Multi-objective combinatorial optimization problems: A survey

In the last 20 years many multi-objective linear programming (MOLP) methods with continuous variables have been developed. However, in many real-world applications discrete variables must be introduced. It is well known that MOLP problems with discrete variables can have special difficulties and so cannot be solved by simply combining discrete programming methods and multi-objective programming methods. The present paper is intended to review the existing literature on multi-objective combinatorial optimization (MOCO) problems. Various classical combinatorial problems are examined in a multi-criteria framework. Some conclusions are drawn and directions for future research are suggested.     

Combined visual illusion effects on the perceived index of difficulty and movement outcomes in discrete and continuous fitts’ tapping

The speed-accuracy trade-off is a fundamental movement problem that has been extensively investigated. It has been established that the speed at which one can move to tap targets depends on how large the targets are and how far they are apart. These spatial properties of the targets can be quantified by the index of difficulty (ID). Two visual illusions are known to affect the perception of target size and movement amplitude: the Ebbinghaus illusion and Muller-Lyer illusion. We created visual images that combined these two visual illusions to manipulate the perceived ID, and then examined people’s visual perception of the targets in illusory context as well as their performance in tapping those targets in both discrete and continuous manners. The findings revealed that the combined visual illusions affected the perceived ID similarly in both discrete and continuous judgment conditions. However, the movement outcomes were affected by the combined visual illusions according to the tapping mode. In discrete tapping, the combined visual illusions affected both movement accuracy and movement amplitude such that the effective ID resembled the perceived ID. In continuous tapping, none of the movement outcomes were affected by the combined visual illusions. Participants tapped the targets with higher speed and accuracy in all visual conditions. Based on these findings, we concluded that distinct visual-motor control mechanisms were responsible for execution of discrete and continuous Fitts’ tapping. Although discrete tapping relies on allocentric information (object-centered) to plan for action, continuous tapping relies on egocentric information (self-centered) to control for action. The planning-control model for rapid aiming movements is supported.     

Towards a Theory of Limited Indeterminism in Branching Space-times

Branching space-times (BST; Belnap, Synthese 92:385–434, 1992) is the most advanced formal framework for representing indeterminism. BST is however based on continuous partial orderings, while our natural way of describing indeterministic scenarios may be called discrete. This paper establishes a theorem providing a discrete data format for BST: it is proved that a discrete representation of indeterministic scenarios leading to BST models is possible in an important subclass of cases. This result enables the representation of limited indeterminism in BST and hopefully paves the way for the representation of substances with capacities in that framework.     

Adaptive executive control: Flexible multiple-task performance without pervasive immutable response-selection bottlenecks

A new theoretical framework, the EPIC (Executive-Process/Interactive-Control) architecture, provides the basis for accurate detailed computational models of human multiple-task performance. Contrary to the traditional response-selection bottleneck hypothesis, EPIC's cognitive processor can select responses and do other procedural operations simultaneously for multiple concurrent tasks. Using this capacity together with flexible executive control of peripheral perceptual-motor components, EPIC computational models account well for various patterns of mean reaction times, systematic individual differences in multiple-task performance, and influences of special training on people's task-coordination strategies. These diverse phenomena, and EPIC's success at modeling them, raise strong doubts about the existence of a pervasive immutable response-selection bottleneck in the human information-processing system. The present research therefore helps further characterize the nature of discrete versus continuous information processing.     

Semantics, conceptual spaces, and the meeting of minds

We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions.     

From objects to names: A cognitive neuroscience approach

To name an object, we need both to recognize it and to access the associated phonological form, and phonological retrieval itself may be constrained by aspects of the visual recognition process. This paper reviews evidence for such constraints, drawing on data from experimental psychology, neuropsychology, functional imaging, and computational modelling. Data on picture identification in normal observers demonstrate that the speed of name retrieval processes differs for natural objects and artifacts, due at least in part to differences in visual similarity between exemplars within these categories. Also, effects of variables on early and late stages of object identification combine in an interactive rather than an additive manner, consistent with object processing stages operating in a continuous rather than a discrete manner. Neuropsychological evidence supports this proposal, demonstrating that subtle perceptual deficits can produce naming problems, even when there is good access to associated semantic knowledge. Functional activation studies further show increased activity in visual processing areas when conditions stress object naming relative to the recognition of familiar object structures. These studies indicate that object naming is based on a series of continuous processing stages and that naming involves increased visual processing relative to recognition tasks. The data can be modelled within an interactive activation and competition framework. Received: 25 November 1997 / Accepted: 16 May 1998     

Resource scarcity and outcome conflict in time-sharing performance

The efficacy of the resource-scarcity and outcome-conflict views in explaining dual-task interference was examined. A discrete—continuous task pair was purposely chosen to allow fine-grained analysis of time-shared performance. The relative priority of the dual task was manipulated by a secondary task technique to test for performance tradeoff that would be indicative of resource allocation. The temporal predictability of the discrete stimuli was manipulated to examine possible strategic avoidance of interference. The moment-by-moment data did not reveal any evidence for a switching strategy. It was concluded that the intricate interference patterns could be more easily interpreted within the resource framework than within the outcome-conflict framework.     

The temporally-integrated causality landscape: A theoretical framework for consciousness and meaning

Theoretical approaches to understanding consciousness have begun to converge upon areas of general agreement, yet substantive differences remain. Here, I introduce a new theoretical framework for the emergence of consciousness from the functional integration of the thalamocortical system: the Temporally-Integrated Causality Landscape (TICL). TICL presents a novel perspective which addresses important phenomenological characteristics of consciousness that other frameworks, such as IIT, do not. First, the TICL is based upon the observation that conscious experiences are temporally continuous, not discrete. Secondly, the TICL establishes a thalamocortical basis for the point-of-view. According to TICL, consciousness is composed of contents that arise from neuronal subsystems that have meaning from the point-of-view of the larger, integrated system in which they are nested. Meaningful contents emerge from the subsystems because they exhibit a level of temporally-integrated causality (TIC) that is distinguishable from that of the larger system.     

Exploring the dynamics of the appraisal–emotion relationship: A constraint satisfaction model of the appraisal process

This paper presents a computational model of emotions that is based in an appraisal theoretical framework. The model explores the dynamics of the appraisal–emotion relationship using parallel constraint satisfaction. It proposes belief coherence, desire coherence and belief–desire coherence as basic principles and specifies how these principles can be realised in a parallel constraint satisfaction system. The model shows that the very same mechanisms that account for the formation of coherence or consistency are also pivotal for the emergence and alteration of emotional states and for the dynamics of the cognition–emotion relationship. Concrete simulation examples show how discrete emotions such as anger, pride, sadness, shame, surprise, relief and disappointment emerge out of these principles.     

Toward Computational Model of Emotion from Individual Difference in Perceiving Facial Expressions

We propose a computational model for identifying emotional state of a facial expression from appraisal scores given by human observers utilizing their differences in perception. The appraisal model of human emotion is adopted as the basis of this evaluation process with appraisal variables as output. We investigated the performance for both categorical and continuous representation of the variables appraised by human observers. Analysis of the data exhibits higher degree of agreement between estimated Indian ratings and the available reference when these are rated through continuous domain. We also observed that emotional state with negative valence are influential in the perception of hybrid emotional state like ‘Surprise’, only when appraisal variables are labeled through categories of emotions. Thus, the proposed method has implications in developing software to detect emotion using appraisal variables in continuous domain, perceived from facial expression of an agent (or human subject). Further, this model can be customized to include cultural variability in recognizing emotions.     

Homogeneous case of the continuous response model

In line with the latent trait model, the continuous response level is defined and considered, in contrast to the discrete response levels, which have already been explored by the author. Discussions are mainly focused on the homogeneous case and the open response situation. The operating density characteristic of the continuous item score is defined. Also the basic function, information functions and the positive-exponent family are discussed on the continuous response level, in connection with the sufficient condition that a unique maximum estimate is provided for the response pattern, which consists of the continuous item scores.     

Generalising principles in spite of procedural differences: Children's understanding of division

Between ages 5 and 7, children are known to be quite good at sharing discrete quantities but very bad at sharing continuous quantities. Our aim was to find whether they can transfer their understanding of logical relations from discrete to continuous quantities though the procedures used in sharing these quantities are markedly different.Two samples of 5- to 7-year-olds participated in two studies. In the first study, the items involved partitive division; in the second, quotitive division tasks. In both studies, the children solved tasks with discrete and continuous quantities.Performance varied significantly across age level and logical principle (equivalence between different rounds of sharing versus inverse relation between the divisor and the quotient) but not across type of quantity (discrete versus continuous). There was a very strong relation between performance across type of quantity. We conclude that children can generalise reasoning principles in division across type of quantity in spite of the difference in sharing procedures.     

Neural Computation and the Computational Theory of Cognition

We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non‐neural notions of computation ought to be replaced or reinterpreted in terms of neural computation.     

Judgments of discrete and continuous quantity: an illusory Stroop effect

Evidence from human cognitive neuroscience, animal neurophysiology, and behavioral research demonstrates that human adults, infants, and children share a common nonverbal quantity processing system with nonhuman animals. This system appears to represent both discrete and continuous quantity, but the proper characterization of the relationship between judgments of discrete and continuous quantity remains controversial. Some researchers have suggested that both continuous and discrete quantity may be automatically extracted from a scene and represented internally, and that competition between these representations leads to Stroop interference. Here, four experiments provide evidence for a different explanation of adults’ performance on the types of tasks that have been said to demonstrate Stroop interference between representations of discrete and continuous quantity. Our well-established tendency to underestimate individual two-dimensional areas can provide an alternative explanation (introduced here as the “illusory-Stroop” hypothesis). Though these experiments were constructed like Stroop tasks, and they produce patterns of performance that initially appear consistent with Stroop interference, Stroop interference effects are not involved. Implications for models of the construction of cumulative area representations and for theories of discrete and continuous quantity processing in large sets are discussed.     

Perception-action coupling and S-R compatibility

How is an aiming movement toward a visual target amended when the target suddenly steps to a new position just before or after the movement has started? Three hypotheses are examined: (1) the initial movement needs to be actively terminated before the new movement can be planned and executed, (2) substitution of the initial target position code results, after a normal RT, in the simultaneous termination of the initial movement and initiation of the movement to the new target position, or (3) a second movement from the initial to the second target is initiated after a normal RT, and superimposed on the ongoing movement toward the initial target. The substitution hypothesis assumes a highly continuous and parallel mode of operation of the perceptual-motor system, whereas the other hypotheses assume a distinctly discrete mode of operation. Detailed analyses of double-step movement trajectories clearly favored the substitution hypothesis. These results are discussed with reference to current views on motor control, overlapping-task performance, and the discrete-continuous issue. It is argued that the nature of the perception-action interface depends on the ideomotor compatibility of the task. Perceptual and motor processes operate in a highly continuous and parallel fashion in ideomotor compatible tasks, whereas the interposition of a limited-capacity response selection mechanism results in a discrete and intermittent mode of communication between these processes in non-ideomotor compatible tasks.     

Visual analogue scales for mode-independent measurement in self-administered questionnaires

Previous research has shown evidence for mode differences between computer-assisted self-administered interviews (CASI) and paper-and-pencil interviews, especially in the case of sensitive questions. Some of these differences are explained by higher degrees of self-disclosure for CASI than for paper-and-pencil interviews, due to the more private situation with CASIs. This analysis examines the existence of different degrees of self-disclosure for CASI versus paper-and-pencil questionnaires and whether these differences can be reduced by the use of a specific response format. Judgments of items on a self-control scale with discrete 5-point (Likert-type) scales are compared with judgments on continuous visual analogue scales (VAS). Because a categorization effect for Likert-type items is assumed when pressure for social desirability is present, it is hypothesized that VAS compared to Likert-type response formats are less sensitive to mode differences.