相关论文: Kolmogorov Complexity, String Information, Pansper…

First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…

The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…

Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements in the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical…

Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…

Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the…

As we learn more about the frequency and size distribution of exoplanets, we are discovering that terrestrial planets are exceedingly common. The distribution of orbital periods in turn results in many of these planets being the occupants…

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of…

The (prefix-free) Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This gives rise to some `standard' lowness notions for reals: A is K-trivial if its initial segments have the lowest…

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…

The idea to find the "maximal number that can be named" can be traced back to Archimedes (see his Psammit). From the viewpoint of computation theory the natural question is "which number can be described by at most n bits"? This question…

Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$ denotes mutual…

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…

Cosmic strings provide a radically different paradigm for the formation of structure to the prevailing inflationary one. They afford some extra technical complications: for example, the calculation of the power spectrum of matter and…

The Fermi paradox highlights the dichotomy between the lack of physical contact with other civilizations and the expectation that technological civilizations are assumed likely to evolve in many locations in the Milky Way galaxy, given the…

Spurious correlations are common in time-series analysis because simple, low-complexity patterns can produce high Pearson correlations even between unrelated series. We argue that Kolmogorov complexity, interpreted as resistance to…

In this paper we consider the extent to which a lack of observations from SETI may be used to quantify the Fermi paradox. Building on previous research, we construct a geometrical model to compute the probability of at least one detection…

Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we…

We study practical approximations to Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the interpreter optimality for this language as the reference machine for the Coding Theorem…

Currently, string theory represents the only advanced approach to a unification of all interactions, including gravity. In spite of the more than thirty years of its existence it did not make any empirically testable predictions. And it is…

In direct response to requests for a logico-mathematical test of the conjecture, we formally disprove a recently conjectured artificial intelligence trade-off between epistemic certainty and scope in its published universal hyperbolic…