Application of the results

The examples shown in the dissertation clearly highlight the main characteristics of the stochastic selection. We can claim that they are generally valid. Because of this, the meth-ods and implementations are also valid, and the cellular, localized selection can be used as a substitution of the global method. Considering this, my method as an example can also help to show, how a non-topographic problem can be transformed into a topographic one, and how it can be solved by topographic algorithms on topographic architectures.

Not only the general method on the virtual machine, but also the implementation on the Xenonv3 architecture can help to solve optimization problems. This way the com-monly used (mostly in image processing tasks) CNN chips can also applied in tasks where parameter optimizations and/or state estimations are required. These topographic algo-rithm are ideal, where complex problems have to be solve with strict time limits and low power consumption. The extremely good low power consumption of theXenon_v3 (under 20mW) could be ideal in mobile application such as robotics, mobile-communication or navigation.

100

Also not only the implementation can be applied and useful, but the similar implemen-tation of these (or related) algorithms on other devices and architectures can be crucial e.g: implementation on FPGA-s or GPU-s.

The architectures described in the second part of the dissertation could be useful in designing computers with extremely low power consumption. These simple computational models can be extended in cases where the storing essence of the information is the spin and not the charge. The cores of these architectures are feasible even when only a few atoms are used, this makes them as a true alternative for Beyond Moore’s low computation. The analytic solution of the differential equation system could help the investigation of spin-torque oscillators. Apart from the theoretical results I have shown through two simple examples how an STO array can be used for simple computational problems. Although these networks are not feasible in these days because of the physical constraints, but I hope in the future I can measure the dynamics of STOs in practice and the development of STO devices it could speed up the process since only the equation system has to be solved instead of simulating a complex differential equation system.

In the dissertation I wanted to show, how obtaining the topographic constraints can modify the algorithm development, and what we can do to avoid these limitations, also how this limits can help to solve non-topographic problems. I hope in this way topographic thinking, and considering two dimensional constraints and the precedence of locality can help in the solution of new problem classes and in their mapping on many-core architec-tures as well.

101

Chapter 9

Conclusion

In this dissertation I have shown through general models, how local selection can be ap-plied instead of the global selection mechanism. I have shown, that the local selection is not a completely different or specialized algorithm, but a more generalized version of the global process, where by setting the neighborhood radius optimally the exploitation/exploration ratio of stochastic optimization can be set. In case of the case studies I have examined how the neighborhood radius can tune the speed of information propagation. This can result more diverse cohorts, helping us to avoid local extrema, which is one of the most serious problems in stochastic optimization.

The dissertation also shows how these general models can be applied in practice. In case of the practical problems I have considered how this method can be implemented on existing CNN chips and also I have shown a sample implementation on the Xenon_v3 architecture.

I examined the idea of local selection mechanisms in two practical algorithms: in the genetic algorithm and also with the particle filter algorithm. In both cases I have pointed out how easily this method is parallelizable and scalable. This means that in case of difficult problems we do not have to alter our method our increase the processing speed, the addition of extra computing cores – what can be done easily– is enough.

Later on it would be useful to examine other problems, problem classes which can be mapped ideally on topographic many-core architectures. I would also like to use this method in practice, there are promising problems from the field of tracking, navigation and speech processing. Mobile applications with strict time constraint could be the best environment, because the low power consumption and high computational power of the CNN chip could result optimal implementation of such algorithms. It would be also useful to enhance the current implementation in those parts which are not ideal because of the design of the Xenon_v3 architecture. Implementation on other architectures like FPGA, GPU implementations could be also useful in case of complex problems from the field of financial mathematics.

In the second part of this thesis I have also investigated special topographic architec-102

tures. I briefly describe, how topographic architectures can be applied beyond Moore’s law.

I have shown a simple example how spin (the magnetization vector of a nano-device) can be used instead of the charge as a unit to store information dynamically. I have shown who the steady-state frequency and plane of oscillation of an STO can be calculated analyti-cally from the differential equation system. I have done an approximation about a general coupled network of STOs, with this giving a mapping between the frequency-encoded input and the phaseshift-encoded output of an STO array.

I have examined how the phase shift between two oscillators depend on the input current difference and the coupling weight. these equations can be used to design simple coupling of oscillatory network.

I have shown through two examples how these methods can be used in practice. I have calculated and simulated two different networks for topographic, image processing tasks:

one for simple edge detection and one for a complex spatial change detection.

In this dissertation I wanted two show, how we have to consider topographic constraints during algorithm development. What we can do to avoid these constraints, and also how they can help us to design topographic algorithms to solve even non-topographic problems.

In the following year topographic thinking and topographic algorithm will be extremely important, because on the nanoscale only cellular, local couplings are feasible in an efficient way.

103

Chapter 10