Mathematical model for an evolutive and hierarchical living system, based on the theory of categories

The notion of an evolutive hierarchical system proposed here retains the following characteristics of some natural systems, like living organisms: they have an internal organization consisting of more or less complex components with interrelations; they maintain their organization in time although their components are changing; they may be studied at several complexity levels (e.g., molecular, cellular, ...). The idea is to model the state of the system at a given instant by a category, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (its own organization). The emergence of new properties for a complex object is measured, and a development process is described.     

Applications of a new subspace clustering algorithm (COSA) in medical systems biology

A novel clustering approach named Clustering Objects on Subsets of Attributes (COSA) has been proposed (Friedman and Meulman, (2004). Clustering objects on subsets of attributes. J. R. Statist. Soc. B 66, 1–25.) for unsupervised analysis of complex data sets. We demonstrate its usefulness in medical systems biology studies. Examples of metabolomics analyses are described as well as the unsupervised clustering based on the study of disease pathology and intervention effects in rats and humans. In comparison to principal components analysis and hierarchical clustering based on Euclidean distance, COSA shows an enhanced capability to trace partial similarities in groups of objects enabling a new discovery approach in systems biology as well as offering a unique approach to reveal common denominators of complex multi-factorial diseases in animal and human studies. Doris Damian, Matej Orešič, and Elwin Verheij contributed equally to this work.     

Biocomplexity: adaptive behavior in complex stochastic dynamical systems

Existing methods of complexity research are capable of describing certain specifics of bio systems over a given narrow range of parameters but often they cannot account for the initial emergence of complex biological systems, their evolution, state changes and sometimes-abrupt state transitions. Chaos tools have the potential of reaching to the essential driving mechanisms that organize matter into living substances. Our basic thesis is that while established chaos tools are useful in describing complexity in physical systems, they lack the power of grasping the essence of the complexity of life. This thesis illustrates sensory perception of vertebrates and the operation of the vertebrate brain. The study of complexity, at the level of biological systems, cannot be completed by the analytical tools, which have been developed for non-living systems. We propose a new approach to chaos research that has the potential of characterizing biological complexity. Our study is biologically motivated and solidly based in the biodynamics of higher brain function. Our biocomplexity model has the following features, (1) it is high-dimensional, but the dimensionality is not rigid, rather it changes dynamically; (2) it is not autonomous and continuously interacts and communicates with individual environments that are selected by the model from the infinitely complex world; (3) as a result, it is adaptive and modifies its internal organization in response to environmental factors by changing them to meet its own goals; (4) it is a distributed object that evolves both in space and time towards goals that is continually re-shaping in the light of cumulative experience stored in memory; (5) it is driven and stabilized by noise of internal origin through self-organizing dynamics. The resulting theory of stochastic dynamical systems is a mathematical field at the interface of dynamical system theory and stochastic differential equations. This paper outlines several possible avenues to analyze these systems. Of special interest are input-induced and noise-generated, or spontaneous state-transitions and related stability issues.     

Homochirality and the Need for Energy

The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object—that can be intrinsically asymmetric—and a collection of objects—whose racemic state is the more stable one—must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.     

Interactions among biological systems: An analysis of asymptotic stability

An analysis of the interactions among asymptotically stable dynamical systems is formulated by making use of the dynamical system theory. Some results coming from previous mathematical analyses have been slightly modified to take into account some typical biological constraints as the boundedness properties of the solutions. In particular it has been shown that when the “coupling” among the subsystems is “loose” enough (in a sense that has to be made mathematically precise) the asymptotic behaviour of a complex system is the same of that of its individual components. The mathematical theory has been used to analyze two systems of biological significance: the coupling among chemical reactions and the stability properties of a 4-dimensional system describing the kinetics of a chemical transmitter.     

Other developments regarding the concept of energy in biological systems

In order to recognize the realizability of inputs with different physical natures through a component, Yoneda's Lemma is applied. The major utility of this Lemma is when the components produce only energy. From this, it is assumed that a new material input must exist which was not recognized in the original developments in biological systems representation. Moreover, simple transfers of energy, between objects, components, and among both objects and components are developed under the generic name; energetical evolution. Thus, energetical evolution appears as anew element in the abstract representation of biological systems. These new concepts are incorporated into a new abstract diagram and a newM _β category. This paper was made possible by a Fellowship from the Consejo Nacional de Investigaciones Científicas y Técnicas of the República Argentina.     

A systems approach to animal communication

Why animal communication displays are so complex and how they have evolved are active foci of research with a long and rich history. Progress towards an evolutionary analysis of signal complexity, however, has been constrained by a lack of hypotheses to explain similarities and/or differences in signalling systems across taxa. To address this, we advocate incorporating a systems approach into studies of animal communication—an approach that includes comprehensive experimental designs and data collection in combination with the implementation of systems concepts and tools. A systems approach evaluates overall display architecture, including how components interact to alter function, and how function varies in different states of the system. We provide a brief overview of the current state of the field, including a focus on select studies that highlight the dynamic nature of animal signalling. We then introduce core concepts from systems biology (redundancy, degeneracy, pluripotentiality, and modularity) and discuss their relationships with system properties (e.g. robustness, flexibility, evolvability). We translate systems concepts into an animal communication framework and accentuate their utility through a case study. Finally, we demonstrate how consideration of the system-level organization of animal communication poses new practical research questions that will aid our understanding of how and why animal displays are so complex.     

An Object-Oriented Modeling and Simulation Environment for Reactive Systems Development

An environment to support the modeling, analysis, simulation, and development of state transition models, SMOOCHES (State Machines for Object-Oriented Concurrent Hierarchical Engineering Specifications), is presented. SMOOCHES allows the hierarchical construction, analysis, and simulation of state transition models in an object-oriented distributed environment. Statecharts (see Harel 1987b), a powerful mechanism for state transition specification, are fundamental to the development of SMOOCHES. To assist in the specification of hierarchical state transition models for distributed and reactive systems, statecharts are extended by introducing the concept of exit-safe states. SMOOCHES allows the specification of objects in the system with hierarchical state transition models and the derivation of new classes of objects through inheritance. A graphical monitoring system has been developed to represent and simulate the object state life cycles and monitor event generations. The example presented illustrates the modeling and simulation of different state life cycles of an assembly robot.     

The Hierarchical Structure of Ecosystems: Connections to Evolution

Ecologic systems, which are involved mainly in the processing of energy and materials, are actually nested one inside another—they are simultaneously parts and wholes. This fundamental hierarchical organization is easy to detect in nature but has been undervalued by ecologists as a source of new insights about the structure and development of ecosystems and as a means of understanding the crucial connections between ecologic processes and large-scale evolutionary patterns. These ecologic systems include individual organisms bundled into local populations, populations as functional components of local communities or ecosystems, local systems making up the working parts of larger regional ecosystems, and so on, right up to the entire biosphere. Systems at any level of organization can be described and interpreted based on aspects of scale (size, duration, and “membership” in more inclusive entities), integration (all the vital connections both at a particular focal level and across levels of hierarchical organization), spatiotemporal continuity (the “life history” of each system), and boundaries (either membranes, skins, or some other kind of border criterion). Considering hierarchical organization as a general feature of ecologic systems could reinvigorate theoretical ecology, provide a realistic scaling framework for paleoecologic studies, and – most importantly – forge new and productive connections between ecology and evolutionary theory.     

Autogenesis: the evolution of replicative systems

Questions concerning the nature and origin of living systems and the hierarchy of their evolutionary processes are considered, and several problems which arise in connection with formerly developed theories--the autopoiesis of Maturana & Varela, the POL theory of Haukioja and the earlier developed evolutionary theory of Csányi--are discussed. The organization of living systems, the use of informational terms and the question how reproduction can enter into their characterization, problems of autonomy and identity are included in the list. It is suggested that replication--a copying process achieved by a special network of interrelatedness of components and component-producing processes that produces the same network as that which produced them--characterizes the living organization. The information "used" in this copying process, whether it is stored by special means or distributed in the whole system, is called replicative information. A theoretical model is introduced for the spontaneous emergence of replicative organization, called autogenesis. Autogenesis commences in a system by an organized "small" subsystem, referred to as AutoGenetic System Precursor (AGSP), which conveys replicative information to the system. During autogenesis, replicative information increases in system and compartment(s) form. A compartment is the co-replicating totality of components. The end state of autogenesis is an invariantly self-replicating organization which is unable to undergo further intrinsic organizational changes. It is suggested that replicative unities--such as living organisms--evolve via autogenesis. Levels of evolution emerge as a consequence of the relative autonomy of the autogenetic unities. On the next level they can be considered as components endowed with functions and a new autogenetic process can commence. Thus evolution proceeds towards its end state through the parallel autogenesis of the various levels. In terms of applications, ontogenesis is dealt with in detail as an autogenetic process as is the autogenesis of the biosphere and the global system.     

Simulation modelling of ecological hierarchies in constructive dynamical systems

Organized complexity is a characteristic feature of ecological systems with heterogeneous components interacting at several spatio-temporal scales. The hierarchy theory is a powerful epistemological framework to describe such systems by decomposing them vertically into levels and horizontally into holons. It was at first developed in a temporal and functional perspective and then, in the context of landscape ecology, extended to a spatial and structural approach. So far, most ecological applications of this theory were restricted to observational purposes, using multi-scale analysis to describe hierarchies. In spite of an increasing attention to dynamics of hierarchically structured ecological systems, current simulation models are still very limited in their representation of self-organization in complex adaptive systems. An ontological conceptualization of the hierarchy theory is outlined, focusing on key concepts, such as levels of organization and the compound and component faces of the holons. Various existing formalisms are currently used in simulation modelling, such as system dynamics, discrete event and agent based paradigms. Their ability to express the hierarchical organization of dynamical ecological systems is discussed. It turns out that a multi-modelling approach linking all these formalisms and oriented toward the specification of a constructive dynamical system would be able to express the dynamical structure of the hierarchy (creation, destruction and change of holons) and the functional and structural links between levels of organization.     

Parasitic systems and the structure of parasite populations

 The analysis of population systems is carried out on the basis of the spatial and functional classification of populations developed by V.N. Beklemishev. The population system is a functional part of a particular community. Steady interrelationships between population systems of different species within the community (referred to as ”community links”) appear to be a prerequisite for the formation of a complex of population systems. A prominent example of this is the parasitic system. The parasitic system is the population system of a parasite with all the connected populations of its hosts. The complexity of a parasitic system depends on: (1) peculiarities of the life cycle of the parasite, since its population system is the organizing component of the parasitic system and (2) subdivision of the environment for the parasites. The first trait is discussed from the standpoint of the phase structure of populations, which is clearly seen in parasites. The second one comprises the organization of the parasites’ environment according to the scale of variability (interspecies, interpopulation or intrapopulation) of hosts. These make it possible to recognize spatial and functional parts in the framework of the parasitic system. A critical review of the terminology is presented together with a list of the pertaining vocabulary. Received: 15 January 1998 / Accepted: 15 October 1998     

A hierarchical probabilistic model for rapid object categorization in natural scenes

Humans can categorize objects in complex natural scenes within 100-150 ms. This amazing ability of rapid categorization has motivated many computational models. Most of these models require extensive training to obtain a decision boundary in a very high dimensional (e.g., ～6,000 in a leading model) feature space and often categorize objects in natural scenes by categorizing the context that co-occurs with objects when objects do not occupy large portions of the scenes. It is thus unclear how humans achieve rapid scene categorization.To address this issue, we developed a hierarchical probabilistic model for rapid object categorization in natural scenes. In this model, a natural object category is represented by a coarse hierarchical probability distribution (PD), which includes PDs of object geometry and spatial configuration of object parts. Object parts are encoded by PDs of a set of natural object structures, each of which is a concatenation of local object features. Rapid categorization is performed as statistical inference. Since the model uses a very small number (～100) of structures for even complex object categories such as animals and cars, it requires little training and is robust in the presence of large variations within object categories and in their occurrences in natural scenes. Remarkably, we found that the model categorized animals in natural scenes and cars in street scenes with a near human-level performance. We also found that the model located animals and cars in natural scenes, thus overcoming a flaw in many other models which is to categorize objects in natural context by categorizing contextual features. These results suggest that coarse PDs of object categories based on natural object structures and statistical operations on these PDs may underlie the human ability to rapidly categorize scenes.     

Non-visual environmental imaging and object detection through active electrolocation in weakly electric fish

Weakly electric fish orient at night by employing active electrolocation. South American and African species emit electric signals and perceive the consequences of these emissions with epidermal electroreceptors. Objects are detected by analyzing the electric images which they project onto the animal’s electroreceptive skin surface. Electric images depend on size, distance, shape, and material of objects and on the morphology of the electric organ and the fish’s body. It is proposed that the mormyrid Gnathonemus petersii possesses two electroreceptive “foveae” at its Schnauzenorgan and its nasal region, both of which resemble the visual fovea in the retina of many animals in design, function, and behavioral use. Behavioral experiments have shown that G. petersii can determine the resistive and capacitive components of an object’s complex impedance in order to identify prey items during foraging. In addition, fish can measure the distance and three-dimensional shape of objects. In order to determine object properties during active electrolocation, the fish have to determine at least four parameters of the local signal within an object’s electric image: peak amplitude, maximal slope, image width, and waveform distortions. A crucial parameter is the object distance, which is essential for unambiguous evaluation of object properties.     

The complex structure of hunter-gatherer social networks

In nature, many different types of complex system form hierarchical, self-similar or fractal-like structures that have evolved to maximize internal efficiency. In this paper, we ask whether hunter-gatherer societies show similar structural properties. We use fractal network theory to analyse the statistical structure of 1189 social groups in 339 hunter-gatherer societies from a published compilation of ethnographies. We show that population structure is indeed self-similar or fractal-like with the number of individuals or groups belonging to each successively higher level of organization exhibiting a constant ratio close to 4. Further, despite the wide ecological, cultural and historical diversity of hunter-gatherer societies, this remarkable self-similarity holds both within and across cultures and continents. We show that the branching ratio is related to density-dependent reproduction in complex environments and hypothesize that the general pattern of hierarchical organization reflects the self-similar properties of the networks and the underlying cohesive and disruptive forces that govern the flow of material resources, genes and non-genetic information within and between social groups. Our results offer insight into the energetics of human sociality and suggest that human social networks self-organize in response to similar optimization principles found behind the formation of many complex systems in nature.     

Levels of organization of living systems: Cooperons

All creatures living on Earth are traditionally discussed in the context of structuralmorphological approach, in frame of which there are considered various systems (for instance, organisms and ecosystems) that have different sizes and organization and use different resources for their existence. These characteristics are sometimes added by some particular functional and ecological characteristics, but usually with respect to the structural ones. We believe that such traditional approach, although illustrating, but distracts from the circumstance that any living systems is to be considered an integrated structural-functional complex, the maintenance of existence of this system being impossible without the processes occurring constantly in it and aimed at preserving this complex. This leads us to the concept of cooperons—the self-preserved dynamic structures existing only as a result of various specifically organized cooperative processes (their intensities can vary depending on circumstances). From our point of view, all living systems are cooperons of different hierarchy levels. Some other systems, specifically the symbiotic ones, also are cooperons. In frame of this concept, it is possible to discuss functioning of living systems of different types of organization in a new context closer to physiologists, both for the case of “norm” and for the situation when the cooperative interrelations of parts of the system are impaired (for instance, in systemic diseases).     

The evolution of hormonal signalling systems.

1. A comparative analysis was made of chemosignalling systems responsible for the action of hormones, hormone-like substances, pheromones, etc. in vertebrates--multicellular invertebrates--unicellular eukaryotes. Many common features revealed in structural-functional organization of the above systems give evidence of their evolutionary conservatism. 2. It was shown that some molecular components as well as signal transduction mechanisms similar to those of higher eukaryote hormonal signalling systems are present in such early organisms as bacteria. This allowed a suggestion that the roots of chemosignalling systems are likely to be found in prokaryotes. 3. The evolution of hormonal signalling systems is discussed in terms of current theories of the origin of eukaryotic cell, its organelles and components. A hypothesis is put forward about endosymbiotic genesis of these signal transduction systems in eukaryotes. 4. A possible evolutionary scenario of the formation of hormonocompetent systems is proposed with hormone-sensitive adenylate cyclase complex taken as an example.     

Non-locality in biological systems results from hierarchy

The concept of non-locality is deduced from a new concept for biological systems, the functional interaction. It is shown that a biological system, which is expressed in terms of functional interactions, can be constructed as a hierarchical system, the dynamics of which are represented by a non-local field at each level of organization. The two following constraints: continuous representation of state variables and hierarchy of the system, result in non-locality, i.e., a space property according to which the system depends on mechanisms that are located elsewhere in the space. Concepts and theory are illustrated in the case of the nervous system, where two levels of organization are considered, the level of neurons and the level of synapses. Non-local versus local field operators are discussed, and an interpretation of the field equation terms is proposed. A general formulation of non-local operators for hierarchical systems is given.     

Broca's area and the hierarchical organization of human behavior

The prefrontal cortex subserves executive control, i.e., the organization of action or thought in relation to internal goals. This brain region hosts a system of executive processes extending from premotor to the most anterior prefrontal regions that governs the temporal organization of behavior. Little is known, however, about the prefrontal executive system involved in the hierarchical organization of behavior. Here, we show using magnetic resonance imaging in humans that the posterior portion of the prefrontal cortex, including Broca's area and its homolog in the right hemisphere, contains a system of executive processes that control start and end states and the nesting of functional segments that combine in hierarchically organized action plans. Our results indicate that Broca's area and its right homolog process hierarchically structured behaviors regardless of their temporal organization, suggesting a fundamental segregation between prefrontal executive systems involved in the hierarchical and temporal organization of goal-directed behaviors.