Related papers: Incomplete information and fractal phase space

We demonstrate that the concept of information offers a more complete description of complementarity than the traditional approach based on observables. We present the first experimental test of information complementarity for two-qubit…

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…

In frameworks of the phenomenological approach we analyze of the phase diagram of mixed compounds. We obtain space groups of symmetry of the real structures as result of phase transition from close-packed degenerate structure. The theory of…

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…

Nature is full of random networks of complex topology describing such apparently disparate systems as biological, economical or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections…

The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…

We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in…

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing…

Model selection and assessment with incomplete data pose challenges in addition to the ones encountered with complete data. There are two main reasons for this. First, many models describe characteristics of the complete data, in spite of…

For convex optimization problems Bregman divergences appear as regret functions. Such regret functions can be defined on any convex set but if a sufficiency condition is added the regret function must be proportional to information…

Most statistical tools used to characterize the complex structures of the interstellar medium can be related to the power spectrum, and therefore to the Fourier amplitudes of the observed fields. To tap into the vast amount of information…

We study the geometrical features of the order parameter's fluctuations near the critical point of mixed-order phase transitions in randomly interdependent spatial networks. In contrast to continuous transitions, where the structure of the…

The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…

We discuss the issue of complementarity between the confining phase and the Higgs phase for gauge theories in which there are no light particles below the scale of confinement or spontaneous symmetry breaking. We show with a number of…

The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces,…

Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of experimental data may not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the…

According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and…

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a…

We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…