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Welcome !! |
Lev
Goldfarb
Diploma Math/CS ( Ph.D. in Systems Design
Engineering ( Inductive Information Systems tel: (506) 455-4323 |
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Proposal for a book:
“Redoing
Our Mathematics and Science: Integrating Mind into the Universe”
*****
A
general description of the fundamentally new, event-based, representational formalism (ETS) proposed by us :
It is
the first and so far the only general formal framework for modeling evolving forms of (object and class)
representations.
While
all of modern science is based on the formalism that is precise elaboration of
the ‘continuous’, ETS can be considered as a proposal for a precise and general
elaboration of the ‘discrete’. Moreover,
and what is more, while in the conventional scientific models syntax is not
related to semantics—and hence, of necessity, we have no choice but to project onto
reality their formal structures,
e.g. the vector space structure—ETS is the first
formalism which has been designed in such a way that syntax
and semantics are congruent, so that the proposed formal structures are
supposed to be the blueprints of the corresponding structures in nature.
Also, in
contrast to the conventional scientific models—which
do not make any explicit assumptions about the structure of objects in nature and represent objects as ‘points’—in ETS, objects are viewed and represented as irreversible structural processes, i.e. as
(non-linear, temporal) streams
of interconnected structured events.
On the
philosophical side, the opposition between the ‘mind’ and ‘matter’ has been
overcome, since now both ‘rely’ on the same form of representation.
Is there a different mathematics, of generatively
structured entities,
which would clarify the nature of the structural ‘measurement’
processes?
Natural numbers—think of them
as strings
of •'s—which have gradually emerged over many
millennia, served as the basis of the ubiquitous numeric forms for representing
information about objects or events. All
our basic scientific paradigms are built on the foundation of this
representation. Measurement, as conventionally understood, is the corresponding
process for (numeric) representation of objects, i.e. it is a procedure or
device that realizes the mapping from the set of objects to the set of numbers.
Accordingly, in science, there has existed only one underlying (i.e. numeric)
representational model, and it has served as a universal blueprint for
building all known measurement devices.
Moreover, we, collectively, have had no experience with any other kind
of measurement device! Thus, when
contemplating the transition from the classical measurement processes to the
structural ones, we are faced with the situation absolutely unprecedented in
the history of science, with the ensuing benefits far outweighing the
difficulties.
When considering structural generalization of the
classical measurement, or representation, theory, one has to keep in mind that
any ‘measurement device’ can be conceived (and constructed) provided we have
identified the underlying formal
structure. This formal structure—in contrast to the conventional mathematical, point-like, view of objects entrenched
in the concept of the set—is supposed to provide a
fundamentally new, structural, form of object representation, and the
developments associated with such formal structure will constitute a new,
structural, mathematics.
A crucial feature of the ETS representation that we have
proposed is related to the observation that all objects in nature (including mental objects) have a formative history. We have gradually realized that the concept of
formative object history and the concept of object representation are very
similar. Thus, a ‘true’ representational formalism must provide a unified formal structure
for capturing an object's formative ‘history’: both, complete history (as in
Nature itself) or subjective (as perceived by an agent). It is not difficult to see that the numeric
representation possesses this feature but only in a very rudimentary form: numeric representation records the process of
object formation relying on the extremely limited concatenation operation for strings over a single letter
alphabet {•} (because this is how a natural number is
built). Such trivially temporal
representation intrinsically cannot
capture any non-trivial structural formative history, in which the
corresponding events are of more complex structure (than the concatenation
operation).
Accordingly, all conventional
discrete ‘representations’—such
as strings over an alphabet of size > 1, trees, and graphs—cannot be viewed as true object representations, since they do not
capture the formative history. For
example, the formative history of a string is not part of the string
representation. Hence a string is not a
reliable form of object representation, since it has an exponential number of
formative histories associated with its generation, creating a computationally
insurmountable problem for inductive learning process, which is supposed to
discover the (generative) class representation.
Returning to the measurement process, one can say that all
classical measurement processes ‘produce’ numbers as their outputs, while the
generalized measurement process is supposed to output non-numeric entities,
which we call structs. Thus, the generalized measurement process
captures the temporal, or informational,
structure of objects in an inductive manner, through a more dynamic
interaction with the environment.
I am convinced that gradually, as the development of
various applications of the ETS formalism progresses, the new form of object
representation should supersede such preliminary and incomplete ones as the
string, tree, graph, etc.
ETS group
Muhammad Al-Digeil
Lev Goldfarb
Ian Scrimger
Research areas of interest
Inductive informatics :
·
structural representations (equivalently: evolutionary-, or inductively-,
structured environments);
structural (inductive, intelligent) measurement processes
connections with:
physics, chemistry, biochemistry,
biology, neurobiology, neuroscience,
cognitive science
· fundamental limitations of the classical
(numeric) representations and measurement processes
· inductive learning processes (natural
and artificial)
· ETS
(theory and applications)
· fundamental limitations of numeric
learning models
· pattern recognition/machine learning
· protein representation &
classification
· inductive databases and data (including image and web) mining
· bioinformatics &
cheminformatics
· information retrieval
· inductive models of vision and their
applications
· speech recognition and understanding
· cognitive models based on ETS formalism
Journal editorial
boards
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· Pattern Recognition (1991 – 2008) |
Selected publications,
talks, and workshops
My
second (updated) FQXi essay “Nature
is fundamentally discrete but our basic formalism is not” and its discussion
My
first FQXi essay and its discussion “What is possible in
physics depends on the chosen representational formalism”
A
simplified visual illustration of the
process of spatial instantiation of the ETS representation for the Bubble
Man example from Part III of our main paper (produced by Reuben Peter-Paul)
Slightly
modified talk at MPI ,
Tübingen, July 2007 (PowerPoint slides:
if you want to see the “hidden” slides and notes, save the file first; the
latter option is also faster)
IIT,
"Pattern representation and the future
of pattern recognition: a program for action" ICPR 2004 satellite workshop,
Cornell Biophysics March 2003 talk "Can a formal model unify biology?"
Topic for "Birds of
a Feather" discussion at ISMB 2002 (MSWord version)
· Four papers for the ETS book
· Dmitry Korkin and Lev Goldfarb, "Multiple genome rearrangement: A General approach via the evolutionary genome graph" (PDF version), ISMB 2002 (also to appear in a special issue of Bioinformatics).
· Lev Goldfarb and Oleg Golubitsky, "What is a structural measurement process?" (PDF version), Faculty of Computer Science, U.N.B., Technical Report TR01-147, October 2001.
· Lev Goldfarb, Oleg Golubitsky, and Dmitry Korkin, "What is a structural representation?" (PDF version), Faculty of Computer Science, U.N.B., Technical Report TR00-137, December 2000.
· Lev Goldfarb, Oleg Golubitsky, and Dmitry Korkin, "What is a structural representation in chemistry: Towards a unified framework for CADD?" (PDF version), Faculty of Computer Science, U.N.B., Technical Report TR00-138, December 2000.
· Lev Goldfarb and Jaroslav Hook, "Why classical models for pattern recognition are not pattern recognition models", in International Conference on Advances in Pattern Recognition, ed. Sameer Singh, Springer, pp.405-414, 1998.
· Lev Goldfarb, Sanjay S. Deshpande and Virendra C. Bhavsar, " Inductive theory of vision", Faculty of Computer Science", U.N.B., Technical Report TR96-108, April 1996.
·
Sanjay
· Lev Goldfarb, John Abela, Virendra C. Bhavsar and Vithal N. Kamat, "Can a vector space based learning model discover inductive class generalization in a symbolic environment?", Pattern Recognition Letters 16, pp. 719-726, 1995.
· Lev Goldfarb and Sandeep Nigam, "The unified learning paradigm: A foundation for AI", in V. Honavar and L. Uhr, eds., Artificial Intelligence and Neural Networks: Steps towards Principled Integration, Academic Press, Boston, MA, 1994.
· Lev Goldfarb, "What is distance and why do we need the metric model for pattern learning?", Pattern Recognition 25, pp. 431-438, 1992.
· Tony Y. T. Chan and Lev Goldfarb, "Primitive pattern learning", Pattern Recognition 25, pp. 883-889, 1992.
· Lev Goldfarb, "On the foundations of intelligent processes - I: An evolving model for pattern learning", Pattern Recognition 23, pp. 595-616, 1990. (Received an annual Pattern Recognition Society Award)
Graduate
thesis supervised since 1990
· Ian Scrimger (2007) Structural Representation of the Game of Go, Master's Thesis
· Mohammad S. Al-Digeil (2005) Towards an ETS Representation of Proteins, Master's Thesis
· David Clement (2003) Information Retrieval via the ETS Model, Master's Thesis
·
John M. Abela (2002) ETS Learning of Kernel Languages, Ph.D. Thesis
· Jaroslav Hook (1998) Are Artificial Neural Networks Learning Machines?, Master's Thesis
· Sanjay S. Deshpande (1996) On the Foundations of Vision, Master's Thesis
· Vithal N. Kamat (1995) Inductive Learning with the Evolving Tree Transformation System, Ph.D. Thesis
· John M. Abela (1994) Topics in Evolving Transformation Systems, Master's Thesis
· Sandeep Nigam (1993) Metric Model Based Generalization and Generalization Capabilities of Connectionist Models, Master's Thesis
· Wiranto B. Santoso (1992) Learning Algorithm for the Reconfigurable Learning Machine, Master's Thesis
· Tony Y. T. Chan (1992) Learning as Optimization, Ph.D. Thesis
· Sonya Dewi (1991) Dynamic Selection of Primitives in the Metric Model for Pattern Learning, Master's Thesis
· Ahmady Satriawan (1990) A Tree Transformation System for
Pattern Learning, Master's
Thesis
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