Comparisons

of

finite

element

and

Rayleigh

methods

for

the

study

of

conical

Bloch

waves

in

arrays

of

metallic

cylinders

Abstract

This

paper

investigates

new

technological

devices

to

be

utilised

in

future

optical

communications,

by

means

of

variational

method

(FEM)

and

multipole

scattering

approach

(Rayleigh

method).

This

last

one

provides

interesting

asymptotic

results

in

the

long-wavelength

limit.

The

so-called

photonic

crystal

fibres

(PCF)

possess

radically

different

guiding

properties

due

to

photonic

band

gap

guidance:

removing

a

hole

within

a

macro-cell

leads

to

a

defect

state

within

the

gap.

In

the

case

of

multi-core

PCF,

the

localised

modes

start

talking

to

each

other

which

possibly

leads

to

a

new

generation

of

multiplexer/demultiplexers.

Nanostructured

materials

containing

ordered

arrays

of

cylindrical

holes

pave

the

way

of

an

optoelectronics

revolution,

doing

for

light

what

silicon

did

for

electrons.

The

microelectronics

revolution

was

based

on

the

elaborate

control

of

electric

currents

achieved

with

semiconductors

as

silicon.

That

control

depends

on

a

phenomenon

called

the

band

gap,

i.e.

a

range

of

energies

in

which

electrons

are

blocked

from

travelling

through

the

semiconductor.

By

analogy

with

semiconductors,

physicist

have

produced

materials

with

a

photonic

band

gap

-a

range

of

wavelengths

of

light

that

is

blocked

by

the

material

-by

structuring

the

material

in

carefully

designed

patterns

at

the

nanoscopic-size

scale.

These

so-called

photonic

crystals

(PC)

act

as

semiconductors

for

light

and

promise

innumerable

technological

applications.

Such

structures

can

be

stretched

along

the

third

dimension,

forming

a

new

kind

of

optical

fibres,

christened

"photonic

crystal

fibres"

(PCF).

Conventional

optical

fibres

have

a

high

refractive

index

at

their

core,

which

confines

light

by

total

internal

reflection.

Philip

St

J.

Russell

of

the

University

of

Bath

in

England

demonstrated

in

how

to

make

photonic

band-gap

fibres

(Knight

et

al.,

In

one

version,

light

travels

along

a

central

hole

in

the

fibre,

confined

there

by

the

two-dimensional

band

gap

of

a

surrounding

periodic

cladding.

More

optical

power

can

be

sent

through

such

a

central

void

than

through

glass,

enabling

greater

information-carrying

capacity,

perhaps

times

that

of

conventional

telecommunications

fibres.

Specialty

fibres

have

advanced

the

most

as

commercial

photonic

band-gap

products.

Two

companies,

one

of

them

being

based

in

UK

("www.blazephotonics.com")

and

led

by

Philip

St

J.

Russell,

have

already

distributed

sample

quantities

and

will

soon

begin

volume

production

of

PCF.

We

present

analysis

of

electromagnetic

waves

propagating

through

such

doubly

periodic

array

of

cylindrical

channels

in

oblique

incidence.

We

use

Floquet-Bloch

quasi-periodicity

conditions

to

take

into

account

the

periodicity

of

the

problem

Although

one

may

argue

that

the

PCF

reportedly

have

a

finite

size

in

real

world

(Knight

et

al.,

this

model

enables

us

to

construct

dispersion

curves

for

the

corresponding

periodic

structure.

We

exhibit

band

gaps

in

conical

incidence

and

study

localised

modes

associated

with

a

defect

in

a

macrocell..

Rayleigh

method

Set

up

of

the

spectral

problem

Maxwell's

equations

at

work.

We

consider

a

periodic

heterogeneous

lossless

medium.

This

micro-structure

is

characterised

by

its

permittivity

¼

r

is

the

permittivity

of

vacuum)

and

its

permeability

m

¼

m

r

m

(m

is

the

permeability

of

vacuum).

We

assume

an

implicit

time

dependence

exp

of

the

electric

field

Eðx;

y;

zÞ

and

the

magnetic

field

Hðx;

y;

zÞ,

which

are

therefore

solutions

of

the

time

harmonic

Maxwell's

equations

(in

the

sense

of

distributions

in

R

Since

we

are

studying

propagation

of

modes

in

a

periodic

medium,

the

well

posedness

of

this

spectral

problem

is

ensured

by

the

Floquet-Bloch

quasi-periodicity

conditions

which

hold

on

the

boundary

of

a

basic

cell

(provided

that

r

and

m

r

are

real

functions

with

strictly

positive

lower

and

upper

bounds)..

In

the

case

of

propagating

waves

in

conical

incidence

in

a

medium

invariant

along

the

z-axis,

V

V

denoting

either

E

or

H

is

sought

in

the

form:.

where

g

is

the

(strictly

positive)

propagation

constant

and

r

and

F

denote

the

radial

and

angular

variables

of

V

which

is

associated

with

one

of

the

basic

cells

(Figure

which

we

denote

as

Y

¼

d

d

(d

is

the

pitch

of

the

square

array)..

From

now

on,

we

will

study

piecewise-constant

permittivity

and

permeability:

we

restrict

our

analysis

to

the

important

case

of

a

periodic

assembly

of

infinite

conducting

cylindrical

inclusions

of

circular

cross-section

C

Knight

et

al.,

Using

the

vector

Helmholtz

decomposition.

Study

of

conical

Bloch

waves

we

find

that

in

the

medium

between

the

metallic

inclusions,

the

electric

and

magnetic

field

satisfies

the

vector

Helmholtz

equation.

where

the

spectral

parameter

k

denotes

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffi

v

r

m

m

r

p

r

and

m

r

being,

respectively,

the

relative

permittivity

and

permeability

in

the

matrix..

Because

the

rods

are

infinitely

extended

in

the

z-direction,

the

x

and

y

components

of

the

E

and

H

fields

can

be

reconstructed

from

their

z-components,

via

the

equations.

It

should

be

noted

that

in

the

subsequent

analysis

we

retain

the

z-dependence

of

the

fields.

The

mathematical

model

of

infinite

conducting

inclusions

amounts

to

assuming

that

the

tangential

part

of

the

electric

field

n

E

be

vanishing

on

their

boundary,

unlike

the

tangential

part

of

the

magnetic

field

n

H

which

involves

the

(unknown)

current.

If

we

write

the

tangent

vector

at

any

given

point

on

the

inclusion

surface

›C

as

e

t

and

the

normal

vector

as

n

then.

Conical

mounting

for

metallic

cylinders:

miracle

making.

Noting

that

e

t

and

e

z

are

perpendicular,

we

can

express

the

boundary

conditions

as

a

set

of

restrictions

on

the

z-components

of

the

fields.

These

are

But

that

is

not

all,

we

should

also

note

that

equations

and

hold

both

for

E

z

H

z

and

(E

z

,H

z

due

to

the

definition

and

the

fact

that

n

is

perpendicular

to

the

z-axis..

Recast

of

the

problem

into

longitudinal

components.

Finally,

the

boundary

value

problem

splits

in

two

fundamental

polarisations,

namely

T.E.

polarisation.

›H

z

›n

›C

¼

on

the

boundary

of

each

cylinder

on

the

boundary

of

each

cylinder

It

should

be

noted

that

v

should

be

greater

than

the

so-called

cut-off

frequency

v

c

¼

g=.

to

ensure

a

real

(positive)

transverse

wave-number

k

The

Bloch

conditions:

from

boundary

value

to

spectral

problems.

For

the

spectral

problem

to

be

completely

specified,

we

further

assume

that

the

longitudinal

part

V

z

of

the

vector

field

V

satisfies

an

appropriate

quasi-periodicity

condition

known

as

the

Floquet-Bloch

condition.

where

k

is

known

as

the

Bloch

wave-vector

and

R

p

¼

p

a

þ

p

a

is

the

vector

attached

to

the

nodes

p

¼

p

p

Z

of

the

lattice

of

translations

vectors

a

and

a

which

form

the

basis

for

the

lattice

as

a

whole

(Figure

An

orphan:

the

TEM

case.

Most

of

the

studies

dealing

with

the

infinite

array

of

metallic

cylinders

light-heartedly

skip

the

important

issue

of

the

most

peculiar

class

of

so-called

transverse

electric-magnetic

waves,

except

in

the

noticeable

work

of

McPhedran

et

al.

These

modes

are

of

the

form

but

otherwise

they

should

also

fullfil

the

restrictive

condition.

within

the

PCF.

Let

us

check

whether

or

not

such

a

constraint

is

achievable.

Firstly,

it

follows

from

either

equation

or

together

with

equation

that

the

propagation

constant

g

has

to

be

equal

to

the

wavenumber

k

¼

v

r

m

m

r

p

if

we

want

non

zero

E

t

or

H

t

Hence,

in

the

transverse

case

ðg

¼

0Þ

TEM

modes

would

only

stand

a

chance

to

exist

in

the

static

limit..

Secondly,

plugging

E

¼

E

t

e

ig

z

and

H

¼

H

t

e

ig

z

in

equation

we

find.

The

second

equality

in

equation

holds

true

if

and

only

if

curl

E

t

¼

in

the

sense

of

distributions,

since

both

H

t

and

e

z

E

t

are

orthogonal

to

e

z

unlike

curl

E

t

which

is

COMPEL

colinear

to

e

z

Owing

to

equation

and

E

t

j

›C

is

also

null.

Hence,

E

t

is

irrotational

in

classical

sense

and

it

therefore

derives

from

a

potential

W

TE

A

similar

reasoning

can

be

led

for

H

t

but

we

notice

that

only

its

normal

derivative

will

vanish

of

the

boundary

C

and

therefore

it

is

only

irrotational

in

distributional

sense

(due

to

the

existence

of

a

current

n

H

t

on

›C

Now,

from

equations

and

we

have.

both

in

distributional

and

classical

sense

(due

to

Dirichlet

boundary

conditions

on

›C)..

At

this

stage,

we

remark

that

Y

n

C

is

a

not

simply

connected

set

(it

would

be

simply

connected

if

we

would

consider

an

array

of

dielectric

cylinders).

Therefore,

equation

does

not

imply

that

the

(quasi-periodic)

potential

W

TE

be

constant

over

the

basic

cell

(which

would

lead

to

E

t

¼

It

is

important

to

note

also

that

the

potential

W

TE

is

bound

to

take

a

value

W

i

TE

on

the

boundary

›C

in

the

ith

basic

cell

within

the

array

which

is

distinct

from

its

value

W

j

TE

on

the

boundary

›C

in

the

jth

basic

cell

if

i

-j.

We

are

therefore

in

presence

of

a

quasi-periodic

potential

solution

of

a

problem

of

electrostatic

type.

The

analysis

of

the

quasi-static

limit

led

by

Poulton

et

al.

reveals

the

following

relationships

between

on

the

one

hand,

the

dynamic

field

quantities

H

z

and

our

electrostatic

potential

W

TE

where.

is

the

quasi-static

wavenumber..

On

the

other

hand,

in

the

T.M.

case

it

is

shown

in

Poulton

et

al.

that.

where.

which

is

supplied

with

Bloch

conditions

on

opposite

sides

of

Y

and

some

Neumann

boundary

condition

›W

TM

=›n

¼

on

the

boundary

›C.

Remarkedly,

the

electrostatic

solutions

W

TE,x

and

W

TM,

y

(repectively

corresponding

to

fields

directed

along

the

x-and

y-axes)

form

a

Cauchy-Riemann

pair

and

are

related

by

Keller's

theorem

(Keller,

according

to

grad

W

TE;x

¼

z

TM;

y

where

R(w)

denotes

a

rotation

by

an

angle

w.

From

this,

it

can

be

deduced

that,

in

the

quasi-static

limit,

the

transverse

field

modes

E

t

and

H

t

(which

are

respectively

proportional

to

e

z

gradW

TE

and

gradW

TM

form

a

linearly

independent

(orthogonal)

pair

of

TEM

modes,

identical

up

to

a

rotation

through

angle

Actually,

for

a

square

array

of

circular

metallic

inclusions,

it

can

be

shown

that

the

potential

W

TE

solution

of

equation

can

be

expressed

as.

Study

of

conical

Bloch

waves

where

A

and

B

are

some

integration

constants

deduced

from

the

boundary

conditions

(quasi-periodicity

of

W

on

opposite

sides

of

the

basic

cell

Y

as

well

as

vanishing

normal

derivative

on

the

boundary

r

¼

r

c

In

this

paper,

we

have

presented

two

algorithms

by

which

one

can

construct

some

band

diagrams

associated

with

conical

Bloch

waves

in

arrays

of

metallic

cylinders.

The

first

one,

the

so-called

Rayleigh

method,

is

an

analytic

algorithm

well

suited

for

various

asymptotic

purposes

such

as

the

long-wavelength

limit

(homogenisation)

and

leads

to

an

infinite

algebraic

system

which

is

typically

truncated

as

a

matrix.

The

second

one,

the

so-called

finite

element

method,

leads

to

large

sparse

systems,

but

can

tackle

problems

of

more

complex

geometries

(such

as

arrays

of

cylinders

of

arbitrary

cross-section

or

models

for

periodic

structures

with

defects

as

in

Figure

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Oral messages improve visual search Input multimodality combining speech and hand gestures has motivated numerous usability studies. Contrastingly, issues relating to the design and ergonomic evaluation of multimodal output messages combining speech with visual modalities have not yet been addressed extensively. The experimental study presented here addresses one of these issues. Its aim is to assess the actual efficiency and usability of oral system messages including some brief spatial information for helping users to locate objects on crowded displays rapidly and without effort. Target presentation mode, scene spatial structure and task difficulty were chosen as independent variables. Two conditions were defined: the visual target presentation mode (VP condition) and the multimodal target presentation mode (MP condition). Each participant carried out two blocks of visual search tasks (120 tasks per block, and one block per condition). Scene target presentation mode, scene structure and task difficulty were found to be significant factors. Multimodal target presentation mode proved to be more efficient than visual target presentation. In addition, participants expressed very positive judgments on multimodal target presentations which were preferred to visual presentations by a majority of participants. Besides, the contribution of spatial messages to visual search speed and accuracy was influenced by scene spatial structure and task difficulty. First, messages improved search efficiency to a lesser extent for 2D array layouts than for some other symmetrical layouts, although the use of 2D arrays for displaying pictures is currently prevailing. Second, message usefulness increased with task difficulty. Most of these results are statistically significant. We have presented an experimental study that aims at assessing the actual contribution of voice system messages to visual search efficiency and comfort. Messages comprised one or two spatial phrases conveying coarse information on the target location on the display. 24 participants carried out 240 visual search tasks in two conditions differing from each other in initial target presentation only: visual presentation of the target versus multimodal presentation, that is, visual presentation of the target simultaneously with oral indications on its location on the screen. Oral messages improved participants' selection times and accuracy noticeably. However, their influence varied according to display spatial layout: the benefits were smaller for 2D array layouts than for Radial layouts, although the use of 2D arrays for displaying pictures is currently prevailing. In addition, message usefulness increased with task difficulty. Most of these results are statistically significant. According to subjective judgments, oral messages were well accepted, and multimodal target presentations were preferred to visual presentations by a majority of participants. Therefore, designers of graphical user interfaces might consider resorting to short oral messages including coarse spatial information for drawing users' attention to some displayed object. As such messages are likely to be well accepted by users, they may provide designers of advanced conversational user interfaces with a useful alternative "pointing" technique which may appropriately replace visual enhancement in interaction contexts where gaze activity is intense and where there is a risk of visual attention overload and eyestrain. However, these results need to be consolidated and further refined before reliable recommendations inferred from them can be proposed to designers. Their actual scope has first to be assessed. In particular, is the influence of spatial layout on visual search efficiency and comfort independent of the number of items displayed simultaneously and of their type (e.g., textual labels, graphical icons, drawings, etc.)? To what extent are the efficiency and user acceptance of oral spatial information messages dependent on their length and complexity? We are considering addressing some of these issues in the near future. Averaged selection times, error numbers and percentages were computed over all subjects (24) by condition, scene structure and task difficulty. First, we applied a n-factors ANOVA procedure on the data, then, paired t-tests whenever possible. Table 1 shows that scene target presentation mode, scene structure and task difficulty are significant factors. Considering selection times, results are highly significant for both target presentation mode and task difficulty; considering error numbers, they are highly significant for the target presentation mode only. These results suggest that scene structure has less influence on results than target presentation mode and task difficulty. The overall experimental protocol is first presented. Then, the description focuses on the design of the visual material. Target presentation mode, scene spatial structure and task difficulty were chosen as independent variables. Two dependent variables were used to assess participants' performances: target selection time (from scene display onset until first mouse click), and accuracy (i.e., mouse click on the target vs elsewhere); in addition, participants' subjective judgements were elicited through post-session questionnaires and debriefing interviews. To assess hypothesis A, two conditions were defined: the VP condition (target visual presentation) and the MP condition (target multimodal presentation). Each participant carried out two blocks including 120 visual search tasks each, one block per condition. In addition, the order of blocks was counterbalanced between participants so as to neutralize possible task learning effects. To assess hypothesis B, we had to create specific visual material, due to the great structural diversity and complexity of real objects and scenes. To control spatial structure variations, scenes were build from sets of photographs, each scene including 30 photographs arranged along one out of four standard symmetrical structures (see figure 1 ):. • Matrix-like, the layout most frequently used for presenting collections of pictures [7] ; • Elliptic (two concentric ellipses), a useful structure for displaying several sets of pictures simultaneously; • Radial (8 radii along the screen medians and diagonals), another possible structure for visualizing sets of pictures, especially ordered sets; \item • Random (random placing of items), the reference layout. We used the same 120 scenes for the VP and MP conditions in order to eliminate target visual and semiotic characteristics as possible factors of influence on participants' performances. We used 3600 different photographs collected from popular sites on the Internet to build the required 120 scenes (30 photographs per scene), so as to enhance the realism and attraction of the experimental visual search tasks as well as to obtain useful results for the design of picture browsers. Photographs were sorted out into 40 themes (e.g., sport, monuments, animals) and sub-themes (e.g., snakes or cats, for animals), then formatted (125x95 pixels, i.e., 4/3). Scenes were exclusively composed of photographs belonging to the same theme or sub-theme so as to reduce intrascene diversity in visual salience and subjective appeal. They were presented to participants in random order, regardless of their structure, their visual properties and those of the target. In addition, a different order was assigned to each subject so as to neutralize possible sequence effects. Target position varied from one scene to the other. For each scene, participants had to locate a pre-viewed photograph in the scene, and to select it as fast as they could, using the mouse. In the VP condition, the isolated target was displayed in the centre of the screen during 3 seconds. In the MP condition, a short oral message containing information on the TL was played simultaneously with the target visual presentation. Messages were composed of one or two short spatial phrases, for instance, "On the left (of the screen)" or "At the bottom (of the screen), on the right". Following target presentation, participants had to click on a button in the centre of the screen for launching the scene display. Thus, the position of the mouse at the beginning of the search was identical for all tasks. Three levels of task difficulty were defined, based mainly on the target visual complexity and the number of photographs in the scene that might be mistaken for it because of their visual similarity to it [2] . Levels of task difficulty were evenly distributed among the four structures (i.e., 10 scenes by level and structure). A gender-balanced group of 24 experienced computer users with ages between 24 and 29 and normal eyesight (assessed using the Bioptor test kit) participated in the experiment. Thus, all participants were expert mouse users with alike quick motor reactions; they were also experienced in visual search activities on computer displays. Therefore, target selection time and spotting accuracy were likely to reflect visual search performance reliably, and task learning effects were prevented.

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 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 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 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 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 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 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 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


Lot sizing and furnace scheduling in small foundries Abstract: A lot-sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (1) the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature.Finally, foundry-based tests with a real order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice. Foundries are common in every region of Brazil, producing many types of products, ranging from simple items for domestic use to sophisticated parts for the automobile and machine tool industries. According to the Brazilian Foundry Association [1] , the sector is growing rapidly, having produced over 12,000 tonnes a day (October/2005) and directly employing about 60,000 people.. Foundries can be classified as either captive or market-driven. The former tend to be part of large companies, such as car manufacturers, that totally absorb the foundry production, composed of large quantities of a small number of parts with relatively stable demand. On the other hand, market-driven foundries are generally small or medium sized companies that nevertheless produce a huge range of items with vastly varying demand. While captive foundries use a small number of different metal alloys, market-driven foundries need to work with a wide variety due to the diversity of their clients. This paper focuses on the problem of planning and scheduling production in small market-driven foundries.. Numerous researchers have studied lot sizing and setup scheduling problems, with reviews by [2] [3] [4] [5] [6] [7] [8] [9] [10] . However, there is little published research on such problems in foundries, and even less concerned with market-driven foundries. Santos-Meza et al. [11] studied the problem in small and medium-sized foundries, while Araujo and Arenales [12] researched a large captive foundry.. Sounderpandian et al. [13] and Gravel et al. [14] also studied to large foundries, but dealt specifically with the problem of job sequencing on machines. Most papers on this topic are concerned with production scheduling in large steel plants. By their nature, such plants do not have moulding sections since they produce steel sheets, of varying sizes and types, in rolling machines with cylinders that are configured according to the sheet specifications. Tang et al. [15] published a review of research on production planning and scheduling in steel production, while a variety of papers have studied the practical problems found in large steel plants, including [16] [17] [18] [19] [20] [21] [22] [23] .. In practice, the problem is tackled sequentially. The lot sizing of foundry products is carried out first, taking into account their demand and due dates. The production of alloys is then scheduled as a function of the lot sizes of the end products. However, this approach can result in a poor furnace schedule given the lack of two-way linkage between the lot sizing of end products and the scheduling of alloys. In this paper, we propose an optimization model where the two problems are solved in an integrated manner. The model put forward in this paper is closely related to the General Lot Sizing and Scheduling Problem (GLSP) and its extensions [8, [24] [25] [26] [27] [28] . The GLSP schedules multiple products on a single machine and allows many setups in each single 'large-bucket' time period. This paper adapts the GLSP to include backlogs and product-group setups, with an emphasis on rolling horizon use.. speed and solution quality for this kind of model as an important research area. Recent research by Gupta and Magnusson [29] into capacitated lot sizing with sequence-dependent setup costs states that it is still difficult to obtain near-optimal solutions for industrial-size problems. Dillenberger et al. [30] formulated a lot sequencing and sizing model with representation of sequence-independent setup times on multiple machines. The resulting mixed integer programming (MIP) model is difficult to solve optimally for large realistic problems, and so the authors resorted to the fix-andrelax method (Beraldi et al. [31] ), more widely known as relax-and-fix (Wolsey [32] , Kelly and Mann [33] ). The current paper uses a similar basic approach. Dillenberger et al. [30] illustrated the viability and value of the relax-and-fix method, applying it to sizeable real problems from three IBM plants, and obtaining acceptable solutions in reasonable computing time, even on the slower machines of the 1990s. Section 2 describes the lot sequencing and sizing in the context of found while section 3. presents the results MIP model. An initial attempt to optimally solve this model using advanced optimisation software was not successful. To try to overcome this, section 4 presents rolling horizon solution strategy, but the software still failed to find good solutions within reasonable computational time. The relax-and-fix heuristic approach was then applied on a rolling horizon basis in section 5, giving good results. Relax-and-fix involves the solution of a period-by-period sequence of partially-relaxed MIPs, each one with just a reduced set of binary variables whose number is small enough to obtain good solutions. As the horizon rolls forward in time over the periods, each set of binary variables is permanently fixed at their solution values.. For comparison, three methods involving neighbourhood search on the reduced set of binary variables were developed, namely, descent heuristic, diminishing neighbourhood search and simulated annealing. Several authors have already explored a similar approach, among them Kuik et al. [34] who used simulated annealing and tabu search on a lot-sizing problem with sequenceindependent setups, Teghem et al. [35] who employed linear programming within a simulated annealing for a combinatorial production planning problem, and Fleischman and Meyr [26] who applied threshold accepting search on the general lot sizing problem (GLSP) with sequenceindependent setup costs (but not times), denoted GLSPST. Similarly, Meyr [27] developed an efficient algorithm for the GLSPST that uses multiple runs on a local search for lot sequencing with linear programming (LP) dual reoptimization for rapid lot-sizing.. Computational tests comparing all the methods are presented and analysed in section 6, including in-foundry comparisons with practiced schedules.

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


Permutable fuzzy consequence and interior operators and their connection with fuzzy relations Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type.We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf-! composition. For this cases, we connect permutability of the fuzzy relations (using the sup-⁄ composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces. Fuzzy consequence operators and fuzzy interior operators are an essential tool in most of the different frameworks were fuzzy logic appears. As prominent examples, we find approximate reasoning and fuzzy mathematical morphology. In approximate reasoning, fuzzy consequence operators are used to obtain conclusions from certain fuzzy premises and fuzzy relations [13, 18, 19, 30] . Fuzzy interior operators appear as a dual notion of fuzzy consequence operators in the lattice of truth values [5] . In fuzzy mathematical morphology, fuzzy consequence operators and fuzzy interior operators are called fuzzy closings and openings respectively and they act as morphological filters used for image processing [7, 8, 15, 16] . Operators induced by fuzzy relations appear in this context as a generalization of morphological filters defined in sets were an additive operation does not necessarily exist [20, 22] . In these cases, the fuzzy relation plays the role of structuring element. This abstraction allows to use certain techniques from fuzzy mathematical morphology into data mining problems [21] . Other places where fuzzy consequence and interior operators appear are modal logic [10] , fuzzy topology [23] [24] [25] , fuzzy rough sets [9, 28, 34] , fuzzy relation equations [29] and fuzzy concept analysis [1, 3] . In all these contexts there is a need of concatenating two or more operators and it is important to know when this composition preserves their properties. A very relevant question is whether the composition of two fuzzy consequence (interior) operators is such an operator. As will be shown it this paper, it turns out to be closely related to their permutability or commutativity.. The objective of this paper is to characterize permutability in the case of composition of either two fuzzy consequence operators or two fuzzy interior operators. We study two particular cases of operators induced by fuzzy relations: fuzzy operators induced by means of Zadeh compositional rule and fuzzy operators induced by the inf-! composition, mainly focusing on the cases of operators induced by fuzzy preorders and similarities. As we shall see, permutability of fuzzy relations is closely related to permutability of their induced fuzzy operators and preservation of their properties.. The paper is organized as follows. In Section 2 we set the framework and we recall the main definitions and results that will be used throughout the paper.. In Section 3 we recollect several definitions and results that show connections between fuzzy relations and fuzzy operators. We recall the operators C Ã R and C ! R given by Zadeh's compositional rule and inf-! composition respectively, several of their properties and extend the notion of C Ã R to a more general process to obtain fuzzy operators from a fuzzy relation and another fuzzy operator. We introduce the notion of concordance between a fuzzy operator and a fuzzy relation, which is the key to preserve the properties of fuzzy consequence operator of the induced operator.. Sections 4 and 5 are devoted to the analysis of permutability for certain cases of fuzzy relations and fuzzy operators. In Section 4, we study permutability of general fuzzy preorders and the particular case of fuzzy indistinguishability relations. In Section 5, permutability of fuzzy consequence operators is characterized and dual results are obtained for the case of fuzzy interior operators.. Sections 6 and 7 show the relationship between permutability of fuzzy relations and permutability of fuzzy operators by using the connections established in Section 3. In Section 6, we relate permutability of fuzzy relations with permutability of the operators that they induce through Zadeh's compositional rule. In Section 7, a similar study is made for operators induced through inf-! composition. We use the results developed in Sections 4 and 5 in order to study the cases of fuzzy operators induced by fuzzy preorders and similarities.. In Section 8 we analyze under which conditions different properties of the induced operators are satisfied even if permutability does not hold. Some of these properties are used to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.. Finally, in Section 9 we present the conclusions. Permutability of fuzzy consequence operators and fuzzy interior operators does not always occur. However, there are cases for which the order of composition does not affect the result. We have shown that this fact is completely connected to the preservation of the operator type through composition.. For the particular cases of fuzzy consequence operators induced through Zadeh's compositional rule and fuzzy interior operators induced using the inf-! composition we proved that permutability of the relations is connected to permutability of the induced operators. In fact, permutability of the starting relations appears to be a necessary and sufficient condition in order to obtain permutability of the induced operators.. Finally, we have seen that for reflexive relations, the operator induced by the transitive closure of their composition coincides with the closure of the operator that their composition induces.. To conclude, we summarize the most important results that we have obtained. First of all, we enumerate the results about permutability of fuzzy preorders and fuzzy indistinguishability relations that have been the key to analyze permutability of their induced fuzzy operators:. 1. R; P fuzzy Ã-preorders. Then, R P ¼ P R () R P and P R are fuzzy Ã-preorders. 2. E; F fuzzy Ã-similarities. Then, E F ¼ F E () E F is a fuzzy Ã-similarity.. 3. R P preserves type (similarity or preorder) , R P ¼ maxðR; PÞ.. Permutability of general fuzzy consequence and interior operators can be summarized in the following two 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 O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B 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 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 B I I 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 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 B O O O O B O O O O O O O O O O O O O O O O B 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 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 O O O O O O O O O O O O O O O O O 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 B 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 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 B O O O O O O O O O O O O O O O


Probabilistic information retrieval approach for ranking of database query results We investigate the problem of ranking the answers to a database query when many tuples are returned. In particular, we present methodologies to tackle the problem for conjunctive and range queries, by adapting and applying principles of probabilistic models from information retrieval for structured data. Our solution is domain independent and leverages data and workload statistics and correlations. We evaluate the quality of our approach with a user survey on a real database. Furthermore, we present and experimentally evaluate algorithms to efficiently retrieve the top ranked results, which demonstrate the feasibility of our ranking system. Database systems support a simple Boolean query retrieval model, where a selection query on a SQL database returns all tuples that satisfy the conditions in the query. This often leads to the Many-Answers Problem: when the query is not very selective, too many tuples may be in the answer. We use the following running example throughout the article:. Example: Consider a realtor database consisting of a single table with attributes such as (TID, Price, City, Bedrooms, Bathrooms, LivingArea, SchoolDistrict, View, Pool, Garage, BoatDock . . . ). Each tuple represents a home for sale in the US.. Consider a potential home buyer searching for homes in this database. A query with a not very selective condition such as "City=Seattle and View= Waterfront" may result in too many tuples in the answer, since there are many homes with waterfront views in Seattle.. The Many-Answers Problem has also been investigated in information retrieval (IR), where many documents often satisfy a given keyword-based query. Approaches to overcome this problem range from query reformulation techniques (e.g., the user is prompted to refine the query to make it more selective), to automatic ranking of the query results by their degree of "relevance" to the query (though the user may not have explicitly specified how) and returning only the top-k subset.. It is evident that automated ranking can have compelling applications in the database context. For instance, in the earlier example of a homebuyer searching for homes in Seattle with waterfront views, it may be preferable to first return homes that have other desirable attributes, such as good school districts, boat docks, etc. In general, customers browsing product catalogs will find such functionality attractive.. In this article we propose an automated ranking approach for the ManyAnswers Problem for database queries. Our solution is principled, comprehensive, and efficient. We summarize our contributions below.. Any ranking function for the Many-Answers Problem has to look beyond the attributes specified in the query, because all answer tuples satisfy the specified conditions. 1 However, investigating unspecified attributes is particularly tricky since we need to determine what the user's preferences for these unspecified attributes are. In this article we propose that the ranking function of a tuple depends on two factors: (a) a global score which captures the global importance of unspecified attribute values, and (b) a conditional score which captures the strengths of dependencies (or correlations) between specified and unspecified attribute values. For example, for the query "City = Seattle and View = Waterfront" (we also consider IN queries, e.g., City IN (Seattle, Redmond)), a home that is also located in a "SchoolDistrict = Excellent" gets high rank because good school districts are globally desirable. A home with also "BoatDock = Yes". • S. Chaudhuri et al. gets high rank because people desiring a waterfront are likely to want a boat dock. While these scores may be estimated by the help of domain expertise or through user feedback, we propose an automatic estimation of these scores via workload as well as data analysis. For example, past workload may reveal that a large fraction of users seeking homes with a waterfront view have also requested boat docks. We extend our framework to also support numeric attributes (e.g., age), in addition to categorical, by exploiting state-of-the-art bucketing methods based on histograms.. The next challenge is: how do we translate these basic intuitions into principled and quantitatively describable ranking functions? To achieve this, we develop ranking functions that are based on probabilistic information retrieval (PIR) ranking models. We chose PIR models because we could extend them to model data dependencies and correlations (the critical ingredients of our approach) in a more principled manner than if we had worked with alternative IR ranking models such as the Vector-Space model. We note that correlations are sometimes ignored in IR data-important exceptions are relevance feedback-based IR systems-because they are very difficult to capture in the very high-dimensional and sparsely populated feature spaces of text whereas there are often strong correlations between attribute values in relational data (with functional dependencies being extreme cases), which is a much lower-dimensional, more explicitly structured, and densely populated space that our ranking functions can effectively work on. Furthermore, we exploit possible functional dependencies in the database to improve the quality of the ranking.. The architecture of our ranking has a preprocessing component that collects database as well as workload statistics to determine the appropriate ranking function. The extracted ranking function is materialized in an intermediate knowledge representation layer, to be used later by a query processing component for ranking the results of queries. The ranking functions are encoded in the intermediate layer via intuitive, easy-to-understand "atomic" numerical quantities that describe (a) the global importance of a data value in the ranking process, and (b) the strengths of correlations between pairs of values (e.g., "if a user requests tuples containing value y of attribute Y , how likely is she to be also interested in value x of attribute X ?"). Although our ranking approach derives these quantities automatically, our architecture allows users and/or domain experts to tune these quantities further, thereby customizing the ranking functions for different applications.. We report on a comprehensive set of experimental results. We first demonstrate through user studies on real datasets that our rankings are superior in quality to previous efforts on this problem. We also demonstrate the efficiency of our ranking system. Our implementation is especially tricky because our ranking functions are relatively complex, involving dependencies/correlations between data values. We use interesting precomputation techniques which reduce this complex problem to a problem efficiently solvable using top-k algorithms.. The rest of this article is organized as follows. In Section 2 we discuss related work. In Section 3 we define the problem. In Section 4 we discuss our approach to ranking based on probabilistic models from information retrieval, along with various extensions and special cases. In Section 5 we describe an efficient implementation of our ranking system. In Section 6 we discuss the results of our experiments, and we conclude in Section 7. We propose a completely automated approach for the Many-Answers Problem which leverages data and workload statistics and correlations. Our ranking functions are based upon the probabilistic IR models, judiciously adapted for structured data. We presented results of preliminary experiments which demonstrate the efficiency as well as the quality of our ranking system. Our work brings forth several intriguing open problems. For example, many relational databases contain text columns in addition to numeric and categorical columns. It would be interesting to see whether correlations between text and nontext data can be leveraged in a meaningful way for ranking. Second, rather than just query strings present in the workload, can more comprehensive user interactions be leveraged in ranking algorithms-for example, tracking the actual tuples that the users select in response to query results? Finally, comprehensive quality benchmarks for database ranking need to be established. This would provide future researchers with a more unified and systematic basis for evaluating their retrieval algorithms. A preliminary version of this article appeared in Chaudhuri et al. [2004] , where we presented the basic principles of using probabilistic information retrieval models to answer database queries. However, our earlier article only handled point queries (see Section 3). In this work, we show how IN and range queries can be handled and how this makes the algorithms to produce efficiently the top results more challenging (Sections 4.4.1 and 5.4). Furthermore Chaudhuri et al. [2004] focused on only categorical attributes, whereas we have a complete study of numerical attributes as well (Section 4.4.2). Chaudhuri et al. [2004] also ignored functional dependencies, which as we show can improve the quality of the results (Section 4.2.2). In this work, we also present specialized solutions for cases where no workload is available (Section 4.3.1), and no dependencies exist between attributes (Section 4.3.2). We also generalize to the case where the data resides on multiple tables (Section 4.4.3). Finally, we extend Chaudhuri et al. [2004] with a richer set of quality and performance experiments. On the quality level, we show results for IN queries and also compare them to the results of a "random" algorithm. On the performance level, we include experiments on how the number k of requested results affects the performance of the algorithms.. Ranking functions have been extensively investigated in information retrieval. The vector space model as well as probabilistic information retrieval (PIR) models [Baeza-Yates and Ribeiro-Neto 1999; Grossman and Frieder 2004; , 2000b and statistical language models [Croft and Lafferty 2003; Grossman and Frieder 2004] are very successful in practice. Feedback-based IR systems (e.g., relevance feedback [Harper and Van Rijsbergen 1978] , pseudorelevance feedback [Xu and Croft 1996] ) are based on inferring term correlations and modeling term dependencies, which are related to our approach of inferring correlations within workloads and data. While our approach has been inspired by PIR models, we have adapted and extended them in ways unique to our situation, for example, by leveraging the structure as well as correlations present in the structured data and the database workload.. In database research, there has been significant work on ranked retrieval from a database. The early work of Motro [1988] considered vague/imprecise similarity-based querying of databases. Probabilistic databases have been addressed in Barbara et al. [1992] , Cavallo and Pittarelli [1987] , Dalvi and Suciu [2005] , and Lakshmanan et al. [1997] . Recently, a broader view of the needs for managing uncertain data has been evolving (see, e.g., Widom [2005] ).. The challenging problem of integrating databases and information retrieval systems has been addressed in a number of seminal papers [Cohen 1998a [Cohen , 1998b Fuhr 1990 Fuhr , 1993 Roelleke 1997, 1998 ] and has gained much attention lately Amer-Yahia et al. [2005a] . More recently, information retrieval-based approaches have been extended to XML retrieval [Amer-Yahia et al. 2005b; Chinenyanga and Kushmerick 2002; Carmel et al. 2003; S. Chaudhuri et al. and Grossjohann 2004; Guo et al. 2003; Hristidis et al. 2003b; Lalmas and Roelleke 2004; Theobald and Weikum 2002; Theobald et al. 2005] . The articles , Ortega-Binderberger et al. [2002] , Rui et al. [1997] , and Wu et al. [2000] employed relevance-feedback techniques for learning similarity in multimedia and relational databases. Our approach of leveraging workloads is motivated by and related to IR models that aim to leverage querylog information (e.g., see Radlinski and Joachims [2005] and Shen et al. [2005] ). Keyword-query-based retrieval systems over databases have been proposed in Agrawal et al. [2002] , Bhalotia et al. [2002] , Hristidis and Papakonstantinou [2002] , and Hristidis et al. [2003a] . In Kiessling [2002] and Nazeri et al. [2001] , the authors proposed SQL extensions in which users can specify ranking functions via soft constraints in the form of preferences. The distinguishing aspect of our work from the above is that we espouse automatic extraction of PIR-based ranking functions through data and workload statistics.. The work most closely related to our article is Agrawal et al. [2003] , which briefly considered the Many-Answers Problem (although its main focus was on the Empty-Answers Problem, which occurs when a query is too selective, resulting in an empty answer set). It too proposed automatic ranking methods that rely on workload as well as data analysis. In contrast, however, our article has the following novel strengths: (a) we use more principled probabilistic PIR techniques rather than ad hoc techniques "loosely based" on the vector-space model, and (b) we take into account dependencies and correlations between data values, whereas Agrawal et al. [2003] only proposed a form of global score for ranking.. Ranking is also an important component in collaborative filtering research [Breese et al. 1998 ]. These methods require training data using queries as well as their ranked results. In contrast, we require workloads containing queries only.. A major concern of this article is the query processing techniques for supporting ranking. Several techniques have been previously developed in database research for the top-k problem [Bruno et al. 2002a [Bruno et al. , 2002b Fagin 1998; Fagin et al. 2001; Wimmers et al. 1999] . We adopt the Threshold Algorithm of Fagin et al. [2001 ] Güntzer et al. [2000 , and Nepal and Ramakrishna [1999] for our purposes, and develop interesting precomputation techniques to produce a very efficient implementation of the Many-Answers Problem. In contrast, an efficient implementation for the Many-Answers Problem was left open in Agrawal et al. [2003] . In this section we discuss the architecture and the implementation of our database ranking system. Figure 1 shows the architecture of our proposed system for enabling ranking of database query results. As mentioned in the introduction, the main components are the preprocessing component, an intermediate knowledge representation layer in which the ranking functions are encoded and materialized, and a query processing component. The modular and generic nature of our system allows for easy customization of the ranking functions for different applications. In this section we report on the results of an experimental evaluation of our ranking method as well as some of the competitors. We evaluated both the quality of the rankings obtained, as well as the performance of the various approaches. We mention at the outset that preparing an experimental setup for testing ranking quality was extremely challenging, as unlike IR, there are no standard benchmarks available, and we had to conduct user studies to evaluate the rankings produced by the various algorithms.. For our evaluation, we used real datasets from two different domains. The first domain was the MSN HomeAdvisor database (http:// houseandhome.msn.com/), from which we prepared a table of homes for sale in the U.S., with a mix of categorical as well as numeric attributes such as Price, Year, City, Bedrooms, Bathrooms, Sqft, Garage, etc. The original database table also had a text column called Remarks, which contained descriptive information about the home. From this column, we extracted additional Boolean attributes such as Fireplace, View, Pool, etc. To evaluate the role of the size of the database, we also performed experiments on a subset of the HomeAdvisor database, consisting only of homes sold in the Seattle area.. The second domain was the Internet Movie Database (http://www. imdb.com), from which we prepared a table of movies, with attributes such as Title, Year, Genre, Director, FirstActor, SecondActor, Certificate, Sound, Color, etc. We first selected a set of movies by the 30 most prolific actors for our experiments. From this we removed the 250 most well-known movies, as we did not wish our users to be biased with information they already might know about these movies, especially information that is not captured by the attributes that we had selected for our experiments. The sizes of the various (single-table) datasets used in our experiments are shown in Table I . The quality experiments were conducted on the Seattle Homes and Movies tables, while the performance experiments were conducted on the Seattle Homes and the U.S. Homes tables-we omitted performance experiments on the Movies table on account of its small size. We used Microsoft SQL Server 2000 RDBMS on a P4 2.8-GHz PC with 1 GB of RAM for our experiments. We implemented all algorithms in C#, and connected to the RDBMS through DAO. We created single-attribute indices on all table attributes, to be used during the selection phase of the Scan algorithm. Note that these indices are not used by the List Merge algorithm.

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 B 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 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 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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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B I O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Efficient fork-linearizable access to untrusted shared memory When data is stored on a faulty server that is accessed concurrently by multiple clients, the server may present inconsistent data to different clients. For example, the server might complete a write operation of one client, but respond with stale data to another client. Mazières and Shasha (PODC 2002) introduced the notion of forkconsistency, also called fork-linearizability, which ensures that the operations seen by every client are linearizable and guarantees that if the server causes the views of two clients to differ in a single operation, they may never again see each other's updates after that without the server being exposed as faulty. In this paper, we improve the communication complexity of their fork-linearizable storage access protocol with n clients from Ω(n 2 ) to O(n). We also prove that in every such protocol, a reader must wait for a concurrent writer. This explains a seeming limitation of their and of our improved protocol. Furthermore, we give novel characterizations of fork-linearizability and prove that it is neither stronger nor weaker than sequential consistency. Many users no longer keep all their data on local storage. Instead, their data often resides on remote, online service providers. Systems with such remotely stored information include network filesystems, online collaboration servers such as Wikis, source code repositories using versioning tools like CVS, and web-based email providers. Users rely on the provider to maintain the integrity of the stored data, but there is no generally available technology that allows a user to easily verify that no subtle modification has been Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. August 12-15, 2007 , Portland, Oregon, USA . introduced to the data. In other words, users must trust the storage provider.

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


Initial Synchronisation of Wideband and UWB Direct Sequence Systems: Single- and Multiple-Antenna Aided Solutions Abstract-This survey guides the reader through the open literature on the principle of initial synchronisation in singleantenna-assisted single-and multi-carrier Code Division Multiple Access (CDMA) as well as Direct Sequence-Ultra WideBand (DS-UWB) systems, with special emphasis on the DownLink (DL). There is a paucity of up-to-date surveys and review articles on initial synchronization solutions for MIMO-aided and cooperative systems -even though there is a plethora of papers on both MIMOs and on cooperative systems, which assume perfect synchronization. Hence this paper aims to fill the related gap in the literature. C ODE Division Multiple Access (CDMA) [1] based mobile communication systems have been widely advocated by the standardisation bodies, leading to the IS-95 [1] and the Third-Generation (3G) [2] systems. In the inter-cell synchronous CDMA-2000 system, the Mobile Station's (MS) receiver must be capable of coarsely synchronously aligning a locally generated Pseudo-Noise (PN) code with the received composite multi-user signals containing the desired user's PN sequence [3] - [6] before the transmission of the desired signal. This process is referred to as 'initial code acquisition', followed by optimum post-initial code acquisition [7] , [8] , where the term 'post-initial code acquisition' [7] refers to identifying the timing instants of the affordable-complexitydependent number of delayed received signal paths, which will be combined by Rake receiver.. In general, the initial synchronisation is achieved in two consecutive steps. Code acquisition is invoked first for coarse code alignment and code phase tracking for fine alignment [3] , [5] , [9] . Substantial research efforts have been devoted to the design of code acquisition techniques [4] - [6] . A variety of serial search [3] , [4] , parallel search [10] , [11] , as well as sequential estimation [12] - [14] based code acquisition techniques have been proposed in the literature. In order to achieve a high performance, numerous detector structures such as multiple dwell based search schemes [3] - [5] , PostDetection Integration (PDI) [3] , [15] , [16] and Differentially Coherent (DC) [17] - [19] schemes have also been studied in the literature. Then, the code acquisition performance of Multi-Carrier (MC) DS-CDMA evaluated with the aid of serial and parallel search based schemes has been investigated in [6] , [20] , [21] , respectively.. Most code acquisition schemes have originally been designed for Single-Input Single-Output (SISO) systems [3] , [16] , [22] . However, there is a paucity of in-depth studies in the open literature representing the fundamental characteristics of code acquisition schemes, regardless whether co-located or cooperative Multiple Input/Multiple Output (MIMO) scenarios considered. Hence, we have reviewed a variety of code acquisition schemes designed for antenna arrays, since they may be considered an important generic MIMO family [23] - [27] . The recent contributions disseminated in [28] - [33] aimed for the fundamental characterization of code acquisition schemes assisted by either co-located or cooperative MIMOs. Furthermore, the research of Ultra WideBand (UWB) systems has recently attracted a significant interest in both the academic and industrial research community [34] , [35] . However, initial code and timing acquisition in the DS-UWB DL constitutes a particularly challenging problem owing to the extremely short signalling chip-duration employed [36] , [37] . Accordingly, in this survey we dedicate special attention to the employment of iterative code acquisition schemes designed for diverse MIMOs.. In Section II we commence our discourse by introducing the related terminology, definitions and various approaches regarding code acquisition. In Section III we guide the reader through the extensive literature, commencing from the conception of the various schemes and portray a variety of search strategies as well as schemes, leading to the concept of initial and post-initial code acquisition concepts appliable to both single-carrier and MC-DS-CDMA systems. In Section IV a brief historical perspective is provided, leading to the current state-of-the-art associated with code acquisition schemes employed in DS-UWB systems. We then proceed further to provide insights on the pertinent issues associated with the family of iterative Message Passing (MP) aided acquisition approaches. The associated performance versus complexity trade-offs are illustrated in terms of serial, hybrid, parallel and iterative MP acquisition schemes. Subsequently, in Section V we consider antenna array aided MIMO scenarios as well as both co-located and cooperative MIMO environments. Then, in Section VI we detail a range of current research endeavors 1553-877X/12/$25.00 c 2012 IEEE II. PRELIMINARIES In this section, we will strive to elucidate, code acquisition procedures, the interaction between the synchronisation module and Rake receiver, the associated decision strategy and the concept of Mean Acquisition Time (MAT) in a simple and concise manner. Our discourse will be limited to the following topics:. • Code acquisition procedures in the DownLink (DL) and UpLink (UL); • The procedures of the synchronisation module and Rake receiver; • The basic principle of the decision strategy;. • Characterization of the MAT. Each point will be treated separately in the forthcoming subsections. We would like to direct the attention of those readers, who wish to delve into further detail, to some excellent textbooks such as [3] - [6] , amongst others. In this article, we have provided a comprehensive survey of the associated open literature that is related to the principle of initial synchronisation in the single-and multi-carrier CDMA as well as DS-UWB DL. We have commenced our discourse by outlining the related basic terminology and definitions in Section II. We have limited our elaborations to the basic principles of code acquisition procedures, the interaction between the synchronisation module and Rake receiver, the associated decision strategy and the concept of MAT. Following these preliminaries, in Section III we proceeded to provide various search strategies, widely used detector structures, the initial and post-initial code acquisition as well as code acquisition schemes designed for both the MC-DS-CDMA DL and for DS-UWB DL. More specifically, we focused our attention on the literature concerning various search strategies. The underlying serial search based code acquisition was presented, followed by the parallel search (ML) based code acquisition scheme. Then the set of known sequential estimation based code acquisition schemes were classified into four categories. Finally, random search based code acquisition was presented. Then, we outlined a variety of widely used detector structures. Subsequently, we detailed NC code acquisition as well as both a chip based-DC detection scheme and a FPC based DC detection scheme. We also discussed the widely-used PDI concept of practical code acquisition receivers. Additionally, we summarised the historic evolution of sequential estimation based code acquisition as well as that of DC acquisition schemes in Tables II and III, respectively. We have provided a concise portrayal of both initial and post-initial code acquisition schemes designed for both the MC-DS-CDMA DL and for DS-UWB DL. More specifically, the last subsection constitutes an overview of a variety of schemes, such as iterative MP aided code acquisition and two-stage iterative arrangements. The subsection has portrayed how the most popular iterative detection schemes usually employed for channel coding schemes in the literature have been adopted in terms of code acquisition approaches [37] , [49] , [56] , [76] , [77] , [79] - [81] .. In Section IV, we have focused our attention on current research topics related to code acquisition in both the colocated and cooperative MIMOs. We proceeded by explaining some basic scecnarios regarding code acquisition in colocated MIMOs. More explicitly, we attempted to illustrate the behaviours of the NC co-located MIMOs in terms of code acquisition, then the related information theoretic considerations in the NC MIMO aided scenarios were portrayed in a concise manner. Finally, we have outlined a three-stage code acquisition scenario encountered in fixed RS-aided environments, closing with the characteristics of code acquisition in both the co-located and cooperative MIMOs. Based on our elaborations regarding the diverse code acquisition scenarios relying on both cooperative MIMOs and iterative acquisition schemes, a range of further sophisticated approaches may be considered for future research.

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


Learning to select distinctive landmarks for mobile robot navigation In landmark-based navigation systems for mobile robots, sensory perceptions (e.g., laser or sonar scans) are used to identify the robot's current location or to construct internal representations, maps, of the robot's environment. Being based on an external frame of reference (which is not subject to incorrigible drift errors such as those occurring in odometry-based systems), landmark-based robot navigation systems are now widely used in mobile robot applications.The problem that has attracted most attention to date in landmark-based navigation research is the question of how to deal with perceptual aliasing, i.e., perceptual ambiguities. In contrast, what constitutes a good landmark, or how to select landmarks for mapping, is still an open research topic. The usual method of landmark selection is to map perceptions at regular intervals, which has the drawback of being inefficient and possibly missing 'good' landmarks that lie between sampling points.In this paper, we present an automatic landmark selection algorithm that allows a mobile robot to select conspicuous landmarks from a continuous stream of sensory perceptions, without any pre-installed knowledge or human intervention during the selection process. This algorithm can be used to make mapping mechanisms more efficient and reliable. Experimental results obtained with two different mobile robots in a range of environments are presented and analysed. To make predictions, the robot has to move in straight-line segments between consecutive perceptions. It is conceivable that the approach can be expanded to arbitrary motions between perceptions. Furthermore, for the experiments described here, the robots have sampled perceptual data in regular intervals. Clearly, the proposed algorithm is intended to select landmarks from continuous observations of the environment and although a robot will always only be able to sample the environment in discrete time steps, it is no problem to increase the sampling rate beyond that used in the experiments discussed in this paper.. Finally, how useful the selected landmarks are for actual navigation has not yet been investigated. The purpose of this research was to investigate the consistency of landmark selection. The construction of an entire mobile robot navigation system, incorporating the landmark selection algorithm presented here, is subject to ongoing research. A number of methods of selecting landmarks are described in the literature. Some systems [3, 15] take sonar scans at regular intervals, such as every 150 cm of travel in an environment, with every sonar scan being used as a landmark that is put into the map. This avoids the problem of ensuring that landmarks should be detected consistently, but since in many environments -such as corridors -a large number of perceptions are almost identical, the map is filled up with information that does not aid navigation.. Another problem with mapping at regular intervals is that perceptions that lie between sampling locations are missed. It may well be that these missed perceptions include considerably more distinctive landmarks than those perceived at the user-defined sampling locations.. A number of researchers have considered selecting suitable landmarks for mobile robot navigation. These can be split into off-line approaches that are not suitable for use on the robot as it explores, and systems that can be used on-line.. In the first category is the technique of asking the user to define the landmarks before the robot explores. Humans typically select objects that they find easy to recognise, such as doors, or line segments extracted from camera images recorded as the robot travels [6] . These approaches suffer from the same problem -the robot's perceptions of the world are very different to those of a human, and so features that the researcher thinks are distinctive may not be noticeable by the robot.. In contrast to this, Thrun [13] addressed the problem of Bayesian learning to select an optimal set of landmarks for performing self-localisation in one specific environment, where the landmarks consisted of a projection from the robot's raw sensory perceptions (camera images) onto vectors in a lower-dimensional space. This optimisation was performed by minimising directly the quantity of interest, namely the robot's error in self-localisation. Thrun showed that his method produced better performance than localisation using designer-determined landmarks including doors and ceiling lights. A similar, but computationally cheaper technique, was developed by Vlassis et al. [14] , who showed that their optimisation method produced better results than principal component analysis. Our approach differs in that we do not carry out any analysis of the utility of the landmarks selected, but instead use a self-acquired model of 'typical' sequences of perceptions, which is independent of any particular task or environment.. Neither of the above approaches are suitable for on-line selection of landmarks, because they rely on an acquired model of a previously explored environment. Zimmer [16] considered the problem of selecting landmarks in a topological map through a process of 'life-long learning', where the robot's map was continuously adapted on-line during exploration. This approach used global statistical information, based on comparison of accumulated error statistics at each of the nodes, to decide where to add and delete nodes in the map.. A related idea can be found in Bourque and Dudek [2] , who addressed the 'vacation snapshot' problem of deciding in which locations to take camera images in order to obtain a set of images that best represent an entire environment. This approach kept running statistics on what is a 'typical' perception, together with backtracking to previously visited locations that were subsequently found to be 'atypical'. Our method differs from these approaches in that we only use local sensory information to decide when to add landmarks to the map.. Simhon and Dudek [12] also use only local information. They addressed the problem of deciding the best locations in which to create local metric maps, using a distinctiveness function based on the robot's ability to localise itself within such a map. However, this approach relies heavily on the designer's intuition in selecting an appropriate distinctiveness function. For a mobile agent, the ability to navigate is of fundamental importance. Over short distances, this capability of goal-oriented motion may be achieved by path integration through dead reckoning, but very quickly odometry drift errors render dead reckoning navigation systems too inaccurate for useful navigation.. The alternative is to use perceptual landmarks for navigation. Typical landmark-based navigation systems either log perceptions at regular intervals, or match perceptions with pre-supplied templates of 'desirable' landmarks. The former approach is inefficient and runs the risk of missing out clearly visible landmarks that lie between sampling points. The latter approach runs the risk of being based on landmarks that are easily visible to a human, but not to a robot, or (equally undesirable) of missing landmarks that are easily visible to a robot, but that remain unselected because they are not important for human navigation.. A suitable way to address these problems is to devise an automatic landmark selection mechanism that allows the robot to select suitable landmarks without a pre-defined model of those landmarks, or human supervision. This paper has described an algorithm that can be used to achieve this.

O O O O O O O O O O B 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 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 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 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