### Browsing by Author "Golubitsky, Oleg"

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Item On the generating process and the class typicality measure(2002) Golubitsky, OlegIn this paper, we consider the stochastic generating process—one of the key concepts of the Evolving Transformation System model [1]—from the formal perspective. First, we give an informal definition of the generating process supported by some intuitive assumptions and consider several examples. Then, we formally define the concept of the generating process as a continuous parameter (c.p.) Markov chain. Some important random variables associated with this c.p. Markov chain are introduced next, followed by the definition of the typicality measure. Two methods for the computation of the typicality measure are proposed. In conclusion, we discuss the problem of compactification of the state space for the c.p. Markov chain. This problem is not only interesting from the points of view of topology and of the c.p. Markov chains theory, but also has important implications for the ETS model, since it is related to the problem of class comparison and to the proper formulation of the learning problem. Reference: [1] L. Goldfarb, O. Golubitsky, D. Korkin, What is a structural representation? Technical Report TR00-137, Faculty of Computer Science, U.N.B., October 2001.Item What Is a Structural Measurement Process?(2001) Goldfarb, Lev; Golubitsky, OlegNumbers have emerged historically as by far the most popular form of representation. All our basic scientific paradigms are built on the foundation of these, numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects or events, i.e., it is a procedure or device that realizes the mapping from the set of objects to the set of numbers. Any (including a future) measurement device is constructed based on the underlying mathematical structure that is thought appropriate for the purpose. It has gradually become clear to us that the classical numeric mathematical structures, and hence the corresponding (including all present) measurement devices, impose on “real” events/objects a very rigid form of representation, which cannot be modified dynamically in order to capture their combinative, or compositional, structure. To remove this fundamental limitation, a new mathematical structure—evolving transformation system (ETS)—was proposed earlier. This mathematical structure specifies a radically new form of object representation that, in particular, allows one to capture (inductively) the compositional, or combinative, structure of objects or events. Thus, since the new structure also captures the concept of number, it offers one the possibility of capturing simultaneously both the qualitative (compositional) and the quantitative structure of events. In a broader scientific context, we briefly discuss the concept of a fundamentally new, biologically inspired, “measurement process”, the inductive measurement process, based on the ETS model. In simple terms, all existing measurement processes “produce” numbers as their outputs, while we are proposing a measurement process whose outputs capture the representation of the corresponding class of objects, which includes the class progenitor (a non-numeric entity) plus the class transformation system (the structural class operations). Such processes capture the structure of events/objects in an inductive manner, through a direct interaction with the environment.Item What Is a Structural Representation in Chemistry: Towards a Unified Framework for CADD?(2001) Goldfarb, Lev; Golubitsky, Oleg; Korkin, DmitryA fundamentally new formal framework for structural representation of organic compounds based on the first "true" (general) formalism for structural object representation recently proposed by us|evolving transformation system (ETS) model is outlined. The applied orientation of the paper is towards the molecular design in general and computer aided drug design (CADD) in particular. Inadequacies of the conventional models used in (CADD) for molecular representation and classification as well as the advantages of the proposed ETS model are discussed. Some advantages of the ETS model is its capability to represent naturally all important structural features of molecules, e.g. different atoms and their bonding types (including hydrogen bonding), basic 2D and 3D isometries, the molecular class structure. The model allows one not only to classify a new compound, but also to construct a chemically valid new compound from the class of compounds that was previously learned based on a small set of examples. The model also guarantees the inheritance of the chemical structural class information from the parent class to all its subclasses. In general, the ETS model offers a much more precise "language" for chemical structural formulas. The central role of the class learning problem in CADD is suggested. Moreover, we propose the ETS model as a unified framework for the class learning problem and therefore as a unified formal framework for CADD. This would allow considerable streamlining of the CADD by assigning to the chemist the role of an interactive user of the system rather that a role of a human weak link within the CADD process.Item What Is a Structural Representation?(2001) Goldfarb, Lev; Golubitsky, Oleg; Korkin, DmitryWe outline a formal foundation for a “structural” (or “symbolic”) object/event representation, the necessity of which is acutely felt in all sciences, including mathematics and computer science. The proposed foundation incorporates two hypotheses: 1) the object’s formative history must be an integral part of the object representation and 2) the process of object construction is irreversible, i.e. the “trajectory” of the object’s formative evolution does not intersect itself. The last hypothesis is equivalent to the generalized axiom of (structural) induction. Some of the main difficulties associated with the transition from the classical numeric to the structural representations appear to be related precisely to the development of a formal framework satisfying these two hypotheses. The concept of (inductive) class representation—which has inspired the development of this approach to structural representation—differs fundamentally from the known concepts of class. In the proposed, evolving transformations system (ETS), model, the class is defined by the transformation system—a finite set of weighted transformations acting on the class progenitor—and the generation of the class elements is associated with the corresponding generative process which also induces the class typicality measure. Moreover, in the ETS model, a fundamental role of the object’s class in the object’s representation is clarified: the representation of an object must include the class. From the point of view of ETS model, the classical discrete representations, e.g. strings and graphs, appear now as incomplete special cases, the proper completion of which should incorporate the corresponding formative histories, i.e. those of the corresponding strings or graphs.Item What is a structural representation? A proposal for an event-based representational formalism: Sixth Variation(2007) Goldfarb, Lev; Gay, David; Golubitsky, Oleg; Korkin, Dmitry; Scrimger, IanWe outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt not just in artificial intelligence and pattern recognition, but also in the natural sciences, particularly biology. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important (to society) and interesting (to science), but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural entities/processes that we aim to formally address here, in contrast to theubiquitous mathematical view of objects as points in some abstract space. In light of the above, the paper is addressed to a very broad group of scientists. One can gain an initial intuitive understanding of the proposed representation by generalizing the temporal process of the (Peano) construction of natural numbers: replace the single structureless unit out of which a number is built by multiple structural ones. An immediate and important consequence of the distinguishability (or multiplicity) of units in the construction process is that we can now see which unit was attached and when. Hence, the resulting (object) representation for the first time embodies temporal structural information in the form of a formative, or generative, object “history” recorded as a series of (structured) events. Each such event stands for a “standard” interaction of several objects/processes. We introduce the new concept of class representation via the concept of class generating system, which outputs structural entities belonging to that class. Hence, the concept of class is introduced as that of a class of similar structural entities, where the “similarity” of such entities is ensured by them being outputs of the same class generating system and hence having similar formative histories. In particular, such a concept of class representation implies that—in contrast to all existing formalisms—no two classes have elements in common. The evolving transformation system (ETS) formalism proposed here is the first one developed to support such a new vision of classes. Most important, since the operations that participated in the object’s construction are, for the first time, made explicit in the representation, it makes the inductive recovery of class representation (on the basis of object representation) much more reliable. As a result, ETS offers a formalism that outlines, for the first time, a tentative framework for understanding what a class is. Even this tentative framework makes it quite clear that the term “class” has been improperly understood, used, and applied: many, if not most, of the current “classes” should not be viewed as such. A detailed example of a class representation is included. In light of ETS, the classical discrete “representations” (strings, graphs) appear as incomplete special cases at best, the proper adaptation of which should incorporate corresponding formative histories, as is done here. The gradual emergence of ETS—including the concepts of structural object and class representations, the resulting radically different (temporal) view of “data”, as well as the associated inductive learning processes and the representational levels—points to the beginning of a new field, inductive informatics, which is intended as a class oriented rival to conventional information processing paradigms.Item What is a structural representation?: Second version(2004) Goldfarb, Lev; Gay, David; Golubitsky, Oleg; Korkin, DmitryWe outline a formalism for “structural”, or “symbolic”, representation, the necessity of which is acutely felt in all sciences. One can develop an initial intuitive understanding of the proposed representation by simply generalizing the process of construction of natural numbers: replace the identical structureless units out of which numbers are built by several structural ones, attached consecutively. Now, however, the resulting constructions embody the corresponding formative/generative histories, since we can see what was attached and when. The concept of class representation—which inspired and directed the development of this formalism—differs radically from the known concepts of class. Indeed, the evolving transformation system (ETS) formalism proposed here is the first one developed to support that concept; a class representation is a finite set of weighted and interrelated transformations (“structural segments”), out of which class elements are built. The formalism allows for a very natural introduction of representational levels: a next-level unit corresponds to a class representation at the previous level. We introduce the concept of “intelligent process”, which provides a suitable scientific environment for the investigation of structural representation. This process is responsible for the actual construction of levels and of representations at those levels; conventional “learning” and “recognition” processes are integrated into this process, which operates in an unsupervised mode. Together with the concept of structural representation, this leads to the delineation of a new field—inductive informatics—which is intended as a rival to conventional information processing paradigms. From the point of view of the ETS formalism, classical discrete “representations” (strings, graphs) now appear as incomplete special cases at best, the proper “completion” of which should incorporate corresponding generative histories (e.g. those of strings or graphs).