This paper explores the interactions between knot theory and quantum computing. On one side, knot theory has been used to create models of quantum computing, and on the other, it is a source of computational problems. Knot theory is often used to introduce topological idea to people without a formal mathematical background, and we are building on this tradition to discuss some of the deeper ideas of quantum computing.

El objetivo de este artículo es sencillo: por un lado, esbozar brevemente las líneas maestras que han marcado y marcan los pensamientos desarrollados por Sigfrido Samet Letichevsky (SSL), José Antonio López Díaz (JALD) y Javier Pérez Jara (JPJ) en lo tocante al debate que nos ocupa; y, por otro lado, matizar ciertos comentarios que Javier Pérez Jara hila sobre mis coordenadas filosóficas en su reciente artículo «La cosmología moderna como fuente de teorías metafísicas, monistas y míticas» (El Catoblepas, nº 32, pág. 18). En ningún caso es mi propósito embarcarme en una polémica que ya zarpó y lleva en alta mar más de diez meses, con los riesgos que eso conlleva. Principalmente, por una razón doble.

In this article, we provide and overview of what we consider to be some of the most pressing research questions facing the field of artificial intelligence (AI); as well as its sub-field of computational intelligence (CI). We demarcate these questions using five unique Rs – namely, (i) rationalizability, (ii) resilience, (iii) reproducibility, (iv) realism, and (v) responsibility. Just as air serves as the basic element of biological life, the term AIR5 – cumulatively referring to the five aforementioned Rs – is introduced herein to mark some of the basic elements of artificial life (supporting the sustained growth of AI and CI). A brief summary of each of the Rs is presented, highlighting their relevance as pillars of future research in this arena.

Mobile and general-purpose robots increasingly support our everyday life, requiring dependable robotics control software. Creating such software mainly amounts to implementing their complex behaviors known as missions. Recognizing the need, a large number of domain-specific specification languages has been proposed. These, in addition to traditional logical languages, allow the use of formally specified missions for synthesis, verification, simulation, or guiding the implementation. For instance, the logical language LTL is commonly used by experts to specify missions, as an input for planners, which synthesize the behavior a robot should have. Unfortunately, domain-specific languages are usually tied to specific robot models, while logical languages such as LTL are difficult to use by non-experts. We present a catalog of 22 mission specification patterns for mobile robots, together with tooling for instantiating, composing, and compiling the patterns to create mission specifications.

The black hole information paradox is a contradiction between fundamental principles which has puzzled physicists for over forty years. The crux of the problem lies in an assumption about the structure of entanglement across the event horizon, namely, that the Hilbert space factorizes. While valid in quantum mechanics, this fails drastically in quantum field theory, and hence a deeper understanding of entanglement is required if further progress is to be made. Recently, ideas from algebraic quantum field theory have provided new insight into this issue, and show promise for elucidating the connection between entropy and horizons that underlies black hole thermodynamics.

We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture—called the {em universal memory architecture} (UMA)—maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems Z and Z+). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the Sageev-Roller duality between discrete poc sets and discrete median algebras provides a two-way dictionary from inference to geometry, leading to immense savings in computation, at a cost in the quality of representation that can be quantified in terms of topological invariants.

Statistical and multiscaling characteristics of WTI Crude Oil prices expressed in US dollar in relation to the most traded currencies as well as to gold futures and to the E-mini S&P500 futures prices on 5 min intra-day recordings in the period January 2012 – December 2017 are studied. It is shown that in most of the cases the tails of return distributions of the considered financial instruments follow the inverse cubic power law. The only exception is the Russian ruble for which the distribution tail is heavier and scales with the exponent close to 2. From the perspective of multiscaling the analysed time series reveal the multifractal organization with the left-sided asymmetry of the corresponding singularity spectra. Even more, all the considered financial instruments appear to be multifractally cross-correlated with oil, especially on the level of medium-size fluctuations, as the multifractal cross-correlation analysis carried out by means of the multifractal cross-correlation analysis (MFCCA) and detrended cross-correlation coefficient ρq show.

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a ‘good’ model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called ‘measure problem’ in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices.

Computational chemistry grew in a new era of “desktop modeling”, which coincided with a growing demand for modeling software, especially from the pharmaceutical industry. Parameterization of models in computational chemistry is an arduous enterprise, and we argue that this activity leads, in this specific context, to tensions among scientists regarding the lack of epistemic transparency of parameterized methods and the software implementing them. To explicit these tensions, we rely on a corpus which is suited for revealing them, namely the Computational Chemistry mailing List (CCL), a professional scientific discussion forum. We relate one flame war from this corpus in order to assess in detail the relationships between modeling methods, parameterization, software and the various forms of their enclosure or disclosure. Our claim is that parameterization issues are a source of epistemic opacity and that this opacity is entangled in methods and software alike. Models and software must be addressed together to understand the epistemological tensions at stake.

In the 16th century, Simon Stevin initiated a modern approach to decimal representation of measuring numbers, marking a transition from the discrete arithmetic practised by the Greeks to the arithmetic of the continuum taken for granted today. However, how to perform arithmetic directly on infinite decimals remains a long-standing problem, which has seen the popular degeometrisation of real numbers since the first constructions were published in around 1872. Our article is devoted to solving this historical problem. An issue that Hardy called “a fatal defect” is also settled.