Csiszar’s ϕ-divergences for testing the order in a Markov chain

x ₁, ..., x _n+r can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H ₀ that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: _ϕ-Divergences. More precisely, if p _{a 1 ....., a r}: _{a r +1} denotes the transition probability for a r ^th order Markov chain, the hypothesis to be tested is H ₀:p _{a 1 ....., a r}: _{a r +1} = p _{a 2 ....., a r}: _{a r +1}, a _i ∈{1, ..., s}, i = 1, ..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic. Received: August 3, 1998; revised version: November 25, 1999     

Continuity of utility functions representing fuzzy preferences

In a previous paper, we established necessary and sufficient conditions for a given binary fuzzy relation to be representable by a utility function. In this article, we construct a crisp order topology associated to a given weakly complete fuzzy pre-order and introduce the notion of “continuous fuzzy pre-order.” We show that this new condition and the conditions introduced in the previous paper are together necessary and sufficient for a numerical representation of a given weakly complete fuzzy pre-order by a continuous utility function.     

Tests of hypotheses based on ranks in the general linear model

A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished.     

Mental Rotation of Dynamic,Three‐Dimensional Stimuli by 3‐Month‐Old Infants

Mental rotation involves transforming a mental image of an object so as to accurately predict how the object would look if it were rotated in space. This study examined mental rotation in male and female 3‐month‐olds, using the stimuli and paradigm developed by Moore and Johnson (2008) . Infants were habituated to a video of a three‐dimensional object rotating back and forth through a 240° angle around the vertical axis. After habituation, infants were tested both with videos of the same object rotating through the previously unseen 120° angle, and with the mirror image of that display. Unlike females, who fixated the test displays for approximately equal durations, males spent significantly more time fixating the familiar object than the mirror‐image object. Because familiarity preferences like this emerge when infants are relatively slow to process a habituation stimulus, the data support the interpretation that mental rotation of dynamic three‐dimensional stimuli is relatively difficult—but possible—for 3‐month‐old males. Interpretation of the sex differences observed in 3‐ and 5‐month‐olds’ performances is discussed.     

From Provocation and Combustibility Toward Mutuality: Once More with Less Rage,Please

This paper presents a summary and excerpts taken from the psychoanalytic treatment, spanning over 16 years, of a highly disturbed and provocative male patient. Prior to referral, the man had been unsuccessfully treated psychopharmacologically for a depressive illness with severe somatic and affective symptoms and behavioral disturbances. A highlight of the case is the emergence of a therapeutic impasse that developed around the patient's attempt to connect intensely with the analyst; the patient attempted to repair his own damaged phallic narcissism by demanding that the analyst participate in a ritualized sexual enactment, which threatened the destruction of the treatment process. The resolution of the impasse was accomplished through the analyst's reaffirming the frame and recovering his own disrupted composure and ref lectiveness, while maintaining a compassionate and caring attitude toward the patient.     

«Land of East Wind»: mise en forme d'une mémoire mi'gmaq*

This essay follows from an historical study of Heron Island (Baie des Chaleurs), and in particular, the relationship between the island and the members, past and present, of the Eel River Bar Band, from the reserve of the same name. It aims to explore elements brought to light through my observation of members of the band, and notably the processes by which the latter strive to fashion a renewed connection with Heron Island; that is, to Self and to the world. Purposefully multidisciplinary, this study focusses on the representation/construction of space and on the manner in which it acts upon its derivatives in the form of collective memory and identity. Situated at the intersection of the symbolic and material realms, this essay endeavours to shed light on the formation of the narratives that, in this instance, constitute the production (mise en scene) of a perspective space of symbolization and social objectification—a process articulated on the enunciation of goals related to socio‐economic development and autonomy. At the same time, it is an attempt to account for a number of correlates to discourse, particularly practices related to social reconfiguration and the exercise of power, in a context marked by a quest for self‐determination and revitalism. In short, it is an examination of a case of resistance and accommodation by a small indigenous group seeking a new world‐vision. Le présent essai découle d'une étude historique portant sur l'île au Héron (Baie‐des‐Chaleurs) et en particulier sur les liens qui s'éta‐blissent entre celle‐ci et les membres, passés et présents, de la bande Eel River Bar, de la réserve du même nom. Il vise à explorer les éléments mis en relief par des observations faites dans le cadre de mes relations avec des membres de la bande, notamment les processus de l'élaboration d'un rapport renouveléà l'île au Héron, c'est‐à‐dire au Soi et au monde. Résolument multidisciplinaire, c'est une étude de cas qui porte sur la représentation/construction de l'espace et sur la façon dont celle‐ci influe sur la mémoire collective et sur l'identité qui en dérive. Sis à l'intersection de l'univers symbolique et de l'univers matériel, cet essai cherche à mettre au jour la formation des récits qui, dans ce cas, constituent la mise en scène d'un espace perspectif de symbolisation et d'objectivation sociale, un processus articulé sur l'énonciation de desseins de développement socio‐économique et d'autonomie. Parallèlement, il s'attache àéclairer les pratiques corrélatives au discursif, qui se nomment reconfiguration sociale et déploiement du pouvoir, dans un contexte de prise en main et de velléités revitalistes. En somme, il s'agit d'examiner un cas de résistance et d'accommodement de la part d'un groupe autochtone de petite taille, en mal de vision‐monde.     

Higher Education's Role in the Dialogue on Race

The university is a logical locus for discussionof the role race has played in our society. Perhaps noAmerican institution is more committed to free andopen dialogue than the university. Higher educationcan thus provide a context for the recognition ofissues as well as a forum for the resolution ofinitiatives. To date, however, university attempts atdiversity training have often imbued recipients withself-consciousness, usurping the unity implicit in theword `university' and evoking an even greater tendencytoward separatism. The university's traditional questfor truth has been subverted by a subtle and pervasivesense that some views are more correct than others,that openness is dangerous, and that some issues mighteven be taboo. At best, such an approach to diversityleads to a fragile stalemate among self-containedenclaves. By championing President Clinton's call fora dialogue on race, the university can restore itselfas an institution that puts honesty above all else.Not only is there a resonant rationale for theuniversity's central responsibility in this debate,but there is also a pedagogical means by which itsrole can be realized. This paper proposes a model forethnic dialogue relevant to either a text-based orissues-based class. Borrowing from pedagogy developedin professional schools, we believe that the tenets ofthe `case method' can create a climate conducive tothe substantive scrutiny of race, ethnicity, andprejudice in general. We argue that this dialogueshould not be a mere add-on to college life, butintegrated into existing curricula in the socialsciences, literature, and history. Heated debate canthen occur without anger, and race/ethnicity can bediscussed without fear of recrimination.Paradoxically, the very expression of ethnicity may bethe catalyst that eventually moves multiculturalismtoward interculturalism – where differences are nolonger articulated, measurable or even discernible.