Presentazione Progetto eVACUATE - polito.itPresentazione Progetto Evacuate 5. Rapporto con la ricerca accademica Esiste un rapporto con la ricerca accademica se i soggetti coinvolti

Presentazione Progetto eVACUATE



Presentazione Progetto Evacuate

Description”The dynamic capture of situational awareness concerning crowds in

specific mass gathering venues and its intelligent enablement into emergency

management information systems, using smart communication devices and spaces is

critical for achieving rapid, timely guidance and safe evacuation of people out of

dangerous areas. Humans could be overwhelmed by fast changes of potentially

dangerous incidents occurring at confined environments with mass-gathering. This

condition may lead to mass panic and make emergency management more

challenging. In eVACUATE, the intelligent fusion of sensors, geospatial and

contextual information, with advanced multi-scale crowd behaviour detection and

recognition will be developed.

1. FAQ: Frequently Asked Questions

2. Bibliography and Reasonings on Mathematical Tools for Complex Systems

3. Models, Preliminary Simulations, and Open Problems

– p. 1/27


– p. 2/27



1. Cosa si intende per rete di collaborazione di ricerca?

2. Che impegno e quali competenze richiede?

3. Finanziamenti e Incentivi?

4. Che tipo di problemi matematici implica?

5. E possibile un rapporto con la ricerca di tipo accademico?

7. Come si compete per un progetto di ricerca?

8. Altre?

– p. 3/27



1. Cosa si intende per rete di collaborazione di ricerca?

E una rete di grandi dimensioni che sviluppa un progetto dettagliato ed articolato con

un preciso “work-plan” con avanzamento lavoro per l’interadurata del progetto. In

questo caso 4 anni.Le verifiche sono periodiche di norma ogni 6 mesi e ogni Partner

deve presentare il proprio avanzamento lavori al Coordinatore Centrale. Le verifiche

da parte delle Comunit Europea sono ogni 12 – 18 mesi.

2. Che impegno e quali competenze richiede?

Il progettoe interdisciplinare e richiede competenze specifiche e capacita di dialogo

congli altri Partner comprese collaborazioni di ricerca. Le competenze richieste a

POLITO sono: modellizzazione e relativa simulazione delladinamica delle folle con

particolare attenzione all’evacuazione da aree con geometria complessa in condizioni

di panico; raccolta dati empirici e validazione dei modelli. L’impegno none

trascurabile e va rendicontato sui “time-sheets”. Il temporendicontato corrisponde piu

o meno all’impegno effettivo.La mia esperienza porta a dire chee in pratica

impossibile essere tecnicamente coinvolti in un progetto senza aver svolto o svolgere

ricerca scientifica sulle tematiche del progetto stesso. – p. 4/27


3. Finanziamenti e Incentivi?

L’ordine di grandezza di un finanziamento per una piccola unita teoricae di oltre

200ML Euro per 4 anni finanziato al75% circa circa. Dopo aver coperto le spese vive

sostenute per il progetto (assegni di ricerca, attrezzaure, mobilit) e le eventuali spese

che non possibile ricondurre direttamente allattivit di progetto (luce, gas, IRAP ecc.)

la parte di contributo non utilizzata per i costi vivi pu essere utilizzata per ulteriore

ricerca o per compensi al personale docente e ricercatore coinvolto. Un gruppo che

scelga di utilizzarla per ricerca deve essere lasciato libero di farlo con una certa

flessibilita, altrimenti viene a mancare l’incentivo.

4. Problemi matematici?

La trattazione matematica, sia modellistica che computazionale, richiede lo sviluppo di

metodi matematici nuovi basati su sviluppi delle teorie cinetiche e della teoria dei

giochi per lo studio di sistemi complessi. Le variabili dipendenti sono distribuzioni di

probabilita e le equazioni hanno struttura iperbolica con nonlinearita di tipo

quadratico. Inoltre, le interazioni “individual based” sono nonlinearmente additive,

non locali nello spazio, e condizionate dalle variabili dipendenti.

– p. 5/27


5. Rapporto con la ricerca accademica

Esiste un rapporto con la ricerca accademica se i soggetti coinvolti nel progetto sono

realmente interessati al tema ed alle difficolta matematiche che questo implica.

Comunque none una questione da ritagli di tempo e none da non sottovalutare il

rischio che per occuparsi di temi diversi si finisca con perdere il filo conduttore della

linea di ricerca abitualmente seguita.

6. Come si compete per un progetto di ricerca?

I progetti sono inseriti nelle grandi linee di intervento della EU. Il tema della sicurezza

e particolarmente importante e sara di certo presente anche nel prossimo programma

quadro. La presenza dei matematicie richiesta, tuttavia i Coordinatori puntano a

soggetti di grande visibilita. Ho verificato il ruolo fondamentale di una pagina “WEB”

di gruppo, purche sia ben progettata e curata nei dettagli e includa solo elementi di

reale spessore scientifico, una pagina WEB superficiale ha invece un impatto negativo.

Un team competitivo deve riuscire a coprire tutte le competenze: modellistiche, analisi

qualitativa, e metodi computazionali. Infine, se DISMA vuole partecipare a piu

progetti deve anche coordinare i gruppi di lavoro in quanto il numero di ore uomo

impegnabili ha un tetto da verificare sui “time-sheets”.– p. 6/27


2. Bibliography and Reasonings on Mathematical Tools

N. B and C. Dogbe, On the modelling of traffic and crowds - a survey of models,

speculations, and perspectives, SIAM Review, 53(3) (2011), 409–463.

N. B, and A. Bellouquid, On The Modeling of Crowd Dynamics: Looking at the

Beautiful Shapes of Swarms, Netw. Heter. Media., 6 (2011), 383–399.

N. B, B. Piccoli, and A. Tosin, Modeling crowd dynamics from a complex system

viewpoint, Math. Models Methods Appl. Sci., 22, (2012) 1230004, (29 pages).

N. B, A. Bellouquid, and D. Knopoff, On The Kinetic Theory Approach to Crowd

Dynamics: Modeling and Mathematical Problems, SIAM Multiscale Modeling

Simulation, (2013), to appear.

D. Knopoff and A. Tosin, ”A kinetic theory approach to crowd dynamics by

stochastic mean-field interactions”, (2013), work in progress.

– p. 7/27



1. Ability to express a strategy: Living entities are capable to develop

specificstrategies andorganization abilitiesthat depend on the state of the

surrounding environment. These can be expressed without the application of any

external organizing principle. In general, they typicallyoperate

out-of-equilibrium. For example, a constant struggle with the environment is

developed to remain in a particular out-of-equilibrium state, namely stay alive.

2. Heterogeneity: The ability to express a strategy is not the same for all

entities:Heterogeneitycharacterizes a great part of living systems, namely, the

characteristics of interacting entities can even differ from an entity to another

belonging to the same structure.In developmental biology, this is due to different

phenotype expressions generated by the same genotype.

3. Learning ability: Living systems receive inputs from their environments and

have the ability to learn from past experience. Therefore their strategic ability and the

characteristics of interactions among living entities evolve in time.Societies can

induce a collective strategy toward individual learning

– p. 8/27



4. Nonlinear Interactions: Interactions nonlinearly additive and involve

immediate neighbors, but in some cases also distant particles. Indeed, living systems

have the ability to communicate and may possibly choose different observation paths.

In some cases, the topological distribution of a fixed numberof neighbors can play a

prominent role in the development of the strategy and interactions. Interactions modify

their state according to the strategy they develop. Living entitiesplay a game at

each interaction with an output that is technically related to their strategyoften

related to surviving and adaptation ability.Individual interactions in swarms can

depend on the number of interacting entities rather that on their distance.

5. Darwinian selection and time as a key variable: All living

systems are evolutionary. For instance birth processes cangenerate individuals more

fitted to the environment, who in turn generate new individuals again more fitted to the

outer environment. Neglecting this aspect means that the time scale of observation and

modeling of the system itself is not long enough to observe evolutionary events.

Micro-Darwinian occurs at small scales, while Darwinian evolution is generally

interpreted at large scales.– p. 9/27



Validation of models

Should mathematics attempt to reproduce experiments by equations whose parameters

are identified on the basis of empirical data, or develop new structures, hopefully a new

theory able to capture the complexity of biological phenomena and subsequently to

base experiments on theoretical foundations?

This question witnesses the presence of adilemma, which occasionally is the object

of intellectual conflicts within the scientific community. However, we are inclined to

assert the second perspective, since we firmly believe that it can also give a

contribution to further substantial developments of mathematical sciences.

Should a conceivable mathematical theory show common features in all field of

applications?

Although a theory should be linked to a specific class of systems, all theories should

have common features.

– p. 10/27



Validation of models

The collective dynamics of complex systems is determined byinteractions at the

micro-scale ruled by the strategy that interacting entities are able to express. This

collective dynamics exhibits emerging behaviors as well assome aspects of the

dynamics which may not be specifically related to complexity, such as steady

conditions uniform in space that are reproduced in analogy with classical systems.

These considerations lead to state that models should have the ability to depict both

emerging behaviors far from steady cases and the steady ones. This also implies that

both should not be artificially imposed in the structure of the model, rather should be

induced by interactions at the micro-scale.

Accordingly, empirical data should be used toward the assessment of models at

the micro-scale and subsequently validation of models should be obtained byinvestigating their ability to depict emerging behaviors.However, the process can

be implemented if the modeling at the micro-scale is consistent with the physics ofthe real system, and if the tuning method leads to a unique solution of the inverse

problem of parameters identification.– p. 11/27



Guidelines Towards Modeling Approach

• understanding the links between the dynamics of living systems and their

complexity features;

• derivation a general mathematical structure, consistent with the aforesaid features,

with the aim of offering the conceptual framework toward thederivation of

specific models;

• design of specific models corresponding to well defined classes of systems by

implementing the said structure with suitable model of individual-based

interactions according to a detailed interpretation of thedynamics at the

micro-scale;

• validation of models by comparison of the dynamics predicted by them with that

one resulting from empirical data;

• analysis of the gap between modeling and mathematical theory.

– p. 12/27



• The overall system is subdivided intofunctional subsystemsconstituted by

entities, calledactive particles, whose individual state is calledactivity;

• The state of each functional subsystem is defined by a suitable, time dependent,

probability distribution over the microscopic state, which includes position,

velocity, and activity variables;

• Interactions are modeled by games, more precisely stochastic games, where the

state of the interacting particles and the output of the interactions are known in

probability;

• The evolution of the probability distribution is obtained by a balance of particles

within elementary volume of the space of the microscopic states, where the

dynamics of inflow and outflow of particles is related to interactions at the

microscopic scale.

– p. 13/27



Dynamics in open domains

– p. 14/27



Crowds in Bounded Domain with Obstacles

P

T

∂ΩΩ

P′

~ν(P)

~ν(P′)

T

∂Ω

P∗ ~ν(P∗)

Λ∗

– p. 15/27



Towards a Modeling Approach

The assumptions which lead to a specific model are as follows:

H.1. The testparticlex,v is subject to an action of the whole storm of the type:

F [f ](t,x) =1

ρM

∫

Σt

ϕ(x,x∗,v,v

∗,U[f ](t))f(t,x∗

,v∗) dx∗

dv∗,

whereΣt is the domain occupied by the swarm,ϕ is the individual action of the field

particle(x∗,v∗) over the test particle. This acceleration term depends on the distance

between particles inducing a flocking action, but also induces an attraction towards the

mean direction of the swarm:

ϕ =1

ε+ |x− x∗|aψ(v, ~νS) , a > 0, ~νS =

U

|U|,

whereε is a small positive dimensionless quantity. The termψ models the attraction of

individuals toward the main stream of the swarm. It increases with increasing angle

between the individual direction and the mean direction of the swarm.

– p. 16/27



H.2. There is an interaction rateη related toρΩβas follows:

η[f ](t,x) = η0(t,x)µ[f ] where, depending on time and position,

µ[f ] =

(ρΩβ

ρΩint

)b

, b > 0 ,

and whereρΩint(t) represents the mean density onΩint andη0 represents the

interaction rate when the two domains coincide.

H.3. Thecandidateparticle with microscopic state(x∗,v∗) at the timet interacts with

fieldparticles(x∗,v∗) with rateη and acquires the state of thetestparticles. The

candidate particle modifies its state according to the probability densityA which

depends on the state of the interacting particles and on the mean velocityV:

A[f ](v∗ → v|V[f ]) ,

∫

Dv

A[f ](v∗ → v|V[f ]) dv = 1 ,

for all conditioning inputs, whiletestparticles interact with field particles and lose

their state. More precisely, Candidate particles have a trend to adjust their velocity

both to the mean velocity of the cluster and to that of the fieldparticles.– p. 17/27



(∂t + v · ∂x + ∂vF [f ]

)f(t,x,v) = J [f ](t,x,v)

=

∫

Ωβ [f ]

∫

(Dv)2µ[f ]A(v∗ → v|v∗,v

∗,V[f ])f(t,x,v∗) f(t,x

∗,v

∗) dx∗dv∗ dv

∗

−f(t,x,v)

∫

Ωβ [f ]

∫

Dv

µ[f ] f(t,x∗,v

∗) dx∗dv

∗.

This structure can be rapidly generalized to the presence ofa hierarchy, as follows:

(∂t + v · ∂x +

p∑

j=1

∂vFij [f ]

)fi(t,x,v) = Ji[f ](t,x,v) =

p∑

j=1

Jij [f ](t,x,v) ,

Jij =

∫

Ωβ [f ]

∫

(Dv)2µ[f ]Aij [f ](v∗ → v)fi(t,x,v∗) fj(t,x

∗,v

∗) dx∗dv∗ dv

∗

−fi(t,x,v)

∫

Ωβ [f ]

∫

Dv

µ[f ] fj(t,x∗,v

∗) dx∗dv

∗.

– p. 18/27


3. Models, Preliminary Simulations, and Open ProblemsThe density within the interaction domainΩβ is computed as follows:

ρΩβ(t) = ρΩβ

[f ](t) =

∫

Dv

∫

Ωβ

f(t,x,v) dx dv.

Moreover, the mean velocity of the particles included inΩ is computed by

VΩβ(t) = VΩβ

[f ](t) =1

ρΩβ(t)

∫

Dv

∫

Ωβ

v f(t,x,v) dx dv.

This is the mean velocity within the cluster and we define the direction

~νΩβ(t) =

VΩβ(t)

|VΩβ(t)|

.

An additional quantity of interest is the mean velocity of the whole storm:

U(t) = U[f ](t) =1

ρ(t)

∫

Dv

∫

Σt

v f(t,x,v) dx dv ,

ρ(t) = ρ[f ](t) =

∫

Dv

∫

Σt

f(t,x,v) dx dv.

– p. 19/27


3. Models, Preliminary Simulations, and Open ProblemsPolar coordinates with discrete values are used for the velocity variablev = v, θ:

Iθ = θ1 = 0 , . . . , θi , . . . , θn =n

n− 12π, Iv = v1 = 0 , . . . , vj , . . . , vm = 1.

f(t,x,v, u) =

n∑

i=1

m∑

j=1

fij(t,x, u) δ(θ − θi)⊗ δ(v − vj).

Some specific cases can be considered. For instance the case of two different groups,

labeled with the superscriptσ = 1, 2, which move towards two different targets.

fσ(t,x,v, u) =

n∑

i=1

m∑

j=1

fσij(t,x) δ(θ − θi)⊗ δ(v − vj)⊗ δ(u− u0) ,

wherefσij(t,x) = f(t,x, θi, vj) corresponding, for each groupσ = 1, 2, to the

ij-particle, namely to the pedestrian moving in the directionθi with velocityvj .

ρ(t,x) =

2∑

σ=1

ρσ(t,x) =

2∑

σ=1

n∑

i=1

m∑

j=1

fσij(t,x) ,

– p. 20/27


3. Models, Preliminary Simulations, and Open Problems(∂t + vij · ∂x

)fσij(t,x) = J [f ](t,x)

=n∑

h,p=1

m∑

k,q=1

∫

Λ

η[ρ(t,x∗)]Aσhk,pq(ij)[ρ(t,x

∗)]fσhk(t,x) f

σpq(t,x

∗) dx∗

− fσij(t,x)

n∑

p=1

m∑

q=1

∫

Λ

η[ρ(t,x∗)] fσpq(t,x

∗) dx∗,

wheref = fij, while the termAσhk,pq(ij) should be consistent with the probability

density property:

n∑

i=1

m∑

j=1

Aσhk,pq(ij) = 1, ∀ hp ∈ 1, . . . , n, ∀ kq ∈ 1, . . . ,m ,

for σ = 1, 2, and for all conditioning local density.

Pedestrians have a visibility zoneΛ = Λ(x), which does not coincide with the whole

domainΩ due to the limited visibility angle of each individual.

– p. 21/27



• Interaction rate:

η(ρ(t,x)) = η0(1 + ρ(t,x)) exp

(− ρ(t,x)

).

• Transition probability density: The approach proposed here is based on the

assumption that particles are subject to three different influences, namely thetrend to

the exit point, theinfluence of the streaminduced by the other pedestrians, and the

selection of the path with minimal density gradient. A simplified interpretation of the

phenomenological behavior is obtained by assuming the factorization of the two

probability densities modeling the modifications of the velocity direction and modulus:

Aσhk,pq(ij) = Bσ

hp(i)(θh → θi|ρ(t,x)

)× Cσ

kq(j)(vk → vj |ρ(t,x)

).

– Interaction with a upper stream and target directions, namely θp > θh, θν > θh:

Bσhp(i) = αu0(1− ρ) + αu0 ρ if i = h+ 1 ,

Bσhp(i) = 1− αu0(1− ρ)− αu0 ρ if i = h ,

Bσhp(i) = 0 if i = h− 1.

– p. 22/27



– Interaction with a upper stream and low target directionθp > θh; θν < θh:

Bσhp(i) = αu0 ρ if i = h+ 1 ,


Bσhp(i) = αu0 (1− ρ) if i = h− 1.

– Interaction with a lower stream and upper target directionθp < θh; θν > θh:

Bσhp(i) = αu0(1− ρ) if i = h+ 1 ,


Bσhp(i) = αu0 ρ if i = h− 1.

– Interaction with a lower stream and target directionsθp < θh; θν < θh:

Bσhp(i) = 0 if i = h+ 1 ,


Bσhp(i) = αu0 (1− ρ) + αu0 ρ if i = h− 1.

– p. 23/27



– Interaction with faster particlesvk < vq and slower particlesvk > vq

Cσkq(j) =

1− β u0ρ, j = k;

βu0ρ, j = k + 1;

0, otherwise.

Cσkq(j) =

β u0ρ, j = k;

1− β u0ρ, j = k − 1;

0, otherwise.

– Interaction with equal velocity particlesvk = vq

Cσkq(j) =

1− 2β u0ρ, j = k;

β u0ρ, j = k − 1;

β u0ρ, j = k + 1.

– for k = 1 the candidate particle cannot reduce velocity, while fork = k cannot

increase it:

Cσkq(j) =

1− β u0 ρ, j = 1;

β u0 ρ, j = 2;

0, otherwise;

Cσkq(j) =

β u0 ρ, j = m− 1;

1− β u0 ρ, j = m;

0, otherwise.– p. 24/27


3. Models, Preliminary Simulations, and Open ProblemsExistence Theory - Mild form of the initial value problem

fσij(t,x) = φ

σij(x) +

∫ t

0

(Γσij [f , f ](s,x)− fσ

ij(s, x)L[f ](s, x)

)ds,

i ∈ 1, . . . , n, j ∈ 1, . . . ,m, σ ∈ 1, 2,

where the following notation has been used for any given vector f(t,x):

fσij(t,x) = fσ

ij(t, x+ vj cos(θi)t, y + vj sin(θi)t).

H.1. For all positiveR, there exists a constantCη > 0 so that

0 < η(ρ) ≤ Cη , whenever 0 ≤ ρ ≤ R.

H.2. Both the encounter rateη[ρ] and the transition probabilityAσhk,pq(ij)[ρ] are

Lipschitz continuous functions of the macroscopic densityρ, i.e., that there exist

constantsLη, LA is such that

| η[ρ1]−η[ρ2] |≤ Lη | ρ1−ρ2 |, | Aσhk,pq(ij)[ρ1]−Aσ

hk,pq(ij)[ρ2] |≤ LA | ρ1−ρ2 |

whenever0 ≤ ρ1 ≤ R, 0 ≤ ρ2 ≤ R, and alli, h, p = 1, .., n andj, k, q = 1, ..,m.

– p. 25/27



Existence TheoryLet φσ

ij ∈ L∞ ∩ L1, φσij ≥ 0, then there existsφ0 so that, if‖ φ ‖1≤ φ0, there exist

T , a0, andR so that a unique non-negative solution to the initial value problem exists

and satisfies:

f ∈ XT , supt∈[0,T ]

‖ f(t) ‖1≤ a0 ‖ φ ‖1,

ρ(t,x) ≤ R, ∀t ∈ [0, T ], x ∈ Ω.

Moreover, if∑2

σ=1

∑n

i=1

∑m

j=1 ‖ φσij ‖∞≤ 1, and‖ φ ‖1 is small, one has

ρ(t,x) ≤ 1, ∀t ∈ [0, T ], x ∈ Ω.

There existφr, (r = 1, ..., p− 1) such that if‖ φ ‖1≤ φr, there existsar so that it is

possible to find a unique non-negative solution to the initial value problem satisfying

for anyr ≤ p− 1 the followingf(t) ∈ X[0, (p− 1)T ],

supt∈[0,T ]

‖ f(t+ (r − 1)T ) ‖1≤ ar−1 ‖ φ ‖1,

andρ(t+ (r − 1)T,x) ≤ R, ∀t ∈ [0, T ], x ∈ Ω. Moreover,

ρ(t+ (r − 1)T,x) ≤ 1, ∀t ∈ [0, T ], x ∈ Ω.– p. 26/27



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t = t2– p. 27/27

Documents

Presentazione Progetto eVACUATE - polito.itPresentazione Progetto Evacuate 5. Rapporto con la ricerca accademica Esiste un rapporto con la ricerca accademica se i soggetti coinvolti