Related papers: State Complexity Approximation
In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…
The combinatorial explosion that plagues planning and reinforcement learning (RL) algorithms can be moderated using state abstraction. Prohibitively large task representations can be condensed such that essential information is preserved,…
The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
This paper constructs a finite state abstraction of a possibly continuous-time and infinite state model in two steps. First, a finite external signal space is added, generating a so called $\Phi$-dynamical system. Secondly, the strongest…
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…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
This paper defines a complexity between states in quantum field theory by introducing a Finsler structure based on ladder operators (the generalization of creation and annihilation operators). Two simple models are shown as examples to…
Analysis of the process of accumulation of the results of measurements shows that the success of this process substantially depends on the possibility of coordination of actions of two participants of the process - preparator who prepares…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…
In increasingly digitalized and metered distribution networks, state estimation is generally recognized as a key enabler of advanced network management functionalities. However, despite decades of research, the real-life adoption of state…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…