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Hector Zenil

Publications and source records attributed to Hector Zenil.

At least 91 records · Page 5Linked to original sources

Evaluating Network Inference Methods in Terms of Their Ability to Preserve the Topology and Complexity of Genetic Networks

Network inference is a rapidly advancing field, with new methods being proposed on a regular basis. Understanding the advantages and limitations of different network inference methods is key to their effective application in different circumstances. The common structural properties shared by diverse networks naturally pose a challenge when it comes to devising accurate inference methods, but surprisingly, there is a paucity of comparison and evaluation methods. Historically, every new methodology has only been tested against \textit{gold standard} (true values) purpose-designed synthetic and real-world (validated) biological networks. In this paper we aim to assess the impact of taking into consideration aspects of topological and information content in the evaluation of the final accuracy of an inference procedure. Specifically, we will compare the best inference methods, in both graph-theoretic and information-theoretic terms, for preserving topological properties and the original information content of synthetic and biological networks. New methods for performance comparison are introduced by borrowing ideas from gene set enrichment analysis and by applying concepts from algorithmic complexity. Experimental results show that no individual algorithm outperforms all others in all cases, and that the challenging and non-trivial nature of network inference is evident in the struggle of some of the algorithms to turn in a performance that is superior to random guesswork. Therefore special care should be taken to suit the method to the purpose at hand. Finally, we show that evaluations from data generated using different underlying topologies have different signatures that can be used to better choose a network reconstruction method.

q-bio.MN↗

Fractal dimension versus process complexity

Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields are related to each other in a non-trivial fashion. Here we study small Turing machines (TMs) with two symbols, and two and three states. For any particular such machine $τ$ and any particular input $x$ we consider what we call the 'space-time' diagram which is the collection of consecutive tape configurations of the computation $τ(x)$. In our setting, we define fractal dimension of a Turing machine as the limiting fractal dimension of the corresponding space-time diagram. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the above-specified type and its runtime complexity. In particular, a TM with three states and two colors runs in at most linear time iff its dimension is 2, and its dimension is 1 iff it runs in super-polynomial time and it uses polynomial space. If a TM runs in time $O(x^n)$ we have empirically verified that the corresponding dimension is $(n+1)/n$, a result that we can only partially prove. We find the results presented here remarkable because they relate two completely different complexity measures: the geometrical fractal dimension on the one side versus the time complexity of a computation on the other side.

cs.CC↗

Causality, Information and Biological Computation: An algorithmic software approach to life, disease and the immune system

Biology has taken strong steps towards becoming a computer science aiming at reprogramming nature after the realisation that nature herself has reprogrammed organisms by harnessing the power of natural selection and the digital prescriptive nature of replicating DNA. Here we further unpack ideas related to computability, algorithmic information theory and software engineering, in the context of the extent to which biology can be (re)programmed, and with how we may go about doing so in a more systematic way with all the tools and concepts offered by theoretical computer science in a translation exercise from computing to molecular biology and back. These concepts provide a means to a hierarchical organization thereby blurring previously clear-cut lines between concepts like matter and life, or between tumour types that are otherwise taken as different and may not have however a different cause. This does not diminish the properties of life or make its components and functions less interesting. On the contrary, this approach makes for a more encompassing and integrated view of nature, one that subsumes observer and observed within the same system, and can generate new perspectives and tools with which to view complex diseases like cancer, approaching them afresh from a software-engineering viewpoint that casts evolution in the role of programmer, cells as computing machines, DNA and genes as instructions and computer programs, viruses as hacking devices, the immune system as a software debugging tool, and diseases as an information-theoretic battlefield where all these forces deploy. We show how information theory and algorithmic programming may explain fundamental mechanisms of life and death.

cs.NE↗

Asymptotic Intrinsic Universality and Reprogrammability by Behavioural Emulation

We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative behaviour of computer programs. Our method may quantify the trust and confidence of the computing capabilities of natural and classical systems, and quantify computers by their degree of reprogrammability. We test the method to provide evidence in favour of a conjecture concerning the computing capabilities of Busy Beaver Turing machines as candidates for Turing universality. The method has recently been used to quantify the number of 'intrinsically universal' cellular automata, with results that point towards the pervasiveness of universality due to a widespread capacity for emulation. Our method represents an unconventional approach to the classical and seminal concept of Turing universality, and it may be extended and applied in a broader context to natural computation, by (in something like the spirit of the Turing test) observing the behaviour of a system under circumstances where formal proofs of universality are difficult, if not impossible to come by.

cs.CC↗

Interacting Behavior and Emerging Complexity

Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited available resources. We implement Global Rules that determine the interaction between two Elementary Cellular Automata on the same grid. Global Rules change the complexity of the state evolution output which suggests that some complexity is intrinsic to the interaction rules themselves. The largest increases in complexity occurred when the interacting elementary rules had very little complexity, suggesting that they are able to accept complexity through interaction only. We also found that some Class 3 or 4 CA rules are more fragile than others to Global Rules, while others are more robust, hence suggesting some intrinsic properties of the rules independent of the Global Rule choice. We provide statistical mappings of Elementary Cellular Automata exposed to Global Rules and different initial conditions onto different complexity classes.

cs.NE↗

The Information-theoretic and Algorithmic Approach to Human, Animal and Artificial Cognition

We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to computational and algorithmic complexity. We start by arguing that passing the Turing test is a trivial computational problem and that its pragmatic difficulty sheds light on the computational nature of the human mind more than it does on the challenge of artificial intelligence. We then review our proposed algorithmic information-theoretic measures for quantifying and characterizing cognition in various forms. These are capable of accounting for known biases in human behavior, thus vindicating a computational algorithmic view of cognition as first suggested by Turing, but this time rooted in the concept of algorithmic probability, which in turn is based on computational universality while being independent of computational model, and which has the virtue of being predictive and testable as a model theory of cognitive behavior.

cs.AI↗

Methods of Information Theory and Algorithmic Complexity for Network Biology

We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdos-Renyi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data. We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs, characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.

q-bio.MN↗

Natural scene statistics mediate the perception of image complexity

Humans are sensitive to complexity and regularity in patterns. The subjective perception of pattern complexity is correlated to algorithmic (Kolmogorov-Chaitin) complexity as defined in computer science, but also to the frequency of naturally occurring patterns. However, the possible mediational role of natural frequencies in the perception of algorithmic complexity remains unclear. Here we reanalyze Hsu et al. (2010) through a mediational analysis, and complement their results in a new experiment. We conclude that human perception of complexity seems partly shaped by natural scenes statistics, thereby establishing a link between the perception of complexity and the effect of natural scene statistics.

cs.AI↗

Quantifying Loss of Information in Network-based Dimensionality Reduction Techniques

To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been clear. Here we develop a framework, based on algorithmic information theory, to quantify the extent to which information is preserved when network motif analysis, graph spectra and spectral sparsification methods are applied to over twenty different biological and artificial networks. We find that the spectral sparsification is highly sensitive to high number of edge deletion, leading to significant inconsistencies, and that graph spectral methods are the most irregular, capturing algebraic information in a condensed fashion but largely losing most of the information content of the original networks. However, the approach shows that network motif analysis excels at preserving the relative algorithmic information content of a network, hence validating and generalizing the remarkable fact that despite their inherent combinatorial possibilities, local regularities preserve information to such an extent that essential properties are fully recoverable across different networks to determine their family group to which they belong to (eg genetic vs social network). Our algorithmic information methodology thus provides a rigorous framework enabling a fundamental assessment and comparison between different data dimensionality reduction methods thereby facilitating the identification and evaluation of the capabilities of old and new methods.

q-bio.MN↗

Two-Dimensional Kolmogorov Complexity and Validation of the Coding Theorem Method by Compressibility

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing machine. The technique is interesting because it provides a natural algorithmic process for symmetry breaking generating complex $n$-dimensional structures from perfectly symmetric and fully deterministic computational rules producing a distribution of patterns as described by algorithmic probability. Algorithmic probability also elegantly connects the frequency of occurrence of a pattern with its algorithmic complexity, hence effectively providing estimations to the complexity of the generated patterns. Experiments to validate estimations of algorithmic complexity based on these concepts are presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability. We then use the output frequency of the set of 2-dimensional Turing machines to classify the algorithmic complexity of the space-time evolutions of Elementary Cellular Automata.

cs.CC↗

Rare Speed-up in Automatic Theorem Proving Reveals Tradeoff Between Computational Time and Information Value

We show that strategies implemented in automatic theorem proving involve an interesting tradeoff between execution speed, proving speedup/computational time and usefulness of information. We advance formal definitions for these concepts by way of a notion of normality related to an expected (optimal) theoretical speedup when adding useful information (other theorems as axioms), as compared with actual strategies that can be effectively and efficiently implemented. We propose the existence of an ineluctable tradeoff between this normality and computational time complexity. The argument quantifies the usefulness of information in terms of (positive) speed-up. The results disclose a kind of no-free-lunch scenario and a tradeoff of a fundamental nature. The main theorem in this paper together with the numerical experiment---undertaken using two different automatic theorem provers AProS and Prover9 on random theorems of propositional logic---provide strong theoretical and empirical arguments for the fact that finding new useful information for solving a specific problem (theorem) is, in general, as hard as the problem (theorem) itself.

cs.LO↗

Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed \emph{coding theorem method} the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.

cs.CC↗

Numerical Investigation of Graph Spectra and Information Interpretability of Eigenvalues

We undertake an extensive numerical investigation of the graph spectra of thousands regular graphs, a set of random Erdös-Rényi graphs, the two most popular types of complex networks and an evolving genetic network by using novel conceptual and experimental tools. Our objective in so doing is to contribute to an understanding of the meaning of the Eigenvalues of a graph relative to its topological and information-theoretic properties. We introduce a technique for identifying the most informative Eigenvalues of evolving networks by comparing graph spectra behavior to their algorithmic complexity. We suggest that extending techniques can be used to further investigate the behavior of evolving biological networks. In the extended version of this paper we apply these techniques to seven tissue specific regulatory networks as static example and network of a naïve pluripotent immune cell in the process of differentiating towards a Th17 cell as evolving example, finding the most and least informative Eigenvalues at every stage.

cs.IT↗

Quantifying Natural and Artificial Intelligence in Robots and Natural Systems with an Algorithmic Behavioural Test

One of the most important aims of the fields of robotics, artificial intelligence and artificial life is the design and construction of systems and machines as versatile and as reliable as living organisms at performing high level human-like tasks. But how are we to evaluate artificial systems if we are not certain how to measure these capacities in living systems, let alone how to define life or intelligence? Here I survey a concrete metric towards measuring abstract properties of natural and artificial systems, such as the ability to react to the environment and to control one's own behaviour.

cs.AI↗

On the Complexity and Behaviour of Cryptocurrencies Compared to Other Markets

We show that the behaviour of Bitcoin has interesting similarities to stock and precious metal markets, such as gold and silver. We report that whilst Litecoin, the second largest cryptocurrency, closely follows Bitcoin's behaviour, it does not show all the reported properties of Bitcoin. Agreements between apparently disparate complexity measures have been found, and it is shown that statistical, information-theoretic, algorithmic and fractal measures have different but interesting capabilities of clustering families of markets by type. The report is particularly interesting because of the range and novel use of some measures of complexity to characterize price behaviour, because of the IRS designation of Bitcoin as an investment property and not a currency, and the announcement of the Canadian government's own electronic currency MintChip.

q-fin.ST↗

Turing Minimalism and the Emergence of Complexity

Not only did Turing help found one of the most exciting areas of modern science (computer science), but it may be that his contribution to our understanding of our physical reality is greater than we had hitherto supposed. Here I explore the path that Alan Turing would have certainly liked to follow, that of complexity science, which was launched in the wake of his seminal work on computability and structure formation. In particular, I will explain how the theory of algorithmic probability based on Turing's universal machine can also explain how structure emerges at the most basic level, hence reconnecting two of Turing's most cherished topics: computation and pattern formation.

cs.CC↗

Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines

Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The method is an alternative to the traditional lossless compression algorithms, which it may complement, the two being serviceable for different string lengths. We provide a thorough analysis for all $\sum_{n=1}^{11} 2^n$ binary strings of length $n<12$ and for most strings of length $12\leq n \leq16$ by running all $\sim 2.5 \times 10^{13}$ Turing machines with 5 states and 2 symbols ($8\times 22^9$ with reduction techniques) using the most standard formalism of Turing machines, used in for example the Busy Beaver problem. We address the question of stability and error estimation, the sensitivity of the continued application of the method for wider coverage and better accuracy, and provide statistical evidence suggesting robustness. As with compression algorithms, this work promises to deliver a range of applications, and to provide insight into the question of complexity calculation of finite (and short) strings.

cs.IT↗

Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks

We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We show that approximations of K characterise synthetic and natural networks by their generating mechanisms, assigning lower algorithmic randomness to complex network models (Watts-Strogatz and Barabasi-Albert networks) and high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) measure, based on algorithmic probability theory.

cs.IT↗