相关论文: Integrated Information, a Complexity Measure for o…
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the…
We study a separable design for computing information measures, where the information measure is computed from learned feature representations instead of raw data. Under mild assumptions on the feature representations, we demonstrate that a…
Since its introduction, the partial information decomposition (PID) has emerged as a powerful, information-theoretic technique useful for studying the structure of (potentially higher-order) interactions in complex systems. Despite its…
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
Integrated Computational Materials Engineering (ICME) calls for the integration of computational tools into the materials and parts development cycle, while the Materials Genome Initiative (MGI) calls for the acceleration of the materials…
We study a family of models for an $N_1 \times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…
One of the most complex tasks of decision making and planning is to gather information. This task becomes even more complex when the state is high-dimensional and its belief cannot be expressed with a parametric distribution. Although the…
Size uniformity is one of the main criteria of superpixel methods. But size uniformity rarely conforms to the varying content of an image. The chosen size of the superpixels therefore represents a compromise - how to obtain the fewest…
Categorization is an important topic both for biological and artificial neural networks. Here, we take an information theoretic approach to assess the efficiency of the representations induced by category learning. We show that one can…
We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass…
We demonstrate how the key notions of Tononi et al.'s Integrated Information Theory (IIT) can be studied within the simple graphical language of process theories, i.e. symmetric monoidal categories. This allows IIT to be generalised to a…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
The property of isoscaling in nuclear fragmentation is studied using a simple bond percolation model with ``isospin'' added as an extra degree of freedom. It is shown analytically, first, that isoscaling is expected to exist in such a…