The prospects of a quantitative measurement of agility: A validation study on an agile maturity model Agile Development has now become a well-known approach to collaboration in professional work life. Both researchers and practitioners want validated tools to measure agility. This study sets out to validate an agile maturity measurement model with statistical tests and empirical data. First, a pretest was conducted as a case study including a survey and focus group. Second, the main study was conducted with 45 employees from two SAP customers in the US. We used internal consistency (by a Cronbach's alpha) as the main measure for reliability and analyzed construct validity by exploratory principal factor analysis (or PFA). The results suggest a new categorization of a subset of items existing in the tool and provides empirical support for these new groups of factors. Since there are few validated tools to measure agile maturity, researchers cannot correlate quantitative agile maturity measurements to other variables in Software Engineering research and be confident that the results are correct. Practitioners cannot either use these tools to guide their journey towards agility. Based on the results we suggest a new partly validated set of items from the tested tool. However, we argue that maturity models do not measure agility in a way that is desired. The study of agile development and management practices is a relatively new field of research. The term itself, "agile development", was first coined in the area of software development but similar concepts preceded it in the literature on manufacturing. Today it has become a general project management concept/tool, and the word "agile" is frequently used in the general business and project management literature, e.g. Miles (2013) ; Poolton et al. (2006) ; Vinodh et al. (2010) .. Agile methods in software engineering evolved during the 1990s and in 2001 it became a recognized concept due to "The manifesto for agile software development" written by a group of software developers (Fowler & Highsmith, 2001 ). According to Cobb (2011) the background to the agile ideas was that projects in crisis sometimes took on more flexible ways of thinking and working and then were more successful. This style was named "agile", which literally means to be able to move quickly and easily (Fowler & Highsmith, 2001) , and emerged in reaction to more traditional project management methods were detailed planning typically precedes any implementation work.. During the 1990s the traditional way of doing procurement, elicitation of requirements, contract negotiations and then production and, finally, delivery (e.g. what is often termed the waterfall model in software development literature), sometimes helped create computer and software systems that were obsolete before they were delivered. To try to solve these challenges the agile community thus defined a set of principles that they summarized in The Agile Manifesto (Fowler & Highsmith, 2001 ):. • Individuals and interactions over processes and tools.. • Working software over comprehensive documentation.. • Customer collaboration over contract negotiation.. • Responding to change over following a plan. Laanti et al. (2011) claim that scientific and quantitative studies on agile methods were still rare in 2011, while requesting such studies since they can give more general advice about the practices involved. Overall, if an organization wants to transition to more agile ways of working, regardless of whether they are a software organization or not, the decision-makers will benefit from measuring agility both before, during, and after such a transition. The question is if this is possible since agility is a cultural change (described in the agile manifesto above) as well as a smorgasbord of practices to support them (Williams, 2012; Ranganath, 2011; Zieris & Salinger, 2013) .. There is a diversity of agile measurement tools out there, both scientific and commercial but almost none of them has been statistically validated. In order to measure measure agility and trust in the given results/output, both researchers and practitioners need validated tools to guide their process. The problem is what to focus on and on what level, since the agile approach is on a diversity of levels in the organization. This empirical study will evaluate one of the agility maturity models found in research through a statistical validation process. This tool focuses a bit more on behavior and not only lists a set of practices for the research subjects to tick yes or no regarding if they are implemented or not. We also connect a Likert scale to the evaluation in order to capture more variance in connection to each item. Section 2 will outline existing agile measurement tools found in the literature, Section 3 will present how our main statistical investigation was conducted, but also describe a pretest conducted before the main study including its findings under Subsection 2.2, Section 4 will present main study findings, Section 5 will analyze and discuss these overall results, and, finally, Section 6 will present conclusions and suggest future work.. This study aims to contribute with the following: 1. A test to evaluate if the Agile Adoption Framework can be used to measure current agility (instead of agile potential).. 2. If practitioners think such an evaluation is relevant through a case study pretest. 3. Expand the Agile Adoption Framework to include a Likert scale evaluation survey filled out by all the team members and not just by the assessor/researcher and connect a confidence interval to the item results. 4. Partly validate the Agile Adoption Framework with statistical tests. 5. Suggest changes Agile Adoption Framework and/or highlight the issues connected to agility measurement. In conclusion, this study has shown that quantitative data do not support the categorization of a subset of items in the Agile Adoption Framework. This is not surprising since no quantitative validation has been done on the tool, but troublesome for both research and practice since no thoroughly validated tool is a their disposal. Since this is the case researchers cannot correlate quantitative agile maturity measurements to other variables in Software Engineering research and be confident that the results are correct. Practitioners cannot either use these tools to guide their journey towards agility. In order to create a validated survey, the items must be iterated with real data until supported and reliable. By first doing a pretest with a small sample (N = 15) we qualitatively validated the items. After a few alterations we ran a factor analysis and a reliability test on the tool (N = 45). Data did not support the division of a subset of items selected from the Agile Adoption Framework. However, the data gave new categorizations of the items in the Agile Adoption Framework. As far as we know, this gives one of the first partially validated agile maturity model.. To summarize this study has contributed with:. 1. A positive result/feedback from practitioners on the usage if the Agile Adoption Framework as measure of current agility (instead of agile potential), in a pretest case study. 2. Evolvement of the method of the Agile Adoption Framework to include a Likert scale evaluation survey filled out by all the team members and not just by the assessor/researcher and connect confidence intervals to the item results. This way of assessing agility is less time consuming for the assessor. 3. Validation tests for internal consistency and construct validity on the Agile Adoption Framework on additional data suggest the data collected did not support the way the indicators are related to the agile practices (on Level 1) in the framework under investigation. 4. This study finds support for a new division of items to measure agility but concludes that much validation is needed to even state that the items measure the agile practices. Furthermore, we question agile maturity models as a good way to assess agility and propose that tools look more into other dimensions like culture and innovation propensity. 5. This study also highlights the tradeoff between quick quantitative measurements to guide agile adoption that is much wanted by practitioners and time-consuming contextual and more qualitative assessments in organizations that might be closer to the real situation.. We believe the next step for this kind of research would be to combine the items from many agile maturity models and see where they overlap. These items should then be subjected to the same analysis conducted in this study with a larger data set. Obviously, the larger the sample the better when validating a tool and it would be good to validate all maturity models (including the Agile Adoption Framework) with an even larger sample. However, we believe new separate agile maturity models have ceased to contribute to the development of measuring agility, and we want to stress the importance of creating one validated combination instead. We also see the importance of adding other dimensions than agile practices to these measurements, such as validated measurements of organizational culture and innovation propensity. In this study we first tested how practitioners rate the use of the Agile Adoption Framework through a focus group. The result of this was positive. However, the statistical tests did not support the categorization of factors in the framework and can therefore not be considered to measure distinct constructs (i.e. being a valid measurement for agility, in this case).. The pretest showed that the teams found the categories of the Agile Adoption Framework relevant and measured how the teams worked in their new process. However, the statistical analyses suggest this measurement needs more work in order to be a valid measurement of agile practices implemented in a team. This can be due to a diversity of reasons; first, a cultural change in an organization is by definition hard to assess and very contextual. Perhaps this set of items do not reflect what agility is, however, we believe a set of items that considers a cultural as well as a behavioral dimension could be constructed in the future.. Even if the Agile Adoption Framework does not measure the agility construct as expected and therefore the hypothesis was rejected, the items were still developed and checked for content validity by Sidky (2007) , i.e. it is coherent with what some practitioners define as "agility". However, as mentioned in the introduction, a statistical analysis must support the items to be considered a valid measurement. None of the Figure 2 : Overview of which items we found support for.. categories defined in the Agile Adoption Framework were statistically verified. Even though this was the case, the set of items that Sidky generated are covering much of the behavior connected to agile development processes. Practitioners seem to be keen on measuring agility since they want to show proof of their success for a set of reasons, however, this does not mean the measurements really reflect agility as shown by this study.. Another possible explanation could be that our sample is too small (or skewed) to say that Sidky's categories are not supported. However, when constructing a survey tool (or "scale" in psychology) one must verify the categorizations made qualitatively through a quantitative validation. Hence, any of the mentioned agile maturity models need more development before they can be considered reliable. Furthermore, to trust the result in this study another independent PFA should be done and compared to this one. If two or more independent PFAs give the same result, we would be certain our results hold. Therefore, this result is only a first step in creating a validated tool.. Over the last decade, a diversity of agile maturity models have surfaced, as described in the introduction (Leppänen, 2013) . It is a pity that researchers keep inventing new ones instead of validating (or even merging) existing tools to actually find a couple that works. Even the same year as the work of Leppänen (2013) was presented, more models have been suggested (by e.g. Soundararajan (2013) ). New ideas and models are good but in this context what is really needed is to validate the existing ones so practitioners can be comfortable using them.. However, there is another fundamental issue with agile maturity models. Even if we can develop a statistically valid set of items to measure agile practices, a team's score on such a scale might not reflect what is actually meant by an agile team. The term "agile process" is undefined and many researchers and practitioners have their own definition and perception of what it exactly means. It is clear, though, that agile processes are not such a set of hands-on practices. Since agile principles are more about culture than a set of implemented methods, maybe a maturity level approach is not the way to go. Or we need another focus in the measurements that include cultural assessments instead of degree of used practices.. The fact that the different agile maturity models have the same agile practice in a range of different levels (Leppänen, 2013) , also indicates that the maturity levels of agility are not evident. Maybe this is a syndrome of not letting go of the control mechanisms that agile principles suggest should be more in the periphery. Since agile methods are more about people and culture we suggest social psychological measurements are more appropriate if organizations want to measure their level of agility. The only study we found on social psychology and agile development processes is the article Perceptive Agile Measurement: New Instruments for Quantitative Studies in the Pursuit of the Social-Psychological Effect of Agile Practices by So & Scholl (2009) . Their work deserves more attention since they created a tool and validated it on a sample of N = 227. Since we want to measure agility in organizations, this tool will make such a measurement feasible since it excludes specific practices and focuses on behavior connected to the underlying agile principles.. The Agile Adoption Framework is intended to assess agility before these ideas have been introduced into the organization, however, we believe an organization that has no clue what the wording "Agile Processes" means could still be agile in their ways of working. We also believe the opposite is true; an organization can have implemented agile practices without really being agile. Therefore, the measurement of agility should not be dependent on what the organization calls a "manager", "team lead" or "agile coach" etc., but focus on what these people are doing. This is a threat to this study since questions regarding the manager were reported to be hard to interpret. However, this is also part of our critique we just mentioned regarding building a tool that is not dependent on such jargon. The other aspects of the tool did not form factors anyways, but we have suggested new categories for the Agile Adoption Framework. These were: "Dedication to Teamwork and Results", "Open Communication", "Agile Planning", "Leadership Style", and "Honest Feedback to Management". This makes the Agile Adoption Framework (Sidky, 2007 ) one of few agile maturity level now partially statistically validated (on level 1 in one of the step described by Sidky). However, the questions still includes some ambiguity regarding manager and agile leader. Furthermore, the Agile Adoption Framework uses the same items to assess both results for developers and managers, which makes statistical analysis cumbersome. However, as mentioned, in our validation we also only used the survey for developers.. Sidky's tool was not intended to measure agility of a team but agile potential. This separation of perspectives is the reason why his survey for managers does not include Agile Management concepts like the definition of "Done". We argue, though, that a team can be agile without having implemented agile practices and therefore this type of Boolean response to if a team is agile or not before the measurement is conducted, does not cover what agility is, according to us.. We should also mention that the largest contribution by Sidky (2007) , as we see it, is not his agile team level potential assessment, but the overall items regarding a go/no go decision process at an early stage to see if agile methods is a good idea for a specific organization. This part is not presented in this study but is a great contribution to the field.. We believe the work of So & Scholl (2009) could be combined with the Agile Adoption Framework to reflect more aspects of agility in such an assessment. Then the dimensions presented in the Perceptive Agile Measurement:. • Iteration Planning • Dedication to Teamwork and Results In this section we will present the result of statistical tests for for internal consistency and construct validity. The former will be tested by a Cronbach's α and the latter by exploratory principal factor analysis (or PFA).. However, before these statistical tests we would like to highlight a problem with using the Agile Adoption Framework to measure agility. The terms "Manager" and "Scrum Master/Agile Coach" could be a source of confusion. Two respondents gave the open-ended feedback of "We have a PM and an Agile coach. I consider their agile skills to be far apart which lead to some ambiguity when answering questions around 'manager'." and "Some of the questions on my manager are irrelevant or could be misinterpreted. My manager isn't part of the IT organization." This ambiguity probably affected the responses since some of the individuals evidently have both a Manager and a Scrum Master. Some researchers suggest qualitative approaches like interviewing as a method for assessing agility in teams (Boehm & Turner, 2003; Sidky et al., 2007; Pikkarainen & Huomo, 2005) . Hoda et al. (2012) even suggest the use of grounded theory which is an even more iterative and domain specific analysis method (Glaser & Strauss, 2006) . Interviewing is a good way to deal with interviewee misinterpretations and other related biases. The work proposed by Lee & Xia (2010) compares a few agility dimensions with performance and draw conclusions about the complexity of if agile methods increase performance or not, which they do. Datta (2009) describes an Agility Measurement Index as an indicator for determining which method of Waterfall, Unified Software Development Process (UP), or eXtreme Programming (XP) should be used. Where Waterfall is plan-driven and XP is an agile method, UP is considered to have elements of both and is a more general framework that can be adapted to specific needs but that is often used as a kind of middle ground between the other two. The author suggests that the five dimensions: Duration, Risk, Novelty, Effort, and Interaction should be taken into account when selecting development method. Their method is, however, a company-specific assessment, which makes comparisons between different organizations cumbersome.. A process control method often used within IT is the CMMI (Capability Maturity Model Integration). This method also divides the organization into different maturity levels and is essentially a set of requirements for engineering processes, particularly those involved in product development. Just like stage-gate project management these older methods often co-exist with agile methods when implemented (Turner & Jain, 2002) , i.e. CMMI is constructed to measure a more traditional project management approach.. To be able to compare and guide organization in their agile implementations a diversity of agile maturity models have been suggested, as mentioned in the introduction. Leppänen (2013) presents a nice overview of these agile maturity tools selected with the following criteria: "Domain" (the domains the models are targeted to), "Purpose" (the purposes the models have been developed for), "Conceptual and Theoretical Bases" (the conceptual and theoretical backgrounds upon which the models have been built), "Approaches and Principles" (the approaches and principles used to construct the models), "Structure" (the architectures of the models), and "Use and Validation" (extent of deployment and validation). Based on these criteria eight tools were selected: The Agile Maturity Model (Ambler, 2010) , A Road Map for Implementing eXtreme Programming (Lui & Chan, 2006) , Toward Maturity Model for Extreme Programming (Nawrocki et al., 2001) , The Agile Maturity Map (Packlick, 2007) , Agile Maturity Model (Patel & Ramachandran, 2009) , Agile Maturity Model (Pettit, 2006) , A Framework to Support the Evaluation, Adoption and Improvement of Agile Methods in Practice (Qumer & Henderson-Sellers, 2008) , and The Agile Adoption Framework . According to Leppänen (2013) some of them are merely based on conceptual studies, others are developed only in one organization, a third group has gathered more experience from organizations, and some are discussed with practitioners. However, as also Leppänen (2013) concludes, none of them are validated. He also states that higher maturity levels could partially be assessed by more lightweight methods.. In this study we selected to focus on the Sidky's Agile Adoption Framework, and in order to keep the number of items as low as possible, we selected only level one of this tool. We should also mention that there is a set of commercial tools available, however, their scientific foundation is hard to assess.. We would like to highlight the difficulty of measuring something that is an ambiguous construct, such as agility. Maturity is of course even harder to assess in connection to agility since maturing with a unspecific concept is even harder. However, there are some behaviors connect to "being agile" in software development and behavior connected to this way of working, which is our definition of agile maturity in this case. We do not aim to find a way to quantitatively measure agility in this study (and we neglect the agile practices effectiveness as well), but instead to test one of the existing tools and try to understand how to proceed in measuring/dealing agility transformations in organizations.

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In

this

review,

we

present

an

automated

method

to

segment

blood

vessels

of

fundus

retinal

image.

The

proposed

method

could

be

used

to

support

a

non-intrusive

diagnosis

in

modern

ophthalmology

for

early

detection

of

retinal

diseases,

treatment

evaluation

or

clinical

study.

This

study

combines

the

bias

correction

and

an

adaptive

histogram

equalisation

to

enhance

the

appearance

of

the

blood

vessels.

Then

the

blood

vessels

are

extracted

using

probabilistic

modelling

that

is

optimised

by

the

expectation

maximisation

algorithm.

The

method

is

evaluated

on

fundus

retinal

images

of

STARE

and

DRIVE

datasets.

The

experimental

results

are

compared

with

some

recently

published

methods

of

retinal

blood

vessels

segmentation.

The

experimental

results

show

that

our

method

achieved

the

best

overall

performance

and

it

is

comparable

to

the

performance

of

human

experts.

Automated

segmentation

of

retinal

structures

allows

ophthalmologist

and

eye

care

specialists

to

perform

large

population

vision

screening

exams

for

early

detection

of

retinal

diseases

and

treatment

evaluation.

This

non-intrusive

diagnosis

in

modern

ophthalmology

could

prevent

and

reduce

blindness

and

many

cardiovascular

diseases

around

the

world.

An

accurate

segmentation

of

retinal

blood

vessels

(vessel

diameter,

colour

and

tortuosity)

plays

an

important

role

in

detecting

and

treating

symptoms

of

both

the

retinal

abnormalities

and

diseases

that

affect

the

blood

circulation

and

the

brain

such

as

haemorrhages,

vein

occlusion,

neo-vascularisation.

However,

the

intensity

inhomogeneity

and

the

poor

contrast

of

the

retinal

images

cause

a

significant

degradation

to

the

performance

of

automated

blood

vessels

segmentation

techniques.

The

intensity

inhomogeneity

of

the

fundus

retinal

image

is

generally

attributed

to

the

acquisition

of

the

image

under

different

conditions

of

illumination..

Previous

methods

of

blood

vessels

segmentation

can

be

classified

into

two

categories:

pixels

processing

based

tracking-based

or

vectorial

tracking

or

tracing

methods

Pixel

processing

based

methods

use

filtering

and

morphological

pre-processing

techniques

to

enhance

the

appearance

of

the

blood

vessels

in

the

image.

The

enhanced

image

is

then

processed

using

techniques

such

as

thinning

or

branching

to

classify

pixel

as

either

belonging

to

vessels

or

background.

Hoover

et

al.

proposed

a

framework

to

extract

blood

vessel

from

retinal

images

using

a

set

of

twelve

directional

kernels

to

enhance

the

vessels

before

applying

threshold-probing

technique

for

segmentation.

Mendoca

et

al.

presented

a

method

to

extract

a

vessel

centreline

then

filled

it

using

the

global

intensity

characteristics

of

the

image

and

the

local

vessel

width

information.

Maritiner-perez

et

al.

proposed

a

new

segmentation

method

of

blood

vessels

from

red-free

and

fluorescein

retinal

images.

This

method

is

based

on

multiscale

feature

extraction,

which

used

the

first

and

second

spatial

derivatives

of

the

image

intensity

that

provides

information

about

vessel

topology.

A

multiple

pass

region

growing

procedure

is

applied

to

segment

the

vessels

using

both

vessels

feature

information

and

spatial

information.

Zhang

et

al.

extracted

the

blood

vessel

tree

by

matched

filter

with

first-order

derivative

of

Gaussian.

The

method

detects

the

blood

vessels

by

thresholding

the

retinal

image's

response

to

the

matched

filter,

while

the

threshold

is

adjusted

by

the

response

of

the

image

to

the

first-order

derivative

of

Gaussian.

Cinsdikici

et

al.

proposed

a

method

of

retinal

blood

vessel

detection

using

a

combination

of

a

hybrid

model

of

matched

filter

and

ant

colony

algorithm..

The

drawback

of

these

techniques

is

that

some

proprieties

of

blood

vessels

can

only

be

applied

in

the

segmentation

process

after

a

low

level

preprocessing

and

they

generally

output

poor

segmentation

results

on

unhealthy

retinal

images

that

have

the

presence

of

lesions.

They

also

need

more

computational

power

when

the

size

of

an

image

increases,

thus

a

special

hardware

is

required

for

real

time

processing..

The

tracking

based

approaches

or

vectorial

tracking

or

tracing

included

semi

automated

tracing

and

automated

tracing.

In

the

semi

automated

tracing

methods,

the

user

manually

selects

the

initial

vessel

seed

point.

The

methods

are

generally

used

in

quantitative

coronary

angiography

analysis.

In

fully

automated

tracing,

the

algorithms

select

automatically

the

initial

vessel

points

and

most

of

them

use

Gaussian

functions

to

characterise

a

vessel

profile

model,

which

locates

a

vessel

points

for

the

vessel

tracing.

The

tracking

based

methods

are

seen

as

single

pass

operations,

which

perform

the

vessels'

structure

detection

and

recognition

simultaneously.

The

advances

of

using

these

techniques

are

that,

they

are

computational

efficient

and

much

faster

than

pixels

processing

methods

because

the

algorithms

avoid

the

processing

of

every

pixels

in

the

image

and

use

only

the

pixels

in

the

neighbourhood

of

the

vessels

structure..

Xu

et

al.

combined

the

adaptive

local

thresholding

method

and

the

tracking

growth

technique

to

segment

retinal

blood

vessels.

Staal

et

al.

proposed

a

retinal

blood

vessel

segmentation

in

two

dimensional

colour

retinal

images.

The

method

extracts

the

images

ridges,

which

are

used

to

compose

primitives

in

the

form

of

line

elements.

The

line

elements

are

used

to

partition

an

image

into

patches,

then

a

feature

vectors

are

computed

for

every

pixel

and

classified

a

kappa

NN-classifier

and

sequential

forward

feature

selection.

Chaudhuri

et

al.

presented

a

framework

to

segment

the

blood

vessels

in

the

retina.

The

method

is

based

on

the

optical

and

spatial

properties

of

the

vessels,

where

the

gray-level

profile

of

the

cross

section

of

a

blood

vessel

is

approximated

by

a

Gaussianshaped

curve

and

a

matched

filter

is

used

to

define

the

piecewise

linear

segments

of

blood

vessels.

Finally

twelve

different

templates

are

designed

to

search

for

vessel

segments

along

all

possible

directions.

Salazar

et

al.

used

an

adaptive

histogram

equalisation

and

the

distance

transform

algorithm

to

enhance

the

vessels

appearance,

then

applied

the

graph

cut

technique

to

segment

vessels.

In

Yin

et

al.

proposed

an

automated

tracking

approach

to

segment

blood

vessels

in

retinal

images.

The

technique

detects

vessel

edge

points

iteratively

using

a

Bayesian

model

based

on

statistical

sampling

approach

and

the

intensity

profile

of

the

vessel

are

approximated

by

a

Gaussian

model.

New

vessel

edge

points

are

defined

based

on

local

grey

level

statistics

and

expected

vessel

features..

The

limitations

of

the

tracking

based

approaches

are

that

the

multiple

branches

models

are

not

always

applicable

and

they

do

not

perform

well

on

disease

retinal.

The

semi

automated

tracking

methods

also

require

manual

input,

which

required

more

times.

Thus

they

are

not

suitable

for

real

time

retinal

image

analysis.

In

this

paper,

we

present

a

new

automated

method

to

extract

blood

vessels

in

retinal

fundus

images.

The

proposed

method

is

divided

into

two

main

stages:

the

preprocessing

and

the

probabilistic

modelling.

Our

approach

takes

as

first

step

the

correction

of

the

intensity

inhomogeneity

of

the

retinal

image

using

a

bias

correction

algorithm

then

the

appearance

of

blood

vessels

are

enhanced

with

an

adaptive

histogram

equalisation.

A

probabilistic

model

optimised

by

an

expectation

maximisation

(EM)

algorithm

is

used

to

extract

the

vascular

tree

from

the

processed

images.

Finally,

a

length

filter

is

applied

on

the

output

of

the

EM

algorithm

to

eliminate

all

the

non-vessels

pixels..

The

experimental

results

are

performed

on

two

publicly

available

datasets.

The

STARE

(STructured

Analysis

of

the

Retina)

images

were

provided

by

the

Shiley

Eye

Center

at

the

University

of

California,

San

Diego,

and

by

the

Veterans

Administration

Medical

Centre

in

San

Diego.

The

images

of

the

DRIVE

were

obtained

from

a

diabetic

retinopathy-screening

program

in

The

Netherlands

and

the

screening

population

consisted

of

diabetic

subjects

between

years

of

age.

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


Population-Based Continuous Optimization, Probabilistic Modelling and Mean Shift Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems. Evolutionary Algorithms (EAs) are a broad class of methods that apply mechanisms inspired by biological evolution to the solution of optimization problems. An optimization problem can be constructed through the representation of a problem solution as an (n-dimensional) parameter vector, x = (x 1 , . . . , x n ), together with an objective function f (x) : S → IR, where S is the set of feasible solutions. EAs are applicable where no further information is available regarding the optimization problem, for example derivatives of f . Although the ultimate goal is to find a globally optimal solution vector x * = argmaxf (x) in practice, the aim is often to find as good a solution as possible given constraints such as available computation time (Törn andŽilinskas, 1989) . The objective function may present difficulties such as local maxima, discontinuities or be subject to noise. In such situations, EAs and other heuristic and meta-heuristic methods have gained wide popularity and demonstrated impressive performance. By convention, an EA produces an iterative search process using a population X = {x 1 , . . . , x k } of sample points (candidate solutions). Beginning with a typically randomly generated population, each iteration (generation) of the EA involves the application of a set of genetic operators (e.g, selection, recombination and mutation) to evolve the population for the following generation. In this way an EA explores the search space, using information about the objective function obtained from individual candidate solutions to direct future search. To take a slightly different view, the population (being the only "information" that persists into the next generation) can be thought of as an implicit model of the potentially promising regions of the search space .. In recent years, a number of researchers have focused specifically on this notion of modelling the search space. That is, the model is made an explicit part of the search process, and the algorithm is viewed as performing optimization via the construction and utilization of an inductive model of the solution space. Although several different modelling techniques have been adopted from statistics and machine learning (Boyan et al., 2000) , most of the work within the EA community has employed a probabilistic model of the solution space. These methods have become known as Estimation of Distribution Algorithms (EDAs) , Optimization by Building and Using Probabilistic Models (OBUPM) (Pelikan et al., 2002) or Probabilistic Modelling Evolutionary Algorithms (Gallagher, 2000) . To avoid confusion, in this paper we will refer to these methods as EDAs. A general outline of an EDA is:. 1. Initialize the probability model, Q(x). This paper has developed a theoretical framework to interpret the dynamics of continuous evolutionary algorithms based on probabilistic modelling. Under this framework, the basic continuous-PBIL algorithm and the (1, λ)-ES approximate a stochastic gradient descent of the Kullback-Leibler divergence between the chosen probability model and an assumed target density. The framework also leads to an alternative algorithm assuming a simple Gaussian probability model, which uses all of the information obtained during search (i.e. the entire population and its associated objective function values) to update the probability model. We have shown that the framework complements an existing theoretical framework developed for discrete model-based EAs, and also with the generalised mean shift framework developed in the context of clustering algorithms. The experimental results presented illustrate the stability and fluctuations of the algorithm on a simple problem, and indicate that the proposed algorithm has a robustness to noise in the objective function, and has a more stochastic behaviour than PBIL.. There are several interesting possibilities for future work using the ideas presented in this paper. A comprehensive empirical study of the P KLD algorithm is needed to investigate its performance at solving more challenging problems (including multidimensional and real-world problems), as well as investigating the behaviour of the method across a range of values of its adjustable parameters. From a more theoretical perspective, we are interested in exploring the application of the framework to more flexible probability models. The relationship to mean shift clustering also deserves further investigation, particularly in the context of existing EDAs based on kernel and Gaussian mixture model density estimators (Bosman and Thierens, 1999; Bosman and Thierens, 2000; Gallagher et al., 1999; Gallagher, 2000) .

O B I 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 B I I 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 B I I 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 O O 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 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 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


More Efficient Algorithms and Analyses for Unequal Letter Cost Prefix-Free Coding There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally, there are many good heuristics that all provide additive errors to optimal. The additive error in these algorithms usually depends linearly upon the largest encoding letter size. This paper was motivated by the problem of finding optimal codes when the encoding alphabet is infinite. Because the largest letter cost is infinite, the previous analyses could give infinite error bounds. We provide a new algorithm that works with infinite encoding alphabets. When restricted to the finite alphabet case, our algorithm often provides better error bounds than the best previous ones known. L ET be an encoding alphabet; represents all finite words written using . Word is a prefix of word if where is a nonempty word. A code over is a collection of words . Code is prefix-free if for all is not a prefix of . See Fig. 1 .. Let be the length or number of characters in . Given a set of associated probabilities , the cost of the code is . The prefix coding problem, sometimes known as the Huffman encoding problem is to find a prefix-free code over of minimum cost. This problem is very well studied and has a wellknown -time greedy algorithm due to Huffman [1] ( -time if the are sorted in non-decreasing order). Alphabetic coding is the same problem with the additional constraint that the codewords must be chosen in increasing alphabetic order (with respect to the words to be encoded). This corresponds, for example, to the problem of constructing optimal (with respect to average search time) search trees for items Fig. 1 . In this example, 6 = fa; bg. The code on the left is faaa; aab; ab; bg which is prefix-free. The code on the right is faaa; aab; ab; aabag which is not prefix-free because aab is a prefix of aaba. The second row of the tables contain the costs of the codewords when cost(a) = 1 and cost(b) = 3.. with the given access probabilities or frequencies. Such a code can be constructed in time [2] . One well studied generalization of the problem is to let the encoding letters have different costs. That is, let have associated cost . The cost of codeword will be , i.e., the sum of the costs of its letters (rather than the length of the codeword) with the cost of the code still being defined as with this new cost function.. The existing, large, literature on the problem of finding a minimal-cost prefix-free code when the are no longer equal, which will be surveyed below, assumes that is a finite alphabet, i.e., that . The original motivation of this paper was to address the problem when is unbounded. As will briefly be described in Section II, this models certain types of language restrictions on prefix-free codes and the imposition of different cost metrics on search trees. The tools developed, though, turn out to provide improved approximation bounds for many of the finite cases as well.. More specifically, it was known [3] , [4] 1 that where is the entropy of the distribution, is the unique positive root of the characteristic equation and is the minimum cost of any prefix-free code for those . Note that in this paper, will always denote . For , the known efficient algorithms create a code that satisfies (1) where is the cost of code and is some function of the letter costs , with the actual value of depending upon the particular algorithm. Since , code has an additive error at most from . The corresponding to the different algorithms shared an almost linear dependence upon the value 1 Note that if t = 2 with c = c = 1 then c = 1 and this reduces to the standard entropy lower bound for prefix-free coding. Although the general lower bound is usually only explicitly derived for finite t, Krause [3] showed how to extend it to infinite t in cases where a positive root of 1 = 2 exists.. 0018-9448/$25.00 © 2008 IEEE Fig. 2 . Two min-cost prefix-free codes for probabilities 2=6; 2=6; 1=6; 1=6; and their tree representations. The code on the left is optimal for c = c = 1 while the code on the right, the prefix-free code from Fig. 1 , is optimal for c = 1; c = 3.. the largest letter cost. They therefore cannot be used for infinite . In this paper, we present a new algorithmic variation (most algorithms for this problem start with the same splitting procedure so they are all, in some sense, variations of each other) with a new analysis.. • (Theorems 2 and 3) For finite , we derive new additive error bounds which, in many cases, are much better than the old ones. • (Lemma 9) If is infinite but is bounded, then we can still give a bound of type (1) . For example, if , i.e., exactly two letters each of length , then we can show that . • (Theorem 4) If is infinite but is unbounded then we cannot provide a bound of type (1) but, as long as , we can show that (2) where is some constant based only on and . We now provide some more history and motivation. For a simple example, refer to Fig. 2 . Both codes written there have minimum cost for the frequencies but under different letter costs. The code has minimum cost for the standard Huffman problem in which and , i.e., the cost of a word is the number of bits it contains. The code has minimum cost for the alphabet in which the cost of an " " is and the cost of a " " is , i.e., . The unequal letter cost coding problem was originally motivated by coding problems in which different characters have different transmission times or storage costs [5] - [9] . One example is the telegraph channel [3] , [10] , [11] in which and , i.e., in which dashes are twice as long as dots. Another is the run-length-limited codes used in magnetic and optical storage [12] , [13] , in which the codewords are binary and constrained so that each must be preceded by at least , and at most 's. (This example can be modeled by the unequal-cost letter problem by using an encoding alphabet of characters with associated costs. .). The unequal letter cost alphabetic coding problem arises in designing testing procedures in which the time required by a test depends upon the outcome of the test [14, Sec. 6.2.2, Example 33] and has also been studied under the names dichotomous search [15] or the leaky shower problem [16] .. The literature contains many algorithms for the unequal-cost coding problem. Blachman [5] , Marcus [6] , and (much later) Gilbert [11] give heuristic constructions without analyses of the costs of the codes they produced. Karp gave the first algorithm yielding an exact solution (assuming the letter costs are integers); Karp's algorithm transforms the problem into an integer program and does not run in polynomial time [7] . Later, exact algorithms based on dynamic programming were given by Golin and Rote [13] for arbitrary and a slightly more efficient one by Bradford et al. [17] for . These algorithms run in time where is the cost of the largest letter. Despite the extensive literature, there is no known polynomial-time algorithm for the generalized problem, nor is the problem known to be NP-hard. Golin, Kenyon, and Young [18] provide a polynomial time approximation scheme (PTAS). Their algorithm is mainly theoretical and not useful in practice. Finally, in contrast to the nonalphabetic case, alphabetic coding has a polynomial-time algorithm time algorithm [2] . Karp's result was followed by many efficient algorithms [3] , [4] , [19] - [21] . As mentioned above, ; almost 2 all of these algorithms produce codes of cost at most and therefore give solutions within an additive error of optimal. An important observation is that the additive error in these papers somehow incorporate the cost of the largest letter . Typical in this regard is Mehlhorn's algorithm [4] which provides a bound of (3). Thus, none of the algorithms described can be used to address infinite alphabets with unbounded letter costs.. The algorithms all work by starting with the probabilities in some given order, grouping consecutive probabilities together according to some rule, assigning the same initial codeword prefix to all of the probabilities in the same group and then recursing. They therefore actually create alphabetic codes. Another unstated assumption in those papers (related to their definition of alphabetic coding) is that the order of the is given and must be maintained.. In this paper, we are only interested in the general coding problem and not the alphabetic one and will therefore have freedom to dictate the original order in which the are given and the ordering of the . We will actually always assume that and . These assumptions are the starting point that will permit us to derive better bounds. Furthermore, for simplicity, we will always assume that . If not, we can always force this by uniformly scaling all of the .. For further references on Huffman coding with unequal letter costs, see Abrahams' survey on source coding [22, Sec. 2.7] , which contains a section on the problem.

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


A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis Data envelopment analysis (DEA) is a linear programming methodology to evaluate the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. It has been widely used to measure performance in many areas. A weakness of the traditional DEA model is that it cannot deal with negative input or output values. There have been many studies exploring this issue, and various approaches have been proposed.In this paper, we develop a variant of the traditional radial model whereby original values are replaced with absolute values as the basement to quantify the proportion of improvements to reach the frontier. The new radial measure is units invariant and can deal with all cases of the presence of negative data. In addition, the VRM model preserves the property of proportionate improvement of a traditional radial model, and provides the exact same results in the cases that the traditional radial model can deal with. Examples show the advantages of the new approach. Data envelopment analysis (DEA), originally developed by Charnes et al. (1978) , is a linear programming methodology for evaluating the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs (Charnes et al., 1978) . It has been widely used to measure performance in many areas. A weakness of a traditional DEA model is that it requires the assumption that all the inputs and outputs have non-negative values, while in many situations negative values, especially those of outputs, such as profit, could exist.. Among the various approaches proposed for dealing with negative data, the simplest one is to exchange the role between inputs and outputs. If inputs are all negative or non-positive, they can be treated as positive outputs so that their absolute values can be increased, which means a decrease of negative inputs. And vice versa if outputs are all negative or non-positive, they can be treated as positive inputs so that their absolute values can be reduced, which means an increase of negative outputs (Scheel, 2001; Zhu, 2009) . However this method cannot be applied to variables with both positive and negative values. In addition, treating negative outputs as positive inputs may not reflect the true production process.. The commonly used approach to dealing with negative data is based on the property of "translation invariance". A DEA model is expected to be translation invariant if translating the original input and/or output data values results in a new model that has the same optimal solution as the old one (Ali and Seiford, 1990; Cooper et al., 2007) . For DEA models with translation invariance, negative values can be turned into positive values by imposing a big enough positive value to the variable with negative values so that all the values of the variable become positive (Charnes et al., 1983; Lovell and Pastor, 1995; Seiford and Zhu, 2002) . The additive model under variable returns to scale (VRS) is translation invariant, which means that the results will not change after a positive scalar is added to any input or output in the additive model ( Charnes et al., 1985; Ali and Seiford, 1990; Lovell and Pastor, 1995; Pastor, 1996) . Lovell et al. (1995) developed a normalized weighted additive model that is both translation invariant and units invariant. However, both the traditional additive model and the normalized additive model have some drawbacks. Firstly, they yield the 'furthest' targets on the production frontier for inefficient units; and secondly they cannot provide an efficiency score for an inefficient unit (Portela et al., 2004) .. Another translation-invariant model is the radial model under VRS technology (BCC model), but it only has restricted translation invariance. Input-translation invariance exists only in output-oriented models and output-translation invariance exists only in input-oriented models. The efficiency status (efficient or inefficient) of the evaluated DMU is translation invariant in both input and output-oriented BCC models, though, its efficiency score is not (classification invariance only) (Ali and Seiford, 1990; Lovell and Pastor, 1995; Pastor, 1996; Cooper et al., 2007) . Portela et al. (2004) put forth a directional distance model (range directional measure, RDM) using range values (absolute gap between the initial evaluated value and the best observed value of a variable) as the direction vector, which can deal with inputs or outputs with positive and/or negative values (Portela et al., 2004) . The advantage of the RDM over the generic directional distance model, which can natively deal with negative data, is that it is units invariant and it yields efficiency scores between 0 and 1 for inefficient units. The efficiency measurement process applied is similar to but not the same as that of radial model. The results obtained from the RDM model are generally different than those delivered by the conventional radial model in the cases that the latter model can deal with, such as non-negative value data or negative value free DMUs.. On the basis of the idea proposed by Portela et al. (2004) , Sharp et al. (2006) introduced a modified slack-based measure (MSBM) which can deal with data with positive and/or negative values (Sharp et al., 2007) . Similar to the RDM model, MSBM model is broadly unable to yield same results in the cases the traditional slack-based measure (SBM) model can deal with. Emrouznejad et al. (2010) propose a semi-oriented radial measure (SORM), which is applicable to datasets include variables which can take both negative and positive values (Emrouznejad et al., 2010a; Emrouznejad et al., 2010b) . The essence of SORM is that it breaks down each variable into two variables, one assigned the negative values and the other the positive values of the original variable. Similarly to RDM and MSBM, SORM is able to deal with negative data without changes of origin (data translation). The preservation of the origin means a form of radial pursuit of targets to a certain extent, although it is in terms of the positive or negative part of a variable but not in terms of the variable as a whole. SORM yields the same results as those determined by the traditional radial model in case no negative data exist for the evaluated DMUs. The disadvantage of the SORM is the artificial increase of the number of variables (inputs and/or outputs). As a result, the method may not necessarily determine Pareto efficient targets. In addition, SORM may lead to targets worse than the observed values.. In this paper, we propose a variant of radial measure (VRM) that yields a measure of efficiency and also is able to handle variables consisting of positive values for some and negative values for other sample DMUs. This paper unfolds as follows.. Section 2 introduces the VRM model. Section 3 provides a brief comparison between VRM and two more approaches focused on negative data handling in DEA. Moreover, in the next section, numerical examples are quoted to demonstrate the differences between the related methods, as well as advantages and defects of the VRM method are revealed. Conclusive remarks are presented in the last section. In the presence of negative input or output data, the traditional input or output-oriented radial models, respectively, lead to flawed results due to their weakness to identify the magnitude of the negative-signed data to the optimization process. In this context, the target values obtained towards efficiency attainment express worsened input or output levels compared with the original values introduced.. The (normalized) additive model, the range directional measures (RDM), the modified slack-based model (MSBM) and the semi-oriented radial model (SORM) could be applied in order to tackle the disorientation problem raised in case negative values exist within the dataset under assessment, though without lacking weaknesses.. Namely, the (normalized) additive model does not provide efficiency measure. The RDM model may be unbounded when the evaluated DMU performs the maximum values for every output variable or engages the minimum levels for all the inputs.. Following, the SORM model may get deteriorated targets and suffer from disorientation for the sample units that either all their input or all their output values are negative.. In this paper, we developed a variant of the traditional radial model, in which the original values are replaced by their absolute values to quantify the proportion of improvements in order to reach the best-practice frontier. The VRM model is units invariant and can deal omnipotently with every case of negative values presence in the dataset under assessment. In addition, the VRM model preserves the proportionate improvement property of the traditional radial model, and also yields the same results with the traditional model in the cases in which the latter one is applicable.

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


The Reconfigurable Ring of Processors: Fine-Grain Tree-Structured Computations We study ne-grain computation on the Recon gurable Ring of Processors (RRP), a parallel architecture whose processing elements (PEs) are interconnected via a multiline recon gurable bus, each of whose lines has one-packet width and can be con gured, independently of other lines, to establish an arbitrary PE-to-PE connection. We present a message-passing protocol, Comet, that will, in the presence of suitable implementation technology, endow an RRP with message latency that is logarithmic in the number of PEs a message passes over in transit. Our study focusses on the computational consequences of such latency in such an architecture. Denoting by (N; L)-RRP an N -PE ring whose bus has L lines, we establish the following computational properties of logarithmic-latency RRPs. Hence, when L is as large as N 1= log log N , the RRP performs a sweep within time 2 log N log log N + l.o.t.(b) The performance of RRPs on LTS algorithms can be improved by at most a constant factor, both when the buswidth L is \small," so that the rst term of bound (1) dominates, and when L is \large," so that the second term dominates. Our lower bound extends to a much broader range of architectures than RRPs: all of these architectures require time proportional to log N log log N to perform any N -argument 1-sweep LTS algorithm, such as broadcast. 2. We expose an architecture-independent limitation imposed by the logarithmic communication latency of RRPs: for a broad range of N -PE parallel architectures, including N -RRPs, any operation that requires one PE to receive and/or send information|directly or indirectly|from and/or to all other PEs, requires time proportional to log N log log N .2 We study ne-grain computation on the Recon gurable Ring of Processors (RRP), a parallel architecture whose processing elements (PEs) are interconnected via a multiline recon gurable bus: each line of the bus has one-packet width and can be con gured, independently of other lines, to establish an arbitrary PE-to-PE connection.. Our study is inspired by a novel strategy for (a) designing the bus of an RRP and for (b) passing one-word messages along the lines of the bus in a way that yields message latency that is logarithmic in the number of PEs the message traverses|at least for (MOS) wafer-scale implementations of RRPs. We are currently working on estimating the technological parameters that would enable our Cooperative Message Transmission (Comet) strategy to be realized. Our goal in the current paper, as in its companion paper 7] , is to understand the computational consequences of a ne-grain logarithmic delay model for RRPs: su ciently good news would provide powerful motivation for paying the technological cost that would enable the model to be realized. Henceforth, we focus only on RRPsthat have been implemented so as to achieve logarithmic message latency|perhaps, but not necessarily, via Comet. The interested reader should see 6] for another theoretical study of recon gurable architectures with logarithmic message latency.. In the remainder of this section, we describe, in turn, our main results, the detailed architecture of RRPs, and the Comet message-passing protocol. The subsequent sections of the paper describe our results and their proofs in detail.

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


The

GMOseek

matrix:

a

decision

support

tool

for

optimizing

the

detection

of

genetically

modified

plants

Background:

Since

their

first

commercialization,

the

diversity

of

taxa

and

the

genetic

composition

of

transgene

sequences

in

genetically

modified

plants

(GMOs)

are

constantly

increasing.

To

date,

the

detection

of

GMOs

and

derived

products

is

commonly

performed

by

PCR-based

methods

targeting

specific

DNA

sequences

introduced

into

the

host

genome.

Information

available

regarding

the

GMOs'

molecular

characterization

is

dispersed

and

not

appropriately

organized.

For

this

reason,

GMO

testing

is

very

challenging

and

requires

more

complex

screening

strategies

and

decision

making

schemes,

demanding

in

return

the

use

of

efficient

bioinformatics

tools

relying

on

reliable

information.Description:

The

GMOseek

matrix

was

built

as

a

comprehensive,

online

open-access

tabulated

database

which

provides

a

reliable,

comprehensive

and

user-friendly

overview

of

GMO

events

and

different

genetic

elements

(status:

The

GMOseek

matrix

is

aiming

to

facilitate

GMO

detection

from

plant

origin

at

different

phases

of

the

analysis.

It

assists

in

selecting

the

targets

for

a

screening

analysis,

interpreting

the

screening

results,

checking

the

occurrence

of

a

screening

element

in

a

group

of

selected

GMOs,

identifying

gaps

in

the

available

pool

of

GMO

detection

methods,

and

designing

a

decision

tree.

The

GMOseek

matrix

is

an

independent

database

with

effective

functionalities

in

a

format

facilitating

transferability

to

other

platforms.

Data

were

collected

from

all

available

sources

and

experimentally

tested

where

detection

methods

and

certified

reference

materials

(CRMs)

were

available.GMOseek

matrix

is

currently

a

unique

and

very

valuable

tool

with

reliable

information

on

GMOs

from

plant

origin

and

their

present

genetic

elements

that

enables

further

development

of

appropriate

strategies

for

GMO

detection.

It

is

flexible

enough

to

be

further

updated

with

new

information

and

integrated

in

different

applications

and

platforms.

The

GMOseek

matrix

currently

constitutes

the

most

complete

and

comprehensive

database

gathering

information

on

GMO

events

with

different

elements

present

in

their

respective

GM

constructs.

Handling

all

these

data

requires

a

user-friendly

system.

For

this

reason,

the

herein

described

Excel

environment

offers

several

functionalities

facilitating

data

searches,

the

development

of

GMO

detection

strategies,

data

analysis,

and

decision

making

for

GMO

detection.

The

GMOseek

matrix

also

provides

information

useful

for

the

selection

of

additional

screening

targets

for

which

new

singleplex

or

multiplex

qPCR

detection

assays

need

to

be

developed.

It

serves

as

a

comprehensive

tool

useful

to

GMO

testing

laboratories

and

control

authorities.

The

flexibility

of

the

GMOseek

matrix

facilitates

its

adaption

for

use

in

many

countries,

taking

into

account

their

respective

legislations.

The

authors

strongly

recommend

that

users

of

the

GMOseek

matrix

consider

the

recommendations

and

limitations

of

the

matrix

approach

In

the

future,

the

data

of

the

GMOseek

matrix

will

be

integrated

into

the

larger

web-based

EUginius

database

EUginius

(European

GMO

Initiative

for

a

Unified

Database

System)

will

be

a

user-friendly

retrieval

system

providing

information

on

GMOs

concerning

their

phenotypic

and

molecular

characterisation

(DNA

sequences),

detection

methods,

reference

material,

as

well

as

their

GMO

world-wide

regulatory

status.

The

GMOseek

matrix

can

be

used

also

with

a

so-called

GMOseek

algorithm,

another

central

part

of

the

GMOseek

project

This

mathematical

algorithm

selects

from

the

matrix

an

optimal

set

of

genetic

elements

that

need

to

be

targeted

for

the

detection

of

GMOs

and

should

allow

streamlining

different

GMO

screening

applications..

Building

such

a

matrix

was

a

time

consuming

task

and

would

not

have

been

possible

without

the

international

collaboration

of

the

GMOseek

partners.

Further

effort

will

be

needed

to

maintain

and

update

the

matrix

with

new

GMO

events

and

genetic

elements,

and

to

experimentally

confirm

the

presence

of

genetic

elements

in

GMOs.

It

will

require

developing

new

detection

methods

and,

when

certified

GMO

reference

material

is

not

available,

using

precisely

defined

alternative

reference

material.

In

order

to

avoid

duplication

of

work

and

to

ensure

harmonization

of

GMO

testing,

the

authors

are

calling

for

a

broader

collaboration

of

the

laboratories

involved

in

GMO

detection

within

and

outside

of

Europe.

Genetically

modified

organisms

(GMOs)

of

plant

origin

have

been

widely

approved

for

commercialisation

at

a

global

scale

To

allow

consumer

freedom

of

choice,

many

countries

regulate

the

authorization,

labelling,

and

compliance

control

of

GMOs.

The

constantly

increasing

number

of

GMOs

on

the

world

market

raises

a

new

major

challenge

for

testing

laboratories:

limiting

the

cost

increase

while

meeting

all

test

criteria

and

requirements

demands

higher

throughput

to

keep

GMO

monitoring

efficient

and

cost-affordable

for

enforcement

purposes..

To

date,

PCR-based

detection

methods

are

the

standards

to

routinely

analyse

the

GMO

presence

in

the

food/feed

chain

Approaches

for

targeting

DNA

sequences

of

GMOs

in

food

and

feed

samples

can

be

based

on

the

detection

of

commonly

used

genetic

elements

(or

groups

of

genetic

elements)

for

screening

purposes

(screening

tests)

or

solely

on

the

identification

of

the

specific

GMO

events

(event-specific

tests)

For

the

screening

approach,

the

choice

of

tests

covering

a

wide

range

of

GMOs

has

become

less

obvious

and

is

hampered

by

the

lack

of

available

information

regarding

the

genetic

elements

introduced

into

the

different

GMOs.

The

use

of

event-specific

tests

is

extremely

costly

given

the

high

number

of

GMO

events

to

be

scrutinized,

and

it

only

enables

the

detection

of

known

events..

The

common

strategy

followed

by

laboratories

in

the

European

Network

of

GMO

Laboratories

(ENGL)

is

based

on

the

so-called

"matrix

approach"

which

combines

both

types

of

tests

A

first

step

consists

of

screening

tests

chosen

to

allow

large

coverage

of

GMOs.

By

comparing

the

test

results

with

tabulated

data

describing

the

presence/absence

of

the

targeted

sequences

in

individual

events

(matrix),

the

analyst

evaluates

the

possible

presence

of

individual

GMO

events.

Confirmation

and

identification

of

GMOs

in

a

second

step

is

performed

using

event-specific

tests.

When

a

screening

test

pattern

cannot

be

explained

by

a

registered

GMO,

a

sample

is

considered

as

noncompliant

and

additional

testing

(e.g.

insertional

cloning

or

genome

walking

combined

with

DNA

sequence

analysis)

is

required

to

elucidate

the

origin

of

the

unexplained

positive

signals

A

matrix-based

screening

approach

enables

the

smart

selection

of

a

minimum

set

of

tests

that

can

cover

a

maximum

number

of

GMOs,

thus

reducing

the

number

of

costly

event-specific

tests

to

be

performed.

A

major

requisite

for

applying

a

"matrix

approach"

in

GMO

detection

is

the

availability

of

reliable

information

on

the

molecular

targets

present

in

the

GMOs

under

investigation

Existing

databases

mainly

collect

the

information

for

GMO

risk

assessment

and

the

methods

available

for

detection

Several

target/GMO

tables

demonstrate

the

use

of

the

matrix

approach

in

GMO

analysis

In

most

cases,

the

scope

of

the

GMOs

and

the

listed

targets

have

been

restricted,

such

as

for

the

GMOs

authorized

for

commercial

use

in

the

European

Union

(EU)

at

a

particular

time.

Moreover,

most

of

the

existing

datasets

are

not

presented

in

a

format

appropriate

for

decisionmaking

in

GMO

detection,

or

data

are

missing

because

some

early

attempts

utilized

a

limited

amount

of

data..

The

main

purpose

of

the

present

work

was

to

fill

these

essential

gaps

by

building

an

extensive

database

on

GMOs

and

their

genetic

elements

(hereafter

named

"GMO

elements")

by

the

partners

of

the

GMOseek

project.

The

aim

of

the

GMOseek

matrix

is

to

focus

on

the

genetically

modified

plants

that

can

be

found

in

food

or

feed

products.

The

information

compiled

in

the

GMOseek

matrix

originates

from

all

available

sources

at

the

time

of

building

it.

When

the

detection

method

and

(certified)

reference

material

were

available,

data

were

also

experimentally

verified.

The

GMOseek

matrix

is

presented

with

effective

functionalities

for

flexible

data

retrieval

in

a

format

enabling

easy

modification

and

addition

of

new

information

and

even

implementation

into

larger

database

platforms.

The

GMOseek

matrix

facilitates

a

quick,

easy

overview

of

all

genetic

elements

and

their

presence

or

absence

in

numerous

GMO

events

that

can

be

found

on

the

global

market.

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


A Contrario Selection of Optimal Partitions for Image Segmentation Abstract-We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the a contrario reasoning when applied to the segmentation problem, and to overcome the limitations of current algorithms within that framework. This exploratory approach has three main goals.Our first goal is to extend the search space of greedy merging algorithms to the set of all partitions spanned by a certain hierarchy, and to cast the segmentation as a selection problem within this space. In this way we increase the number of tested partitions and thus we potentially improve the segmentation results. In addition, this space is considerably smaller than the space of all possible partitions, thus we still keep the complexity controlled.Our second goal aims to improve the locality of region merging algorithms, which usually merge pairs of neighboring regions. In this work, we overcome this limitation by introducing a validation procedure for complete partitions, rather than for pairs of regions.The third goal is to perform an exhaustive experimental evaluation methodology in order to provide reproducible results.Finally, we embed the selection process on a statistical a contrario framework which allows us to have only one free parameter related to the desired scale.

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