A NUMERICAL METHOD FOR INTERFACE RECONSTRUCTION OF TRIPLE POINTS WITHIN A VOLUME TRACKING ALGORITHM Abstract. A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple-point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a triple-point is described as the minimum of a constrained minimization problem inside an interfacial cell of the discretization. For given volume fractions of materials in the cell, an interior-point/Newton method is used for the reconstruction of the local geometry and the localization of the triple-point. Initialization of the Newton method is performed with a derivative-free algorithm. Numerical results are presented for static and pure advection cases to illustrate the efficiency and robustness of the algorithm. Free surface flows appear in many fields of science and engineering, such as mold filling [10, 22] , welding [7] or combustion and atomization [19] .. In volume tracking finite volume based methods, see e.g. [29] , the geometrical reconstruction of the interfaces between the various materials is a crucial issue in order to estimate accurately the propagation fronts. In volume-of-fluid methods, the description of the position of each material relies on the characteristic function of the domain filled with each material [20] . For both incompressible or compressible flows, the equations modeling the flow in each material are coupled with the advection equations governing the behavior of the volume fractions of materials [18] . In order to reconstruct a sharp approximation of the interfaces, a geometrical reconstruction locally in each interface cell of the discretization is needed to reduce the numerical diffusion and blurring of the propagation fronts induced by most algorithms. Several methods can be found in the literature for the reconstruction of an interface in two-phases flows, the most popular ones being the SLIC (Simple line interface calculation) [9, 24, 26] or the PLIC (Piecewise linear interface calculation) [29, 30, 37, 32] procedures, the parabolic reconstruction of interfaces [28] or markers methods [2, 3] . In the SLIC method, the interface is reconstructed by determining the local normal vector to the interface and constructing a linear interface between two media that matches the volume fractions of materials in the cell, via a bisection method for instance [12, 29] .. The two-dimensional case is discussed in this article. When three phases are adjacent in one cell, they can be arranged in layers or in a triple-point configuration where one point is located at the intersection of the three interface planes between pairs of materials [1, 14, 15, 31] . At equilibrium, the position of a triple-point and the orientation of the interfaces between pairs of materials can be determined by giving the contact angles between the interfaces, based on physical models or experimental data [17, 34] . However, in non-stationary cases, when the equilibrium between the different phases is not reached, the position of the triple-point and the orientation of the interfaces have to be reconstructed without relying on equilibrium angles. The reconstruction can rely on the approximation of normal vectors [1, 8] or be based on power diagrams [5, 31] .. The approach presented here is an extension of the PLIC algorithm. The computation of a triple-point configuration requires i) the determination of the normal vectors of the interfaces between pairs of materials and ii) the localization of the triple-point in order to match the volume fractions of materials in the cell given by the finite volume method and the geometric volumes delimited by the triplepoint and the three interfaces. The determination of the normal vectors is based on a finite element approach [6, 23] . For given normal vectors, the localization of the triple-point is based on a constrained minimization problem, solved with an interior-point method [25] , coupled with a Newton iteration [36] and pattern-search techniques [13] . The procedure is based on the minimization of the difference between normalized computed volumes and volume fractions produced by the finite volume scheme, provided that the triple-point remains in the cell. As an extension of the PLIC algorithm, the proposed approach reconstruct linear interfaces and is therefore first order accurate.. The structure of this article is the following. In Section 2, the model for the flow and the volume fractions of materials is briefly presented. In Section 3, the computation of the normal vectors is presented and in Section 4, the problem of the localization of the triple-point is detailed. Finally, numerical results are presented in Section 5, in particular for the reconstruction of T-shape and Y-shape configurations. In multiphase flows, the determination of the topology (or geometric configuration) inside cells containing more than two materials is a difficult challenge. A new method for the reconstruction of triple-point interfaces has been presented as an alternative to onion-skin methods. It has been designed to treat any configuration

O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A

testbed

for

coverage

control

using

mixed

wireless

sensor

networks

Wireless

Sensor

Networks

(WSNs)

is

a

relatively

new

technology

that

has

been

proposed

for

several

applications

including

wide

area

monitoring.

Such

applications

may

include

stationary

or

mobile

sensor

platforms

or

they

may

include

several

stationary

and

some

mobile-robotic

sensor

nodes

that

can

move

in

the

area

in

order

to

achieve

certain

objectives,

e.g.,

monitor

areas

that

are

not

adequately

covered

or

assist

in

the

transfer

of

data

to

prevent

the

energy

depletion

of

certain

critical

nodes.

Such

networks

that

consist

of

both

stationary

and

mobile

nodes

are

referred

to

as

mixed

WSNs.

This

paper

presents

the

development

of

an

experimental

testbed

for

mixed

WSNs

consisting

of

stationary

and

mobile

sensor

nodes

that

collaborate

to

improve

the

sensing

coverage

and

event

detection

of

the

network

in

a

given

deployment

area.

The

paper

describes

the

hardware

and

infrastructure

of

the

testbed

as

well

as

a

case

study

for

coverage

control

that

was

investigated

using

the

testbed.

We

point

out

that

the

developed

testbed

can

be

used

for

the

evaluation

and

validation

of

different

algorithms

for

coverage

control

that

involve

collaboration

between

stationary

and

mobile

sensors

to

improve

the

WSN's

monitoring

capabilities.

In

addition,

it

can

also

be

used

to

investigate

other

objectives

as

well

as

other

concepts

(e.g.,

network

control).

Recent

advancements

in

wireless

communication

and

microelectronics

have

enabled

the

development

of

simple

nodes

that

can

communicate

wirelessly

to

form

a

Wireless

Sensor

Network

(WSN).

Such

networks

have

great

potential

in

many

applications

such

as

area

monitoring,

smart

buildings,

precision

agriculture

and

traffic

control.

Their

unique

feature

is

that

they

can

capture

the

spatial

and

temporal

dynamics

of

the

environment

or

process

they

monitor..

Depending

on

the

applications,

a

WSN

may

consists

of

either

stationary

sensor

nodes

or

mobile

sensors,

e.g.,

sensors

installed

on

robots

or

aerial

vehicles.

Another

possibility

are

the

mixed

WSNs

which

consist

of

several

stationary

nodes

together

with

some

mobile

nodes

that

collaborate

in

order

to

achieve

objectives

like

improved

coverage,

improved

network

connectivity,

or

prolonged

network

life.

This

paper

provides

an

overview

of

a

mixed

WSN

experimental

testbed.

The

testbed

includes

several

stationary

This

work

is

partly

supported

by

the

European

Structural

Funds,

the

Cyprus

Government,

the

Cyprus

Research

Promotion

Foundation

and

the

European

Project

CONtrol

for

COORDination

of

distributed

systems

Corresponding

author

Email

addresses:

faniseng@ucy.ac.cy

(Theofanis

P.

Lambrou),

christosp@ucy.ac.cy

(Christos

G.

Panayiotou)

URL:

(Theofanis

P.

Lambrou)

nodes

as

well

as

some

nodes

mounted

on

mobile

robots.

A

main

objective

of

the

testbed

is

to

demonstrate

and

validate

algorithms

that

allow

the

mobile

nodes

to

move

autonomously

in

the

area

in

order

to

achieve

their

objectives.

For

the

purposes

of

this

paper,

the

objective

is

to

improve

the

network's

sensing

coverage.

Furthermore,

the

testbed

can

be

used

to

demonstrate

the

collaboration

between

the

sensor

nodes.

Moreover,

we

emphasize

that

the

testbed

can

also

be

used

to

demonstrate

other

objectives

(e.g.,

network

connectivity)

as

well

as

other

concepts

such

as

networked

control

or

control

over

wireless

networks,

however,

these

objectives

are

out

of

the

scope

of

this

paper..

In

monitoring

applications

that

involve

a

large

area,

coverage

holes

(areas

not

sufficiently

monitored,

where,

if

an

event

occurs

it

may

not

be

detected)

are

inevitable;

either

due

to

an

effort

to

reduce

the

overall

cost,

or

due

to

random

failures

of

some

nodes.

An

approach

to

address

the

problem

of

coverage

holes

is

to

employ

mobile

sensor

nodes

that

collaborate

with

stationary

nodes

in

order

to

improve

the

area

coverage

and/or

to

detect

an

event

as

fast

as

possible.

We

are

particularly

interested

in

approaches

where

the

mobile

nodes

(agents)

autonomously

decide

their

own

path

based

only

on

"local"

information

in

order

to

sample

areas

that

have

not

been

sampled

by

other

nodes,

stationary

or

mobile.

To

achieve

this,

mobile

nodes

collaborate

by

exchanging

some

information

so

that

they

do

not

sample

the

same

areas.

The

node

collaboration

approaches

investigated

in

this

paper

have

been

presented

in

The

underlying

principle

of

these

approaches

is

that

the

mobile

nodes

search

in

a

small

area

around

their

current

location

for

the

points

least

covered

(not

adequately

monitored

by

other

sensors)

and

try

to

move

towards

those

points

but,

along

the

way

they

also

navigate

such

that

they

avoid

areas

that

are

sufficiently

covered

by

other

nodes..

The

overwhelming

majority

of

approaches

for

solving

the

sensing

coverage

problem

has

been

validated

and

evaluated

based

only

on

simulation

models.

Experimental

work

with

WSNs

and

teams

of

cooperative

autonomous

robots

has

been

limited,

primarily

due

to

cost

and

practical

implementation

challenges.

Nevertheless,

experimental

validation

is

particularly

important

in

distributed

WSNs

and

multi-robot

systems

research

since

several

factors

that

can

significantly

affect

the

behavior

and

performance

of

various

approaches

may

not

be

accurately

modeled.

Such

factors

may

include

asynchronous

communication,

delayed

or

dropped

packets,

hardware

limitations,

inaccurate

sensing

etc.

While

several

experimental

testbeds

involving

either

stationary

sensors

or

cooperative

autonomous

robots

have

been

proposed

(e.g.

to

the

best

of

our

knowledge,

non

of

these

specifically

addresses

the

development

of

mixed

WSNs..

This

paper

presents

the

development

of

an

inexpensive

testbed

that

enables

validation

and

evaluation

of

mixed

WSNs

and

multi-robot

cooperation

algorithms

through

both

simulation

and

experimentation.

A

case

study

for

coverage

control

is

also

presented..

The

remaining

of

the

paper

is

organized

as

follows.

Section

reviews

related

work.

Section

presents

an

overview

of

the

developed

testbed

and

describes

its

main

components.

Section

defines

the

coverage

control

problem

while

Section

presents

a

case

study

that

is

investigated

using

the

testbed

and

involves

the

distributed

coverage

control

problem.

This

section

presents

all

algorithms

executed

by

the

mobiles

for

their

collaborative

path

planning.

Section

presents

the

results

obtained

from

the

testbed

under

different

scenarios.

Finally,

the

paper

concludes

with

Section

where

some

limitations

of

the

testbed

as

well

as

plans

for

future

developments

are

presented.

Motivated

by

the

need

for

an

experimental

platform

to

validate

distributed

path

planning

algorithms

in

mixed

sensor

networks,

we

have

developed

a

new

testbed

for

studying

collaborative

path

planning

algorithms

for

multirobot

systems

and

distributed

area

monitoring

techniques

for

mixed

WSNs.

This

paper

presents

an

overview

of

the

testbed

developed

together

with

details

on

the

static

and

mobile

sensor

nodes

used

and

the

overall

infrastructure

developed.

The

testbed

has

been

used

to

validate

a

coverage

control

case

study

where

mobile

nodes

collaboratively

sample

areas

not

adequately

monitored

by

the

static

sensor

network.

The

case

study

has

also

indicated

some

of

the

limitations

of

the

testbed

mainly

due

to

the

selected

mobile

platform

which

turned

out

to

be

a

little

difficult

to

accurately

control..

In

the

future

we

plan

to

upgrade

the

hardware

and

software

of

our

testbed

in

order

to

make

it

faster

and

more

robust.

Particular

attention

will

be

given

to

the

controlled

motion

of

the

mobile

platforms.

In

the

current

version,

it

was

evident

that

the

mobile

nodes

could

not

accurately

implement

the

path

suggested

by

the

path

planning

algorithm.

In

addition,

we

plan

to

use

the

testbed

to

come

up

with

more

accurate

simulation

models

such

that

the

discrepancies

between

simulation

and

experimentation

are

eliminated.

This

approach

can

lead

to

better

simulation

models

but

more

importantly

to

more

robust

algorithms

that

can

tolerate

unexpected

events.

Experimental

work

with

teams

of

cooperative

mobile

robots

in

the

context

of

WSNs

has

been

limited,

primarily

due

to

the

cost

and

the

implementation

overhead

required

for

the

experimental

validation

of

the

algorithms

developed

for

WSNs.

Some

experimental

testbeds

involving

only

cooperative

autonomous

robots

have

been

proposed

in

the

literature..

In

the

authors

develop

a

testbed

with

multiple

mobile

khepera

robots

that

form

a

team

which

cooperates

to

visit

multiple

target

points

to

collect

the

rewards

associated

with

them.

The

objective

is

to

maximize

the

total

reward

accumulated

over

a

given

time

interval.

This

testbed

has

also

been

used

to

address

dynamic

network

deployment

in

the

context

of

coverage

control

using

only

mobile

nodes.

Khepera

robots,

though

ideal

for

such

testbeds

due

to

their

small

size

and

functionality,

they

are

quite

expensive

(each

wireless

Khepera

robot

costs

approximately

euros).

Therefore,

several

attempts

have

been

made

to

develop

small,

inexpensive,

modular

and

open-source

platforms

for

developing

large-scale

mobile

robot

applications

In

the

authors

develop

an

experimental

testbed

to

study

several

issues

associated

with

the

convergence

of

control,

communication

and

computation.

The

testbed

consists

of

remotely

controlled

cars

and

each

car

is

controlled

by

its

own

dedicated

laptop.

An

overhead

camera

provides

positioning

information

and

communication

between

laptops

is

based

on

IEEE

The

authors

have

tested

many

scenarios

on

this

testbed

ranging

from

traffic

control

to

collision

avoidance..

Another

mobile

robot

platform

that

has

been

incorporated

in

a

testbed

is

presented

in

In

this

case

study

authors

develop

a

mobile

sensor

node

based

on

the

board

developed

by

Crossbow

Technology.

Their

main

objective

is

to

create

a

network

of

mobile

nodes

that

trace

the

boundaries

of

a

diffusion

contamination

process..

In

an

experimental

testbed

for

studying

multi-vehicle,

networked

control

has

been

developed.

The

authors

use

ducted

fans

to

control

the

vehicles

and

develop

real-time

feedback

control

algorithms

to

stabilize

the

system

while

performing

cooperative

tasks.

Several

other

researchers

have

also

demonstrated

experimentally

leader

following

cooperation

using

two

Unmanned

Aerial

Vehicles

(UAVs)

Recently,

MIT's

Distributed

Robotics

Laboratory

developed

an

energy

efficient

four

rotor

flying

robot

for

indoor

and

outdoor

navigation

Also

researches

at

Utah

State

University

have

develop

another

low

cost

UAV

platform

for

aerial

surveillance

missions..

The

testbed

presented

in

this

paper

involves

a

mixed

WSN

consisting

of

stationary

and

mobile

sensor

nodes

and

its

objective

is

to

study

collaborative

algorithms

that

improve

the

sensing

coverage

and

event

detection.

The

developed

testbed

enables

also

validation

and

evaluation

of

mixed

WSNs

collaboration

algorithms

through

both

simulation

and

experimentation

and,

to

the

best

of

our

knowledge,

non

of

aforementioned

testbeds

specifically

addresses

the

development

of

mixed

WSNs.

O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Expressive speech-driven facial animation Speech-driven facial motion synthesis is a well explored research topic. However, little has been done to model expressive visual behavior during speech. We address this issue using a machine learning approach that relies on a database of speech-related high-fidelity facial motions. From this training set, we derive a generative model of expressive facial motion that incorporates emotion control, while maintaining accurate lip-synching. The emotional content of the input speech can be manually specified by the user or automatically extracted from the audio signal using a Support Vector Machine classifier. Facial animation is an essential component of many applications such as video games, online virtual reporters, and other interactive human-computer interfaces. However, realistic facial animation remains one of the most challenging problems in computer graphics. Hundreds of individual muscles work in coordinated fashion to generate complex facial expressions and speech. Even though the dynamics of each of these muscles is well understood, their combined effect is very difficult to simulate precisely and efficiently. Motion capture provides us with the ability to record high-fidelity facial motions. But this technique is mostly useful for specific shots since the recorded motions are difficult to modify. Motion capture by itself cannot be used for efficient facial animation synthesis unless it is combined with some manual or automated editing tools.. A great deal of research addresses this issue using data-driven or machine learning approaches. In these approaches, face movement is no longer viewed as the result of a complex biomechanical system, but rather as the output of some abstract functions that can be estimated by the analysis of recorded motion capture data. The strength of data-driven approaches is to provide a yardstick against which to compare the synthesized motions: the quality of synthesized motions can be evaluated by how much they deviate from the recorded data. Machine learning approaches typically extract statistical or generative models from sets of high-fidelity recorded data. Novel animations are then synthesized by performing suitable operations within the interpolation space of the learned models.. Data-driven approaches have yielded some of the most high-fidelity facial animation systems to date. However, most of this work has focused on the issue of lip-synching or, in other words, synthesizing a face motion that matches the content of an input speech. In reality, facial motion is not only a function of speech. For example, the same sentence spoken in an angry way would look very different if spoken in a happy way. In computer graphics, it is traditional to refer to emotions in order to classify facial expressions. For instance, a smiling face is often associated with happiness or raised eyebrows with surprise (see Figure 1 ). This association between emotions and facial expression has long been studied by psychologists, anthropologists, and animal biologists. Emotions provide only a coarse parameterization of the space of facial expressions. However, because emotions have intuitive meanings that we can all relate to, they provide a simple way of restricting the space of facial expressions to a few intuitive categories.. In this article, we present a set of novel techniques for automatically synthesizing speech-driven expressive facial animation. Our approach relies on a database of high-fidelity recorded facial motions which includes speech-related motions with variations across multiple emotions. The input of our system, shown in Figure 2 , is a spoken utterance and a set of emotional tags. These emotional tags can be specified by a user or extracted from the speech signal using a classifier. Its output is a realistic facial animation that is synched to the input audio and conveys faithfully the specified emotions. Thus, our contributions are primarily twofold. First, we present a novel method for high-fidelity lip-synching based on motion capture data. Second, we develop a new approach to control the emotional content of the resulting facial motion.. The remainder of the article is organized as follows. Section 2 reviews the related literature. Section 3 presents the initial and laborious data collection and processing phase. In Section 4, we introduce our novel lip-synching approach. Section 5 describes how we map the emotional content of a synthesized facial motion to a desired emotion. Section 6 describes our emotion classifier. In Section 7, we present the details of our rendering method. Section 8 discusses our results. Lastly, Section 9 concludes this article and describes future work. In this article, we present a novel approach that, given an input utterance, can automatically synthesize matching and expressive facial motion. Our approach organizes a large set of recorded motions and associated speech into a novel data structure, the Anime Graph. Lip-synching with accurate coarticulation is solved by the proposed constrained search of the Anime Graph. We design our algorithms such that the fidelity of the recorded data is preserved at every stage of the motion synthesis process.. We also introduce a novel approach that maps facial motion between different emotion spaces. Our approach is based on the decomposition proposed by Cao et al. [2003] that separates facial motion into content and emotion components. Using sentences from our database that share content but differ in emotion, we create a large set of correspondences that serve as samples of our mapping model. Using scattered data interpolation, we turn these samples into a powerful mapping model that can map any facial motion to the desired emotion space.. We are planning to deploy this animation system in various educational software where a synthetic mentor is needed. These educational tools impose another requirement on our system: real-time performance. Efforts are under way to make this technique efficient enough for real-time motion synthesis and to interface it with a real-time speech synthesis system.. Despite the quality of the results, there is a lot of room for improvement. First, we would like to incorporate a visual attention model that controls the gaze of the speaking avatar. Lee et al. [2003] describes an interesting first attempt toward this problem. We are also investigating ways of producing motion in the absence of an input speech signal, for example, during a long pause. Synthesizing expressive head motion is also at the top our investigation list.. We realize that manipulating the emotional content of the motion without changing the content of the speech is not optimal. We are studying this problem in the wider context of combined facial motion and speech synthesis. We believe that there is much to be gained by studying and modeling these two highly correlated signals (motion and speech) in the same framework.. The main limitation of our approach is its dependency on motion and speech data. The quality of the output can only be as good as the motions in the training set. In addition, although our algorithm is automatic, building the database requires manual processing. In particular, during the data processing stage, we sometime have to manually fix the phoneme, labeling. To date, we have not found a completely reliable automatic phoneme-labeling software. Our contribution, however, is not in the field of phoneme labeling but in facial motion synthesis. Moreover, because it is costly to gather a second database of three-dimensional face motion, we were not able to test our approach with a second face. However, the techniques described in this article do not depend on the particular person that is being modeled. We believe that they would apply to any human face since human faces share a lot of similarities. In addition, we can retarget the facial motion produced by our method to other face models using a motion retargeting approach such as Pyun et al. [2003] . We tested the effectiveness of our method with a number of experiments. Figure 1 demonstrates the ability of the system to produce a high-quality rendered animation of the synthesized expressive facial motion. Figure 10 shows snapshots of a novel synthesized motion. Our system produces a high-quality synthesized motion that follows the speech signal closely. Figure 9 demonstrates the ability of the system to map motion between different emotional states. In the example, a frustrated motion is mapped to a happy motion. Our system is capable of handling both short and long sentences and a variety of emotional states. The longest sentence we have synthesized to date is 62 seconds.

O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Correctness of gossip-based membership under message loss Due to their simplicity and effectiveness, gossip-based membership protocols have become the method of choice for maintaining partial membership in large P2P systems. A variety of gossip-based membership protocols were proposed. Some were shown to be effective empirically, lacking analytic understanding of their properties. Others were analyzed under simplifying assumptions, such as lossless and delay-less network. It is not clear whether the analysis results hold in dynamic networks where both nodes and network links can fail.In this paper we try to bridge this gap. We first enumerate the desirable properties of a gossip-based membership protocol, such as view uniformity, independence, and load balance. We then propose a simple Send & Forget protocol, and show that even in the presence of message loss, it achieves the desirable properties. Large-scale dynamic systems are nowadays being deployed in many places, including peer-to-peer networks over the Internet, in data centers, and computation grids. Such systems are subject to churn, i.e., their membership constantly changes, as nodes dynamically join and leave. Moreover, such systems are often comprised of unreliable components, where node failures and message losses are frequent.. In order to allow nodes to communicate with each other, each node must know the ids (for example, IP addresses and ports), of some other nodes. Such ids are stored at each node in a local view (sometimes called membership), or view for short. In large systems, it is uncommon to store full views including all nodes in the system, not only because of the amount of memory this would require, but also because of the high maintenance overhead that churn would induce. Instead, one typically stores small views, e.g., logarithmic in system size [8, 2] . Local views are maintained by a distributed group membership protocol.. The views of all nodes induce a membership graph (overlay network), over which communication takes place. Two nodes are neighbors if one of their views includes the id of the other. The properties of local views have significant consequences for the respective graph's diameter, connectivity, load-balance, and robustness. Our goal in this paper is to mathematically analyze the proprieties of such views, and in particular, to understand the impact that message loss has on these properties.. We begin, in Section 2, by identifying the goals that a membership service strives to achieve: First, to bound the load on each node, each node has to maintain a small view and have a bounded degree (number of neighbors). Additionally, the "holy grail" for a membership service is to choose view entries independently of each other (we call this spatial independence) and uniformly at random [8, 21, 7] . Indeed, such choices result in an expander graph, with good connectivity and robustness, and low diameter [9] , ensuring fast and reliable communication. Note that in a dynamic system subject to churn, local views must evolve to reflect joining nodes and exclude ones that left or failed, and the system should converge to independent uniform views from any initial topology.. Beyond maintaining the membership graph for communication, independent random node id samples are useful for a variety of additional applications, such as gathering statistics, gossip-based aggregation, and choosing locations for data caching [17, 12, 5] . Such applications constantly require fresh random node ids, independent of past views, which requires views to evolve even in the absence of churn or failures. We thus identify an additional goal for a membership service: temporal independence-evolving into new graphs whose dependence on the past decays rapidly.. The most common approach to maintaining small local views is using gossip-based membership protocols [11, 8, 2, 23, 16] . In such protocols, nodes exchange ("gossip about") ids from their views with their neighbors, and use this information to update their views (see Section 3) . Such protocols make random choices, and their evolution is therefore a random process. Gossip-based membership has been empirically shown to lead to good load balance of node degrees [8, 16] , and certain variants of gossip were proven to ensure low probability for partitions [2] . On the other hand, most gossip-based protocols do, in fact, induce spatial dependencies among neighboring nodes. This is because an id that is gossiped to a neighbor typically remains in the sender's view.. Spatial dependencies can be eliminated by deleting ids sent to a neighbor. In order to avoid having unused entries in views, this is usually done in actions involving bidirectional communication, where the id received in a reply replaces the sent id [2, 18, 19] . However, such actions were previously analyzed under the assumption that they occur atomically, without overlapping in time with any other action, even though they involve multiple nodes. In practice, it is unclear how overlap can be avoided, as protocol actions are initiated from different nodes asynchronously, and a node might receive a message initiating a new action while it is already engaged in another. Moreover, implementing such atomic actions requires bookkeeping at each node, and is of course impossible in the presence of message loss [14] or node failures.. In Section 4, we present a model for studying gossip-based membership without atomicity assumptions. We follow [18, 19] , and model protocol actions as random graph transformations. In order to apply this methodology to real systems, we break up protocol actions into steps that can be executed atomically at a single node, allowing the analysis to account for message loss.. In Section 5, we present Send & Forget (S&F ), a simple and practical protocol that eliminates bidirectional communication, at the cost of allowing for unused (empty) entries in views. Message loss increases the number of unused entries. The protocol compensates for loss by creating new, dependent view entries. The goal is to create as little dependencies as possible.. In Section 6, we analyze node degree distributions induced by S&F . Our analysis shows that S&F can operate with small views-constant (e.g., with 40 entries), or logarithmic in system size. It further shows that the distribution of node degrees is very well balanced-close to the binomial distribution.. In Section 7 we study the distribution of membership graphs the protocol evolves to (i.e., the protocol's properties in the steady state). We define a Markov Chain (MC) on the global states (membership graphs) reachable by S&F starting from any weakly connected membership graph. We show that without loss, S&F achieves the desired properties of uniformity and independence. With positive loss, uniformity still holds but there exist spatial dependencies among entries in the same view as well as among views of neighboring nodes. These dependencies increase very moderately with the loss rate: The fraction of dependent entries in views is bounded, and grows like twice the loss rate. As the loss is typically in the order of 1% [22, 4] , the vast majority of view entries are expected to be independent. From this bounded spatial dependence, we prove that the temporal independence is preserved. We show that in a system of size n, starting from a random state (membership graph) G in the MC, once each node initiates O(s log n) actions, where s is a view size and n is the number of nodes in the system, the system evolves to a state whose dependence on G can be made arbitrarily small. For space limitations, some formal proofs are deferred to the full paper [15] .. In summary, we make the following contributions:. • We spell out the desired properties of membership protocols that maintain small views.. • We provide a model for studying membership graph evolution with non-atomic protocol actions.. • We present a practical membership protocol, S&F , which is amenable to formal analysis.. • In the absence of message loss, S&F provides all the desired properties of a membership service.. • We present the first formal analysis of a membership protocol in the presence of message loss. The salient properties of S&F are preserved even under reasonable loss rates. We formalized the desired properties of distributed membership service: small local views, bounded number of node neighbors, uniformity of views, and their low correlation with past and neighbors' views. We proposed a formal model for studying membership graph evolutions with non-atomic protocol actions. We presented a simple and practical membership protocol, S&F and showed that it provides all the desired properties of a membership service. This is the first analysis of a membership protocol in the presence of message loss that we are aware of. It might be interesting to apply our methodology in order to analyze additional gossip-based protocols under message loss.

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Parabolic finite element equations in nonconvex polygonal domains Let Ω be a bounded nonconvex polygonal domain in the plane. Consider the initial boundary value problem for the heat equation with homogeneous Dirichlet boundary conditions and semidiscrete and fully discrete approximations of its solution by piecewise linear finite elements in space. The purpose of this paper is to show that known results for the stationary, elliptic, case may be carried over to the time dependent parabolic case. A special feature in a polygonal domain is the presence of singularities in the solutions generated by the corners even when the forcing term is smooth. These cause a reduction of the convergence rate in the finite element method unless refinements are employed.: 65M60, 65N30.

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A Complexity Analysis of Bisimilarity for Value-Passing Processes We study the complexity of deciding bisimilarity between non-deterministic processes with explicit primitives for manipulating data values. In particular, we consider a language with value-passing (input/output of data) and parametric de nitions of processes. We distinguish the case in which data cannot be tested and the case in which a simple equality test over data is permitted.In the rst case, our main result shows that the problem is PSPACE-hard for the full calculus. In the second case, we rst show that the problem is coNP-complete in the fragment with value-passing and no parametric de nitions. We then de ne a compositional polynomial-time translation of the full calculus to the fragment with parametric de nitions but no value-passing. The translation preserves bisimilarity: this fact establishes the decidability of the full calculus and shows that the fragment without value-passing is computationally equivalent to the full calculus. For the latter, bisimilarity is then proved to be EXP-complete. Finally, we add to our language a parallel composition operator and show that, for a certain restricted syntactic format, the bisimilarity problem is still decidable and EXP-complete. Recently, there has been a renewed interest in process calculi with explicit primitives to manipulate data values. In particular, several enriched versions of Milner's CCS Mil80, Mil89, JP93, HL95, HL93] have been studied. In pure, i.e. data-less, process calculi such as CCS, beside standard operators for describing behaviours of processes (such as non-determinism + and parallel composition j) only pure-synchronization actions (also called \pure" actions) are provided. By contrast, process calculi with explicit treatment of data contain primitives for expressing transmission and receipt of values at communication ports: this feature is known as value-passing. Using the notation of Mil80], output of v at port a is written av:, while input at a is written a(x):; here the variable x acts as a formal parameter. Besides being exchanged, usually data values can be used as parameters in recursively de ned processes and tested by means of predicates to control the execution ow. Languages with explicit manipulation of values permit a natural description of realistic systems.. As an example, the recursively de ned process C(x):. C(x) ( x < o](a(y):C(y) + bx:C(x)) + x o]Error(x) speci es a memory cell whose initial content is a number x; as long as this content is less than an over ow value o, the cell can either receive a new value at a, or transmit its content at b; as soon as the value x equals or exceeds o, a recovery process Error is called.. A very peculiar kind of value-passing language is Milner, Parrow and Walker's -calculus MPW92] , where the values being exchanged among processes are communication ports themselves (name-passing). This permits the description of systems with dynamical communication linkage.. When analysing concurrent systems, a central problem is to be able to decide whether two given descriptions (usually regarded as a speci cation and as an implementation) are equivalent or not, according to a chosen notion of equivalence (veri cation). The algebraic aspects of this problem are becoming now well-understood, also for value-passing processes HL93, PS95, BD94]. On the contrary, a lot of questions concerning the decidability and the computational complexity of veri cation remain unanswered. A basic problem is to determine meaningful fragments of the calculi with values over which the veri cation problem is decidable. Then, a fundamental issue is to determine the abstract computational complexity of each of these fragments w.r.t. verication. Answering such questions would improve our understanding of the mathematical nature of processes. In practical cases, it could provide us with useful information to locate sources of ine ciency. In the present work, we will try to address some of these issues. We will restrict our attention to one of the most widely studied equivalences, Milner's bisimulation equivalence (also called \bisimilarity"), written and described e.g. in Mil89] .. For processes manipulating values, a non-trivial aspect of the problem is that they have usually an operational description in terms of an in nite state-transition graph (they are in nite state), at least if the domain of data values is in nite. This is due to the fact that each input action a(x): gives rise to in nitely many actual transitions, one for each di erent value. In JP93], Jonsson and Parrow concentrate on a particular class of processes with values, the data independent ones, which cannot test data nor perform any kind of operation over them. They prove that the bisimilarity problem for such processes can be transformed into a bisimilarity problem for nite-state processes. For the latter, decision algorithms exist PT87, KS90] , which are polynomial in the sizes of the involved graphs (that can be however much larger than the syntactical size of the processes). A detailed comparison of our work with JP93] is contained in Section 9.. In the present paper, we consider a calculus for describing non-deterministic processes that should be naturally embedded in every \reasonable" language with explicit data manipulation.. More precisely, besides permitting the execution of pure actions, we allow data values to be exchanged, used as parameters in recursive de nitions and tested for equality. The latter is done via the matching predicate a = b], also considered in the -calculus MPW92] . This is perhaps the most elementary form of test one would admit on data. Not even negative tests, to decide inequality of data, are permitted.. Our goal is to classify and separate the computational complexity, w.r.t. the syntactical size of processes, of the two basic operations for manipulating data, value-passing and parametric recursive de nitions. This will be done both for the data-independent case (where matching is excluded) and for the data-dependent one (where matching is included). More precisely, in each of the two cases, we consider separately three (sub-)languages, obtained from the calculus with pure actions and non-deterministic choice by adding either or both of value-passing and recursive de nitions. Then we asses the decidability and the di erence in complexity of these languages. In this analysis, we refer to the complexity classes NP, coNP, PSPACE and EXP (the latter contains the rst three and PSPACE contains the rst two, see e.g. BC93] ).. In the data-independent regime, we rst note that the bisimilarity problem is solvable in polynomial time for the calculi allowing either, but not both, of recursive de nitions or value-passing. For the calculus allowing both these primitives, we then prove that the problem is PSPACE-hard. This improves on a NP-hardness result due to Jonsson and Parrow. In the data-dependent regime, we rst show that, in the sublanguage with value-passing but no recursive de nitions, the bisimilarity problem is decidable and coNP-complete. Then we analyze the complexity of the full language, with both value-passing and recursive de nitions. We show that this language can be compositionally translated down to the fragment without value-passing, in a way that preserves bisimulation equivalence. The translation can be carried out in a time polynomial in the sizes of the processes. The result is interesting for two reasons. First, it gives us a procedure for deciding the bisimilarity problem in the full language, since the problem is easily seen to be decidable in the fragment without value-passing. Second, it ensures that the problem for the fragment without value-passing is just as complex as for the full language. It is important to point out that the matching predicate plays a crucial role in the de nition of the translation. We then prove that bisimilarity for the full language is EXP-hard. To the best of authors' knowledge, the latter represents the highest complexity lower-bound ever determined for a decidable bisimilarity over a meaningful language.. Finally, we consider adding to the language a binary parallel composition operator (P j Q).. We show that, for a restricted format of the resulting calculus, where parallel composition does not appear inside recursive de nitions ( nite-control processes), the bisimilarity problem is still decidable and EXP-complete (this implies that the fragments without parallel compositions are all in EXP).. To sum up, in the absence of matching, value-passing and recursive de nitions are separately tractable, but if we join them together the bisimilarity problem becomes very complex (PSPACEhard). If matching is allowed, the presence of value-passing itself makes the problem coNP-complete. By contrast, the presence of recursive de nitions themselves makes the problem EXP-complete; then, the adding of value-passing and of (a limited form of) parallel composition does not increase neither the expressive nor the computational power. These results are also summarized in Table 1 .. The most important conclusion we can draw out of this analysis is that, in the presence of values, most of the complexity is not due to value-passing, nor to parallel composition, but to parametric recursive de nitions.. The rest of the paper is organized as follows. In Section 2, syntax and semantics of the considered language are presented, and a few notions from complexity theory are recalled. Section 3 establishes some basic properties of operational semantics and bisimulation that will be used throughout the rest of the paper. Section 4 deals with the complexity of data-independent processes. As to datadependent processes, value-passing is dealt with in Section 5, while the relationship between the language with all the primitives for handling values and the fragment without value-passing is investigated in Section 6. In Section 7, we establish that these two calculi are EXP-hard. Section 8 deals with a language with parallel composition in addition. Comparison with related work and conclusive remarks are contained in Section 9. In this paper we have studied the decidability and the complexity of bisimilarity in fragments of CCS with values and of the -calculus. We considered both a data-independent setting, in which processes are allowed to send and receive data, but cannot do any test on them, and a simple data-dependent one, in which processes can only perform equality tests.. In the literature, some variants of bisimulation have been proposed, such as late bisimilarity MPW92, PS95] and open bisimilarity San93]. Many of the results presented in the paper extend to these equivalences. In particular, both late and open bisimilarity are PSPACE-hard over the data-independent processes, because the three equivalences coincide in this case (see e.g. PS95]).. Our paper is mainly related to JP93]. There, Jonsson and Parrow prove that bisimilarity is decidable in the data-independent language L v;r , by showing that the in nitely many transitions due to an input action can be reduced to a single, suitably chosen, schematic action JP93]. The latter is characterized as the receipt of the least value (w.r.t. to a xed ordering of values) not \used" in the considered process. This approach yields the polynomial-time tractability of some restricted cases. On the other hand, the technique cannot be used in a data-dependent setting, mainly because in the presence of the equality test, determining the set of \used" values of a process becomes very complex (perhaps undecidable). In this paper, we have taken a less radical approach to deal with the in nite-state problem: instead of substituting in nitely many actions with a single one, we replace them with a \moderate" number of actions (the ones corresponding to the set V 0 ). Jonsson and Parrow also show that L v;r is NP-hard, by means of a quite involved reduction from the clique problem. Here, we have for the same language a stronger result with an easier technique.. A question that is left open by the present work is the exact complexity of bisimilarity in L v;r . This language looks quite simpler than L m;v;r . Indeed, it is possible to show that a process of L m;v;r exists that is not bisimilar to any process of L v;r , that is, L m;v;r has more expressive power than L v;r . Even if such observation has no immediate complexity-theoretic implication, we suspect that a polynomial-space algorithm exists for the bisimilarity problem in L v;r .. In the data-dependent setting, we showed the EXP-completeness of the bisimilarity problem. This is the stronger intractability result proved to date for a decidable bisimilarity problem. The reduction establishing such result does not make use of the value-passing operators: this is hardly surprising in view of our proof that the full language can be compositionally translated in polynomial time into the fragment L m;r without value-passing.. The parallel composition operator is known to create an exponential blow-up of the size of the labeled transition systems. This motivates the common belief that adding such operator to a language generally increases the complexity of the bisimilarity problem. Indeed, we have showed that if the parallel composition operator is never used inside recursive de nition, then adding it to L m;v;r does not increase the complexity of bisimilarity, that remains EXP-complete (Theorem 8.2). The latter result implies that, given two processes P and Q in L m;v;r;p , we can compute in polynomial time two processes P 0 and Q 0 in L m;r such that P Q if and only if P 0 Q 0 . However, the result does not imply any apparent relationship between the syntactic structure of P and Q and that of P 0 and Q 0 . It would be interesting to nd, in the spirit of the translation from L m;v;r;p to L m;r;p , a compositional reduction from L m;r;p to L m;r that would show how to \express" the parallel composition operator using the other operators.. In HL95, HL93, San93, BD94], notions of symbolic bisimulation are investigated for both CCS with value-passing and -calculus, aiming at a more e cient representation of bisimilarity. Our results show that, even for very simple fragments, it is very unlikely that e cient algorithms exist. It remains to be seen whether symbolic techniques give some bene ts on the average.

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Assessing the Effect of Visualizations on Bayesian Reasoning through Crowdsourcing Abstract-People have difficulty understanding statistical information and are unaware of their wrong judgments, particularly in Bayesian reasoning. Psychology studies suggest that the way Bayesian problems are represented can impact comprehension, but few visual designs have been evaluated and only populations with a specific background have been involved. In this study, a textual and six visual representations for three classic problems were compared using a diverse subject pool through crowdsourcing. Visualizations included area-proportional Euler diagrams, glyph representations, and hybrid diagrams combining both. Our study failed to replicate previous findings in that subjects' accuracy was remarkably lower and visualizations exhibited no measurable benefit. A second experiment confirmed that simply adding a visualization to a textual Bayesian problem is of little help, even when the text refers to the visualization, but suggests that visualizations are more effective when the text is given without numerical values. We discuss our findings and the need for more such experiments to be carried out on heterogeneous populations of non-experts. Both laymen and professionals have difficulty making inferences and decisions based on statistical and probabilistic data [18, 26, 32] . This can have severe consequences in many domains.. Physicians need to diagnose diseases based on the outcome of unreliable medical tests. Patients need to decide whether they should undertake heavy medical treatment. Wrong judgments are common and often result in overdiagnosis [55] , e.g., up to two thirds of breast can-. • Luana Micallef is with INRIA and School of Computing, University of Kent, UK, e-mail: lm304@kent.ac.uk.. • Pierre Dragicevic is with INRIA, e-mail: dragice@lri.fr.. • Jean-Daniel Fekete is with INRIA, e-mail: jean-daniel.fekete@inria.fr. cers detected by mammography can be overdiagnosed [58] . In other cases, patients with a positive HIV test result attempted or committed suicide before further tests turned out negative [13, 25, 50] . In this domain, a crucial piece of information for effective decision making is the probability that a patient has a disease given that a test is positive.. In legal trials, juries have to convict or acquit defendents based on unreliable evidence and here too, wrong judgments abound [36] . A respected professor and advisor to defense lawyers claimed on U.S. television that since only 0.1% of wife batterers murder their wives, evidence of battering should be ignored in murder trials [29] . This reasoning is however fallacious, since the only important information is the probability that a husband was the murderer given that he battered his wife and she was killed.. These two scenarios involve Bayesian inference, which is known to be counterintuitive and subject to fallacious reasoning. As an illustration, consider the following classic problem [21] :. The probability that a woman at age 40 has breast cancer is 1%. According to the literature, the probability that the disease is detected by a mammography is 80%. The probability that the test misdetects the disease although the patient does not have it is 9.6%. If a woman at age 40 is tested as positive, what is the probability that she indeed has breast cancer?. Out of 100 doctors, 95 estimated this probability to be between 70% and 80%, while the correct probability is only 7.8% [21] . The probability is low because the prevalence of the disease in the population, i.e., the base rate, is low. When making Baysian inference, this information is often ignored [27, 32] , thus leading to the base rate fallacy [4, 5] . Using natural frequencies 1 instead of probabilities reduces the fallacy [18, 27, 31] . However, it is still difficult to comprehend how the different numerical quantities relate to each other 2 .. Previously proposed solutions involve the use of heuristics [34] and theories of mental models [33] . Others use visual representations. A study confirms that when Bayes' theorem is introduced to students through visualizations, students learn faster and report higher temporal stability than without a visualization [48] . However, prior training is not always possible. A few studies were conducted to assess the immediate benefits of visualizations, but it is still unclear which is the most effective representation for Bayesian reasoning. Moreover, studies have been carried out on populations with a specific background (usually highly-focused university students), making it difficult to generalize their findings to a more diverse population of laypeople of various backgrounds and ages.. We present the first study that tests the effectiveness of six different visualizations (i.e., Euler diagrams, glyph representations, and combinations of the two) on a large, diverse group of participants through crowdsourcing. Two new textual problem formats, specially designed to be used with visualizations, are also proposed and evaluated.. We first discuss current visualizations for Bayesian reasoning (Section 2). Then, we introduce the rationale of our study design (Section 3) and we report our two experiments together with our findings and their implications (Sections 4 and 5). Finally, we summarize our work and contributions (Section 6). We used crowdsourcing to assess the effect of six visualizations (based on Euler diagrams, glyphs and combinations of both) on probabilistic reasoning using three classic Bayesian problems in psychology. Our findings were inconsistent with previous studies in that subjects' accuracy was remarkably low and did not significantly improve when a visualization was provided with the text. A follow-up experiment confirmed that simply adding a visualization to a textual Bayesian problem is of little help for crowdsource workers. It however revealed that communicating statistical information with a diagram, giving no numbers and using text to merely set the scene significantly reduces probability estimation errors. Thus, novel representations that holistically combine text and visualizations and that promote the use of estimation rather than calculation need to be investigated.. We also argue for the need to carry out more studies in settings that better capture real-life rapid decision making than laboratories. We propose the use of crowdsourcing to partly address this concern, as crowdsourcing captures a more diverse and less intensely focused population than university students. Doing so, we hope that appropriate representations that facilitate reasoning for both laymen and professionals, independent of their background, knowledge, abilities and age will be identified. By effectively communicating statistical and probabilistic information, physicians will interpret diagnostic results more adequately, patients will take more informed decisions when choosing medical treatments, and juries will convict criminals and acquit innocent defendants more reliably. Though we used the best known textual representation (natural frequencies) [27] and the same text and text+visualization format as in previous studies, we failed to replicate previous findings as our subjects' accuracy was remarkably lower. For instance, considering V0 (text and no visualization), previous studies reported 35% [8] , 46% [27] , 51% [49] and 72% [18] exact answers with the natural frequency format, which are considerably higher than the 6% we obtained.. Yet, everything seems to suggest that our participants completed the tasks seriously. Only workers with a high HIT accept rate (95%) could participate and, since such a selection criteria is common practice, they have incentives to maintain a high rate. In addition, they were overall successful at the tests, the paper folding test being particularly attention-demanding. Finally, they often reported being confident in their answers and wrote a number of positive comments.. Of much concern is the fact that nearly all of our subjects were at least reasonably confident in their answer. In a real world situation, fallacious reasoning combined with overconfidence can easily lead to wrong decisions, with potentially harmful consequences (e.g., choosing whether to undertake chemotherapy after being diagnosed with cancer). Since we found that bias was close to zero overall, bad judgments could go either way.. We believe that far from invalidating the choice of the crowdsourcing method, these poor results motivate the need for more studies of this sort. It is important that techniques that aid probabilistic reasoning and decision making can benefit untrained people with different backgrounds and age ranges and, remain effective in situations where little time and attention are available.. In addition to a low accuracy overall, none of the visualizations we tested seemed to help. Although there is surely an effect [14] , Figure 3 suggests that effects on our metrics of interest (see Section 3.4) are small. This contrasts with conclusions drawn from studies on proportions of correct answers [8] . Girotto and Gonzalez go as far as arguing that with appropriate use of visualizations, anyone (including 'naive' subjects) could solve Bayesian problems [28] . However, our results are also consistent with previous studies finding no significant improvement with visualizations over text alone [18] .. Although Cosmides and Tooby suggest that passive visualizations are ignored when solving Bayesian problems [18] , 89% of our 53 participants who completed the follow-up questionnaire confirmed that they at least "somehow" used the diagram. Most of them reported finding the diagram very useful and commented that they generally like being given diagrams to solve problems. So it seems that subjects tended to overestimate the degree to which diagrams are helpful.. It is worth noting that despite positive comments overall, various participants commented that they did not fully understand the diagram, that having two representations was confusing, that they ignored it and that the information provided in the text was sufficient. A few others doubted the credibility of the diagram and chose to trust the text.. Several solutions have already been suggested. Teaching Bayesian reasoning is one of them. It can be extremely effective [48] but again, we chose to focus on techniques that can be used without prior training or background. Another well known approach is the use of active rather than passive visualizations [18] (but see also [8] ). Having people draw their own visualization can be effective, but it is not practical in many situations, including in scientific press, informative pamphlets, or in broadcasted visual adverts [26] . For similar reasons, static visualizations should probably be considered before interactive ones.. Since the answer to the Bayesian problem is in the diagram itself, it should be possible to increase the chances that people find it, either by i) helping them make the link between the text and the diagram [28] ; ii) encouraging them to search for the solution in the diagram; and iii) forcing them to search for the solution in the diagram.. We propose two alternative presentation techniques that only involve moderate modifications to the text: a) adding short instructions in the text that refer to the diagram (thereby supporting i and possibly ii), b) removing all numerical quantities from the text (supporting iii). The last technique is based on the idea that a rough estimation can be better than a plain wrong calculation and should further eliminate any possible doubt that the visualization is not credible.. We conducted a second experiment in order to i) confirm that simply adding a visualization to a Bayesian problem is of little help, and ii) testing whether an improvement can be obtained by the above two presentation techniques. In order to test i, we only included V0 and V4 and increased statistical power with larger sample sizes (from N = 24 to N = 120 each). V4 was the diagram with the lowest mean error and combined both Euler diagrams and glyphs. To further simplify the design, we only included the Mam problem. We chose it because it is a classic problem which has been used in various studies [21, 27] .. Our first experiment revealed that crowdsource workers were quite unsuccessful at solving Bayesian problems. Our second experiment had two objectives: i) confirm that simply adding a Euler/Glyph visualization to a Bayesian problem is not a viable solution (we increased sample size from N = 24 to N = 120 to get more statistical power) and ii) start exploring possible solutions to this problem.. We met our first objective by measuring a statistically significant difference between text alone and text+diagram, but showing that the practical difference was small (no more than 0.1 points of mean error as confirmed by an equivalence test).. We incidentally found that subjects were even less accurate than in our previous experiment, although the reasons for this are unclear. The design differed in two respects: a) subjects were initially instructed they could use any tool but they did not have to; b) those who reported having previously seen the HIT without submitting were discarded from the analysis (11%). So subjects might have been primed in trying to get exact answers and failed in their calculations, or alternatively, our previous experiment could have overestimated subjects' accuracy by including workers who possibly acquainted themselves with the problem way before carrying out the task.. With respect to our second objective, we tried two alternative presentations and found that referring to the diagram within the text (V4a) did not help, whereas removing the actual numbers from the text (V4b) yielded clear improvements. This is an important finding, since it is a simple and effective technique that can be easily applied to many reallife situations. Previously proposed techniques are more difficult to apply since they either involve prior training, or like active constructions, they require a pen and paper, time and possibly assistance [18] . We do not know of any previous study on Bayesian reasoning which proposed a technique similar to V4b, possibly due to the fact that most of them focused on increasing the number of exact answers rather than reducing estimation errors.. Our particular study focused on how to reduce inaccuracy, excluding investigations on why exactly subjects make mistakes and what these mistakes are. Some previous studies have observed different types of miscalculations in Bayesian reasoning tasks [27] and such investigations are likely crucial for designing effective visualizations and text formats. The distributions in Figure 4 do suggest that typical miscalculations or reasoning errors have occurred in our experiments. Some of them (close to bias 1) seem less common when a visualization is provided, possibly resulting in more miscalculations of a different type (close to bias -1) and a lower bias overall ( Figure 5 ). Trying to address specific mistakes might help to further increase accuracy, including when no numbers are provided, since diagrams can be misinterpreted. However, recurrent mistakes seem to vary across problems ( Figure 2 ) and finding general solutions might be challenging.. Our findings on visualization-friendly textual formats are only another step towards helping people being more accurate in Bayesian reasoning: even when shown a diagram without numbers, workers were still inaccurate at estimating probabilities (with a typical estimation about 3 times lower or higher). There are further possible improvements to our presentation techniques, such as showing numbers on the visualization. The text (story) could also be overlaid on the visualization, or alternatively, miniature visualizations could be embedded in the text [53] . Although we focused on static representations due to their wider applicability, interactive techniques can not only help users understand the relationship between text and diagrams, but also let them explore variants and generalize the problems [54] .. Other directions for future work include extending our design space with other types of Bayesian visualizations and comparing their efficiency. Although our initial comparison was inconclusive, we anticipate that using problem formats that are more adapted to visualizations will encourage subjects to actually use them and will ultimately make these visualization designs easier to compare in terms of both speed and estimation accuracy. .

O O O O O O B I O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Quantum complementarity and logical indeterminacy Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system. I will show that certain mathematical propositions on a d-valent function of a binary argument can be encoded in d-dimensional quantum states of mutually unbiased basis (MUB) sets, and truth values of the propositions can be tested in MUB measurements. I will then show that a proposition is undecidable within the system of axioms encoded in the state, if and only if the measurement associated with the proposition gives completely random outcomes.The theorems of Bell [1], Kochen and Specker [2] as well as of Greenberger, Horne and Zeilinger [3] showed that the mere concept of co-existence of local elements of physical reality is in a contradiction with quantum mechanical predictions. Apart from the known loopholes, which are considered by the majority of physicists to be of technical nature, all experiments confirmed the quantum predictions. This implies that either the assumption of "elements of reality", or "locality" or both must fail. Most working scientists seem to hold fast to the concept of "elements of reality". One of the reasons for this tendency might be that it is not clear how to base a theory without this concept. While one should leave all options open, it should be noted that maintaining the assumption of realism and denying locality faces certain conceptual problems [4] . But, perhaps more importantly in my view is that so far this approach could not encourage any new phenomenology that might result in the hope for a progressive research program.An alternative to this is to arrive at a new understanding of probabilities which is not based on our ignorance about some prederminated properties. What is then the origin of probabilities? What makes the probabilities different at all? Here I will show that certain mathematical propositions on a d-valent function of a binary argument can be encoded in d-dimensional quantum states (qudits), and truth values of the propositions can be tested in corresponding quantum measurements. I will then show that logically independent propositions correspond to measurements in mutually unbiased basis (MUB) sets. In quantum theory, a pair of orthonormal bases {|k }, 0 ≤ k ≤ d − 1 and {|l }, 0 ≤ l ≤ d − 1 in a Hilbert space C d are said to be unbiased if the modulus square of the inner product between any basis vector from {|k } with any other basis vector from {|l } satisfies | k|l | 2 = 1/d. A set of bases for which each pair of bases are unbiased is said to be mutually unbiased [5] . If one assumes that there is a fundamental limit on how much information a quantum system can carry ("a single qudit carries one dit of information"), and that this information is exhausted in defining one of the propositions (taken as an axiom), then the measurements that correspond to logically independent propositions must give irreducibly random outcomes. This allows to derive the probabilities (= 1/d) for outcomes of the MUB measurements without directly invoking quantum theory, but by looking if the proposition is definite or "undecidable" within the axiomatic set.In 1982, Chaitin gave an information theoretical formulation of mathematical undecidability suggesting that it arises whenever a proposition to be proven and the axioms contain together more information than the set of axioms alone [6, 7] . In this work, when relating mathematical undecidability to quantum randomness, I will exclusively refer to the incompleteness in Chaitin's sense and not to the original work of Gödel. Furthermore, I will consider mathematical undecidability in those axiomatic systems which can be completed and which therefore are not subject to Gödel's incompleteness theorem [8] .Consider a d-valent function f (x) ∈ 0, ..., d − 1 of a single binary argument x ∈ {0, 1}, with d a prime number [9] . There are d 2 such functions. We will partition the functions into d + 1 different ways following the procedure of Ref. [10] . In a given partition, the d 2 functions will be divided into d different groups each containing d functions. Enumerating the first d partitions by the integer a = 0, ..., d − 1 and the groups by b = 0, ..., d − 1, the groups of functions are generated from the formula:where the sum is modulo d. In the last partition, enumerated by a = d, the functions are divided into groups b = 0, ..., d − 1 according to the functional value f (0) = b.

B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O