Recent

Technical

Report

List

May

-LCB-

New

York

University

Courant

Institute

of

Mathematical

Sciences

Computer

Science

Department

ON-LINE

SCHEDULERS

FOR

OVERLOADED

REAL-TIME

SYSTEMS

G.

Koren

B.

Mishra

A.

Raghunathan

D.

Shasha

May

There

are

several

scheduling

algorithms

proposed

for

real-time

systems

with

sporadic

tasks

that

exhibit

optimal

behavior

if

the

system

is

underloaded

Examples

of

such

scheduling

algorithms

include

earliest-deadline-first

-LRB-

D

-RRB-

smallest-slack-timefirst

-LRB-

SL

-RRB-

etc.

However

these

algorithms

performs

poorly

when

the

system

is

overloaded

This

is

a

serious

problem

since

even

the

best-modeled

systems

may

not

be

able

to

avoid

intermittent

overloading

situations

In

this

paper

we

propose

an

on-line

scheduling

algorithm

for

a

uniprocessor

in

an

environment

of

sporadic

tasks

that

addresses

this

issue

We

assume

that

the

value

of

each

task

is

proportional

to

its

computation

time

provided

it

completes

by

its

deadline

if

it

misses

its

deadline

its

value

is

zero

An

optimal

scheduling

algorithm

then

maximizes

the

sum

of

the

values

of

the

completed

tasks

Even

for

a

clairvoyant

model

this

problem

is

NP-hard

In

this

paper

we

formalize

the

notions

of

when

a

system

is

overloaded

and

when

it

is

underloaded

We

devise

a

scheduling

algorithm

called

D

that

provides

the

following

performance

guarantee

Informally

speaking

D

achieves

optimal

performance

while

the

system

is

underloaded

and

achieves

a

value

that

is

at

least

times

the

length

of

the

overloaded

period

while

the

system

is

overloaded

To

the

best

of

our

knowledge

this

is

the

only

algorithm

that

makes

such

a

non-trivial

guarantee

for

a

real-time

system

that

may

face

intermittent

overloading

We

implement

D

using

simple

data

structures

at

a

cost

of

O

-LRB-

log

n

-RRB-

time

per

task

where

n

bounds

the

number

of

tasks

in

the

system

at

any

instant

We

also

show

that

no

on-line

algorithm

can

guarantee

a

value

that

is

better

than

times

the

value

obtained

by

a

clairvoyant

algorithm

Our

experimental

data

indicate

that

the

proposed

algorithm

-LRB-

referred

to

as

D

algorithm

-RRB-

is

comparable

to

Locke

's

best

effort

scheduler

-LRB-

BE

-RRB-

in

the

uniform

arrival

case

while

guaranteeing

the

one-fifth

bound

even

for

the

pathological

cases

that

would

cripple

Locke

's

scheduler

OPTIMAL

MOTION

PLANNING

FOR

A

FALLING

CAT

C.

Fernandes

L.

Gurvits

Z.

X.

Li

May

How

does

a

falling

cat

change

her

orientation

in

midair

without

violating

the

angular

momentum

constraint

This

has

become

an

interesting

question

to

both

control

engineers

and

robotists

In

this

paper

we

address

this

problem

together

with

a

constructive

solution

First

we

show

that

a

falling

cat

problem

is

equivalent

to

the

constructive

nonlinear

controllability

problem

Thus

the

same

principle

and

algorithm

used

by

a

falling

cat

can

be

used

for

space

robotic

applications

such

as

reorientation

of

a

satellite

using

rotors

attitude

control

of

a

space

structure

using

internal

motion

and

for

other

robotic

tasks

such

as

dextrous

manipulation

with

multifingered

robotic

hands

and

nonholonomic

motion

planning

for

mobile

robots

Then

using

ideas

from

Ritz

Approximation

Theory

we

develop

a

simple

algorithm

for

motion

planning

by

a

falling

cat

Finally

we

test

the

algorithm

through

simulation

on

two

widely

accepted

models

of

a

falling

cat

It

is

interesting

to

note

that

one

set

of

simulated

trajectories

is

close

to

trajectories

used

by

a

real

cat

A

THEORY

OF

NATURAL

LEARNING

A.

Botta

May

Unsupervised

learning

is

based

on

capturing

regularities

in

data

We

formalize

the

vague

notion

of

regularity

using

the

concept

of

algorithmic

information

-LRB-

Solomonoff

Chaitin

Koppel

-RRB-

We

present

a

theory

on

how

regularities

are

induced

and

accumulated

A

generative

model

captures

a

regularity

if

it

achieves

compression

A

basic

regularity

is

a

building

block

for

hierarchical

structures

We

prove

that

a

basic

regularity

may

be

identified

as

a

local

maximum

in

compressibility

Stepwise

induction

is

a

polynomial-time

approach

to

structures

whose

basic

components

have

bound

complexity

Agents

exploring

a

universe

engage

in

active

learning

The

regularities

of

their

sensory-motor

streams

are

similar

to

Piaget

's

schemes

and

constituents

of

an

induced

ontology

We

illustrate

these

ideas

on

three

microworlds

First

are

Moore

automata

State

representations

are

constructed

incrementally

from

results

of

tests

when

in

that

state

and

from

outputs

perceived

on

the

way

to

that

state

The

second

world

contains

loosely

coupled

geometric

objects

They

are

basic

regularities

identifiable

by

stepwise

induction

In

the

third

world

the

agent

has

an

elaborate

eye

and

can

move

objects

on

a

tiled

surface

Statistical

correlations

between

sets

of

stimuli

are

induced

then

models

are

constructed

to

generate

instances

of

new

correlations

from

already

known

ones

Algorithmic

information

theory

allows

a

unified

perspective

on

many

areas

of

learning

research

We

define

analysis

as

the

separation

of

novelty

in

data

from

the

already

known

We

present

explanation

based

generalization

as

a

well

formalized

instance

of

analysis

and

constructive

induction

as

an

ill

defined

instance

We

show

EBG

to

specialize

a

theory

through

positive

examples

and

we

prove

it

a

language

independent

method

valid

beyond

the

predicate

calculus

representations

AMORTIZED

COMPLEXITY

OF

DATA

STRUCTURES

R.

Sundar

May

This

thesis

investigates

the

amortized

complexity

of

some

fundamental

data

structure

problems

and

introduces

interesting

ideas

for

proving

lower

bounds

on

amortized

complexity

and

for

performing

amortized

analysis

The

problems

are

as

follows

ffl

Dictionary

Problem

A

dictionary

is

a

dynamic

set

that

supports

searches

of

elements

and

changes

under

insertions

and

deletions

of

elements

It

is

open

whether

there

exists

a

dictionary

data

structure

that

takes

constant

amortized

time

per

operation

and

uses

space

polynomial

in

the

dictionary

size

We

prove

that

dictionary

operations

require

log-logarithmic

amortized

time

under

a

multilevel

hashing

model

that

is

based

on

Yao

's

cell

probe

model

ffl

Splay

Algorithm

's

Analysis

Splay

is

a

simple

efficient

algorithm

for

searching

binary

search

trees

devised

by

Sleator

and

Tarjan

that

uses

rotations

to

reorganize

the

tree

Tarjan

conjectured

that

Splay

takes

linear

time

to

process

deque

operation

sequences

on

a

binary

tree

and

proved

a

special

case

of

this

conjecture

called

the

Scanning

Theorem

We

prove

tight

bounds

on

the

maximum

numbers

of

various

types

of

right

rotations

in

a

sequence

of

right

rotations

performed

on

a

binary

tree

One

of

the

lower

bounds

refutes

a

conjecture

of

Sleator

We

apply

the

upper

bounds

to

obtain

a

nearly

linear

upper

bound

for

Tarjan

's

conjecture

We

give

two

new

proofs

of

the

Scanning

Theorem

one

of

which

is

a

potential-based

proof

that

solves

a

problem

of

Tarjan

ffl

Set

Equality

Problem

The

task

of

maintaining

a

dynamic

collection

of

sets

under

various

operations

arises

in

many

applications

We

devise

a

fast

data

structure

for

maintaining

sets

under

equality-tests

and

under

creations

of

new

sets

through

insertions

and

deletions

of

elements

Equality-tests

require

constant

time

and

set-creations

require

logarithmic

amortized

time

This

improves

previous

solutions

DECOMPOSITION

AND

FICTITIOUS

DOMAINS

METHODS

FOR

ELLIPTIC

BOUNDARY

VALUE

PROBLEMS

S.

V.

Nepomnyaschikh

May

Boundary

value

problems

for

elliptic

second

order

equations

in

three-dimensional

domains

with

piecewise

smooth

boundaries

are

considered

Discretization

of

the

problem

is

performed

using

a

conventional

version

of

the

finite

element

method

with

piecewise

linear

basis

functions

The

main

purpose

of

the

paper

is

the

construction

of

a

preconditioning

operator

for

the

resulting

system

of

grid

equations

The

method

is

based

on

two

approaches

decomposition

of

the

domain

into

subdomains

and

using

a

new

version

of

the

method

of

fictitious

domains

The

rate

of

convergence

of

the

corresponding

conjugate

gradient

method

is

independent

of

both

the

grid

size

and

the

number

of

subdomains

A

QUOTIENT

SPACE

HOUGH

TRANSFORM

FOR

SPACE-VARIANT

VISUAL

ATTEN

TION

A.

S.

Rojer

E.

L.

Schwartz

June

We

consider

the

problem

of

visual

attention

in

the

context

of

space-variant

machine

vision

Is

there

a

general

theoretical

and

practical

formulation

for

the

next-look

problem

to

guide

a

space-variant

sensor

to

a

rapid

choice

for

its

next

fixation

point

This

topic

is

developed

in

the

context

of

Hough

transform

methods

by

the

addition

of

a

third

space

to

the

usual

feature

and

object

spaces

considered

in

traditional

Hough

methods

This

third

space

is

a

behavioural

or

motor

space

which

is

typically

low-dimensional

with

respect

to

the

feature

and

object

spaces

For

example

the

motor

space

of

particular

interest

for

us

is

the

two-dimensional

manifold

of

monocular

eye

positions

By

collapsing

the

generalized

Hough

transform

into

a

low

dimensional

motor

space

we

show

that

it

is

possible

to

avoid

a

practical

difficulty

in

applying

Hough

transform

methods

which

is

the

exponential

dependence

of

the

accumulator

array

on

the

dimensionality

of

the

object

space

Beginning

with

a

simple

and

very

general

Bayesian

scheme

we

derive

in

stages

the

generalized

Hough

transform

as

a

special

case

Since

attentional

applications

by

their

nature

require

only

partial

knowledge

about

objects

computation

of

all

the

parameters

characterizing

a

scene

object

is

superfluous

and

wasteful

of

computational

resources

This

suggests

that

for

an

attentional

application

collapsing

the

-LRB-

large

-RRB-

object

space

onto

the

-LRB-

small

-RRB-

motor

space

provides

a

computationally

grounded

definition

of

the

term

visual

attention

We

illustrate

these

ideas

with

an

example

of

choosing

fixation

points

for

a

space-variant

sensor

in

a

machine

vision

application

for

real-time

reading

of

license

plates

of

moving

vehicles

THE

HOUGH

TRANSFORM

AS

BAYESIAN

INFERENCE

A.

S.

Rojer

E.

L.

Schwartz

June

Although

the

Hough

transform

and

its

generalizations

have

been

used

for

many

years

in

computer

vision

and

pattern

recognition

its

conceptual

grounding

has

been

largely

heuristic

We

demonstrate

here

that

the

generalized

Hough

transform

may

be

viewed

as

a

special

case

of

Bayesian

inference

Starting

from

a

simple

and

very

general

Bayesian

scheme

we

derive

in

stages

the

generalized

Hough

transform

-LRB-

of

Ballard

-RRB-

By

doing

so

we

explicate

a

series

of

assumptions

concerning

featural

independence

and

equal

a

priori

occurrence

of

objects

which

are

implicit

in

the

use

of

the

generalized

Hough

transform

When

-LRB-

if

ever

-RRB-

these

assumptions

are

satisfied

Hough

transform

methods

are

optimal

-LRB-

in

a

Bayesian

sense

-RRB-

for

object

recognition

Consideration

of

the

assumptions

also

illuminates

conditions

under

which

performance

degradation

of

the

Hough

approach

is

expected

The

goal

of

this

paper

is

not

to

yet

more

variations

on

the

Hough

transform

but

rather

to

clarify

the

implicit

assumptions

associated

with

this

methodology

and

to

suggest

future

research

in

which

these

assumptions

can

verified

or

relaxed

VIVID

REPRESENTATIONS

E.

Davis

June

This

paper

criticizes

the

widespread

idea

that

knowledge

bases

in

AI

systems

should

be

complete

and

that

representations

should

be

model-like

The

arguments

in

favor

of

such

representations

are

less

cogent

and

more

ambiguous

than

they

appear

at

first

Levesque

's

suggestion

that

representations

should

be

vivid

is

extremely

restrictive

particularly

in

its

uniform

imposition

of

a

closed-world

assumption

Spatial

representations

that

are

adequate

for

reasoning

about

a

wide

range

of

physical

phenomena

must

ultimately

either

use

complex

symbolic

reasoning

or

deal

with

partial

and

imperfect

approximations

Requiring

that

temporal

representations

be

fully

detailed

simulations

will

often

be

extremely

inefficient

Finally

a

flexible

intelligent

system

must

necessarily

deal

with

partial

information

of

all

kinds

and

the

techniques

for

carrying

out

reasoning

about

partial

information

using

complete

representations

are

very

limited

in

their

application

OPTIMALITY

CONDITIONS

AND

DUALITY

THEORY

FOR

MINIMIZING

SUMS

OF

THE

LARGEST

EIGENVALUES

OF

SYMMETRIC

MATRICES

M.

L.

Overton

R.

S.

Womersley

June

This

paper

gives

max

characterizations

for

the

sum

of

the

largest

eigenvalues

of

a

symmetric

matrix

The

elements

which

achieve

the

maximum

provide

a

concise

characterization

of

the

generalized

gradient

of

the

eigenvalue

sum

in

terms

of

a

dual

matrix

The

dual

matrix

provides

the

information

required

to

either

verify

first-order

optimality

conditions

at

a

point

or

to

generate

a

descent

direction

for

the

eigenvalue

sum

from

that

point

splitting

a

multiple

eigenvalue

if

necessary

A

model

minimization

algorithm

is

outlined

and

connections

with

the

classical

literature

on

sums

of

eigenvalues

are

explained

Sums

of

the

largest

eigenvalues

in

absolute

value

are

also

addressed

ON

THE

SUBDIFFERENTIABILITY

OF

FUNCTIONS

OF

A

MATRIX

SPECTRUM

I

MATHEMATICAL

FOUNDATIONS

J.

V.

Burke

M.

L.

Overton

June

We

consider

analytic

matrix

valued

mappings

A

C

Cn?n

and

study

the

variational

properties

of

the

spectrum

of

A

-LRB-

ffl

-RRB-

Of

particular

interest

are

ff

-LRB-

ffl

-RRB-

and

ae

-LRB-

ffl

-RRB-

respectively

the

spectral

abscissa

and

the

spectral

radius

of

A

-LRB-

ffl

-RRB-

In

this

paper

we

introduce

the

mathematical

techniques

required

for

this

analysis

We

begin

with

polynomials

and

discuss

the

bifurcation

of

the

roots

of

a

polynomial

having

analytic

coefficients

It

is

this

bifurcation

phenomenon

that

leads

to

the

nonlipschitzian

behavior

of

the

types

of

functions

that

we

wish

to

study

Puiseux-Newton

series

and

diagrams

are

then

introduced

as

a

means

for

analyzing

these

bifurcations

It

is

shown

how

these

techniques

can

be

used

to

describe

the

tangent

cone

to

certain

sets

of

stable

polynomials

Matrices

and

polynomials

are

connected

via

characteristic

polynomials

Further

properties

of

the

spectrum

of

a

matrix

A

-LRB-

-RRB-

are

obtained

from

a

block

diagonalization

of

A

-LRB-

-RRB-

where

the

kth

diagonal

block

is

an

nk

by

nk

upper

triangular

matrix

with

a

constant

diagonal

whose

value

is

an

eigenvalue

of

A

-LRB-

-RRB-

with

multiplicity

nk

By

using

results

of

Arnold

on

the

versal

deformation

of

a

matrix

we

show

how

the

results

concerning

polynomials

can

be

translated

into

into

results

about

matrices

In

the

case

that

the

block

diagonal

form

is

the

Jordan

form

the

conditions

which

are

obtained

reduce

to

conditions

on

generalized

traces

of

a

matrix

ON

THE

SUBDIFFERENTIABILITY

OF

FUNCTIONS

OF

A

MATRIX

SPECTRUM

II

SUBDIFFERENTIAL

FORMULAS

J.

V.

Burke

M.

L.

Overton

June

Variational

properties

for

the

spectral

radius

and

spectral

abscissa

of

an

analytic

matrix

valued

mapping

A

Cs

Cn?n

are

considered

A

notion

of

directional

differentiability

is

introduced

that

allows

us

to

exploit

the

perturbation

results

of

Part

I

of

this

study

Lower

bounds

for

the

directional

derivative

are

established

which

yield

formulas

for

the

directional

derivative

when

a

natural

nondegeneracy

condition

is

satisfied

These

formulas

are

interpreted

in

the

extreme

cases

where

the

eigenvalues

attaining

either

the

spectral

radius

or

the

spectral

abscissa

are

nonderogatory

or

semisimple

-LRB-

nondefective

-RRB-

We

conclude

by

investigating

the

relationship

with

the

proximal

normal

subdifferential

In

particular

it

is

shown

that

the

proximal

normal

subdifferential

is

always

nonempty

APPLICATIONS

AND

ANALYSIS

OF

PROBABILISTIC

TECHNIQUES

P.

V.

Tetali

June

The

thesis

illustrates

the

strength

of

randomness

by

applying

some

recent

probabilistic

techniques

to

solve

problems

in

number

theory

graph

theory

and

computer

science

The

first

part

of

the

thesis

is

concerned

with

random

construction

of

integer

sequences

with

certain

additive

properties

A

set

of

natural

numbers

is

called

an

asymptotic

basis

of

order

k

if

every

number

-LRB-

sufficiently

large

-RRB-

can

be

expressed

as

a

sum

of

k

distinct

numbers

from

the

set

We

prove

that

for

every

fixed

k

there

exists

an

asymptotic

basis

of

order

k

such

that

the

number

of

representations

of

n

is

Theta

-LRB-

logn

-RRB-

The

case

k

was

proved

in

by

Paul

Erdos

The

second

part

deals

with

analysis

of

random

walks

on

graphs

Random

walks

on

graphs

have

been

known

to

have

interesting

analogies

in

electrical

networks

A

precise

characterization

of

effective

resistance

in

electrical

networks

is

provided

in

this

thesis

in

terms

of

random

walks

on

the

underlying

graphs

The

interpretation

of

effective

resistance

yields

interesting

new

results

and

new

proofs

for

some

known

results

The

main

result

here

is

an

exact

formula

for

the

hitting

time

between

two

vertices

in

terms

of

the

effective

resistances

in

the

network

settling

an

open

question

This

is

much

in

the

spirit

of

the

commute

time

result

by

Ashok

Chandra

et

al.

The

final

part

of

the

thesis

addresses

problems

involving

Discrepancy

Discrepancy

is

a

combinatorial

problem

that

arises

in

various

contexts

such

as

communication

complexity

in

multi-party

protocols

quasi-randomness

in

graphs

and

hypergraphs

hypergraph

coloring

and

the

Gale-Berlekamp

switching

game

In

k-dimensions

the

game

consists

of

an

nXn

array

A

-LRB-

of

size

nk

-RRB-

of

lights

There

are

kn

switches

each

controlling

a

hyperplane

of

nk

lights

Each

switch

when

thrown

changes

each

light

in

its

control

from

on

to

off

or

from

off

to

on

Discrepancy

is

defined

as

the

maximum

difference

between

the

number

of

lights

on

and

off

that

one

can

obtain

given

any

initial

configuration

for

the

lights

It

follows

from

a

result

of

Erdos

and

Spencer

that

discrepancy

Theta

-LRB-

n

-LRB-

k

-RRB-

-RRB-

This

result

however

is

existential

due

to

its

critical

use

of

randomness

An

optimal

deterministic

sequential

and

an

NC

algorithm

are

given

in

this

thesis

The

basic

idea

is

to

use

Spencer

's

method

of

conditional

expectation

to

remove

randomness

But

the

crucial

part

of

the

derandomization

is

in

justifying

the

efficient

computation

of

the

conditional

expectations

involved

For

the

NC

algorithm

we

prove

that

independent

random

setting

for

the

switches

works

ADDITIVE

SCHWARZ

METHODS

FOR

ELLIPTIC

FINITE

ELEMENT

PROBLEMS

IN

THREE

DIMENSIONS

M.

Dryja

O.

B.

Widlund

June

Many

domain

decomposition

algorithms

and

certain

multigrid

methods

can

be

described

and

analyzed

as

additive

Schwarz

methods

When

designing

and

analyzing

domain

decomposition

methods

we

encounter

special

difficulties

in

the

case

of

three

dimensions

and

if

the

coefficients

are

discontinuous

and

vary

over

a

large

range

In

this

paper

we

first

introduce

a

general

framework

for

Schwarz

methods

Three

classes

of

applications

are

then

considered

certain

wire

basket

based

iterative

substructuring

methods

Neumann-Neumann

algorithms

with

low

dimensional

global

subspaces

and

a

modified

form

of

a

multilevel

algorithm

introduced

by

Bramble

Pasciak

and

Xu

EFFICIENT

ALGORITHMS

FOR

CYCLIC

SCHEDULING

F.

Gasperoni

U.

Schwiegelshohn

July

This

work

addresses

the

problem

of

non-preemptively

scheduling

a

cyclic

set

of

interdependent

operations

representing

for

instance

a

program

loop

when

p

identical

processors

are

available

For

p

we

give

a

simple

efficient

polynomial

time

algorithm

producing

optimum

results

When

p

the

problem

becomes

NP-hard

and

a

slight

modification

of

our

algorithm

generates

provably

close

to

optimum

results

AN

OPTIMAL

SCHEDULING

ALGORITHM

WITH

A

COMPETITIVE

FACTOR

FOR

REAL

TIME

SYSTEMS

G.

Koren

D.

Shasha

July

We

consider

real-time

systems

in

which

the

value

of

a

task

is

proportional

to

its

computation

time

The

system

obtains

the

value

of

a

given

task

if

the

task

completes

by

its

deadline

Otherwise

the

system

obtains

no

value

for

the

task

When

such

a

system

is

underloaded

-LRB-

i.e.

there

exists

a

schedule

for

which

all

tasks

meet

their

deadlines

-RRB-

Dertouzos

showed

that

the

earliest

deadline

first

algorithm

will

achieve

of

the

possible

value

We

consider

the

case

of

a

possibly

overloaded

system

and

present

an

algorithm

which

behaves

like

the

earliest

deadline

first

algorithm

when

the

system

is

underloaded

obtains

at

least

of

the

maximum

value

that

an

optimal

clairvoyant

algorithm

could

obtain

even

when

the

system

is

overloaded

We

implement

our

algorithm

with

an

amortized

cost

of

O

-LRB-

log

n

-RRB-

time

per

task

where

n

bounds

the

number

of

tasks

in

the

system

at

any

instant

ONLINE

ALGORITHMS

FOR

FINGER

SEARCHING

R.

Cole

A.

Raghunathan

August

A

well-known

technique

for

speeding

up

access

into

search

structures

is

to

maintain

fingers

that

point

to

various

locations

of

the

search

structure

The

advantage

of

maintaining

fingers

is

that

accessing

information

near

a

finger

is

normally

faster

than

the

usual

method

of

access

In

this

paper

we

consider

the

problem

of

choosing

locations

in

a

large

search

structure

at

which

to

maintain

fingers

In

particular

we

consider

a

server

problem

in

which

k

servers

move

along

a

line

segment

of

length

m

where

m

is

the

number

of

keys

in

the

search

structure

Since

fingers

may

be

arbitrarily

copied

we

allow

a

server

to

jump

or

fork

to

a

location

currently

occupied

by

another

server

We

present

online

algorithms

and

analyze

their

competitiveness

We

show

that

the

case

k

behaves

differently

from

the

case

k

by

showing

that

there

is

a

algorithm

for

k

that

never

forks

its

fingers

For

k

we

show

that

any

online

algorithm

that

does

not

fork

its

fingers

can

be

at

most

-LRB-

-RRB-

competitive

By

contrast

in

the

main

result

of

the

paper

we

show

that

for

k

there

is

an

online

algorithm

that

forks

and

is

constant

competitive

-LRB-

independent

of

m

the

size

of

the

search

structure

-RRB-

Our

algorithm

is

simple

and

implementable

although

our

analysis

is

complicated

The

existence

of

a

constant

competitive

algorithm

for

k

is

left

as

an

open

question

THE

EXPECTED

ADVANTAGE

OF

ASYNCHRONY

R.

Cole

O.

Zajicek

September

This

paper

studies

the

implicit

costs

of

synchronization

and

the

advantage

that

may

be

gained

by

avoiding

synchronization

in

asynchronous

environments

An

asynchronous

generalization

of

the

PRAM

model

called

the

APRAM

model

is

used

and

appropriate

complexity

measures

are

defined

The

advantage

asynchrony

provides

is

illustrated

by

analyzing

two

algorithms

a

parallel

summation

algorithm

which

proceeds

along

an

implicit

complete

binary

tree

and

a

recursive

doubling

algorithm

which

proceeds

along

a

linked

list

SEGMENTATION

AND

SURFACE-BASED

MODELING

OF

OBJECTS

IN

THREE

DIMENSIONAL

BIOMEDICAL

IMAGES

A.

Kalvin

September

The

rapid

development

of

technologies

for

imaging

the

human

body

has

led

to

a

growing

interest

in

the

extraction

and

analysis

of

objects

in

biomedical

images

for

applications

in

fields

such

as

clinical

medicine

biomedical

research

and

physical

anthropology

This

dissertation

examines

the

problem

of

creating

surface-based

geometric

models

of

biomedical

objects

that

are

suitable

for

analysis

through

visualization

mensuration

and

manipulation

This

is

a

two-stage

problem

First

the

objects

are

identified

by

segmenting

the

image

into

regions

of

interest

and

then

surface-based

models

of

the

objects

are

created

We

discuss

the

issues

of

segmentation

and

surface

construction

and

introduce

the

following

new

methods

for

solving

these

problems

First

we

present

the

MLO

algorithm

a

general-purpose

domain-independent

segmentation

algorithm

that

has

been

applied

successfully

to

identify

skulls

in

CT

images

the

ventricle

walls

of

the

heart

in

MR

images

brain

ventricles

in

CT

images

and

carotid

arteries

in

MR

angiography

images

It

uses

an

iterative

cooperative

procedure

to

segment

an

image

by

optimizing

a

cost

function

To

achieve

a

fast

segmentation

a

coarse-to-fine

strategy

is

employed

using

a

multiresolution

pyramid

The

GRG

algorithm

is

a

model-driven

special-purpose

algorithm

for

identifying

thin

bone

in

CT

head

images

The

algorithm

developed

specifically

for

craniofacial

surgical

planning

uses

anatomical

knowledge

in

the

segmentation

process

and

can

handle

the

abnormal

anatomy

of

craniofacial

patients

It

successfully

finds

most

of

the

thin

bone

that

can

not

be

found

using

previous

methods

ALLIGATOR

is

a

surface

construction

algorithm

that

creates

models

using

the

winged-edge

data

structure

of

Baumgart

enabling

efficient

access

to

the

topological

and

geometric

information

of

the

surfaces

and

permitting

efficient

topologically

consistent

modifications

to

the

representations

Unlike

previous

surface

construction

algorithms

ALLIGATOR

is

suitable

not

just

for

visualizing

biomedical

objects

but

for

measuring

and

manipulating

them

as

well

Another

important

feature

of

ALLIGATOR

is

that

it

uses

an

adaptive

facemerging

process

to

create

surface

models

that

are

significantly

more

concise

in

terms

of

vertices

edges

and

faces

than

the

models

produced

by

other

surface

construction

algorithms

ATTITUDE

CONTROL

OF

SPACE

PLATFORM/MANIPULATOR

SYSTEM

USING

INTER

NAL

MOTION

C.

Fernandes

L.

Gurvits

Z.

Li

September

Attitude

control

of

a

space

platform/manipulator

system

using

internal

motion

is

an

example

of

a

Nonholonomic

Motion

Planning

-LRB-

NMP

-RRB-

problem

arising

from

symmetry

and

conservation

laws

Common

to

NMP

problems

are

that

an

admissible

configuration

space

path

is

constrained

to

a

given

nonholonomic

distribution

We

formulate

the

dynamic

equations

of

a

system

consisting

of

a

F

Puma

like

manipulator

attached

to

a

space

platform

-LRB-

e.g.

a

space

station

or

a

satellite

-RRB-

as

a

NMP

problem

and

discuss

controllability

of

the

system

Then

we

describe

the

application

of

a

simple

algorithm

for

obtaining

approximate

optimal

solutions

We

conclude

with

a

description

of

simulation

software

implementing

the

algorithm

and

simulation

results

for

two

experiments

FOUNDATIONS

OF

NONHOLONOMIC

MOTION

PLANNING

C.

Fernandes

L.

Gurvits

Z.

Li

September

Nonholonomic

Motion

Planning

-LRB-

NMP

-RRB-

problems

arise

not

only

from

classic

nonholonomic

constraints

-LRB-

e.g.

rolling

contact

-RRB-

but

also

from

symmetries

and

conservation

laws

of

holonomic

mechanic

-LRB-

or

biological

-RRB-

systems

In

real

life

NMP

systems

exist

in

abundance

a

-LRB-

kinematic

-RRB-

unicycle

a

front-wheel-drive

cart

a

system

of

two

contacting

bodies

with

rolling

constraint

a

system

consisted

of

a

dextrous

robotic

hand

and

an

object

to

be

manipulated

a

spring-board

diver

an

astronaut

a

falling-cat

a

free-flying

robot

with

a

floating

base

a

satellite

with

a

number

of

rotors

a

space

station

and

the

Hubble

Space

Telescope

Common

to

these

systems

are

that

an

admissible

configuration

space

path

is

constrained

to

a

given

nonholonomic

distribution

Thus

NMP

deals

with

the

problem

of

optimal

path

planning

subject

to

a

nonholonomic

distribution

and

possibly

additional

holonomic

constraints

e.g.

collision

avoidance

In

this

preliminary

report

we

describe

our

recent

work

in

NMP

First

we

study

examples

of

NMP

problems

examine

the

constraints

or

symmetries

associated

with

these

systems

and

show

the

derivation

of

nonholonomic

distributions

We

transform

a

NMP

problem

into

a

nonlinear

control

problem

so

that

analytic

techniques

from

nonlinear

control

theory

can

be

used

Second

we

study

the

existence

of

motion

using

Frobenius

theory

and

Chow

's

theorem

We

also

develop

several

new

results

for

checking

controllability

for

a

class

of

NMP

systems

Third

we

apply

variational

principles

to

study

optimal

trajectories

of

NMP

We

show

that

an

optimal

solution

necessarily

satisfies

Hamilton

's

equation

for

some

well-defined

Hamiltonian

function

Furthermore

we

prove

the

equivalence

of

two

different

formulations

of

NMP

Fourth

we

present

a

numerical

algorithm

called

the

Basis

Algorithm

for

computing

approximate

optimal

solutions

of

NMP

We

show

that

the

objective

function

is

locally

convex

and

has

desirable

convergence

property

Finally

we

describe

a

simulation

environment

developed

at

our

laboratory

for

the

study

of

NMP

along

with

simulation

results

obtained

using

the

Basis

Algorithm

STABILITY

PROOF

OF

RAIBERT

'S

FOUR-LEGGED

HOPPER

IN

BOUNDING

GAIT

A.

Neishtadt

Z.

Li

September

M.

Raibert

and

his

co-workers

have

designed

and

built

a

four-legged

hopper

or

a

quadruped

Using

the

notion

of

virtual

legs

and

a

control

algorithm

they

have

achieved

stable

hopping

motion

of

the

system

in

bounding

gait

as

well

as

in

trotting

and

pacing

gaits

In

this

paper

we

provide

a

proof

of

stability

of

the

system

The

mathematical

tools

we

use

in

the

proof

derives

from

dynamical

system

theory

in

particular

perturbation

techniques

The

main

results

of

the

paper

are

as

follows

When

the

touch-down

angle

is

small

there

is

exactly

one

periodic

solution

for

each

fixed

energy

level

of

the

Hamiltonian

system

j

is

a

necessary

-LRB-

and

also

sufficient

when

the

touch-down

angle

is

small

-RRB-

condition

for

Hamiltonian

stability

of

the

system

where

j

I

is

a

dimensionless

parameter

of

the

system

For

fixed

levels

of

leg

dissipation

and

thrusting

there

exists

a

unique

periodic

solution

along

which

energy

change

is

balanced

The

system

is

asymptotically

stable

with

respect

to

change

in

energy

With

a

damping

term

from

the

attitude

control

law

added

the

system

becomes

asymptotically

stable

DIFFERENTIAL

PROPERTIES

OF

EIGENVALUES

J.

Burke

M.

Overton

September

We

define

and

study

a

directional

derivative

for

two

functions

of

the

spectrum

of

an

analytic

matrix

valued

function

These

are

the

maximum

real

part

and

the

maximum

modulus

of

the

spectrum

Results

are

first

obtained

for

the

roots

of

polynomials

with

analytic

coefficients

by

way

of

Puiseux-Newton

series

In

this

regard

the

primary

analytic

tool

is

the

so

called

Puiseux-Newton

diagram

These

results

are

then

translated

into

the

context

of

matrices

Precise

results

are

obtained

when

the

eigenvalues

that

achieve

the

maximum

value

for

the

function

under

consideration

are

all

either

nondefective

or

nonderogatory

In

the

defective

derogatory

cases

a

general

lower

bound

for

the

directional

derivative

is

given

which

in

particular

describes

those

directions

in

which

the

directional

derivative

attains

an

infinite

value

AN

ADDITIVE

SCHWARZ

METHOD

FOR

THE

P-VERSION

FINITE

ELEMENT

METHOD

L.

Pavarino

September

The

additive

Schwarz

method

was

originally

proposed

for

the

h-version

finite

element

method

for

elliptic

problems

In

this

paper

we

apply

it

to

the

p-version

in

which

increased

accuracy

is

achieved

by

increasing

the

degree

of

the

elements

while

the

mesh

is

fixed

We

obtain

a

constant

bound

independent

of

p

for

the

condition

number

of

the

iteration

operator

in

two

and

three

dimensions

The

result

holds

for

linear

self

adjoint

second

order

elliptic

problems

and

for

quadrilateral

elements

SOME

SCHWARZ

METHODS

FOR

SYMMETRIC

AND

NONSYMMETRIC

ELLIPTIC

PROBLEMS

O.

Widlund

September

This

paper

begins

with

an

introduction

to

additive

and

multiplicative

Schwarz

methods

A

two-level

method

is

then

reviewed

and

a

new

result

on

its

rate

of

convergence

is

established

for

the

case

when

the

overlap

is

small

Recent

results

by

Xuejun

Zhang

on

multi-level

Schwarz

methods

are

formulated

and

discussed

The

paper

is

concluded

with

a

discussion

of

recent

joint

results

with

Xiao-Chuan

Cai

on

nonsymmetric

and

indefinite

problems

MULTILEVEL

ADDITIVE

SCHWARZ

METHODS

X.

Zhang

September

We

consider

the

solution

of

the

algebraic

system

of

equations

which

result

from

the

discretization

of

elliptic

equations

A

class

of

multilevel

algorithms

are

studied

using

the

additive

Schwarz

framework

We

establish

that

in

the

general

case

the

condition

number

of

the

iterative

operator

grows

at

most

linearly

with

the

number

of

levels

The

bound

is

independent

of

the

mesh

sizes

and

the

number

of

levels

under

the

assumption

of

the

equation

This

is

an

improvement

on

Dryja

and

Widlund

's

result

on

a

multilevel

additive

Schwarz

algorithm

as

well

as

Bramble

Pasciak

and

Xu

's

result

on

the

BPX

algorithm

DOMAIN

DECOMPOSITION

ALGORITHMS

FOR

THE

BIHARMONIC

DIRICHLET

PROB

LEM

X.

Zhang

September

We

consider

additive

Schwarz

methods

for

the

biharmonic

Dirichlet

problem

and

show

that

the

algorithms

have

optimal

convergence

properties

for

some

conforming

finite

elements

Some

multilevel

methods

are

also

discussed

STUDIES

IN

DOMAIN

DECOMPOSITION

MULTILEVEL

METHODS

AND

THE

BIHAR

MONIC

DIRICHLET

PROBLEM

X.

Zhang

September

A

class

of

multilevel

methods

for

second

order

problems

is

considered

in

the

additive

Schwarz

framework

It

is

established

that

in

the

general

case

the

condition

number

of

the

iterative

operator

grows

at

most

linearly

with

the

number

of

levels

The

bound

is

independent

of

the

mesh

sizes

and

the

number

of

levels

under

a

regularity

assumption

This

is

an

improvement

of

a

result

by

Dryja

and

Widlund

on

a

multilevel

additive

Schwarz

algorithm

and

the

theory

given

by

Bramble

Pasciak

and

Xu

for

the

BPX

algorithm

Additive

Schwarz

and

iterative

substructuring

algorithms

for

the

biharmonic

equation

are

also

considered

These

are

domain

decomposition

methods

which

have

previously

been

developed

extensively

for

second

order

elliptic

problems

by

Bramble

Pasciak

and

Schatz

Dryja

and

Widlund

and

others

Optimal

convergence

properties

are

established

for

additive

Schwarz

algorithms

for

the

biharmonic

equation

discretized

by

certain

conforming

finite

elements

The

number

of

iterations

for

the

iterative

substructuring

methods

grows

only

as

the

logarithm

of

the

number

of

degrees

of

freedom

associated

with

a

typical

subregion

It

is

also

demonstrateed

that

it

is

possible

to

simplify

the

basic

algorithms

This

leads

to

a

decrease

of

the

cost

but

not

of

the

rate

of

convergence

of

the

iterative

methods

In

the

analysis

new

tools

are

developed

to

deal

with

Hermitian

elements

Certain

new

inequalities

for

discrete

norms

for

finite

element

spaces

are

also

used

EFFICIENT

LOOP-LEVEL

PARALLELISM

IN

ADA

M.

Hind

September

Parallelism

in

scientific

applications

can

most

often

be

found

at

the

loop

level

Although

Ada

supports

parallelism

via

the

task

construct

its

coarseness

renders

it

unsuitable

for

this

light-weight

parallelism

In

this

work

we

propose

Ada

constructs

to

achieve

efficient

loop-level

parallelism

in

ANSI-Ada

This

is

accomplished

in

two

steps

First

we

present

an

idiom

that

allows

the

specification

of

light-weight

tasks

Second

we

give

an

efficient

implementation

of

this

idiom

that

is

considerably

more

efficient

than

a

standard

Ada

task

In

addition

we

present

an

idiom

that

makes

the

fetch

and

add

synchronization

primitive

available

at

the

Ada

level

Our

implementation

of

this

idiom

is

more

efficient

in

both

time

and

space

than

previous

results

In

addition

to

providing

universal

synchronization

using

fetch

and

add

simplifies

program

analysis

-LRB-

e.g.

proving

the

absence

of

race

conditions

in

the

implementation

of

a

parallel

algorithm

-RRB-

Since

all

these

idioms

are

written

in

standard

Ada

they

maintain

the

portability

that

is

central

to

the

mandated

uses

of

the

language

ON

SHAPE

OPTIMIZING

THE

RATIO

OF

THE

FIRST

TWO

EIGENVALUES

OF

THE

LAPLACIAN

J.

Haeberly

October

We

investigate

numerically

a

conjecture

of

Payne

Polya

and

Weinberger

The

conjecture

asserts

that

the

ratio

of

the

first

two

eigenvalues

of

the

Laplacian

on

a

bounded

domain

of

the

plane

with

Dirichlet

boundary

conditions

reaches

its

minimum

value

precisely

when

is

a

disk

A

crucial

feature

of

this

problem

is

the

loss

of

smoothness

of

the

objective

function

at

the

solution

The

following

results

form

the

core

of

our

numerical

treatment

First

we

construct

finite

dimensional

families

of

deformations

of

a

disk

equipped

with

a

uniform

triangulation

This

permits

the

formulation

of

a

discrete

model

of

the

problem

via

finite

element

techniques

Second

we

build

on

the

work

of

M.

Overton

to

derive

optimality

conditions

in

terms

of

Clarke

's

generalized

gradients

for

nonsmooth

functions

These

ideas

are

then

combined

into

an

algorithm

and

implemented

in

Fortran

NEW

THEORETICAL

AND

COMPUTATIONAL

RESULTS

FOR

REGULAR

LANGUAGES

C.

Chang

R.

Paige

October

We

show

how

to

turn

a

regular

expression

into

an

O

-LRB-

s

-RRB-

space

representation

of

McNaughton

and

Yamada

's

NFA

where

s

is

the

number

of

NFA

states

The

standard

adjacency

list

representation

of

McNaughton

and

Yamada

's

NFA

takes

up

s

space

in

the

worst

case

The

adjacency

list

representation

of

the

NFA

produced

by

Thompson

takes

up

between

and

space

where

r

s

in

general

and

can

be

arbitrarily

larger

than

s.

Given

any

set

T

of

NFA

states

our

representation

can

be

used

to

compute

the

set

N

of

states

one

transition

away

from

the

states

in

T

in

optimal

time

O

-LRB-

jT

j

jN

j

-RRB-

McNaughton

and

Yamada

's

NFA

requires

-LRB-

jT

j

jN

j

-RRB-

in

the

worst

case

Using

Thompson

's

NFA

the

equivalent

calculation

requires

-LRB-

r

-RRB-

time

in

the

worst

case

An

implementation

of

our

NFA

representation

confirms

that

it

takes

up

an

order

of

magnitude

less

space

than

McNaughton

and

Yamada

's

machine

An

implementation

to

produce

a

DFA

from

our

NFA

representation

by

subset

construction

shows

linear

and

quadratic

speedups

over

subset

construction

starting

from

both

Thompson

's

and

McNaughton

and

Yamada

's

NFA

's

It

also

shows

that

the

DFA

produced

from

our

NFA

is

as

much

as

one

order

of

magnitude

smaller

than

DFA

's

constructed

from

the

two

other

NFA

's

A

MINIATURIZED

ACTIVE

VISION

SYSTEM

B.

B.

Bederson

R.

S.

Wallace

E.

L.

Schwartz

November

We

have

developed

a

prototype

miniaturized

active

vision

system

whose

sensor

architecture

is

based

on

a

logarithmic

structured

space-variant

pixel

geometry

This

system

integrates

a

CCD

sensor

mini

pan-tilt

actuator

controller

general

purpose

processor

and

display

Due

to

the

ability

of

space-variant

sensors

to

cover

large

work-spaces

yet

provide

high

acuity

with

an

extremely

small

number

of

pixels

space-variant

active

vision

system

architectures

provide

the

potential

for

radical

reductions

in

system

size

and

cost

In

this

paper

we

describe

a

prototype

space-variant

active

vision

system

which

performs

such

tasks

as

connected

components

analysis

and

motion

tracking

The

potential

application

domains

for

systems

of

this

type

include

vision

systems

for

mobile

robots

and

robot

manipulators

traffic

monitoring

systems

security

and

surveillance

and

consumer

video

communications

SPACE-VARIANT

IMAGE

PROCESSING

R.

S.

Wallace

P.

Ong

B.

B.

Bederson

E.

L.

Schwartz

November

Space-variant

sensors

have

nonuniform

sampling

across

the

image

plane

Partially

motivated

by

the

observation

that

human

vision

is

strongly

space-variant

yielding

an

image

compression

for

the

human

system

that

is

estimated

to

be

as

much

as

four

orders

of

magnitude

a

number

of

research

groups

have

been

experimenting

with

space-variant

sensors

Such

systems

cover

wide

solid

angles

yet

maintain

high

acuity

in

their

central

regions

Implementation

of

space-variant

systems

pose

at

least

two

outstanding

problems

First

such

a

system

must

be

active

in

order

to

utilize

its

high

acuity

region

second

there

are

fascinating

image

processing

problems

introduced

by

the

non-uniform

pixel

size

shape

and

connectivity

Familiar

image

processing

operations

such

as

connected

components

convolution

template

matching

and

even

image

translation

take

on

new

and

different

forms

when

defined

on

space-variant

arrays

The

present

paper

provides

a

general

method

for

space-variant

image

processing

based

on

a

connectivity

graph

which

represents

the

neighbor-relations

in

an

arbitrarily

structured

sensor

We

illustrate

this

approach

with

the

following

applications

ffl

Connected

components

is

reduced

to

its

graph

theoretic

counterpart

We

illustrate

this

on

a

logmap

sensor

which

possesses

a

difficult

topology

due

to

the

branch

cut

associated

with

the

complex

logarithm

function

ffl

We

show

how

to

write

local

image

operators

in

the

connectivity

graph

that

are

independent

of

the

sensor

geometry

and

solve

a

sensor

calibration

problem

with

these

operations

ffl

We

relate

the

connectivity

graph

to

pyramids

over

irregular

tessalations

and

implement

a

local

binarization

operator

in

a

pyramid

ffl

Finally

we

expand

the

connectivity

graph

into

a

structure

we

call

a

translation

graph

representing

the

effects

of

translation

in

space-variant

image

sensors

Using

the

translation

graph

we

define

an

efficient

algorithm

for

translation

in

the

logmap

image

and

solve

the

template

matching

problem

for

space-variant

images

Because

of

the

very

small

number

of

pixels

typical

of

logarithmic

structured

space-variant

arrays

the

connectivity

graph

approach

to

image

processing

is

suitable

for

real-time

implementation

and

provides

a

generic

solution

to

a

wide

range

of

image

processing

applications

with

space-variant

sensors

A

WAVELET

BASED

SPACE-TIME

ADAPTIVE

NUMERICAL

METHOD

FOR

PARTIAL

DIFFERENTIAL

EQUATIONS

E.

Bacry

S.

Mallat

November

We

describe

a

time

and

space

adaptive

numerical

method

for

solving

partial

differential

equations

based

on

wavelet

orthonormal

bases

The

multiresolution

structure

of

wavelet

orthonormal

bases

provide

a

simple

approach

to

adapt

computation

refinements

to

the

local

regularity

of

the

solution

High

resolution

computations

are

performed

only

in

regions

where

singularities

or

sharp

transitions

occur

For

many

evolution

equations

to

maintain

the

stability

and

precision

of

the

numerical

scheme

it

is

necessary

to

adapt

the

time

steps

to

the

spatial

resolution

We

describe

an

algorithm

that

modifies

the

time

discretization

at

each

resolution

depending

upon

the

properties

of

the

partial

differential

equation

The

stability

of

this

space-time

adaptive

scheme

is

studied

for

the

heat

equation

and

the

linear

advection

equation

We

explain

how

this

algorithm

applies

to

the

one-dimensional

Burgers

equation

with

periodic

boundary

conditions

Numerical

results

on

the

precision

and

complexity

of

the

algorithm

are

given

CHARACTERIZATION

OF

SIGNALS

FROM

MULTISCALE

EDGES

S.

Mallat

S.

Zhong

December

A

multiscale

Canny

edge

detection

is

equivalent

to

finding

the

local

maxima

of

a

wavelet

transform

We

study

the

properties

of

multiscale

edges

through

the

wavelet

formalism

For

pattern

recognition

one

often

needs

to

discriminate

different

types

of

edges

We

show

that

the

evolution

of

wavelet

local

maxima

across

scales

characterize

the

local

shape

of

irregular

structures

Numerical

descriptors

of

edge

types

are

derived

The

completeness

of

a

multiscale

edge

representation

is

also

studied

We

describe

an

algorithm

that

reconstructs

a

close

approximation

of

one

and

two-dimensional

signals

from

their

multiscale

edges

For

images

the

reconstruction

errors

are

below

our

visual

sensitivity

As

an

application

we

implement

a

compact

image

coding

algorithm

that

selects

important

edges

and

compresses

the

image

data

by

factors

over

CORTICAL

HYPERCOLUMNS

AND

THE

TOPOLOGY

OF

RANDOM

ORIENTATION

MAPS

E.

Schwartz

A.

Rojer

December

If

a

set

of

points

is

assigned

a

random

choice

of

orientations

and

then

is

locally

smoothed

patterns

appear

consisting

of

orientation

vortices

containing

central

regions

of

weak

amplitude

This

pattern

is

reminiscent

of

the

puff-extra-puff

pattern

of

orientation

tuning

in

monkey

visual

cortex

and

of

the

pin-wheels

that

have

been

recently

observed

in

cat

area

We

show

in

this

paper

that

the

formation

of

such

patterns

is

a

consequence

of

the

topology

-LRB-

non-retraction

of

-RRB-

and

stochastic

properties

of

random

orientation

distributions

These

observations

provide

insight

into

experimental

theoretical

and

descriptive

aspects

of

functional

architecture

in

visual

cortex

Specifically

-RRB-

Observation

of

vortex

structure

in

any

visually

excitable

neural

tissue

must

be

evaluated

in

the

light

of

the

hypothesis

that

these

patterns

are

readily

formed

from

random

orientation

distributions

This

is

particularly

problematic

for

observational

techniques

which

bin

together

local

neuronal

orientation

response

-LRB-

e.g.

multiple

unit

recording

optical

dye/blood

flow

-RRB-

We

show

that

similar

patterns

could

in

principle

be

artifactually

observed

in

the

retina

LGN

or

any

other

visually

responsive

tissue

-RRB-

Since

observed

hypercolumn

patterns

in

cat

and

monkey

cortex

are

similar

to

noise

patterns

in

orientation

maps

it

is

possible

that

the

developmental

specification

of

the

brain

for

creating

hypercolumns

need

be

nothing

more

than

a

local

correlation

of

orientation

tuning

in

an

otherwise

random

or

weakly

correlated

map

-RRB-

Since

similar

applications

of

-LRB-

band-pass

-RRB-

filtered

noise

can

be

shown

to

accurately

reproduce

the

ocular

dominance

column

patterns

of

cats

and

monkeys

it

appears

that

the

columnar

structure

of

visual

cortex

in

higher

vertebrates

may

be

described

most

economically

as

the

result

of

a

Wiener

process

a

linear

filter

applied

to

an

array

of

random

variables

AN

OPTIMAL

ON-LINE

SCHEDULING

ALGORITHM

FOR

OVERLOADED

REAL-TIME

SYSTEMS

G.

Koren

D.

Shasha

January

Every

task

in

a

real-time

system

has

a

deadline

by

which

time

it

should

complete

and

a

value

that

it

obtains

only

if

it

completes

by

its

deadline

The

problem

is

to

design

an

on-line

scheduling

algorithm

-LRB-

i.e.

the

scheduler

has

no

knowledge

of

a

task

until

it

is

released

-RRB-

that

maximizes

the

obtained

value

When

such

a

system

is

underloaded

-LRB-

i.e.

there

exists

a

schedule

for

which

all

tasks

meet

their

deadlines

-RRB-

Dertouzos

showed

that

the

earliest

deadline

first

algorithm

will

achieve

of

the

possible

value

Locke

showed

that

earliest

deadline

first

performs

very

badly

when

the

system

is

overloaded

and

proposed

heuristics

to

deal

with

overload

Baruah

et

al.

showed

that

the

best

that

an

on-line

algorithm

can

guarantee

is

-LRB-

pk

-RRB-

of

the

value

that

an

offline

-LRB-

clairvoyant

-RRB-

algorithm

can

obtain

where

k

is

the

ratio

between

the

highest

value

density

and

the

lowest

value

density

task

in

the

system

-LRB-

where

the

value

density

of

a

task

is

its

value

divided

by

its

computation

time

-RRB-

This

paper

presents

three

results

ffl

An

on-line

algorithm

that

achieves

the

above

best

possible

guarantee

when

computation

time

is

known

exactly

when

the

task

is

released

and

a

task

obtains

no

value

if

it

completes

after

its

deadline

-LRB-

the

model

studied

by

Baruah

et

al.

-RRB-

The

algorithm

also

obtains

of

the

possible

value

when

the

system

is

underloaded

ffl

The

same

guarantee

in

certain

situations

where

tasks

still

obtain

some

value

if

they

complete

after

their

deadlines

ffl

A

weaker

guarantee

of

-LRB-

pk

-RRB-

-LRB-

ffl?k

-RRB-

-LRB-

pk

-RRB-

of

the

value

of

a

clairvoyant

algorithm

when

the

exact

computation

time

of

a

task

is

not

given

upon

its

release

That

is

for

every

task

T

an

upper

bound

on

its

possible

computation

time

denoted

by

cmax

is

given

The

actual

computation

time

of

T

denoted

by

c

satisfies

-LRB-

ffl

-RRB-

cmax

c

cmax

MULTIPLICATIVE

SCHWARZ

ALGORITHMS

FOR

SOMENONSYMMETRIC

AND

INDEF

INITE

PROBLEMS

X.-C

Cai

O.

Widlund

February

The

classical

Schwarz

alternating

method

has

recently

been

generalized

in

several

directions

This

effort

has

resulted

in

a

number

of

new

powerful

domain

decomposition

methods

for

elliptic

problems

in

new

insight

into

multigrid

methods

and

in

the

development

of

a

very

useful

framework

for

the

analysis

of

a

variety

of

iterative

methods

Most

of

this

work

has

focused

on

positive

definite

symmetric

problems

In

this

paper

a

general

framework

is

developed

for

multiplicative

Schwarz

algorithms

for

nonsymmetric

and

indefinite

problems

Several

applications

are

then

discussed

including

two

and

multi-level

Schwarz

methods

and

iterative

substructuring

algorithms

Some

new

results

on

additive

Schwarz

methods

are

also

presented

SHORTEST

PATHS

FOR

LINE

SEGMENTS

C.

Icking

G.

Rote

E.

Welzl

C.

Yap

February

We

study

the

problem

of

shortest

paths

for

a

line

segment

in

the

plane

As

a

measure

of

the

distance

traversed

by

a

path

we

take

the

average

curve

length

of

the

orbits

of

prescribed

points

on

the

line

segment

This

problem

is

nontrivial

even

in

free

space

-LRB-

i.e.

in

the

absence

of

obstacles

-RRB-

We

characterize

all

shortest

paths

of

the

line

segment

moving

in

free

space

under

the

measure

the

average

orbit

length

of

the

two

endpoints

The

problem

of

optimal

motion

has

been

solved

by

Gurevich

and

also

by

Dubovitskij

who

calls

it

Ulam

's

problem

Unlike

previous

solutions

our

basic

tool

is

Cauchy

's

surface-area

formula

This

new

approach

is

relatively

elementary

and

yields

new

insights

SEMANTIC

ANALYSES

FOR

STORAGE

MANAGEMENT

OPTIMIZATIONS

IN

FUNC

TIONAL

LANGUAGE

IMPLEMENTATIONS

Y.

G.

Park

February

One

of

the

major

overheads

in

implementing

functional

languages

is

the

storage

management

overhead

due

to

dynamic

allocation

and

automatic

reclamation

of

indefinite-extent

storage

This

dissertation

investigates

the

problems

of

statically

inferring

lifetime

information

about

dynamically-allocated

objects

in

higher-order

polymorphic

functional

languages

both

strict

and

non-strict

and

of

applying

that

information

to

reduce

the

storage

management

overhead

We

have

developed

a

set

of

compile-time

semantic

analyses

for

a

higher-order

monomorphic

strict

functional

language

based

on

denotational

semantics

and

abstract

interpretation

They

are

-RRB-

escape

analysis

which

provides

information

about

the

relative

lifetimes

of

objects

such

as

arguments

and

local

objects

defined

within

a

function

with

respect

to

an

activation

of

the

function

call

-RRB-

refined

escape

analysis

which

as

a

refinement

of

escape

analysis

provides

information

about

the

lifetimes

of

components

of

aggregate

structures

and

-RRB-

reference

escape

analysis

which

provides

information

about

the

relative

lifetimes

of

references

created

within

a

function

with

respect

to

an

activation

of

the

function

We

also

have

developed

a

compile-time

semantic

analysis

called

order-of-demand

analysis

for

higher-order

monomorphic

non-strict

functional

languages

which

provides

information

about

the

order

in

which

the

values

of

bound

variables

are

demanded

and

thus

allows

one

to

compute

a

range

of

information

including

strictness

evaluation-order

and

evaluationstatus

information

Using

the

notion

of

polymorphic

invariance

we

describe

a

method

for

analyzing

a

polymorphic

language

by

using

the

analyses

for

a

monomorphic

language

We

then

extend

those

analyses

for

a

strict

language

to

a

non-strict

language

using

non-strict

program

transformation

and

evaluation-status

information

Based

on

statically

inferred

escape

information

we

propose

a

combination

of

storage

management

optimization

techniques

including

stack

allocation

explicit

reclamation

in-place

reuse

reference

counting

elimination

block

allocation/reclamation

and

improving

generational

garbage

collection

SMOOTH

TIME-PERIODIC

FEEDBACK

SOLUTIONS

FOR

NONHOLONOMIC

MOTION

PLANNING

L.

Gurvits

and

Z.

X.

Li

February

In

this

paper

we

present

an

algorithm

for

computing

time-periodic

feedback

solutions

for

nonholonomic

motion

planning

with

collision-avoidance

For

a

first-order

Lie

bracket

system

we

begin

by

computing

a

holonomic

collision-free

path

using

the

potential

field

method

Then

we

compute

a

nonholonomic

path

approximating

the

collision-free

path

within

a

predetermined

bound

For

this

we

first

solve

for

extended

inputs

of

an

extended

system

using

Lie

bracket

completion

vectors

We

then

use

averaging

techniques

to

calculate

the

asymptotic

trajectory

of

the

nonholonomic

system

under

application

of

a

family

of

highly-oscillatory

inputs

Comparing

the

limiting

trajectories

with

the

extended

system

we

obtain

a

system

of

nonlinear

equations

from

which

the

desired

admissible

control

inputs

can

be

solved

For

higher-order

Lie

bracket

systems

we

use

multi-scale

averaging

and

apply

recursively

the

algorithm

for

first-order

Lie

bracket

systems

Based

on

averaging

techniques

we

also

provide

error

bounds

between

a

nonholonomic

system

and

its

averaged

system

INFINITE

LOOPS

IN

FINITE

TIME

SOME

OBSERVATIONS

E.

Davis

February

Formulating

physical

theories

using

real-valued

space

and

time

often

raises

the

difficult

issue

of

clustered

variation

states

that

change

their

value

infinitely

often

in

a

finite

interval

or

infinite

sequences

of

events

that

occur

in

a

finite

interval

Some

physical

theories

permit

nonsensical

models

unless

clustered

variation

is

prohibited

others

force

clustered

variation

to

occur

This

paper

surveys

a

number

of

technical

issues

involved

with

clustered

variation

without

attempting

to

find

a

uniform

treatment

of

the

issue

We

present

examples

of

theories

where

clustered

variation

must

be

allowed

and

of

theories

where

it

must

be

prohibited

We

discuss

the

meaning

of

plans

containing

infinite

series

of

events

We

present

constraints

on

real-valued

fluents

and

spatial

fluents

that

guarantee

discrete

variation

of

important

associated

states

We

show

that

requiring

discrete

variation

may

be

inconsistent

with

allowing

infinitely

many

objects

in

the

universe

even

if

each

object

is

individually

well-behaved

We

show

how

the

need

for

requiring

discrete

variation

may

depend

subtly

on

the

particular

ontology

chosen

for

the

domain

A

SOLUTION

TO

KRONECKER

'S

PROBLEM

G.

Gallo

B.

Mishra

March

Kronecker

believed

God

made

the

natural

numbers

and

all

the

rest

was

man

's

work

We

only

know

of

this

opinion

by

hearsay

evidence

however

and

his

paper

Ueber

den

Zahlbegriff

indicates

to

me

that

he

thought

God

made

a

bit

more

Buchstabenrechnung

or

calculation

with

letters

In

modern

terms

Kronecker

seems

to

envisage

a

cosmic

computer

which

computes

not

just

with

natural

numbers

but

with

polynomials

with

natural

number

coefficients

-LRB-

in

any

number

of

indeterminates

-RRB-

-LRB-

see

the

article

by

Harold

M.

Edwards

entitled

Kronecker

's

Views

on

the

Foundations

of

Mathematics

-RRB-

The

preceding

notion

of

constructive

mathematics

as

postulated

by

Kronecker

can

be

expanded

further

and

leads

to

some

very

interesting

algorithmic

problems

While

it

is

quite

apparent

that

Kronecker

regarded

these

algorithmic

questions

as

at

the

heart

of

his

formulation

of

mathematics

it

is

unclear

whether

Kronecker

had

been

able

to

resolve

these

questions

in

a

satisfactory

manner

The

present

notes

make

a

fresh

attempt

at

resolving

the

algorithmic

questions

raised

by

Kronecker

while

remaining

faithful

to

the

notion

of

constructivity

espoused

by

Kronecker

A

MINIATURE

PAN-TILT

ACTUATOR

THE

SPHERICAL

POINTING

MOTOR

B.

Bederson

R.

Wallace

E.

Schwartz

April

A

pan-tilt

mechanism

is

a

computer-controlled

actuator

designed

to

point

an

object

such

as

a

camera

sensor

For

applications

in

active

vision

a

pan-tilt

mechanism

should

be

accurate

fast

small

inexpensive

and

have

low

power

requirements

We

have

designed

and

constructed

a

new

type

of

actuator

meeting

these

requirements

which

incorporates

both

pan

and

tilt

into

a

single

two

degree

of

freedom

device

The

Spherical

Pointing

Motor

-LRB-

SPM

-RRB-

consists

of

three

orthogonal

motor

windings

in

a

permanent

magnetic

field

configured

to

move

a

small

camera

mounted

on

a

gimbal

It

is

an

absolute

positioning

device

and

is

run

open

loop

The

SPM

is

capable

of

panning

and

tilting

a

load

of

grams

for

example

a

CCD

image

sensor

at

rotational

velocities

of

several

hundred

degrees

per

second

with

an

accuracy

of

degrees

We

have

also

built

a

miniature

camera

consisting

of

a

single

CCD

sensor

chip

and

miniature

lens

assembly

that

fits

on

the

rotor

of

this

motor

In

this

paper

we

discuss

the

theory

of

the

SPM

which

includes

its

basic

electromagnetic

principles

and

derive

the

relationship

between

applied

currents

and

resultant

motor

position

We

present

an

automatic

calibration

procedure

and

discuss

open

and

closed-loop

control

strategies

Finally

we

present

the

physical

characteristics

and

results

of

our

prototype

AN

O

-LRB-

mlogn

-RRB-

TIME

ALGORITHM

FOR

THE

MAXIMAL

PLANAR

SUBGRAPH

PROBLEM

J.

Cai

X.

Han

R.

Tarjan

April

Based

on

a

new

version

of

Hopcroft

and

Tarjan

's

planarity

testing

algorithm

we

develop

an

O

-LRB-

mlogn

-RRB-

time

algorithm

to

find

a

maximal

planar

subgraph

COUNTING

EMBEDDINGS

OF

PLANAR

GRAPHS

USING

DFS

TREES

J.

Cai

April

Previously

counting

embeddings

of

planar

graphs

used

P

Q

trees

and

was

restricted

to

biconnected

graphs

Although

the

P

Q

tree

approach

is

conceptually

simple

its

implementation

is

complicated

In

this

paper

we

solve

this

problem

using

DFS

trees

which

are

easy

to

implement

We

also

give

formulas

that

count

the

number

of

embeddings

of

general

planar

graphs

-LRB-

not

necessarily

connected

or

biconnected

-RRB-

in

O

-LRB-

n

-RRB-

arithmetic

steps

where

n

is

the

number

of

vertices

of

the

input

graph

Finally

our

algorithm

can

be

extended

to

generate

all

embeddings

of

a

planar

graph

in

linear

time

with

respect

to

the

output

MORE

EFFICIENT

BOTTOM-UP

MULTI-PATTERN

MATCHING

IN

TREES

J.

Cai

R.

Paige

R.

Tarjan

April

Pattern

matching

in

trees

is

fundamental

to

a

variety

of

programming

language

systems

However

progress

has

been

slow

in

satisfying

a

pressing

need

for

general

purpose

pattern

matching

algorithms

that

are

efficient

in

both

time

and

space

We

offer

asymptotic

improvements

in

both

time

and

space

to

Chase

's

bottom-up

algorithm

for

pattern

preprocessing

A

preliminary

implementation

of

our

algorithm

runs

ten

times

faster

than

Chase

's

implementation

on

the

hardest

problem

instances

Our

preprocessing

algorithm

has

the

advantage

of

being

on-line

with

respect

to

pattern

additions

and

deletions

It

also

adapts

to

favorable

input

instances

and

on

Hoffmann

and

O'Donnell

's

class

of

Simple

Patterns

it

performs

better

than

their

special

purpose

algorithm

tailored

to

this

class

We

show

how

to

modify

our

algorithm

using

a

new

decomposition

method

to

obtain

a

space/time

tradeoff

Finally

we

trade

a

log

factor

in

time

for

a

linear

space

bottom-up

pattern

matching

algorithm

that

handles

a

wide

subclass

of

Hoffmann

and

O'Donnell

's

Simple

Patterns

COMPLEXITY

ISSUES

IN

COMPUTATIONAL

ALGEBRA

G.

Gallo

May

The

ideal

membership

problem

for

the

ring

of

multivariate

polynomials

is

a

central

problem

in

Computational

Algebra

Relatively

tight

computational

complexity

bounds

for

this

problem

are

known

in

the

case

of

polynomials

with

coefficients

in

a

field

After

reviewing

these

results

we

give

an

algorithm

together

with

an

upper

bound

on

its

complexity

for

the

solution

of

the

membership

problem

in

the

case

of

polynomials

with

integer

coefficients

This

result

is

obtained

adapting

Buchberger

's

algorithm

to

the

integer

case

As

an

application

we

also

provide

a

more

general

upper

bound

on

the

length

of

strictly

ascending

chain

of

ideals

in

the

ring

Z

-LSB-

xn

-RSB-

Many

applications

of

Computational

Algebra

however

do

not

require

the

complete

solution

of

the

membership

problems

and

alternative

approaches

are

available

In

this

thesis

we

survey

the

method

of

the

characteristic

sets

originally

introduced

by

Ritt

in

the

forties

and

now

widely

applied

particularly

in

Elementary

Geometry

Theorem

Proving

We

present

optimal

algorithms

for

computing

a

characteristic

set

with

simple-exponential

sequential

and

polynomial

parallel

time

complexities

We

finally

present

an

attempt

to

generalize

some

of

the

constructive

methods

of

Commutative

Algebra

to

the

Algebra

of

differential

polynomials

Rings

of

differential

polynomials

do

not

resemble

their

purely

algebraic

counterparts

we

prove

that

there

exist

non-recursive

differential

ideals

in

Zx

and

hence

that

in

general

no

effective

method

can

be

devised

to

solve

the

membership

problem

in

this

case

However

special

classes

of

ideals

can

be

algorithmically

approached

and

toward

this

goal

we

generalize

the

concept

of

H-basis

first

introduced

by

Macaulay

for

algebraic

ideals

to

differential

rings

DOMAIN

DECOMPOSITION

ALGORITHMS

WITH

SMALL

OVERLAP

M.

Dryja

O.

Widlund

May

Numerical

experiments

have

shown

that

two-level

Schwarz

methods

often

perform

very

well

even

if

the

overlap

between

neighboring

subregions

is

quite

small

This

is

true

to

an

even

greater

extent

for

a

related

algorithm

due

to

Barry

Smith

where

a

Schwarz

algorithm

is

applied

to

the

reduced

linear

system

of

equations

that

remains

after

that

the

variables

interior

to

the

subregions

have

been

eliminated

In

this

paper

a

supporting

theory

is

developed

GMRES/CR

AND

ARNOLDI/LANCZOS

AS

MATRIX

APPROXIMATION

PROBLEMS

A.

Greenbaum

L.

Trefethen

May

The

GMRES

and

Arnoldi

algorithms

which

reduce

to

the

CR

and

Lanczos

algorithms

in

the

symmetric

case

both

minimize

kp

-LRB-

A

-RRB-

bk

over

polynomials

p

of

degree

n

The

difference

is

that

p

is

normalized

at

z

for

GMRES

and

at

z

inf

for

Arnoldi

Analogous

ideal

GMRES

and

ideal

Arnoldi

problems

are

obtained

if

one

removes

b

from

the

discussion

and

minimizes

kp

-LRB-

A

-RRB-

k

instead

Investigation

of

these

true

and

ideal

approximation

problems

gives

insight

into

how

fast

GMRES

converges

and

how

the

Arnoldi

iteration

locates

eigenvalues

MATRICES

THAT

GENERATE

THE

SAME

KRYLOV

RESIDUAL

SPACES

A.

Greenbaum

Z.

Strakos

May

Given

an

n

by

n

nonsingular

matrix

A

and

an

n-vector

v

we

consider

the

spaces

of

the

form

AKk

-LRB-

A

v

-RRB-

k

n

where

Kk

-LRB-

A

v

-RRB-

is

the

kth

Krylov

space

equal

to

spanfv

Av

Ak

We

characterize

the

set

of

matrices

B

that

with

the

given

vector

v

generate

the

same

spaces

i.e.

those

matrices

B

for

which

BKk

-LRB-

B

v

-RRB-

AKk

-LRB-

A

v

-RRB-

for

all

k

n

It

is

shown

that

any

such

sequence

of

spaces

can

be

generated

by

a

unitary

matrix

If

zero

is

outside

the

field

of

values

of

A

then

there

is

a

Hermitian

positive

definite

matrix

that

generates

the

same

spaces

and

moreover

if

A

is

close

to

Hermitian

then

there

is

a

nearby

Hermitian

matrix

that

generates

the

same

spaces

It

is

also

shown

that

any

such

sequence

of

spaces

can

be

generated

by

a

matrix

having

any

desired

eigenvalues

Implications

about

the

convergence

rate

of

the

GMRES

method

are

discussed

A

new

proof

is

given

that

if

zero

is

outside

the

field

of

values

of

A

then

convergence

of

the

GMRES

algorithm

is

strictly

monotonic

It

is

shown

that

if

A

is

close

to

Hermitian

then

the

eigenvalues

of

A

essentially

determine

the

behavior

of

the

GMRES

iteration

but

that

in

general

eigenvalue

information

alone

is

never

sufficient

to

ensure

rapid

convergence

of

the

GMRES

algorithm

MULTISET

DISCRIMINATION

A

METHOD

FOR

IMPLEMENTING

PROGRAMMING

LANGUAGE

SYSTEMS

WITHOUT

HASHING

J.

Cai

R.

Paige

June

It

is

generally

assumed

that

hashing

is

essential

to

many

algorithms

related

to

efficient

compilation

e.g.

symbol

table

formation

and

maintenance

grammar

manipulation

basic

block

optimization

and

global

optimization

This

paper

questions

this

assumption

and

initiates

development

of

an

efficient

alternative

compiler

methodology

without

hashing

or

sorting

Underlying

this

methodology

are

several

generic

algorithmic

tools

among

which

special

importance

is

given

to

Multiset

Discrimination

which

partitions

a

multiset

into

blocks

of

duplicate

elements

We

show

how

multiset

discrimination

together

with

other

tools

can

be

tailored

to

rid

compilation

of

hashing

without

loss

in

asymptotic

performance

Because

of

the

simplicity

of

these

tools

our

results

may

be

of

practical

as

well

as

theoretical

interest

The

various

applications

presented

culminate

with

a

new

algorithm

to

solve

iterated

strength

reduction

folded

with

useless

code

elimination

that

runs

in

worst

case

asymptotic

time

and

auxiliary

space

-LRB-

jLj

jL?j

-RRB-

where

jLj

and

jL?j

represent

the

lengths

of

the

initial

and

optimized

programs

respectively

The

previous

best

solution

due

to

Cocke

and

Kennedy

takes

-LRB-

-RRB-

hash

operations

in

the

worst

case

HESFCN

A

FORTRAN

PACKAGE

OF

HESSIAN

SUBROUTINES

FOR

TESTING

NON

LINEAR

OPTIMIZATION

SOFTWARE

V.

Averbukh

S.

Figueroa

T.

Schlick

June

We

report

the

development

of

Hessian

FORTRAN

routines

for

testing

unconstrained

nonlinear

optimization

An

existing

package

Algorithm

-LRB-

J.

Mor?e

B.

G.

Garbow

and

K.

Hillstrom

ACM

Trans

Math

Softw

-LCB-

and

-LCB-

-RRB-

provides

function

and

gradient

subroutines

of

test

functions

for

multivariate

minimization

Our

supplementary

Hessian

segments

will

enable

users

to

test

optimization

software

that

requires

second

derivative

information

Eigenvalue

analysis

throughout

the

minimization

will

also

be

possible

in

the

goal

of

better

understanding

minimization

progress

by

different

algorithms

and

the

relation

of

progress

to

eigenvalue

distribution

and

condition

number

MINIATURE

SPACE-VARIANT

ACTIVE

VISION

SYSTEM

CORTEX-I

B.

Bederson

July

We

have

developed

a

prototype

miniaturized

active

vision

system

whose

sensor

architecture

is

based

on

a

logarithmically

structured

space-variant

pixel

geometry

A

space-variant

image

's

resolution

changes

across

the

image

Typically

the

central

part

of

the

image

has

a

very

high

resolution

and

the

resolution

falls

off

gradually

in

the

periphery

Our

system

integrates

a

miniature

CCD-based

camera

pan-tilt

actuator

controller

general

purpose

processors

and

display

Due

to

the

ability

of

space-variant

sensors

to

cover

large

work-spaces

yet

provide

high

acuity

with

an

extremely

small

number

of

pixels

spacevariant

active

vision

system

architectures

provide

the

potential

for

radical

reductions

in

system

size

and

cost

We

have

realized

this

by

creating

an

entire

system

that

takes

up

less

than

a

third

of

a

cubic

foot

In

this

thesis

we

describe

a

prototype

space-variant

active

vision

system

-LRB-

V

-RRB-

which

performs

such

tasks

as

tracking

moving

objects

and

license

plate

reading

and

functions

as

a

video

telephone

We

report

on

the

design

and

construction

of

the

camera

-LRB-

which

is

-RRB-

its

readout

and

a

fast

mapping

algorithm

to

convert

the

uniform

image

to

a

space-variant

image

We

introduce

a

new

miniature

pan-tilt

actuator

the

Spherical

Pointing

Motor

-LRB-

SPM

-RRB-

which

is

The

basic

idea

behind

the

SPM

is

to

orient

a

permanent

magnet

to

the

magnetic

field

induced

by

three

orthogonal

coils

by

applying

the

appropriate

ratio

of

currents

to

the

coils

Finally

we

present

results

of

integrating

the

system

with

several

applications

Potential

application

domains

for

systems

of

this

type

include

vision

systems

for

mobile

robots

and

robot

manipulators

traffic

monitoring

systems

security

and

surveillance

telerobotics

and

consumer

video

communications

The

long-range

goal

of

this

project

is

to

demonstrate

that

major

new

applications

of

robotics

will

become

feasible

when

small

low-cost

machine

vision

systems

can

be

mass-produced

This

notion

of

commodity

robotics

is

expected

to

parallel

the

impact

of

the

personal

computer

in

the

sense

of

opening

up

new

application

niches

for

what

has

until

now

been

expensive

and

therefore

limited

technology

THE

SPIDERWEB

ALGORITHM

FOR

SURFACE

CONSTRUCTION

FROM

MEDICAL

VOL

UME

DATA

GEOMETRIC

PROPERTIES

OF

ITS

SURFACE

D.

Karron

J.

Cox

B.

Mishra

July

The

SpiderWeb

algorithm

is

a

set

of

rules

to

construct

a

triangular

mesh

isosurface

-LRB-

simplicial

complex

-RRB-

from

density

data

The

algorithm

is

robust

in

the

presence

of

noisy

data

in

the

sense

that

the

surface

grown

will

be

an

oriented

two

manifold

surface

Further

the

algorithm

constructs

the

triangulation

using

only

local

triangle-spinning

rules

thus

needing

no

additional

global

information

The

triangle

spinning

rules

use

local

geometric

symmetries

that

translate

into

face-hit

rules

These

rules

are

not

artifacts

of

the

algorithm

or

any

data

assumptions

but

rather

inherent

in

the

nature

of

density

data

sampled

at

a

given

resolution

or

spatial

frequency

SpiderWeb

does

not

require

ad

hoc

rules

to

deal

with

inconsistencies

caused

by

so-called

nongeometric

noise

Thus

the

algorithm

conforms

to

and

strongly

exploits

previously

unrecognized

geometric

properties

of

density

data

while

requiring

minimal

assumptions

on

the

distribution

of

such

data

COMPUTING

READY

SIMULATIONS

EFFICIENTLY

B.

Bloom

R.

Paige

September

Ready

simulation

is

the

finest

fully

abstract

notion

of

process

equivalence

in

the

CCS

setting

We

give

an

O

-LRB-

mn

-RRB-

time

algorithm

for

deciding

when

n-state

m-transition

processes

are

ready

similar

a

substantial

improvement

on

the

-LRB-

-RRB-

algorithm

presented

in

Bard

Bloom

's

Thesis

SOME

SCHWARZ

ALGORITHMS

FOR

THE

P-VERSION

FINITE

ELEMENT

METHOD

L.

Pavarino

September

Domain

decomposition

methods

based

on

the

Schwarz

framework

were

originally

proposed

for

the

h-version

finite

element

method

for

elliptic

problems

In

this

paper

we

consider

instead

the

p-version

in

which

increased

accuracy

is

achieved

by

increasing

the

degree

of

the

elements

while

the

mesh

is

fixed

We

consider

linear

scalar

self

adjoint

second

order

elliptic

problems

and

quadrilateral

elements

in

the

finite

element

discretization

For

a

class

of

overlapping

additive

Schwarz

methods

we

prove

a

constant

bound

independent

of

the

degree

p

and

the

number

of

elements

N

for

the

condition

number

of

the

iteration

operator

This

optimal

result

holds

in

two

and

three

dimensions

for

additive

and

multiplicative

schemes

as

well

as

variants

on

the

interface

We

then

study

local

refinement

for

the

same

class

of

overlapping

methods

in

two

dimensions

A

constant

bound

holds

under

certain

hypotheses

on

the

refinement

region

while

in

general

an

almost

optimal

bound

with

logarithmic

growth

in

p

is

obtained

SOME

RECENT

RESULTS

ON

SCHWARZ

TYPE

DOMAIN

DECOMPOSITION

ALGO

RITHMS

M.

Dryja

O.

Widlund

September

Numerical

experiments

have

shown

that

two-level

Schwarz

methods

for

the

solution

of

discrete

elliptic

problems

often

perform

very

well

even

if

the

overlap

between

neighboring

subregions

is

quite

small

This

is

true

to

an

even

greater

extent

for

a

related

algorithm

due

to

Barry

Smith

where

a

Schwarz

algorithm

is

applied

to

the

reduced

linear

system

of

equations

that

remains

after

that

the

variables

interior

to

the

subregions

have

been

eliminated

A

supporting

theory

is

outlined

DOMAIN

DECOMPOSITION

ALGORITHMS

FOR

THE

P-VERSION

FINITE

ELEMENT

METHOD

FOR

ELLIPTIC

PROBLEMS

L.

Pavarino

September

Domain

decomposition

algorithms

based

on

the

Schwarz

framework

were

originally

proposed

for

the

h-version

finite

element

method

for

elliptic

problems

In

this

thesis

we

study

some

Schwarz

algorithms

for

the

p-version

finite

element

method

in

which

increased

accuracy

is

achieved

by

increasing

the

degree

p

of

the

elements

while

the

mesh

is

fixed

These

iterative

algorithms

often

of

conjugate

gradient

type

are

both

parallel

and

scalable

and

therefore

very

well

suited

for

massively

parallel

computing

We

consider

linear

scalar

self

adjoint

second

order

elliptic

problems

and

quadrilateral

elements

in

the

finite

element

discretization

For

a

class

of

overlapping

methods

we

prove

a

constant

bound

independent

of

the

degree

p

the

mesh

size

H

and

the

number

of

elements

N

for

the

condition

number

of

the

iteration

operator

This

optimal

result

holds

in

two

and

three

dimensions

for

additive

and

multiplicative

schemes

as

well

as

variants

on

the

interface

We

consider

then

local

refinement

for

the

same

class

of

overlapping

methods

in

two

dimensions

Optimal

bounds

are

obtained

under

certain

hypothesis

on

the

choice

of

refinement

points

while

in

general

almost

optimal

bounds

with

logarithmic

growth

in

p

are

obtained

In

the

analysis

of

these

local

refinement

methods

we

prove

some

results

of

independent

interest

such

as

a

polynomial

discrete

Sobolev

inequality

and

a

bounded

decomposition

of

discrete

harmonic

polynomials

Iterative

substructuring

methods

in

two

dimensions

are

also

considered

We

use

the

additive

Schwarz

framework

to

prove

almost

optimal

bounds

as

in

the

h-version

finite

element

method

Results

of

numerical

experiments

confirming

the

theoretical

results

are

conducted

in

two

dimensions

for

model

problems

AN

EFFICIENT

ALGORITHM

TO

DECIDE

PLANAR

IMMOBILITY

M.

Teichmann

B.

Mishra

October

-LRB-

Out

of

Print

-RRB-

In

robotics

it

is

necessary

to

immobilize

an

object

by

placing

fingers

-LRB-

clamps

or

fixtures

-RRB-

whose

contacts

with

the

object

prevent

its

motion

Depending

on

the

areas

of

applications

the

problem

has

been

variously

labelled

as

grasping

workholding

part-mating

Also

there

have

been

a

wide

class

of

definitions

of

grasping

for

instance

force/torque

closure

grasps

form

closure

grasps

stable

grasps

zero

total

freedom

and

recently

a

new

simple

geometric

formulation

called

immobility

In

this

paper

we

propose

a

characterization

of

the

sets

of

immobilizing

points

which

leads

to

an

algorithm

to

test

whether

a

given

set

immobilizes

a

polygon

This

algorithm

runs

in

time

linear

in

the

number

of

points

in

the

set

ON

THE

NUMBER

OF

CELLS

DEFINED

BY

A

SET

OF

POLYNOMIALS

R.

Pollack

M.

Roy

October

We

show

that

the

sum

of

the

number

of

connected

components

of

all

non

empty

realizations

of

sign

conditions

of

s

polynomials

in

n

variables

each

of

degree

at

most

d

is

bounded

by

-LRB-

O

-LRB-

sd

n

-RRB-

-RRB-

n

The

previously

known

bound

based

on

a

result

of

J.

Heintz

was

-LRB-

sd

-RRB-

O

-LRB-

n

-RRB-

-LRB-

see

for

example

-LSB-

-RSB-

-RRB-

MATCHING

PURSUITS

WITH

TIME-FREQUENCY

DICTIONARIES

S.

Mallat

Z.

Zhang

October

Revised

August

We

introduce

an

algorithm

called

matching

pursuit

that

decomposes

any

signal

into

a

linear

expansion

of

waveforms

that

are

selected

from

a

redundant

dictionary

of

functions

These

waveforms

are

chosen

in

order

to

best

match

the

signal

structures

Matching

pursuits

are

general

procedures

to

compute

adaptive

signal

representations

With

a

dictionary

of

Gabor

functions

a

matching

pursuit

defines

an

adaptive

time-frequency

transform

We

derive

a

signal

energy

distribution

in

the

time-frequency

plane

which

does

not

include

interference

terms

unlike

Wigner

and

Cohen

class

distributions

-LSB-

-RSB-

A

matching

pursuit

isolates

the

signal

structures

that

are

coherent

with

respect

to

a

given

dictionary

An

application

to

pattern

extraction

from

noisy

signals

is

described

We

compare

a

matching

pursuit

decomposition

with

a

signal

expansion

over

an

optimized

wavepacket

orthonormal

basis

selected

with

the

algorithm

of

Coifman

and

Wickerhauser

BACKWARD

ANALYSIS

FOR

HIGHER-ORDER

FUNCTIONS

USING

INVERSE

IMAGES

T-R

Chuang

B.

Goldberg

November

We

propose

a

method

for

performing

backward

analysis

on

higher

-LCB-

order

functional

programming

languages

based

on

computing

inverse

images

of

functions

over

abstract

domains

This

method

can

be

viewed

as

abstract

interpretation

done

backward

Given

an

abstract

semantics

which

supports

forward

analysis

we

can

transform

it

into

an

abstract

semantics

which

performs

backward

analysis

We

show

that

if

the

original

abstract

semantics

is

correct

and

computable

then

the

transformed

version

of

the

abstract

semantics

is

also

correct

and

computable

More

specifically

given

a

forward

abstract

semantics

of

a

higher

-LCB-

order

functional

language

which

is

expressed

in

terms

of

Scott

-LCB-

closed

powerdomains

we

derive

an

backward

abstraction

semantics

which

is

expressed

in

terms

of

Scott

-LCB-

open

powerdomains

The

derivation

is

shown

to

be

correct

and

the

relationships

between

forward

analysis

and

backward

analysis

is

established

We

apply

this

method

to

the

classic

strictness

analysis

in

functional

languages

and

obtain

promising

results

We

show

that

the

time

complexity

of

inverse

image

based

backward

analysis

is

not

much

worse

than

the

forward

analysis

from

which

it

is

derived

We

then

compare

this

work

with

previous

works

of

Wadler

and

Hughes

-LRB-

-RRB-

Hughes

-LRB-

-RRB-

and

Burn

-LRB-

-RRB-

showing

that

some

special

restrictions

and

constructions

in

previous

works

have

natural

interpretation

in

the

Scott

-LCB-

closed/Scott

-LCB-

open

powerdomain

framework

A

brief

outline

of

applying

the

inverse

image

method

to

other

backward

semantics

analysis

is

also

given

STATISTICAL

APPROACH

TO

AFFINE

INVARIANT

MATCHING

WITH

LINE

FEATURES

F.

Tsai

November

One

of

the

most

important

goals

of

computer

vision

research

is

object

recognition

Currently

most

object

recognition

algorithms

assume

reliable

quality

of

image

segmentation

which

in

practice

is

often

not

the

case

This

report

examines

the

combination

of

the

Hough

Transform

with

a

variation

of

Geometric

Hashing

as

a

technique

for

model-based

object

recognition

in

seriously

degraded

single

intensity

images

There

is

recently

much

focus

on

the

performance

analysis

of

geometric

hashing

However

to

our

knowledge

all

of

them

are

focusing

on

applying

the

paradigm

to

point

features

and

show

that

the

technique

is

sensitive

to

noise

There

is

as

yet

no

exploration

of

line

features

In

this

report

we

use

lines

as

the

primitive

features

to

compute

the

geometric

invariants

for

fast

indexing

into

the

geometric

hash

table

containing

the

pre-processed

model

information

In

addition

we

analytically

determine

the

effect

of

perturbations

of

line

parameters

on

the

computed

invariant

for

the

case

where

models

are

allowed

to

undergo

affine

transformation

We

have

implemented

the

system

with

a

series

of

experiments

on

polygonal

objects

which

are

modeled

by

lines

It

shows

that

the

technique

is

noise

resistant

and

suitable

in

an

environment

containing

many

occlusions

POLYMORPHIC

TYPE

INFERENCE

AND

ABSTRACT

DATA

TYPES

K.

L?aufer

December

Many

statically-typed

programming

languages

provide

an

abstract

data

type

construct

such

as

the

package

in

Ada

the

cluster

in

CLU

and

the

module

in

However

in

most

of

these

languages

instances

of

abstract

data

types

are

not

first-class

values

Thus

they

can

not

be

assigned

to

a

variable

passed

as

a

function

parameter

or

returned

as

a

function

result

The

higher-order

functional

language

ML

has

a

strong

and

static

type

system

with

parametric

polymorphism

In

addition

ML

provides

type

reconstruction

and

consequently

does

not

require

type

declarations

for

identifiers

Although

the

ML

module

system

supports

abstract

data

types

their

instances

can

not

be

used

as

first-class

values

for

type-theoretic

reasons

In

this

dissertation

we

describe

a

family

of

extensions

of

ML

While

retaining

ML

's

static

type

discipline

type

reconstruction

and

most

of

its

syntax

we

add

significant

expressive

power

to

the

language

by

incorporating

first-class

abstract

types

as

an

extension

of

ML

's

free

algebraic

datatypes

In

particular

we

are

now

able

to

express

ffl

multiple

implementations

of

a

given

abstract

type

ffl

heterogeneous

aggregates

of

different

implementations

of

the

same

abstract

type

and

ffl

dynamic

dispatching

of

operations

with

respect

to

the

implementation

type

Following

Mitchell

and

Plotkin

we

formalize

abstract

types

in

terms

of

existentially

quantified

types

We

prove

that

our

type

system

is

semantically

sound

with

respect

to

a

standard

denotational

semantics

We

then

present

an

extension

of

Haskell

a

non-strict

functional

language

that

uses

type

classes

to

capture

systematic

overloading

This

language

results

from

incorporating

existentially

quantified

types

into

Haskell

and

gives

us

first-class

abstract

types

with

type

classes

as

their

interfaces

We

can

now

express

heterogeneous

structures

over

type

classes

The

language

is

statically

typed

and

offers

comparable

flexibility

to

object-oriented

languages

Its

semantics

is

defined

through

a

type-preserving

translation

to

a

modified

version

of

our

ML

extension

We

have

implemented

a

prototype

of

an

interpreter

for

our

language

including

the

type

reconstruction

algorithm

in

Standard

ML

RESIDUAL

RELATIONSHIPS

WITHIN

THREE

PAIRS

OF

ITERATIVE

ALGORITHMS

FOR

SOLVING

Ax

b

J.

Cullum

A.

Greenbaum

February

In

-LSB-

Brown

SIAM

Jour

Sci

Stat

Comput

pp.

-RSB-

a

relationship

was

established

between

the

norms

of

the

residuals

produced

by

the

Arnoldi

algorithm

and

those

produced

by

the

GMRES

algorithm

This

combined

with

the

relationship

between

successive

GMRES

residual

norms

obtained

in

-LSB-

Saad

and

Schultz

SIAM

Jour

Sci

Stat

Comput

pp.

-RSB-

shows

that

when

the

GMRES

algorithm

is

converging

rapidly

the

norms

of

the

Arnoldi

residuals

are

approximately

equal

to

those

of

the

GMRES

residuals

while

when

the

GMRES

algorithm

is

converging

very

slowly

the

norms

of

the

Arnoldi

residuals

are

significantly

larger

than

those

of

the

GMRES

residuals

We

state

this

relationship

in

a

slightly

different

form

showing

the

precise

connection

between

the

residual

norm

reduction

at

a

particular

GMRES

step

and

the

ratio

of

the

Arnoldi

to

GMRES

residual

norms

at

that

step

Assuming

exact

arithmetic

we

show

that

a

similar

relationship

exists

between

the

residuals

of

the

biconjugate

gradient

algorithm

and

the

quasi-residuals

of

the

QMR

algorithm

where

the

quasi-residuals

are

the

vectors

whose

norms

are

actually

minimized

by

the

QMR

algorithm

It

is

demonstrated

numerically

that

the

norms

of

the

quasi-residuals

are

of

the

same

order

of

magnitude

as

the

norms

of

the

actual

residuals

We

then

consider

this

relationship

for

the

corresponding

real

symmetric

procedures

Lanczos

and

MINRES

We

prove

that

for

a

certain

class

of

real

symmetric

problems

the

relationship

holds

to

a

close

approximation

even

in

finite

precision

arithmetic

In

particular

we

show

that

for

well-conditioned

problems

the

nonsymmetric

bidiagonalization

procedures

considered

in

-LSB-

Cullum

IBM

Res

Rept

RC

-RSB-

fall

into

this

class

and

hence

satisfy

the

residual

relationship

to

a

close

approximation

in

finite

precision

arithmetic

A

HYBRID

ALGORITHM

FOR

OPTIMIZING

EIGENVALUES

OF

SYMMETRIC

DEFINITE

PENCILS

J.

Haeberly

M.

Overton

February

We

present

an

algorithm

for

the

optimization

of

the

maximum

eigenvalue

of

a

symmetric

definite

pencil

depending

affinely

on

a

vector

of

parameters

The

algorithm

uses

a

hybrid

approach

combining

a

scheme

based

on

the

method

of

centers

developed

by

Boyd

and

El

Ghaoui

with

a

new

quadratically

convergent

local

scheme

A

convenient

expression

for

the

generalized

gradient

of

the

maximum

eigenvalue

of

the

pencil

is

also

given

expressed

in

terms

of

a

dual

matrix

The

algorithm

computes

the

dual

matrix

which

establishes

the

optimality

of

the

computed

solution

USING

LINE

INVARIANTS

FOR

OBJECT

RECOGNITION

BY

GEOMETRIC

HASHING

F.

Tsai

February

Geometric

Hashing

is

a

model-based

object

recognition

technique

for

detecting

objects

which

can

be

partially

overlapping

or

partly

occluded

It

precompiles

from

local

geometric

features

redundant

transformation-invariant

information

of

the

models

in

a

hash

table

and

uses

the

invariants

computed

from

a

scene

for

fast

indexing

into

the

hash

table

to

hypothesize

possible

matches

between

object

instances

and

object

models

during

recognition

In

its

simplest

form

the

geometric

hashing

method

assumes

relatively

noise-free

data

and

is

applied

to

objects

with

points

as

local

features

However

extracting

of

the

locations

of

point

features

is

inherently

error-prone

and

the

analysis

of

geometric

hashing

on

point

sets

shows

considerable

noise

sensitivity

Line

features

can

generally

be

extracted

with

greater

accuracy

We

investigate

the

use

of

line

features

for

geometric

hashing

applied

to

-LRB-

or

flat

-RRB-

object

recognition

and

derive

from

a

combination

of

line

features

invariants

for

lines

under

various

geometric

transformations

SCHWARZ

METHODS

OF

NEUMANN-NEUMANN

TYPE

FOR

THREE-DIMENSIONAL

ELLIPTIC

FINITE

ELEMENT

PROBLEMS

M.

Dryja

O.

Widlund

March

Several

domain

decomposition

methods

of

Neumann-Neumann

type

are

considered

for

solving

the

large

linear

systems

of

algebraic

equations

that

arise

from

discretizations

of

elliptic

problems

by

finite

elements

We

will

only

consider

problems

in

three

dimensions

Several

new

variants

of

the

basic

algorithm

are

introduced

in

a

Schwarz

method

framework

that

provides

tools

which

have

already

proven

very

useful

in

the

design

and

analysis

of

other

domain

decomposition

and

multi-level

methods

The

Neumann-Neumann

algorithms

have

several

advantages

over

other

domain

decomposition

methods

The

subregions

which

define

the

subproblems

only

share

the

boundary

degrees

of

freedom

with

their

neighbors

The

subregions

can

also

be

of

quite

arbitrary

shape

and

many

of

the

major

components

of

the

preconditioner

can

be

constructed

from

subprograms

available

in

standard

finite

element

program

libraries

However

in

its

original

form

the

algorithm

lacks

a

mechanism

for

global

transportation

of

information

and

its

performance

therefore

suffers

when

the

number

of

subregions

increases

In

the

new

variants

of

the

algorithms

considered

in

this

paper

the

preconditioners

include

global

components

of

low

rank

to

overcome

this

difficulty

Bounds

are

established

for

the

condition

number

of

the

iteration

operator

which

are

independent

of

the

number

of

subregions

and

depend

only

polylogarithmically

on

the

number

of

degrees

of

freedom

of

individual

local

subproblems

Results

are

also

given

for

problems

with

arbitrarily

large

jumps

in

the

coefficients

across

the

interfaces

separating

the

subregions

SECOND

DERIVATIVES

FOR

OPTIMIZING

EIGENVALUES

OF

SYMMETRIC

MATRICES

M.

Overton

R.

Womersley

March

Let

A

denote

an

n?n

real

symmetric

matrix-valued

function

depending

on

a

vector

of

real

parameters

x

m.

Assume

that

A

is

a

twice

continuously

differentiable

function

of

x

with

the

second

derivative

satisfying

a

Lipschitz

condition

Consider

the

following

optimization

problem

minimize

the

largest

eigenvalue

of

A

-LRB-

x

-RRB-

Let

x

denote

a

minimum

Typically

the

maximum

eigenvalue

of

A

-LRB-

x

-RRB-

is

multiple

so

the

objective

function

is

not

differentiable

at

x

and

straightforward

application

of

Newton

's

method

is

not

possible

Nonetheless

the

formulation

of

a

Newton-based

method

with

local

quadratic

convergence

is

possible

This

formulation

is

derived

by

parameterizing

the

eigenvectors

using

a

matrix

exponential

representation

introducing

an

appropriate

Lagrangian

function

Consideration

of

the

Hessian

of

this

Lagrangian

function

leads

to

the

second

derivative

matrix

used

by

Newton

's

method

The

derivation

of

the

method

and

the

proof

of

quadratic

convergence

take

into

account

the

following

key

fact

the

number

of

variables

used

in

the

eigenvector

parameterization

drops

in

the

limit

by

t

-LRB-

t

-RRB-

where

t

is

the

multiplicity

of

the

maximum

eigenvalue

of

A

-LRB-

x

-RRB-

In

the

special

case

t

the

maximum

eigenvalue

is

a

smooth

function

and

the

method

reduces

to

the

standard

Newton

method

The

same

ideas

are

applicable

to

a

wide

variety

of

other

eigenvalue

and

singular

value

optimization

problems

THE

COMPLEXITY

OF

RESOLVENT

RESOLVED

G.

Gallo

B.

Mishra

March

The

concept

of

a

resolvent

of

a

prime

ideal

was

originally

introduced

by

J.F.

Ritt

along

with

the

notion

of

a

characteristic

set

The

motivation

for

studying

resolvents

comes

from

its

connections

with

the

birational

isomorphisms

that

describe

structures

of

irreducible

algebraic

varieties

by

means

of

an

equivalent

hypersurface

and

a

one-to-one

rational

map

As

a

result

these

ideas

have

a

wide

range

of

applications

in

such

areas

as

solid

modeling

computer

aided

design

and

manufacturing

An

algorithm

to

compute

the

resolvent

by

means

of

characteristic

sets

was

first

proposed

by

Ritt

This

and

some

related

algorithms

have

resurfaced

as

interest

in

resolvent

structures

have

grown

spurred

by

its

applicability

Unfortunately

the

algebraic

complexity

of

the

resolvent

and

the

computational

complexity

of

the

associated

algorithms

have

never

been

satisfactorily

explored

In

this

paper

we

give

single

exponential

upper

and

lower

bounds

for

the

degrees

of

the

resolvent

and

its

associated

parametrizing

polynomials

We

also

show

that

the

resolvent

can

be

computed

deterministically

in

single

exponential

sequential

and

polynomial

parallel

time

complexity

All

previous

algorithms

for

resolvent

had

relied

on

a

random

choice

of

certain

extraneous

parameters

TWO-LEVEL

SCHWARZ

METHODS

FOR

NONCONFORMING

FINITE

ELEMENTS

AND

DISCONTINUOUS

COEFFICIENTS

M.

Sarkis

March

A

two-level

domain

decomposition

methods

are

developed

for

a

simple

nonconforming

approximation

of

second

order

elliptic

problems

A

bound

is

established

for

the

condition

number

of

these

iterative

methods

which

grows

only

logarithmically

with

the

number

of

degrees

of

freedom

in

each

subregion

This

bound

holds

for

two

and

three

dimensions

and

is

independent

of

jumps

in

the

value

of

the

coefficients

THE

CELL

PROGRAMMING

LANGUAGE

P.

Agarwal

March

We

describe

the

Cell

Programming

Language

-LRB-

CPL

-RRB-

which

we

have

designed

to

write

programs

that

mimic

the

life

of

a

biological

cell

The

aim

is

to

study

the

complex

interactions

between

cells

which

lead

to

diverse

shapes

of

cellular

aggregates

Each

cell

is

treated

as

a

two-dimensional

homogeneous

polygon

with

a

specific

area

A

cell

goes

through

a

series

of

states

in

its

lifetime

In

each

state

one

can

specify

the

cell

's

growth

rate

information

about

cell

division

and

cell

differentiation

the

chemical

constituents

of

the

cell

and

their

interactions

and

cell

motion

This

behavior

may

be

conditional

based

on

the

cell

's

own

status

-LRB-

chemical

concentrations

and

size

-RRB-

or

on

its

neighborhood

-LRB-

the

type

of

cells

surrounding

it

the

contact

lengths

with

each

of

them

their

areas

the

directions

to

these

cells

and

their

chemical

concentrations

-RRB-

The

language

is

explored

by

modeling

cellular

sorting

in

vitro

and

aggregation

in

the

Dictyostelium

discoidea

-LRB-

cellular

slime

mold

-RRB-

TOWARDS

SECOND-ORDER

METHODS

FOR

STRUCTURED

NONSMOOTH

OPTIMIZA

TION

M.

Overton

X.

Ye

April

Structured

nonsmooth

optimization

objectives

often

arise

in

a

composite

form

f

h

ffi

a

where

h

is

convex

-LRB-

but

not

necessarily

polyhedral

-RRB-

and

a

is

smooth

We

consider

the

case

where

the

structure

of

the

nonsmooth

convex

function

h

is

known

Specifically

we

assume

that

for

any

given

point

in

the

domain

of

h

a

parameterization

of

a

manifold

on

which

h

reduces

locally

to

a

smooth

function

is

given

We

discuss

two

affine

spaces

the

tangent

space

to

the

manifold

at

a

point

and

the

affine

hull

of

the

subdifferential

of

h

at

the

same

point

and

explain

that

these

are

typically

orthogonal

complements

We

indicate

how

the

construction

of

locally

second-order

methods

is

possible

even

when

h

is

nonpolyhedral

provided

the

appropriate

Lagrangian

modeling

the

structure

is

used

We

illustrate

our

ideas

with

two

important

convex

functions

the

ordinary

max

function

and

the

max

eigenvalue

function

for

symmetric

matrices

and

we

solicit

other

interesting

examples

with

genuinely

different

structure

from

the

community

HIGHLY

EFFICIENT

DICTIONARY

MATCHING

IN

PARALLEL

S.

Muthukrishnan

K.

Palem

April

We

present

highly

efficient

parallel

algorithms

for

several

well-studied

dictionary

matching

problems

Our

algorithms

are

faster

and

more

efficient

in

terms

of

their

parallel

work

compared

to

previously

known

results

ffl

For

static

dictionary

matching

we

present

an

algorithm

that

preprocesses

the

dictionary

and

matches

the

text

in

O

-LRB-

logm

-RRB-

parallel

time

and

O

-LRB-

M

n

log

m

-RRB-

work

given

any

dictionary

of

size

M

whose

longest

pattern

is

m

characters

long

and

a

text

of

size

n

We

have

further

improved

this

algorithm

to

solve

static

dictionary

matching

with

only

O

-LRB-

-LRB-

M

n

-RRB-

p

log

m

-RRB-

work

if

the

characters

are

drawn

from

an

alphabet

of

constant

size

A

distinguishing

feature

of

these

algorithms

and

the

one

stated

below

for

matching

in

higher

dimensions

is

that

in

contrast

with

previous

work

the

running

times

and

work

overheads

when

applicable

are

dependent

only

on

the

length

of

the

longest

pattern

m.

ffl

We

present

a

parallel

algorithm

for

d-dimensional

dictionary

matching

that

runs

in

O

-LRB-

logm

-RRB-

time

and

matches

the

text

in

O

-LRB-

M

n

log

m

-RRB-

work

for

any

fixed

d.

ffl

We

present

a

new

and

more

efficient

parallel

algorithm

for

dynamic

dictionary

matching

Insertions

into

and

deletions

from

the

dictionary

as

well

as

matching

the

text

can

be

done

with

optimal

speedup

in

O

-LRB-

log

M

-RRB-

work

and

O

-LRB-

logM

-RRB-

time

Here

denotes

the

length

of

the

string

to

be

inserted

deleted

or

matched

into

a

dictionary

of

size

M

All

of

the

above

algorithms

are

designed

by

applying

the

shrink-and-spawn

technique

that

we

introduce

in

this

paper

We

also

show

that

this

technique

leads

to

parallel

algorithms

that

only

do

optimal

-LRB-

linear

-RRB-

work

for

multi-dimensional

pattern

matching

and

related

problems

in

-LSB-

-RSB-

-LSB-

-RSB-

Our

algorithms

are

deterministic

as

those

in

-LSB-

-RSB-

but

however

are

much

simpler

and

preserve

the

efficiency

as

well

as

the

speed

of

those

presented

there

SPACE

VARIANT

IMAGE

PROCESSING

R.

S.

Wallace

P.-W

Ong

B.

B.

Bederson

E.

L.

Schwartz

April

This

paper

describes

a

graph-based

approach

to

image

processing

intended

for

use

with

images

obtained

from

sensors

having

space

variant

sampling

grids

The

connectivity

graph

-LRB-

CG

-RRB-

is

presented

as

a

fundamental

framework

for

posing

image

operations

in

any

kind

of

space

variant

sensor

Partially

motivated

by

the

observation

that

human

vision

is

strongly

space

variant

a

number

of

research

groups

have

been

experimenting

with

space

variant

sensors

Such

systems

cover

wide

solid

angles

yet

maintain

high

acuity

in

their

central

regions

Implementation

of

space

variant

systems

pose

at

least

two

outstanding

problems

First

such

a

system

must

be

active

in

order

to

utilize

its

high

acuity

region

second

there

are

significant

image

processing

problems

introduced

by

the

non-uniform

pixel

size

shape

and

connectivity

Familiar

image

processing

operations

such

as

connected

components

convolution

template

matching

and

even

image

translation

take

on

new

and

different

forms

when

defined

on

space

variant

images

The

present

paper

provides

a

general

method

for

space

variant

image

processing

based

on

a

connectivity

graph

which

represents

the

neighbor-relations

in

an

arbitrarily

structured

sensor

We

illustrate

this

approach

with

the

following

applications

-LRB-

-RRB-

Connected

components

is

reduced

to

its

graph

theoretic

counterpart

We

illustrate

this

on

a

logmap

sensor

which

possesses

a

difficult

topology

due

to

the

branch

cut

associated

with

the

complex

logarithm

function

-LRB-

-RRB-

We

show

how

to

write

local

image

operators

in

the

connectivity

graph

that

are

independent

of

the

sensor

geometry

-LRB-

-RRB-

We

relate

the

connectivity

graph

to

pyramids

over

irregular

tessalations

and

implement

a

local

binarization

operator

in

a

pyramid

-LRB-

-RRB-

Finally

we

expand

the

connectivity

graph

into

a

structure

we

call

a

transformation

graph

which

represents

the

effects

of

geometric

transformations

in

space

variant

image

sensors

Using

the

transformation

graph

we

define

an

efficient

algorithm

for

matching

in

the

logmap

images

and

solve

the

template

matching

problem

for

space

variant

images

Because

of

the

very

small

number

of

pixels

typical

of

logarithmic

structured

space

variant

arrays

the

connectivity

graph

approach

to

image

processing

is

suitable

for

real-time

implementation

and

provides

a

generic

solution

to

a

wide

range

of

image

processing

applications

with

space

variant

sensors

MINIATURE

DIRECT

DRIVE

ROTARY

ACTUATORS

R.

S.

Wallace

April

This

paper

reports

the

development

of

direct

drive

DC

motor

actuators

for

miniature

robots

The

motors

are

based

on

Nd-Fe-B

rare

earth

permanent

magnets

and

controlled

by

low

cost

microcontrollers

The

motors

have

low

friction

small

size

high

speed

low

construction

cost

no

gear

backlash

operate

safely

without

limit

switches

have

limited

self-braking

and

generate

moderate

torque

Significantly

one

motor

can

generate

enough

torque

to

lift

a

second

motor

of

about

the

same

size

against

the

force

of

gravity

at

a

distance

approximately

equal

to

the

size

of

the

motor

without

resorting

to

the

use

of

a

counterweight

We

demonstrated

the

feasibility

of

using

these

actuators

to

make

a

two-link

robot

finger

or

leg

A

LANGUAGE

FOR

SEMANTIC

ANALYSIS

J.

Cai

May

Semantic

analysis

is

important

for

compilers

In

the

APTS

program

transformation

system

semantics

is

specified

by

rules

in

the

language

RSL

The

semantic

rules

are

interpreted

by

APTS

to

generate

the

semantic

information

of

the

program

which

is

then

used

by

the

rewriting

engine

for

program

translation

This

approach

has

proved

to

be

convenient

and

powerful

in

our

construction

of

a

SETL-to-C

compiler

In

this

paper

we

discuss

the

features

applications

implementation

strategy

and

performance

of

RSL

VOICE-BANDWIDTH

VISUAL

COMMUNICATION

THROUGH

LOGMAPS

THE

TELECORTEX

R.

Wallace

B.

Bederson

E.

Schwartz

May

We

present

a

robotic

video

telephone

application

of

the

miniaturized

space-variant

active

vision

system

The

embedded

processor

architecture

of

enables

it

to

implement

a

variety

of

functions

not

found

in

conventional

video

telephones

for

example

the

camera

tracks

moving

users

with

its

pantilt

mechanism

We

also

report

an

analog

channel

coding

scheme

to

transmit

logmap

video

images

through

band-limited

analog

channels

such

as

the

public

switched

telephone

network

-LRB-

PSTN

-RRB-

The

transmitter

divides

the

voice

frequency

band

into

channels

and

modulates

two

values

in

quadrature

on

each

channel

Some

channels

are

reserved

for

special

calibration

signals

enabling

the

receiver

to

recover

both

the

phase

and

magnitude

of

the

transmitted

signal

The

remaining

channels

carry

pixel

intensities

We

synthesize

the

signal

in

the

frequency

domain

and

run

the

FFT

algorithm

to

implement

a

fast

conversion

to

a

real

time-domain

signal

A

phase-lock

loop

keeps

the

receiver

frame-synchronized

with

the

transmitter

We

constructed

an

experimental

video

telephone

that

sends

pixel

logmap

images

at

frames

per

second

through

the

PSTN

Using

the

analog

channel

coding

scheme

we

achieve

an

effective

data

transfer

rate

in

excess

of

bits

per

second

KNOWLEDGE

PRECONDITIONS

FOR

PLANS

E.

Davis

May

For

an

agent

to

be

able

to

rely

on

a

plan

he

must

know

both

that

he

is

physically

capable

of

carrying

out

the

physical

actions

involved

and

that

he

knows

enough

to

carry

out

the

plan

In

this

talk

we

advance

and

discuss

new

definitions

of

knowing

enough

to

carry

out

a

plan

for

the

case

of

a

single

agent

carrying

out

a

sequence

of

primitive

actions

one

at

a

time

We

consider

both

determinate

and

indeterminate

plans

Definition

A

plan

P

-LRB-

determinate

or

indeterminate

-RRB-

is

executable

for

agent

A

at

time

T

if

and

only

if

a.

P

terminates

when

executed

starting

in

T

and

b

After

any

beginning

of

the

execution

of

P

starting

in

T

b.i

A

will

know

whether

P

has

successfully

finished

b.ii

A

will

know

of

every

action

whether

or

not

it

is

a

next

step

of

P

and

b.iii

All

the

next

steps

of

P

are

feasible

Definition

An

indeterminate

plan

P

is

epistemically

feasible

as

a

task

for

agent

A

at

time

T

if

there

exists

a

plan

P

such

that

A

knows

in

T

that

a.

P

is

executable

for

A

at

T

and

b.

Any

execution

of

P

starting

in

T

will

constitute

an

execution

of

P

starting

in

T

We

show

how

these

definition

can

be

expressed

in

a

formal

logic

using

a

situation

calculus

model

of

time

and

a

possible

worlds

model

of

knowledge

The

definitions

strictly

subsume

previous

theories

for

the

single-agent

case

without

concurrent

actions

We

illustrate

the

power

of

the

definition

by

showing

that

it

supports

results

of

the

following

kinds

ffl

Positive

verification

Showing

that

a

plan

is

feasible

ffl

Negative

verification

Showing

that

a

plan

is

infeasible

ffl

Monotonicity

The

more

an

agent

knows

the

more

plans

are

executable

ffl

Reduction

for

omniscient

agent

For

an

omniscient

agent

a

plan

is

executable

if

and

only

if

it

is

necessarily

physically

feasible

and

a

plan

is

epistemically

feasible

as

task

if

and

only

if

it

is

possibly

physically

feasible

ffl

Simple

recursive

rules

that

are

sufficient

conditions

for

the

feasibility

of

a

plan

described

as

a

sequence

or

a

conditional

combination

of

subplans

SCHWARZ

ANALYSIS

OF

ITERATIVE

SUBSTRUCTURING

ALGORITHMS

FOR

ELLIP

TIC

PROBLEMS

IN

THREE

DIMENSIONS

M.

Dryja

B.

Smith

O.

Widlund

May

Domain

decomposition

methods

provide

powerful

preconditioners

for

the

iterative

solution

of

the

large

systems

of

algebraic

equations

that

arise

in

finite

element

or

finite

difference

approximations

of

partial

differential

equations

The

preconditioners

are

constructed

from

exact

or

approximate

solvers

for

the

same

partial

differential

equation

restricted

to

a

set

of

subregions

into

which

the

given

region

has

been

divided

In

addition

the

preconditioner

is

often

augmented

by

a

coarse

second

level

approximation

that

provides

additional

global

exchange

of

information

and

which

can

enhance

the

rate

of

convergence

considerably

The

iterative

substructuring

methods

based

on

decompositions

of

the

region

into

non-overlapping

subregions

form

one

of

the

main

families

of

such

Many

domain

decomposition

algorithms

can

conveniently

be

described

and

analyzed

as

Schwarz

methods

These

algorithms

are

fully

defined

in

terms

of

a

set

of

subspaces

and

auxiliary

bilinear

forms

A

general

theoretical

framework

has

previously

been

developed

and

in

this

paper

these

techniques

are

used

in

an

analysis

of

iterative

substructuring

methods

for

elliptic

problems

in

three

dimensions

A

special

emphasis

is

placed

on

the

difficult

problem

of

designing

good

coarse

models

and

obtaining

robust

methods

for

which

the

rate

of

convergence

is

insensitive

to

large

variations

in

the

coefficients

of

the

differential

equation

Domain

decomposition

algorithms

can

conveniently

be

built

from

modules

which

represent

local

and

global

components

of

the

preconditioner

In

this

paper

a

number

of

such

possibilities

is

explored

and

it

is

demonstrated

how

a

great

variety

of

fast

algorithms

can

be

designed

and

analyzed

COMPETITIVE

ALGORITHMS

AND

LOWER

BOUNDS

FOR

ON-LINE

SCHEDULING

OF

MULTIPROCESSOR

REAL-TIME

SYSTEMS

G.

Koren

D.

Shasha

June

We

study

competitive

on-line

scheduling

in

multi-processor

real-time

environments

In

our

model

every

task

has

a

deadline

and

a

value

that

it

obtains

only

if

it

completes

by

its

deadline

A

task

can

be

assigned

to

any

processor

all

of

which

are

equally

powerful

The

problem

is

to

design

an

on-line

scheduling

algorithm

-LRB-

i.e.

the

scheduler

has

no

knowledge

of

a

task

until

it

is

released

-RRB-

with

worst

case

guarantees

as

to

the

total

value

obtained

by

the

system

We

study

systems

with

two

or

more

processors

and

with

uniform

or

non-uniform

value

density

We

present

an

inherent

limit

on

the

best

competitive

guarantee

that

any

on-line

parallel

real-time

scheduler

can

give

Then

we

present

a

competitive

algorithm

that

achieves

a

worst

case

guarantee

which

is

only

within

a

factor

of

from

the

best

possible

guarantee

in

many

cases

These

are

the

most

general

results

yet

known

for

parallel

overloaded

real-time

scheduling

A

PROBABILISTIC

APPROACH

TO

GEOMETRIC

HASHING

USING

LINE

FEATURES

F.

Tsai

June

Most

current

object

recognition

algorithms

assume

reliable

image

segmentation

which

in

practice

is

often

not

available

We

examine

the

combination

of

the

Hough

Transform

with

a

variation

of

Geometric

Hashing

as

a

technique

for

model-based

object

recognition

in

seriously

degraded

single

intensity

images

Prior

work

on

the

performance

analysis

of

geometric

hashing

has

focused

on

point

features

and

shown

its

noise

sensitivity

This

paper

uses

line

features

to

compute

recognition

invariants

in

a

potentially

more

robust

way

We

investigate

the

statistical

behavior

of

these

line

features

analytically

Various

viewing

transformations

which

-LRB-

or

flat

-RRB-

objects

undergo

during

image

formation

are

considered

For

the

case

of

affine

transformations

which

are

often

suitable

substitutes

for

more

general

perspective

transformations

we

show

experimentally

that

the

technique

is

noise

resistant

and

can

be

used

in

highly

occluded

environments

CHARACTERIZATION

OF

SELF-SIMILAR

MULTIFRACTALS

WITH

WAVELET

MAXIMA

W.-L

Hwang

S.

Mallat

August

Self-similar

multifractals

have

a

wavelet

transform

whose

maxima

define

self-similar

curves

in

the

scale-space

plane

We

introduce

an

algorithm

that

recovers

the

affine

self-similarity

parameters

through

a

voting

procedure

in

the

corresponding

parameter

space

The

voting

approach

is

robust

with

respect

to

renormalization

noises

and

can

recover

the

value

of

parameters

having

random

fluctuations

We

describe

numerical

applications

to

Cantor

measures

dyadique

multifractals

and

to

the

study

of

Diffusion

Limited

Aggregates

CONTROL

OF

A

DEXTEROUS

ROBOT

HAND

THEORY

IMPLEMENTATION

AND

EX

PERIMENT

N.

Silver

August

Advanced

robotic

systems

such

as

multi-fingered

hands

are

becoming

more

complex

and

as

yet

many

of

the

basic

questions

involved

remain

unanswered

What

control

law

should

we

use

What

constitutes

a

good

control

law

How

should

we

describe

motions

What

constitutes

a

broad

yet

efficient

description

of

motions

for

a

grasped

object

In

addition

to

the

complexity

robotic

systems

frequently

undergo

upgrades

and

it

is

therefore

necessary

to

design

the

system

in

an

organized

manner

This

includes

such

things

as

hierarchical

software

system

independent

descriptions

of

motion

system

independent

control

laws

In

this

thesis

we

address

these

issues

for

a

less

complex

system

We

have

focused

our

attention

on

describing

motions

for

objects

being

grasped

by

a

multi-fingered

hand

We

present

a

formulation

for

motion

primitives

which

allow

object

manipulation

and

require

limited

parameter

specification

We

have

attempted

to

find

a

control

law

which

will

perform

under

adverse

conditions

We

have

built

the

system

and

tested

it

on

the

NYU

Four

Finger

Manipulator

which

is

a

two

dimensional

hand

Even

for

this

simplified

problem

there

remains

a

large

degree

of

complexity

and

there

are

as

yet

no

definitive

solutions

to

these

problems

ED

I

NYU

EDUCATIONAL

ROBOT

DESIGN

AND

EVALUATION

B.

Mishra

M.

Antoniotti

August

The

primary

goal

of

the

NYU

educational

robot

project

is

to

create

a

disseminable

multi-functional

and

inexpensive

laboratory

course

sequence

aimed

at

improving

the

practical

skills

of

undergraduate

students

specializing

in

robotics

vision

AI

and

manufacturing

disciplines

The

main

work-horse

of

the

NYU

educational

project

was

chosen

to

be

a

multi-functional

ED

I

robot

system

consisting

of

a

DOF

DD

arm

and

several

auxiliary

devices

The

system

was

designed

to

be

simple

inexpensive

flexible

and

safe

In

this

report

we

describe

the

history

design

structure

and

evaluation

of

this

robot

system

We

also

describe

several

robotics

and

related

course

sequence

that

can

use

the

ED

I

system

effectively

We

also

provide

some

example

experiments

that

have

been

run

on

ED

I

successfully

This

report

has

benefited

from

the

labor

contribution

discussions

advice

and

criticisms

of

several

people

on

the

ED

I

project

team

and

the

credit

for

the

final

product

goes

to

the

entire

team

NEW

TECHNIQUES

FOR

THE

ANALYSIS

AND

IMPLEMENTATION

OF

FUNCTIONAL

PROGRAMS

T.-R

Chuang

August

Functional

programming

languages

provide

programmers

with

clean

semantics

and

side

-LCB-

effect

free

computation

which

make

easier

the

tasks

of

designing

programs

and

reasoning

about

them

Efficient

implementations

of

purely

functional

programs

however

can

pose

certain

challenges

Our

purpose

in

this

dissertation

is

to

develop

new

techniques

for

the

efficient

analysis

and

implementation

of

functional

programs

Our

first

goal

is

to

investigate

a

syntactic

approach

contrary

to

the

usual

semantic

approaches

of

finding

the

least

fixed

points

of

higher

-LCB-

order

functions

over

finite

domains

The

second

objective

is

to

develop

implementation

techniques

for

aggregate

data

structures

for

functional

programs

such

that

accesses

to

aggregates

are

both

efficient

and

side

-LCB-

effects

free

Finding

the

least

fixed

point

of

a

monotonic

function

over

a

finite

domain

is

an

essential

task

when

analyzing

a

functional

program

in

the

framework

of

abstract

interpretation

Previous

methods

for

least

fixed

point

finding

have

primarily

used

semantic

approaches

which

often

traverse

large

portions

of

the

semantic

domain

and

may

be

very

inefficient

even

for

simple

programs

We

propose

a

syntactic

method

based

on

an

augmented

simply

typed

lambda

calculus

It

is

shown

that

for

finite

domains

the

syntactic

method

is

both

sound

and

complete

with

respect

to

the

semantics

Moreover

we

demonstrate

that

the

proposed

syntactic

method

can

be

quite

effective

in

cases

where

the

usual

semantic

method

is

very

inefficient

Efficient

implementations

of

aggregate

data

structures

for

functional

programs

has

been

an

active

research

topic

The

problem

arises

because

once

an

aggregate

is

updated

both

the

old

version

and

newly

updated

copy

must

be

preserved

to

maintain

the

side

-LCB-

effect

free

semantics

of

functional

languages

We

modify

the

shallow

binding

scheme

of

Baker

to

implement

functional

arrays

for

efficient

incremental

updates

and

voluminous

reads

The

scheme

however

uses

side

-LCB-

effects

and

can

not

be

implemented

in

purely

functional

languages

themselves

We

then

investigate

the

possibility

of

implementing

efficient

aggregates

without

using

side

-LCB-

effects

and

show

that

real

-LCB-

time

deques

can

be

implemented

in

a

purely

functional

way

We

describe

several

interesting

applications

of

this

technique

NORMS

OF

FUNCTIONS

OF

MATRICES

A.

Greenbaum

August

Let

A

be

an

n

by

n

matrix

and

let

be

a

diagonal

matrix

of

eigenvalues

of

A

An

expression

is

given

for

the

smallest

number

such

that

kp

-LRB-

A

-RRB-

kF

kp

-LRB-

-RRB-

kF

for

all

polynomials

p

where

k

kF

denotes

the

Frobenius

norm

It

is

shown

that

if

A

has

distinct

eigenvalues

then

the

well-known

bound

-LCB-

minV

F

-LRB-

V

-RRB-

where

F

denotes

the

Frobenius

norm

condition

number

and

the

minimum

is

taken

over

all

eigenvector

matrices

V

of

A

-LCB-

is

within

a

factor

of

n

of

the

optimal

constant

Classes

of

matrices

A

and

polynomials

p

for

which

the

sharp

upper

bound

is

also

a

reasonable

estimate

of

kp

-LRB-

A

-RRB-

kF

are

described

BIDIRECTIONAL

EDGES

PROBLEM

PART

I

A

SIMPLE

ALGORITHM

B.

Mishra

September

The

bidirectional

edges

problem

is

to

find

an

edge-labelling

of

an

undirected

network

G

-LRB-

V

E

-RRB-

with

a

source

and

a

sink

such

that

an

edge

-LSB-

u

v

-RSB-

in

E

is

labelled

u

v

or

v

u

-LRB-

or

both

-RRB-

depending

on

the

existence

of

a

-LRB-

simple

-RRB-

path

from

the

source

to

sink

that

visits

the

vertices

u

and

v

in

the

order

u

v

or

v

u

respectively

We

provide

several

algorithms

for

this

problem

in

the

current

paper

and

the

accompanying

sequel

In

this

paper

we

show

the

relation

between

this

problem

and

the

classical

two-vertex-disjoint-paths

problem

and

then

devise

a

simple

algorithm

with

a

time

complexity

of

O

-LRB-

jEjjV

-RRB-

In

the

sequel

we

improve

the

time

complexity

to

O

-LRB-

jEjjV

j

-RRB-

The

main

technique

exploits

a

clever

partition

of

the

graph

into

a

set

of

paths

and

bridges

which

are

then

analyzed

recursively

Bidirectional

edges

problem

arises

naturally

in

the

context

of

the

simulation

of

an

MOS

transistor

network

in

which

a

transistor

may

operate

as

a

unilateral

or

a

bilateral

device

depending

on

the

voltages

at

its

source

and

drain

nodes

For

efficient

simulation

it

is

required

to

detect

the

set

of

transistors

that

may

operate

as

bilateral

devices

Also

sometimes

it

is

intended

to

propagate

information

in

one

direction

only

and

propagation

in

the

wrong

direction

-LRB-

resulting

in

a

sneak

path

can

cause

functional

error

Our

algorithms

can

be

used

to

detect

all

the

sneak

paths

BIDIRECTIONAL

EDGES

PROBLEM

PART

II

AN

EFFICIENT

ALGORITHM

B.

Mishra

September

The

bidirectional

edges

problem

is

to

find

an

edge-labelling

of

an

undirected

network

G

-LRB-

V

E

-RRB-

with

a

source

and

a

sink

such

that

an

edge

-LSB-

u

v

-RSB-

in

E

is

labelled

u

v

or

v

u

-LRB-

or

both

-RRB-

depending

on

the

existence

of

a

-LRB-

simple

-RRB-

path

from

the

source

to

sink

that

visits

the

vertices

u

and

v

in

the

order

u

v

or

v

u

respectively

In

this

paper

building

upon

the

machinery

developed

in

a

prequel

we

devise

an

efficient

algorithm

for

this

problem

with

a

time

complexity

of

O

-LRB-

E

V

-RRB-

The

main

technique

exploits

a

clever

partition

of

the

graph

into

a

set

of

paths

and

bridges

which

are

then

analyzed

recursively

Bidirectional

edges

problem

arises

naturally

in

the

context

of

the

simulation

of

an

MOS

transistor

network

in

which

a

transistor

may

operate

as

a

unilateral

or

a

bilateral

device

depending

on

the

voltages

at

its

source

and

drain

nodes

Here

it

is

required

to

detect

the

set

of

transistors

that

may

operate

as

bilateral

devices

ITERATIVE

SUBSTRUCTURING

METHODS

FOR

SPECTRAL

ELEMENTS

IN

THREE

DI

MENSIONS

L

Pavarino

Olof

B.

Widlund

September

Iterative

substructuring

methods

form

an

important

family

of

domain

decomposition

algorithms

for

elliptic

finite

element

problems

The

p-version

finite

element

method

based

on

continuous

piecewise

Qp

functions

is

considered

for

second

order

elliptic

problems

in

three

dimensions

this

special

method

can

also

be

viewed

as

a

spectral

element

method

An

iterative

method

is

designed

for

which

number

of

the

relevant

operator

grows

only

in

proportion

to

-LRB-

log

p

-RRB-

ITERATIVE

SOLUTION

OF

ELLIPTIC

FINITE

ELEMENT

PROBLEMS

ON

PARTIALLY

REFINED

MESHES

AND

THE

EFFECT

OF

USING

INEXACT

SOLVERS

H.

Cheng

October

We

will

consider

some

solution

methods

for

the

linear

systems

of

algebraic

equations

which

arise

from

second-order

elliptic

finite

element

problems

We

first

consider

iterative

refinement

methods

Historically

these

methods

were

called

FAC

and

AFAC

methods

Optimal

bounds

of

the

condition

number

for

the

AFAC

iterative

operator

are

established

by

proving

a

strengthened

Cauchy-Schwarz

inequality

using

an

interpolation

theorem

for

Hilbert

scales

This

work

completes

earlier

work

by

Dryja

and

Widlund

We

also

apply

an

extension

theorem

for

finite

element

functions

to

get

a

weaker

bound

under

a

more

general

assumption

The

optimality

of

the

FAC

method

when

spectrally

equivalent

inexact

solvers

are

used

is

also

proved

by

using

similar

techniques

We

next

consider

multilevel

additive

Schwarz

methods

with

partial

refinement

These

algorithms

are

generalizations

of

the

multilevel

additive

Schwarz

methods

developed

by

Dryja

and

Widlund

and

many

others

We

use

quasi-interpolants

to

prove

that

this

class

of

methods

has

an

optimal

condition

number

which

is

independent

of

the

selection

of

refinement

subregions

under

quite

general

assumptions

The

third

algorithm

which

we

develop

is

a

domain

decomposition

parallel

preconditioning

method

-LRB-

DD-PPM

-RRB-

The

preconditioner

is

closely

related

to

the

construction

of

an

operator

providing

a

uniformly

bounded

extension

from

the

boundary

of

the

nonoverlapping

subdomains

to

the

interior

of

these

subdomains

This

method

is

well

suited

for

the

computation

of

finite

element

solutions

on

multiprocessor

computer

architectures

We

also

obtain

a

new

condition

number

estimate

for

general

DD-PPM

which

is

sharper

than

those

previously

known

by

using

the

framework

of

additive

Schwarz

methods

Finally

we

develop

an

iterative

substructuring

method

which

is

a

variation

of

Smith

's

vertex

space

method

by

using

the

similar

idea

of

the

previous

algorithm

Some

numerical

experiments

illustrate

the

difference

between

this

algorithm

and

that

of

Smith

A

SURVEY

OF

COMPUTATIONAL

DIFFERENTIAL

ALGEBRA

B.

Mishra

October

In

this

note

we

explore

the

computational

aspects

of

several

problems

in

differential

algebra

with

concrete

applications

in

dynamics

and

motion-planning

problems

in

robotics

automatic

synthesis

of

control

schemes

for

nonlinear

systems

and

simulation

of

physical

systems

with

fixed

degrees

of

freedom

Our

primary

aim

is

to

study

compute

and

structurally

describe

the

solution

of

a

system

of

differential

equations

with

coefficients

in

a

field

-LRB-

say

the

field

of

complex

numbers

-RRB-

There

seem

to

have

been

various

approaches

in

this

direction

e.g.

ideal

theoretic

approach

of

Ritt

Galois

theoretic

approach

of

Kolchin

and

Singer

and

group

theoretic

technique

of

Lie

It

is

interesting

to

study

their

interrelationship

and

effectivity

of

various

problems

they

suggest

In

general

these

problems

are

known

to

be

uncomputable

thus

we

need

to

understand

under

what

situations

these

problems

become

feasible

As

related

computer

science

questions

we

also

need

to

study

the

complexity

of

these

problems

underlying

data-structures

effects

of

the

representation

-LRB-

e.g.

sparsity

-RRB-

Of

related

interest

are

some

closely-related

problems

such

as

symbolic

integration

problem

solving

difference

equations

integro-differential

equations

and

differential

equations

with

algebraic

constraints

Miniature

Direct

Drive

Rotary

Actuators

II

Eye

Finger

and

Leg

R.

Wallace

November

We

have

developed

miniature

direct

drive

DC

motor

actuators

for

robotics

These

actuators

have

low

friction

small

size

high

speed

low

construction

cost

no

gear

backlash

operate

safely

without

the

use

of

limit

switches

and

generate

moderate

torque

at

a

high

torque

to

weight

ratio

Our

initial

experiments

indicated

the

feasibility

of

constructing

a

variety

of

new

high

speed

low

cost

actuators

for

applications

in

camera

pointing

robot

hands

and

robot

legs

In

this

work

we

study

some

prototype

devices

in

each

of

these

categories

Feedback

Control

of

Miniature

Direct

Drive

Devices

D.

Max

R.

Wallace

We

discuss

dynamics

and

control

of

miniature

direct

drive

actuators

specifically

for

the

two

axis

spherical

pointing

motor

and

for

the

one

axis

direct

drive

finger

joint

These

actuators

can

move

both

accurately

and

at

high

speed

however

the

capabilities

of

these

devices

can

not

be

fully

exploited

using

open

loop

control

techniques

We

derive

an

ideal

PID

feedback

control

scheme

Our

initial

experiments

indicate

that

PID

feedback

control

for

the

SPM

and

finger

joint

is

highly

feasible

and

a

significant

improvement

over

open

loop

methods

NYU

Educational

Robotics

Project

A

Pedagogic

Overview

B.

Mishra

M.

Antoniotti

F.

Hansen

and

R.

Wallace

November

The

primary

goal

of

the

NYU

educational

robotics

project

-LRB-

NYU-ED

-RRB-

is

to

create

a

disseminable

multi-functional

and

inexpensive

laboratory

course

sequence

aimed

at

improving

the

practical

skills

of

undergraduate

students

specializing

in

robotics

vision

AI

and

manufacturing

disciplines

The

earlier

approaches

to

robotics

laboratory

education

have

been

to

use

either

industrial

robot

arms

or

commerciallyavailable

low-power

arms

In

each

case

there

have

been

considerable

problems

in

the

lack

of

an

ideal

interface

in

not

providing

enough

flexibility

to

add

other

devices

or

in

the

absence

of

adequate

safety

Also

the

underlying

dynamical

model

is

usually

so

complicated

that

performing

any

control

experiment

has

been

beyond

the

scope

of

all

but

advanced

graduate

students

In

this

report

we

describe

our

approach

to

deal

with

these

problems

in

constructing

a

modern

robotics

laboratory

The

main

work-horse

of

the

NYU

educational

project

was

chosen

to

be

a

multi-functional

ED

I

robot

system

consisting

of

a

DOF

DD

arm

and

several

auxiliary

devices

The

system

was

designed

to

be

simple

inexpensive

flexible

and

safe

We

also

describe

our

experience

with

some

advanced

laboratory

experiments

using

miniature

direct

drive

robots

that

have

proven

to

be

ideal

for

teaching

as

they

are

reconfigurable

safe

and

easy

to

program

Multilevel

Schwarz

Methods

with

Partial

Refinement

H.

Cheng

We

consider

multilevel

additive

Schwarz

methods

with

partial

refinement

These

algorithms

are

generalizations

of

the

multilevel

additive

Schwarz

methods

developed

by

Dryja

and

Widlund

and

many

others

We

will

give

two

different

proofs

by

using

quasi-interpolants

under

two

different

assumptions

on

selected

refinement

subregions

to

show

that

this

class

of

methods

has

an

optimal

condition

number

The

first

proof

is

based

purely

on

the

localization

property

of

quasi-interpolants

However

the

second

proof

use

some

results

on

iterative

refinement

methods

As

a

by-product

the

multiplicative

versions

which

corresponds

to

the

FAC

algorithms

with

inexact

solvers

consisting

of

one

Gauss-Seidel

or

damped

Jacobi

iteration

have

optimal

rates

of

convergence

Finally

some

numerical

results

are

presented

for

these

methods

Pscheme

Extending

Continuations

to

Express

Control

and

Synchronization

in

a

Parallel

LISP

C.

Yao

B.

Goldberg

March

In

this

paper

we

describe

Pscheme

a

parallel

dialect

of

Scheme

The

primary

construct

for

specifying

parallelism

synchronization

and

communication

is

a

natural

extension

of

first-class

continuations

which

we

call

a

port

We

describe

the

behavior

of

ports

along

with

the

other

parallel

constructs

of

Pscheme

Because

the

user

has

precise

control

over

the

parallel

computation

the

Pscheme

constructs

can

be

used

to

build

higher-level

parallel

programming

abstractions

such

as

futures

semaphores

and

Ada-style

rendezvous

We

provide

the

Pscheme

code

for

these

abstractions

and

discuss

the

current

implementation

of

Pscheme

on

a

shared-memory

multiprocessor

Adaptive

Time-Frequency

Approximations

with

Matching

Pursuits

G.

Davis

S.

Mallat

Z.

Zhang

Computing

the

optimal

expansion

of

a

signal

in

a

redundant

dictionary

of

waveforms

is

an

NP-complete

problem

We

introduce

a

greedy

algorithm

called

a

matching

pursuit

which

computes

a

sub-optimal

expansion

The

dictionary

waveforms

which

best

match

a

signal

's

structures

are

chosen

iteratively

An

orthogonalized

version

of

the

matching

pursuit

is

also

developed

Matching

pursuits

are

general

procedures

for

computing

adaptive

signal

representations

With

a

dictionary

of

Gabor

functions

a

matching

pursuit

defines

an

adaptive

time-frequency

transform

We

derive

a

signal

energy

distribution

in

the

time-frequency

plane

which

does

not

contain

interference

terms

unlike

the

Wigner

and

Cohen

class

distributions

A

matching

pursuit

is

a

chaotic

map

whose

asymptotic

properties

are

studied

We

describe

an

algorithm

which

isolates

the

coherent

structures

of

a

signal

and

show

an

application

to

pattern

extraction

from

noisy

signals

Stability

Theory

for

Dissipatively

Perturbed

Hamiltonian

Systems

J.

Maddocks

M.

Overton

It

is

shown

that

for

an

appropriate

class

of

dissipatively

perturbed

Hamiltonian

systems

the

number

of

unstable

modes

of

the

dynamics

linearized

at

a

nondegenerate

equilibrium

is

determined

solely

by

the

index

of

the

equilibrium

regarded

as

a

critical

point

of

the

Hamiltonian

In

addition

the

movement

of

the

associated

eigenvalues

in

the

limit

of

vanishing

dissipation

is

analyzed

A

New

Primal-Dual

Interior-Dual

Interior-Point

Method

for

Semidefinite

Programming

F.

Alizadeh

J.P.

Haeberly

M.

Overton

Semidefinite

programming

-LRB-

SDP

-RRB-

is

a

convex

optimization

problem

in

the

space

of

symmetric

matrices

Primal-dual

interiorpoint

methods

for

SDP

are

discussed

These

generate

primal

and

dual

matrices

X

and

Z

which

commute

only

in

the

limit

A

new

method

is

proposed

which

iterates

in

the

space

of

commuting

matrices

Optimizing

Eigenvalues

of

Symmetric

Definite

Pencils

J.P.

Haeberly

M.

Overton

We

consider

the

following

quasiconvex

optimization

problem

minimize

the

largest

eigenvalue

of

a

symmetric

definite

matrix

pencil

depending

on

parameters

A

new

form

of

optimality

conditions

is

given

emphasizing

a

complementarity

condition

on

primal

and

dual

matrices

Newton

's

method

is

then

applied

to

these

conditions

to

give

a

new

quadratically

convergent

interior-point

method

which

works

well

in

practice

The

algorithm

is

closely

related

to

primal-dual

interior-point

methods

for

semidefinite

programming

A

Polylogarithmic

Bound

for

an

Iterative

Substructuring

Method

for

Special

Elements

in

Three

Dimensions

L.

Pavarino

O.

Widlund

Iterative

substructuring

methods

form

an

important

family

of

domain

decomposition

algorithms

for

elliptic

finite

element

problems

A

p-version

finite

element

method

based

on

continuous

piecewise

Qp

functions

is

considered

for

second

order

elliptic

problems

in

three

dimensions

this

special

method

can

also

be

viewed

as

a

conforming

spectral

element

method

An

iterative

method

is

designed

for

which

the

condition

number

of

the

relevant

operator

grows

only

in

proportion

to

-LRB-

log

p

-RRB-

This

bound

is

independent

of

jumps

in

the

coefficient

of

the

elliptic

problem

across

the

interfaces

between

the

subregions

Numerical

results

are

also

reported

which

support

the

theory

Multilevel

Schwarz

Methods

for

Elliptic

Problems

with

Discontinous

Coefficients

in

Three

Dimensions

M.

Dryja

M.

Sarkis

O.

Widlund

Multilevel

Schwarz

methods

are

developed

for

a

conforming

finite

element

approximation

of

second

order

elliptic

problems

We

focus

on

problems

in

three

dimensions

with

possibly

large

jumps

in

the

coefficients

across

the

interface

separating

the

subregions

We

establish

a

condition

number

estimate

for

the

iterative

operator

which

is

independent

of

the

coefficients

and

grows

at

most

as

the

square

of

the

number

of

levels

We

also

characterize

a

class

of

distributions

of

the

coefficients

called

quasi-monotone

for

which

the

weighted

is

stable

and

for

which

we

can

use

the

standard

piecewise

linear

functions

as

a

coarse

space

In

this

case

we

obtain

optimal

methods

i.e.

bounds

which

are

independent

of

the

number

of

levels

and

subregions

We

also

design

and

analyze

multilevel

methods

with

new

coarse

spaces

given

by

simple

explicit

formulas

We

consider

nonuniform

meshes

and

conclude

by

an

analysis

of

multilevel

iterative

substructuring

methods

Iterative

Substructuring

Methods

for

Spectral

Elements

Problems

in

Three

Dimensions

Based

on

Numerical

Quadrature

L.

Pavarino

O.

Widlund

Iterative

substructuring

methods

form

an

important

family

of

domain

decomposition

algorithms

for

elliptic

finite

element

problems

Two

preconditioners

for

p-version

finite

element

methods

based

on

continuous

piecewise

Qp

functions

are

considered

for

second

order

elliptic

problems

in

three

dimensions

these

special

methods

can

also

be

viewed

as

spectral

element

methods

The

first

iterative

method

is

designed

for

the

Galerkin

formulation

of

the

problem

The

second

applies

to

linear

systems

for

a

discrete

model

derived

by

using

Gauss-Lobatto-Legendre

quadrature

For

both

methods

it

is

established

that

the

condition

number

of

the

relevant

operator

grows

only

in

proportion

to

-LRB-

log

p

-RRB-

These

bounds

are

independent

of

the

number

of

elements

into

which

the

given

region

has

been

divided

their

diameters

as

well

as

the

jumps

in

the

coefficients

of

the

elliptic

equation

between

elements

Results

of

numerical

computations

are

also

given

which

provide

upper

bounds

on

the

condition

numbers

as

functions

of

p

and

which

confirms

the

correctness

of

our

theory

Conceptual

and

Pragmatic

Tools

for

Design

and

Control

of

Manufacturing

Systems

M.

Antoniotti

In

this

survey

we

explore

two

conceptual

tools

that

have

been

used

in

recent

-LRB-

and

not

so

recent

-RRB-

years

to

build

models

of

and

to

control

various

Manufacturing

Systems

-LRB-

MS

-RRB-

and

processes

Our

aim

is

to

investigate

some

computational

frameworks

that

could

be

interpreted

and

used

to

-LRB-

partially

-RRB-

perform

the

tasks

of

Simulation

of

an

-LRB-

arbitrary

-RRB-

MS

Preventive

Verification

of

some

of

its

properties

Evaluation

of

some

of

its

characteristic

parameters

Control

of

its

behavior

These

tasks

require

well

defined

computational

models

that

should

be

easily

equipped

with

an

appropriate

semantics

capable

of

expressing

several

properties

of

MS

's

Petri

Nets

and

RW-Systems

satisfy

these

requirements

generalized gradient
spectral radius
symmetric matrix

max characterization
maximum eigenvalues
minimax problem