Neil J. Gunther
Encyclopedia
Neil Gunther, is a computer
information systems
researcher
best known internationally for developing the open-source performance modeling software Pretty Damn Quick and developing the Guerrilla approach to computer capacity planning and performance analysis. He has also been cited for his contributions to the theory of large transients
in computer systems and packet networks, and his universal law of computational scalability
.
Gunther is a Senior Member of both the Association for Computing Machinery
(ACM) and the Institute of Electrical and Electronics Engineers
(IEEE), as well as a member of the American Mathematical Society
(AMS), American Physical Society
(APS), Computer Measurement Group
(CMG) and ACM SIGMETRICS
.
He is currently focused on developing quantum information
system technologies.
and Scots
ancestry, born in Melbourne
on 15 August 1950. He attended Preston East Primary School from 1955 to 1956, and Balwyn North Primary School from 1956 until 1962. For his tenth birthday, Gunther received a copy of the now famous book entitled The Golden Book of Chemistry Experiments
from an older cousin. Inspired by the book, he started working on various experiments, making use of various chemicals that could be found around in his house. After he spilled some potassium permanganate
solution on his bedroom carpet his mother confined him to an alcove in the garage which he turned into a small laboratory
, replete with industrial chemicals and second-hand laboratory glassware
. Gunther was interested in finding out how things like detergents and oils were composed by cracking
them in his fractionating column
. He took particular interest in mixing paints for his art classes, as well as his chemistry classes in Balwyn High School
. His father, being the Superintendent of Melbourne's electrical power station, borrowed an organic chemistry text from the chemists in the quality control laboratory. This ultimately led to an intense interest in synthesizing Azo dyes
. At around age 14, Gunther attempted to predict the color of azo dyes based on the chromophore
-auxochrome
combination. Apart from drawing up empirical tables, this effort was largely unsuccessful due to his lack of knowledge of quantum theory
.
from 1980-1981. He then joined Syncal Corporation, a small company contracted by NASA
and JPL to develop thermoelectric materials for their deep-space missions. Gunther was asked to analyze the thermal stability
test data from the Voyager
RTG
s. He discovered that the stability of the silicon
-germanium
(Si-Ge) thermoelectric alloy was controlled by a soliton
-based precipitation mechanism. JPL used his work to select the next generation of RTG materials for the Galileo mission launched in 1989.
to develop parametric and functional test software for PARC's small-scale VLSI design fabrication line. Ultimately, he was recruited onto the Dragon multiprocessor workstation project where he also developed the PARCbench multiprocessor benchmark. This was his first fore into computer performance analysis.
1989, he developed a Wick-rotated
version of Richard Feynman
's quantum path integral formalism
for analyzing performance degradation in large-scale computer systems and packet networks.
(now part of Fujitsu Siemens Computers) where he held positions as Senior Scientist and Manager of the Performance Analysis Group that was responsible for attaining industry-high TPC
benchmarks on their Unix
multiprocessors. He also performed simulations for the design of the Reliant RM1000 parallel database server.
in 1994, to provide consulting and educational services for the management of high performance computer systems with an emphasis on performance analysis
and enterprise-wide capacity planning
. He went on to release and develop his own open-source performance modeling
software called "PDQ (Pretty Damn Quick)" around 1998. That software also accompanied his first textbook on performance analysis entitled The Practical Performance Analyst. Several other books have followed since then.
. During the course of his research in this area, he has developed a theory of photon bifurcation that is currently being tested experimentally at École Polytechnique Fédérale de Lausanne
. This represents yet another application of path integral formulation
to circumvent the wave-particle duality of light.
In its simplest rendition, this theory can be considered as providing the quantum
corrections to the Abbe
-Rayleigh diffraction
theory of imaging and the Fourier theory
of optical information processing.
and information visualization
. In 1991, he developed a tool called Barry, which employs barycentric coordinates
to visualize sampled CPU usage data on large-scale multiprocessor
systems. More recently, he has applied the same 2-simplex
barycentric coordinates to visualizing the Apdex
application performance metric, which is based on categorical response time data. A barycentric 3-simplex] (a tetrahedron
), that can be swivelled on the computer screen using a mouse
, has been found useful for visualizing packet network performance data. In 2008, he co-founded the PerfViz google group.
where N represents either the number of physical processors in the hardware
configuration or the number of users driving the software application. The parameters
and 
represent respectively the levels of contention (e.g., queueing for shared resources) and coherency delay (i.e., latency for data to become consistent) in the system. The 
parameter also quantifies the retrograde throughput seen in many stress tests but not accounted for in either Amdahl's law
or event-based simulations
.
This scalability law was originally developed by Gunther in 1993 while he was employed at Pyramid Technology
. Since there are no topological dependencies, C(N) can model symmetric multiprocessors
, multicores
, clusters
, and GRID
architectures. Also, because each of the three terms has a definite physical meaning, they can be employed as a heuristic
to determine where to make performance improvements in hardware platforms or software applications.
At a more fundamental level, the above equation can be derived from the Machine Repairman queueing model:
The following corollary (Gunther 2008 with
) corresponds to Amdahl's law:
, not with the goal of developing a technical proof
of the original conjecture but rather, using computers as a tool to examine it for structure that might lead to better computer-generated visualizations
of this and related problems in number theory
. In one early attempt along these lines he employed VRML
. Paul Erdös famously stated about the 3x+1 problem, "Mathematics is not yet ready for such problems." Gunther thinks that perhaps computers are.
More formally, Gunther has developed a functional Diophantine equation
that generalizes Terra’s theorem (1976) and is based on a graphical primitive: the G-set. The G-set is related to the predecessor sets of Wirsching by the following theorem.
The proof is unpublished. This theorem leads to the following conjecture for the construction of
.
Ironically, given his lack of intent to find a proof, the formal associations with the theorems of Terras and Wirsching, make it plausible that this method of sub-graph enumeration might form the basis of an inductive proof.
B.Sc. Honors dissertation, Department of Physics, Oct. (1974)
University (AUS), M.Sc. dissertation, Department of Applied Mathematics, Nov. (1976)
dissertation, Department of Physics, Dec. (1979)
Heidelberg, Germany, October 2001, ISBN 3540421459 (Contributed chapter)
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
information systems
Information systems
Information Systems is an academic/professional discipline bridging the business field and the well-defined computer science field that is evolving toward a new scientific area of study...
researcher
Researcher
A researcher is somebody who performs research, the search for knowledge or in general any systematic investigation to establish facts. Researchers can work in academic, industrial, government, or private institutions.-Examples of research institutions:...
best known internationally for developing the open-source performance modeling software Pretty Damn Quick and developing the Guerrilla approach to computer capacity planning and performance analysis. He has also been cited for his contributions to the theory of large transients
Transient (computer programming)
-Java:In the Java programming language, transient is a keyword used as a field modifier. When a field is declared transient, it would not be serialized even if the class to which it belongs is serialized...
in computer systems and packet networks, and his universal law of computational scalability
Scalability
In electronics scalability is the ability of a system, network, or process, to handle growing amount of work in a graceful manner or its ability to be enlarged to accommodate that growth...
.
Gunther is a Senior Member of both the Association for Computing Machinery
Association for Computing Machinery
The Association for Computing Machinery is a learned society for computing. It was founded in 1947 as the world's first scientific and educational computing society. Its membership is more than 92,000 as of 2009...
(ACM) and the Institute of Electrical and Electronics Engineers
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers is a non-profit professional association headquartered in New York City that is dedicated to advancing technological innovation and excellence...
(IEEE), as well as a member of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
(AMS), American Physical Society
American Physical Society
The American Physical Society is the world's second largest organization of physicists, behind the Deutsche Physikalische Gesellschaft. The Society publishes more than a dozen scientific journals, including the world renowned Physical Review and Physical Review Letters, and organizes more than 20...
(APS), Computer Measurement Group
Computer Measurement Group
The Computer Measurement Group , founded in 1974, is a worldwide non-profit organization of data processing professionals whose work involves measuring and managing the performance of computing systems...
(CMG) and ACM SIGMETRICS
SIGMETRICS
SIGMETRICS is the Association for Computing Machinery's Special Interest Group on Measurement and Evaluation, which specializes in the field of performance analysis of computer systems.The group have organised an annual conference of the same name since 1973....
.
He is currently focused on developing quantum information
Quantum information
In quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...
system technologies.
Biography
Gunther is an Australian of GermanGermans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
and Scots
Scottish people
The Scottish people , or Scots, are a nation and ethnic group native to Scotland. Historically they emerged from an amalgamation of the Picts and Gaels, incorporating neighbouring Britons to the south as well as invading Germanic peoples such as the Anglo-Saxons and the Norse.In modern use,...
ancestry, born in Melbourne
Melbourne
Melbourne is the capital and most populous city in the state of Victoria, and the second most populous city in Australia. The Melbourne City Centre is the hub of the greater metropolitan area and the Census statistical division—of which "Melbourne" is the common name. As of June 2009, the greater...
on 15 August 1950. He attended Preston East Primary School from 1955 to 1956, and Balwyn North Primary School from 1956 until 1962. For his tenth birthday, Gunther received a copy of the now famous book entitled The Golden Book of Chemistry Experiments
The Golden Book of Chemistry Experiments
The Golden Book of Chemistry Experiments was a children's chemistry book written in the 1960s by Robert Brent and illustrated by Harry Lazarus and published by Western Publishing in their Golden Books series. Many of the experiments contained in the book are now considered "dangerous for...
from an older cousin. Inspired by the book, he started working on various experiments, making use of various chemicals that could be found around in his house. After he spilled some potassium permanganate
Potassium permanganate
Potassium permanganate is an inorganic chemical compound with the formula KMnO4. It is a salt consisting of K+ and MnO4− ions. Formerly known as permanganate of potash or Condy's crystals, it is a strong oxidizing agent. It dissolves in water to give intensely purple solutions, the...
solution on his bedroom carpet his mother confined him to an alcove in the garage which he turned into a small laboratory
Laboratory
A laboratory is a facility that provides controlled conditions in which scientific research, experiments, and measurement may be performed. The title of laboratory is also used for certain other facilities where the processes or equipment used are similar to those in scientific laboratories...
, replete with industrial chemicals and second-hand laboratory glassware
Laboratory glassware
Laboratory glassware refers to a variety of equipment, traditionally made of glass, used for scientific experiments and other work in science, especially in chemistry and biology laboratories...
. Gunther was interested in finding out how things like detergents and oils were composed by cracking
Cracking (chemistry)
In petroleum geology and chemistry, cracking is the process whereby complex organic molecules such as kerogens or heavy hydrocarbons are broken down into simpler molecules such as light hydrocarbons, by the breaking of carbon-carbon bonds in the precursors. The rate of cracking and the end products...
them in his fractionating column
Fractionating column
A fractionating column or fractionation column is an essential item used in the distillation of liquid mixtures so as to separate the mixture into its component parts, or fractions, based on the differences in their volatilities...
. He took particular interest in mixing paints for his art classes, as well as his chemistry classes in Balwyn High School
Balwyn High School
Balwyn High School is a state-run high school in the suburb of Balwyn North, in Melbourne, Victoria, Australia. It was established in 1954. As of 2009 it has some 2,000 students and over 180 staff, making it one of the largest schools in the inner-eastern suburbs of Melbourne or the third largest...
. His father, being the Superintendent of Melbourne's electrical power station, borrowed an organic chemistry text from the chemists in the quality control laboratory. This ultimately led to an intense interest in synthesizing Azo dyes
Azo compound
Azo compounds are compounds bearing the functional group R-N=N-R', in which R and R' can be either aryl or alkyl. IUPAC defines azo compounds as: "Derivatives of diazene , HN=NH, wherein both hydrogens are substituted by hydrocarbyl groups, e.g. PhN=NPh azobenzene or diphenyldiazene." The more...
. At around age 14, Gunther attempted to predict the color of azo dyes based on the chromophore
Chromophore
A chromophore is the part of a molecule responsible for its color. The color arises when a molecule absorbs certain wavelengths of visible light and transmits or reflects others. The chromophore is a region in the molecule where the energy difference between two different molecular orbitals falls...
-auxochrome
Auxochrome
An auxochrome is a group of atoms attached to a chromophore which modifies the ability of that chromophore to absorb light. Examples include the hydroxyl group , the amino group , and an aldehyde group ....
combination. Apart from drawing up empirical tables, this effort was largely unsuccessful due to his lack of knowledge of quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
Post-Doc years
Gunther taught physics at San Jose State UniversitySan José State University
San Jose State University is a public university located in San Jose, California, United States...
from 1980-1981. He then joined Syncal Corporation, a small company contracted by NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
and JPL to develop thermoelectric materials for their deep-space missions. Gunther was asked to analyze the thermal stability
Thermal stability
Thermal stability is the stability of a molecule at high temperatures; i.e. a molecule with more stability has more resistance to decomposition at high temperatures....
test data from the Voyager
Voyager program
The Voyager program is a U.S program that launched two unmanned space missions, scientific probes Voyager 1 and Voyager 2. They were launched in 1977 to take advantage of a favorable planetary alignment of the late 1970s...
RTG
Radioisotope thermoelectric generator
A radioisotope thermoelectric generator is an electrical generator that obtains its power from radioactive decay. In such a device, the heat released by the decay of a suitable radioactive material is converted into electricity by the Seebeck effect using an array of thermocouples.RTGs can be...
s. He discovered that the stability of the silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
-germanium
Germanium
Germanium is a chemical element with the symbol Ge and atomic number 32. It is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors tin and silicon. The isolated element is a semiconductor, with an appearance most similar to elemental silicon....
(Si-Ge) thermoelectric alloy was controlled by a soliton
Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
-based precipitation mechanism. JPL used his work to select the next generation of RTG materials for the Galileo mission launched in 1989.
Xerox years
In 1982, Gunther joined Xerox PARCXerox PARC
PARC , formerly Xerox PARC, is a research and co-development company in Palo Alto, California, with a distinguished reputation for its contributions to information technology and hardware systems....
to develop parametric and functional test software for PARC's small-scale VLSI design fabrication line. Ultimately, he was recruited onto the Dragon multiprocessor workstation project where he also developed the PARCbench multiprocessor benchmark. This was his first fore into computer performance analysis.
1989, he developed a Wick-rotated
Wick rotation
In physics, Wick rotation, named after Gian-Carlo Wick, is a method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable...
version of Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
's quantum path integral formalism
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
for analyzing performance degradation in large-scale computer systems and packet networks.
Pyramid years
In 1990 Gunther joined Pyramid TechnologyPyramid Technology
Pyramid Technology Corporation was a computer company that produced a number of RISC-based minicomputers at the upper end of the performance range. They also became the second company to ship a multiprocessor Unix system , in 1985, which formed the basis of their product line into the early 1990s...
(now part of Fujitsu Siemens Computers) where he held positions as Senior Scientist and Manager of the Performance Analysis Group that was responsible for attaining industry-high TPC
Transaction Processing Performance Council
Transaction Processing Performance Council is a non-profit organization founded in 1988 to define transaction processing and database benchmarks and to disseminate objective, verifiable TPC performance data to the industry...
benchmarks on their Unix
Unix
Unix is a multitasking, multi-user computer operating system originally developed in 1969 by a group of AT&T employees at Bell Labs, including Ken Thompson, Dennis Ritchie, Brian Kernighan, Douglas McIlroy, and Joe Ossanna...
multiprocessors. He also performed simulations for the design of the Reliant RM1000 parallel database server.
Consulting practice
Gunther founded Performance Dynamics Company as a sole proprietorship, registered in CaliforniaCalifornia
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...
in 1994, to provide consulting and educational services for the management of high performance computer systems with an emphasis on performance analysis
Performance analysis
In software engineering, profiling is a form of dynamic program analysis that measures, for example, the usage of memory, the usage of particular instructions, or frequency and duration of function calls...
and enterprise-wide capacity planning
Capacity planning
Capacity planning is the process of determining the production capacity needed by an organization to meet changing demands for its products. In the context of capacity planning, "capacity" is the maximum amount of work that an organization is capable of completing in a given period of time...
. He went on to release and develop his own open-source performance modeling
Performance analysis
In software engineering, profiling is a form of dynamic program analysis that measures, for example, the usage of memory, the usage of particular instructions, or frequency and duration of function calls...
software called "PDQ (Pretty Damn Quick)" around 1998. That software also accompanied his first textbook on performance analysis entitled The Practical Performance Analyst. Several other books have followed since then.
Quantum information systems
In 2004, Gunther has embarked on joint research into quantum information systems based on photonicsPhotonics
The science of photonics includes the generation, emission, transmission, modulation, signal processing, switching, amplification, detection and sensing of light. The term photonics thereby emphasizes that photons are neither particles nor waves — they are different in that they have both particle...
. During the course of his research in this area, he has developed a theory of photon bifurcation that is currently being tested experimentally at École Polytechnique Fédérale de Lausanne
École polytechnique fédérale de Lausanne
The École polytechnique fédérale de Lausanne is one of the two Swiss Federal Institutes of Technology and is located in Lausanne, Switzerland.The school was founded by the Swiss Federal Government with the stated mission to:...
. This represents yet another application of path integral formulation
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
to circumvent the wave-particle duality of light.
In its simplest rendition, this theory can be considered as providing the quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
corrections to the Abbe
Ernst Karl Abbe
- See also :*Abbe prism*Abbe refractometer*Abbe error*Aberration in optical systems*Calculation of glass properties* German inventors and discoverers-External links:*...
-Rayleigh diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
theory of imaging and the Fourier theory
Fourier optics
Fourier optics is the study of classical optics using Fourier transforms and can be seen as the dual of the Huygens-Fresnel principle. In the latter case, the wave is regarded as a superposition of expanding spherical waves which radiate outward from actual current sources via a Green's function...
of optical information processing.
Performance visualization
Inspired by the work of Tukey, Gunther explored ways to help systems analyst visualize performance in a manner similar to that already available in scientific visualizationScientific visualization
Scientific visualization is an interdisciplinary branch of science according to Friendly "primarily concerned with the visualization of three-dimensional phenomena , where the emphasis is on realistic renderings of volumes, surfaces, illumination sources, and so forth, perhaps...
and information visualization
Information visualization
Information visualization is the interdisciplinary study of "the visual representation of large-scale collections of non-numerical information, such as files and lines of code in software systems, library and bibliographic databases, networks of relations on the internet, and so forth".- Overview...
. In 1991, he developed a tool called Barry, which employs barycentric coordinates
Barycentric coordinates (mathematics)
In geometry, the barycentric coordinate system is a coordinate system in which the location of a point is specified as the center of mass, or barycenter, of masses placed at the vertices of a simplex . Barycentric coordinates are a form of homogeneous coordinates...
to visualize sampled CPU usage data on large-scale multiprocessor
Multiprocessor
Computer system having two or more processing units each sharing main memory and peripherals, in order to simultaneously process programs.Sometimes the term Multiprocessor is confused with the term Multiprocessing....
systems. More recently, he has applied the same 2-simplex
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
barycentric coordinates to visualizing the Apdex
Apdex
Apdex is an open standard developed by an alliance of companies. It defines a standard method for reporting and comparing the performance of software applications in computing...
application performance metric, which is based on categorical response time data. A barycentric 3-simplex] (a tetrahedron
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
), that can be swivelled on the computer screen using a mouse
Mouse (computing)
In computing, a mouse is a pointing device that functions by detecting two-dimensional motion relative to its supporting surface. Physically, a mouse consists of an object held under one of the user's hands, with one or more buttons...
, has been found useful for visualizing packet network performance data. In 2008, he co-founded the PerfViz google group.
Universal Law of Computational Scalability
The relative capacity C(N) of a computational platform is given by:
where N represents either the number of physical processors in the hardware
Hardware
Hardware is a general term for equipment such as keys, locks, hinges, latches, handles, wire, chains, plumbing supplies, tools, utensils, cutlery and machine parts. Household hardware is typically sold in hardware stores....
configuration or the number of users driving the software application. The parameters
and represent respectively the levels of contention (e.g., queueing for shared resources) and coherency delay (i.e., latency for data to become consistent) in the system. The parameter also quantifies the retrograde throughput seen in many stress tests but not accounted for in either Amdahl's lawAmdahl's law
Amdahl's law, also known as Amdahl's argument, is named after computer architect Gene Amdahl, and is used to find the maximum expected improvement to an overall system when only part of the system is improved...
or event-based simulations
Discrete Event Simulation
In discrete-event simulation, the operation of a system is represented as a chronological sequence of events. Each event occurs at an instant in time and marks a change of state in the system...
.
This scalability law was originally developed by Gunther in 1993 while he was employed at Pyramid Technology
Pyramid Technology
Pyramid Technology Corporation was a computer company that produced a number of RISC-based minicomputers at the upper end of the performance range. They also became the second company to ship a multiprocessor Unix system , in 1985, which formed the basis of their product line into the early 1990s...
. Since there are no topological dependencies, C(N) can model symmetric multiprocessors
Symmetric multiprocessing
In computing, symmetric multiprocessing involves a multiprocessor computer hardware architecture where two or more identical processors are connected to a single shared main memory and are controlled by a single OS instance. Most common multiprocessor systems today use an SMP architecture...
, multicores
Multi-core (computing)
A multi-core processor is a single computing component with two or more independent actual processors , which are the units that read and execute program instructions...
, clusters
Cluster (computing)
A computer cluster is a group of linked computers, working together closely thus in many respects forming a single computer. The components of a cluster are commonly, but not always, connected to each other through fast local area networks...
, and GRID
Grid computing
Grid computing is a term referring to the combination of computer resources from multiple administrative domains to reach a common goal. The grid can be thought of as a distributed system with non-interactive workloads that involve a large number of files...
architectures. Also, because each of the three terms has a definite physical meaning, they can be employed as a heuristic
Heuristic
Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...
to determine where to make performance improvements in hardware platforms or software applications.
At a more fundamental level, the above equation can be derived from the Machine Repairman queueing model:
Theorem (Gunther 2008): The universal scalability law is equivalent to the synchronous queueing bound on throughput in a modified Machine Repairman with state-dependent service times.
The following corollary (Gunther 2008 with
) corresponds to Amdahl's law:
Theorem (Gunther 2002): Amdahl's law for parallel speedup is equivalent to the synchronous queueing bound on throughput in a Machine Repairman model of a multiprocessor.
Computational mathematics
Over the past fifteen years, Gunther has had an abiding interest in of the 3x+1 problemCollatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture , Kakutani's problem , the Thwaites conjecture , Hasse's algorithm The Collatz conjecture is a...
, not with the goal of developing a technical proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
of the original conjecture but rather, using computers as a tool to examine it for structure that might lead to better computer-generated visualizations
Scientific visualization
Scientific visualization is an interdisciplinary branch of science according to Friendly "primarily concerned with the visualization of three-dimensional phenomena , where the emphasis is on realistic renderings of volumes, surfaces, illumination sources, and so forth, perhaps...
of this and related problems in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. In one early attempt along these lines he employed VRML
VRML
VRML is a standard file format for representing 3-dimensional interactive vector graphics, designed particularly with the World Wide Web in mind...
. Paul Erdös famously stated about the 3x+1 problem, "Mathematics is not yet ready for such problems." Gunther thinks that perhaps computers are.
More formally, Gunther has developed a functional Diophantine equation
Diophantine equation
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
that generalizes Terra’s theorem (1976) and is based on a graphical primitive: the G-set. The G-set is related to the predecessor sets of Wirsching by the following theorem.
Theorem (Gunther 1999): The G-set () is a directed subgraph in
(Collatz tree) formed by acyclic predecessor sets starting at b and terminating at vertex a with exactly k = 1 edges arising from
, i.e.,
.
The proof is unpublished. This theorem leads to the following conjecture for the construction of
.
Conjecture (Gunther 1999):, where
, enumerates all G-cells in
such that the unique G-set
contains the degenerate cycle
.
Ironically, given his lack of intent to find a proof, the formal associations with the theorems of Terras and Wirsching, make it plausible that this method of sub-graph enumeration might form the basis of an inductive proof.
Awards
- Senior Member ACM (elected April 2009).
- Senior Member IEEE (elected February 2009).
- Recipient of the A. A. Michelson Award, December 2008.
- Summer Research Institute visitor, EPFL 2006 and 2007.
- Lecturer, Western Institute of Computer Science, Stanford UniversityStanford UniversityThe Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
, 1997-2000. - Best paper award, CMGComputer Measurement GroupThe Computer Measurement Group , founded in 1974, is a worldwide non-profit organization of data processing professionals whose work involves measuring and managing the performance of computing systems...
conference 1996. - Visiting Scholar in Materials Science, Stanford University, 1981-1982.
- Science Research Council Studentship, U.K. 1976-1980.
- Commonwealth Postgraduate Scholarship, Australia 1975-1976.
Quotes
- As a consultant, I offer more harangue for the buck.
- Lately, I've been solicited to give so many talks I feel like Mister Ed The Talking Whore.
- It's better to have wrong expectations, than no expectations.
- Best Practices are an admission of failure.
- A queueQueueing theoryQueueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
is a line of customers waiting to be severed. - The only dumb question is the one never asked.
- A quantum leap is neither.
- Art irritates life.
- If you want to be more productive, go to sleep.
- All meaning has a pattern, but not all patterns have a meaning.
Theses
- The Feynman Path Integral in Non-Relativistic Quantum Mechanics and Quantum Electrodynamics, La Trobe University (AUS),
B.Sc. Honors dissertation, Department of Physics, Oct. (1974)
- Dynamical Symmetry Groups: The Study and Interpretation of Certain Invariants as Group Generators in Quantum Mechanics, La Trobe
University (AUS), M.Sc. dissertation, Department of Applied Mathematics, Nov. (1976)
- Broken Dynamical Symmetries in Quantum Field Theory and Phase Transition Phenomena, University of Southampton (U.K.), Ph.D.
dissertation, Department of Physics, Dec. (1979)
Books
- The Practical Performance Analyst, McGraw-HillMcGraw-HillThe McGraw-Hill Companies, Inc., is a publicly traded corporation headquartered in Rockefeller Center in New York City. Its primary areas of business are financial, education, publishing, broadcasting, and business services...
, New York, New York 1998, ISBN 0079129463 (Out of print) - The Practical Performance Analyst, iUniverse.com Press, Lincoln, Nebraska 2000, ISBN 059512674X (Reprint edition)
- Performance Engineering: State of the Art and Current Trends, Lecture Notes in Computer Science, Springer-VerlagSpringer Science+Business Media- Selected publications :* Encyclopaedia of Mathematics* Ergebnisse der Mathematik und ihrer Grenzgebiete * Graduate Texts in Mathematics * Grothendieck's Séminaire de géométrie algébrique...
Heidelberg, Germany, October 2001, ISBN 3540421459 (Contributed chapter)
- Analyzing Computer System Performance with Perl::PDQ, Springer, Heidelberg 2005, ISBN 3540208658
- Guerrilla Capacity Planning, Springer, Heidelberg 2007, ISBN 3540261389
Invited presentations
- Goldstone Modes in First-order Phase Transitions, Sixth West Coast Conference on Statistical Mechanics, IBM Research Laboratories, San Jose, June (1980)
- Instanton Techniques for Queueing Models of Large Computer Systems: Getting a Piece of the Action, SIAM Conference on Applied Probability in Science and Engineering, New Orleans, Louisiana, March (1990)
- (Numerical) Investigations into Physical Power-law Models of Internet Traffic Using the Renormalization Group, IFORS Conference of Operations Research Societies, Honolulu, Hawaii, July 11–15 (2005)
Papers
- Goldstone Modes in Vacuum Decay and First-order Phase Transitions, Journal of Physics, A, 13, 1755-1767 (1980)
- A Benchmark for Image Retrieval using Distributed Systems over the Internet (2000 with G. Beretta)
- Performance and Scalability Models for a Hypergrowth e-Commerce Web Site (2000)
- Characterization of the Burst Stabilization Protocol for the RR/CICQ Switch (2003 with K. J. Christensen and K. Yoshigoe)
- Unification of Amdahl's Law, LogP and Other Performance Models for Message-Passing Architectures (2005)
- Towards Practical Design Rules for Quantum Communications and Quantum Imaging Devices (2005 with G. Beretta)
- The Virtualization Spectrum from Hyperthreads to GRIDs, Proc. CMG Conf., Reno, Nevada, Dec. (2006)
External links
- Performance Dynamics Company(SM)
- Performance blog
- The Mathematics Genealogy Project
- OEIS Binary Carry Sequence: Mathematica code (May 23 2009)
- M.Sc. Thesis at National Library of Australia
- List of papers on arXiv
- List of papers on computer performance analysis
- Dirac Number 2
- Guerrilla Manifesto
- PDQ performance modeling software
- Performance Visualization
- Linked-in profile