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Denis V. Juriev

Publications and source records attributed to Denis V. Juriev.

At least 19 recordsLinked to original sources
arXiv2000

Tactics, dialectics, representation theory

This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory (representative dynamics) are specially investigated in detail, they correlate with the hypothesis on the dialectical features of human thinking in general and mathematical thought (the constructing of a solution of mathematical problem) in particular.

math.GM↗
arXiv1999

Tactical games & behavioral self-organization

The interactive game theoretical approach to tactics and behavioral self-organization is developed. Though it uses the interactive game theoretical formalization of dialogues as psycholinguistic phenomena, the crucial role is played by the essentially new concept of a tactical game. Applications to the perception processes and related subjects (memory, recollection, image understanding, imagination) are discussed together with relations to the computer vision and pattern recognition (the dynamical formation of patterns and perception models during perception as a result of its self-organization) and computer games (modelling of the tactical behavior and self-organization, tactical RPG and elaboration of new tactical game techniques). The appendix is devoted to the operative computer games and the user programming of operative units in a multi-user online operative computer game.

math.GM↗
arXiv1999

Representative dynamics

This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to solve it means to correspond a representative dynamics to the controlled system.

math.HO↗
arXiv1999

Interactive forces

This short article is devoted to the dynamics of controlled (and, therefore, open) systems. The internal forces, which appear only in the presence of external free controls and depend explicitely on them, are considered. Such interactive forces may be regarded as feedbacks generated in the system by the external free controls. In particular, one is able to interpret the interactive controls as couplings of free controls with the action of interactive forces; such dynamical approach to the interactive systems often simplifies their analysis and allows to perform their synthesis on a systematic level. The field theoretic counterparts of interactive forces, the fields of interactive forces, are also considered.

math.HO↗
arXiv1999

Games, predictions, interactivity

This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such predictions. A method to improve the predictions is proposed. Applications to the strategical analysis of interactive games are also briefly specified.

math.OC↗
arXiv1999

Caleidoscope-roulette: the resonance phenomena in perception games

Kaleidoscope-roulettes, a proper class of perception games, is described. Kaleidoscope-roulette is defined as a perception and, hence, verbalizable interactive game, whose hidden dialogue consists of quasirandom sequences of ``words''. The resonance phenomena in such games and their controlling are discussed.

math.HO↗
arXiv1999

Perception games, the image understanding and interpretational geometry

The interactive game theoretical approach to the description of perception processes is proposed. The subject is treated formally in terms of a new class of the verbalizable interactive games which are called the perception games. An application of the previously elaborated formalism of dialogues and verbalizable interactive games to the visual perception allows to combine the linguistic (such as formal grammars), psycholinguistic and (interactive) game theoretical methods for analysis of the image understanding by a human that may be also useful for the elaboration of computer vision systems. By the way the interactive game theoretical aspects of interpretational geometries are clarified.

math.HO↗
arXiv1999

Interactive games, dialogues and the verbalization

The note is devoted to an interactive game theoretic formalization of dialogues as psycholinguistic phenomena and the unraveling of a hidden dialogue structure of 2-person differential interactive games. In the field-theoretic description of interactive games the dialogues are defined naively as interactive games of discrete time with intention fields of continuous time; the correct mathematical formulation is proposed. The states and the controls of a dialogue correspond to the speech whereas the intention fields describe the understanding. In the case of dialogues the main inverse problem is to describe geometrical and algebraical properties of the understanding. On the other hand, a precise mathematical definition of dialogues allows to formulate a problem of the unraveling of a hidden dialogue structure of any 2-person differential interactive game. Such procedure is called the verbalization. It means that the states of a differential interactive game are interpreted as intention fields of a hidden dialogue and the problem is to describe such dialogue completely. If a 2-person differential interactive game is verbalizable one is able to consider many linguistic (e.g. the formal grammar of a related hidden dialogue) or psycholinguistic (e.g. the dynamical correlation of various implications) aspects of it.

math.HO↗
arXiv1999

The laced interactive games and their a posteriori analysis

An important class of differential interactive games, namely, one of the laced interactive games is considered. A posteriori analysis of such games (including the virtual a posteriori decomposition of a collective control) is discussed. Approximations of the laced interactive games by the ordinary differential games, the frozen feedback approximation and the retarded control approximation, are constructed. Applications are briefly specified.

math.HO↗
arXiv1998

Droems: experimental mathematics, informatics and infinite dimensional geometry

The article is devoted to a problem of elaboration of the real-time interactive videosystems for accelerated nonverbal cognitive computer and telecommunications. The proposed approach is based on the using of droems (dynamically reconstructed objects of experimental mathematics) and interpretational figures as pointers to them. Four paragraphs of the article are devoted to (1) an exposition of basic notions of the interpretational geometry, (2) the operator methods in the theory of interactive dynamical videosystems, (3) the general concept of organization of the integrated interactive real-time videocognitive systems, (4) the droems and processes of their dynamical reconstruction, where the general notions are illustrated by a concrete example related to the infinite dimensional geometry. The exposition is presumably heuristic and conceptual (the first and the third paragraphs) though some particular aspects such as content of the second and the fourth paragraphs, which allow deeper formalization and detailing in present, are exposed on the mathematical level of rigor.

cs.HC↗
arXiv1998

Infinite dimensional geometry of $M_1=Diff_+(S^1)/PSL(2,R)$ and $q_R$-conformal symmetries. II. Geometric quantization and hidden symmetries of Verma modules over Virasoro algebra

Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via $q_R$-conformal symmetries in the Verma modules over the Lie algebra $sl(2,C)$ is found. The analysis and the unraveling of the algebraic structure of these families of hidden symmetries are performed.

math.RT↗