A spatial perturbation technique for the investigation of discrete internal representations of visual patterns

A technique is proposed for the investigation of discrete internal representations assumed to be formed by the visual system in response to pattern stimuli. The proposed technique involves applying a local 1-parameter group of spatial transformations to a pattern to generate a continuum of patterns. The visual discriminability of pairs of perturbed patterns corresponding to small fixed increments in the transformation parameter is determined at various points in the parameter range. By means of a simple rule, the characteristics of this discrimination performance are then related to the probability density functions assumed to underlie the hypothesized discrete internal representations. Two experimental applications of the proposed technique are described. The first is concerned with a discrete internal representation involving the specification of the collinearity or non-collinearity of the points in a pattern; the second is concerned with a discrete internal representation involving the specification of the acuteness or obtuseness of the angle between two lines in a pattern.     

Characterization of discrete and continuous modes of visual pattern discrimination

Discrete and continuous modes of visual pattern discrimination performance are analyzed using a model for the investigation of discrete internal pattern representations described in previous papers (Foster, 1980a, b). A simple quantitative criterion is derived to characterize the two kinds of visual discrimination performance. Values predicted by this criterion are then compared with values obtained from experimental data.     

Speech perception at the interface of neurobiology and linguistics

Speech perception consists of a set of computations that take continuously varying acoustic waveforms as input and generate discrete representations that make contact with the lexical representations stored in long-term memory as output. Because the perceptual objects that are recognized by the speech perception enter into subsequent linguistic computation, the format that is used for lexical representation and processing fundamentally constrains the speech perceptual processes. Consequently, theories of speech perception must, at some level, be tightly linked to theories of lexical representation. Minimally, speech perception must yield representations that smoothly and rapidly interface with stored lexical items. Adopting the perspective of Marr, we argue and provide neurobiological and psychophysical evidence for the following research programme. First, at the implementational level, speech perception is a multi-time resolution process, with perceptual analyses occurring concurrently on at least two time scales (approx. 20-80 ms, approx. 150-300 ms), commensurate with (sub)segmental and syllabic analyses, respectively. Second, at the algorithmic level, we suggest that perception proceeds on the basis of internal forward models, or uses an 'analysis-by-synthesis' approach. Third, at the computational level (in the sense of Marr), the theory of lexical representation that we adopt is principally informed by phonological research and assumes that words are represented in the mental lexicon in terms of sequences of discrete segments composed of distinctive features. One important goal of the research programme is to develop linking hypotheses between putative neurobiological primitives (e.g. temporal primitives) and those primitives derived from linguistic inquiry, to arrive ultimately at a biologically sensible and theoretically satisfying model of representation and computation in speech.     

Representations of the human circulatory system

There is no agreement about the robustness of intuitive representations of the circulatory system and their susceptibility to change by instruction. In this paper, we analyse to what extent students with varying degrees of biology instruction and different ages (High School Health Science and Social Science students and first and final year University Psychology students) have been able to change their intuitive beliefs into scientific representations of the workings of the human circulatory system. We analysed two aspects of the representation of the circulatory system: models of the circulatory system (the relationship between the heart and lungs in the blood pathway) and the circulatory system pattern (the blood pathway between organs). In relation to the models of the circulatory system, we found differences among the different groups of students according to the amount of biological instruction they had. The majority of participants (High School Social Science students and both University Psychology student groups) had an incomplete model, which did not include the lungs while the High School Health Science students group had a scientific representation. As for the circulatory system pattern, we did not find differences among groups. However, we cannot conclude that the representations of the two aspects of the circulatory system (model and pattern) are independent. The data in this study show that compulsory human physiology instruction did not enhance the acquisition of a scientific representation of the human circulatory system.     

ROOTMAP—a model in three-dimensional coordinates of the growth and structure of fibrous root systems

A model is described which simulates the growth of fibrous root systems. The root growth is specified in terms of growing time, numbers of axes, initiation times of axes, growth rates and branching characteristics of the roots, and characteristics governing the direction of root growth. The model generates a representation of the root system in which the locations of all branches and root tips are recorded in three-dimensional coordinates, and updates this representation in discrete time steps until the specified growing time is reached. Data are presented from a simulation of wheat root growth by the model. The simulated root system is represented pictorially and also graphically in the form of root length and root tip number profiles which are stratified by branching order class. The pictorial representations produced by the model are much more realistic than any which have been produced by past root growth models, and the graphical representations show trends in root length and root tip numbers which are the same as those commonly observed in real roots.     

Shifting attention within memory representations involves early visual areas

Prior studies have shown that spatial attention modulates early visual cortex retinotopically, resulting in enhanced processing of external perceptual representations. However, it is not clear whether the same visual areas are modulated when attention is focused on, and shifted within a working memory representation. In the current fMRI study participants were asked to memorize an array containing four stimuli. After a delay, participants were presented with a verbal cue instructing them to actively maintain the location of one of the stimuli in working memory. Additionally, on a number of trials a second verbal cue instructed participants to switch attention to the location of another stimulus within the memorized representation. Results of the study showed that changes in the BOLD pattern closely followed the locus of attention within the working memory representation. A decrease in BOLD-activity (V1-V3) was observed at ROIs coding a memory location when participants switched away from this location, whereas an increase was observed when participants switched towards this location. Continuous increased activity was obtained at the memorized location when participants did not switch. This study shows that shifting attention within memory representations activates the earliest parts of visual cortex (including V1) in a retinotopic fashion. We conclude that even in the absence of visual stimulation, early visual areas support shifting of attention within memorized representations, similar to when attention is shifted in the outside world. The relationship between visual working memory and visual mental imagery is discussed in light of the current findings.     

From theory to data: Representing neurons in the 1940s

Recent literature on the role of pictorial representation in the life sciences has focused on the relationship between detailed representations of empirical data and more abstract, formal representations of theory. The standard argument is that in both a historical and epistemic sense, this relationship is a directional one: beginning with raw, unmediated images and moving towards diagrams that are more interpreted and more theoretically rich. Using the neural network diagrams of Warren McCulloch and Walter Pitts as a case study, I argue that while in the empirical sciences, pictorial representation tends to move from data to theory, in areas of the life sciences that are predominantly theoretical, when abstraction occurs at the outset, the relationship between detail and abstraction in pictorial representations can be of a different character.     

Measuring internal representations from behavioral and brain data

The study of internal knowledge representations is a cornerstone of the research agenda in the interdisciplinary study of cognition. An influential proposal assumes that the brain uses its internal knowledge of the external world to constrain, in a top-down manner, high-dimensional sensory data into a lower-dimensional representation that enables perceptual decisions and other higher-level cognitive functions [1-9]. This proposal relies on a precise formulation of the observer-specific internal knowledge (i.e., the internal representations, or models) that guides reduction of the high-dimensional retinal input onto a low-dimensional code. Here, we directly revealed the content of subjective internal representations by instructing five observers to detect a face in the presence of only white noise, to force a pure top-down, knowledge-based task. We used reverse correlation methods to visualize each observer's internal representation that supports detection of an illusory face. Using reverse correlation again, this time applied to observers' electroencephalogram activity, we established where and when in the brain specific internal knowledge conceptually interprets the input white noise as a face. We show that internal representations can be reconstructed experimentally from behavioral and brain data, and that their content drives neural activity first over frontal and then over occipitotemporal cortex.     

Multilevel structure in behaviour and in the brain: a model of Fuster's hierarchy

A basic question, intimately tied to the problem of action selection, is that of how actions are assembled into organized sequences. Theories of routine sequential behaviour have long acknowledged that it must rely not only on environmental cues but also on some internal representation of temporal or task context. It is assumed, in most theories, that such internal representations must be organized into a strict hierarchy, mirroring the hierarchical structure of naturalistic sequential behaviour. This article reviews an alternative computational account, which asserts that the representations underlying naturalistic sequential behaviour need not, and arguably cannot, assume a strictly hierarchical form. One apparent liability of this theory is that it seems to contradict neuroscientific evidence indicating that different levels of sequential structure in behaviour are represented at different levels in a hierarchy of cortical areas. New simulations, reported here, show not only that the original computational account can be reconciled with this alignment between behavioural and neural organization, but also that it gives rise to a novel explanation for how this alignment might develop through learning.     

On adaptation: A reduction of the Kauffman-Levin model to a problem in graph theory and its consequences

It is shown that complex adaptations are best modelled as discrete processes represented on directed weighted graphs. Such a representation captures the idea that problems of adaptation in evolutionary biology are problems in a discrete space, something that the conventional representations using continuous adaptive landscapes does not. Further, this representation allows the utilization of well-known algorithms for the computation of several biologically interesting results such as the accessibility of one allele from another by a specified number of point mutations, the accessibility of alleles at a local maximum of fitness, the accessibility of the allele with the globally maximum fitness, etc. A reduction of a model due to Kauffman and Levin to such a representation is explicitly carried out and it is shown how this reduction clarifies the biological questions that are of interest.Thanks are due to William Wimsatt, James F. Crow, and the referees for Biology and Philosophy for comments on an earlier version of this paper. Remarks by members of the audience, especially Abner Shimony, of a seminar at Boston University, February 19, 1988, were also very helpful. The diagrams were prepared with the assistance of Tracy Lubas.     

Knowledge-based vision and simple visual machines.

The vast majority of work in machine vision emphasizes the representation of perceived objects and events: it is these internal representations that incorporate the ''knowledge'' in knowledge-based vision or form the ''models'' in model-based vision. In this paper, we discuss simple machine vision systems developed by artificial evolution rather than traditional engineering design techniques, and note that the task of identifying internal representations within such systems is made difficult by the lack of an operational definition of representation at the causal mechanistic level. Consequently, we question the nature and indeed the existence of representations posited to be used within natural vision systems (i.e. animals). We conclude that representations argued for on a priori grounds by external observers of a particular vision system may well be illusory, and are at best place-holders for yet-to-be-identified causal mechanistic interactions. That is, applying the knowledge-based vision approach in the understanding of evolved systems (machines or animals) may well lead to theories and models that are internally consistent, computationally plausible, and entirely wrong.     

Vision as temporal trace

Most current models of human and animal vision assume that the processes of vision involve 2D (or even 3D) internal representations of the external world--an iconic representation. Within these models, recognition involves some form of lineal, areal or volumetric comparison of these internal representations (either learned or innate) with current sensory inputs. However, this view has recently come under criticism. In this paper, a neural model of vision is explored in which this iconic world view is replaced by a temporally ordered trace of (essentially) local features. The model employs hierarchical, recurrently linked, self-organizing topological maps.     

Are binary synapses superior to graded weight representations in stochastic attractor networks?

Synaptic plasticity is an underlying mechanism of learning and memory in neural systems, but it is controversial whether synaptic efficacy is modulated in a graded or binary manner. It has been argued that binary synaptic weights would be less susceptible to noise than graded weights, which has impelled some theoretical neuroscientists to shift from the use of graded to binary weights in their models. We compare retrieval performance of models using both binary and graded weight representations through numerical simulations of stochastic attractor networks. We also investigate stochastic attractor models using multiple discrete levels of weight states, and then investigate the optimal threshold for dilution of binary weight representations. Our results show that a binary weight representation is not less susceptible to noise than a graded weight representation in stochastic attractor models, and we find that the load capacities with an increasing number of weight states rapidly reach the load capacity with graded weights. The optimal threshold for dilution of binary weight representations under stochastic conditions occurs when approximately 50% of the smallest weights are set to zero.     

Capacity optimization and scheduling of a multiproduct manufacturing facility for biotech products

A general mathematical framework has been proposed in this work for scheduling of a multiproduct and multipurpose facility involving manufacturing of biotech products. The specific problem involves several batch operations occurring in multiple units involving fixed processing time, unlimited storage policy, transition times, shared units, and deterministic and fixed data in the given time horizon. The different batch operations are modeled using state‐task network representation. Two different mathematical formulations are proposed based on discrete‐ and continuous‐time representations leading to a mixed‐integer linear programming model which is solved using General Algebraic Modeling System software. A case study based on a real facility is presented to illustrate the potential and applicability of the proposed models. The continuous‐time model required less number of events and has a smaller problem size compared to the discrete‐time model. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:1221–1230, 2014     

Markov invariants and the isotropy subgroup of a quartet tree

The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results directly to Markov invariants, thereby extending previous theoretical results by systematically identifying linear combinations that vanish for a given quartet. We also note that the theory is fully generalizable to arbitrary trees and is equally applicable to the related case of phylogenetic invariants. All results follow from elementary consideration of the representation theory of finite groups.