Лекции 27 сентября

Среда, 27 сентября, Морской зал ДВФУ

Lecture 7

Lecture 8

Lecture 9

Multidimensional Visualization: Part II

The second part is foundational and mathematical. The results/theorems are explored in depth discussing the special properties of Parallel Coordinates and how they are used. The representation of linear flats is constructed recursively (in increasing dimension). Then the representation of smooth hypersurfaces is obtained by considering them as envelopes of their tangent hyperplanes. The resulting patterns provide some new geometrical insights. Our intuition, obtained from our 3-dimensional habitation, together with the new representations becomes a laboratory to make conjectures from the picture, in the true spirit of Geometry,  and then try to prove a new result.   Geometrically based/motivated algorithms like convex hypersurface interior point construction with applications to Intelligent Process Control and elsewhere are presented. Research topics will be pointed out.

Lecture 10

Lecture 11

The Primary Language III: Discovering No-Search Approach to Opposing Games

This lecture continues a series of lectures on the Primary Language, a Language of Visual Streams (mental movies). The Algorithm of Discovery (AD) is the major algorithm based directly on the Primary Language. In this lecture, the AD is applied to rediscover Linguistic Geometry (LG), a type of game theory that permits solving a class of opposing games by constructing (not searching) the solution and this way avoid combinatorial explosion. This lecture consists of two parts:

The first part includes theoretical account into the LG Game Solving. It includes step-by-step manual execution of the AD to obtain the major result in LG, the so-called No-Search Approach. This Approach shows that LG generates optimal solutions for a class of opposing games without search and demonstrates construction of those solutions. At first, the AD initiates the Terminal Set Expansion, i.e., expansion of the subsets of terminal states into “bubbles,” the larger sets of states. For each of the states from those bubbles the AD determines a strategy leading to the respective terminal states. Then, it realizes that the bubbles of states permit to decompose the whole game state space into subspaces. This decomposition is implemented via constructing a visual model called a State Space Chart. This Chart is intended to serve as a strategic “geographical map” of the state space by providing guidelines for “travel” from state to state. Then the AD utilizes this Chart for constructing classes of potential strategies for all the opposing sides and for pruning those classes that cannot be implemented for a given problem. Subsequent application of the non-pruned potential strategies leads to construction of the optimal solution – the only real strategy existing in this problem.

The second part includes brief introduction to the LG Game Construction for solving real world defense problems (with a short movie). The LG Game Construction includes construction of the Abstract Board Games (ABG) and the LG Hypergames including abstract boards, abstract pieces, and relations of reachability.