Logical model of Personality and Cognition with possible Applications

Although the cognition is significant in strategic reasoning, its role has been weakly analyzed, because only the average intelligence is usually considered. For example, prisoner's dilemma in game theory, would have different outcomes for persons with different intelligence. I show how various levels of intelligence influence the quality of reasoning, decision, or the probability of psychosis. I explain my original methodology developed for my MA thesis in clinical psychology in 1998, and grant research in 1999, demonstrating the bias of the classic IQ method, and how the intelligence limits thinking. Based on that I defined Personality Model, providing insight into understanding of psychosis (schizophrenia, bi-polar), which has not been explained yet by psychology or psychiatry. In addition, it enables to analyze and assess non-linear problems, utilizable in computer programming, visualization (animation) or other fields including Baduk game. I've already applied some principles in complex information system www.each.co.uk, and video-animations exhibited in London, Germany, Tokyo. I need to mention my experience in chess composition between 1994 and 2000, winning a few international prizes and inventing a special class of fairy rules redefining the mate. The chess composition principles or patterns show the way to organize logical series to higher advanced mechanisms (like calculus), applicable to other fields. One of such principles is a logical aesthetic innovation: new strategy, defined by Italian composers. Finally I show how the simple redefinition of the classic utility concept links economics and psychology to explain irrational / destructive behavior. All presented results (from the research) can be repeated

A note on the multiplicity of determinantal ideals

Herzog, Huneke, and Srinivasan have conjectured that for any homogeneous $k$-algebra, the multiplicity is bounded above by a function of the maximal degrees of the syzygies and below by a function of the minimal degrees of the syzygies. The goal of this paper is to establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay algebras over a field $k$ for $k$-algebras $k[x_1, ..., x_n]/I$ being $I$ a determinantal ideal of arbitrary codimension

Investigations into an optimal approach for on-line robot trajectory planning and control.

The purpose of this thesis is to present a comprehensive and practical approach for the time-optimal motion planning and control of a general purpose industrial manipulator. In particular, the case of point-to-point path unconstrained motions is considered, with special emphasis towards strategies suitable for efficient on-line implementations. From a dynamic model description of the plant, and using an advanced graphical robotics simulation environment, the control algorithms are formulated. Experimental work is then conducted to verify the proposed algorithms, by interfacing the industrial manipulator to the master controller, implemented on a personal computer. The full rigid-body non-linear dynamics of the open-chain manipulator have been accommodated into the modelling, analysis and design of the control algorithms. For path unconstrained motions, this leads to a model-based regulating strategy between set points, which combines conventional trajectory planning and subsequent control tracking stages into one. Theoretical insights into these two robot motion disciplines are presented, and some are experimentally demonstrated on a CRS A251 industrial arm. A critical evaluation of current approaches which yield optimal trajectory planning and control of robot manipulators is undertaken, leading to the design of a control solution which is shown to be a combination of Pontryagin's Maximum Principle and state-space methods of design. However, in a real world setting, consideration of the relationship between optimal control and on-line viability highlights the need to approximate manipulator dynamics by a piecewise linear and decoupled function, hence rendering a near-time-optimal solution in feedback form. The on-line implementation of the proposed controller is presented together with a comparison between simulation and experimental results. Furthermore, these are compared with measurements from the industrial controller. It is shown that the model-based near-optimal-time feedback control algorithms allow faster manipulator motions, with an average speed-up of 14%, clearly outperforming current industrial controller practices in terms of increased productivity. This result was obtained by setting an acceptable absolute error limit on the target location of the joint (position and velocity) to within [2.0E-02 rad, 8.7E-03 rad/s], when the joint was regarded at rest

The renormalized Hamiltonian truncation method in the large ETE_T expansion

Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in Refs. [1-3]. The method is general but as an example we calculate the exact $g^2$ and some of the $g^3$ contributions for the $\phi^4$ theory in two dimensions. The coefficients of the local expansion calculated in Ref. [1] are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.Comment: JHEP version, typos fixed in Appendix and eq. (23

Ideals generated by submaximal minors

The goal of this paper is to study irreducible families W(b;a) of codimension 4, arithmetically Gorenstein schemes X of P^n defined by the submaximal minors of a t x t matrix A with entries homogeneous forms of degree a_j-b_i. Under some numerical assumption on a_j and b_i we prove that the closure of W(b;a) is an irreducible component of Hilb^{p(x)}(P^n), we show that Hilb^{p(x)}(P^n) is generically smooth along W(b;a) and we compute the dimension of W(b;a) in terms of a_j and b_i. To achieve these results we first prove that X is determined by a regular section of the twisted conormal sheaf I_Y/I^2_Y(s) where s=deg(det(A)) and Y is a codimension 2, arithmetically Cohen-Macaulay scheme of P^n defined by the maximal minors of the matrix obtained deleting a suitable row of A.Comment: 22 page