Related papers: Product Representations and the Quantization of Co…
We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz…
We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We present a computational framework for analyzing and quantifying system flexibility. Our framework incorporates new features that include: general uncertainty characterizations that are constructed using composition of sets, procedures…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of…
The construction and operation of large scale quantum information devices presents a grand challenge. A major issue is the effective control of coherent evolution, which requires accurate knowledge of the system dynamics that may vary from…
Qualitative modelling is a technique integrating the fields of theoretical computer science, artificial intelligence and the physical and biological sciences. The aim is to be able to model the behaviour of systems without estimating…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take…
Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…
Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
The method of complex Langevin simulations is a tool that can be used to tackle the complex-action problem encountered, for instance, in finite-density lattice quantum chromodynamics or real-time lattice field theories. The method is based…
With the tracking condition, the stability of quintessence solutions are examined. It is found that there is only one physically relevant fixed point for the system generically. Two specific examples of quintessence potentials are worked…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…