶✮

■♥❞✐❝❛t♦rs ❈♦♥✢✐❝t ✐♥t❡♥s✐t② ❈♦♥✢✐❝t ✐♠♠✐♥❡♥❝❡ ❈♦♥✢✐❝t ❞✉r❛t✐♦♥ ❈♦♥✢✐❝t ♣r♦❜❛❜✐❧✐t② ■♥❢♦ ♣r♦✈✐❞❡❞ ❘✐s❦ ♦❢ ❝♦❧❧✐s✐♦♥ ❯r❣❡♥❝② ❊①♣❡❝t❡❞ ✇♦r❦❧♦❛❞ Pr✐♦r✐t② ❚❤❡② ❞❡✜♥❡ t❤❡ s❡✈❡r✐t② ❛♥❞ ❝r✐t✐❝❛❧✐t② ♦❢ t❤❡ ❝♦♥✢✐❝t

✼ ✴ ✶✾

❈♦♥✢✐❝t ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ✭✷✮

■♥❞✐❝❛t♦rs ❈♦♥✢✐❝t ✐♥t❡♥s✐t② ❈♦♥✢✐❝t ✐♠♠✐♥❡♥❝❡ ❈♦♥✢✐❝t ❞✉r❛t✐♦♥ ❈♦♥✢✐❝t ♣r♦❜❛❜✐❧✐t② ❙✉♣♣♦rt✐♥❣ ♠❡tr✐❝s ▼✐♥✐♠✉♠ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛✴❝ ❙t❛rt✐♥❣ t✐♠❡ ♦❢ ❝♦♥✢✐❝t ❉✉r❛t✐♦♥ ♦❢ ❧♦ss ♦❢ s❡♣❛r❛t✐♦♥ P[dmin ≤ D] ✭D ✲ ❣✐✈❡♥ s❡♣❛r❛t✐♦♥ r❡q✉✐r❡♠❡♥t✮ ✭✐♥ t❤✐s ✇♦r❦ D❂✺ ◆▼❂✾✷✻✵ ♠✮

✽ ✴ ✶✾

❆ss✉♠♣t✐♦♥s

❚✇♦ ❛✐r❝r❛❢t✱ ❆ ❛♥❞ ❇✱ ✢② ✇✐t❤ ❛♣♣r♦❛❝❤✐♥❣ tr❛❥❡❝t♦r✐❡s ❛t t❤❡ s❛♠❡ ❛❧t✐t✉❞❡✱ ✇✐t❤ ❝♦♥st❛♥t ❦♥♦✇♥ ❛✐rs♣❡❡❞s ✭VA ❛♥❞ VB✮✳ ❚❤❡ ✐♥✐t✐❛❧ s❡♣❛r❛t✐♦♥ ❜❡t✇❡❡♥ ❛✐r❝r❛❢t ✐s ❣r❡❛t❡r t❤❛♥ D ✳ ❚❤❡ ❛✐r❝r❛❢t ❝♦✉rs❡s ✐♥ s❡❣♠❡♥ts i ❛♥❞ j r❡s♣✳ ✭ψAi ❛♥❞ ψBj✮ ❛r❡ ❝♦♥st❛♥t ❛♥❞ ❦♥♦✇♥✳ ❚❤❡ ❛✐r❝r❛❢t ❛r❡ ❛✛❡❝t❡❞ ❜② t❤❡ s❛♠❡ ✉♥❝❡rt❛✐♥ ❝♦♥st❛♥t ✇✐♥❞ ✭ w(wx,wy)✮✳ ❚❤❡ ❣r♦✉♥❞ s♣❡❡❞s ✭Vg,Ai ❛♥❞ Vg,Bj✮ ❛r❡ ✉♥❝❡rt❛✐♥✳

✾ ✴ ✶✾

❈♦♥✢✐❝t s❝❡♥❛r✐♦

❆✐r❝r❛❢t ♠♦t✐♦♥ ✭s❡❣♠❡♥ts i✱ j✮

• sAi (t) =

s✵,Ai + Vg,Ai t

• Vg,Ai =

VAi + w

• sBj (t) =

s✵,Bj + Vg,Bj t

• Vg,Bj =

VBj + w ❘❡❧❛t✐✈❡ ♠♦t✐♦♥

• sij(t) =

sBj (t)− sAi (t) =

• s✵,Bj −

s✵,Ai

• +
• Vg,Bj −

Vg,Ai

• t
• sij(t) =

s✵ij + Vgij t r❡❧❛t✐✈❡ ✐♥✐t✐❛❧ ♣♦s✐t✐♦♥ s✵ij (✉♥❝❡rt❛✐♥) r❡❧❛t✐✈❡ ❣r♦✉♥❞ s♣❡❡❞

• Vgij (✉♥❝❡rt❛✐♥)

✶✵ ✴ ✶✾

❈♦♥✢✐❝t ❞❡✜♥✐t✐♦♥

❉✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ t✇♦ ❛✐r❝r❛❢t✿ dij(t) =

• sij(t)
• =
• s✷

✵ij +✷

s✵ij · Vgij t +V ✷

gij t✷

▼✐♥✐♠✉♠ ❞✐st❛♥❝❡ dmin = min{(dmin)ij} = g(wx,wy) (✉♥❝❡rt❛✐♥) ❈♦♥✢✐❝t ❡①✐st❡♥❝❡ dmin ≤ D (❉ ✲ ❣✐✈❡♥ s❡♣❛r❛t✐♦♥ r❡q✉✐r❡♠❡♥t) Pr♦❜❛❜✐❧✐t② ♦❢ ❝♦♥✢✐❝t Pcon = P[dmin ≤ D]

✶✶ ✴ ✶✾

Pr♦❜❛❜✐❧✐st✐❝ ❛♣♣r♦❛❝❤

Pr♦❜❛❜✐❧✐st✐❝ ❚r❛♥s❢♦r♠❛t✐♦♥ ▼❡t❤♦❞ ✭P❚▼✮

PTM

❚❤❡ ❡①♣❡❝t❡❞ ✈❛❧✉❡✱ st❛♥❞❛r❞ ❞❡✈✳ ❛♥❞ ♣r♦❜❛❜✐❧✐t② ♦❢ ❝♦♥✢✐❝t ❛r❡ ❣✐✈❡♥ ❜② E[dmin] =

∞

−∞ ρfdmin(ρ)dρ

σ[dmin] = ∞

−∞ ρ✷fdmin(ρ)dρ −(E[dmin])✷

✶/✷ P[dmin ≤ D] =

D

−∞ fdmin(ρ)dρ

✶✷ ✴ ✶✾

❈♦♥✢✐❝t r❡s♦❧✉t✐♦♥

▼♦❞✐❢② ❜♦t❤ tr❛❥❡❝t♦r✐❡s ✭✈❡❝t♦r✐♥❣✮ ✐♥ s✉❝❤ ❛ ✇❛② t❤❛t t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❝♦♥✢✐❝t ❜❡ s♠❛❧❧❡r t❤❛♥ ❛ ❣✐✈❡♥ t❤r❡s❤♦❧❞ δ✱ ❛♥❞ t❤❡ ❞❡✈✐❛t✐♦♥ ❢r♦♠ t❤❡ ♥♦♠✐♥❛❧ tr❛❥❡❝t♦r✐❡s ❜❡ ♠✐♥✐♠✉♠ ❚❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ♠♦❞✐✜❛❜❧❡ ✇❛②♣♦✐♥ts ❛r❡ ❝♦❧❧❡❝t❡❞ ✐♥ t❤❡ ✈❡❝t♦r ①✳ ❚❤❡ ♥♦♠✐♥❛❧ tr❛❥❡❝t♦r✐❡s ❛r❡ ❝♦♥s✐❞❡r❡❞ ❛s t❤❡ ♣r❡❢❡rr❡❞ ♦♥❡s ❛♥❞ t❤❡② ❛r❡ ❞❡♥♦t❡❞ ❜② ①n P❛r❛♠❡tr✐❝ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠ minimize

q

∑

k=✶

• (xk −xn

k )✷ +(yk −yn k )✷

subject to Pcon(①) ≤ δ (q is the number of modifiable waypoints)

✶✸ ✴ ✶✾

❆♣♣❧✐❝❛t✐♦♥ ✭✶✮

Pr♦❜❛❜✐❧✐st✐❝ ✇✐♥❞

❊P❙✿ ▼été♦ ❋r❛♥❝❡ P❊❆❘P ✭✸✺ ♠❡♠❜❡rs✮✳ ✻✿✵✵ ♦♥ ✵✺✲▼❛②✲✷✵✶✻ ✐♥ t❤❡ ❙♦✉t❤❡❛st ♦❢ ❙♣❛✐♥ ✭✸✽◦◆✱ ✷.✺◦❲✮❀ ❋♦r❡❝❛st ❤♦r✐③♦♥ ♦❢ ✵ ❤♦✉rs✳ P❉❋✿ wx✱ wy ✖ ✉♥✐❢♦r♠ ❞✐str✐❜✉t✐♦♥ fwi (wi) =

• ✶

✷δwi ,

wi ∈ [ ¯ wi −δwi , ¯ wi +δwi ] ✵

• therwise

✇❤❡r❡ i ∈ x,y✱ ❛♥❞ s✉♣♣♦s❡❞ t♦ ❜❡ st❛t✐st✐❝❛❧❧② ✐♥❞❡♣❡♥❞❡♥t✿ fwx,wy (wx,wy) = fwx (wx)·fwy (wy) ▼❡r✐❞✐♦♥❛❧ ✇✐♥❞✿ ¯ wx = ✷✵.✵✽ ♠✴s✱ δwx = ✽.✸✸ ♠✴s ❩♦♥❛❧ ✇✐♥❞✿ ¯ wy = ✶✼.✽✾ ♠✴s✱ δwy = ✼.✻✺ ♠✴s

5 10 15 20 25 30 0.02 0.04 0.06 0.08 0.1 0.12 0.14

fwx[s/m] wx[m/s]

5 10 15 20 25 30 0.02 0.04 0.06 0.08 0.1 0.12 0.14

fwy[s/m] wy[m/s]

✶✹ ✴ ✶✾

❆♣♣❧✐❝❛t✐♦♥ ✭✷✮

◆♦♠✐♥❛❧ s❝❡♥❛r✐♦ ❛✐r❝r❛❢t ❢♦❧❧♦✇✐♥❣ ❘◆❆❱ r♦✉t❡s ❯▼✶✾✷ ❛♥❞ ❯◆✽✻✾ VA = ✷✹✵ ♠✴s✱ VB = ✷✸✵ ♠✴s

5000 10000 15000 0.2 0.4 0.6 0.8 1 x 10

−4

fdmin [1/m] dmin [m] D

E[dmin] = ✼✵✹✹ ♠✱ σ[dmin] = ✸✶✼✵ ♠ Pcon = ✼✵.✹✪

ROLAS ARPEX BAZAS BLN MORAL VTB NASOS ANZAN MGA 5° W 4° W 3° W 2° W 36° N 37° N 38° N 39° N AMR AGIDO 40° N

✶✺ ✴ ✶✾

❆♣♣❧✐❝❛t✐♦♥ ✭✸✮

❉❡❝♦♥✢✐❝t❡❞ s❝❡♥❛r✐♦

0.5 1 1.5 2 2.5 x 10

4

0.2 0.4 0.6 0.8 1 1.2 x 10

−4

fdmin [1/m] dmin [m] D

E[dmin] = ✶✹✸✷✾ ♠✱ σ[dmin] = ✷✽✾✼ ♠

Pcon = ✵.✶✪ ▼❛① ❞❡✈✐❛t✐♦♥ ❛✴❝ ❆✿ ✹✽✷✻ ♠ ✭❅❇▲◆✮ ▼❛① ❞❡✈✐❛t✐♦♥ ❛✴❝ ❇✿ ✺✵✷✾ ♠ ✭❅❇▲◆✮ ✭❘❡s♦❧✉t✐♦♥ ❝♦st✿ ✻✾✼✸ ♠✮

5° W 4° W 3° W 2° W 36° N 37° N 38° N 39° N AMR AGIDO ROLAS ARPEX BAZAS ANZAN NASOS VTB MORAL BLN MGA 40° N

Nominal waypoints resolution waypoints nominal trajectories resolution trajectories

✶✻ ✴ ✶✾

❆♣♣❧✐❝❛t✐♦♥ ✭✸✮

❉❡❝♦♥✢✐❝t❡❞ s❝❡♥❛r✐♦

0.5 1 1.5 2 2.5 x 10

4

0.2 0.4 0.6 0.8 1 1.2 x 10

−4

fdmin [1/m] dmin [m] D

E[dmin] = ✶✹✸✷✾ ♠✱ σ[dmin] = ✷✽✾✼ ♠

Pcon = ✵.✶✪ ▼❛① ❞❡✈✐❛t✐♦♥ ❛✴❝ ❆✿ ✹✽✷✻ ♠ ✭❅❇▲◆✮ ▼❛① ❞❡✈✐❛t✐♦♥ ❛✴❝ ❇✿ ✺✵✷✾ ♠ ✭❅❇▲◆✮ ✭❘❡s♦❧✉t✐♦♥ ❝♦st✿ ✻✾✼✸ ♠✮

5° W 4° W 3° W 2° W 36° N 37° N 38° N 39° N AMR AGIDO ROLAS ARPEX BAZAS ANZAN NASOS VTB MORAL BLN MGA 40° N

Nominal waypoints resolution waypoints nominal trajectories resolution trajectories

✶✻ ✴ ✶✾

❙✉♠♠❛r② ✲ ❋✐♥❛❧ r❡♠❛r❦s ✭✶✮

❲❡ ❤❛✈❡ ❛❞❞r❡ss❡❞ ❛♥ ✐♠♣♦rt❛♥t t♦♣✐❝ ❢♦r t❤❡ ❢✉t✉r❡ ♦❢ ❚❇❖✳ ❚❤❡ ♣r♦❜❛❜✐❧✐st✐❝ ♠❡t❤♦❞♦❧♦❣② ♣r❡s❡♥t❡❞

✐s ❛❜❧❡ t♦ q✉❛♥t✐❢② t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❝♦♥✢✐❝t✱ ✐s ❛❜❧❡ t♦ r❡s♦❧✈❡ t❤❡ ❝♦♥✢✐❝t✱ ❣❡♥❡r❛t✐♥❣ ♥❡✇ tr❛❥❡❝t♦r✐❡s t❤❛t ❧♦✇❡r t❤❡ ♣r♦❜❛❜❧✐t② ♦❢ ❝♦♥✢✐❝t t♦ s♠❛❧❧ ❛❝❝❡♣t❛❜❧❡ ❧❡✈❡❧s✱ ✐s ✈❡r② ✢❡①✐❜❧❡ ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ✇❡❛t❤❡r ✐♥♣✉t✿ ✐t ❝❛♥ t❛❦❡ ❛s ✐♥♣✉t ❛♥② t②♣❡ ♦❢ ✇✐♥❞ ❞✐str✐❜✉t✐♦♥ ❞❡r✐✈❡❞ ❢r♦♠ ❛♥② ✇❡❛t❤❡r ❞❛t❛ s♦✉r❝❡✳✳

❚❤❡ ✐♥❞✐❝❛t♦rs ❞❡✜♥❡❞ ❝❛♥ ❜❡ ♦❢ ✐♥t❡r❡st ❢♦r ❆❚❈✱ ❜❡❝❛✉s❡ t❤❡② ♣r♦✈✐❞❡

r❡❧❡✈❛♥t ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ❝♦♥✢✐❝t✱ ❛♥❞✱ t❤❡r❡❢♦r❡✱ s✉♣♣♦rt ❢♦r ❜❡tt❡r ❞❡❝✐s✐♦♥ ♠❛❦✐♥❣✳

✶✼ ✴ ✶✾

❙✉♠♠❛r② ✲ ❋✐♥❛❧ r❡♠❛r❦s ✭✷✮

❆♣♣❧✐❝❛t✐♦♥ ❢♦r❡s❡❡♥✿ ▼❡❞✐✉♠ ❚❡r♠ ❈♦♥✢✐❝t ❉❡t❡❝t✐♦♥ ✭▼❚❈❉✮✳

◆♦t✐✜❝❛t✐♦♥ ♦❢ ❝♦♥✢✐❝ts t♦ ❆❚❈ ❛❝❝♦r❞✐♥❣ t♦ t❤❡✐r ♣r♦❜❛❜✐❧✐t②❀ r❡❞✉❝t✐♦♥ ♦❢ ♠✐ss❡❞ ❛♥❞ ❢❛❧s❡ ❛❧❡rts✳ ❊✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ ✈✐❛❜✐❧✐t② ✭✐♥ t❡r♠s ♦❢ ❝♦♥✢✐❝t ♣r♦❜❛❜✐❧✐t②✮ ♦❢ ♣r♦♣♦s❡❞ r❡s♦❧✉t✐♦♥ ♠❛♥❡✉✈❡rs❀ str❛t❡❣✐❝❛❧❧② ❞❡❝♦♥✢✐❝t✐♥❣ t❤❡ ❛✐r tr❛✣❝✳

❋✉t✉r❡ ❲♦r❦

❞✐✛❡r❡♥t t②♣❡s ♦❢ ✇✐♥❞ ❞✐str✐❜✉t✐♦♥ ✈❛r✐❛❜❧❡✱ ❝♦rr❡❧❛t❡❞ ✇✐♥❞ ✜❡❧❞s ❛❧t✐t✉❞❡ ❛♥❞ s♣❡❡❞ ❝❤❛♥❣❡s ✭❢♦r ❚▼❆ ❛♥❛❧②s✐s✮

✶✽ ✴ ✶✾

❆❝❦♥♦✇❧❡❞❣❡♠❡♥ts

THANK YOU

❙✉♣♣♦rt❡❞ ❜② t❤❡ ❙♣❛♥✐s❤ ▼✐♥✐st❡r✐♦ ❞❡ ❊❝♦♥♦♠í❛ ② ❈♦♠♣❡t✐t✐✈✐❞❛❞ ❝♦✲✜♥❛♥❝❡❞ ✇✐t❤ ❋❊❉❊❘ ❢✉♥❞s Pr♦❥❡❝t ❖♣t▼❡t ❚❘❆✷✵✶✹✲✺✽✹✶✸✲❈✷✲✶✲❘

✶✾ ✴ ✶✾