相关论文: On Ultrametric Algorithmic Information

Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…

The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without…

TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…

Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…

The possibility of calculation of the conditional and unconditional complexity of description of information objects in the algorithmic theory of information is connected with the limitations for the set of the used languages of programming…

Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…

We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…

We present a method for estimating the complexity of an image based on Bennett's concept of logical depth. Bennett identified logical depth as the appropriate measure of organized complexity, and hence as being better suited to the…

Object parsing -- the task of decomposing an object into its semantic parts -- has traditionally been formulated as a category-level segmentation problem. Consequently, when there are multiple objects in an image, current methods cannot…

Feature selection for a given model can be transformed into an optimization task. The essential idea behind it is to find the most suitable subset of features according to some criterion. Nature-inspired optimization can mitigate this…

Machine-learning algorithms offer immense possibilities in the development of several cognitive applications. In fact, large scale machine-learning classifiers now represent the state-of-the-art in a wide range of object…

Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…

Learning with complete or partial supervision is powerful but relies on ever-growing human annotation efforts. As a way to mitigate this serious problem, as well as to serve specific applications, unsupervised learning has emerged as an…

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…

In the theoretical modelling of a physical system a crucial step consists in the identification of those degrees of freedom that enable a synthetic, yet informative representation of it. While in some cases this selection can be carried out…

At this point in time there is a need for a new representation of different information, to identify and organize descending its characteristics. Today, science is a powerful tool for the description of reality - the numbers. Why the most…

We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…

As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…

Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers…