Abstract representations of biological systems in supercategories

An abstract representation of biological systems from the standpoint of the theory of supercategories is presented. The relevance of such representations forG-relational biologies is suggested. In section A the basic concepts of our representation, that is class, system, supercategory and measure are introduced. Section B is concerned with the mathematical representation starting with some axioms and principles which are natural extensions of the current abstract representations in biology. Likewise, some extensions of the principle of adequate design are introduced in section C. Two theorems which present the connection between categories and supercategories are proved. Two other theorems concerning the dynamical behavior of biological and biophysical systems are derived on the basis of the previous considerations. Section D is devoted to a general study of oscillatory behavior in enzymic systems, some general quantitative relations being derived from our representation. Finally, the relevance of these results for a quantum theoretic approach to biology is discussed.     

Abstract and associatively based representations in human sequence learning

We give an analysis of performance in an artificial neural network for which the claim had been made that it could learn abstract representations. Our argument is that this network is associative in nature, and cannot develop abstract representations. The network thus converges to a solution that is solely based on the statistical regularities of the training set. Inspired by human experiments that have shown that humans can engage in both associative (statistical) and abstract learning, we present a new, hybrid computational model that combines associative and more abstract, cognitive processes. To cross-validate the model we attempted to predict human behaviour in further experiments. One of these experiments reveals some evidence for the use of abstract representations, whereas the others provide evidence for associatively based performance. The predictions of the hybrid model stand in line with our empirical data.     

Pattern computation in neural communication systems

Biological data suggests that activity patterns emerging in small- and large-scale neural systems may play an important role in performing the functions of the neural system, and in particular, neural computations. It is proposed in this paper that neural systems can be understood in terms of pattern computation and abstract communication systems theory. It is shown that analysing high-resolution surface EEG data, it is possible to determine abstract probabilistic rules that describe how emerging activity patterns follow earlier activity patterns. The results indicate the applicability of the proposed approach for understanding the working of complex neural systems.     

Notation-dependent and -independent representations of numbers in the parietal lobes

It is a commonly held view that numbers are represented in an abstract way in both parietal lobes. This view is based on failures to find differences between various notational representations. Here we show that by using relatively smaller voxels together with an adaptation paradigm and analyzing subjects on an individual basis it is possible to detect specialized numerical representations. The current results reveal a left/right asymmetry in parietal lobe function. In contrast to an abstract representation in the left parietal lobe, the numerical representation in the right parietal lobe is notation dependent and thus includes nonabstract representations. Our results challenge the commonly held belief that numbers are represented solely in an abstract way in the human brain.     

On the computational architecture of the neocortex

This paper proposes that each area of the cortex carries on its calculations with the active participation of a nucleus in the thalamus with which it is reciprocally and topographically connected. Each cortical area is responsible for maintaining and updating the organism's knowledge of a specific aspect of the world, ranging from low level raw data to high level abstract representations, and involving interpreting stimuli and generating actions. In doing this, it will draw on multiple sources of expertise, learned from experience, creating multiple, often conflicting, hypotheses which are integrated by the action of the thalamic neurons and then sent back to the standard input layer of the cortex. Thus this nucleus plays the role of an 'active blackboard' on which the current best reconstruction of some aspect of the world is always displayed. Evidence for this theory is reviewed and experimental tests are proposed. A sequel to this paper will discuss the cortico-cortical loops and propose quite different computational roles for them.     

Core systems of geometry in animal minds

Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds.     

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.     

Creating abstract topographic representations: Implications for coding,learning and reasoning

Topographic maps are a fundamental and ubiquitous feature of the sensory and motor regions of the brain. There is less evidence for the existence of conventional topographic maps in associational areas of the brain such as the prefrontal cortex and parietal cortex. The existence of topographically arranged anatomical projections is far more widespread and occurs in associational regions of the brain as well as sensory and motor regions: this points to a more widespread existence of topographically organised maps within associational cortex than currently recognised. Indeed, there is increasing evidence that abstract topographic representations may also occur in these regions. For example, a topographic mnemonic map of visual space has been described in the dorsolateral prefrontal cortex and topographically arranged visuospatial attentional signals have been described in parietal association cortex. This article explores how abstract representations might be extracted from sensory topographic representations and subsequently code abstract information. Finally a simple model is presented that shows how abstract topographic representations could be integrated with other information within the brain to solve problems or form abstract associations. The model uses correlative firing to detect associations between different types of stimuli. It is flexible because it can produce correlations between information represented in a topographic or non-topographic coordinate system. It is proposed that a similar process could be used in high-level cognitive operations such as learning and reasoning.     

On the Semio-Mathematical Nature of Codes

The relational structure of RNA, DNA, and protein bears an interesting similarity to the determination problem in category theory. In this paper, we present this deep-structure similarity and use it as a springboard for discussing some abstract properties of coding in various systems. These abstract properties, in turn, may shed light on the evolution of the DNA world from a semiotic perspective. According to the perspective adopted in this paper, living systems are not information processing systems but “meaning-making” systems. Therefore, what flows in the genetic system is not “information” but “value.” We define meaning, meaning-making, and value and then use these terms to explain the abstract dynamics of coding, which can illuminate many forms of sign-mediated activities in biosystems.     

Modelling brain representations of abstract concepts

Abstract conceptual representations are critical for human cognition. Despite their importance, key properties of these representations remain poorly understood. Here, we used computational models of distributional semantics to predict multivariate fMRI activity patterns during the activation and contextualization of abstract concepts. We devised a task in which participants had to embed abstract nouns into a story that they developed around a given background context. We found that representations in inferior parietal cortex were predicted by concept similarities emerging in models of distributional semantics. By constructing different model families, we reveal the models’ learning trajectories and delineate how abstract and concrete training materials contribute to the formation of brain-like representations. These results inform theories about the format and emergence of abstract conceptual representations in the human brain.     

Structural systems biology: modelling protein interactions

Much of systems biology aims to predict the behaviour of biological systems on the basis of the set of molecules involved. Understanding the interactions between these molecules is therefore crucial to such efforts. Although many thousands of interactions are known, precise molecular details are available for only a tiny fraction of them. The difficulties that are involved in experimentally determining atomic structures for interacting proteins make predictive methods essential for progress. Structural details can ultimately turn abstract system representations into models that more accurately reflect biological reality.     

Heterarchy in biological systems: a logic-based dynamical model of abstract biological network derived from time-state-scale re-entrant form

Heterarchical structure is important for understanding robustness and evolvability in a wide variety of levels of biological systems. Although many studies emphasize the heterarchical nature of biological systems, only a few computational representations of heterarchy have been created thus far. We propose here the time-state-scale re-entrant form to address the self-referential property derived from setting heterarchical structure. In this paper, we apply the time-state-scale re-entrant form to abstract self-referential modeling for a functional manifestation of biological network presented by [Tsuda, I., Tadaki, K., 1997. A logic-based dynamical theory for a genesis of biological threshold. BioSystems 42, 45-64]. The numerical results of this system show different intermittent phase transitions and power-law distribution of time spent in activating functional manifestation. The Hierarchically separated time-scales obtained from spectrum analysis imply that the reactions at different levels simultaneously appear in a dynamical system. The results verify the mutual inter-relationship between heterarchical structure in biological systems and the self-referential property of computational heterarchical systems.     

Modality-independent coding of spatial layout in the human brain

In many nonhuman species, neural computations of navigational information such as position and orientation are not tied to a specific sensory modality [1, 2]. Rather, spatial signals are integrated from multiple input sources, likely leading to abstract representations of space. In contrast, the potential for abstract spatial representations in humans is not known, because most neuroscientific experiments on human navigation have focused exclusively on visual cues. Here, we tested the modality independence hypothesis with two functional magnetic resonance imaging (fMRI) experiments that characterized computations in regions implicated in processing spatial layout [3]. According to the hypothesis, such regions should be recruited for spatial computation of 3D geometric configuration, independent of a specific sensory modality. In support of this view, sighted participants showed strong activation of the parahippocampal place area (PPA) and the retrosplenial cortex (RSC) for visual and haptic exploration of information-matched scenes but not objects. Functional connectivity analyses suggested that these effects were not related to visual recoding, which was further supported by a similar preference for haptic scenes found with blind participants. Taken together, these findings establish the PPA/RSC network as critical in modality-independent spatial computations and provide important evidence for a theory of high-level abstract spatial information processing in the human brain.     

Multiple time-scales and the developmental dynamics of social systems

To build a theory of social complexity, we need to understand how aggregate social properties arise from individual interaction rules. Here, I review a body of work on the developmental dynamics of pigtailed macaque social organization and conflict management that provides insight into the mechanistic causes of multi-scale social systems. In this model system coarse-grained, statistical representations of collective dynamics are more predictive of the future state of the system than the constantly in-flux behavioural patterns at the individual level. The data suggest that individuals can perceive and use these representations for strategical decision-making. As an interaction history accumulates the coarse-grained representations consolidate. This constrains individual behaviour and provides the foundations for new levels of organization. The time-scales on which these representations change impact whether the consolidating higher-levels can be modified by individuals and collectively. The time-scales appear to be a function of the 'coarseness' of the representations and the character of the collective dynamics over which they are averages. The data suggest that an advantage of multiple timescales is that they allow social systems to balance tradeoffs between predictability and adaptability. I briefly discuss the implications of these findings for cognition, social niche construction and the evolution of new levels of organization in biological systems.     

Espaces de représentation et psychopathologie

A subjective world can be conceptualized as a “representational space” — that is, as a universe displayed from memory, in which the subject “is sailing”. Recent cognitive theory provides some conceptual tools for describing such a space in a relevant way for clinical purposes. The construction of a representational space is based on mental representations: (a) analogical representations, which display a content in working memory; (b) symbolic representations, which code and link up analogical representations to form a represented world. The dynamics of representations and affects is ruled by a principle of unification of representational space. The topology of a representational space depends on objective and subjective constraints which cause some “folds” and limit the display of such a space. The interaction between an event and a subjective memory can be analyzed within this framework, so that the concepts of trauma and defence processes can be defined. Clinical syndromes are defensive configurations that tend to close the representational space.     

Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition

A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary collection. The classical account supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to--compatible with--their structure. Classical compositionality, however, does not explain why these two components must be compatible; they are only compatible by the ad hoc assumption (convention) of employing the same mode of (concatenative) compositionality (e.g., prefix/postfix, where a relation symbol is always prepended/appended to the symbols for the related entities). Architectures employing mixed modes do not support systematicity. Recently, we proposed an alternative explanation without ad hoc assumptions, using category theory. Here, we extend our explanation to domains that are quasi-systematic (e.g., aspects of most languages), where the domain includes some but not all possible combinations of constituents. The central category-theoretic construct is an adjunction involving pullbacks, where the primary focus is on the relationship between processes modelled as functors, rather than the representations. A functor is a structure-preserving map (or construction, for our purposes). An adjunction guarantees that the only pairings of functors are the systematic ones. Thus, (quasi-)systematicity is a necessary consequence of a categorial cognitive architecture whose basic processes are functors that participate in adjunctions.     

Multimodal phylogeny for taxonomy: integrating information from nucleotide and amino acid sequences

The crucial role played by the analysis of microbial diversity in biotechnology-based innovations has increased the interest in the microbial taxonomy research area. Phylogenetic sequence analyses have contributed significantly to the advances in this field, also in the view of the large amount of sequence data collected in recent years. Phylogenetic analyses could be realized on the basis of protein-encoding nucleotide sequences or encoded amino acid molecules: these two mechanisms present different peculiarities, still starting from two alternative representations of the same information. This complementarity could be exploited to achieve a multimodal phylogenetic scheme that is able to integrate gene and protein information in order to realize a single final tree. This aspect has been poorly addressed in the literature. In this paper, we propose to integrate the two phylogenetic analyses using basic schemes derived from the multimodality fusion theory (or multiclassifier systems theory), a well-founded and rigorous branch for which its powerfulness has already been demonstrated in other pattern recognition contexts. The proposed approach could be applied to distance matrix-based phylogenetic techniques (like neighbor joining), resulting in a smart and fast method. The proposed methodology has been tested in a real case involving sequences of some species of lactic acid bacteria. With this dataset, both nucleotide sequence- and amino acid sequence-based phylogenetic analyses present some drawbacks, which are overcome with the multimodal analysis.     

A support vector machine approach to the identification of phosphorylation sites

We describe a bioinformatics tool that can be used to predict the position of phosphorylation sites in proteins based only on sequence information. The method uses the support vector machine (SVM) statistical learning theory. The statistical models for phosphorylation by various types of kinases are built using a dataset of short (9-amino acid long) sequence fragments. The sequence segments are dissected around post-translationally modified sites of proteins that are on the current release of the Swiss-Prot database, and that were experimentally confirmed to be phosphorylated by any kinase. We represent them as vectors in a multidimensional abstract space of short sequence fragments. The prediction method is as follows. First, a given query protein sequence is dissected into overlapping short segments. All the fragments are then projected into the multidimensional space of sequence fragments via a collection of different representations. Those points are classified with pre-built statistical models (the SVM method with linear, polynomial and radial kernel functions) either as phosphorylated or inactive ones. The resulting list of plausible sites for phosphorylation by various types of kinases in the query protein is returned to the user. The efficiency of the method for each type of phosphorylation is estimated using leave-one-out tests and presented here. The sensitivities of the models can reach over 70%, depending on the type of kinase. The additional information from profile representations of short sequence fragments helps in gaining a higher degree of accuracy in some phosphorylation types. The further development of an automatic phosphorylation site annotation predictor based on our algorithm should yield a significant improvement when using statistical algorithms in order to quantify the results.     

A graph-based reflexive artificial chemistry

The conceptual divide between formal systems of computation and abstract models of chemistry is considered. As an attempt to concretely bridge this divide, a formalism is proposed that describes a constructive artificial chemistry on a space of directed graph structures. The idea for the formalism originates in computer science theory, with the traditional abstraction of a physical machine, the finite-state machine (FSM). In the FSM, the machine (state-transition graph) and input string (series of binary digits) are fundamentally distinct objects, separated by nature of the underlying formalism. This distinction is dissolved in the proposed system, resulting in a construction process that is reflexive: graphs interact with their own topological structure to generate a product. It is argued that this property of reflexivity is a key element missing from earlier model chemistries. Examples demonstrate the continuous emergence complex self-similar topologies, novel reaction pathways, and seemingly open-ended diversity. Implications of these findings are discussed.