The geometry of decision-making in individuals and collectives

Choosing among spatially distributed options is a central challenge for animals, from deciding among alternative potential food sources or refuges to choosing with whom to associate. Using an integrated theoretical and experimental approach (employing immersive virtual reality), we consider the interplay between movement and vectorial integration during decision-making regarding two, or more, options in space. In computational models of this process, we reveal the occurrence of spontaneous and abrupt “critical” transitions (associated with specific geometrical relationships) whereby organisms spontaneously switch from averaging vectorial information among, to suddenly excluding one among, the remaining options. This bifurcation process repeats until only one option—the one ultimately selected—remains. Thus, we predict that the brain repeatedly breaks multichoice decisions into a series of binary decisions in space–time. Experiments with fruit flies, desert locusts, and larval zebrafish reveal that they exhibit these same bifurcations, demonstrating that across taxa and ecological contexts, there exist fundamental geometric principles that are essential to explain how, and why, animals move the way they do.

Relations and Influences in the Process of Conventionalization of Organic Markets in the Southern Region of Brazil: A Multilevel Perspective Analysis

The organic markets from all around the world are changing fast. An example is the proliferation of standards and the entrance of new actors in the organic market, as the processors. In this paper, organic farmers, agro industries, retailers, consumers, and rural extension agents were consulted through qualitative research methods to better understand these changes and to assess the conventionalization-bifurcation process of organic markets in the Southern Region of Brazil. The relations and influences that exist between these actors were identified and analyzed. The theoretical approach used in this study comes from the Multilevel Perspective. This approach sustains that a novelty, like organic farming, can produce radical or incremental changes in a socio-technical regime, as the dominant agro-food regime, while connections between both are built. We observed that these relations and influences are of three main types: outsourcing and elongation of supply chains; restrictions in the commercialization of the farmer’s production; and the consequences, adjustments and commercial conditions established through contracts with retail chains besides commercialization in alternative networks. Through these findings, we identified a bifurcation in the organic markets where some actors demonstrate practices similar to agrifood dominant regime. In this process, the regime is changing, but so are the alternative networks. It indicates that once again the alternative agriculture is capable of reaffirmation by some ways.

The geometry of decision-making

Choosing among spatially-distributed options is a central challenge for animals, from deciding among alternative potential food sources or refuges, to choosing with whom to associate. Using an integrated theoretical and experimental approach (employing immersive virtual reality), we consider the interplay between movement and vectorial integration during decision-making regarding two, or more, options in space. In computational models of this process we reveal the occurrence of spontaneous and abrupt "critical" transitions (associated with specific geometrical relationships) whereby organisms spontaneously switch from averaging vectorial information among, to suddenly excluding one, among the remaining options. This bifurcation process repeats until only one option---the one ultimately selected---remains. Thus we predict that the brain repeatedly breaks multi-choice decisions into a series of binary decisions in space-time. Experiments with fruit flies, desert locusts, and larval zebrafish reveal that they exhibit these same bifurcations, demonstrating that across taxa and ecological context, we show that there exist fundamental geometric principles that are essential to explain how, and why, animals move the way they do.

Bifurcation and Chaos of Spontaneous Oscillations of Hair Bundles in Auditory Hair Cells

Various spontaneous oscillations and Hopf bifurcation have been observed in hair bundles of auditory hair cells, which play very important roles in the auditory function. In the present paper, the bifurcations and chaos of spontaneous oscillations of hair bundles are investigated in a theoretical model to explain the experimental observations. Firstly, the equivalent negative stiffness and symmetrical characteristic of the model are acquired. The model exhibits coexisting attractors symmetrical to each other or an attractor with symmetry by itself. The attractors include stable focus, stable periodic oscillations, and chaotic oscillations. Secondly, except for the well-known subcritical and supercritical Hopf bifurcations from the stable focus to period-1 limit cycle, the complex bifurcations of spontaneous oscillation patterns such as period-doubling bifurcation cascade to chaos and intermittency between periodic limit cycles and chaos, are observed. Various chaotic oscillations are distinguished. Lastly, a complex bifurcation process containing multiple modes of oscillations and bifurcations mentioned above is obtained, which provides the relationships between different spontaneous oscillation patterns. The results present not only the well-known Hopf bifurcation, but also the various spontaneous oscillations including periodic and chaotic patterns, which are consistent with the recent experimental results. The complex bifurcation process presents a global view of the nonlinear dynamics of complex spontaneous oscillations of hair bundles, which is very important for the auditory function.

Speciation in the face of gene flow within the toothed whale superfamily Delphinoidea

Understanding speciation is a central aspect in Biology. The formation of new species was once thought to be a simple bifurcation process. However, recent advances in genomic resources now provide the opportunity to investigate the role of post-divergence gene flow in the speciation process. The diversification of lineages in the presence of gene flow appears almost paradoxical. However, with enough time and in the presence of incomplete physical and/or ecological barriers to gene flow, speciation can and does occur. Speciation without complete isolation seems especially likely to occur in highly mobile, wide ranging marine species, such as cetaceans, which face limited geographic barriers. The toothed whale superfamily Delphinoidea represents a good example to further explore speciation in the presence of interspecific gene flow. Delphinoidea consists of three families (Delphinidae, Phocoenidae, and Monodontidae) and within all three families, contemporary interspecific hybrids have been reported. Here, we utilise publicly available genomes from nine species, representing all three families, to investigate signs of post-divergence gene flow across their genomes, and to address the speciation processes that led to the diversity seen today within Delphinoidea. We use a multifaceted approach including: (i) phylogenetics, (ii) the distribution of shared derived alleles, and (iii) demography-based. We find that the divergence and evolution of lineages in Delphinoidea did not follow a simple bifurcating pattern, but were much more complex. Our results indicate multiple, long-lasting ancestral gene flow events both within and among families, which continued for millions of years after initial divergence.

Geomorphologic Analysis of Small River Basin within the Framework of Fractal Tree

This paper presents the modified framework of geomorphologic analysis based on the concept of fractal tree. Especially, it is intended to provide hydrologic practitioners with the information on the fractal property of small river basins. To this end, the complete drainage path network is applied to a growth process of a fractal tree for the basin of interest by connecting a channel network to overland drainage pathways. The growth process of a fractal tree would occur only within the limited region possessing channel flow properties in a natural river basin. The exponent of the intra basin type of Hack’s law could show a variable trend in small river basins mainly due to anisotropic property of the catchment planform. The bifurcation process of a drainage path network might be more sensitive to the growth step of the fractal tree than the meandering process of drainage path segment. The fractal dimension from the sinuosity of a channel segment is relatively stable compared to the one from the bifurcation process of the network, so that the geomorphologic features of a small river basin can be characterized by the anisotropic property of catchment planform as well as the bifurcation property of drainage path network with the growth of the fractal tree.

The concept of “chaos measure” in the aspect of social synergetics

We understand chaos as a bifurcation process, the quantitative characteristic of which is reduced to the number of possibilities for the further evolution of the system, which in real time is directly expressed by self-oscillations of chaos and order (bifurcation cascade). The questions are being investigated: the scientific correctness of such formulations as ―chaos measure‖, ―evolution of chaos‖, correlation of the concepts ―measure of chaos‖ and ―magnitude of entropy‖; does the concept of ―measure of chaos‖ correlate with the concept of entropy; how the concepts of ―measure of chaos‖ and ―measure of order‖ relate, and is it possible to ―control‖ chaos? Models that study the evolution of open systems provide a bifurcation picture of development opportunities in at least two directions: complication and simplification, progress and regression, hierarchization of systems and their de-hierarchization, where a quantitative measure of chaos corresponds to the number of possible outcomes. The conclusion drawn from this is that human influence on the vector of the evolutionary process is reduced to a deliberate impact on the structure, which is commonly called the norm: an individual is able to comprehend the "measure of chaos" of the system of which he is an element, correlate it with the "measure of order" of the system and, setting the norm, thereby determine the direction to the superattractor.

Vertical Stratification

This chapter considers national system stratification in high participation systems (HPS) of higher education. As demand for higher education increases, the social value of places within a system becomes more differentiated on a binary basis, between places offering exceptionally high positional value and others offering little value. Three prepositions about stratification are advanced. The first expands on the tendency to system bifurcation in HPS, with a small and elite ‘artisanal’ sector, mostly research-intensive universities, opposed to a larger and undistinguished ‘demand-absorbing’ sector. The second proposition identifies a set of drivers that push the bifurcation process. The third proposition recognizes that bifurcation is always incomplete and focuses on the contradictory dynamics of the ‘middle’ layer of higher education institutions in most HPS. Nationally specific factors that accentuate or limit stratification are identified.