Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.Comment: 52 pages, 12 figure

Models of adaptation and behavioural patterns in complex systems in crisis

“Change is the only constant in life,” said the Greek philosopher Heraclitus. In order to function and develop under uncertainty, our complex society, as well as its elementary agents, must exhibit an appropriate adaptation. Hence, it is imperative to understand how adaptation takes place in complex systems. This understanding should include a theory of adaptation that would enable us to model and predict its outcomes using the language of mathematics.  In this work, we provide an attempt to present such a theory. A review of major directions is provided in Chapter 1 of the thesis. Chapter 2 provides a hierarchy of models of adaptation. These models are based on Hans Selye’s and Bernard Goldstone’s axioms of adaptation: an organism (or a group of individuals) is represented as a system which optimizes distribution of the internal adaptation resource (“Adaptation Energy”) for neutralization of an aggressive factor. A general analysis of these models is presented in the same chapter. In this Chapter 3, we provide an example of the application of these principles and models to the problem of understanding complex spontaneous activity of neural cultures. We demonstrate that the rich dynamics of activity patterns in neural cultures can be described by very simple equations modelling “adaptation” in such systems. In Chapter 4 we present another take on adaptation through correlation graphs measuring correlations between agents in complex systems. We discuss a potential of using these graphs for early warning of crisis for various systems. We demonstrate this on examples of the thirty largest companies from the Financial Times Stock Exchange 100 Index during the two major crises – the global financial crisis of 2008 and the first wave of the COVID-19 pandemic in March 2020. Chapter 5 concludes the thesis and discusses directions for future work.</p

Invariant template matching in systems with spatiotemporal coding: a matter of instability. Neural Netw

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition

General Laws of Adaptation to Environmental Factors: From Ecological Stress to Financial Crisis

We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the correlation increases too. If the stress continues to increase then the second threshold appears: the correlation achieves maximal value, and start to decrease, but the variance continue to increase. In many applications this second threshold is a signal of approaching of fatal outcome.
This effect is supported by many experiments and observation of groups of humans, mice, trees, grassy plants, and on financial time series. A general approach to explanation of the effect through dynamics of adaptation is developed. H. Selye introduced “adaptation energy" for explanation of adaptation phenomena. We formalize this approach in factors – resource models and develop hierarchy of models of adaptation. Different organization of interaction between factors (Liebig's versus synergistic systems) lead to different adaptation dynamics. This gives an explanation to qualitatively different dynamics of correlation under different types of load and to some deviation from the typical reaction to stress.
In addition to the “quasistatic" optimization factor – resource models, dynamical models of adaptation are developed, and a simple model (three variables) for adaptation to one factor load is formulated explicitly

Invariant template matching in systems with spatiotemporal coding: A matter of instability

We consider the design principles of algorithms that match templates to images subject to spatiotemporal encoding. Both templates and images are encoded as temporal sequences of samplings from spatial patterns. Matching is required to be tolerant to various combinations of image perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, and, as special cases, invariant transformation groups such as translation and rotations, as well as unmodeled uncertainties (noise). For a system to deal with such perturbations in an efficient way, they are to be handled through a minimal number of channels and by simple adaptation mechanisms. These normative requirements can be met within the mathematical framework of weakly attracting sets. We discuss explicit implementation of this principle in neural systems and show that it naturally explains a range of phenomena in biological vision, such as mental rotation, visual search, and the presence of multiple time scales in adaptation. We illustrate our results with an application to a realistic pattern recognition problem