A theory of causality: Causality=interaction (as defined by a suitable quantum field theory)

In this paper I put forward a suggestion for identifying causality in micro-systems with the specific quantum field theoretic interactions that occur in such systems. I first argue — along the lines of general transference theories — that such a physicalistic account is essential to an understanding of causation; I then proceed to sketch the concept of interaction as it occurs in quantum field theory and I do so from both a formal and an informal point of view. Finally, I present reasons for thinking that only a quantum field theoretic account can do the job — in particular I rely on a theorem by D. Currie and to the effect that interaction cannot be described in (a Hamiltonian formulation of) Classical Mechanics. Throughout the paper I attempt to suggest that the widespread scepticism about the ability of quantum theory to support a theory of causality is mistaken and rests on several misunderstandings.     

The approximation of two-mode proximity matrices by sums of order-constrained matrices

A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered define Q-forms (or anti-Q-forms) for a two-mode matrix, where after suitable and separate row and column reorderings, the entries within each row and within each column are nondecreasing (or nonincreasing) to a maximum (or minimum) and thereafter nonincreasing (or nondecreasing). Several other types of order constraints are also mentioned to show how alternative structures can be considered using the same computational strategy.     

Involutions defined by monadic terms

We prove that there are two involutions defined by monadic terms that characterize Monadic Algebras. We further prove that the variety of Monadic Algebras is the smallest variety of Interior Algebras where these involutions give rise to an interpretation from the variety of Bounded Distributive Lattices into it.Research funded by Fondecyt, project N 764-1987.     

The finite inseparability of the first-order theory of diagonalisable algebras

In a recent paper, Montagna proved the undecidability of the first-order theory of diagonalisable algebras. This result is here refined — the set of finitely refutable sentences is shown effectively inseparable from the set of theorems. The proof is quite simple.     

Attentional capture by globally defined objects

The abrupt appearance of a new perceptual object in the visual field typically captures visual attention. However, if attention is focused in advance on a different location, onsets can fail to capture attention (Yantis & Jonides, 1990). In the present experiments, we investigated the extent to which the deployment of attention to the local level of a hierarchical scene may be affected by the abrupt appearance of a new object at the global level. Participants searched for a semi-disk target in an array of randomly oriented segmented disks (“pacmen”). On half the trials, a subset of the segmented disks induced a subjective square. On these critical trials, participants were significantly slower to respond to the presence of a local target even though the local features of the display were qualitatively identical across all conditions. This slowing was absent when outline pacmen were used (which do not induce subjective figures) and when the subjective square was perceptually old. When the participants’ task was defined at the global level of the display, a new local element failed to capture attention, suggesting an asymmetry in the ability of objects at different levels of a hierarchical scene to capture attention. In a control experiment, a new local element captured attention, however, when the participants’ task was defined at the local level, indicating that the local item was in principle capable of capturing attention. It is argued that global objects capture attention because they convey important information about the environment that is not available at the local level.     

Recognizing faces defined by texture gradients

Texture gradients can reveal surface orientation in a manner similar to shape from shading, and therefore provide an important cue for object recognition. In this study, we tested whether a complex 3-D object, such as a face, can be identified from texture gradients alone. The stimuli were laser-scanned faces for which the texture element was a fractal-noise pattern mapped onto the 3-D surface. An eight-alternative forced choice task was used in which participants matched a face defined by texture gradients to one of eight faces defined by shape from shading (Experiment 1) or by texture gradients (Experiment 2). On average, participants scored 24% and 18%, respectively, above chance in these experiments. Although this performance was much poorer than the performance based entirely on shape-from-shading stimuli (Experiment 3), the results suggest that texture gradient information may be used to recover surface geometry of complex objects.     

Attentional capture by globally defined objects.

The abrupt appearance of a new perceptual object in the visual field typically captures visual attention. However, if attention is focused in advance on a different location, onsets can fail to capture attention (Yantis & Jonides, 1990). In the present experiments, we investigated the extent to which the deployment of attention to the local level of a hierarchical scene may be affected by the abrupt appearance of a new object at the global level. Participants searched for a semi-disk target in an array of randomly oriented segmented disks ("pacmen"). On half the trials, a subset of the segmented disks induced a subjective square. On these critical trials, participants were significantly slower to respond to the presence of a local target even though the local features of the display were qualitatively identical across all conditions. This slowing was absent when outline pacmen were used (which do not induce subjective figures) and when the subjective square was perceptually old. When the participants' task was defined at the global level of the display, a new local element failed to capture attention, suggesting an asymmetry in the ability of objects at different levels of a hierarchical scene to capture attention. In a control experiment, a new local element captured attention, however, when the participants' task was defined at the local level, indicating that the local item was in principle capable of capturing attention. It is argued that global objects capture attention because they convey important information about the environment that is not available at the local level.     

A simple procedure for rearranging matrices

Guttman's scalogram board technique for reordering the columns and rows of a matrix is described and its disadvantages are pointed out. A simple and inexpensive procedure for doing the same job without these disadvantages is outlined.I am grateful to Professor Jozef Cohen of the University of Illinois for a five-minute conversation which greatly simplified the procedure described here.     

Mimic automata: A novel formal model for mimic computing

In this paper, we aim to establish a mathematical model for mimic computing. To this end, we present a novel automaton called a mimic automaton. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a computing unit, a sequential automaton is employed to describe some state transitions, a hierarchical automaton is employed to express the different granularities of some computing units, and a probabilistic automaton is used to depict some random changes of a computing unit. Second, a mimic automaton is obtained by combining the various types of automata mentioned above in a certain logical relationship. Compared with the existing models of mimic computing, the new model portrays the operational semantics for a mimic computing system, and it can directly describe the behaviors of a system. Furthermore, the new model possesses a stronger generality.     

A finite God reconsidered

International Journal for Philosophy of Religion -     

The detection of surface curvatures defined by optical motion

The detectability of surface curvatures defined by optical motion was evaluated in three experiments. Observers accurately detected very small amounts of curvature in a direction perpendicular to the direction of rotation, but they were less sensitive to curvatures along the direction of rotation. Variations in either the number of points (between 91 and 9) or the number of views (from 15 to 2) had little or no effect on discrimination accuracy. The results of this study demonstrate impressive visual sensitivity to surface curvature. Several characteristics of this sensitivity to curvature are inconsistent with many computational models for deriving three-dimensional structure from motion.     

Attention to object files defined by transparent motion

Two interspersed and differently colored sets of dots were rotated in opposite directions and were perceived as superimposed transparent surfaces. Probes consisting of brief changes in dot motion direction were reported. Two probes affecting the same surface were discriminated accurately. The 2nd probe was discriminated poorly if it affected a surface different from the 1st and if the time between probes was less than 600 ms. This reflects a difficulty in switching attention rapidly between surfaces. Spatial proximity increased the interference. Controls were incompatible with traditional spatial mechanisms (2- or 3-dimensional) or with simple sensory filters. Instead, probes were apparently selected by object files. The interference is not simply due to an inability to process 2 objects at once but requires close spatial proximity of incompatible motion signals.     

Parallel discrimination of subjective contours defined by offset gratings

Recent physiological studies (von der Heydt & Peterhans, 1989) suggest that the orientation of subjective contours is encoded very early in the visual system (V2 in monkey). This result is seemingly at odds with existing psychophysical data which suggest that the detection of subjective contours involves selective attention. It is argued that certain subjective contours are registered in a reflexive (bottom-up) manner by the visual system but that selective attention may be needed to gain access to this representation. To assess this suggestion, a visual-search task was used in which subjects were to detect the presence of a horizontal (vertical) subjective contour (defined by offset gratings) in a variable number of vertical (horizontal) subjective contours (also defined by offset gratings). When there were no competing organizations within the display, detection was indeed independent of the number of nontarget distractors, that is, selective attention was unnecessary. In a second experiment, we found that a curved form (a crescent defined by subjective contours) was easier to detect in a background of vertical bars (also defined by subjective contours) than vice versa, namely, a search asymmetry paralleling those found by Treisman and Gormican (1988). A final experiment showed that when the horizontal and vertical bars of the first experiment formed textured regions, they could be discriminated at very brief display durations (30–120 msec), However, when the line terminations aligned along the subjective contour were tapered rather than abrupt, discrimination dropped off with the degree of tapering. The latter result is consistent with the assumption that the registration of subjective contours in V2 involves the integration of responses from aligned, end-stopped cells found in VI (von der Heydt & Peterhans, 1989).     

An application of signal detection theory with finite mixture distributions to source discrimination

A mixture extension of signal detection theory is applied to source discrimination. The basic idea of the approach is that only a portion of the sources (say A or B) of items to be discriminated is encoded or attended to during the study period. As a result, in addition to 2 underlying probability distributions associated with the 2 sources, there is a 3rd distribution that represents items for which sources were not attended to. Thus, over trials, the observed response results from a mixture of an attended (A or B) distribution and a nonattended distribution. The situation differs in an interesting way from detection in that, for detection, there is mixing only on signal trials and not on noise trials, whereas for discrimination, there is mixing on both A and B trials. Predictions of the mixture model are examined for data from several recent studies and in a new experiment.     

A phonological interpretation of two acoustic confusion matrices

Multidimensional scaling and principal component analysis methods are used to examine two acoustic confusion matrices. It is suggested that three of the dimensions isolated by means of these techniques can be identified with phonological phenomena which could have contributed to the confusions.