Question

Discuss a minimum of two complex systems that you have encountered in your profession. Define why you think that they were complex.

Answer 1

Complex systems

A system is considered to be complex if it imparts characteristic phenomenology which has multiple outcomes, providing with the capacity to choose, to explore and to adapt.

The emerging characteristics of the system as a whole cannot be deduced back to the properties of its constituent parts. The properties of the system reflect the primeval role of instructions between the parts of the system. These are manifested by the generation of self-organized states of a hierarchical and modular type, where order and coherence are ensured by a bottom up approach rather than the typical top up design and control.

The coexistence of the similarities and differences raises the issue of future evolution of the complex system on the basis of the records available. Typical examples are the reliable weather forecast for few days as well as extremely devasting geological and environmental phenomena like earthquakes, floods etc.

In addition to the macroscopic level manifestations, complex systems are also persistent at microscopic level. Systems with built-in disorder like glassy materials give way to a rich variety of evolutionary processes driven by microscopic level interactions. A variety of systems operating on the nonmetric scale, reveal complex behaviors like energy transduction and anomalous transport, arising from the interplay between microscopically generated spontaneous fluctuations and systematic environmental constraints. The very origin of irreversibility is related to the intrinsic complexity of the dynamics of the atoms constituting a macroscopic system under the effect of their mutual interactions.

Boundary value problem

In general a boundary value is a way to predict solution to specific case using the physically available conditions. Mathematically, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.

A boundary value problem is a system of differential equations with solutions and derivative values specified at more than one point mostly two points.

A two-point boundary value problem (BVP) of total order n on a finite interval [a,b] may be written as an explicit first order system of ordinary differential equations (ODEs) with boundary values evaluated at two points as

y(x)), x∈(a,b), g(y(a),y(b))=0

where, y,,g∈Rn and the system is called explicit because the derivative y′ appears explicitly. And the n boundary conditions defined must be independent, i.e, they cannot be expressed in terms of each other (physically change in one should not effect the other). Furthermore, If g is linear, the boundary conditions must also be linearly independent. In general, the boundary value problems are not there directly but instead are present as a combination of equations equations defineing various order of derivatives of all the n variables.

Artificial Neural Network

An Artificial Neural Network is an information processing model that is inspired by the way biological nervous systems, such as the brain, process information. They are loosely modeled after the neuronal structure of the mamalian cerebral cortex but on much smaller scales. In simpler terms it is a simple mathematical model of the brain which is used to process nonlinear relationships between inputs and outputs in parallel like a human brain does every second.

Artificial Neural Networks are used for a variety of tasks, a popular use is for classification. You can collect datasets of images for example of different breeds of dogs and then train a neural network on the images, then if you supply a new image of a dog it will give a statistical score on how closely the new image matches the model and then will output what breed of dog the image is. Neural Networks are also used in Self Driving cars, Character Recognition, Image Compression, Stock Market Prediction, and lots of other interesting applications.