Game logic and its applications I

This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II.The authors thank Hiroakira Ono for helpful discussions and encouragements from the early stage of this research project, and Philippe Mongin, Mitio Takano and a referee of this journal for comments on earlier versions of this paper. The first and second authors are partially supported, respectively, by Tokyo Center of Economic Research and Grant-in-Aids for Scientific Research 04640215, Ministry of Education, Science and Culture.Presented by H. Ono     

Science and its applications: INSERM reflections

The history of science must be introduced onto the curriculum, scientific culture must be developed if the young are to receive a global, healthy understanding of science and technology.

The experiment pioneered by INSERM clubs is, from this point of view, exemplary.     

Matrix differential calculus with applications to simple,hadamard, and kronecker products

Several definitions are in use for the derivative of an m × p matrix function F(X) with respect to its n × q matrix argument X. We argue that only one of these definitions is a viable one, and that to study smooth maps from the space of n × q matrices to the space of m × p matrices it is often more convenient to study the map from nq-space to mp-space. Also, several procedures exist for a calculus of functions of matrices. It is argued that the procedure based on differentials is superior to other methods of differentiation, and leads inter alia to a satisfactory chain rule for matrix functions.     

A theory of phenomenal geometry and its applications

The geometry of perceived space (phenomenal geometry) is specified in terms of three basic factors: the perception of direction, the perception of distance or depth, and the perception of the observer's own position or motion. The apparent spatial locations of stimulus points resulting from these three factors thereupon determine the derived perceptions of size, orientation, shape, and motion. Phenomenal geometry is expected to apply to both veridical and illusory perceptions. It is applied here to explain a number of representative illusions, including the illusory rotation of an inverted mask (Gregory, 1970), a trapezoidal window (Ames, 1952), and any single or multiple point stimuli in which errors in one or more of the three basic factors are present. It is concluded from phenomenal geometry that the size-distance and motion-distance invariance hypotheses are special cases of the head motion paradigm, and that proposed explanations in terms of compensation, expectation, or logical processes often are unnecessary for predicting responses to single or multiple stimuli involving head or stimulus motion. Two hypotheses are identified in applying phenomenal geometry. It is assumed that the perceptual localization of stimulus points determines the same derived perceptions, regardless of the source of perceptual information supporting the localizations. This assumption of cue equivalence or cue substitution provides considerable parsimony to the geometry. Also, it is assumed that the perceptions specified by the geometry are internally consistent. Departures from this internal consistency, such as those which occur in the size-distance paradox, are considered to often reflect the intrusion of nonperceptual (cognitive) processes into the responses. Some theoretical implications of this analysis of phenomenal geometry are discussed.     

Matrix derivatives with chain rule and rules for simple,Hadamard, and Kronecker products

The differential calculus for scalars is used to develop theorems for a calculus of functions of matrices. No appeal to scalar notation is necessary in the resulting calculus, so that the given chain and matrix product rules have wide applicability to matrix theory and models. The chain and product rules of scalar calculus become a special case of the matrix rules. The methods are illustrated by application to a generalized stochastic process model potentially relevant to long- and short-term memory.     

金属蛋白酶-9(MMP-9)及其组织抑制物-1(TIMP-1)在胰腺癌中的表达

探讨MMP-9和TIMP-1在胰腺癌癌细胞及间质的表达与胰腺癌分化程度、分期之间的关系.采用免疫组织化学方法,检测MMP-9和TIMP-1在胰腺癌细胞及间质细胞的表达.MMP-9在胰腺癌细胞和间质组织中均有表达.TlMP-1主要表达在胰腺癌细胞中.MMP-9在胰腺癌间质细胞中的表达高于胰腺癌癌旁组织间质细胞,与胰腺癌的病理分级、分期呈正相关.结论认为MMP-9在胰腺癌间质细胞的表达可能参与胰腺癌的浸润和转移,对预后判断、诊断及治疗具有一定的意义.     

金属蛋白酶-9（MMP-9）及其组织抑制物-1（TIMP-1）在胰腺癌中的表达

探讨MMP-9和TIMP—1在胰腺癌癌细胞及间质的表达与胰腺癌分化程度、分期之间的关系。采用免疫组织化学方法,检测MMP-9和TIMP—1在胰腺癌细胞及间质细胞的表达。MMP-9在胰腺癌细胞和间质组织中均有表达。TIMP—1主要表达在胰腺癌细胞中。MMP-9在胰腺癌间质细胞中的表达高于胰腺癌癌旁组织间质细胞,与胰腺癌的病理分级、分期呈正相关。结论认为MMP-9在胰腺癌间质细胞的表达可能参与胰腺癌的浸润和转移,对预后判断、诊断及治疗具有一定的意义。     

On the logic of informational independence and its applications

We shall introduce in this paper a language whose formulas will be interpreted by games of imperfect information. Such games will be defined in the same way as the games for first-order formulas except that the players do not have complete information of the earlier course of the game. Some simple logical properties of these games will be stated together with the relation of such games of imperfect information to higher-order logic. Finally, a set of applications will be outlined.     

Experience and problem representation in statistics

This research investigated experience level differences in problem representation in statistics. A triad judgment task was designed so that source problems shared either surface similarity (story narrative) or structural (inferential level) features (t test, correlation, or chi-square) with the target problem. Graduate students with varying levels of experience in statistics were asked to choose which source problem "goes best" with the target problem for each triad. Given a choice between a problem that shares surface-level characteristics and one that shares inferential-level characteristics, students who had taken 0 to 4 courses in statistics tended to represent problems on the basis of surface-level features. Students who had more than 4 courses did not consistently make choices on the basis of surface-level features, nor did they consistently rely on structural features. However, all students with statistics course backgrounds noticed structural features when competition between different types of features was eliminated. The role of surface and structural features in determining problem representations is discussed.     

Perfectionism and statistics anxiety

The purpose of this study was to investigate the relationship between perfectionism and statistics anxiety, using a multivariate approach. Participants were 107 students enrolled in graduate-level research methodology courses. A canonical correlation analysis revealed that graduate students who hold unrealistic standards for significant others (i.e. other-oriented perfectionists) and those who maintain a perceived need to attain standards and expectations prescribed by significant others (i.e. socially-prescribed perfectionists) tend to have higher levels of statistics anxiety associated with interpretation anxiety, test and class anxiety, computational self-concept and fear of asking for help. The implications of these findings are discussed.     

On the partitioning of squared Euclidean distance and its applications in cluster analysis

The partitioning of squared Eucliean distance between two vectors in M-dimensional space into the sum of squared lengths of vectors in mutually orthogonal subspaces is discussed and applications given to specific cluster analysis problems. Examples of how the partitioning idea can be used to help describe and interpret derived clusters, derive similarity measures for use in cluster analysis, and to design Monte Carlo studies with carefully specified types and magnitudes of differences between the underlying population mean vectors are presented. Most of the example applications presented in this paper involve the clustering of longitudinal data, but their use in cluster analysis need not be limited to this arena.     

Computer aids in teaching statistics and methodology

Detailed information is provided on the use of a computer as an aid in the teaching of statistics. A review of the state of the art is included.     

Employability: A psycho-social construct, its dimensions, and applications

We examine the idea that an individual’s employability subsumes a host of person-centered constructs needed to deal effectively with the career-related changes occurring in today’s economy. We argue that employability represents a form of work specific (pro)active adaptability that consists of three dimensions—career identity, personal adaptability, and social and human capital. Reciprocal relationships among these dimensions are also discussed. The impact of employability on organizational behavior is illustrated through applications to the research literatures on job loss and job search.