Enabling network inference methods to handle missing data and outliers Background: The inference of complex networks from data is a challenging problem in biological sciences, as well as in a wide range of disciplines such as chemistry, technology, economics, or sociology. The quantity and quality of the data greatly affect the results. While many methodologies have been developed for this task, they seldom take into account issues such as missing data or outlier detection and correction, which need to be properly addressed before network inference. Results: Here we present an approach to (i) handle missing data and (ii) detect and correct outliers based on multivariate projection to latent structures. The method, called trimmed scores regression (TSR), enables network inference methods to analyse incomplete datasets by imputing the missing values coherently with the latent data structure. Furthermore, it substitutes the faulty values in a dataset by proper estimations. We provide an implementation of this approach, and show how it can be integrated with any network inference method as a preliminary data curation step. This functionality is demonstrated with a state of the art network inference method based on mutual information distance and entropy reduction, MIDER.The methodology presented here enables network inference methods to analyse a large number of incomplete and faulty datasets that could not be reliably analysed so far. Our comparative studies show the superiority of TSR over other missing data approaches used by practitioners. Furthermore, the method allows for outlier detection and correction. This work has presented an enhancement of network inference methods consisting of two preprocessing modules for handling incomplete and faulty datasets. The first one is capable of imputing values for lost measurements coherently with the latent structure of data. The second module detects univariate and multivariate outliers and replaces the faulty measurements with new values coherently with the available data.. A comparison of different methodologies for handling missing data has led to two main conclusions. First, traditional approaches used by practitioners, like complete case analysis (CC), linear interpolation (LI), nearest neighbor algorithm (NN) and unconditional mean imputation (MI), have problems when the datasets have high percentages of missing values and when the complexity of the network increases. Second, since trimmed scores regression (TSR) performs significantly better than the previous methods in BM1-BM4, including the iterative algorithm (IA), it represents the best approach to deal with missing values in network inference.. Likewise, the module for detecting and correcting outliers proposed here also applies TSR for replacing faulty observations. The good performance of this approach has been shown by means of simulations with five benchmark problems. The results of the network inference in four benchmarks with simulated multivariate outliers are statistically better when the new module is used as a preprocessing step; results obtained with univariate outliers in the fourth benchmark are not statistically significant. Due to the long computation time required to analyse the fifth benchmark, a single simulation is performed in this large-scale network. Therefore, no statistical differences are computed in this case study. However, the results of TSR in the comparative study and the outlier detection and correction are coherent with the results of BM4.. By extending MIDER with these new functionalities we have combined two different approaches for data analysis: information-theoretic and variance-based. The joint use of both methodologies increases significantly the number of datasets that can be used for network inference.. Crucially, both MIDER and the new preprocessing modules are general-purpose methods, which may be applied to networks of any kind -not only biological, but also from other areas of science -without requiring prior knowledge from the user. Furthermore, the missing data and outlier detection and correction modules can be used as a preprocessing step for other network inference methods. The problem of inferring complex networks is frequently addressed in several research areas [1, 2] such as social sciences (networks between academics, labor relations), engineering (electric power grid), chemistry (chemical reaction networks) or biology (ecological or cellular networks). In the context of cellular networks the individuals (network nodes) are biochemical entities such as genes, proteins, or metabolites. Many different approaches have been applied to date in this area, none of which can be singled out as the best one for all problems. Comparisons often find large discrepancies between the predictions of *Correspondence: abfolfor@upv.es 1 Departamento de Estadística e Investigación Operativa Aplicadas y Calidad, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain Full list of author information is available at the end of the article different algorithms, making network inference an open problem in bioinformatics research [3] [4] [5] [6] [7] .. Network reconstruction usually begins with collecting data from each individual that participates in the network. Then, based on the relationships detected among them, links between the individuals are established. When no prior knowledge is introduced, the reconstruction of complex networks depends solely on the available data. In many cases, the data collection represents a challenge itself when experimental measurements are involved. Network inference methods rely on estimating quantities such as correlation or mutual information, whose calculation requires simultaneous measurements of several variables. When the data collection in a time point fails for a particular variable, resulting in an unmeasured value, the scientist has to decide whether to discard the information regarding the entire experiment at this time point or to impute an appropriate value. This problem is also faced in process monitoring, for example when sensors fail, when a particular measurement is outside the range of the instrument, or when a failure is produced between the control system and the instrumentation [8, 9] .. The problem of missing data has been widely studied using projection to latent structure methods such as principal component analysis (PCA) [10] . Several methods have been developed using PCA in their cores, like the iterative algorithm (IA) [11] , the NIPALS algorithm [12] , and regression-based methods like known data regression (KDR) and trimmed scores regression (TSR) [13] , of which the latter has been shown to be one of the best performers [14] . These methods exploit the existing correlations between variables to impute the missing values coherently with the latent structure of the dataset. Other methods commonly applied to impute missing data are based on clustering algorithms, like the k-nearest neighbor algorithm and its variants [15] .. Projection to latent structure methods, especially PCA, can also be used for outlier detection [16] . Multivariate statistical process control allows the detection of abnormal situations during process monitoring [17] . Latent structure-based methods allow monitoring a large number of process variables, reducing the dimensionality of the original space to a few latent variables and statistics that are easy to control using charts. These methods are able to detect not only univariate outliers (i.e. values outside the usual range of a particular variable) but also changes in the latent structure (i.e. correlation structure) of the original variables, which classical univariate control charts usually miss [18] . Latent structure-based monitoring methods can be easily extrapolated to network inference. In this context, the outliers would be abnormal behaviors for certain individuals of the original dataset, or odd measurements for concentrations in time points during an experiment.. In this work we provide two new functional modules for curating the data that will be used as input to network inference procedures. The first module is devoted to handle missing data. If the toolbox detects that the raw dataset has missing values, the TSR method is applied in order to fill the holes in the dataset coherently with the latent structure of data. The second module detects extreme outliers in the raw dataset, and if there exist, they are first replaced by missing values and then recalculated using TSR. TSR was originally proposed in [14] for PCA model building with missing data, however, the application of TSR to correct outliers is new. The way both preprocessing modules act can be visualized in Fig. 1 . To evaluate the performance of TSR a comparison with other missing data methods commonly used by practitioners is carried out using several network inference benchmark problems. Likewise, several univariate and multivariate outliers are included in the datasets in order to check the ability of the outlier detection module.. Additionally, to illustrate how a network inference method can be augmented with these functionalities, we use them here in combination with a state of the art technique called MIDER (Mutual Information Distance and Entropy Reduction) [19] . MIDER is a general purpose method that exploits information-theoretic concepts such as entropy and mutual information [20, 21] . Informationtheoretic methods have strengths such as good scalability and the ability of detecting nonlinear relationships, and are widely used for the reverse-engineering of biological networks [22] , with examples such as CLR [23] , ARACNE [24] , MRNET [25] , MI3 [26] , or TD-ARACNE [27] . In [19] the performance of MIDER was benchmarked against these methods, obtaining competitive results. We emphasize that MIDER is used for demonstration purposes, but any other network inference method -such as those mentioned before -could be used as well. The data curation modules presented here are of general purpose, and work on the data independently of the reverse engineering procedure.. To facilitate their use, a Matlab/Octave implementation of the two data curation modules is included in the Additional files section (Additional files 1 and 2). Additionally, they have been included in a new version of the MIDER toolbox, MIDERv2 (http://gingproc.iim.csic. es/~gingproc/mider.html and https://sites.google.com/ site/midertoolbox/).. Network inference studies that take into account the missing data imputation problem have been more common in the social sciences than in the biological sciences; however, some examples of the latter type can also be found. Thus, the works [28] [29] [30] [31] [32] report network inference results obtained with datasets with missing values. Wu et al. [28] presented a network inference method with an interpolation controller, providing three selections of data interpolation approaches. In [29, 30] missing data is handled with a weighted k-nearest neighbor method. Hurley et al. [32] illustrated the use of a suite of GRN analysis tools imputing missing data using the LSImpute missing value estimation method. It should be noted that the aforementioned methods [28] [29] [30] 32] are specific for GRN inference with gene expression data, and the approaches chosen to handle missing data are not justified nor compared to other alternatives. In [31] a network inference tool designed for GRNs, NetGenerator, is extended in several ways in order to predict pathogen-host interactions (PHIs). Remarkably, NetGenerator is applicable to datasets with missing values, although it requires complete data for the last time point, which means that missing data imputation procedures may still be needed in some cases. There are also studies that have addressed the Fig. 1 Missing data and outlier detection and correction modules. Initially, if there are missing values in the raw dataset, trimmed scores regression (TSR) method is used to impute the missing data. Then, if the dataset has extreme outliers, first a missing value is generated for the faulty observation, and secondly the observation is reconstructed using again TSR issue of missing data in biological applications, but outside the context of network inference, e.g. [33] .. The present contribution differs from the aforementioned works in that it (i) presents a general method for handling missing data and outliers, (ii) compares its performance with that of other common approaches, (iii) provides an implementation of the methodology, and (iv) combines it with a freely available general-purpose network inference method. In this respect, there may be more resemblances with a recently published paper [34] , which presents a framework for network inference in Cytoscape and includes the possibility of using three built-in missing data "apps": row average, zero imputation, and Bayesian principal component analysis. The present manuscript is complementary to [34] since (i) the missing data imputation methods are different, and (ii) here, outlier detection and correction is also taken into account. This section begins with a description of the methodology for handling missing data, presenting the different methods used in the comparative study. Afterwards, the procedure for the detection and correction of outliers is defined. Then the main features of the MIDER network inference method are summarized, including an introduction of the concepts of entropy and mutual information, which are common to other information-theoretic methods. Finally, the case studies used for testing the methodology are described.

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


dbVOR:

a

database

system

for

importing

pedigree,

phenotype

and

genotype

data

and

exporting

selected

subsets

Background:

When

studying

the

genetics

of

a

human

trait,

we

typically

have

to

manage

both

genome-wide

and

targeted

genotype

data.

There

can

be

overlap

of

both

people

and

markers

from

different

genotyping

experiments;

the

overlap

can

introduce

several

kinds

of

problems.

Most

times

the

overlapping

genotypes

are

the

same,

but

sometimes

they

are

different.

Occasionally,

the

lab

will

return

genotypes

using

a

different

allele

labeling

scheme

(for

example

vs

A/C).

Sometimes,

the

genotype

for

a

person/marker

index

is

unreliable

or

missing.

Further,

over

time

some

markers

are

merged

and

bad

samples

are

re-run

under

a

different

sample

name.

We

need

a

consistent

picture

of

the

subset

of

data

we

have

chosen

to

work

with

even

though

there

might

possibly

be

conflicting

measurements

from

multiple

data

sources.

Results:

We

have

developed

the

dbVOR

database,

which

is

designed

to

hold

data

efficiently

for

both

genome-wide

and

targeted

experiments.

The

data

are

indexed

for

fast

retrieval

by

person

and

marker.

In

addition,

we

store

pedigree

and

phenotype

data

for

our

subjects.

The

dbVOR

database

allows

us

to

select

subsets

of

the

data

by

several

different

criteria

and

to

merge

their

results

into

a

coherent

and

consistent

whole.

Data

may

be

filtered

by:

family,

person,

trait

value,

markers,

chromosomes,

and

chromosome

ranges.

The

results

can

be

presented

in

columnar,

or

PLINK

format.

Conclusions:

dbVOR

serves

our

needs

well.

It

is

freely

available

from

Documentation

for

dbVOR

can

be

found

at

might

be

carried

out

on

a

subset

of

the

samples.

Managing

and

reconciling

these

multiple

sources

of

data,

often

with

different

sample

IDs,

allele

labels,

and

marker

names,

is

best

managed

using

a

database

system.While

several

database

systems

have

been

developed

for

managing

genetic

when

we

tried

some

of

these,

we

found

that

some

relied

on

commercial

database

systems

that

were

so

complicated

that

they

required

a

database

administrator

to

routinely

maintain

and

apply

regular

security

updates.

Others

did

not

scale

well

as

the

numbers

of

markers

genotyped

per

experiment

rapidly

increased.

Some

were

written

with

sophisticated

webbased

interfaces,

that,

while

elegant,

were

difficult

to

extend

and

customize

as

needed.

Therefore,

we

set

out

to

build

our

own

database

system,

based

on

open-source

We

have

created

a

series

of

programs

and

a

database

called,

dbVOR,

to

store,

manage,

and

retrieve

genetic

data.

Figure

illustrates

the

overall

operations

of

dbVOR.

The

raw

data

flows

into

the

database

tables

using

one

of

several

programs.

Finally,

the

genout

program

can

be

used

to

filter

and

merge

data

to

be

output

in

one

of

several

file

formats..

The

rest

of

this

document

is

organized

as

follows:

in

the

Implementation

section,

we

first

describe

dbVOR's

ancillary

database

tables

used

to

store

pedigree,

trait,

and

marker

data.

Then

we

show

the

tables

used

for

storing

genotype

data:

one

for

targeted

experiments

and

the

other

set

for

genome-wide

experiments.

The

key

difference

between

these

is

that

for

genome-wide

data

we

store

multiple

genotypes

per

record,

in

blocks.

We

next

discuss

the

programs

that

are

used

to

enter

data

into

the

aforementioned

tables.

A

subsequent

program

is

presented

that

extracts

data

from

the

database

tables.

The

next

few

sections

are

intended

to

give

a

feel

for

details

of

the

implementation:

configuration

files,

log

files,

note

storage,

and

database

commit

policy.

The

Example

section

illustrates

the

format

and

use

of

the

targeted

and

genome-wide

genotype

tables.

It

also

illustrates

how

multiple

conflicting

genotypes

for

the

same

person

and

marker

coming

from

multiple

or

even

the

same

experiment

get

resolved.

The

Data

statistics

section

show

how

conflicting

genotype

information

is

summarized

for

user

review.

The

Results

section

compares

the

efficiency

of

the

genome-wide

multiple

genotypes

per

record

representation

to

that

of

the

simpler

single

genotype

per

record

representation.

The

performance

is

also

illustrated

in

the

Discussion

section

via

comparisons

with

existing

systems.

Finally,

the

Appendix

shows

the

full

database

schema..

We

maintain

the

following

typographic

conventions:

All

programs

and

subcommands

are

shown

in

a

bold

typeface.

The

names

of

database

tables

are

shown

in

bold

italic.

Our

dbVOR

database

provides

useful

solutions

to

data

management

problems

commonly

encountered

during

an

ongoing

study

of

the

genetics

of

a

complex

trait.

In

such

a

study,

oftentimes

genome-wide

data

are

first

generated,

and

then

later

regions

of

interest

are

followed

up

via

targeted

custom

genotyping

using

a

different

technology.

Differing

technologies

may

return

different

allele

labels

for

a

given

marker.

Genotyping

experiments

may

partially

fail,

and

so

need

to

be

redone.

Clinical

data

may

be

presented

with

identifiers

that

differ

from

the

identifiers

used

in

the

laboratory.

Accordingly,

dbVOR

was

designed

to

handle

data

from

multiple

sources

with

possibly

conflicting

measurements

as

well

as

conflicting

codings

when

the

underlying

data

are

actually

the

same.

It

was

designed

to

process

not

only

targeted

experiments

but

also

genome-wide

experiments

and

to

merge

their

results

into

a

coherent

whole.

dbVOR

allows

you

to

select

subsets

of

the

data

by

several

different

criteria

and

to

output

the

results

in

tabular,

or

PLINK

format..

We

now

enumerate

some

of

the

strengths

of

our

dbVOR

database:.

dbVOR

was

designed

to

be

easy

to

install,

maintain,

and

modify.

It

is

purposely

lean,

requiring

just

two

software

components

(Python

and

MySQL),

and

it

is

open

source..

Our

dbVOR

database

handles

both

genome-wide

scale

data,

as

well

as

targeted

follow-up

data

of

limited

scale.

While

the

genome-wide

data

are

stored

in

a

special

way

that

maximizes

efficiency,

our

database

is

capable

of

merging

the

two

types

of

data

together

during

export.

dbVOR

handles

not

only

unrelated

individuals,

but

also

handles

family

data.

It

can

keep

family

structures

intact

after

filtering.

Our

database

is

capable

of

handling

multiple

different

phenotypes,

both

categorical

and

quantitative,

and

provides

summary

statistics.

dbVOR

is

designed

to

handle

the

reconciliation

of

overlapping

genotype

data

from

different

experiments.

In

the

process,

it

provides

feedback

to

the

user

in

the

form

of

agreement

matrices,

clearly

showing

how

many

repeated

genotypes

agreed

with

each

other

and

how

many

did

not.

Our

database

can

resolve

multiple

ID

systems,

alternate

marker

names,

and

differing

marker

allele

labels.

dbVOR

retains

all

original

data

while

providing

the

ability

to

selectively

turn

off

untrusted

portions

of

the

data.

Our

database

supports

flexible

and

powerful

filtering

during

export.

For

example,

specific

pedigrees

or

persons

can

be

excluded

or

included,

and

markers

can

be

selected

by

name,

chromosomal

position,

or

chromosomal

range.

dbVOR

supports

the

storage

of

multiple

builds

of

map

information,

as

well

as

supports

genetic

maps.

Our

database

uses

a

command-line

interface,

augmented

with

flexible

configuration

files.

dbVOR

has

the

ability

to

do

a

test

run

of

requested

actions

before

committing

such

changes

to

the

database.

This

permits

iterative

improvement

to

the

choice

of

configuration

options.

dbVOR

provides

a

system

for

storing

and

retrieving

notes.

The

data

analyst

can

use

these

notes

to

document

data

cleaning

decisions

and

data

manipulation

choices.

dbVOR

supports

Illumina,

Affymetrix,

and

flat

file

input,

largely

by

letting

the

user

choose

columns

from

the

input

files.

It

also

supports

input

in

PLINK

binary

'bed'

format..

As

with

all

software

projects,

dbVOR

is

a

work

in

progress,

and

so

there

are

a

number

of

possible

improvements

that

could

be

made

in

the

future.

These

include:.

dbVOR

could

be

extended

to

use

multiple

cores

in

parallel

when

available.

Such

an

extension

should

enable

the

speed

up

of

some

currently

slow

operations.

A

number

of

database

systems

for

handling

human

genetics

data

have

been

proposed,

starting

as

early

as

when

the

"Human

Genetics

Database

Management

System"

was

developed;

this

database

system

handled

not

only

marker

data

on

pedigrees,

but

also

clinical

and

laboratory

data

Before

embarking

on

writing

our

own

database

software,

we

explored

other

options.

As

a

small

research

group

with

limited

funds,

the

capable

Integrated

Genotyping

System

was

not

an

option

for

us

because

we

were

not

prepared

to

set

up

and

maintain

a

Windows

server

machine.

However,

we

did

have

a

Sun

Solaris

machine,

and

so

explored

using

GeneLink

GeneLink

was

originally

developed

using

Sybase

SQL

server,

but

we

chose

to

get

the

Oracle

version

working,

as

we

had

a

site

license

for

Oracle.

While

we

got

it

working,

we

found

that

keeping

Oracle

secure

and

updated

was

a

major

undertaking,

requiring

the

skills

of

an

experienced

database

system

administrator.

We

failed

at

our

attempts

to

extend

GeneLink

to

handle

non-integer

pedigree

IDs

-changing

the

pedigree

ID

type

in

the

database

tables

was

simple,

but

adjusting

the

sophisticated

web

interface

to

accommodate

this

change

was

beyond

our

skill

set.

These

experiences

led

us

to

focus

on

creating

a

database

system,

modeled

on

GeneLink,

that

used

open

source

free

components,

was

easy

to

install

and

maintain,

and

has

a

simple

interface,

enhancing

the

ability

to

subsequently

modify

it

as

needed..

In

passing,

we

note

that

PLINK

is

a

formidable

data

analysis

tool

and

it

provides

at

least

as

much

filtering

capabilities

as

dbVOR.

PLINK

can

do

a

variety

of

tasks

-it

can

recode

allele

labels,

flip

strands,

update

individual

information,

zero

out

a

set

of

genotypes,

and

merge

sets

of

genotypes.

However,

PLINK

only

supports

flat

files;

it

has

no

database

capabilities.

Further,

it

cannot

easily

manage

collections

of

experiments

to

process.

Merging

data

sets

with

PLINK

requires

that

both

data

sets

use

the

same

sets

of

person

IDs

and

allele

labels,

while

dbVOR

allows

one

to

resolve

these

issues

via

the

use

of

appropriate

aliases.

And,

having

been

written

primarily

for

data

sets

of

unrelated

individuals,

when

working

with

family

data

it

can

be

challenging

with

PLINK

to

avoid

filtering

out

ungenotyped

individuals

required

to

maintain

family

structures.

While

our

final

merged

and

cleaned

data

sets

are

often

analyzed

with

PLINK,

in

our

experience

dbVOR

greatly

facilitates

the

process

of

preparing

a

single

PLINK-ready

data

set..

We

have

compared

dbVOR

to

SNPpy,

a

recently

developed

database

system

Both

SNPpy

and

dbVOR

are

database

systems

that

store

and

retrieve

genotype

information

from

experiments.

Both

systems

access

their

database

in

Python

and

by

a

command

line

interface.

They

both

deal

with

the

large

amount

of

marker

data

in

current

genome-wise

studies,

but

in

different

ways.

SNPpy

more

heavily

uses

database

features

and

uses

C++

code

embedded

in

Python

to

improve

database

performance.

In

addition,

SNPpy

can

take

advantage

of

multiple

cores,

when

available.

However,

SNPpy

supports

only

one

phenotype

and

no

parental

information.

dbVOR

is

specifically

designed

for

linkage

studies

containing

families,

and

so

stores

parent

data.

It

also

stores

marker

genetic

positions

(as

well

as

base

pair

positions);

in

addition,

it

stores

map

information

for

multiple

builds.

dbVOR

stores

all

the

data

as

it

was

originally

sourced

from

flat

files,

Illumina

files,

or

Affymetrix

files.

But

it

allows

for

later

marker

aliasing,

person

name

aliasing,

and

allele

value

remapping.

It

provides

statistics

to

show

patterns/anomalies

in

the

data

without

judging

them

as

errors..

On

data

extraction,

dbVOR

allows

poor

data

to

be

marked

and

ignored.

It

resolves

multiple

measurements

of

the

same

person/marker

in

an

automated

but

customizable

way.

dbVOR

can

filter

subsets

of

the

database

via

simple

lists

and

ranges

and

does

not

required

the

construction

of

complicated

SQL

expressions

(as

is

necessary

for

SNPpy).

Further,

filtering

can

be

constrained

to

keep

the

family

structures

intact.

dbVOR

reports

data

out

in

the

less

compact

text-based

PLINK

formats

like

SNPpy

does,

as

well

as

in

the

compact

binary

PLINK

format.

It

also

can

output

files

dbVOR's

data

representation

is

particularly

efficient

for

fetching

all

the

markers

from

a

given

chromosome

or

chromosome

range.

Table

compares

the

Illumina

HapMap

loading

times

with

the

corresponding

times

for

SNPpy.

Recall,

these

data

contain

markers

and

and

samples

for

CEU,

YRI,

and

CHB+JPT,

respectively.

We

use

an

iMac

with

a

GHz

Intel

Core

Duo

processor

having

between

bp

to

write

to

ped

file.

The

timings

under

Cold

Database

are

for

performing

a

task

just

after

the

database

server

is

started.

The

Hot

Database

timing

are

for

repeating

the

task

a

second

(or

third)

time.

The

Cold

numbers

are

averaged

over

three

runs

and

the

Hot

numbers

are

averaged

over

six

runs..

GB

memory.

The

dbVOR

configuration

files

used

in

these

comparisons

are

provided

in

Additional

file

the

process

for

developing

the

timing

data

is

described

in

detail

in

Additional

file

The

dbVOR

calculation

is

done

with

the

genotypes

stored

in

the

genome-wide

block

representation.

The

SNPpy

calculation

is

done

with

genotypes

stored

in

the

shard

representation

with

multiprocessing

activity

set

to

one

processor

(j

Regarding

the

average

loading

times

seen

in

the

first

line

of

Table

SNPpy

is

faster

than

dbVOR.

Similarly,

when

selecting

and

writing

out

all

the

genotypes,

SNPpy

is

much

faster

than

dbVOR.

However,

when

smaller

portions

of

the

data

are

selected,

dbVOR

is

faster

than

SNPpy.

The

'cold'

timings

indicate

performance

right

after

the

database

has

been

started,

while

the

'hot'

timings

indicate

the

effect

of

repeating

a

task

that

has

previously

been

carried

out.

Both

systems

show

improvements

in

'hot'

mode

when

reading

a

chromosome

or

less;

presumably

because

data

are

cached

in

the

server

and

so

do

not

have

to

be

fetched

from

the

database

files

One

might

question

why

our

database

system

contains

two

different

subsystems

for

storing

genotypes:

the

Genotypes

table

is

used

for

storing

small

volumes

of

data,

while

the

Genotypesblocks

table

approach

is

used

for

genomewide

large-scale

genotype

data.

One

reason

is

historical:

we

developed

the

Genotypes

table

approach

first

for

targeted

experiments.

The

other

reason

is

that

in

our

experience,

in

a

given

research

project,

it

is

common

to

start

with

genome-wide

large-scale

data

and

then

followup

with

much

smaller

scale

targeted

follow-up

data.

The

genome-wide

representation

is

more

efficient

for

reading

and

writing

large-scale

genotype

data;

however,

it

is

less

space

efficient

for

targeted

data

(as

storing

small-scale

data

in

a

large

block

structure

would

waste

space).

The

Genotypes

table

representation

is

just

the

opposite;

it

is

efficient

where

the

genome-wide

representation

is

not

and

vice

versa.

The

genome-wide

representation

for

reading

and

writing

uses

fewer

database

records.

The

database

must

maintain

indices,

consistency

constraints

and

atomicity

of

operations

for

each

record.

With

fewer

records,

there

is

less

total

time

overhead..

Finally,

it

is

important

to

note

that

efficiency

is

context

dependent:

the

genome-wide

representation

is

inefficient

in

the

case

when

one

is

selecting

a

small

number

of

markers,

each

in

a

separate

block.

Such

a

selection

would,

when

using

the

Genotypeblocks

representation,

require

extraction

and

handling

of

a

lot

of

unneeded

marker

data,

as

each

block

containing

a

selected

marker

would

need

to

be

pulled

in

its

entirety

from

the

database.

Here

we

discuss

some

timing

data

based

on

a

real

data

set,

as

well

as

compare

dbVOR

to

other

previously

published

database

software.

Genetic

studies

of

complex

human

diseases

typically

involve

multiple

iterations

of

genetic

marker

generation.

For

example,

a

set

of

individuals

may

first

be

assayed

with

a

genome-wide

chip

that

measures

genotypes

at

hundreds

of

thousands

of

markers.

Then

a

subset

of

interesting

signals

may

be

followed

up

by

custom

genotyping

using

a

different

technology.

If

there

are

technical

problems,

yet

another

round

of

custom

genotyping

using

a

third

MySQL,

driven

by

command-line

programs

written

in

Python.

We

named

our

database

system

"dbVOR",

after

Vör,

the

inquiring

Norse

goddess

of

wisdom

from

whom

nothing

can

be

concealed.

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


IMPROVEMENT OF POWER SUPPLY ELECTROMAGNETIC COMPATIBILITY BY EXTENSION OF CHAOS ANTICONTROL Switch-mode power supplies usually emit electromagnetic interferences at the switching frequency and its harmonics. Inducing chaos in these systems has recently been suggested as a means of reducing these spectral emissions, yet at the expense of aggravating the overall magnitude of the ripple in the output voltage. We propose here a new nonlinear feedback control method, which induces chaos, and which is able at the same time to achieve low spectral emission and to maintain a small ripple in the output. The feasibility and usefulness of this new and simple method is shown here with a numerical example, which includes a comparison with the previous control method. DC-DC converters are some of the most widely used circuits in power electronics. The purpose of this paper is to introduce an original method of chaos generation in switching systems in general and power electronic circuits in particular.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


RF breast cancer detection employing a noncharacterized vivaldi antenna and a MUSIC-inspired algorithm A novel microwave breast cancer detection system consisting of an Evolutionary Global Optimized Vivaldi antenna and an algorithm inspired by MUltiple SIgnal Classification (MUSIC) is presented. Its performance is assessed by using a simplified numerical breast phantom for a number of critical conditions including the presence of fibroglandular tissues. Breast cancer is the most common cancer in women and X-ray mammography is the most widely used diagnostic technology in mass screening. However, its detection capabilities have been shown to be limited due to poor benign/malignant tissue contrast. Indeed, between 4% and 34% of all breast cancers are missed and nearly 70% of all breast lesions turn out to be benign [1] . In addition, as X-ray mammography requires breast compression, chest wall adjacent regions are left unscreened. Furthermore, the exposure to low levels of ionizing radiation may reduce patient compliance with screening recommendations and limit frequent check-ups.. These concerns motivated the search for techniques that image other physical tissue properties or metabolic changes. Among them, active microwave based diagnostic techniques have triggered great interest. At UHF frequencies, normal and malignant breast tissues exhibit a sharper dielectric contrast which can be greater than 2 : 1, i.e., notably superior to the radiographic density exploited by X-ray mammography [2] . At the same time, the need for breast compression and ionizing screening are eliminated.. Over the last two decades, significant research activities were focused on the early detection of breast cancer by microwave imaging which led to several techniques for detecting, localizing and characterizing tumors in breast tissues. Such methods can be broadly grouped into two categories: one which aims at reconstructing the dielectric and conductivity maps of the breast and another which detects and localizes in-homogeneities in the breast. In both cases, an electromagnetic inverse scattering problem exists [3] .. In the first case the intrinsic non-linearity of inverse scattering problems is taken into account. Accordingly, retrieving the dielectric and conductivity profiles entails running optimization schemes which are computationally intensive [4] . Those imaging solutions also suffer from reliability problems due to the occurrence of false solutions. This is a common consequence of deterministic minimization algorithms [5] .. For the second class, simplified scattering models are employed, so that the detection problem requires linear procedures. Delay and sum procedure (and their different variants [6] ), time-reversal algorithm [7] and the distributional approach [8] are a few of focusing algorithms based on linear inversion. Of course, as simplified models are employed, only "qualitative" information can be gathered and, hence, a further classification step is generally needed [9] . However, problems of reliability and computational burden are avoided.. In 2007 Lazebnik [10] , [11] conducted a large scale study to experimentally determine the microwave dielectric properties of a variety of normal, malignant and benign breast tissues obtained from cancer surgeries. Those results stimulated improvement of beam-forming algorithms to take into account the reduced benign/malignant breast tissue dielectric contrast. Dielectrically heterogeneous MRI-derived breast models and ideal radiating elements were used to assess tumor localization for different radar configurations and contrast enhancement techniques. However, if ideal sources are very useful to promptly evaluate imaging algorithms, the design of the front-end of an RF breast cancer imaging system has fundamental importance for the overall performance. In particular, antennas must fulfil specific requirements including operating band, field penetration inside the breast, phase-center stability, compactness and cost.. Ultra-Wideband (UWB) antennas emerge as suitable candidates for this application due to their properties such as large operating band, phase-linearity and compactness. Therefore, different antenna geometries have been proposed in literature. Planar monopole antennas are able to combine a miniaturized low-profile design with very broad impedance matched bandwidth and good stability when placed close to the breast [12] , [13] . However, their omnidirectional behavior can lead to interference coming from unwanted directions. The same drawback might affect a dipole antenna placed conformally around the breast phantom as investigated in [14] . Horn antennas have been also proposed for their large operating bandwidth and directive pattern [15] . But their bulky structure is suitable just for multi-monostatic configurations with only one TX/RX antenna that moves across a certain number of scanning positions. In [16] , [17] a wide-slot antenna is introduced as a radiator for a 31-element conformal array. Its size is affordable in the frequency range 4 − 8 GHz, where the limited field penetration is compensated for the large number of array elements. Vivaldi antennas combine a large impedance matching bandwidth together with a directive pattern, so that they can divert more power towards the target and reduce backscattering coming from obstacles outside the volume under investigation. In [18] Vivaldi antennas are miniaturized by corrugating the external flanges to operate as breast cancer sensors in the frequency range 3.1 − 6.85 GHz. Efficient Global Optimization (EGO) techniques can also be employed in order to improve their UWB features [19] , [20] . EGO optimisation was used in [13] , where a planar antipodal Vivaldi antenna is evaluated in terms of operating bandwidth, fidelity factor and field penetration into a planar breast phantom. In this paper a novel breast cancer detection system consisting of a planar antipodal Vivaldi antenna and a detection algorithm inspired based by MUltiple SIgnal Classification (MUSIC) [21] is presented. As an a priori characterization of the antenna is not required, a complex optimized geometry can be chosen without the necessity of further algorithm tailoring. The performance of such antenna + algorithm system can be compared to what was obtained by using an ideal dipole source as presented in [22] . In particular, the antenna phase response is not required to be known a priori, neither is this calibrated before achieving tumor detection. Indeed, such characterization is not required at all in any detection stage of the proposed procedure. In order to focus on this aspect, a simplified breast model is considered, although in combination with a non-ideal antenna as commonly done in the literature [14] , [23] , [24] . When the antenna is located close to an unknown breast structure, its behavior changes and its a priori characterization becomes extremely difficult. This issue dramatically reduce the performance of RF tomographic techniques that require coherent data where at least the antenna phase frequency response must be known for obtaining properly focused reconstructions. A MUSIC-inspired detection algorithm is here proposed to address this problem of great relevance in practical situations and its performance is assessed across a large number of scenarios. In particular, the analysis encompasses the cases where: · a single tumor is located at different position within the breast tissue; · the co-presence of three tumors which are positioned at different distances from the skin layer; · fibroglandular structures are also considered for critical benign/malignant tissue contrast. As the primary task of this investigation is to detect and localize tumors inside the breast tissue, a linear model in conjunction to a MUSIC-like algorithm is adopted to develop detection algorithm. This avoids the disadvantages associated with non-linear optimization. In particular, a multi-monostatic/multifrequency configuration is employed.. The paper is organized as follows. Sections II, III and IV, are respectively devoted to the introduction of the adopted phantom, the antenna design and the detection algorithm description. Numerical analysis is discussed in Section V. A novel RF breast cancer detection system has been introduced in this paper. The system components consisting of a simplified phantom, a MUSIC-inspired detection algorithm and a ParEGO Vivaldi antenna have been described in detail. A simplified 2-D phantom was used to assess the performance, while the system was implemented with a realistic antenna and tested in different critical scenarios. Together with visual reconstruction of the detection algorithm results, its performance was measured by suitable metrics such as Full-Width-Half-Maximum (FWHM), Signal-to-Clutter Ratio (SCR), Signal-to-Mean Ratio (SMR) and Spatial displacement (SD). Detection was successful in the presence of a single 5-mm tumor when positioned at different distances from the skin layer. But also when 3 tumoral in-homogeneities are introduced the detecting system is proven to be successful. Finally, the system was tested in the presence of fibro-glandular structures (FGS) that strongly reduce the dielectric contrast between benign and malignant tissues. For both scattered and large FGS, the tumor was correctly detected with a high degree of precision. In conclusion, the proposed RF detection system here presented offers encouraging performance for early-stage breast cancer diagnostics. Its MUSIC-like algorithm proves to be suitable for a non-ideal antenna and performs correctly in critical scenarios. In particular, this algorithm does not require any antenna calibration or phase response estimation. The employment of efficient and complex antenna geometries is allowed without difficult algorithm redefinitions. In fact, multifrequency data are not used for de-correlation purposes [29] or to construct a wideband estimator [34] . In those cases, data might be coherent and thus information about the antenna would be necessary. Alternatively, we separately performed different reconstructions at each frequency. This eliminates the necessity of a priori antenna phase response characterization. Moreover, the broadband antenna requirement is more relaxed compared to other UWB approaches, as the system operates on a discrete set of frequencies rather than on continuous spectrum.

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


Application of global sensitivity analysis to a tire model with correlated inputs When a vehicle equipped with tire is manoeuvred on the ground, the tires are submitted to a number of forces -longitudinal force when driving or braking torque is applied to the wheel and/or lateral force when the wheel is steered to turn at a corner. Pacejka model describes these forces that represent the reaction of the road onto the tire. This nonlinear model depends on correlated parameters such as the friction coefficient, the vertical load, the cornering stiffness, . . . which have to be identified from some measurements.The sensitivity of Pacejka model to these correlated parameters are studied using an approach based on polynomial chaos. It consists in decorrelating the parameters using the Nataf transformation and then, in expanding the model output onto polynomial chaos. The sensitivity indices are then obtained straightforwardly from the algebraic expression of the coefficients of the polynomial expansion. In the automotive and aeronautical fields, modelling the tire/road interface is fundamental. Indeed, the tire model is one of the major elements to integrate into a ground vehicle or aircraft model, as the tires are the only contact surface with the road. When a vehicle equipped with tires is manoeuvred on the ground, they are subject to a number of forces -longitudinal force when driving or braking torque is applied to the wheel and lateral force when the wheel is steered to turn at a corner. The tire models available in the literature describe the efforts and moments corresponding to the road reaction of the tire (see for instance [1, 2, 3, 4] ).. One of the most famous model was proposed by Pacejka ([1] ) and is often used ( [5] ) nowadays by industrials (Michelin, SAE, Adams tire software, ...). This model is nonlinear, complex and depends on a certain number of parameters (friction coefficient, vertical load, side slip angle, ...) that can be obtained from experimentation. Unfortunately, experimental data are often sparse or incomplete, especially in the aircraft domain and their measurements are very expensive. On the one hand, some parameters only have a negligible influence on the model response and therefore, do not need to be determined accurately. On the other hand, some others are relevant for the model response and thus influence its uncertainty significantly. These parameters may require additional measurement effort in order to be estimated with relatively high accuracy. In order to prepare and plan future experiments, it is necessary to perform a sensitivity analysis of the Pacejka 2 model.. Several studies have focused on the global sensitivity analysis of nonlinear models with independent inputs (for instance, [6, 7, 8, 9, 10, 11, 12] ). They rely on variance-based sensitivity indices also known as Sobol' indices ( [7] ).. They measure the contribution of input parameters to the model response variance. Such a contribution can be due to a parameter alone or to a group of parameters. Sobol' indices are unique and easily interpretable when the parameters are independent. But, it is more challenging when they are dependent. Indeed, if a function (i.e. model response) structurally depends on parameter p 1 and not on p 2 , and if p 1 and p 2 are correlated, classical Sobol' indices will lead to the conclusion that both are relevant inputs. Even though actually p 2 is influential only because of its correlation with p 1 .. It may be of high interest to distinguish whether an input is relevant regarding its correlations with the other ones [13] . This information may be of great help for the experimenter in order to guide future experiments.. Mara and Tarantola ( [14] ) have derived a set of variance-based sensitivity indices to cope with parameters dependency. They also proposed a computational method for their estimation. The proposed approach relies on the use of polynomial chaos expansion ( [15] ) in conjunction with a GramSchmidt based decorrelation procedure. They also indicate that Nataf ( Pacejka model is widely used in the automotive and aeronautical fields. The model depends on correlated parameters (friction coefficient, cornering stiffness, vertical load, ...) which must be identified from measurement data.. The most relevant parameters on the lateral force are highlighted, using the approach proposed in [14] .. The paper is organised as follows. Section 2 presents the Pacejka tire model. Section 3 recalls the expression of the Sobol' sensitivity indices for model with independent parameters and their estimation based on polynomial chaos. Section 4 presents the approach used to study the sensitivity for models with correlated parameters. Then, the sensitivity analysis of the Pacejka tire model is performed.

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


Robust energy-aware routing with redundancy elimination Many studies in literature have shown that energy-aware routing (EAR) can significantly reduce energy consumption for backbone networks. Also, as an arising concern in networking research area, the protocol-independent tra c redundancy elimination (RE) technique helps to reduce (a.k.a compress) tra c load on backbone network. Motivation from a formulation perspective, we first present an extended model of the classical multi-commodity flow problem with compressible flows. Moreover, our model is robust with fluctuation of tra c demand and compression rate. In details, we allow any set of a predefined size of traffic flows to deviate simultaneously from their nominal volumes or compression rates. As an applicable example, we use this model to combine redundancy elimination and energy-aware routing to increase energy e ciency for a backbone network. Using this extra knowledge on the dynamics of the tra c pattern, we are able to significantly increase energy e ciency for the network. We formally define the problem and model it as a Mixed Integer Linear Program (MILP). We then propose an e cient heuristic algorithm that is suitable for large networks. Simulation results with real tra c traces on Abilene, Geant and Germany50 networks show that our approach allows for 16 28% extra energy saving with respect to the classical EAR model. Another research topic that has also been active recently is tra c redundancy elimination (RE) [2, 3, 37, 41] . Observing that tra c on the Internet contains a large fraction of redundancy (e.g. popular contents such as new movies are often downloaded several times subsequently), a complementary approach uses redundancy elimination (RE) techniques to reduce link load in backbone networks. It consists in splitting packets into small chunks, each is indexed with a small key, that are cached along tra c flows as long as they are popular. Then, keys are substituted to chunks in tra c flows to avoid sending multiple times the same content, and the original data are recovered on downstream routers based on the cache synchronization between the sending and the receiving routers. Therefore, tra c redundancy is removed and tra c volumes of flows between the two routers are reduced. For simplicity, a tra c flow from which redundancy has been removed is called a compressed flow. We use interchangeably the notation compression rate or RE rate to denote how much tra c redundancy can be eliminated.. From energy saving perspective, RE has a drawback since it increases energy consumption of routers [23] . To find a good trade-o↵, in our previous work, we proposed GreenRE -a model that combines EAR and RE to increase energy e ciency for backbone network [23] . In the GreenRE model, each of the demand has a static tra c volume and is associated with a constant factor of redundant tra c. To handle future changes and guarantee a certain level of quality of service (QoS) (avoiding overloaded links), the peak volumes of tra c demand and the lowest RE rates are used as the worst case realization. Such assumption clearly leads to ine cient usage of network resources and poor energy saving. To alleviate this limitation of the GreenRE model, the uncertainty on tra c volumes and RE rates has to be precisely modeled and taken into account in the optimization process. By using this extra information, we are able to obtain a design which is closely related to the dynamics of the tra c pattern, hence significantly increase energy saving compared to previous proposals.. In mathematical literature, the technology-independent -robustness has been introduced in [8, 9] and then successfully applied to various network design problems [30, 18, 17] . This approach is based on an observation that in real tra c traces, only a few of the demands are simultaneously at their peaks. So, the authors considered a parameter > 0 so that at most demands deviate simultaneously from their nominal tra c volumes. Based on this assumption, the so-called robust solution is a solution that is feasible for any subsets of demands simultaneously at their peaks, other demands are being at their nominal values. The originality of the method is the expression of the maximum sum of deviation over all possible subsets of demands as a unique linear program (LP). However, this LP formulation may have an exponential number of constraints. To overcome this issue, the LP formulation is transformed into a compact one using the duality theorem.. In this work, we first present an extended version of the classical multi-commodity flow problem in which tra c flows can be compressed to smaller volumes (with some costs, e.g. energy cost mentioned in this paper). Previous studies have considered robustness either on tra c volumes [30] or on redundancy rates [18] . To the best of our knowledge, this is the first work combining uncertainties in both tra c demand volumes and compression rates. In summary, we make the following contributions:. • From a theoretical point of view, we present an extended multi-commodity flow problem with compressible tra c flows. In addition, we provide a robust model in which uncertainties in both tra c volumes and compression rates are taken into account.. • This extended model can be applied to a vast range of applications in network flows and tra c management. In this paper, as an applicable example, we use this model to increase energy e ciency for a backbone network. We apply this extended model into energy-aware routing and formally define the Robust-GreenRE problem using Mixed Integer Linear Program (MILP).. • Since robust network design is NP-hard problem [10] , we propose a heuristic algorithm that is e↵ective for large instances.. • By simulation, we show energy saving o↵ered by our methods on backbone networks with real-life data tra c traces and compression rate fluctuations.. 2 Related Works In this paper, we formally define and model the Robust-GreenRE problem. Taking into account the uncertainties of tra c volumes and redundancy elimination rates, the Robust-GreenRE model provides a more accurate evaluation of energy saving for backbone networks. Based on real-life tra c traces, we have shown a significant improvement of energy saving compared with other models. As future work, we shall investigate implementation issues and impacts of Robust-GreenRE model on QoS and fault tolerance.

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


Some Aspects about Vagueness & Imprecision in Computer Network Fault-Tree Analysis Abstract: Based on the available information (eg.multiple functional faults or sensor errors give rise to similar alarm patterns or outcomes), some states in the behaviour of a network can not be distinguished from one another. So, the computer network's fault tree reliability analysis frequently relies on imprecise or vague input data. The paper will use a Dempster-Shafer Theory to accommodate this vagueness and it will show how imprecision can give rise to false-negative, and false-positive inferences; there will be assigned upper and lower bounds for the probability on elements of the state space. After illustrating the computational simplicity of incorporating the Dempster-Shafer Theory probability assignments, we will apply them for analyzing the reliability of the network of our department. The probabilities are no longer appropriate to represent vagueness in risk and reliability analyses; fuzzy set theory was proposed instead to quantify vagueness in this area [1] . Development in DST have shown how probability can be adapted to incomplete or vague information, especially information that is based on human judgment or human-machine interaction.. False positives and false-negatives are often the end products of vagueness or imprecision. They can arise from imprecision due to noise in monitored data, sensor device failure, or from the ambiguity about the logic rules in the fault tree.. So, when the researcher has only imprecise information, he must appeal to fuzzy-set theory techniques, either the common laws or logic his appreciation for the logic relations in fault trees. Fuzzy data can be incorporated through Dempster Shafer Theory (DST) [2] [3] [4] [5] in conventional fault-tree analysis yield meaningful results.

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


Dictionary Learning with Incoherence and Sparsity Constraints for Sparse Representation of Nonnegative Signals †a) , Nonmember and Shuxue DING † †b) , Member SUMMARY This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.key words: dictionary learning, sparse representation, nonnegative matrix factorization (NMF), hierarchical alternating least squares (HALS), overcomplete dictionary, quadratic functionSparse representation of signals has recently received much attention as it has produced some promising results in various applications. However, to date, there are only few reports on sparse representation for nonnegative signals. Such problems are frequently encountered in signal and image processing [1] , in handling of multispectral data [2], in considering nonnegative factorization for recognition [3] , [4] , and other important problems [5] . In this paper, we mainly focus on sparse representation for nonnegative signals.In the model of sparse representation of signals, a basic assumption is that, using an overcomplete dictionary matrix W ∈ R m×r that contains r atoms, or words, of size m × 1 for columns,, each column vector of a signal matrix Y ∈ R m×n can be represented as a linear combination of very few atoms w i of dictionary W. Here, the term "overcomplete" means m < r. Y = WH, or Y ≈ WH satisfying Sparse representation of signals has recently received much attention as it has produced some promising results in various applications. However, to date, there are only few reports on sparse representation for nonnegative signals. Such problems are frequently encountered in signal and image processing [1] , in handling of multispectral data [2] , in considering nonnegative factorization for recognition [3] , [4] , and other important problems [5] . In this paper, we mainly focus on sparse representation for nonnegative signals.. In the model of sparse representation of signals, a basic assumption is that, using an overcomplete dictionary matrix W ∈ R m×r that contains r atoms, or words, of size m × 1 for columns, {w i } Y − WH 2 ≤ ε are two ways to represent Y. The corresponding matrix H ∈ R r×n that contains the representation coefficients of signals Y is called the coefficient matrix. For dictionary W, it can be either generated by a pre-specified set of functions or learned by a given set of training signals. In practice [6] , a learned dictionary has proved critical for achieving superior results in the domains of signal and image processing. In some sense, one can discover and properly understand the crucial causes underlying the sensed signals by the learned dictionary. Therefore, how to learn a dictionary is important for sparse representation.. Naturally, the problem of finding a dictionary and its sparse representation with the fewest number of atoms can be modeled by using the minimization of 0 -norm upon the column vectors of H. Considering the fact that the 0 -norm optimization problem is generally NP-hard, one frequently used heuristic is the 1 -minimization [7] , which returns the vector with the least 1 -norm. A series of studies has led to many dictionary learning algorithms such as LARS [8] , K-SVD [9] , ILS-DLA [10] , and RLS-DLA [11] . Although these algorithms are very efficient in general, they are not always suitable for learning a nonnegative dictionary from nonnegative signals. For example, a nonnegative variant of K-SVD, which is termed "NN-KSVD" [12] , is not as efficient as K-SVD because the negative elements generated in a dictionary matrix are intentionally set to zero to guarantee nonnegativity as the dictionary updates.. In recent years, nonnegative matrix factorization (NMF) [1] , [2] , [13] has been widely applied to data analysis having nonnegativity constraints. NMF aims to factorize a nonnegative matrix into a product of two nonnegative factor matrices with different properties. Intuitively, NMF is similar to sparse representation of nonnegative signals to some extent. However, the standard NMF algorithm [14] does not impose any constraints on the two factors except for the nonnegativity, and so it is not sufficient to lead to a sparse enough representation. In order to obtain a sparser representation, various sparsity constrained NMF methods have been proposed. Hoyer et al. [15] , [16] considered enforcing the sparsity of coefficient matrix using 1 -norm. Hoyer [17] also introduced a measure of sparsity based on the ratio of the 1 -norm of a vector to the 2 -norm. Some authors imposed sparsity constraints using 2 -norm [18] , [19] . Peharz et al. [20] , [21] presented sparse NMF methods that constrain the 0 -(pseudo)-norm of the coefficient matrix. In this paper, we present a new NMF-based method for learning nonnegative, overcomplete dictionaries for sparse Copyright c 2013 The Institute of Electronics, Information and Communication Engineers representation of nonnegative signals. In this method, we force the representation coefficients to be as sparse as possible and simultaneously force the atoms of the dictionary to be as incoherent as possible for obtaining sparser representations. For optimizing our objective function, we propose optimizing each of two factors alternately and separating each optimization into column-wise or row-wise suboptimization problems, which is meant by the terms "alternating" and "hierarchical". In each column-wise or rowwise updating, one can optimize a series of optimal problems sequentially, each of which is an optimization of a quadratic function that can be solved explicitly, so that the whole problem can be efficiently solved. The way of optimizing each subproblem is obviously different from the standard hierarchical alternating least squares (HALS) [1] , which is an efficient method for solving the NMF problem. This optimization method may be regarded as a variation of HALS. Therefore, our proposed algorithm is termed as the sparse HALS (SHALS). Through experimental validations, we observed that our algorithm achieves the best rate of atom recovery compared to the conventional algorithms [12] , [15] , [17] , [21] . In addition, its performance is robust, even if noise is quite heavy. Furthermore, the computation cost of our algorithm is much lower than that of other algorithms, because it does not involve the complicated calculations inherent to factorization.. The remaining part of the paper is organized as follows. In Sect. 2, we formulate the nonnegative dictionary learning problem and review several existing algorithms in the literature. In Sect. 3, we describe our proposed SHALS algorithm in detail. In Sect. 4, we report the results of numerical experiments using SHALS and compare these results with those of several other existing algorithms. Finally, in Sect. 5, we draw our conclusions and discuss related research topics for the future. In this paper, we presented an NMF-based method for learning overcomplete, nonnegative dictionaries and for obtaining the corresponding coefficients for sparse representation of nonnegative signals. In this method, we forced the coefficients to be as sparse as possible and simultaneously forced the atoms of the dictionary to be as incoherent as possible for obtaining sparser representations. The method was implemented by the proposed sparse hierarchical alternating least squares (i.e., SHALS) algorithm that updates the dictionary in a column-wise and the coefficient matrix in a rowwise manner, which is meant by the terms "alternating" and "hierarchical". In each column-wise or row-wise updating, SHALS optimized a series of optimal problems sequentially, each of which was an optimization of a quadratic function that could be solved explicitly, and thus the whole problem could be efficiently solved.. In addition, we demonstrated that the SHALS algorithm could efficiently solve nonnegative dictionary learning problem. Results of experiments on dictionary recovery showed that SHALS could learn a nonnegative, overcomplete dictionary correctly, regardless of whether the objective signals are synthetic data or natural images. Additionally, further experiments supported the potential application of SHALS in the field of image processing such as image denoising, image classification, and large-scale data processing due to its low computational cost. We are currently working on improving the adjustment to the regularization parameters and on applying this method to some practical problems in image processing; e.g., large-scale image classification. The results from these ongoing studies will be presented in the future.

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


Simplifying Character Skins with Analytic Error Metrics Traditionally, levels of detail (LOD) Quantitative (geometric error metrics) and qualititative (user perceptual) experiments confirm that these new extensions provide significant improvements in quality over traditional, naïve simplification; and while there is naturally some impact on the speed of the off-line simplification process, it is not prohibitive. Character animation brings a static model to life by defining how its geometry changes over time. In real-time applications (such as games), the standard approach is to model a stickfigure skeleton, or rig, then weight the influence of each bone on each vertex of the model, or skin. The animator may then control the bones of the rig, and the skin will deform accordingly.. Level of detail (LOD) refers to a class of techniques for managing the complexity of highly detailed models. Multiple representations of the base model are created, with varying amounts of detail, each of which should approximate the original as well as possible. The most appropriate representation is then selected for the task at hand. Standard applications include rendering (with distant models at lower detail), compression, and progressive transmission [Hop96] .. In this paper, we address the problem of combining the fields of character animation and level-of-detail. Traditionally, LOD representations of an animated character have been produced by applying a static LOD algorithm to a single pose of the character, namely the rest pose in which the model was created. Since this is only designed to be a good approximation in that pose, the quality in other poses may suffer. Figure 1 (a) shows an example of this: the rest pose has the horse standing straight, so the naïve approach eliminates the geometry necessary to represent the ankles and makes a poor approximation to the tail in the pose shown. Our approach is based on a particular method of character skinning, AS, which represents vertices as points in a high-dimensional space. We measure the error of approximations directly in this space, rather than in any particular pose. Standard LOD techniques work by reducing the geometric detail of models-eliminating vertices, edges and faces. However, the cost of either storing or rendering a model depends on the number of influences of bones on vertices: in our implementation, a vertex with four influences takes roughly three times as long to transform as a vertex with only one influence. A further contribution is influence simplification, an LOD technique that removes influences from vertices, and adjusts the remaining influences to minimize the resultant error. We also demonstrate that influence simplification may be combined with a progressive mesh in a unified framework. We start with general background on character animation and LOD in Section 2. Section 3 covers previous approaches to merging the two fields. Sections 4 and 5 describe our two contributions, namely progressive meshes in AS and influence simplification. We finish with results in Section 6 and conclusions in Section 7. We have demonstrated two improvements to the quality of LOD for articulated characters. The first is to perform computations in animation space. Unlike previous approaches to the problem, no sampling of the pose space is required. Sampling may be used to estimate the matrix P, but this is done once rather than per-vertex, and so it is practical to use very large sample sizes. While animation-space computations allow this method to be applied to animation-space models, it may also be applied to SSD models, and the output is again a sequence of SSD models due to the half-edge collapse. Thus, while our method is limited to articulated models, it is not necessary to use animation space in either modelling or rendering. As with previous work that samples the pose space [MG03b, DR05] , the algorithm is applied entirely off-line, and there is no special work to be done during rendering. We have not done a direct comparison to this prior work, but we expect visual quality to be at least as good due to the analytic error computations and the use of appearancepreserving simplification.. The second contribution is influence simplification, which eliminates influences rather than geometry. This improves quality and allows for more extreme simplification than is otherwise possible. It is also useful for eliminating redundant influences in a base model (independently of any runtime LOD), for example to meet a hardware limitation on the number of influences per vertex. The disadvantages are the additional computational cost (but only during preprocessing), and the fact that output models may not be representable within SSD. This makes it undesirable for compression or progressive transmission of SSD models, but it is useful for rendering due to the improved quality [MMG06] . While both character animation and LOD are mature fields, there is relatively little research on combining them, and most techniques consider generic animation without taking advantage of the structure of skeletally animated characters.

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