Algorithmic Information Theory

Artykuł opublikowany w 13 numerze czasopisma "Problemy Studiów Nauczycielskich" przedstawia podręcznik dla studentów kształcących się w kierunku nauczania informatyki, wydany nakładem Wyższej Szkoły Pedagogicznej w Krakowie. W artykule uzasadniona jest celowość uwzględnienia teoretycznych podstaw informatyki w profilu wykształcenia przyszłych nauczycieli informatyki, a także przedstawiona jest zawartość (spis treści) wydanego podręcznika.

This paper explores various spiritual traditions of Hinduism from the evolutionary perspective. The term evolution in its contemporary usage is closely associated with Biological Evolution (BE). However, the paper uses the term ‘evolution’ in a more general sense to include not only BE, but also Cultural Evolution (CE), Axiological Evolution (AE), and in general any Developmental Evolution (DE) as a continuous process that develops over a long period of time with or without teleology.

The paper defines Hinduism as a meta-religion - a group of belief systems which originated, coexisted and interacted with each other in the Indian subcontinent with shared traits and common substrata. It then defines the contours of what is known as Shāstra - a corpus of Sanskrit texts which forms the basis of theological and philosophical traditions of Hinduism. The Shāstra corpus is divided into three groups: (a) Primary texts (Nigamas and Agamas), (b) Secondary texts (Smṛitis, Purāṇas, and Epics), (c) Philosophical texts based on primary and secondary sources, including the writings of some of the 19th-20th century protagonists of Hinduism. The evolutionary perspective of Hinduism is explored within and among these three groups with the admission that this particular approach though justified on the basis of sample selection, is incomplete for the very same reason. In this paper, AE is essentially karmic in nature and binds various Hindu belief systems together. The paper explores the relationship between AE, BE, CE, and DE along with their directionality. BE stands out due to its rationalist framework and absence of directionality.

It is unrealistic to expect complete uniformity of views in a meta-religion like Hinduism that gives space to plurality of beliefs. It is also unrealistic to find in Shāstra any explicit support to BE which originated in the 19th century of Common Era and which is being developed since then adding to its explanatory power.

The paper shows that the germinating ground for BE’s ‘common descent’ is available in the monist Upaniṣhads and pantheist hymns of primary texts. The secondary texts (Purāṇas) offer an interesting model of Dashāvatāras (10-incarnations) which is loosely isomorphic to BE. Though this isomorphism is ‘by accident’, it suggests that there is no inherent resistance to the gradual evolution of humans from the lower organisms due to the pantheist, nature worshipping substratum of popular Hinduism. Hindu axiology (AE) too supports such evolution on the karmic basis.

Among the huge corpus of secondary texts however, there are few socio-religious texts which sourced cultural memes of hierarchical patrilineal classes and purity of lineage. Although these memes did not exist in the primary source; and although Advaita - the apex theosophy of Hinduism advises the aspirant to shed off these memes for spiritual knowledge, they still exist and may resist the ‘common descent’ - the basic principle of BE.

The paper discusses Hindu theosophical systems which support cosmic DE. Following the monist, pantheist primary sources and the karmic axiology, these systems offer ground to the ‘gradual development’ and ‘common descent’ of BE. The difficulty of explaining the emergence of qualitative experience in individual life-forms seems to have been anticipated by these schools. Neo-Hindus like Yogi Aurobindo and Swami Vivekānanda offered an integrated evolutionary spiritual model with alternating directionality of evolution and involution. Hindu theosophical traditions allow such constructive view-point which enables the theologian to place himself in a particular position of his choice in the vast empirical spatium and construct his metaphysical and axiological models based on the primary sources.

Generalized Information (GI) is a measurement of the degree to which a program can be said to generalize a dataset. It is calculated by creating a program to model the data set, measuring the Active Information in the model, and subtracting out the size of the model. Active Information allows GI to be usable with both exact and inexact models.

Four general approaches to the metaphysics of causation are current in
Australasian philosophy. One is a development of the regularity theory (attributed to Hume) that uses counterfactuals (Lewis, 1973; 1994). A second is based in the relations of universals, which determine laws, which in turn determine causal interactions of particulars (with the possible exception of singular causation, Armstrong, 1983). This broad approach goes back to Plato, and was also held in this century by Russell, who like Plato, but unlike the more recent version of Armstrong (1983), held there were no particulars as such, only universals. A third view, originating with Reichenbach and revived by Salmon (1984), holds that a causal process is one that can be marked. This view relies heavily on ideas about the transfer of information and the relation of information to probability, but it also needs uneliminable counterfactuals. The fourth view was developed recently by Dowe (1992) and Salmon (1994). It holds that a causal process involves the transfer of a non-zero valued conserved quantity. A considerable advantage of this approach over the others is that it requires neither counterfactuals nor abstracta like universals to explain causation.
The theory of causation offered here is a development of the mark approach that entails Dowe’s conserved quantity approach. The basic idea is that causation is the transfer of a particular token of a quantity of information from one state of a system to another. Physical causation is a special case in
which physical information instances are transferred from one state of a physical system to another. The approach can be interpreted as a Universals approach (depending on ones approach to mathematical objects and qualities), and it sheds some light on the nature of the regularity approach.
After motivating and describing this approach, I will sketch how it can be used to ground natural laws and how it relates to the four leading approaches, in particular how each can be conceived as a special case of my approach. Finally, I will show how my approach satisfies the requirements of Humean supervenience. The approach relies on concrete particulars and computational logic alone, and is the second stage of constructing a minimal metaphysics, started in (Collier 1996, The necessity of natural kinds).

Deep learning and other similar machine learning techniques have a huge advantage over other AI methods: they do function when applied to real-world data, ideally from scratch, without human intervention. However, they have several shortcomings that mere quantitative progress is unlikely to overcome. The paper analyses these shortcomings as resulting from the type of compression achieved by these techniques, which is limited to statistical compression. Two directions for qualitative improvement, inspired by comparison with cognitive processes, are proposed here, in the form of two mechanisms: complexity drop and contrast. These mechanisms are supposed to operate dynamically and not through pre-processing as in neural networks. Their introduction may bring the functioning of AI away from mere reflex and closer to reflection.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness-recently proved to be theoretically incomputable-and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness."

In  this  article,  we  will  show  that  uncomputability  is  a  relative property  not  only  of  oracle  Turing  machines,  but  also  of  subrecursive classes. We will define the concept of a Turing submachine, and a recursive relative  version  for  the  Busy Beaver  function which we  will  call  Busy Beaver Plus function. Therefore, we will prove that the computable Busy Beaver Plus function defined on any Turing submachine is not computable by any program running on this submachine. We will thereby demonstrate the existence of a “paradox” of computability a la Skolem: a function is computable when “seen from the outside” the subsystem, but uncomputable when “seen from within” the same subsystem. Finally, we will raise the possibility of defining universal submachines,  and a hierarchy of negative Turing degrees.

The main topic of the present work are universal machines for plain and prefix-free description complexity and their domains. It is characterised when an r.e. set W is the domain of a universal plain machine in terms of the description complexity of the spectrum function s W mapping each non-negative integer n to the number of all strings of length n in W ; furthermore, a characterisation of the same style is given for supersets of domains of universal plain machines. Similarly the prefix-free sets which are domains or supersets of domains of universal prefix-free machines are characterised. Furthermore, it is shown that the halting probability Ω V of an r.e. prefix-free set V containing the domain of a universal prefix-free machine is Martin-Löf random, while V may not be the domain of any universal prefix-free machine itself. Based on these investigations, the question whether every domain of a universal plain machine is the superset of the domain of some universal prefix-free machine is discussed. A negative answer to this question had been presented at CiE 2010 by Mikhail Andreev, Ilya Razenshteyn and Alexander Shen, while this paper was under review.

Dear Colleagues,

Classical probability theory and traditional statistics have long helped scientists to find meaningful signals amid the noise and thereby make sense of the world. However, classical approaches have proven a little threadbare in today’s landscape of large datasets and complex data, which are driving new insights in disciplines ranging from biology to ecology to economics. This is as true in biology, with the advent of new techniques of genome editing, as it is in astronomy, with telescope surveys charting the entire sky in the search for new Earth-like planets. The data have changed. Maybe it is time our data analysis tools did, too.

Algorithmic information dynamics (AID) is a new type of discrete calculus based on computer programming, employed to study complex systems by exploring the software space of models explaining a system subject to changes or perturbations. The objective is to look for computable mechanistic generating models and first principles, thereby ushering in the next generation of scientific discovery and model-driven machine learning. Following a popular online course sponsored by the Santa Fe Institute, and the publication in recent years of a number of papers (by original authors as well as independent groups) that utilize AID based on new tools such as the coding theorem and the block decomposition method (motivated by algorithmic probability) to discover new knowledge, AID is becoming a tool fully equal to the challenge of studying rich, complex systems. Whereas we had only been using weak (e.g., computable) measures to study complex systems, now it is possible to match data to models in degree of sophistication.

We encourage authors and researchers to continue exploring how AID can help us to understand new aspects of systems science by building rich causal computational models and submitting their results to this Special Issue. They would thereby be contributing to progress in the methodological aspects of systems science, advancing it beyond its current reliance on simplistic data analysis and ad hoc measures.

Dr. Hector Zenil
Dr. Felipe S. Abrahão
Collection Editors

Algorithmic Information Dynamics (AID) is an algorithmic probabilistic framework for causal discovery and causal analysis. It enables a numerical solution to inverse problems based or motivated on principles of algorithmic probability. AID studies dynamical systems in software space where all possible computable models can be found or approximated under the assumption that discrete longitudinal data such as particle orbits in state and phase space can approximate continuous systems by Turing-computable means. AID combines perturbation analysis and algorithmic information theory to guide a search for sets of models compatible with observations and to precompute and exploit those models as testable generative mechanisms and causal first principles underlying data and systems. AID is an alternative or a complement to other approaches and methods of experimental inference, such as statistical machine learning and classical information theory. AID connects with and across other parallel ...

International Journal of Information Science & techniques (IJIST) focuses on system modeling and information techniques in real engineering and scientific problems This journal provides a forum that impacts the development of scientific computing, complex systems, control theory, signal and image processing, scheduling, data mining, discrete systems. It also acts as a path to exchange novel ideas about new modeling techniques.

Podemos chamar o famoso “paradoxo” de Skolem de um pseudoparadoxo metalinguístico da denumerabilidade: de dentro do sistema um conjunto não é enumerável enquanto que de fora do sistema ele pode ser. O mesmo fenômeno aparece em relação à computabilidade, ou seja, existe um pseudoparadoxo metalinguístico da computabilidade? No qual “de dentro” algo é incomputável enquanto que “de fora” esse algo pode ser computável? É na metabiologia que esse fenômeno surge para ajudar a responder a pergunta sobre como ficaria a evolução dos organismos/programas sujeitos a mutações algorítmicas aleatórias numa natureza computável, visto que nos primeiros modelos demonstrados por Gregory Chaitin isso se dá numa natureza oracular, um hipercomputador.

Palavras-Chave: Metabiologia, Paradoxo de Skolem, Teoria da Computabilidade, Computabilidade da Vida, Hipótese do Universo Computável, Teoria da Informação Algorítmica.

Broadly speaking, there are two approaches to quantifying information. The first, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out. The second, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory. After introducing the measure, we show that it provides a non-universal analog of algorithmic information. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies (counted in two different ways for the two different capacities). We also discuss how effective information relates to information gain, Shannon and mutual information.

In spite of being ubiquitous in life sciences, the concept of information is harshly criticized. Uses of the concept other than those derived from Shannon's theory are denounced as metaphoric, We perform a computational experiment to explore whether Shannon's information is adequate to describe the uses of said concept in commonplace scientific practice. Our results show that semantic sequences do not have unique complexity values different from the value of meaningless sequences. This result suggests that quantitative theoretical frameworks do not account fully for the complex phenomenon that the term "information" refers to. We propose restructuring the concept into two related, but independent notions, and conclude that a complete theory of information must account completely not only for both notions, but also for the relationship between them.

Transmission of information in the form of qubits much faster than the speed of light is the important aspects of quantum information theory. Quantum information processing exploits the quantum nature of information that needs to be stored, encoded, transmit, receive and decode the information in the form of qubits. Bosonic channels appear to be very attractive for the physical implementation of quantum communication. This paper does the study of quantum channels and how best it can be implemented with the existing infrastructure that is the classical communication. Multiple access to the quantum network is the requirement where multiple users want to transmit their quantum information simultaneously without interfering with each others.

While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two pictures. We give several natural definitions of a universal information metric, based on length of shortest programs for either ordinary computations or reversible (dissipationless) computations. It turns out that these definitions are equivalent up to an additive logarithmic term. We show that the information distance is a universal cognitive similarity distance. We investigate the maximal correlation of the shortest programs involved, the maximal uncorrelation of programs (a generalization of the Slepian-Wolf theorem of classical information theory), and the density properties of the discrete metric spaces induced by the information distances. A related distance measures the amount of nonreversibility of a computation. Using the physical theory of reversible computation, we give an appropriate (universal, anti-symmetric, and transitive) measure of the thermodynamic work required to transform one object in another object by the most efficient process. Information distance between individual objects is needed in pattern recognition where one wants to express effective notions of "pattern similarity" or "cognitive similarity" between individual objects and in thermodynamics of computation where one wants to analyse the energy dissipation of a computation from a particular input to a particular output.

We show that metabiology is not restricted to the study of the evolution of programs or the evolution of computable systems. Inspired by the concept of hyper-computation, that is, by the idea of programs having access to a Turing oracle, we propose a model for the evolution of hyper-programs, which are non-computable systems. Metabiology´s basic theorem that software living beings will become more and more creative – with Nature as an infinite source of random mutations and new information – still holds. However, in studying the evolution of hyper-programs we need to consider a much more powerful source of new information, our new Nature, that is capable of answering any arithmetical question, in other words, that is a complete system with respect to the arithmetical hierarchy.

Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole.
One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible.
By formalising the act of observing as mutual perturbations between dynamical systems,
we demonstrate that emergence of algorithmic information do depend on the observer's formal knowledge, while robust to other subjective factors, particularly: the choice of the programming language and the measurement method; errors or distortions during the information acquisition; and the informational cost of processing.
This is called observer-dependent emergence (ODE).
In addition, we demonstrate that the unbounded and fast increase of emergent algorithmic information implies asymptotically observer-independent emergence (AOIE).
Unlike ODE, AOIE is a type of emergence for which emergent phenomena will remain considered to be emergent for every formal theory that any observer might devise.
We demonstrate the existence of an evolutionary model that displays the diachronic variant of AOIE and a network model that displays the holistic variant of AOIE.
Our results show that, restricted to the context of finite discrete deterministic dynamical systems, computable systems, and irreducible information content measures, AOIE is the strongest form of emergence that formal theories can attain.

This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked population of randomly generated computable systems with a fixed communication protocol. Then, in order to solve an undecidable problem, we study how nodes (i.e., Turing machines or computable systems) can harness the power of the metabiological selection and the power of information sharing (i.e., communication) through the network. Formally, we show that there is a pervasive network topological condition, in particular, the small-diameter phenomenon, that ensures that every node becomes capable of solving the halting problem for every program with a length upper bounded by a logarithmic order of the population size. In addition, we show that this result implies the existence of a central node capable of emergently solving the halting problem in the minimum number of communication rounds. Furthermore, we introduce an algorithmic-informational measure of synergy for networked computable systems, which we call local algorithmic synergy. Then, we show that such algorithmic network can produce an arbitrarily large value of expected local algorithmic synergy.

Entendendo a metabiologia como uma teoria matemática para evolução de programas ou de sistemas computáveis, inspirada pela – e voltada para – evolução biológica, esse artigo tem como objetivo discutir - e introduzir - sobre a evolução metabiológica de sistemas não computáveis. Estes últimos, chamaremos de hiperprogramas. Tomaremos como referência principal o modelo de evolução cumulativa já apresentado por Gregory Chaitin para, com isso, ver se resultado análogo pode ser obtido para a evolução de hiperprogramas. Ultrapassaremos o computável, passando pela completude da aritmética e indo além.

We introduce a family of unsupervised, domain-free, and asymptotically optimal model-independent algorithms based on the principles of algorithmic probability and information theory designed to minimize the loss of algorithmic information, and thereby avoiding certain deceiving phenomena and distortions known to occur in statistics and entropy-based approaches. Our methods include a lossless-compression-based lossy compression algorithm that can select and coarse-grain data in an algorithmic-complexity fashion (without the use of popular compression algorithms) by collapsing regions that may procedurally be regenerated from a computable candidate model. We show that the method can perform dimension reduction, denoising, feature selection, and network sparsification, while preserving the properties of the objects. As validation case, we demonstrate the methods on image segmentation against popular methods like PCA and random selection, and also demonstrate that the method preserves the graph-theoretic indices measured on a well-known set of synthetic and real-world networks of very different nature, ranging from degree distribution and clustering coefficient to edge betweenness and degree and eigenvector centralities, achieving equal or significantly better results than other data reduction and the leading network sparsification methods (Spectral, Transitive).

—High-throughput technologies for biological measurements generate vast amounts of quantitative data, which necessitate the development of advanced approaches to data analysis to help understand the underlying processes and networks. Reconstruction of biological networks from measured data of different components is a significant challenge in systems biology. We applied an information theoretic approach to reconstruct phosphoprotein-cytokine networks in RAW 264.7 macrophage cells. The information theoretic approach is based on estimation of mutual information of interactions by using kernel density estimators. Mutual information provides a measure of statistical dependencies between interacting components. Using this information theoretic approach, we develop a data-driven parsimonious input-output model of the phosphoprotein-cytokine network. Cytokines are secreted upon activation of a wide range of regulatory signals transduced by the phosphoprotein network. Identifying these components can help identify regulatory modules responsible for the cytokine responses. We demonstrate the applicability of our information theoretic approach to reconstruction of biological networks. This approach not only captures most of the known signaling components involved in cytokine release but also predicts new signaling components involved in releases of cytokines. The results of this study are important for gaining a clear understanding of macrophage activation during the inflammation process.

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 Kolmogorov-Chaitin complexity of a string s. Some attempts have been made to arrive at a framework stable enough for a concrete definition of K, independent of any constant under a programming language, by appealing to the "naturalness" of the language in question. The aim of this paper is to present an approach to overcome the problem by looking at a set of models of computation converging in output probability distribution such that that "naturalness" can be inferred, thereby providing a framework for a stable definition of K under the set of convergent models of computation.

This paper is devoted to large scale aspects of the geometry of the space of isometry classes of Riemannian metrics, with a 2-sided curvature bound, on a fixed compact smooth manifold of dimension at least five. Using a mix of tools from logic/computer science, and differential geometry and topology, we study the diameter functional and its critical points, as well as their distribution (density) within the space and the structure of their neighborhoods.

Different and many times provably-incompatible technical definitions, all claiming to formally characterize the vague notion of randomness, have appeared in the past century. This work is a personal attempt to put a few of these related mathematical developments into a general philosophical perspective. It is not at all a conclusive summary of the modern notion of randomness and its underlying philosophy. Quite the contrary - it is a mere sketch. Nonetheless, one hopefully demonstrating not only the rich technical diversity pertaining to the notion, but the delicate interplay between the technical developments and the evolving philosophical intuitions behind the word, and even more importantly – the possibility of revealing the order underlying that diversity, the structure determining the possibilities for notions of randomness and how they are constrained, as well as the relations among them.

In a genetic algorithm, fluctuations of the entropy of a genome over time are interpreted as fluctuations of the information that the genome's organism is storing about its environment, being this reflected in more complex organisms. The computation of this entropy presents technical problems due to the small population sizes used in practice. In this work we propose and test an alternative way of measuring the entropy variation in a population by means of algorithmic information theory, where the entropy variation between two generational steps is the Kolmogorov complexity of the first step conditioned to the second one. As an example application of this technique, we report experimental differences in entropy evolution between systems in which sexual reproduction is present or absent.

The concept of entropy plays a major part in communication theory. The Shannon entropy is a measure of uncertainty with respect to a priori probability distribution. In algorithmic information theory the information content of a message is measured in terms of the size in bits of the smallest program for computing that message. This paper discusses the classical entropy and entropy rate for discrete or continuous Markov sources, with finite or continuous alphabets, and their relations to program-size complexity and algorithmic probability. The accent is on ideas, constructions and results; no proofs will be given.

The need to act in networks and to function in a society where we relate in complex fashions has fostered the use of data in accordance with distributed models. In a big data context, the individual is often overcome with the sentiment that one's life does not matter, nor does it make a difference. What are sought are trends, and since there is no detached observer, those change things as much as they measure them. Where can we find a vantage point, this 'topsight' that Gelernter deemed necessary before the conception of any program? One could seek it in the direction of a collective figure, somewhat like the Leviathan of Hobbes, made up in its gigantism of smaller figures. Those that have been schooled in the classical tradition, or philosophia perennis, might think that we are abandoning solid realism, which seeks a conformation of statements, propositions, and language to what there is. They might criticize the reign of opinion. But what we entered into is not, upon closer inspection, some overarching paradigm of truth as success. It is rather a rationality of the likely, and it requires assessing the truths that can seem distributed between alternating or competing positions. But then, to seek decisions despite this, is to erase from our world this 'esprit de finesse' which Pascal deemed necessary to balance the illusions of a procedural mathematical rationality claiming that its end-products are simply in correspondence with reality. Some of the challenges are going to be centered around the development of signposts, flags, and warnings if we are not to end-up with a 'governing machine' (Dominique Dubarle's expression). We will even at times hear that persons are transparent right through if one would capture them as information, which we could deem even to constitute a 'common body.' Yet, such a trivialisation of Shannon's model leaves behind the algorithmic informational understanding. It seems that a common body, alongside a common intellect, is some gnostic and self-defeating notion, that calls to mind medieval monopsychistic positions. There is at the same time a ‘new cave’ that has made its appearance. It often masquerades as truth seeking, but it in fact rests on prejudices assumed to be true without discussion. To counter it, we look at science as bearing means of enlightenment,–and it does–, but this does not imply that it knows the answers any more than common sense in situations of uncertainty. When we gather information, we frame it within an ontology for classification purposes, but this does not import with itself the immanence of this information as endogenous power to harmonise and give form. Feeling, as Whitehead construed it, seeks to take within it a receptivity to the world in order to turn it into an internalised representation. For this, it needs to be possible for a part of the world to reflect on itself the whole. Yet, this reflection is not a totalisation in an immaterial data range, it is rather a grounding in the mystery of the flesh, which is found here as a signpost on the way, if we are to heal dreams of complete mastery.

Recent large scale experiments have shown that the Normalized Information Distance, an algorithmic information measure, is among the best similarity metrics for melody classification. This paper proposes the use of this distance as a fitness function which may be used by genetic algorithms to automatically generate music in a given pre-defined style. The minimization of this distance of the generated music to a set of musical guides makes it possible to obtain computer-generated music which recalls the style of a certain human author. The recombination operator plays an important role in this problem and thus several variations are tested to fine tune the genetic algorithm for this application. The superiority of the relative pitch envelope over other music parameters, such as the lengths of the notes, brought us to develop a simplified algorithm that nevertheless obtains interesting results.

As an increasing number of protein structures become available, the need for algorithms that can quantify the similarity between protein structures increases as well. Thus, the comparison of proteins' structures, and their clustering accordingly to a given similarity measure, is at the core of today's biomedical research. In this paper, we show how an algorithmic information theory inspired Universal Similarity Metric (USM) can be used to calculate similarities between protein pairs. The method, besides being theoretically supported, is surprisingly simple to implement and computationally efficient. Results: Structural similarity between proteins in four different datasets was measured using the USM.The sample employed represented alpha, beta, alpha-beta, tim-barrel, globins and serpine protein types. The use of the proposed metric allows for a correct measurement of similarity and classification of the proteins in the four datasets. Availability: All the scripts and programs used for the preparation of this paper are available at http://www.cs.nott.ac.uk/ nxk/USM/protocol.html. In that web-page the reader will find a brief description on how to use the various scripts and programs. Contact: [email protected]; [email protected] Supplementary information: The protein datasets used are collected in

We further deconstruct Heraclitean Quantum Systems giving a model for a universe using pregeometric notions in which the end-game problem is overcome by means of self-referential noise. The model displays self-organisation with the emergence of 3-space and time. The time phenomenon is richer than the present geometric modelling.

Um campo, por essência, transdisciplinar é criado quando a teoria algorítmica da informação se propõe a resolver uma questão da biologia. Possivelmente, a questão mais importante: a evolução dos seres vivos. A partir daí, velhos problemas, tanto biológicos quanto matemáticos, são retomados, assim como, emergem novas questões a serem respondidas ou não. É sobre esta última frase e sobre os trabalhos de Gregory J. Chaitin que a presente discussão se desdobra.  O que é o ser vivo? Podemos responder isso dizendo que o DNA é um software. Na metabiologia um programa de computador é tratado como uma representação do organismo biológico.  Abre-se todo um leque de possibilidades de interpretações sobre que tipos de relações recursivas entre ser vivo e meio-ambiente satisfazem tal hipótese representativa.
Outro pressuposto na base da teoria metabiológica é tomar a aptidão do programa/organismo pelo tamanho do número que ele consegue calcular. Temos aqui uma forma quantitativa de medição de uma propriedade da relação do ser vivo com a natureza. Então, o que esse número que um programa é capaz de calcular poderia simbolizar?
No artigo de referência vários resultados já nos são apresentados. Um tipo de evolução, aquela dada por uma busca exaustiva no espaço de todas as mutações, é indicada como o modelo errado, justamente, pela velocidade da evolução não corresponder (a princípio) com a biológica. Mas estaria, de qualquer forma, esse modelo fadado ao fracasso? O outro modelo que nos trás uma melhor semelhança com o biológico passa por um tipo de progressão na qual as mutações são “direcionadas”, isto é, na qual somente é permitido um tipo específico de mutação – aquele que sempre visa se aproximar cada vez mais do número Omega. Quais características algum outro número oracular precisaria ter para satisfazer esse modelo? De fato, para ele funcionar é necessário algum sistema na natureza equivalente a uma Oracle Machine. Mas esta é a única forma de chegarmos a resultados satisfatórios dentro da metabiologia?
Chegamos, por esse caminho, a possibilidades e algumas perguntas. Além de discuti-las de forma mais ampla, serão apresentadas possíveis soluções.

This paper explores various spiritual traditions of Hinduism from the evolutionary perspective. The term evolution in its contemporary usage is closely associated with Biological Evolution (BE). However, the paper uses the term ‘evolution’ in a more general sense to include not only BE, but also Cultural Evolution (CE), Axiological Evolution (AE), and in general any Developmental Evolution (DE) as a continuous process that develops over a long period of time with or without teleology. The paper defines Hinduism as a meta-religion - a group of belief systems which originated, coexisted and interacted with each other in the Indian subcontinent with shared traits and common substrata. It then defines the contours of what is known as Shāstra - a corpus of Sanskrit texts which forms the basis of theological and philosophical traditions of Hinduism. The Shāstra corpus is divided into three groups: (a) Primary texts (Nigamas and Agamas), (b) Secondary texts (Smṛitis, Purāṇas, and Epics), (c) Philosophical texts based on primary and secondary sources, including the writings of some of the 19th-20th century protagonists of Hinduism. The evolutionary perspective of Hinduism is explored within and among these three groups with the admission that this particular approach though justified on the basis of sample selection, is incomplete for the very same reason. In this paper, AE is essentially karmic in nature and binds various Hindu belief systems together. The paper explores the relationship between AE, BE, CE, and DE along with their directionality. BE stands out due to its rationalist framework and absence of directionality. It is unrealistic to expect complete uniformity of views in a meta-religion like Hinduism that gives space to plurality of beliefs. It is also unrealistic to find in Shāstra any explicit support to BE which originated in the 19th century of Common Era and which is being developed since then adding to its explanatory power. The paper shows that the germinating ground for BE’s ‘common descent’ is available in the monist Upaniṣhads and pantheist hymns of primary texts. The secondary texts (Purāṇas) offer an interesting model of Dashāvatāras (10-incarnations) which is loosely isomorphic to BE. Though this isomorphism is ‘by accident’, it suggests that there is no inherent resistance to the gradual evolution of humans from the lower organisms due to the pantheist, nature worshipping substratum of popular Hinduism. Hindu axiology (AE) too supports such evolution on the karmic basis. Among the huge corpus of secondary texts however, there are few socio-religious texts which sourced cultural memes of hierarchical patrilineal classes and purity of lineage. Although these memes did not exist in the primary source; and although Advaita - the apex theosophy of Hinduism advises the aspirant to shed off these memes for spiritual knowledge, they still exist and may resist the ‘common descent’ - the basic principle of BE. The paper discusses Hindu theosophical systems which support cosmic DE. Following the monist, pantheist primary sources and the karmic axiology, these systems offer ground to the ‘gradual development’ and ‘common descent’ of BE. The difficulty of explaining the emergence of qualitative experience in individual life-forms seems to have been anticipated by these schools. Neo-Hindus like Yogi Aurobindo and Swami Vivekānanda offered an integrated evolutionary spiritual model with alternating directionality of evolution and involution. Hindu theosophical traditions allow such constructive view-point which enables the theologian to place himself in a particular position of his choice in the vast empirical spatium and construct his metaphysical and axiological models based on the primary sources.

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypothesis testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are described.

Effective fractal dimension was defined by Lutz (2003) in order to quantitatively analyze the structure of complexity classes, but then interesting connections of effective dimension with information theory were also found, justifying the long existent intuition that dimension is an information content measure. Considering different bounds on computing power that range from finite memory to constructibility, including time-bounded and space-bounded

This work presents some outcomes of a theoretical investigation of incompressible high-order networks defined by a generalized graph representation. We study some of their network topological properties and how these may be related to real-world complex networks. We show that these networks have very short diameter, high k-connectivity, degrees of the order of half of the network size within a strong-asymptotically dominated standard deviation, and rigidity with respect to automorphisms. In addition, we demonstrate that incompressible dynamic (or dynamic multilayered) networks have transtemporal (or crosslayer) edges and, thus, a snapshot-like representation of dynamic networks is inaccurate for capturing the presence of such edges that compose underlying structures of some real-world networks.