Related papers: Complexity, parallel computation and statistical p…
Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however,…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Classic economic science is reaching the limits of its explanatory powers. Complexity science uses an increasingly larger set of different methods to analyze physical, biological, cultural, social, and economic factors, providing a broader…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…