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ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS
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S. IYANIWURA, M. J. WARD
Journal:

The ANZIAM Journal / Volume 63 / Issue 1 / January 2021

Published online by Cambridge University Press:

01 March 2021, pp. 1-22
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A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as “traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps.

ANZ VOLUME 62 ISSUE 3 COVER AND BACK MATTER
Journal:

The ANZIAM Journal / Volume 62 / Issue 3 / July 2020

Published online by Cambridge University Press:

01 February 2021, pp. b1-b5
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ANZ VOLUME 62 ISSUE 3 COVER AND FRONT MATTER
Journal:

The ANZIAM Journal / Volume 62 / Issue 3 / July 2020

Published online by Cambridge University Press:

01 February 2021, pp. f1-f2
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OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY
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- Operations research and management science
K. G. SIRINANDA, M. BRAZIL, P. A. GROSSMAN, J. H. RUBINSTEIN, D. A. THOMAS
Journal:

The ANZIAM Journal / Volume 62 / Issue 3 / July 2020

Published online by Cambridge University Press:

18 January 2021, pp. 334-351
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The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described in an earlier paper by the authors is applicable to a class of real mine planning problems, by using the algorithm to design a part of the underground access in the Rubicon gold mine near Kalgoorlie in Western Australia. The algorithm is used to design a decline connecting two ore bodies so as to maximize the net present value (NPV) associated with the connector. The connector is to break out from the access infrastructure of one ore body and extend to the other ore body. There is a junction on the connector where it splits in two near the second ore body. The GCDSPA is used to obtain the optimal location of the junction and the corresponding NPV. The result demonstrates that the GCDSPA can be used to solve certain problems in mine planning for which currently available methods cannot provide optimal solutions.

Part Three - Semirandom Models
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 165-166
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9 - Introduction to Semirandom Models
from Part Three - Semirandom Models
- By Uriel Feige
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp 189-211
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7 - Sparse Recovery
from Part Two - Deterministic Models of Data
- By Eric Price
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp 140-164
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10 - Semirandom Stochastic Block Models
from Part Three - Semirandom Models
- By Ankur Moitra
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 212-233
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Part Five - Applications in Machine Learning and Statistics
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp 359-360
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26 - When Simple Hash Functions Suffice
from Part Six - Further Applications
- By Kai-Min Chung, Michael Mitzenmacher, Salil Vadhan
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp 567-585
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29 - Data-Driven Algorithm Design
from Part Six - Further Applications
- By Maria-Florina Balcan
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp 626-645
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Index
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 663-686
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30 - Algorithms with Predictions
from Part Six - Further Applications
- By Michael Mitzenmacher, Sergei Vassilvitskii
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp 646-662
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21 - Why Do Local Methods Solve Nonconvex Problems?
from Part Five - Applications in Machine Learning and Statistics
- By Tengyu Ma
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 465-485
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13 - Smoothed Analysis of Local Search
from Part Four - Smoothed Analysis
- By Bodo Manthey
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 285-308
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Frontmatter
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

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17 December 2020

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14 January 2021, pp i-iv
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12 - Self-Improving Algorithms
from Part Three - Semirandom Models
- By C. Seshadhri
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 259-282
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23 - Instance Optimal Distribution Testing and Learning
from Part Five - Applications in Machine Learning and Statistics
- By Gregory Valiant, Paul Valiant
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 506-526
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16 - Noise in Classification
from Part Five - Applications in Machine Learning and Statistics
- By Maria-Florina Balcan, Nika Haghtalab
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

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14 January 2021, pp 361-381
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Contents
Edited by Tim Roughgarden, Columbia University, New York
Book:

Beyond the Worst-Case Analysis of Algorithms

Published online:

17 December 2020

Print publication:

14 January 2021, pp v-xii
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ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS

ANZ VOLUME 62 ISSUE 3 COVER AND BACK MATTER

ANZ VOLUME 62 ISSUE 3 COVER AND FRONT MATTER

OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY

Part Three - Semirandom Models

9 - Introduction to Semirandom Models

7 - Sparse Recovery

10 - Semirandom Stochastic Block Models

Part Five - Applications in Machine Learning and Statistics

26 - When Simple Hash Functions Suffice

29 - Data-Driven Algorithm Design

Index

30 - Algorithms with Predictions

21 - Why Do Local Methods Solve Nonconvex Problems?

13 - Smoothed Analysis of Local Search

Frontmatter

12 - Self-Improving Algorithms

23 - Instance Optimal Distribution Testing and Learning

16 - Noise in Classification

Contents

Optimization

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3869 results in Optimization