Related papers: From Space and Time to a Deeper Reality as a Possi…
Cyberspace is being more and more tightly linked to the physical space and socioeconomic space to emerge a cyber-physical-socioeconomic space, where humans, machines and physical objects in the natural environment interact with each other,…
The concept of emergence is a powerful concept to explain very complex behaviour by simple underling rules. Existing approaches of producing emergent collective behaviour have many limitations making them unable to account for the…
Human collective intelligence has proved itself as an important factor in a society's ability to accomplish large-scale behavioral feats. As societies have grown in population-size, individuals have seen a decrease in their ability to…
Systems are growing into more complex ones for developing and maintaining. Existing systems which do not have much in common on the first look are connected, due to the technical progress, even if it was never intended that way. It is an…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
We have a lot of relation to the encoding and the Theory of Information, when considering thinking. This is a natural process and, at once, the complex thing we investigate. This always was a challenge - to understand how our mind works,…
Divide and conquer is an established algorithm design paradigm that has proven itself to solve a variety of problems efficiently. However, it is yet to be fully explored in solving problems with a neural network, particularly the problem of…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…
The extent to which the benefits of science can be fully realized depends critically upon the quality of the connection between researchers themselves and between researchers and members of the public. We believe that it is now possible to…
There is nowadays a constant flux of data being generated and collected in all types of real world systems. These data sets are often indexed by time, space or both requiring appropriate approaches to analyze the data. In univariate…
In this paper, I develop a novel version of the multiverse theory of sets called hierarchical pluralism by introducing the notion of `degrees of intentionality' of theories. The presented view is articulated for the purpose of reconciling…
We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…
Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization,…
Cyberspace has gradually replaced the physical reality, its role evolving from a simple enabler of daily live processes to a necessity for modern existence. As a result of this convergence of physical and virtual realities, for all…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…
It is shown that as knowledge is structured, it comes in modules. This provides different " layers of reality ". Each layer of reality has its own distinctive inductive logic which may differ from that of the others. All this is woven…